Bronchiectasis, a progressive chronic airway disease, is characterized by microbial colonization and infection. We present an approach to the multi-biome that integrates bacterial, viral and fungal communities in bronchiectasis through weighted similarity network fusion (https://integrative-microbiomics.ntu.edu.sg). Patients at greatest risk of exacerbation have less complex microbial co-occurrence networks, reduced diversity and a higher degree of antagonistic interactions in their airway microbiome. Furthermore, longitudinal interactome dynamics reveals microbial antagonism during exacerbation, which resolves following treatment in an otherwise stable multi-biome. Assessment of the Pseudomonas interactome shows that interaction networks, rather than abundance alone, are associated with exacerbation risk, and that incorporation of microbial interaction data improves clinical prediction models. Shotgun metagenomic sequencing of an independent cohort validated the multi-biome interactions detected in targeted analysis and confirmed the association with exacerbation. Integrative microbiomics captures microbial interactions to determine exacerbation risk, which cannot be appreciated by the study of a single microbial group. Antibiotic strategies probably target the interaction networks rather than individual microbes, providing a fresh approach to the understanding of respiratory infection.

Objective to establish whether there is any change in mortality from infection with a new variant of SARS-CoV-2, designated a variant of concern (VOC-202012/1) in December 2020, compared with circulating SARS-CoV-2 variants.Design Matched cohort study.Setting Community based (pillar 2) covid-19 testing centres in the UK using the TaqPath assay (a proxy measure of VOC-202012/1 infection).Participants 54 906 matched pairs of participants who tested positive for SARS-CoV-2 in pillar 2 between 1 October 2020 and 29 January 2021, followed-up until 12 February 2021. Participants were matched on age, sex, ethnicity, index of multiple deprivation, lower tier local authority region, and sample date of positive specimens, and differed only by detectability of the spike protein gene using the TaqPath assay.Main outcome measure Death within 28 days of the first positive SARS-CoV-2 test result.Results the mortality hazard ratio associated with infection with VOC-202012/1 compared with infection with previously circulating variants was 1.64 (95% confidence interval 1.32 to 2.04) in patients who tested positive for covid-19 in the community. In this comparatively low risk group, this represents an increase in deaths from 2.5 to 4.1 per 1000 detected cases.Conclusions the probability that the risk of mortality is increased by infection with VOC-202012/01 is high. If this finding is generalisable to other populations, infection with VOC-202012/1 has the potential to cause substantial additional mortality compared with previously circulating variants. Healthcare capacity planning and national and international control policies are all impacted by this finding, with increased mortality lending weight to the argument that further coordinated and stringent measures are justified to reduce deaths from SARS-CoV-2.

Fertility critically depends on the gonadotropin-releasing hormone (GnRH) pulse generator, a neural construct comprised of hypothalamic neurons co-expressing kisspeptin, neurokoinin-B and dynorphin. Here, using mathematical modelling and in-vivo optogenetics we reveal for the first time how this neural construct initiates and sustains the appropriate ultradian frequency essential for reproduction. Prompted by mathematical modelling, we show experimentally using female estrous mice that robust pulsatile release of luteinizing hormone, a proxy for GnRH, emerges abruptly as we increase the basal activity of the neuronal network using continuous low frequency optogenetic stimulation. Further increase in basal activity markedly increases pulse frequency and eventually leads to pulse termination. Additional model predictions that pulsatile dynamics emerge from non-linear positive and negative feedback interactions mediated through neurokinin-B and dynorphin signaling respectively are confirmed neuropharmacologically. Our results shed light on the long-elusive GnRH pulse generator offering new horizons for reproductive health and wellbeing.SIGNIFICANCE STATEMENTThe gonadotropin-releasing hormone (GnRH) pulse generator controls the pulsatile secretion of the gonadotropic hormones LH and FSH and is critical for fertility. The hypothalamic arcuate kisspeptin neurons are thought to represent the GnRH pulse generator, since their oscillatory activity is coincident with LH pulses in the blood; a proxy for GnRH pulses. However, the mechanisms underlying GnRH pulse generation remain elusive. We developed a mathematical model of the kisspeptin neuronal network and confirmed its predictions experimentally, showing how LH secretion is frequency-modulated as we increase the basal activity of the arcuate kisspeptin neurons in-vivo using continuous optogenetic stimulation. Our model provides a quantitative framework for understanding the reproductive neuroendocrine system and opens new horizons for fertility regulation.

Embryo development is a critical and fascinating stage in the life cycle of many organisms. Despite decades of research, the earliest stages of mammalian embryogenesis are still poorly understood, caused by a scarcity of high-resolution spatial and temporal data, the use of only a few model organisms, and a paucity of truly multidisciplinary approaches that combine biological research with biophysical modeling and computational simulation. Here, we explain the theoretical frameworks and biophysical processes that are best suited to modeling the early mammalian embryo, review a comprehensive list of previous models, and discuss the most promising avenues for future work.

AbstractTimely interventions have a proven benefit for people experiencing psychotic illness. One bottleneck to accessing timely interventions is the referral process to the specialist team for early psychosis (STEP). Many general practitioners lack awareness or confidence in recognising psychotic symptoms or state. Additionally, referrals for people without apparent psychotic symptoms, although beneficial at a population level, lead to excessive workload for STEPs. There is a clear unmet need for accurate stratification of STEPs users and healthy cohorts. Here we propose a new approach to addressing this need via the application of digital behavioural tests.To discriminate between the STEPs users (SU; n=32) and controls (n=32, age and sex matched), we employed k-nearest neighbours (kNN) classifier, and applied it to objective, quantitative and interpretable features derived from the ‘mirror game’ (MG) and trail making task (TMT). The MG is a movement coordination task shown to be a potential socio-motor biomarker of schizophrenia, while TMT is a neuropsychiatric test of cognitive function. We show that the proposed classifier achieves an excellent performance, AUC = 0.89 (95%CI 0.73-1), Sensitivity = 0.75 (95%CI 0.5-1), Specificity = 1 (95%CI 0.62-1), evaluated on 25% hold-out and 1000 folds. We demonstrate that this performance is underpinned by the large effect sizes of the differences between the cohorts in terms of the features used for classification. We also find that MG and TMT are unsuitable in isolation to successfully differentiate between SU with and without at-risk-mental-state or first episode psychosis with sufficient level of performance.Our findings show that introduction of standardised battery of digital behavioural tests could benefit both clinical and research practice. Including digital behavioural tests into healthcare practice could allow precise phenotyping and stratification of the highly heterogenous population of people referred to STEPs resulting in quicker and more personalised diagnosis. Moreover, the high specificity of digital behavioural tests could facilitate the identification of more homogeneous clinical high-risk populations, benefiting research on prognostic instruments for psychosis. In summary, our study demonstrates that cheap off-the-shelf equipment (laptop computer and a leap motion sensor) can be used to record clinically relevant behavioural data that could be utilised in digital mental health applications.Author summaryNeuropsychiatric assessment and accurate diagnosis are notoriously challenging. Psychosis represents a classical example of this challenge where many at-risk of psychotic illness individuals (often very young) are misdiagnosed and/or inappropriately treated clinically. Our study demonstrates that combining digital tests with data analytics has potential for simplifying neuropsychiatric assessment. It shows that using measurements from TMT and MG allows to differentiate between people accepted for assessment in specialist team for early psychosis (STEP) and controls with excellent performance (AUROC > 0.9), while achieving 100% specificity (no false positive detections). The study shows feasibility of using cheap, portable equipment, assembled from off-the-shelf components, for collection of clinically relevant data that could be used to inform clinical decision making. Moreover, our study, with its state-of-the-art performance and interpretable results, demonstrate high clinical potential of implementing digital batteries of behavioural tests in clinical practice. Such developments would not only help to stratify STEPs users but would facilitate rapid assessment for all people seeking care in early intervention services. This in turn would contribute to improving the quality of life and wellbeing of individuals at risk of developing psychosis.FundingEPSRC Impact Acceleration Account, Impact & Knowledge Exchange Award, Jean Golding Institute seed corn, Avon & Wiltshire Mental Health Partnership NHS Trust Research Capability Funding.PS was generously supported by the Wellcome Trust Institutional Strategic Support Award 204909/Z/16/Z. KTA gratefully acknowledges the financial support of the EPSRC via grant EP/T017856/1.For the purpose of open access, the authors have applied a ‘Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.

AbstractControl-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of numerical continuation to experiments and provides systematic dynamical analyses without the need for mathematical modelling. CBC has seen considerable success in studying the bifurcation structure of mechanical systems. Nevertheless, the method is not practical for studying relaxation oscillations. Large numbers of Fourier modes are required to describe them, and the length of the experiment significantly increases when many Fourier modes are used, as the system must be run to convergence many times. Furthermore, relaxation oscillations often arise in autonomous systems, for which an appropriate phase constraint is required. To overcome these challenges, we introduce an adaptive B-spline discretisation that can produce a parsimonious description of responses that would otherwise require many Fourier modes. We couple this to a novel phase constraint that phase-locks control target and solution phase. Results are demonstrated on simulations of a slow-fast synthetic gene network and an Oregonator model. Our methods extend CBC to a much broader range of systems than have been studied so far, opening up a range of novel experimental opportunities on slow-fast systems.

The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.

BackgroundVariable clinical outcomes are reported with fungal sensitisation in chronic obstructive pulmonary disease (COPD), and it remains unclear which fungi and what allergens associate with the poorest outcomes. The use of recombinant as opposed to crude allergens for such assessment is unknown.MethodsA prospective multicentre assessment of stable COPD (n=614) was undertaken in five hospitals across three countries: Singapore, Malaysia and Hong Kong. Clinical and serological assessment was performed against a panel of 35 fungal allergens including crude and recombinantAspergillusand non-Aspergillusallergens. Unsupervised clustering and topological data analysis (TDA) approaches were employed using the measured sensitisation responses to elucidate if sensitisation subgroups exist and their related clinical outcomes.ResultsAspergillus fumigatussensitisation was associated with increased exacerbations in COPD. Unsupervised cluster analyses revealed two “fungal sensitisation” groups. The first was characterised byAspergillussensitisation and increased exacerbations, poorer lung function and worse prognosis. Polysensitisation in this group conferred even poorer outcome. The second group, characterised byCladosporiumsensitisation, was more symptomatic. Significant numbers of individuals demonstrated sensitisation responses to only recombinant (as opposed to crude)A. fumigatusallergens f 1, 3, 5 and 6, and exhibited increased exacerbations, poorer lung function and an overall worse prognosis. TDA validated these findings and additionally identified a subgroup withinAspergillus-sensitised COPD of patients with frequent exacerbations.ConclusionAspergillussensitisation is a treatable trait in COPD. Measuring sensitisation responses to recombinantAspergillusallergens identifies an important patient subgroup with poor COPD outcomes that remains overlooked by assessment of only crudeAspergillusallergens.

Antimicrobial resistance is an urgent threat to human health, and new antibacterial drugs are desperately needed, as are research tools to aid in their discovery and development. Vancomycin is a glycopeptide antibiotic that is widely used for the treatment of Gram-positive infections, such as life-threatening systemic diseases caused by methicillin-resistant Staphylococcus aureus (MRSA). Here we demonstrate that modification of vancomycin by introduction of an azide substituent provides a versatile intermediate that can undergo copper-catalysed azide-alkyne cycloaddition (CuAAC) reaction with various alkynes to readily prepare vancomycin fluorescent probes. We describe the facile synthesis of three probes that retain similar antibacterial profiles to the parent vancomycin antibiotic. We demonstrate the versatility of these probes for the detection and visualisation of Gram-positive bacteria by a range of methods, including plate reader quantification, flow cytometry analysis, high-resolution microscopy imaging, and single cell microfluidics analysis. In parallel, we demonstrate their utility in measuring outer-membrane permeabilisation of Gram-negative bacteria. The probes are useful tools that may facilitate detection of infections and development of new antibiotics.

Timely interventions have a proven benefit for people experiencing psychotic illness. One bottleneck to accessing timely interventions is the referral process to the specialist team for early psychosis (STEP). Many general practitioners lack awareness or confidence in recognising psychotic symptoms or state. Additionally, referrals for people without apparent psychotic symptoms, although beneficial at a population level, lead to excessive workload for STEPs. There is a clear unmet need for accurate stratification of STEPs users and healthy cohorts. Here we propose a new approach to addressing this need via the application of digital behavioural tests. To demonstrate that digital behavioural tests can be used to discriminate between the STEPs users (SU; n = 32) and controls (n = 32, age and sex matched), we compared performance of five different classifiers applied to objective, quantitative and interpretable features derived from the 'mirror game' (MG) and trail making task (TMT). The MG is a movement coordination task shown to be a potential socio-motor biomarker of schizophrenia, while TMT is a neuropsychiatric test of cognitive function. All classifiers had AUC in the range of 0.84-0.92. The best of the five classifiers (linear discriminant classifier) achieved an outstanding performance, AUC = 0.92 (95%CI 0.75-1), Sensitivity = 0.75 (95%CI 0.5-1), Specificity = 1 (95%CI 0.75-1), evaluated on 25% hold-out and 1000 folds. Performance of all analysed classifiers is underpinned by the large effect sizes of the differences between the cohorts in terms of the features used for classification what ensures generalisability of the results. We also found that MG and TMT are unsuitable in isolation to successfully differentiate between SU with and without at-risk-mental-state or first episode psychosis with sufficient level of performance. Our findings show that standardised batteries of digital behavioural tests could benefit both clinical and research practice. Including digital behavioural tests into healthcare practice could allow precise phenotyping and stratification of the highly heterogenous population of people referred to STEPs resulting in quicker and more personalised diagnosis. Moreover, the high specificity of digital behavioural tests could facilitate the identification of more homogeneous clinical high-risk populations, benefiting research on prognostic instruments for psychosis. In summary, our study demonstrates that cheap off-the-shelf equipment (laptop computer and a leap motion sensor) can be used to record clinically relevant behavioural data that could be utilised in digital mental health applications.

