ICMS

Mar 17, 2008 - Mar 19, 2008

Royal Society of Edinburgh, 22-26 George Street, Edinburgh

Organisers

Name	Institution
Coombes, Stephen	University of Nottingham
Timofeeva, Yulia	University of Warwick

Training Workshop Organiser
Dr Mark van Rossum, University of Edinburgh

 

This is the first annual meeting of the newly established UK Mathematical Neuroscience Network. The network is focussed on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviour in the applied neurosciences. This three-day conference will provide an overview of the current state of research in mathematical approaches to neuroscience, bringing together both physical and life scientists. Drawing together the field in this way will allow for a critical discussion of the relevant experimental facts and of various mathematical methods and techniques that have been successfully applied to date. Importantly, it will draw attention to, and help develop, those pieces of mathematical theory which are likely to be relevant to future studies of the brain.

The meeting will consist of invited speakers, core members and registered participants. In addition, the schedule will allow for a number of poster presentations.

This event is sponsored by the EPSRC via the UK Mathematical Neuroscience Network

 

Arrangements

Participation
Please note that the workshop is now full.

Venue
The meeting will be held at the the Royal Society of Edinburgh, 22-26 George Street, Edinburgh, EH2 2PQ. The Conference Room is equipped with an OHP, data projector and flipchart.

Registration
Registration will take place from 08.45 - 09.30, on Monday 17 March, in the foyer of the Royal Society of Edinburgh.

Registration fee
The registration fee for this meeting is 50.00 GBP.

Meals and Refreshments
Morning and afternoon refreshments will be provided at the venue.

A poster session and wine reception will be held at ICMS, 14 India Street, Edinburgh on Monday 17 March at 18.00. This is a short walk from the Royal Society of Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.

A Conference Dinner will take place on Tuesday 18 March at 19.00.

Accommodation
Participants are asked to make their own accommodation arrangements. A list of Edinburgh accommodation of various sorts and prices is available here .

Financial Assistance
Some financial assistance is available to assist graduate students who attend BOTH the training workshop and the conference.. Applicants should provide a brief résumé including degrees and at least one recommendation letter explaining their suitability for the activity. The résumé and letter should be e-mailed to Irene Moore. Students requesting financial support will be notified by 4 February 2008.

Training Workshop
A one-day training workshop for PhD students and post-docs entitled “An introduction to Mathematical Neuroscience” will take place prior to the meeting on Sunday 16 March at the University of Edinburgh. This will be organised by Mark van Rossum and will comprise a series of 'primer' lectures designed to introduce the concepts that will be covered in the main conference.

The workshop will run from 12.30 until 18.00 on Sunday 16 March in the Forrest Hill Building, 5 Forrest Hill, Edinburgh EH1 2QL. map

 

Programme

Sunday 16 March - Training Workshop

Please note that the training workshop will take place in a different venue from the main workshop.

12.30 - 12.45	Introduction by Steve Coombes and Mark van Rossum
12.45 - 13.45	Yulia Timofeeva (University of Warwick) Single neuron models
13.45 - 14.45	Mark van Rossum (University of Edinburgh) Synaptic dynamics
14.45 - 15.00	Break
15.00 - 16.00	Steve Coombes (University of Nottingham) Neural field models
16.00 - 17.00	Jon Peirce (University of Nottingham) Simple nonlinear models of V1 neurons
17.00 - 17.15	Break
17.15 - 18.15	Rasmus Peterson (University of Manchester) Neural coding
	Beer and pizza

 

Monday 17 March

09.00 - 10.30	Registration and coffee
10.30 - 10.45	Welcome
10.45 - 11.30	William Kath (Northwestern University) Models of synaptic integration via dendritic spikes in CA1 pyramidal neurons
11.30 - 12.15	Brent Doiron (University of Pittsburgh) Microcircuits and macrodynamics in auditory processing
12.15 - 14.00	Lunch
14.00 - 14.45	Simon Schultz (Imperial College, London) Studying the neuronal population code with in vivo two-photon calcium imaging
14.45 - 15.30	Einevoll Gaute (Norwegian University of Life Sciences) Extraction of cortical-network models from laminar multielectrode recordings
15.30 - 16.15	Coffee/tea
16.15 - 17.00	Wyeth Bair (University of Oxford) Rapid adaptive properties of motion sensitive neurons in the macaque visual cortex
18.00 - 19.30	Poster session and wine reception at ICMS, 14 India Street, Edinburgh EH3 6EZ map

