AbstractThe double-membrane cell envelope of Gram-negative bacteria is a formidable barrier to intracellular antibiotic accumulation. A quantitative understanding of antibiotic transport in these cells is crucial for drug development, but this has proved elusive due to the complexity of the problem and a dearth of suitable investigative techniques. Here we combine microfluidics and time-lapse auto-fluorescence microscopy to quantify antibiotic uptake label-free in hundreds of individual Escherichia coli cells. By manipulating the microenvironment, we showed that drug (ofloxacin) accumulation is higher in growing versus non-growing cells. Using genetic knockouts, we provide the first direct evidence that growth phase is more important for drug accumulation than the presence or absence of individual transport pathways. We use our experimental results to inform a mathematical model that predicts drug accumulation kinetics in subcellular compartments. These novel experimental and theoretical results pave the way for the rational design of new Gram-negative antibiotics.

ABSTRACTNeuroendocrine axes display a remarkable diversity of dynamic signalling 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 modelling 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.

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 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. 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.

SummaryFertility critically depends on the gonadotropin-releasing hormone (GnRH) pulse generator, a neural construct comprised of hypothalamic neurons co-expressing kisspeptin, neurokoinin-B and dynorphin that drives the pulsatile release of GnRH. How this neural network generates and controls the appropriate ultradian frequency essential for gametogenesis and ovulation is unknown. Here, we present a mathematical model of the GnRH pulse generator with theoretical evidence and in vivo experimental data showing 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 of the neural construct. Further increases in basal activity markedly increase pulse frequency. Model predictions that such behaviors are concomitant of non-linear positive and negative feedback interactions mediated through neurokinin-B and dynorphin signaling respectively are confirmed neuropharmacologically. Our mathematical model sheds light on the long-elusive GnRH pulse generator offering new horizons for fertility regulation.

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.

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.

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.

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.

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

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.

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.

We study the chemotaxis of a population of genetically identical swimming
bacteria undergoing run and tumble dynamics driven by stochastic switching
between clockwise and counterclockwise rotation of the flagellar rotary system.
Understanding chemotaxis quantitatively requires that one links the switching
rate of the rotary system in a gradient of chemoattractant/repellant to
experimental measures of the efficiency of a population of bacteria in moving
up/down the gradient. Here we achieve this by using a probabilistic model and
show that the response of a population to the gradient is complex. We find the
changes to a phenotype (the steady state switching rate in the absence of
gradients) affects the average speed of the response as well as the width of
the distribution and both must be taken into account to optimise the overall
response of the population in complex environments. This is due to the
behaviour of individuals in the 'tails' of the distribution. Hence we show that
for chemotaxis, the behaviour of atypical individuals can have a significant
impact on the fitness of a population.

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

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.

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.

Improving in one aspect of a task can undermine performance in another, but how such opposing demands play out in single cells and impact on fitness is mostly unknown. Here we study budding yeast in dynamic environments of hyperosmotic stress and show how the corresponding signalling network increases cellular survival both by assigning the requirements of high response speed and high response accuracy to two separate input pathways and by having these pathways interact to converge on Hog1, a p38 MAP kinase. Cells with only the less accurate, reflex-like pathway are fitter in sudden stress, whereas cells with only the slow, more accurate pathway are fitter in increasing but fluctuating stress. Our results demonstrate that cellular signalling is vulnerable to trade-offs in performance, but that these trade-offs can be mitigated by assigning the opposing tasks to different signalling subnetworks. Such division of labour could function broadly within cellular signal transduction.

Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control reproduction. These are Gq-coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field.

Living cells sense and process environmental cues through noisy biochemical mechanisms. This apparatus limits the scope of engineering cells as viable sensors. Here, we highlight a mechanism that enables robust, population-wide responses to external stimulation based on cellular communication, known as quorum sensing. We propose a synthetic circuit consisting of two mutually repressing quorum sensing modules. At low cell densities the system behaves like a genetic toggle switch, while at higher cell densities the behaviour of nearby cells is coupled via diffusible quorum sensing molecules. We show by systematic coarse graining that at large length and timescales that the system can be described using the Ising model of a ferromagnet. Thus, in analogy with magnetic systems, the sensitivity of the population-wide response, or its 'susceptibility' to a change in the external signal, is highly enhanced for a narrow range of cell-cell coupling close to a critical value. We expect that our approach will be used to enhance the sensitivity of synthetic bio-sensing networks.