AbstractCircle drawing may be a useful task to study upper-limb function in patient populations. However, previous studies rely on expensive and bulky robotics to measure performance. For clinics or hospitals with limited budgets and space, this may be unfeasible. Virtual reality (VR) provides a portable and low-cost tool with integrated motion capture. It offers potentially a more feasible medium by which to assess upper-limb motor function. Prior to use with patient populations, it is important to validate and test the capabilities of VR with healthy users. This study examined whether a VR-based circle drawing task, completed remotely using participant’s own devices, could capture differences between movement kinematics of the dominant and non-dominant hands in healthy individuals. Participants (n = 47) traced the outline of a circle presented on their VR head-mounted displays with each hand, while the positions of the hand-held controllers were continuously recorded. Although there were no differences observed in the size or roundness of circles drawn with each hand, consistent with prior literature our results did show that the circles drawn with the dominant hand were completed faster than those with the non-dominant hand. This provides preliminary evidence that a VR-based circle drawing task may be a feasible method for detecting subtle differences in function in clinical populations.

AbstractKisspeptin neurons in the arcuate nucleus of the hypothalamus generate gonadotrophin‐releasing hormone (GnRH) pulses, and act as critical initiators of functional gonadotrophin secretion and reproductive competency. However, kisspeptin in other brain regions, most notably the posterodorsal subnucleus of the medial amygdala (MePD), plays a significant modulatory role over the hypothalamic kisspeptin population; our recent studies using optogenetics have shown that low‐frequency light stimulation of MePD kisspeptin results in increased luteinsing hormone pulse frequency. Nonetheless, the neurochemical pathways that underpin this regulatory function remain unknown. To study this, we have utilised an optofluid technology, precisely combining optogenetic stimulation with intra‐nuclear pharmacological receptor antagonism, to investigate the neurotransmission involved in this circuitry. We have shown experimentally and verified using a mathematical model that functional neurotransmission of both GABA and glutamate is a requirement for effective modulation of the GnRH pulse generator by amygdala kisspeptin neurons.

The research in this thesis was conducted in collaboration with Somerset NHS
Foundation Trust, and the University of Exeter, during the COVID-19 pandemic.
Prior to COVID-19 this research was directed at determining whether predictive
models of chronic disease, developed from routinely collected clinical data, could be
safely deployed into the clinical workflow. As part of this we published a novel safety
framework for data driven clinical decision support.
When the COVID-19 pandemic emerged, the priorities of the NHS changed, shifting
towards the acute care of unwell patients. Adjusting for this, we re-oriented the
research to answer the many questions about the impact of COVID-19 on the NHS.
Our study on the Alpha variant was one of the earliest to show increased severity.
Our identification of outbreaks of the Delta variant, and its rapid growth, was at
the forefront of decision making in local NHS trusts, NHS England, Public Health
England, the UK Health Security Agency, and ultimately the UK Government.
As we move forward from the acute phase of the pandemic, understanding the longer
term impact on chronic health management, and as a co-morbidity for chronic disease
will become more of a priority for the NHS. A continued collaboration between the
University of Exeter, Somerset NHS Foundation Trust and the UK Health Security
Agency is well placed to address this need.

Abstract
. Background
. Hospital catchment areas define the primary population of a hospital and are central to assessing the potential demand on that hospital, for example, due to infectious disease outbreaks.
.
. Methods
. We present a novel algorithm, based on label propagation, for estimating hospital catchment areas, from the capacity of the hospital and demographics of the nearby population, and without requiring any data on hospital activity.
.
. Results
. The algorithm is demonstrated to produce a mapping from fine grained geographic regions to larger scale catchment areas, providing contiguous and realistic subdivisions of geographies relating to a single hospital or to a group of hospitals. In validation against an alternative approach predicated on activity data gathered during the COVID-19 outbreak in the UK, the label propagation algorithm is found to have a high level of agreement and perform at a similar level of accuracy.
.
. Results
. The algorithm can be used to make estimates of hospital catchment areas in new situations where activity data is not yet available, such as in the early stages of a infections disease outbreak.
.

Phenotypic variations between individual microbial cells play a key role in the resistance of microbial pathogens to pharmacotherapies. Nevertheless, little is known about cell individuality in antibiotic accumulation. Here, we hypothesise that phenotypic diversification can be driven by fundamental cell-to-cell differences in drug transport rates. To test this hypothesis, we employed microfluidics-based single-cell microscopy, libraries of fluorescent antibiotic probes and mathematical modelling. This approach allowed us to rapidly identify phenotypic variants that avoid antibiotic accumulation within populations of Escherichia coli, Pseudomonas aeruginosa, Burkholderia cenocepacia, and Staphylococcus aureus. Crucially, we found that fast growing phenotypic variants avoid macrolide accumulation and survive treatment without genetic mutations. These findings are in contrast with the current consensus that cellular dormancy and slow metabolism underlie bacterial survival to antibiotics. Our results also show that fast growing variants display significantly higher expression of ribosomal promoters before drug treatment compared to slow growing variants. Drug-free active ribosomes facilitate essential cellular processes in these fast-growing variants, including efflux that can reduce macrolide accumulation. We used this new knowledge to eradicate variants that displayed low antibiotic accumulation through the chemical manipulation of their outer membrane inspiring new avenues to overcome current antibiotic treatment failures.

AbstractPredicting the trajectory of rare degenerative diseases can be extremely beneficial, especially when these predictions are personalised to be relevant for a specific patient. These predictions can help inform and advise patients, families, and clinicians about the next stages of treatment and care. Obtaining such predictions, however, can be challenging, especially when data is limited. In particular, it is important that these predictions do not rely too heavily on general trends from the wider afflicted population while not relying exclusively on the, potentially sparse, data from the patient in question. We present a case study, wherein a modelling framework is developed for predicting a patient’s long term trajectory, using a mix of data from the patient of concern and a database of previously observed patients. This framework directly accounts for the temporal structure of a patient’s trajectory, effortlessly handles a large amount of missing data, allows for a wide range of patient progression, and offers a robust quantification of the various uncertainties. We showcase this framework to an example involving Duchenne Muscular Dystrophy, where it provides promising results.

AbstractThe hypothalamus is the central regulator of reproductive hormone secretion. Pulsatile secretion of gonadotropin releasing hormone (GnRH) is fundamental to physiological stimulation of the pituitary gland to release luteinizing hormone (LH) and follicle stimulating hormone (FSH). Furthermore, GnRH pulsatility is altered in common reproductive disorders such as polycystic ovary syndrome (PCOS) and hypothalamic amenorrhea (HA). LH is measured routinely in clinical practice using an automated chemiluminescent immunoassay method and is the gold standard surrogate marker of GnRH. LH can be measured at frequent intervals (e.g. 10 minutely) to assess GnRH/LH pulsatility. However, this is rarely done in clinical practice because it is resource intensive, and there is no user-friendly and accessible method for computational analysis of the LH data available to clinicians. Here we presenthormoneBayes, a novel open-access Bayesian framework that can be easily applied to reliably analyze serial LH measurements to assess LH pulsatility. The framework utilizes parsimonious models to simulate hypothalamic signals that drive LH dynamics, together with state-of-the-art (sequential) Monte-Carlo methods to infer key parameters and latent hypothalamic dynamics. We show that this method provides estimates for key pulse parameters including inter-pulse interval, secretion and clearance rates and identifies LH pulses in line with the current gold-standard deconvolution method. We show that these parameters can distinguish LH pulsatility in different clinical contexts including in reproductive health and disease in men and women (e.g. healthy men, healthy women before and after menopause, women with HA or PCOS). A further advantage ofhormoneBayesis that our mathematical approach provides a quantified estimation of uncertainty. Our framework will complement methods enabling real-timein-vivohormone monitoring and therefore has the potential to assist translation of personalized, data-driven, clinical care of patients presenting with conditions of reproductive hormone dysfunction.

AbstractMathematical modelling is an indispensable tool in modern biosciences, enabling quantitative analysis and integration of biological data, transparent formulation of our understanding of complex biological systems, and efficient experimental design based on model predictions. This review article provides an overview of the impact that mathematical models had on GnRH research. Indeed, over the last 20 years mathematical modelling has been used to describe and explore the physiology of the GnRH neuron, the mechanisms underlying GnRH pulsatile secretion, and GnRH signalling to the pituitary. Importantly, these models have contributed to GnRH research via novel hypotheses and predictions regarding the bursting behaviour of the GnRH neuron, the role of kisspeptin neurons in the emergence of pulsatile GnRH dynamics, and the decoding of GnRH signals by biochemical signalling networks. We envisage that with the advent of novel experimental technologies, mathematical modelling will have an even greater role to play in our endeavour to understand the complex spatiotemporal dynamics underlying the reproductive neuroendocrine system.

the serial interval of an infectious disease, commonly interpreted as the time between the onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections), and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions, and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early coronavirus disease 2019 data. In this paper, we estimate these key quantities in the context of coronavirus disease 2019 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean of 5.9 (95% CI 5.2; 6.7) and SD 4.1 (95% CI 3.8; 4.7) days (empirical distribution), the generation interval with a mean of 4.9 (95% CI 4.2; 5.5) and SD 2.0 (95% CI 0.5; 3.2) days (fitted gamma distribution), and the incubation period with a mean 5.2 (95% CI 4.9; 5.5) and SD 5.5 (95% CI 5.1; 5.9) days (fitted log-normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period, and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modeling coronavirus disease 2019 transmission.

AbstractThe interaction between a cell and its environment shapes fundamental intracellular processes such as cellular metabolism. In most cases growth rate is treated as a proximal metric for understanding the cellular metabolic status. However, changes in growth rate might not reflect metabolic variations in individuals responding to environmental fluctuations. Here we use single-cell microfluidics-microscopy combined with transcriptomics, proteomics and mathematical modelling to quantify the accumulation of glucose within Escherichia coli cells. In contrast to the current consensus, we reveal that environmental conditions which are comparatively unfavourable for growth, where both nutrients and salinity are depleted, increase glucose accumulation rates in individual bacteria and population subsets. We find that these changes in metabolic function are underpinned by variations at the translational and posttranslational level but not at the transcriptional level and are not dictated by changes in cell size. The metabolic response-characteristics identified greatly advance our fundamental understanding of the interactions between bacteria and their environment and have important ramifications when investigating cellular processes where salinity plays an important role.

For more than 4 decades, it has been shown that humans are particularly sensitive to biological motion and extract socially relevant information from it such as gender, intentions, emotions or a person's identity. A growing number of findings, however, indicate that identity perception is not always highly accurate, especially due to large inter-individual differences and a fuzzy self-recognition advantage compared to the recognition of others. Here, we investigated the self-other identification performance and sought to relate this performance to the metric properties of perceptual/physical representations of individual motor signatures. We show that identity perception ability varies substantially across individuals and is associated to the perceptual/physical motor similarities between self and other stimuli. Specifically, we found that the perceptual representations of postural signatures are veridical in the sense that closely reflects the physical postural trajectories and those similarities between people' actions elicit numerous misattributions. While, on average, people can well recognize their self-generated actions, they more frequently attribute to themselves the actions of those acting in a similar way. These findings are consistent with the common coding theory and support that perception and action are tightly linked and may modulate each other by virtue of similarity.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reproduction number has become an essential parameter for monitoring disease transmission across settings and guiding interventions. The UK published weekly estimates of the reproduction number in the UK starting in May 2020 which are formed from multiple independent estimates. In this paper, we describe methods used to estimate the time-varying SARS-CoV-2 reproduction number for the UK. We used multiple data sources and estimated a serial interval distribution from published studies. We describe regional variability and how estimates evolved during the early phases of the outbreak, until the relaxing of social distancing measures began to be introduced in early July. Our analysis is able to guide localized control and provides a longitudinal example of applying these methods over long timescales. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

AbstractClinical classification is essential for estimating disease prevalence but is difficult, often requiring complex investigations. The widespread availability of population level genetic data makes novel genetic stratification techniques a highly attractive alternative. We propose a generalizable mathematical framework for determining disease prevalence within a cohort using genetic risk scores. We compare and evaluate methods based on the means of genetic risk scores’ distributions; the Earth Mover’s Distance between distributions; a linear combination of kernel density estimates of distributions; and an Excess method. We demonstrate the performance of genetic stratification to produce robust prevalence estimates. Specifically, we show that robust estimates of prevalence are still possible even with rarer diseases, smaller cohort sizes and less discriminative genetic risk scores, highlighting the general utility of these approaches. Genetic stratification techniques offer exciting new research tools, enabling unbiased insights into disease prevalence and clinical characteristics unhampered by clinical classification criteria.

AbstractPhenotypic variations between individual microbial cells play a key role in the resistance of microbial pathogens to pharmacotherapies. Nevertheless, little is known about cell individuality in antibiotic accumulation. Here we hypothesize that phenotypic diversification can be driven by fundamental cell-to-cell differences in drug transport rates. To test this hypothesis, we employed microfluidics-based single-cell microscopy, libraries of fluorescent antibiotic probes and mathematical modelling. This approach allowed us to rapidly identify phenotypic variants that avoid antibiotic accumulation within populations ofEscherichia coli, Pseudomonas aeruginosa, Burkholderia cenocepaciaandStaphylococcus aureus. Crucially, we found that fast growing phenotypic variants avoid macrolide accumulation and survive treatment without genetic mutations. These findings are in contrast with the current consensus that cellular dormancy and slow metabolism underlie bacterial survival to antibiotics. Our results also show that fast growing variants display significantly higher expression of ribosomal promoters before drug treatment compared to slow growing variants. Drug-free active ribosomes facilitate essential cellular processes in these fast growing variants, including efflux that can reduce macrolide accumulation. Using this new knowledge, we phenotypically engineered bacterial populations by eradicating variants that displayed low antibiotic accumulation through the chemical manipulation of their outer membrane inspiring new avenues to overcome current antibiotic treatment failures.