Tuesday 18 March

09.15 - 10.00	Henry Tuckwell (Max Planck Institute) Stochastic effects in neurobiological dynamical systems
10.00 - 10.45	Coffee/tea
10.45 - 11.30	Mark van Rossum (University of Edinburgh) Shannon information capacity of synapses
11.30 - 12.15	Nigel Stocks (University of Warwick) Noise enhanced information processing in neural population
12.15 - 14.00	Lunch
14.00 - 14.45	Peter Ashwin (University of Exeter) Winnerless competition and spatio-temporal encoding
14.45 - 15.30	Paul Bressloff (University of Utah) Mathematical models of primary visual cortex (V1)
15.30 - 16.15	Coffee/tea
16.15 - 17.00	Rodica Curtu (University of Iowa) Frequency control in neuronal competition models
17.00 - 17.20	Discussion
19.00	Workshop dinner - Howies, 29 Waterloo Place, Edinburgh map

Wednesday 19 March

09.00 - 09.45	Olivier Faugeras (INRIA) Mean field analysis for neural mass models
09.45 - 10.30	David Liley (Swinburne University of Technology) Macroscopic state transitions in electroencephalographic dynamics
10.30 - 11.00	Coffee/tea
11.00 - 11.45	Piotr Suffczynski (University of Warsaw) Bistable dynamics of epileptic phenomena
11.45 - 12.30	David Terman (University of Ohio) A Neurobiological Model of the Human Sleep/wake Cycle

 

Presentations:

Presentation Details
Ashwin, Peter
Winnerless competition and spatio-temporal encoding
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Winnerless competition models are intriguing dynamical models of neural function that show complicated dynamics, explained in terms of motion between different types of unstable equilibria or periodic orbits. This presentation will investigate how this can be used for spatio-temporal encoding of steady inputs and presents a number of questions as to when and whether this has relevance in mathematical neuroscience.
Bair, Wyeth
Rapid adaptive properties of motion sensitive neurons in the macaque visual cortex
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Computational models of the sensitivity of visual neurons in the early stages of cortical processing have relied heavily on the use of one or a few linear filters to represent the neuronal receptive field (RF). Recently, however, there is a growing appreciation that RF structure and sensitivity can depend strongly on the spatio-temporal structure of the visual stimuli that are used to map the RFs, even early in the primary visual cortex (V1). This adaptation presents a major challenge to conventional linear-filter RF models, including models with some non-linearities. I will focus on recent results in the motion pathway of the macaque, where direction selective cells in V1 and the cortical motion area (V5/MT) have been found to adapt their temporal integration and their response gain to the statistics of the visual stimuli. I will argue that we need to adopt a more flexible approach to modelling visual responses, one that does not rely on filter-based RF maps, if we intend to unify a variety of adaptive phenomenon in the visual cortex and to make accurate predictions of responses to dynamic stimuli like those encountered in natural viewing.
Bressloff, Paul
Mathematical models of primary visual cortex (V1)
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We describe two alternative approaches to modeling V1. The first approach treats cortex as a two-dimensional cortical sheet in which correlations between long-range horizontal connections and stimulus preference feature maps lead to network inhomogeneities. We explore some of the consequences of these inhomogeneirties for neural pattern formation and wave propagation. The second approach treats cortex as a system of coupled modules or hypercolumns. Weakly nonlinear analysis of such a system leads to a nonlocal Ginzburg Landau equation, which can be used to study various aspects of spontaneous and stimulus-evoked activity.
Curtu, Rodica
Frequency control in neuronal competition models
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The notion of competition has been applied in the modeling of various neuronal computational tasks. For example, competition between two neuronal populations, via reciprocal inhibition, and slow adaptation underlie models for alternating rhythmic behavior in central pattern generators (CPGs) and in perceptual bistability. CPGs consist of neural circuits that drive alternately contracting muscle groups. Perceptual bistability refers to a class of phenomena in which a deeply ambiguous stimulus gives rise to two different interpretations that alternate over time, only one being perceived at any given moment. In both cases the question is what mechanism underlies the oscillation's frequency (or period) that is believed to encode information about the stimulus to the neural system. In this talk we focus on a class of competition firing rate models and show that the period of oscillations depends non-monotonically on the stimulus strength. The period increases with input strength for low values of the latter and in this case the dynamics is due to a release mechanism. On the other hand, for large values of input strength the period decreases with it and the dynamics is due to an escape mechanism.
Doiron, Brent
Microcircuits and macrodynamics in auditory processing.
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Cortical circuits have wiring rules that are far more sophisticated than simple independence would predict. Specific connection “motifs” between small numbers of cells, called microcircuits, appear more (or less) often than expected by chance. However, relatively little is known about how specific microcircuit architectures combine with synaptic dynamics to control the behaviour of a macroscopic network. Using a combination of in vitro recordings, computational modeling, and mean field analysis, we explore this question within layer 2/3 of mouse auditory cortex. Simultaneous whole cell current clamp recordings were made from pyramidal cell/interneuron pairs in a mouse thalamocortical slice preparation. We found that for separation distances of less than 30 microns the neuron pair show a high (low) probability of reciprocal (non-reciprocal) connectivity. In addition, we also find that the sustained inhibition is significantly stronger in the non-reciprocal versus reciprocal pair. The synthesis of these two results suggests that the spatial profile of recruited inhibition is ‘volcano’-shaped, with nearby pyramidal neurons being spared from the strong inhibition received by distal pyramidal cells. To assess the functional implication of these findings, we studied a network of excitatory and inhibitory leaky integrate and fire (LIF) model neurons that incorporated the experimentally measured spatial connectivity profile and inhibitory dynamics. When the network architecture and synaptic dynamics match the experimental results the intensity of a synchronous network gamma oscillation (~ 40 Hz) can be controlled by the spatial extent of a driving input – spatially compact inputs result in a strong gamma band rhythm. This result can be replicated with a spatially coarse-grained mean field theory, where the interaction strength of the fields is conditional on the spatial footprint of the stimulus. These results make strong predictions on how feed-forward connectivity should be organized so as to allow a selective gate of network synchrony in layer 2/3, hence allowing further control of cortical processing.
Einevoll, Gaute
Extraction of cortical-network models from laminar multielectrode recordings
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Mathematical modelling relies on experimental data to make progress. For cortical neural network models the essential experimental method in vivo has been extracellular recordings of action potentials with sharp electrodes. Other types of experimental methods, particularly methods that measure population-level activity in vivo, are needed, and large-scale electrical recordings using various types of multielectrodes are one option. Techniques for such recordings are rapidly improving, and there is a need for methods for extraction of relevant information about the underlying neural activity from such data. Here results from several projects aimed at this will be presented: (1) investigation of how neural morphology and electrical parameters affect the shape and size of extracellular action potentials; (2) investigation of how the low-frequency (local field potentials; LFP) and high-frequency parts (multiunit activity; MUA) of extracellular potentials relates to the firing activity and synaptic activity in a neocortical model column; (3) introduction of laminar population analysis (LPA) where stimulus-evoked laminar-electrode data from rat barrel cortex are analysed in a scheme where the MUA and LFP are jointly modelled using physiological constraints; (4) extraction of thalamocortical and intracortical network models based on results from LPA analysis of laminar-electrode data and simultaneous recording of thalamic firing activity recorded in the homologous barreloid.
Faugeras, Olivier
Mean Field Analysis for Neural Mass Models