Simulation of biomolecular networks is now indispensable for studying
biological systems, from small reaction networks to large ensembles of cells.
Here we present a novel approach for stochastic simulation of networks embedded
in the dynamic environment of the cell and its surroundings. We thus sample
trajectories of the stochastic process described by the chemical master
equation with time-varying propensities. A comparative analysis shows that
existing approaches can either fail dramatically, or else can impose
impractical computational burdens due to numerical integration of reaction
propensities, especially when cell ensembles are studied. Here we introduce the
Extrande method which, given a simulated time course of dynamic network inputs,
provides a conditionally exact and several orders-of-magnitude faster
simulation solution. The new approach makes it feasible to demonstrate, using
decision-making by a large population of quorum sensing bacteria, that
robustness to fluctuations from upstream signaling places strong constraints on
the design of networks determining cell fate. Our approach has the potential to
significantly advance both understanding of molecular systems biology and
design of synthetic circuits.

Cells must sense extracellular signals and transfer the information contained about their environment reliably to make appropriate decisions. To perform these tasks, cells use signal transduction networks that are subject to various sources of noise. Here, we study the effects on information transfer of two particular types of noise: basal (leaky) network activity and cell-to-cell variability in the componentry of the network. Basal activity is the propensity for activation of the network output in the absence of the signal of interest. We show, using theoretical models of protein kinase signaling, that the combined effect of the two types of noise makes information transfer by such networks highly vulnerable to the loss of negative feedback. In an experimental study of ERK signaling by single cells with heterogeneous ERK expression levels, we verify our theoretical prediction: in the presence of basal network activity, negative feedback substantially increases information transfer to the nucleus by both preventing a near-flat average response curve and reducing sensitivity to variation in substrate expression levels. The interplay between basal network activity, heterogeneity in network componentry, and feedback is thus critical for the effectiveness of protein kinase signaling. Basal activity is widespread in signaling systems under physiological conditions, has phenotypic consequences, and is often raised in disease. Our results reveal an important role for negative feedback mechanisms in protecting the information transfer function of saturable, heterogeneous cell signaling systems from basal activity.

Mutual information is fundamentally important for measuring statistical
dependence between variables and for quantifying information transfer by
signaling and communication mechanisms. It can, however, be challenging to
evaluate for physical models of such mechanisms and to estimate reliably from
data. Furthermore, its relationship to better known statistical procedures is
still poorly understood. Here we explore new connections between mutual
information and regression-based dependence measures, $\nu^{-1}$, that utilise
the determinant of the second-moment matrix of the conditional mean prediction
error. We examine convergence properties as $\nu\rightarrow0$ and establish
sharp lower bounds on mutual information and capacity of the form
$\mathrm{log}(\nu^{-1/2})$. The bounds are tighter than lower bounds based on
the Pearson correlation and ones derived using average mean square-error rate
distortion arguments. Furthermore, their estimation is feasible using
techniques from nonparametric regression. As an illustration we provide
bootstrap confidence intervals for the lower bounds which, through use of a
composite estimator, substantially improve upon inference about mutual
information based on $k$-nearest neighbour estimators alone.

Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments. © 2013 Bowsher et al.

The accuracy of DNA transcription is crucial for the proper functioning of the cell. Although RNA polymerases demonstrate selectivity for correct nucleotides, additional active mechanisms of transcriptional error correction are required to achieve observed levels of fidelity. Recent experimental findings have shed light on a particular mechanism of transcriptional error correction involving: (i) diffusive translocation of the RNA polymerase along the DNA (backtracking) and (ii) irreversible RNA cleavage. This mechanism achieves preferential cleavage of misincorporated nucleotides by biasing the local rates of translocation. Here, we study how misincorporated nucleotides affect backtracking dynamics and how this effect determines the level of transcriptional fidelity. We consider backtracking as a diffusive process in a periodic, one-dimensional energy landscape, which at a coarse-grained level gives rise to a hopping process between neighbouring local minima. We propose a model for how misincorporated nucleotides deform this energy landscape and hence affect the hopping rates. In particular, we show that this model can be used to derive both the theoretical limit on the fidelity (i.e. the minimum fraction of misincorporated nucleotides) and the actual fidelity relative to this optimum, achieved for specific combinations of the cleavage and polymerization rates. Finally, we study how external factors influencing backtracking dynamics affect transcriptional fidelity. We show that biologically relevant loads, similar to those exerted by nucleosomes or other transcriptional barriers, increase error correction. © 2012 IOP Publishing Ltd.