AbstractObjectivesTo establish whether there is any change in mortality associated with infection of a new variant of SARS-CoV-2, designated a Variant of Concern in December 2020 (VOC-202012/1) compared to that associated with infection with circulating SARS-CoV-2 variants.DesignMatched cohort study. Cases are matched by age, gender, ethnicity, index of multiple deprivation, lower tier local authority region, and sample date of positive specimen, and differing only by detectability of the spike protein gene using the TaqPath assay - a proxy measure of VOC-202012/1 infection.SettingUnited Kingdom, community - based (Pillar 2) COVID-19 testing centres using the TaqPath assay.Participants54,906 pairs of participants testing positive for SARS-CoV-2 in Pillar 2 between 1st October 2020 and 29th January 2021, followed up until the 12th February 2021.Main outcome measuresDeath within 28 days of first positive SARS-CoV-2 test.ResultsThere is a high probability that the risk of mortality is increased by infection with VOC-202012/01 (p <0.001). The mortality hazard ratio associated with infection with VOC-202012/1 compared to infection with previously circulating variants is 1.64 (95% CI 1.32 - 2.04) in patients who have tested positive for COVID-19 in the community. In this comparatively low risk group, this represents an increase from 2.5 to 4.1 deaths per 1000 detected cases.ConclusionsIf this finding is generalisable to other populations, VOC-202012/1 infections have the potential to cause substantial additional mortality compared to previously circulating variants. Healthcare capacity planning, national and international control policies are all impacted by this finding, with increased mortality lending weight to the argument that further coordinated and stringent measures are justified to reduce deaths from SARS-CoV-2.

Bronchiectasis, a progressive chronic airway disease, is characterized by microbial colonization and infection. We present an approach to the multi-biome that integrates bacterial, viral and fungal communities in bronchiectasis through weighted similarity network fusion (https://integrative-microbiomics.ntu.edu.sg). Patients at greatest risk of exacerbation have less complex microbial co-occurrence networks, reduced diversity and a higher degree of antagonistic interactions in their airway microbiome. Furthermore, longitudinal interactome dynamics reveals microbial antagonism during exacerbation, which resolves following treatment in an otherwise stable multi-biome. Assessment of the Pseudomonas interactome shows that interaction networks, rather than abundance alone, are associated with exacerbation risk, and that incorporation of microbial interaction data improves clinical prediction models. Shotgun metagenomic sequencing of an independent cohort validated the multi-biome interactions detected in targeted analysis and confirmed the association with exacerbation. Integrative microbiomics captures microbial interactions to determine exacerbation risk, which cannot be appreciated by the study of a single microbial group. Antibiotic strategies probably target the interaction networks rather than individual microbes, providing a fresh approach to the understanding of respiratory infection.

Pulsatile GnRH release is essential for normal reproductive function. Kisspeptin secreting neurons found in the arcuate nucleus, known as KNDy neurons for co-expressing neurokinin B, and dynorphin, drive pulsatile GnRH release. Furthermore, gonadal steroids regulate GnRH pulsatile dynamics across the ovarian cycle by altering KNDy neurons' signalling properties. However, the precise mechanism of regulation remains mostly unknown. To better understand these mechanisms, we start by perturbing the KNDy system at different stages of the estrous cycle using optogenetics. We find that optogenetic stimulation of KNDy neurons stimulates pulsatile GnRH/LH secretion in estrous mice but inhibits it in diestrous mice. These in vivo results in combination with mathematical modelling suggest that the transition between estrus and diestrus is underpinned by well-orchestrated changes in neuropeptide signalling and in the excitability of the KNDy population controlled via glutamate signalling. Guided by model predictions, we show that blocking glutamate signalling in diestrous animals inhibits LH pulses, and that optic stimulation of the KNDy population mitigates this inhibition. In estrous mice, disruption of glutamate signalling inhibits pulses generated via sustained low-frequency optic stimulation of the KNDy population, supporting the idea that the level of network excitability is critical for pulse generation. Our results reconcile previous puzzling findings regarding the estradiol-dependent effect that several neuromodulators have on the GnRH pulse generator dynamics. Therefore, we anticipate our model to be a cornerstone for a more quantitative understanding of the pathways via which gonadal steroids regulate GnRH pulse generator dynamics. Finally, our results could inform useful repurposing of drugs targeting the glutamate system in reproductive therapy.

Since Noble adapted in 1962 the model of Hodgkin and Huxley to fit Purkinje fibres, the refinement of models for cardiomyocytes has continued. Most of these models are high-dimensional systems of coupled equations so that the possible mathematical analysis is quite limited, even numerically. This has inspired the development of reduced, phenomenological models that preserve qualitatively the main feature of cardiomyocyte’s dynamics. In this paper, we present a systematic comparison of the dynamics between two notable low-dimensional models, the FitzHugh–Nagumo model (FitzHugh in Bull Math Biophys 17:257–269, 1955, J Gen Physiol 43:867–896, 1960, Biophys J 1:445–466, 1961) as a prototype of excitable behaviour and a polynomial version of the Karma model (Karma in Phys Rev Lett 71(7):16, 1993, Chaos 4:461, 1994) which is specifically developed to fit cardiomyocyte’s behaviour well. We start by introducing the models and considering their pure ODE versions. We analyse the ODEs employing the main ideas and steps used in the setting of geometric singular perturbation theory. Next, we turn to the spatially extended models, where we focus on travelling wave solutions in 1D. Finally, we perform numerical simulations of the 1D PDE Karma model varying model parameters in order to systematically investigate the impact on wave propagation velocity and shape. In summary, our study provides a reference regarding key similarities as well as key differences of the two models.

Objective to establish whether there is any change in mortality from infection with a new variant of SARS-CoV-2, designated a variant of concern (VOC-202012/1) in December 2020, compared with circulating SARS-CoV-2 variants.Design Matched cohort study.Setting Community based (pillar 2) covid-19 testing centres in the UK using the TaqPath assay (a proxy measure of VOC-202012/1 infection).Participants 54 906 matched pairs of participants who tested positive for SARS-CoV-2 in pillar 2 between 1 October 2020 and 29 January 2021, followed-up until 12 February 2021. Participants were matched on age, sex, ethnicity, index of multiple deprivation, lower tier local authority region, and sample date of positive specimens, and differed only by detectability of the spike protein gene using the TaqPath assay.Main outcome measure Death within 28 days of the first positive SARS-CoV-2 test result.Results the mortality hazard ratio associated with infection with VOC-202012/1 compared with infection with previously circulating variants was 1.64 (95% confidence interval 1.32 to 2.04) in patients who tested positive for covid-19 in the community. In this comparatively low risk group, this represents an increase in deaths from 2.5 to 4.1 per 1000 detected cases.Conclusions the probability that the risk of mortality is increased by infection with VOC-202012/01 is high. If this finding is generalisable to other populations, infection with VOC-202012/1 has the potential to cause substantial additional mortality compared with previously circulating variants. Healthcare capacity planning and national and international control policies are all impacted by this finding, with increased mortality lending weight to the argument that further coordinated and stringent measures are justified to reduce deaths from SARS-CoV-2.

Developmental coordination disorder (DCD) describes a condition of poor motor performance in the absence of intellectual impairment. Despite being one of the most prevalent developmental disorders, little is known about how fundamental visuomotor processes might function in this group. One prevalent idea is children with DCD interact with their environment in a less predictive fashion than typically developing children. A metric of prediction which has not been examined in this group is the degree to which the hands and eyes are coordinated when performing manual tasks. To this end, we examined hand and eye movements during an object lifting task in a group of children with DCD (n=19) and an age-matched group of children without DCD (n=39). We observed no differences between the groups in terms of how well they coordinated their hands and eyes when lifting objects, nor in terms of the degree by which the eye led the hand. We thus find no evidence to support the proposition that children with DCD coordinate their hands and eyes in a non-predictive fashion. In a follow-up exploratory analysis we did, however, note differences in fundamental patterns of eye movements between the groups, with children in the DCD group showing some evidence of atypical visual sampling strategies and gaze anchoring behaviours during the task.

Recently, pioneering expression quantitative trait loci (eQTL) studies on single cell RNA sequencing (scRNA-seq) data have revealed new and cell-specific regulatory single nucleotide variants (SNVs). Here, we present an alternative QTL-related approach applicable to transcribed SNV loci from scRNA-seq data: scReQTL. ScReQTL uses Variant Allele Fraction (VAFRNA) at expressed biallelic loci, and corelates it to gene expression from the corresponding cell.

Podocytes are key components of the glomerular filtration barrier (GFB). They are insulin-responsive but can become insulin-resistant, causing features of the leading global cause of kidney failure, diabetic nephropathy. Insulin acts via insulin receptors to control activities fundamental to GFB integrity, but the amount of information transferred is unknown. Here we measure this in human podocytes, using information theory-derived statistics that take into account cell-cell variability. High content imaging was used to measure insulin effects on Akt, FOXO and ERK. Mutual Information (MI) and Channel Capacity (CC) were calculated as measures of information transfer. We find that insulin acts via noisy communication channels with more information flow to Akt than to ERK. Information flow estimates were increased by consideration of joint sensing (ERK and Akt) and response trajectory (live cell imaging of FOXO1-clover translocation). Nevertheless, MI values were always

Freezing of gait (FoG) is typically a symptom of advanced Parkinson’s disease (PD) that negatively influences the quality of life and is often resistant to pharmacological interventions. Novel treatment options that make use of auditory or sensory cues might be optimized by prediction of freezing events. These predictions might help to trigger external sensory cues—shown to improve walking performance—when behavior is changed in a manner indicative of an impending freeze (i.e. when the user needs it the most), rather than delivering cue information continuously. A data-driven approach is proposed for predicting freezing events using Random Forrest (RF), Neural Network (NN), and Naive Bayes (NB) classifiers. Vertical forces, sampled at 100 Hz from a force platform were collected from 9 PD subjects as they stepped in place until they at least had one freezing episode or for 90 s. The F1 scores of RF/NN/NB algorithms were computed for different IL (input to the machine learning algorithm), and GL (how early the freezing event is predicted). A significant negative correlation between the F1 scores and GL, highlighting the difficulty of early detection is found. The IL that maximized the F1 score is approximately equal to 1.13 s. This indicates that the physiological (and therefore neurological) changes leading to freezing take effect at-least one step before the freezing incident. Our algorithm has the potential to support the development of devices to detect and then potentially prevent freezing events in people with Parkinson’s which might occur if left uncorrected.

Author summary Epilepsy is a serious neurological condition encompassing a variety of syndromes that affect around 65 million people worldwide. Seizure type in epilepsy is characterized by onset pattern and brain network involved into three categories that do not fully capture the complexity of observed onset patterns. Ambiguity of seizure onset observed in the clinic could result in significant diagnostic delay and inappropriate treatment for an individual. We show how a variety of recruitment patterns across a network arise as the result of interplay between heterogeneous node dynamics and heterogeneous coupling among nodes. Our results demonstrate the important role of brain network dynamics in driving spatiotemporal patterns of seizure onset and provide a dynamic mechanism that could inform novel classifications of seizure types in clinical practice.

Neuroendocrine axes display a remarkable diversity of dynamic signaling processes relaying information between the brain, endocrine glands, and peripheral target tissues. These dynamic processes include oscillations, elastic responses to perturbations, and plastic long term changes observed from the cellular to the systems level. While small transient dynamic changes can be considered physiological, larger and longer disruptions are common in pathological scenarios involving more than one neuroendocrine axes, suggesting that a robust control of hormone dynamics would require the coordination of multiple neuroendocrine clocks. The idea of apparently different axes being in fact exquisitely intertwined through neuroendocrine signals can be investigated in the regulation of stress and fertility. The stress response and the reproductive cycle are controlled by the Hypothalamic-Pituitary-Adrenal (HPA) axis and the Hypothalamic-Pituitary-Gonadal (HPG) axis, respectively. Despite the evidence surrounding the effects of stress on fertility, as well as of the reproductive cycle on stress hormone dynamics, there is a limited understanding on how perturbations in one neuroendocrine axis propagate to the other. We hypothesize that the links between stress and fertility can be better understood by considering the HPA and HPG axes as coupled systems. In this manuscript, we investigate neuroendocrine rhythms associated to the stress response and reproduction by mathematically modeling the HPA and HPG axes as a network of interlocked oscillators. We postulate a network architecture based on physiological data and use the model to predict responses to stress perturbations under different hormonal contexts: normal physiological, gonadectomy, hormone replacement with estradiol or corticosterone (CORT), and high excess CORT (hiCORT) similar to hypercortisolism in humans. We validate our model predictions against experiments in rodents, and show how the dynamic responses of these endocrine axes are consistent with our postulated network architecture. Importantly, our model also predicts the conditions that ensure robustness of fertility to stress perturbations, and how chronodisruptions in glucocorticoid hormones can affect the reproductive axis’ ability to withstand stress. This insight is key to understand how chronodisruption leads to disease, and to design interventions to restore normal rhythmicity and health.

AbstractClinical classification is essential for estimating disease prevalence but is difficult, often requiring complex investigations. The widespread availability of population level genetic data makes novel genetic stratification techniques a highly attractive alternative. We propose a generalizable mathematical framework for determining disease prevalence within a cohort using genetic risk scores. We compare and evaluate methods based on the means of genetic risk scores’ distributions; the Earth Mover’s Distance between distributions; a linear combination of kernel density estimates of distributions; and an Excess method. We demonstrate the performance of genetic stratification to produce robust prevalence estimates. Specifically, we show that robust estimates of prevalence are still possible even with rarer diseases, smaller cohort sizes and less discriminative genetic risk scores, highlighting the general utility of these approaches. Genetic stratification techniques offer exciting new research tools, enabling unbiased insights into disease prevalence and clinical characteristics unhampered by clinical classification criteria.

Delay or failure to view test results in a hospital setting can lead to delayed diagnosis, risk of patient harm, and represents inefficiency. Factors influencing this were investigated to identify how timeliness and completeness of test review could be improved through an evidence-based redesign of the use of clinical test review software.A cross-section of all abnormal hematology and biochemistry results which were published on a digital test review platform over a 3-year period were investigated. The time it took for clinicians to view these results, and the results that were not viewed within 30 days, were analyzed relative to time of the week, the detailed type of test, and an indicator of patient record data quality.The majority of results were viewed within 90 min, and 93.9% of these results viewed on the digital platform within 30 days. There was significant variation in results review throughout the week, shown to be due to an interplay between technical and clinical workflow factors. Routine results were less likely to be reviewed, as were those with patient record data quality issues.The evidence suggests that test result review would be improved by stream-lining access to the result platform, differentiating between urgent and routine results, improving handover of responsibility for result review, and improving search for temporary patient records. Altering the timing of phlebotomy rounds and a review of the appropriateness of routine test requests at the weekend may also improve result review rates.