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Neural mass models are popular rate models for such neuronal entities as cortical columns.They contain large numbers of spiking neurons and it is still somewhat unclear how to relate the mesoscopic behaviour of the columns to the microscopic behaviour of the individual spiking neurons. Starting with a neuronal network with random synaptic weights and stochastic inputs we adopt the new point of view of studying the problem from the functional analysis viewpoint in the "set of trajectories". With this point of view we address the question of existence and uniqueness of solutions for the mean-field equation of the neural network model. To this purpose, we introduce a new metric on the set of stochastic processes for which this set is complete. This allows us to use the theory of fixed points in complete spaces to prove the existence and uniqueness of the solution we are searching for. Our proof is constructive and provides a method to compute explicitly these solutions. We also apply this framework to stationary solutions which have been studied essentially using local or numerical methods. An intriguing outcome of this result is that the mesoscopic models should also take into account the fluctuations around the mean.
Kath, William
Models of synaptic integration via dendritic spikes in CA1 pyramidal neurons
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Neurons integrate input from synapses throughout the dendritic tree, but cable theory and simulations predict that distal synapses attenuate significantly, and thus are at a disadvantage in terms of affecting action potential generation at the spike initiation zone in the axon. In CA1 pyramidal neurons, this distal disadvantage may be overcome by activating voltage-gated conductances to produce dendritic spikes. We show, via both computational models and experiments, that the forward propagation of dendritic spikes can be unreliable, but that the probability of axonal action potential initiation increases dramatically if the distal dendritic inputs are accompanied by small amounts of more proximal synaptic input.
Liley, David
Macroscopic state transitions in electroencephalographic dynamics
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Despite the discovery of the human alpha rhythm over 70 years ago, physiologically plausible theories for its dynamical genesis have met with only limited success. However over the last decade we have developed a general theory of cortical electrorhythmogenesis that is able to explain the origin of this cortically ubiquitous rhythm. This theory predicts that all the major spectral features of the resting electroencephalogram (EEG), the `1/f' low frequency power and the alpha and beta `resonances', are dynamically explicable if the EEG is viewed as arising from a system being perturbed near an instability (or critical point). Here we present recent experimental results in support of this conjecture. By analysing EEG recorded from healthy volunteers it is found that increases in total power and increased low frequency `1/f' power are all predictive for non-linear deterministic structure in the spontaneous EEG. These results when intepreted in the context of our theory imply that macroscopically cortical tissue continually switches between qualitatively distinct dynamical states. This talk will outline these experimental methods and results as well as discussing their physiological implications and cognitive relevance.
Schultz, Simon
Studying the neuronal population code with in vivo two-photon calcium imaging
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Studies of the population code used to represent and process sensory information in mammalian cortex have been based upon experimental data acquired via single-unit recording techniques, and more recently data from micro-electrode arrays (MEAs). These techniques introduce a number of systematic biases: single-unit recording is biased towards selecting cells with high spontaneous activity; MEA recording, while addressing this issue, still grossly undersamples the computational circuitry. Two-photon calcium imaging allows every cell in an area to be recorded, with slightly reduced temporal resolution and SNR compared to electrophysiological techniques. We are using this approach to study the role of correlations between cells in population coding in both the cerebellar and cerebral cortices. This talk will focus on how in vivo two-photon imaging can help us to refine existing models of neural population coding.
Stocks, Nigel
Noise enhanced information processing in neural population
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A number of results will be presented on the effect of noise on the transmission of information through both model and real neural populations. In particular, the effect of suprathreshold stochastic resonance will be discussed and demonstrated for a real neural system. Also, methods of optimising information transmission, including the use of negatively correlated noise, will be discussed. Additionally, different types of noise will be studied such as signal dependent noise (synaptic) and additive noise.
Suffczynski, Piotr
Bistable dynamics of epileptic phenomena
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The essence of epilepsy is that a patient displays (long) periods of normal EEG activity (i.e. non-epileptiform) intermingled occasionally with epileptiform paroxysmal activity. An essential question is how does the transition between the normal ongoing and the seizure activity take place. In order to provide more insight into the dynamics of the neuronal networks leading to seizure generation we developed a computational model based on relevant physiological data. The model exhibits bistability, i.e., it features two operational states, ictal and interictal, that co-exist. The transitions between these two states occur according to a Poisson process. Model predictions are compared with experimental data and clinical implications in terms of seizure predictability and seizure abortion are discussed.
Terman, David
A neurobiological model of the human sleep/wake cycle
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We propose a detailed, biologically based model for the human sleep/wake cycle. The model is based on Saper’s flip/flop switch model of sleep/wake regulation which proposes that sleep-promoting neurons within the ventral lateral preoptic nucleus and wake-promoting neurons in the monoaminergic cell groups inhibit each other resulting in stable wakefulness and sleep. Input from orexin neurons to the monoaminergic cell groups help to stabilize the flip/flop switch; in particular, a loss of orexin may lead to unwanted switching between sleepiness and wakefulness associated with narcolepsy. Saper has also proposed a flip/flop switch for REM/NREM rhythms, which we have incorporated into our model. The model includes interactions between the circadian and homeostatic processes and accounts for certain features of sleep deprivation, as well as, ultradian rhythms.
Tuckwell, Henry
Stochastic effects in neurobiological dynamical systems
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We consider neurobiological systems at three levels. At the single-neuron level we discuss the effects of noise in (a) linear spatially-distributed models involving two-parameter Ornstein-Uhlenbeck processes and (b) nonlinear ordinary differential equation spiking neuron models such as Hodgkin-Huxley. For coupled pairs of neurons we report on findings for a generic model involving type 1 cells. The negative effects of noise are analyzed in both the single and coupled neuron cases. Finally, we report on investigations of 2 and 6 component reaction-diffusion models for cortical spreading depression which include stochasticity, two space dimensions, and action potential generation and which exhibit threshold phenomena together with spiral and stationary waves.