The accuracy of DNA transcription is crucial for the proper functioning of the cell. Although RNA polymerases demonstrate selectivity for correct nucleotides, additional active mechanisms of transcriptional error correction are required to achieve observed levels of fidelity. Recent experimental findings have shed light on a particular mechanism of transcriptional error correction involving: (i) diffusive translocation of the RNA polymerase along the DNA (backtracking) and (ii) irreversible RNA cleavage. This mechanism achieves preferential cleavage of misincorporated nucleotides by biasing the local rates of translocation. Here, we study how misincorporated nucleotides affect backtracking dynamics and how this effect determines the level of transcriptional fidelity. We consider backtracking as a diffusive process in a periodic, one-dimensional energy landscape, which at a coarse-grained level gives rise to a hopping process between neighboring local minima. We propose a model for how misincorporated nucleotides deform this energy landscape and hence affect the hopping rates. In particular, we show that this model can be used to derive both the theoretical limit on the fidelity (i.e. the minimum fraction of misincorporated nucleotides) and the actual fidelity relative to this optimum, achieved for specific combinations of the cleavage and polymerization rates. Finally, we study how external factors influencing backtracking dynamics affect transcriptional fidelity. We show that biologically relevant loads, similar to those exerted by nucleosomes or other transcriptional barriers, increase error correction. © 2012 IOP Publishing Ltd.

The comparative ability of transcriptional and small RNA-mediated negative feedback to control fluctuations or 'noise' in gene expression remains unexplored. Both autoregulatory mechanisms usually suppress the average (mean) of the protein level and its variability across cells. The variance of the number of proteins per molecule of mean expression is also typically reduced compared with the unregulated system, but is almost never below the value of one. This relative variance often substantially exceeds a recently obtained, theoretical lower limit for biochemical feedback systems. Adding the transcriptional or small RNA-mediated control has different effects. Transcriptional autorepression robustly reduces both the relative variance and persistence (lifetime) of fluctuations. Both benefits combine to reduce noise in downstream gene expression. Autorepression via small RNA can achieve more extreme noise reduction and typically has less effect on the mean expression level. However, it is often more costly to implement and is more sensitive to rate parameters. Theoretical lower limits on the relative variance are known to decrease slowly as a measure of the cost per molecule of mean expression increases. However, the proportional increase in cost to achieve substantial noise suppression can be different away from the optimal frontier-for transcriptional autorepression, it is frequently negligible. © the Author(s) 2012.

We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph. © Applied Probability Trust 2010.

Biological cell function crucially relies on the accuracy of RNA sequences, transcribed from the DNA genetic code. To ensure sufficiently high fidelity in the face of high spontaneous error rates during transcription, error correction mechanisms must play an important role. A particular mechanism of transcriptional error correction involves backtracking of the RNA polymerase and RNA cleavage. Motivated by recent single molecule experiments characterizing the dynamics of backtracking, we present a microscopic model of this editing process. We show that such a mechanism can yield error frequencies that are in agreement with in vivo observations. © 2009 the American Physical Society.

Transcription is a vital stage in the process of gene expression and a major contributor to fluctuations in gene expression levels for which it is typically modeled as a single-step process with Poisson statistics. However, recent single molecule experiments raise questions about the validity of such a simple single-step picture. We present a molecular multistep model of transcription elongation that demonstrates that transcription times are in general non-Poisson-distributed. In particular, we model transcriptional pauses due to backtracking of the RNA polymerase as a first passage process. By including such pauses, we obtain a broad, heavy-tailed distribution of transcription elongation times, which can be significantly longer than would be otherwise. When transcriptional pauses result in long transcription times, we demonstrate that this naturally leads to bursts of mRNA production and non-Poisson statistics of mRNA levels. These results suggest that transcriptional pauses may be a significant contributor to the variability in transcription rates with direct implications for noise in cellular processes as well as variability between cells. © 2008 by the Biophysical Society.