Variant allele frequencies (VAF) are an important measure of genetic variation that can be estimated at single-nucleotide variant (SNV) sites. RNA and DNA VAFs are used as indicators of a wide-range of biological traits, including tumor purity and ploidy changes, allele-specific expression and gene-dosage transcriptional response. Here we present a novel methodology to assess gene and chromosomal allele asymmetries and to aid in identifying genomic alterations in RNA and DNA datasets. Our approach is based on analysis of the VAF distributions in chromosomal segments (continuous multi-SNV genomic regions). In each segment we estimate variant probability, a parameter of a random process that can generate synthetic VAF samples that closely resemble the observed data. We show that variant probability is a biologically interpretable quantitative descriptor of the VAF distribution in chromosomal segments which is consistent with other approaches. To this end, we apply the proposed methodology on data from 72 samples obtained from patients with breast invasive carcinoma (BRCA) from the Cancer Genome Atlas (TCGA). We compare DNA and RNA VAF distributions from matched RNA and whole exome sequencing (WES) datasets and find that both genomic signals give very similar segmentation and estimated variant probability profiles. We also find a correlation between variant probability with copy number alterations (CNA). Finally, to demonstrate a practical application of variant probabilities, we use them to estimate tumor purity. Tumor purity estimates based on variant probabilities demonstrate good concordance with other approaches (Pearson’s correlation between 0.44 and 0.76). Our evaluation suggests that variant probabilities can serve as a dependable descriptor of VAF distribution, further enabling the statistical comparison of matched DNA and RNA datasets. Finally, they provide conceptual and mechanistic insights into relations between structure of VAF distributions and genetic events. The methodology is implemented in a Matlab toolbox that provides a suite of functions for analysis, statistical assessment and visualization of Genome and Transcriptome allele frequencies distributions. GeTallele is available at: https://github.com/SlowinskiPiotr/GeTallele.

BACKGROUND Kisspeptin is a key regulator of hypothalamic gonadotropin-releasing hormone (GnRH) neurons and is essential for reproductive health. A specific kisspeptin receptor (KISS1R) agonist could significantly expand the potential clinical utility of therapeutics targeting the kisspeptin pathway. Herein, we investigate the effects of a KISS1R agonist, MVT-602, in healthy women and in women with reproductive disorders.METHODS We conducted in vivo and in vitro studies to characterize the action of MVT-602 in comparison with native kisspeptin-54 (KP54). We determined the pharmacokinetic and pharmacodynamic properties of MVT-602 (doses 0.01 and 0.03 nmol/kg) versus KP54 (9.6 nmol/kg) in the follicular phase of healthy women (n = 9), and in women with polycystic ovary syndrome (PCOS; n = 6) or hypothalamic amenorrhea (HA; n = 6). Further, we investigated their effects on KISS1R-mediated inositol monophosphate (IP1) and Ca2+ signaling in cell lines and on action potential firing of GnRH neurons in brain slices.RESULTS in healthy women, the amplitude of luteinizing hormone (LH) rise was similar to that after KP54, but peaked later (21.4 vs. 4.7 hours; P = 0.0002), with correspondingly increased AUC of LH exposure (169.0 vs. 38.5 IU∙h/L; P = 0.0058). LH increases following MVT-602 were similar in PCOS and healthy women, but advanced in HA (P = 0.004). In keeping with the clinical data, MVT-602 induced more potent signaling of KISS1R-mediated IP1 accumulation and a longer duration of GnRH neuron firing than KP54 (115 vs. 55 minutes; P = 0.0012).CONCLUSION Taken together, these clinical and mechanistic data identify MVT-602 as having considerable therapeutic potential for the treatment of female reproductive disorders.TRIAL REGISTRATION International Standard Randomised Controlled Trial Number (ISRCTN) Registry, ISRCTN21681316.FUNDING National Institute for Health Research and NIH.

Inner hair cells (IHCs) are excitable sensory cells in the inner ear that encode acoustic information. Before the onset of hearing IHCs fire calcium-based action potentials that trigger transmitter release onto developing spiral ganglion neurones. There is accumulating experimental evidence that these spontaneous firing patterns are associated with maturation of the IHC synapses and hence involved in the development of hearing. The dynamics organising the IHCs’ electrical activity are therefore of interest. Building on our previous modelling work we propose a three-dimensional, reduced IHC model and carry out non-dimensionalisation. We show that there is a significant range of parameter values for which the dynamics of the reduced (three-dimensional) model map well onto the dynamics observed in the original biophysical (four-dimensional) IHC model. By estimating the typical time scales of the variables in the reduced IHC model we demonstrate that this model could be characterised by two fast and one slow or one fast and two slow variables depending on biophysically relevant parameters that control the dynamics. Specifically, we investigate how changes in the conductance of the voltage-gated calcium channels as well as the parameter corresponding to the fraction of free cytosolic calcium concentration in the model affect the oscillatory model bahaviour leading to transition from pseudo-plateau bursting to mixed-mode oscillations. Hence, using fast-slow analysis we are able to further our understanding of this model and reveal a path in the parameter space connecting pseudo-plateau bursting and mixed-mode oscillations by varying a single parameter in the model.

MOTIVATION: By testing for associations between DNA genotypes and gene expression levels, expression quantitative trait locus (eQTL) analyses have been instrumental in understanding how thousands of single nucleotide variants (SNVs) may affect gene expression. As compared to DNA genotypes, RNA genetic variation represents a phenotypic trait that reflects the actual allele content of the studied system. RNA genetic variation at expressed SNV loci can be estimated using the proportion of alleles bearing the variant nucleotide (variant allele fraction, VAFRNA). VAFRNA is a continuous measure which allows for precise allele quantitation in loci where the RNA alleles do not scale with the genotype count. We describe a method to correlate VAFRNA with gene expression and assess its ability to identify genetically regulated expression solely from RNA-sequencing (RNA-seq) datasets. RESULTS: We introduce ReQTL, an eQTL modification which substitutes the DNA allele count for the variant allele fraction at expressed SNV loci in the transcriptome (VAFRNA). We exemplify the method on sets of RNA-seq data from human tissues obtained though the Genotype-Tissue Expression (GTEx) project and demonstrate that ReQTL analyses are computationally feasible and can identify a subset of expressed eQTL loci. AVAILABILITY AND IMPLEMENTATION: a toolkit to perform ReQTL analyses is available at https://github.com/HorvathLab/ReQTL. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A novel, rapid single-cell assay for quantifying antibiotic accumulation in Gram-negative bacteria reveals important insights about bacterial drug accumulation.

Introduction COPD is a heterogeneous disease demonstrating inter-individual variation. A high COPD prevalence in Chinese populations is described but little is known about disease clusters and prognostic outcomes in the Chinese population across South-East Asia. We aim to determine if clusters of Chinese patients with COPD exist and their association with systemic inflammation and clinical outcomes. Methods Chinese patients with stable COPD were prospectively recruited into two cohorts (derivation and validation) from six hospitals across three South-East Asian countries (Singapore, Malaysia and Hong Kong; n=1,480). Each patient was followed over two-years. Clinical data (including co-morbidities) were employed in unsupervised hierarchical clustering (followed by validation) to determine the existence of patient clusters and their prognostic outcome. Accompanying systemic cytokine assessments were performed in a subset (n=336) of COPD patients to determine if inflammatory patterns and associated networks characterised the derived clusters. Results Five patient clusters were identified including (1) Ex-tuberculosis (2) Diabetic (3) Low co-morbidity: low-risk (4) Low co-morbidity: high-risk and (5) cardiovascular. The ‘cardiovascular’ and ‘ex-tuberculosis’ clusters demonstrate highest mortality (independent of GOLD assessment) and illustrate diverse cytokine patterns with complex inflammatory networks. Conclusions We describe novel ‘clusters’ of Chinese COPD patients, two of which represent ‘high-risk’ clusters. The ‘cardiovascular’ and ‘ex-tuberculosis’ patient clusters exhibit high mortality, significant inflammation and complex cytokine networks. Clinical and inflammatory risk stratification of Chinese patients with COPD should be considered for targeted intervention to improve disease outcomes.

Ageing has significant effects on circadian behaviour across a wide variety of species, but the underlying mechanisms are poorly understood. Previous work has demonstrated the age-dependent decline in behavioural output in the model organism Drosophila. We demonstrate this age-dependent decline in circadian output is combined with changes in daily activity of Drosophila. Ageing also has a large impact on sleep behaviour, significantly increasing sleep duration whilst reducing latency. We used electrophysiology to record from large ventral lateral neurons (l-LNv) of the Drosophila circadian clock, finding a significant decrease in input resistance with age, but no significant changes in spontaneous electrical activity or membrane potential. We propose this change contributes to observed behavioural and sleep changes in light-dark conditions. We also demonstrate a reduction in the daily plasticity of the architecture of the small ventral lateral neurons (s-LNv), likely underlying the reduction in circadian rhythmicity during ageing. These results provide further insights into the effect of ageing on circadian biology, demonstrating age-related changes in electrical activity in conjunction with the decline in behavioural outputs.

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients’ data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework.
The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient’s treatment therapies.

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients’ data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient’s treatment therapies.

Children with developmental coordination disorder (DCD) struggle with the acquisition of coordinated motor skills. This paper adopts a dynamical systems perspective to assess how individual coordination solutions might emerge following an intervention that trained accurate gaze control in a throw and catch task. Kinematic data were collected from six upper body sensors from twenty-one children with DCD, using a 3D motion analysis system, before and after a 4-week training intervention. Covariance matrices between kinematic measures were computed and distances between pairs of covariance matrices calculated using Riemannian geometry. Multidimensional scaling was then used to analyse differences between coordination patterns. The gaze trained group revealed significantly higher total coordination (sum of all the pairwise covariances) following training than a technique-trained control group. While the increase in total coordination also significantly predicted improvement in task performance, the distinct post-intervention coordination patterns for the gaze trained group were not consistent. Additionally, the gaze trained group revealed individual coordination patterns for successful catch attempts that were different from all the coordination patterns before training, whereas the control group did not. Taken together, the results of this interdisciplinary study illustrate how gaze training may encourage the emergence of coordination via self-organization in children with DCD.

Normal reproductive functioning is critically dependent on pulsatile secretion of luteinising hormone (LH). Assessment of LH pulsatility is important for the clinical diagnosis of reproductive disorders, but current methods are hampered by frequent blood sampling coupled to expensive serial immunochemical analysis. Here, we report the development and application of a Robotic APTamer-enabled Electrochemical Reader (RAPTER) electrochemical analysis system to determine LH pulsatility. Through selective evolution of ligands by exponential enrichment (SELEX), we identify DNA aptamers that bind specifically to LH and not to related hormones. The aptamers are integrated into electrochemical aptamer-based (E-AB) sensors on a robotic platform. E-AB enables rapid, sensitive and repeatable determination of LH concentration profiles. Bayesian Spectrum Analysis is applied to determine LH pulsatility in three distinct patient cohorts. This technology has the potential to transform the clinical care of patients with reproductive disorders and could be developed to allow real-time in vivo hormone monitoring.

Abstract like in mammals, Drosophila circadian clock neurons display rhythms of activity with higher action potential firing rates and more positive resting membrane potentials during the day. This rhythmic excitability has been widely observed but, critically, its regulation remains unresolved. We have characterized and modeled the changes underlying these electrical activity rhythms in the lateral ventral clock neurons (LNvs). We show that currents mediated by the voltage-gated potassium channels Shaw (Kv3) and Shal (Kv4) oscillate in a circadian manner. Disruption of these channels, by expression of dominant negative (DN) subunits, leads to changes in circadian locomotor activity and shortens lifespan. LNv whole-cell recordings then show that changes in Shaw and Shal currents drive changes in action potential firing rate and that these rhythms are abolished when the circadian molecular clock is stopped. A whole-cell biophysical model using Hodgkin-Huxley equations can recapitulate these changes in electrical activity. Based on this model and by using dynamic clamp to manipulate clock neurons directly, we can rescue the pharmacological block of Shaw and Shal, restore the firing rhythm, and thus demonstrate the critical importance of Shaw and Shal. Together, these findings point to a key role for Shaw and Shal in controlling circadian firing of clock neurons and show that changes in clock neuron currents can account for this. Moreover, with dynamic clamp we can switch the LNvs between morning-like and evening-like states of electrical activity. We conclude that changes in Shaw and Shal underlie the daily oscillation in LNv firing rate. This article is protected by copyright. All rights reserved

Fertility critically depends on the gonadotropin-releasing hormone (GnRH) pulse generator, a neural construct comprised of hypothalamic neurons co-expressing kisspeptin, neurokoinin-B and dynorphin. Here, using mathematical modelling and in-vivo optogenetics we reveal for the first time how this neural construct initiates and sustains the appropriate ultradian frequency essential for reproduction. Prompted by mathematical modelling, we show experimentally using female estrous mice that robust pulsatile release of luteinizing hormone, a proxy for GnRH, emerges abruptly as we increase the basal activity of the neuronal network using continuous low frequency optogenetic stimulation. Further increase in basal activity markedly increases pulse frequency and eventually leads to pulse termination. Additional model predictions that pulsatile dynamics emerge from non-linear positive and negative feedback interactions mediated through neurokinin-B and dynorphin signaling respectively are confirmed neuropharmacologically. Our results shed light on the long-elusive GnRH pulse generator offering new horizons for reproductive health and wellbeing.SIGNIFICANCE STATEMENTThe gonadotropin-releasing hormone (GnRH) pulse generator controls the pulsatile secretion of the gonadotropic hormones LH and FSH and is critical for fertility. The hypothalamic arcuate kisspeptin neurons are thought to represent the GnRH pulse generator, since their oscillatory activity is coincident with LH pulses in the blood; a proxy for GnRH pulses. However, the mechanisms underlying GnRH pulse generation remain elusive. We developed a mathematical model of the kisspeptin neuronal network and confirmed its predictions experimentally, showing how LH secretion is frequency-modulated as we increase the basal activity of the arcuate kisspeptin neurons in-vivo using continuous optogenetic stimulation. Our model provides a quantitative framework for understanding the reproductive neuroendocrine system and opens new horizons for fertility regulation.

