Cortical Network Models to Understand Differential Input Response Properties During Active and Silent States - Mathematics - EPSRC DTP funded PhD Studentship Ref: 2903

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Dr James Rankin
Dr Mick Craig.

Streatham Campus, Exeter.

Project Description
Mathematical modelling of neural networks will be used to understand the neuronal computational principles underlying input response properties in neocortex. Methods from dynamical systems theory, including bifurcation analysis, will be applied to analyse the neural field models developed.

The mammalian neocortex is involved in all aspects of brain function, including sensory processing, motor control, decision making and language. Different cortical network states are associated with different types of behaviour. For example, in mice, synchronised large amplitude slow oscillations of cortical activity during quiet wakefulness give way to higher frequency low amplitude fluctuations when the animal is exploring its environment with its whiskers. Spontaneous transitions between synchronous periods of high activity (a so-called Up state) and low activity (Down state) most frequently occur during slow-wave sleep, where they are believed to be important for memory consolidation in mammals.

Sensory cortical areas respond to inputs in different ways depending on whether the network is in an Up state or a Down state, and whether inputs arrive via sensory stimulation (primary inputs) or from other cortical regions (higher order inputs). The governing principles behind these important differences remains to be established. It is an opportune time to achieve this with mathematical modelling, which will shed light on the functional role of Up and Down states.

The project will develop a dynamical model in the neural field framework, which gives a spatially averaged description of neural activity across multiple cortical columns (several mm of cortex). This provides the ideal framework in which to probe differences between primary sensory inputs, which may be local due to receptive field properties, and higher-order inputs. It is hypothesised that during Down states cortical areas are generally responsive to inputs. However, during Up states sensory areas are differentially response to primary and secondary inputs. The modelling work will be done in close collaboration with experiments investigating input responses during slow-wave sleep, activating whiskers for primary inputs and using optogenetic stimulation of cortico-cortical afferents for higher-order inputs. Existing models have focused on local networks and have not considered the spatial aspects that are likely to be crucial for developing a general theory about response properties that depend on both network state and type of input.

The successful candidate will receive training in the development and analysis of neuronal population models. The model will be defined by systems of integro-differential equations describing firing rates of different neuron subtypes and will be analysed with dynamical systems methods. This will allow experimentally testable predictions to be generated on cortical response properties. Collaborators can test these in new experiments to confirm, reject or refine modelling hypotheses. This project provides a unique opportunity to receive training in mathematical modelling alongside close collaboration with experimentalists using cutting-edge optogenetic methods. Experience working on such interdisciplinary projects is highly sought after.

Candidates with quantitative backgrounds (mathematics, physics, engineering) and from neuroscience programmes are encouraged to apply to this 3.5 year PhD Scholarship. Programming experience, knowledge of dynamical systems theory and training in biological modelling are a plus.

Entry Requirements
You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in Mathematics, Physics, Engineering or Neuroscience. Experience in Dynamical Systems, Computational Neuroscience or Mathematical Biology is desirable. If English is not your first language you will need to meet the English language requirements and provide proof of proficiency. Click here for more information and a list of acceptable alternative tests.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email:
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.