Neurodynamics: heterogeneity, noise, delays, and plasticity in neural systems

Lead Research Organisation: University of Nottingham
Department Name: Sch of Mathematical Sciences


The brain is a wonderfully complex organ that sits at the heart of our every thought, action, memory, feeling and experience of the world. Many branches of science have arisen motivated by a desire to understand the workings of this jelly-like mass of tissue, ranging from neuroanatomy to psychiatry. Despite scientific progress in a wide range of areas, including the development of neuroimaging techniques such as fMRI, much about how brains work remains a mystery. The building blocks of brain matter, namely neurons and synapses, are now understood in great detail. However, the way they coordinate their activity in networks of thousands or millions to perform natural computation has been very difficult to fathom. To understand the complexity of the brain it is now timely to tap into the body of mathematics that has been built up over recent years to explain the dynamics of other rich dynamical systems such as the weather, financial markets, social insects, telecommunication networks, and ecologies. There are four key aspects of the brain that mark it out for study with the use of powerful modern techniques from the mathematical sciences. Firstly it is a highly heterogeneous system, comprising of different types of cells, grouped into specialised organs (such as for memory or speech), and it is thus important to understand how activity and information can propagate usefully through such a highly structured system. Secondly, unlike man-made computers, the brain is made from unreliable noisy components, yet still manages to outperform these devices in all real world applications (like recognising faces or picking ones name out from a distant conversation at a noisy cocktail party). It is thus important to model neurons and synapses with the appropriate stochastic description to fully understand their computational power. Thirdly, the brain does not operate at the speed-of-light and is limited by its biology to quite slow time scales. Thus it is important to understand the consequences of unavoidable processing delays at the small scale on emergent whole brain dynamics. Finally, the brain is inherently plastic - meaning that it can adapt in response to stimulation from its environment to learn new things and lay down new memories, whilst preserving the old. This is another form of dynamics (now at the single synapse), and requires a detailed understanding of how molecules are moved around within cells. All of these four key areas are examples of an emerging new area that mathematicians call Neurodynamics. The UK is a leading light in this area and a workshop on Neurodynamics: heterogeneity, noise, delays, and plasticity in neural systems, will secure our continued leadership in this important area of science, to seed future advances in our understanding of the brain.

Planned Impact

The proposed workshop will bring together a wide range of speakers and participants from areas across the spectrum of mathematical neuroscience. It will enable the exchange of results and ideas and provide an update on the current state-of-the-art activities. The main aim is to synchronise work on the open problems outlined in our objectives. We anticipate close collaboration between participants in the future, leading to a more unified approach in the UK Mathematical Neuroscience community.

Coombes and Timofeeva have considerable experience in organising such activities and maximising their impact. They coordinated the EPSRC funded UK Mathematical Neuroscience Network (MNN) from Jan 2008 to May 2011, whose remit was to bring together experimental neuroscientists and mathematicians to tackle outstanding challenges in the neurosciences. MNN ran four major meetings in this period, each with around 100 participants, as well as 8 smaller one-day hot-topic workshops. The MNN web site provides an ongoing international community resource and its mailing list (with around 200 subscribers) continues to be used to disseminate information about activity in the field of Mathematical Neuroscience. Four training events, organised by van Rossum, have also helped to introduce important ideas in Mathematical Neuroscience to the younger generation (with resources made available on the MNN web-site).

We expect the workshop to be of great benefit to participants, particularly for early career researchers whose development will be greatly aided by exposure to the wealth of expertise on offer and the opportunity to form new collaborations, discuss and exchange research ideas, and develop transferable skills.

As well as disseminating output from the workshop as a set of collected articles by the main speakers (in a SpringerBrief) the tutorial material will be made available electronically to the wider (and non-academic) community. We will make use of the existing MNN site to do this. A meeting report will also be prepared and placed with society mailing lists and newsletters (such as the LMS newsletter, UK Nonlinear News, SIAM,, ESMTB Infoletter,, This will benefit the wider neuroscience community and other related fields (especially those that relate to complex systems), by increasing knowledge and highlighting state-of-the-art techniques in Neurodynamics.


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Coombes S (2013) Editorial for special issue on neurodynamics. in Journal of mathematical neuroscience

Description Although mathematical work on Neurodynamics has increased in recent years, the study of heterogeneity, noise, delays, and plasticity needs much further attention. A firmer mathematical framework for treating dynamical systems with these attributes will pave the way for a more comprehensive understanding of the dynamic states of biological neural networks, and their role in facilitating natural computation. This three-day conference brought together experts in these key areas to seed a new phase of theoretical work to develop those pieces of mathematical theory which are critical for future realistic modelling studies of the brain.
Exploitation Route We have helped develop research and activity in mathematical neuroscience.
Sectors Digital/Communication/Information Technologies (including Software)

Description A special issue on Neurodynamics has been produced; S Coombes and Y Timofeeva 2013 Editorial for special issue on Neurodynamics, Journal of Mathematical Neuroscience, 3:10
First Year Of Impact 2013
Sector Digital/Communication/Information Technologies (including Software)