AbstractEssential Tremor (ET) is one of the most common neurological diseases, with an estimated 7 million affected individuals in the US; the pathophysiology of the disorder is poorly understood. Recently, we identified a mutation (KCNS2 (Kv9.2), c.1137 T > A, p.(D379E) in an electrically silent voltage-gated K+ channel α-subunit, Kv9.2, in a family with ET, that modulates the activity of Kv2 channels. We have produced transgenic Drosophila lines that express either the human wild type Kv9.2 (hKv9.2) or the ET causing mutant Kv9.2 (hKv9.2-D379E) subunit in all neurons. We show that the hKv9.2 subunit modulates activity of endogenous Drosophila K+ channel Shab. The mutant hKv9.2-D379E subunit showed significantly higher levels of Shab inactivation and a higher frequency of spontaneous firing rate consistent with neuronal hyperexcitibility. We also observed behavioral manifestations of nervous system dysfunction including effects on night time activity and sleep. This functional data further supports the pathogenicity of the KCNS2 (p.D379E) mutation, consistent with our prior observations including co-segregation with ET in a family, a likely pathogenic change in the channel pore domain and absence from population databases. The Drosophila hKv9.2 transgenic model recapitulates several features of ET and may be employed to advance our understanding of ET disease pathogenesis.

The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer's disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4-12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing. To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable “quiescent” equilibrium to a more stable “active” equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper, we consider a localized form of non-diffusive (i.e. pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However, we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation, we find increasing coefficient of variation of the subsequent escape times.

It is well known that the addition of noise in a multistable system can
induce random transitions between stable states. The rate of transition can be
characterised in terms of the noise-free system's dynamics and the added noise:
for potential systems in the presence of asymptotically low noise the
well-known Kramers' escape time gives an expression for the mean escape time.
This paper examines some general properties and examples of transitions between
local steady and oscillatory attractors within networks: the transition rates
at each node may be affected by the dynamics at other nodes. We use first
passage time theory to explain some properties of scalings noted in the
literature for an idealised model of initiation of epileptic seizures in small
systems of coupled bistable systems with both steady and oscillatory
attractors. We focus on the case of sequential escapes where a steady attractor
is only marginally stable but all nodes start in this state. As the nodes
escape to the oscillatory regime, we assume that the transitions back are very
infrequent in comparison. We quantify and characterise the resulting sequences
of noise-induced escapes. For weak enough coupling we show that a master
equation approach gives a good quantitative understanding of sequential
escapes, but for strong coupling this description breaks down.

It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives an expression for the mean escape time in the asymptotic limit. If a number of multistable systems are coupled into a network structure, a transition at one site may change the transition properties at other sites. We study the case of escape from a "quiescent" attractor to an "active" attractor in which transitions back can be ignored. There are qualitatively different regimes of transition, depending on coupling strength. For small coupling strengths, the transition rates are simply modified but the transitions remain stochastic. For large coupling strengths, transitions happen approximately in synchrony-we call this a "fast domino" regime. There is also an intermediate coupling regime where some transitions happen inexorably but with a delay that may be arbitrarily long-we call this a "slow domino" regime. We characterize these regimes in the low noise limit in terms of bifurcations of the potential landscape of a coupled system. We demonstrate the effect of the coupling on the distribution of timings and (in general) the sequences of escapes of the system.

Biology emerges from interactions between molecules, which are challenging to elucidate with current techniques. An orthogonal approach is to probe for 'response signatures' that identify specific circuit motifs. For example, bistability, hysteresis, or irreversibility are used to detect positive feedback loops. For adapting systems, such signatures are not known. Only two circuit motifs generate adaptation: negative feedback loops (NFLs) and incoherent feed-forward loops (IFFLs). On the basis of computational testing and mathematical proofs, we propose differential signatures: in response to oscillatory stimulation, NFLs but not IFFLs show refractory-period stabilization (robustness to changes in stimulus duration) or period skipping. Applying this approach to yeast, we identified the circuit dominating cell cycle timing. In Caenorhabditis elegans AWA neurons, which are crucial for chemotaxis, we uncovered a Ca2+ NFL leading to adaptation that would be difficult to find by other means. These response signatures allow direct access to the outlines of the wiring diagrams of adapting systems.

AbstractWe present novel, low-cost and non-invasive potential diagnostic biomarkers of schizophrenia. They are based on the ‘mirror-game’, a coordination task in which two partners are asked to mimic each other’s hand movements. In particular, we use the patient’s solo movement, recorded in the absence of a partner, and motion recorded during interaction with an artificial agent, a computer avatar or a humanoid robot. In order to discriminate between the patients and controls, we employ statistical learning techniques, which we apply to nonverbal synchrony and neuromotor features derived from the participants’ movement data. The proposed classifier has 93% accuracy and 100% specificity. Our results provide evidence that statistical learning techniques, nonverbal movement coordination and neuromotor characteristics could form the foundation of decision support tools aiding clinicians in cases of diagnostic uncertainty.

UNLABELLED: the formation and deposition of tau protein aggregates is proposed to contribute to cognitive impairments in dementia by disrupting neuronal function in brain regions, including the hippocampus. We used a battery of in vivo and in vitro electrophysiological recordings in the rTg4510 transgenic mouse model, which overexpresses a mutant form of human tau protein, to investigate the effects of tau pathology on hippocampal neuronal function in area CA1 of 7- to 8-month-old mice, an age point at which rTg4510 animals exhibit advanced tau pathology and progressive neurodegeneration. In vitro recordings revealed shifted theta-frequency resonance properties of CA1 pyramidal neurons, deficits in synaptic transmission at Schaffer collateral synapses, and blunted plasticity and imbalanced inhibition at temporoammonic synapses. These changes were associated with aberrant CA1 network oscillations, pyramidal neuron bursting, and spatial information coding in vivo. Our findings relate tauopathy-associated changes in cellular neurophysiology to altered behavior-dependent network function. SIGNIFICANCE STATEMENT: Dementia is characterized by the loss of learning and memory ability. The deposition of tau protein aggregates in the brain is a pathological hallmark of dementia; and the hippocampus, a brain structure known to be critical in processing learning and memory, is one of the first and most heavily affected regions. Our results show that, in area CA1 of hippocampus, a region involved in spatial learning and memory, tau pathology is associated with specific disturbances in synaptic, cellular, and network-level function, culminating in the aberrant encoding of spatial information and spatial memory impairment. These studies identify several novel ways in which hippocampal information processing may be disrupted in dementia, which may provide targets for future therapeutic intervention.

In 1985, Haken, Kelso and Bunz proposed a system of coupled nonlinear oscillators as a model of rhythmic movement patterns in human bimanual coordination. Since then, the Haken–Kelso–Bunz (HKB) model has become a modelling paradigm applied extensively in all areas of movement science, including interpersonal motor coordination. However, all previous studies have followed a line of analysis based on slowly varying amplitudes and rotating wave approximations. These approximations lead to a reduced system, consisting of a single differential equation representing the evolution of the relative phase of the two coupled oscillators: the HKB model of the relative phase. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space and for general coupling strengths. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bistability between a variety of coordination patterns. Furthermore, we identify the stability boundaries of distinct coordination regimes in the model and discuss the applicability of our findings to interpersonal coordination and other joint action tasks.

The Pinsky-Rinzel model is a non-smooth 2-compartmental CA3 pyramidal cell model that has been used widely within the field of neuroscience. Here we propose a modified (smooth) system that captures the qualitative behaviour of the original model, while allowing the use of available, numerical continuation methods to perform full-system bifurcation and fast-slow analysis. We study the bifurcation structure of the full system as a function of the applied current and the maximal calcium conductance. We identify the bifurcations that shape the transitions between resting, bursting and spiking behaviours, and which lead to the disappearance of bursting when the calcium conductance is reduced. Insights gained from this analysis, are then used to firstly illustrate how the irregular spiking activity found between bursting and stable spiking states, can be influenced by phase differences in the calcium and dendritic voltage, which lead to corresponding changes in the calcium-sensitive potassium current. Furthermore, we use fast-slow analysis to investigate the mechanisms of bursting and show that bursting in the model is dependent on the intermediately slow variable, calcium, while the other slow variable, the activation gate of the afterhyperpolarisation current, does not contribute to setting the intraburst dynamics but participates in setting the interburst interval. Finally, we discuss how some of the described bifurcations affect spiking behaviour, during sharp-wave ripples, in a larger network of Pinsky-Rinzel cells.

Author Summary Hebbian or associative plasticity is triggered by postsynaptic Ca2+ influx which activates calmodulin and CaMKII. The influx of Ca2+ through voltage-dependent NMDA receptors and Ca2+ channels is regulated by Ca2+ -activated K+ channels (SK-channels) providing negative feedback regulation of postsynaptic [Ca2+]. Using 3-dimensional modeling of Ca2+ and calmodulin dynamics within dendritic spines we show that the non-linear relationship between Ca2+ influx and calmodulin activation endows SK-channels with the ability to ?gate? calmodulin activation and therefore the induction of Hebbian synaptic plasticity. Since SK-channels are inhibited by several neuromodulator receptors including acetylcholine and noradrenaline, the gating of synaptic plasticity by SK-channels could represent a common mechanism by which neuromodulators control the induction of synaptic plasticity.

Joint improvisation is often observed among humans performing joint action tasks. Exploring the underlying cognitive and neural mechanisms behind the emergence of joint improvisation is an open research challenge. This paper investigates jointly improvised movements between two participants in the mirror game, a paradigmatic joint task example. First, experiments involving movement coordination of different dyads of human players are performed in order to build a human benchmark. No designation of leader and follower is given beforehand. We find that joint improvisation is characterized by the lack of a leader and high levels of movement synchronization. Then, a theoretical model is proposed to capture some features of their interaction, and a set of experiments is carried out to test and validate the model ability to reproduce the experimental observations. Furthermore, the model is used to drive a computer avatar able to successfully improvise joint motion with a human participant in real time. Finally, a convergence analysis of the proposed model is carried out to confirm its ability to reproduce joint movements between the participants.

Human movement has been studied for decades, and dynamic laws of motion that are common to all humans have been derived. Yet, every individual moves differently from everyone else (faster/slower, harder/smoother, etc.). We propose here an index of such variability, namely an individual motor signature (IMS) able to capture the subtle differences in the way each of us moves. We show that the IMS of a person is time-invariant and that it significantly differs from those of other individuals. This allows us to quantify the dynamic similarity, a measure of rapport between dynamics of different individuals' movements, and demonstrate that it facilitates coordination during interaction. We use our measure to confirm a key prediction of the theory of similarity that coordination between two individuals performing a joint-action task is higher if their motions share similar dynamic features. Furthermore, we use a virtual avatar driven by an interactive cognitive architecture based on feedback control theory to explore the effects of different kinematic features of the avatar motion on coordination with human players.

Motor coordination is an important feature of intra- and inter-personal interactions, and several scenarios — from finger tapping to human-computer interfaces — have been investigated experimentally. In the 1980s, Haken, Kelso and Bunz formulated a coupled nonlinear two-oscillator model, which has been shown to describe many observed aspects of coordination tasks. We present here a bifurcation study of this model, where we consider a delay in the coupling. The delay is shown to have a significant effect on the observed dynamics. In particular, we find a much larger degree of bistablility between in-phase and anti-phase oscillations in the presence of a frequency detuning.

Type 1 diabetes (T1D) is an auto-immune disease characterized by the selective destruction of the insulin secreting beta cells in the pancreas during an inflammatory phase known as insulitis. Patients with T1D are typically dependent on the administration of externally provided insulin in order to manage blood glucose levels. Whilst technological developments have significantly improved both the life expectancy and quality of life of these patients, an understanding of the mechanisms of the disease remains elusive. Animal models, such as the NOD mouse model, have been widely used to probe the process of insulitis, but there exist very few data from humans studied at disease onset. In this manuscript, we employ data from human pancreases collected close to the onset of T1D and propose a spatio-temporal computational model for the progression of insulitis in human T1D, with particular focus on the mechanisms underlying the development of insulitis in pancreatic islets. This framework allows us to investigate how the time-course of insulitis progression is affected by altering key parameters, such as the number of the CD20+ B cells present in the inflammatory infiltrate, which has recently been proposed to influence the aggressiveness of the disease. Through the analysis of repeated simulations of our stochastic model, which track the number of beta cells within an islet, we find that increased numbers of B cells in the peri-islet space lead to faster destruction of the beta cells. We also find that the balance between the degradation and repair of the basement membrane surrounding the islet is a critical component in governing the overall destruction rate of the beta cells and their remaining number. Our model provides a framework for continued and improved spatio-temporal modeling of human T1D. Type 1 diabetes (T1D) is an auto-immune disease characterized by the selective destruction of the insulin secreting beta cells in the pancreas during an inflammatory phase known as insulitis. Patients with T1D are typically dependent on the administration of externally provided insulin in order to manage blood glucose levels. Whilst technological developments have significantly improved both the life expectancy and quality of life of these patients, an understanding of the mechanisms of the disease remains elusive. Animal models, such as the NOD mouse model, have been widely used to probe the process of insulitis, but there exist very few data from humans studied at disease onset. In this manuscript, we employ data from human pancreases collected close to the onset of T1D and propose a spatio-temporal computational model for the progression of insulitis in human T1D, with particular focus on the mechanisms underlying the development of insulitis in pancreatic islets. This framework allows us to investigate how the time-course of insulitis progression is affected by altering key parameters, such as the number of the CD20+ B cells present in the inflammatory infiltrate, which has recently been proposed to influence the aggressiveness of the disease. Through the analysis of repeated simulations of our stochastic model, which track the number of beta cells within an islet, we find that increased numbers of B cells in the peri-islet space lead to faster destruction of the beta cells. We also find that the balance between the degradation and repair of the basement membrane surrounding the islet is a critical component in governing the overall destruction rate of the beta cells and their remaining number. Our model provides a framework for continued and improved spatio-temporal modeling of human T1D.

BACKGROUND: Understanding the influence of stress on human performance is of theoretical and practical importance. An individual's reaction to stress predicts their subsequent performance; with a "challenge" response to stress leading to better performance than a "threat" response. However, this contention has not been tested in truly stressful environments with highly skilled individuals. Furthermore, the effect of challenge and threat responses on attentional control during visuomotor tasks is poorly understood. DESIGN: Thus, this study aimed to examine individual reactions to stress and their influence on attentional control, among a cohort of commercial pilots performing a stressful flight assessment. METHODS: Sixteen pilots performed an "engine failure on take-off" scenario, in a high-fidelity flight simulator. Reactions to stress were indexed via self-report; performance was assessed subjectively (flight instructor assessment) and objectively (simulator metrics); gaze behavior data were captured using a mobile eye tracker, and measures of attentional control were subsequently calculated (search rate, stimulus driven attention, and entropy). RESULTS: Hierarchical regression analyses revealed that a threat response was associated with poorer performance and disrupted attentional control. CONCLUSION: the findings add to previous research showing that individual reactions to stress influence performance and shed light on the processes through which stress influences performance.

the changes in neuronal firing pattern are signatures of brain function, and it is of interest to understand how such changes evolve as a function of neuronal biophysical properties. We address this important problem by the analysis and numerical investigation of a class of mechanistic mathematical models. We focus on a hippocampal pyramidal neuron model and study the occurrence of bursting related to the after-depolarization (ADP) that follows a brief current injection. This type of burst is a transient phenomenon that is not amenable to the classical bifurcation analysis done, for example, for periodic bursting oscillators. In this letter, we show how to formulate such transient behavior as a two-point boundary value problem (2PBVP), which can be solved using well-known continuation methods. The 2PBVP is formulated such that the transient response is represented by a finite orbit segment for which onsets of ADP and additional spikes in a burst can be detected as bifurcations during a one-parameter continuation. This in turn provides us with a direct method to approximate the boundaries of regions in a two-parameter plane where certain model behavior of interest occurs. More precisely, we use two-parameter continuation of the detected onset points to identify the boundaries between regions with and without ADP and bursts with different numbers of spikes. Our 2PBVP formulation is a novel approach to parameter sensitivity analysis that can be applied to a wide range of problems.

Population-level measurements of phenotypic behaviour in biological systems may not necessarily reflect individual cell behaviour. To assess qualitative changes in the behaviour of a single cell, when alone and when part of a community, we developed an agent-based model describing the metabolic states of a population of quorum-coupled cells. The modelling is motivated by published experimental work of a synthetic genetic regulatory network (GRN) used in Escherichia coli cells that exhibit oscillatory behaviour across the population. To decipher the mechanisms underlying oscillations in the system, we investigate the behaviour of the model via numerical simulation and bifurcation analysis. In particular, we study the effect of an increase in population size as well as the spatio-temporal behaviour of the model. Our results demonstrate that oscillations are possible only in the presence of a high concentration of the coupling chemical and are due to a time scale separation in key regulatory components of the system. The model suggests that the population establishes oscillatory behaviour as the system's preferred stable state. This is achieved via an effective increase in coupling across the population. We conclude that population effects in GRN design need to be taken into consideration and be part of the design process. This is important in planning intervention strategies or designing specific cell behaviours.

Many extracellular signals act via the Raf/MEK/ERK cascade in which kinetics, cell-cell variability, and sensitivity of the ERK response can all influence cell fate. Here we used automated microscopy to explore the effects of ERK-mediated negative feedback on these attributes in cells expressing endogenous ERK or ERK2-GFP reporters. We studied acute rather than chronic stimulation with either epidermal growth factor (ErbB1 activation) or phorbol 12,13-dibutyrate (PKC activation). In unstimulated cells, ERK-mediated negative feedback reduced the population-average and cell-cell variability of the level of activated ppERK and increased its robustness to changes in ERK expression. In stimulated cells, negative feedback (evident between 5 min and 4 h) also reduced average levels and variability of phosphorylated ERK (ppERK) without altering the "gradedness" or sensitivity of the response. Binning cells according to total ERK expression revealed, strikingly, that maximal ppERK responses initially occur at submaximal ERK levels and that this non-monotonic relationship changes to an increasing, monotonic one within 15 min. These phenomena occur in HeLa cells and MCF7 breast cancer cells and in the presence and absence of ERK-mediated negative feedback. They were best modeled assuming distributive (rather than processive) activation. Thus, we have uncovered a novel, time-dependent change in the relationship between total ERK and ppERK levels that persists without negative feedback. This change makes acute response kinetics dependent on ERK level and provides a "gating" or control mechanism in which the interplay between stimulus duration and the distribution of ERK expression across cells could modulate the proportion of cells that respond to stimulation.

Sarcoplasmic/endoplasmic reticulum (SR) and nuclear membranes contain two related cation channels named TRIC-A and TRIC-B. In many tissues, both subtypes are co-expressed, making it impossible to distinguish the distinct single-channel properties of each subtype. We therefore incorporated skeletal muscle SR vesicles derived from Tric-a-knockout mice into bilayers in order to characterise the biophysical properties of native TRIC-B without possible misclassification of the channels as TRIC-A, and without potential distortion of functional properties by detergent purification protocols. The native TRIC-B channels were ideally selective for cations. In symmetrical 210 mM K(+), the maximum (full) open channel level (199 pS) was equivalent to that observed when wild-type SR vesicles were incorporated into bilayers. Analysis of TRIC-B gating revealed complex and variable behaviour. Four main sub-conductance levels were observed at approximately 80 % (161 pS), 60 % (123 pS), 46 % (93 pS), and 30 % (60 pS) of the full open state. Seventy-five percent of the channels were voltage sensitive with Po being markedly reduced at negative holding potentials. The frequent, rapid transitions between TRIC-B sub-conductance states prevented development of reliable gating models using conventional single-channel analysis. Instead, we used mean-variance plots to highlight key features of TRIC-B gating in a more accurate and visually useful manner. Our study provides the first biophysical characterisation of native TRIC-B channels and indicates that this channel would be suited to provide counter current in response to Ca(2+) release from the SR. Further experiments are required to distinguish the distinct functional properties of TRIC-A and TRIC-B and understand their individual but complementary physiological roles.

Postsynaptic Ca(2+) transients triggered by neurotransmission at excitatory synapses are a key signaling step for the induction of synaptic plasticity and are typically recorded in tissue slices using two-photon fluorescence imaging with Ca(2+)-sensitive dyes. The signals generated are small with very low peak signal/noise ratios (pSNRs) that make detailed analysis problematic. Here, we implement a wavelet-based de-noising algorithm (PURE-LET) to enhance signal/noise ratio for Ca(2+) fluorescence transients evoked by single synaptic events under physiological conditions. Using simulated Ca(2+) transients with defined noise levels, we analyzed the ability of the PURE-LET algorithm to retrieve the underlying signal. Fitting single Ca(2+) transients with an exponential rise and decay model revealed a distortion of τ(rise) but improved accuracy and reliability of τ(decay) and peak amplitude after PURE-LET de-noising compared to raw signals. The PURE-LET de-noising algorithm also provided a ∼30-dB gain in pSNR compared to ∼16-dB pSNR gain after an optimized binomial filter. The higher pSNR provided by PURE-LET de-noising increased discrimination accuracy between successes and failures of synaptic transmission as measured by the occurrence of synaptic Ca(2+) transients by ∼20% relative to an optimized binomial filter. Furthermore, in comparison to binomial filter, no optimization of PURE-LET de-noising was required for reducing arbitrary bias. In conclusion, the de-noising of fluorescent Ca(2+) transients using PURE-LET enhances detection and characterization of Ca(2+) responses at central excitatory synapses.

We describe a phenomenological model of seizure initiation, consisting of a bistable switch between stable fixed point and stable limit-cycle attractors. We determine a quasi-analytic formula for the exit time problem for our model in the presence of noise. This formula--which we equate to seizure frequency--is then validated numerically, before we extend our study to explore the combined effects of noise and network structure on escape times. Here, we observe that weakly connected networks of 2, 3 and 4 nodes with equivalent first transitive components all have the same asymptotic escape times. We finally extend this work to larger networks, inferred from electroencephalographic recordings from 35 patients with idiopathic generalised epilepsies and 40 controls. Here, we find that network structure in patients correlates with smaller escape times relative to network structures from controls. These initial findings are suggestive that network structure may play an important role in seizure initiation and seizure frequency.

Large-scale collective behaviors such as synchronization and coordination spontaneously arise in many bacterial populations. With systems biology attempting to understand these phenomena, and synthetic biology opening up the possibility of engineering them for our own benefit, there is growing interest in how bacterial populations are best modeled. Here we introduce BSim, a highly flexible agent-based computational tool for analyzing the relationships between single-cell dynamics and population level features. BSim includes reference implementations of many bacterial traits to enable the quick development of new models partially built from existing ones. Unlike existing modeling tools, BSim fully considers spatial aspects of a model allowing for the description of intricate micro-scale structures, enabling the modeling of bacterial behavior in more realistic three-dimensional, complex environments. The new opportunities that BSim opens are illustrated through several diverse examples covering: spatial multicellular computing, modeling complex environments, population dynamics of the lac operon, and the synchronization of genetic oscillators. BSim is open source software that is freely available from http://bsim-bccs.sf.net and distributed under the Open Source Initiative (OSI) recognized MIT license. Developer documentation and a wide range of example simulations are also available from the website. BSim requires Java version 1.6 or higher. © 2012 Gorochowski et al.

By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events. The spatio-temporal mechanisms through which these events occur are however not fully understood, due in part to the inherent challenges in tracking single molecules moving within an intracellular medium. As a result, theoretical predictions of secretion times are still lacking. Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes. Using parameters from Shigella flexneri we are able to test the role that translocators might have to activate the needle complexes and offer semi-quantitative explanations of recent experimental observations.

Legumes form symbioses with rhizobial bacteria and arbuscular mycorrhizal fungi that aid plant nutrition. A critical component in the establishment of these symbioses is nuclear-localized calcium (Ca(2+)) oscillations. Different components on the nuclear envelope have been identified as being required for the generation of the Ca(2+) oscillations. Among these an ion channel, Doesn't Make Infections1, is preferentially localized on the inner nuclear envelope and a Ca(2+) ATPase is localized on both the inner and outer nuclear envelopes. Doesn't Make Infections1 is conserved across plants and has a weak but broad similarity to bacterial potassium channels. A possible role for this cation channel could be hyperpolarization of the nuclear envelope to counterbalance the charge caused by the influx of Ca(2+) into the nucleus. Ca(2+) channels and Ca(2+) pumps are needed for the release and reuptake of Ca(2+) from the internal store, which is hypothesized to be the nuclear envelope lumen and endoplasmic reticulum, but the release mechanism of Ca(2+) remains to be identified and characterized. Here, we develop a mathematical model based on these components to describe the observed symbiotic Ca(2+) oscillations. This model can recapitulate Ca(2+) oscillations, and with the inclusion of Ca(2+)-binding proteins it offers a simple explanation for several previously unexplained phenomena. These include long periods of frequency variation, changes in spike shape, and the initiation and termination of oscillations. The model also predicts that an increase in buffering capacity in the nucleoplasm would cause a period of rapid oscillations. This phenomenon was observed experimentally by adding more of the inducing signal.

A great deal of work has gone into classifying bursting oscillations, periodic alternations of spiking and quiescence modeled by fast-slow systems. In such systems, one or more slow variables carry the fast variables through a sequence of bifurcations that mediate transitions between oscillations and steady states. A rigorous classification approach is to characterize the bifurcations found in the neighborhood of a singularity; a measure of the complexity of the bursting oscillation is then given by the smallest codimension of the singularities near which it occurs. Fold/homoclinic bursting, along with most other burst types of interest, has been shown to occur near a singularity of codimension three by examining bifurcations of a cubic Liénard system; hence, these types of bursting have at most codimension three. Modeling and biological considerations suggest that fold/homoclinic bursting should be found near fold/subHopf bursting, a more recently identified burst type whose codimension has not been determined yet. One would expect that fold/subHopf bursting has the same codimension as fold/homoclinic bursting, because models of these two burst types have very similar underlying bifurcation diagrams. However, no codimension-three singularity is known that supports fold/subHopf bursting, which indicates that it may have codimension four. We identify a three-dimensional slice in a partial unfolding of a doubly-degenerate Bodganov-Takens point, and show that this codimension-four singularity gives rise to almost all known types of bursting.

Gonadotropin-releasing hormone (GnRH) mediates control of reproduction. It is secreted in pulses and acts via intracellular effectors to activate gonadotrophin secretion and gene expression. Sub-maximal GnRH pulse frequency can elicit maximal responses, yielding bell-shaped frequency-response curves characteristic of genuine frequency decoders. GnRH frequency decoding is therapeutically important (pulsatile GnRH can drive ovulation in assisted reproduction whereas sustained activation can treat breast and prostate cancers), but the mechanisms are unknown. Here, we consider the possibility that it is due to convergence of distinct pulsatile signals at the transcriptome. We develop a model that mirrors wet-laboratory data for activation and nuclear translocation of GnRH effectors (extracellular signal regulated kinase and nuclear factors of activated T-cells) and incorporates transcription. The model predicts genuine frequency decoding when two transcription factors (TFs) converge at a cooperative gate, and shows how optimal pulse frequency could reflect TF activation kinetics and affinities. Importantly, this behaviour is revealed as an emergent feature of the network, rather than an intrinsic feature of a given protein or pathway, and since such network topology is extremely common, may well be widespread in biological systems.

GnRH (gonadotropin-releasing hormone) mediates control of reproduction. It is secreted in pulses and acts via intracellular effectors to activate gene expression. Submaximal GnRH pulse frequency can elicit maximal responses, yielding bell-shaped frequency-response curves characteristic of genuine frequency decoders. GnRH frequency decoding is therapeutically important (pulsatile GnRH can drive ovulation in assisted reproduction, whereas sustained activation can treat breast and prostate cancers), but the mechanisms are unknown. In the present paper, we review recent work in this area, placing emphasis on the regulation of transcription, and showing how mathematical modelling of GnRH effects on two effectors [ERK (extracellular-signal-regulated kinase) and NFAT (nuclear factor of activated T-cells)] reveals the potential for genuine frequency decoding as an emergent feature of the GnRH signalling network, rather than an intrinsic feature of a given protein or pathway within it.

We have explored the possible role of dual specificity phosphatases (DUSPs) on acute EGF-mediated ERK signalling using high content imaging and a delayed MEK inhibition protocol to distinguish direct and indirect effects of the phosphatases on ERK activity. Using siRNAs, we were unable to find evidence that any of the MAPK phosphatases (MKPs) expressed in HeLa cells acts directly to dephosphorylate ppERK1/2 (dual phosphorylated ERKs 1 and/or 2) in the acute time-frame tested (0-14 min). Nevertheless, siRNAs against two p38/JNK MKPs (DUSPs 10 and 16) inhibited acute EGF-stimulated ERK activation. No such effect was seen for acute effects of the protein kinase C activator PDBu (phorbol 12,13 dibutyrate) on ERK activity, although effects of EGF and PDBu on ERK-dependent transcription (Egr-1 luciferase activity) were both reduced by siRNA targeting DUSPs 10 and 16. Inhibition of EGF-stimulated ERK activity by these siRNAs was reversed by pharmacological inhibition of p38 MAPK and single cell analysis revealed that the siRNAs did not influence the nuclear-cytoplasmic distribution of ppERK1/2. Thus, DUSPs 10 and 16 are positive regulators of activation, apparently acting by modulating cross-talk between the p38 and ERK pathways. A simplified mathematical model of this scenario accurately predicted the experimental data, supporting the conclusion that the major mechanism by which MKPs influence acute EGF-stimulated ERK responses is the negative regulation of p38, resulting in the positive regulation of ERK phosphorylation and activity.

Transient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism.

Changes in FKBP12.6 binding to cardiac ryanodine receptors (RyR2) are implicated in mediating disturbances in Ca(2+)-homeostasis in heart failure but there is controversy over the functional effects of FKBP12.6 on RyR2 channel gating. We have therefore investigated the effects of FKBP12.6 and another structurally similar molecule, FKBP12, which is far more abundant in heart, on the gating of single sheep RyR2 channels incorporated into planar phospholipid bilayers and on spontaneous waves of Ca(2+)-induced Ca(2+)-release in rat isolated permeabilised cardiac cells. We demonstrate that FKBP12 is a high affinity activator of RyR2, sensitising the channel to cytosolic Ca(2+), whereas FKBP12.6 has very low efficacy, but can antagonise the effects of FKBP12. Mathematical modelling of the data shows the importance of the relative concentrations of FKBP12 and FKBP12.6 in determining RyR2 activity. Consistent with the single-channel results, physiological concentrations of FKBP12 (3 µM) increased Ca(2+)-wave frequency and decreased the SR Ca(2+)-content in cardiac cells. FKBP12.6, itself, had no effect on wave frequency but antagonised the effects of FKBP12.We provide a biophysical analysis of the mechanisms by which FK-binding proteins can regulate RyR2 single-channel gating. Our data indicate that FKBP12, in addition to FKBP12.6, may be important in regulating RyR2 function in the heart. In heart failure, it is possible that an alteration in the dual regulation of RyR2 by FKBP12 and FKBP12.6 may occur. This could contribute towards a higher RyR2 open probability, 'leaky' RyR2 channels and Ca(2+)-dependent arrhythmias.

Activation of muscarinic acetylcholine receptors (mAChR) facilitates the induction of synaptic plasticity and enhances cognitive function. In the hippocampus, M(1) mAChR on CA1 pyramidal cells inhibit both small conductance Ca(2+)-activated KCa2 potassium channels and voltage-activated Kv7 potassium channels. Inhibition of KCa2 channels facilitates long-term potentiation (LTP) by enhancing Ca(2+)calcium influx through postsynaptic NMDA receptors (NMDAR). Inhibition of Kv7 channels is also reported to facilitate LTP but the mechanism of action is unclear. Here, we show that inhibition of Kv7 channels with XE-991 facilitated LTP induced by theta burst pairing at Schaffer collateral commissural synapses in rat hippocampal slices. Similarly, negating Kv7 channel conductance using dynamic clamp methodologies also facilitated LTP. Negation of Kv7 channels by XE-991 or dynamic clamp did not enhance synaptic NMDAR activation in response to theta burst synaptic stimulation. Instead, Kv7 channel inhibition increased the amplitude and duration of the after-depolarisation following a burst of action potentials. Furthermore, the effects of XE-991 were reversed by re-introducing a Kv7-like conductance with dynamic clamp. These data reveal that Kv7 channel inhibition promotes NMDAR opening during LTP induction by enhancing depolarisation during and after bursts of postsynaptic action potentials. Thus, during the induction of LTP M(1) mAChRs enhance NMDAR opening by two distinct mechanisms namely inhibition of KCa2 and Kv7 channels.

In a series of experiments, Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874-1886, 2011) studied relative-frequency judgments of items drawn from two distinct categories. The experiments showed that the judged frequencies of categories of sequentially encountered stimuli are affected by the properties of the experienced sequences. Specifically, a first-run effect was observed, whereby people overestimated the frequency of a given category when that category was the first repeated category to occur in the sequence. Here, we (1) interpret these findings as reflecting the operation of a judgment heuristic sensitive to sequential patterns, (2) present mathematical definitions of the sequences used in Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874-1886, 2011), and (3) present a mathematical formalization of the first-run effect-the judgments-relative-to-patterns model-to account for the judged frequencies of sequentially encountered stimuli. The model parameter w accounts for the effect of the length of the first run on frequency estimates, given the total sequence length. We fitted data from Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874-1886, 2011) to the model parameters, so that with increasing values of w, subsequent items in the first run have less influence on judgments. We see the role of the model as essential for advancing knowledge in the psychology of judgments, as well as in other disciplines, such as computer science, cognitive neuroscience, artificial intelligence, and human-computer interaction.

After-depolarisation is a hallmark of excitability in hippocampal pyramidal cells of CA1 and CA3 regions, because it constitutes the subthreshold relation between inward and outward ionic currents. This relationship determines the nominal response to stimuli and provides the necessary conditions for firing a spike or a burst of action potentials. Nevertheless, after-depolarisation is an inherently transient phenomenon that is not very well understood. We study after-depolarisation using a single-compartment pyramidal-cell model based on recent voltage- and current-clamp experimental data. We systematically investigate CA1 and CA3 behaviour and show that changes to maximal conductances of T-type Ca(2+)-current and muscarinic-sensitive and delayed rectifier K(+)-currents are sufficient to switch the behaviour of the model from a CA3 to a CA1 neuron. We use model analysis to define after-depolarisation and bursting threshold. We also explain the influence of particular ionic currents on this phenomenon. This study ends with a sensitivity analysis that demonstrates the influence of specific currents on excitability. Counter-intuitively, we find that a decrease of Na(+)-current could cause an increase in excitability. Our analysis suggests that a change of high-voltage activated Ca(2+)-current can have a similar effect.

Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudo-plateau bursting, are often observed in neurons and endocrine cells, respectively. These two types of bursting have very different properties and likely serve different functions. This latter point is supported by the divergent expression of the bursting patterns into different cell types, and raises the question of whether it is even possible for a model for one type of cell to produce bursting of the type seen in the other type without large changes to the model. Using fast/slow analysis, we show here that this is possible, and we provide a procedure for achieving this transition. This suggests that the design principles for bursting in endocrine cells are just quantitative variations of those for bursting in neurons.

Six experiments studied relative frequency judgment and recall of sequentially presented items drawn from 2 distinct categories (i.e. city and animal). The experiments show that judged frequencies of categories of sequentially encountered stimuli are affected by certain properties of the sequence configuration. We found (a) a first-run effect whereby people overestimated the frequency of a given category when that category was the first repeated category to occur in the sequence and (b) a dissociation between judgments and recall; respondents may judge 1 event more likely than the other and yet recall more instances of the latter. Specifically, the distribution of recalled items does not correspond to the frequency estimates for the event categories, indicating that participants do not make frequency judgments by sampling their memory for individual items as implied by other accounts such as the availability heuristic (Tversky & Kahneman, 1973) and the availability process model (Hastie & Park, 1986). We interpret these findings as reflecting the operation of a judgment heuristic sensitive to sequential patterns and offer an account for the relationship between memory and judged frequencies of sequentially encountered stimuli.

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts. First, the dynamic interplay between ion channels within the sensory inner hair cells is used to explain some new electrophysiological recordings from early development. Next, the state of the art is reviewed in modelling the electro-motility present within the outer hair cells (OHCs), including the current debate concerning the role of cell body motility versus active hair bundle dynamics. A simplified model is introduced that combines both effects in order to explain observed amplification and compression in experiments. Finally, new modelling evidence is presented that structural longitudinal coupling between OHCs may be necessary in order to capture all features of the observed mechanical responses.

Associative synaptic plasticity is synapse specific and requires coincident activity in pre-synaptic and post-synaptic neurons to activate NMDA receptors (NMDARs). The resultant Ca(2+) influx is the critical trigger for the induction of synaptic plasticity. Given its centrality for the induction of synaptic plasticity, a model for NMDAR activation incorporating the timing of pre-synaptic glutamate release and post-synaptic depolarization by back-propagating action potentials could potentially predict the pre- and post-synaptic spike patterns required to induce synaptic plasticity. We have developed such a model by incorporating currently available data on the timecourse and amplitude of the post-synaptic membrane potential within individual spines. We couple this with data on the kinetics of synaptic NMDARs and then use the model to predict the continuous spine [Ca(2+)] in response to regular or irregular pre- and post-synaptic spike patterns. We then incorporate experimental data from synaptic plasticity induction protocols by regular activity patterns to couple the predicted local peak [Ca(2+)] to changes in synaptic strength. We find that our model accurately describes [Ca(2+)] in dendritic spines resulting from NMDAR activation during pre-synaptic and post-synaptic activity when compared to previous experimental observations. The model also replicates the experimentally determined plasticity outcome of regular and irregular spike patterns when applied to a single synapse. This model could therefore be used to predict the induction of synaptic plasticity under a variety of experimental conditions and spike patterns.

We present a mathematical analysis of the dynamics that underlies plateau bursting in models of endocrine cells under variation of the location of the (unstable) equilibrium around which these bursting patterns are organised. We focus primarily on the less well-studied case of pseudo-plateau bursting, but also consider the square-wave case. The behaviour of such models is explained using the theory for systems with multiple time scales and it is well known that the underlying so-called fast subsystem organises their dynamics. However, such results are valid only in a sufficiently small neighbourhood of the singular limit that defines the fast subsystem. Hence, the slow variable (intracellular calcium concentration) must be very slow, which is actually not the case for pseudo-plateau bursting. Furthermore, the theoretical predictions are also only valid for parameter values such that the equilibrium is close to a homoclinic bifurcation occuring in the fast subsystem. In the present study, we use numerical explorations to discuss what happens outside this theoretically known neighbourhood of parameter space. In particular, we consider what happens as the equilibrium moves outside a small neighbourhood of the homoclinic bifurcation that occurs in the fast subsystem, and relatively fast speeds are allowed for the slow variable which is controlled by a relatively large value of a parameter ε. The results obtained complement our earlier work [Tsaneva-Atanasova et al. (2010) J Theor Biol264, 1133-1146], which focussed on how the bursting patterns vary with the rate of change ε of the slow variable: we fix ε and move the equilibrium over the full range of the bursting regime. Our findings show that the transitions between different bursting patterns are rather similar for square-wave and pseudo-plateau bursting, provided that the value of ε for the pseudo-plateau-bursting model is chosen so that it is much larger than for the square-wave bursting model. Furthermore, the two families of tonic spiking and plateau bursting, which are generally viewed as two separately generated families, are actually connected into a single family in the two-parameter plane through branches of unstable periodic orbits.

Ultradian pulsatile hormone secretion underlies the activity of most neuroendocrine systems, including the hypothalamic-pituitary adrenal (HPA) and gonadal (HPG) axes, and this pulsatile mode of signalling permits the encoding of information through both amplitude and frequency modulation. In the HPA axis, glucocorticoid pulse amplitude increases in anticipation of waking, and, in the HPG axis, changing gonadotrophin-releasing hormone pulse frequency is the primary means by which the body alters its reproductive status during development (i.e. puberty). The prevalence of hormone pulsatility raises two crucial questions: how are ultradian pulses encoded (or generated) by these systems, and how are these pulses decoded (or interpreted) at their target sites? We have looked at mechanisms within the HPA axis responsible for encoding the pulsatile mode of glucocorticoid signalling that we observe in vivo. We review evidence regarding the 'hypothalamic pulse generator' hypothesis, and describe an alternative model for pulse generation, which involves steroid feedback-dependent endogenous rhythmic activity throughout the HPA axis. We consider the decoding of hormone pulsatility by taking the HPG axis as a model system and focussing on molecular mechanisms of frequency decoding by pituitary gonadotrophs.

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.

Secretion is a fundamental cellular process involving the regulated release of intracellular products from cells. Physiological functions such as neurotransmission, or the release of hormones and digestive enzymes, are all governed by cell secretion. Anomalies in the processes involved in secretion contribute to the development and progression of diseases such as diabetes and other hormonal disorders. To unravel the mechanisms that govern such diseases, it is essential to understand how hormones, growth factors and neurotransmitters are synthesized and processed, and how their signals are recognized, amplified and transmitted by intracellular signaling pathways in the target cells. Here, we discuss diverse aspects of the detailed mechanisms involved in secretion based on mathematical models. The models range from stochastic ones describing the trafficking of secretory vesicles to deterministic ones investigating the regulation of cellular processes that underlie hormonal secretion. In all cases, the models are closely related to experimental results and suggest theoretical predictions for the secretion mechanisms.

Gonadotropin-releasing hormone (GnRH) acts via G-protein-coupled receptors on gonadotrophs to stimulate synthesis and secretion of luteinizing hormone and follicle-stimulating hormone. It is secreted in pulses, and its effects depend on pulse frequency, but decoding mechanisms are unknown. Here we have used an extracellular signal regulated kinase-green fluorescent protein (ERK2-GFP) reporter to monitor GnRH signaling. GnRH caused dose-dependent ERK2-GFP translocation to the nucleus, providing a live-cell readout for activation. Pulsatile GnRH caused dose- and frequency-dependent ERK2-GFP translocation. These responses were rapid and transient, showed only digital tracking, and did not desensitize under any condition tested (dose, frequency, and receptor number varied). We also tested for the effects of cycloheximide (to prevent induction of nuclear-inducible MAPK phosphatases) and used GFP fusions containing ERK mutations (D319N, which prevents docking domain-dependent binding to MAPK phosphatases, and K52R, which prevents catalytic activity). These manipulations had little or no effect on the translocation responses, arguing against a role for MAPK phosphatases or ERK-mediated feedback in shaping ERK activation during pulsatile stimulation. GnRH also caused dose- and frequency-dependent activation of the alpha-gonadotropin subunit-, luteinizing hormone beta-, and follicle-stimulating hormone beta- luciferase reporters, and the latter response was inhibited by ERK1/2 knockdown. Moreover, GnRH caused frequency-dependent activation of an Egr1-luciferase reporter, but the response was proportional to cumulative pulse duration. Our data suggest that frequency decoding is not due to negative feedback shaping ERK signaling in this model.

K(ir)6.2[AAA] transgenic mouse islets exhibit mosaicism such that approximately 70% of the beta-cells have nonfunctional ATP-sensitive potassium (K(ATP)) channels, whereas the remainder have normal K(ATP) function. Despite this drastic reduction, the glucose dose-response curve is only shifted by approximately 2 mM. We use a previously published mathematical model, in which K(ATP) conductance is increased by rises in cytosolic calcium through indirect effects on metabolism, to investigate how cells could compensate for the loss of K(ATP) conductance. Compensation is favored by the assumption that only a small fraction of K(ATP) channels are open during oscillations, which renders it easy to upregulate the open fraction via a modest elevation of calcium. We show further that strong gap-junctional coupling of both membrane potential and calcium is needed to overcome the stark heterogeneity of cell properties in these mosaic islets.

Gonadotropin-releasing hormone (GnRH) acts via 7 transmembrane region receptors on gonadotrophs to stimulate synthesis and secretion of the luteinizing hormone and follicle-stimulating hormone. It is secreted in pulses, and its effects depend on pulse frequency, but decoding mechanisms are unknown. Here we have used (nuclear factor of activated T-cells 2 (NFAT2)-emerald fluorescent protein) to monitor GnRH signaling. Increasing [Ca(2+)](i) causes calmodulin/calcineurin-dependent nuclear NFAT translocation, a response involving proteins (calmodulins and NFATs) that decode frequency in other systems. Using live cell imaging, pulsatile GnRH caused dose- and frequency-dependent increases in nuclear NFAT2-emerald fluorescent protein, and at low frequency, translocation simply tracked GnRH exposure (albeit with slower kinetics). At high frequency (30-min intervals), failure to return to basal conditions before repeat stimulation caused integrative tracking, illustrating how the relative dynamics of up- and downstream signals can increase efficiency of GnRH action. Mathematical modeling predicted desensitization of GnRH effects on [Ca(2+)](i) and that desensitization would increase with dose, frequency, and receptor number, but no such desensitization was seen in HeLa and/or LbetaT2 cells possibly because pulsatile GnRH did not reduce receptor expression (measured by immunofluorescence). GnRH also caused dose- and frequency-dependent activation of alphaGSU, luteinizing hormone beta, and follicle-stimulating hormone beta luciferase reporters, effects that were blocked by calcineurin inhibition. Pulsatile GnRH also activated an NFAT-responsive luciferase reporter, but this response was directly related to cumulative pulse duration. This together with the lack of desensitization of translocation responses suggests that NFAT may mediate GnRH action but is not a genuine decoder of GnRH pulse frequency.

Neurite growth is a fundamental process of neuronal development, which requires both membrane expansions by exocytosis and cytoskeletal dynamics. However, the specific contribution of these processes has not been yet assessed quantitatively. To study and quantify the growth process, we construct a biophysical model in which we relate the overall neurite outgrowth rate to the vesicle dynamics. By considering the complex motion of vesicles in the cell soma, we demonstrate from biophysical consideration that the main step of finding the neurite initiation site relies mainly on a two-dimensional diffusion/sequestration/fusion at the cell surface and we obtain a novel formula for the flux of vesicles at the neurite base. In the absence of microtubules, we show that a nascent neurite initiated by vesicular delivery can only reach a small length. By adding the microtubule dynamics to the secretory pathway and using stochastic analysis and simulations, we study the complex dynamics of neurite growth. Within this model, depending on the coupling parameter between the microtubules and the neurite, we find different regimes of growth, which describe dendritic and axonal growth. To validate one aspect of our model, we demonstrate that the experimental flux of TI-VAMP but not Synaptobrevin 2 vesicles contributes to the neurite growth. We conclude that although vesicles can be generated randomly in the cell body, the search for the neurite position using the microtubule network and diffusion is quite fast. Furthermore, when the TI-VAMP vesicular flow is large enough, the interactions between the microtubule bundle and the neurite control the growth process. In addition, all of these processes intimately cooperate to mediate the various modes of neurite growth: the model predicts three different growing modes including, in addition to the stable axonal growth and the stochastic dendritic growth, a fast oscillatory regime. Finally our study demonstrates that cytoskeletal dynamics is necessary to generate long protrusion, while vesicular delivery alone can only generate small neurite.

Cultured pituitary somatotrophs release growth hormone in response to spontaneous Ca(2+) entry through voltage-gated calcium channels (VGCCs) that is governed by plateau-bursting electrical activity and is regulated by several neurohormones, including GH-releasing hormone (GHRH) and somatostatin. Here we combine experiments and theory to clarify the mechanisms underlying spontaneous and receptor-controlled electrical activity. Experiments support a role of a Na(+)-conducting and tetrodotoxin-insensitive channel in controlling spontaneous and GHRH-stimulated pacemaking, the latter in a cAMP-dependent manner; an opposing role of spontaneously active inwardly rectifying K(+) (K(ir)) channels and G-protein-regulated K(ir) channels in somatostatin-mediated inhibition of pacemaking; as well as a role of VGCCs in spiking and large conductance (BK-type) Ca(2+)-activated K(+) channels in plateau bursting. The mathematical model is compatible with a wide variety of experimental data involving pharmacology and extracellular ion substitution and supports the importance of constitutively active tetrodotoxin-insensitive Na(+) and K(ir) channels in maintaining spontaneous pacemaking in pituitary somatotrophs. The model also suggests that these channels are involved in the up- and downregulation of electrical activity by GHRH and somatostatin. In the model, the plateau bursting is controlled by two functional populations of BK channels, characterized by distance from the VGCCs. The rapid activation of the proximal BK channels is critical for the establishment of the plateau, whereas slow recruitment of the distal BK channels terminates the plateau.

STIM1 (stromal interacting molecule 1), an endoplasmic reticulum (ER) protein that controls store-operated Ca(2+) entry (SOCE), redistributes into punctae at the cell periphery after store depletion. This redistribution is suggested to have a causal role in activation of SOCE. However, whether peripheral STIM1 punctae that are involved in regulation of SOCE are determined by depletion of peripheral or more internal ER has not yet been demonstrated. Here we show that Ca(2+) depletion in subplasma membrane ER is sufficient for peripheral redistribution of STIM1 and activation of SOCE. 1 microM thapsigargin (Tg) induced substantial depletion of intracellular Ca(2+) stores and rapidly activated SOCE. In comparison, 1 nM Tg induced slower, about 60-70% less Ca(2+) depletion but similar SOCE. SOCE was confirmed by measuring I(SOC) in addition to Ca(2+), Mn(2+), and Ba(2+) entry. Importantly, 1 nM Tg caused redistribution of STIM1 only in the ER-plasma membrane junction, whereas 1 microM Tg caused a relatively global relocalization of STIM1 in the cell. During the time taken for STIM1 relocalization and SOCE activation, 1 nM Bodipy-fluorescein Tg primarily labeled the subplasma membrane region, whereas 1 microM Tg labeled the entire cell. The localization of Tg in the subplasma membrane region was associated with depletion of ER in this region and activation of SOCE. Together, these data suggest that peripheral STIM1 relocalization that is causal in regulation of SOCE is determined by the status of [Ca(2+)] in the ER in close proximity to the plasma membrane. Thus, the mechanism involved in regulation of SOCE is contained within the ER-plasma membrane junctional region.

In some cell types, oscillations in the concentration of free intracellular calcium ([Ca2+]) are accompanied by oscillations in the concentration of inositol 1,4,5-trisphosphate ([IP3]). However, in most cell types it is still an open question as to whether oscillations in [IP3] are necessary for Ca2+ oscillations in vivo, or whether they merely follow passively. Using a wide range of models, we show that the response to an artificially applied pulse of IP3 can be used to distinguish between these two cases. Hence, we show that muscarinic receptor-mediated, long-period Ca2+ oscillations in pancreatic acinar cells depend on [IP3] oscillations, whereas short-period Ca2+ oscillations in airway smooth muscle do not.

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.

Pancreatic islets of Langerhans display complex intracellular calcium changes in response to glucose that include fast (seconds), slow ( approximately 5 min), and mixed fast/slow oscillations; the slow and mixed oscillations are likely responsible for the pulses of plasma insulin observed in vivo. To better understand the mechanisms underlying these diverse patterns, we systematically analyzed the effects of glucose on period, amplitude, and plateau fraction (the fraction of time spent in the active phase) of the various regimes of calcium oscillations. We found that in both fast and slow islets, increasing glucose had limited effects on amplitude and period, but increased plateau fraction. In some islets, however, glucose caused a major shift in the amplitude and period of oscillations, which we attribute to a conversion between ionic and glycolytic modes (i.e. regime change). Raising glucose increased the plateau fraction equally in fast, slow, and regime-changing islets. A mathematical model of the pancreatic islet consisting of an ionic subsystem interacting with a slower metabolic oscillatory subsystem can account for these complex islet calcium oscillations by modifying the relative contributions of oscillatory metabolism and oscillatory ionic mechanisms to electrical activity, with coupling occurring via K(ATP) channels.

We use a mathematical model of calcium dynamics in pancreatic acinar cells to investigate calcium oscillations in a ring of three coupled cells. A connected group of cells is modeled in two different ways: 1), as coupled point oscillators, each oscillator being described by a spatially homogeneous model; and 2), as spatially distributed cells coupled along their common boundaries by gap-junctional diffusion of inositol trisphosphate and/or calcium. We show that, although the point-oscillator model gives a reasonably accurate general picture, the behavior of the spatially distributed cells cannot always be predicted from the simpler analysis; spatially distributed diffusion and cell geometry both play important roles in determining behavior. In particular, oscillations in which two cells are in synchrony, with the third phase-locked but not synchronous, appears to be more dominant in the spatially distributed model than in the point-oscillator model. In both types of model, intercellular coupling leads to a variety of synchronous, phase-locked, or asynchronous behaviors. For some parameter values there are multiple, simultaneous stable types of oscillation. We predict 1), that intercellular calcium diffusion is necessary and sufficient to coordinate the responses in neighboring cells; 2), that the function of intercellular inositol trisphosphate diffusion is to smooth out any concentration differences between the cells, thus making it easier for the diffusion of calcium to synchronize the oscillations; 3), that groups of coupled cells will tend to respond in a clumped manner, with groups of synchronized cells, rather than with regular phase-locked periodic intercellular waves; and 4), that enzyme secretion is maximized by the presence of a pacemaker cell in each cluster which drives the other cells at a frequency greater than their intrinsic frequency.

It is known that Ca(2+) influx plays an important role in the modulation of inositol trisphosphate-generated Ca(2+) oscillations, but controversy over the mechanisms underlying these effects exists. In addition, the effects of blocking membrane transport or reducing Ca(2+) entry vary from one cell type to another; in some cell types oscillations persist in the absence of Ca(2+) entry (although their frequency is affected), whereas in other cell types oscillations depend on Ca(2+) entry. We present theoretical and experimental evidence that membrane transport can control oscillations by controlling the total amount of Ca(2+) in the cell (the Ca(2+) load). Our model predicts that the cell can be balanced at a point where small changes in the Ca(2+) load can move the cell into or out of oscillatory regions, resulting in the appearance or disappearance of oscillations. Our theoretical predictions are verified by experimental results from HEK293 cells. We predict that the role of Ca(2+) influx during an oscillation is to replenish the Ca(2+) load of the cell. Despite this prediction, even during the peak of an oscillation the cell or the endoplasmic reticulum may not be measurably depleted of Ca(2+).

We construct a mathematical model of Ca(2+) wave propagation in pancreatic and parotid acinar cells. Ca(2+) release is via inositol trisphosphate receptors and ryanodine receptors that are distributed heterogeneously through the cell. The apical and basal regions are separated by a region containing the mitochondria. In response to a whole-cell, homogeneous application of inositol trisphosphate (IP(3)), the model predicts that 1), at lower concentrations of IP(3), the intracellular waves in pancreatic cells begin in the apical region and are actively propagated across the basal region by Ca(2+) release through ryanodine receptors; 2), at higher [IP(3)], the waves in pancreatic and parotid cells are not true waves but rather apparent waves, formed as the result of sequential activation of inositol trisphosphate receptors in the apical and basal regions; 3), the differences in wave propagation in pancreatic and parotid cells can be explained in part by differences in inositol trisphosphate receptor density; 4), in pancreatic cells, increased Ca(2+) uptake by the mitochondria is capable of restricting Ca(2+) responses to the apical region, but that this happens only for a relatively narrow range of [IP(3)]; and 5), at higher [IP(3)], the apical and basal regions of the cell act as coupled Ca(2+) oscillators, with the basal region partially entrained to the apical region.