Participants

Name	Institution
Amat Roca, Miguel	University of Barcelona
Appleby, Peter	Humbolt University Berlin
Ashwin, Peter	University of Exeter
Bah, Idrissa	GDI
Bair, Wyeth	University of Oxford
Barrett, Adam	University of Edinburgh
beim Graben, Peter	University of Reading
Benjamin, Oscar	University of Bristol
Bisky, Stephan	University of Edinburgh
Borisyuk, Roman	University of Plymouth
Bouaouli, Nabil	Group for Neural Theory, DEC-ENS-College de France
Bressloff, Paul	University of Utah
Chik, David	University of Plymouth
Cohen, Netta	University of Leeds
Colliaux, David	CREA-Ecole Polytechnique-1
Coombes, Stephen	University of Nottingham
Cortes, Jesus	University of Edinburgh
Curtu, Rodica	University of Iowa
Cutsuridis, Vassilis	University of Stirling
David, Francois	CNRS
Doiron, Brent	University of Pittsburgh
Einevoll, Gaute	Norwegian University of Life Sciences
El Hady, Ahmed	International Max Planck Research School of Neurosciences, Goettingen
Elliott, Terry	University of Southampton
Faugeras, Olivier	INRIA
Feldwisch, Hinnerk	University of Edinburgh
Gheorghe, Ana Maria	University of Nottingham
Gin, Stephen	Warwick University
Gjorgjieva, Julijana	University of Cambridge
Goodman, Dan	Ecole normale supérieure
Greene, Garrett	Trinity College, Dublin
Grimbert, François	INRIA
Gurney, Kevin	University of Sheffield
Heess, Nicolas	University of Edinburgh
Hlinka, Jaroslav	University of Nottingham
Houghton, Conor	Trinity College Dublin
Hunter, Russell	University of Stirling
Hutt, Axel	LORIA-INRIA
Kaiser, Marcus	Newcastle University
Kang, Jing	University of Warwick
Kath, William	Northwestern University
Khajeh alijani, Azadeh	University of Warwick
Laudanski, Jonathan	University of Nottingham
Leski, Szymon	Nencki Institute of Experimental Biology
Liley, David	Swinburne University of Technology
Lord, Gabriel	Heriot-Watt University
Malik, Naveed	University of Warwick
Marten, Frank	University of Bristol
Masud, Mohammad	University of Plymouth
Mazurkiewicz, Joanna	Warsaw University
Molaee Ardekani, Behnam	LTSI
Montemurro, Marcelo	The University of Manchester
O Donovan, Julie	University College Cork, Ireland
O'Donnell, Cian	University of Edinburgh
Pattaranit, Ratchada	University of Warwick
Peirce, Jonathan	University of Nottingham
Petersen, Rasmus	University of Manchester
Remme, Michiel	Ecole Normale Superieure
Rodrigues, Serafim	University of Bristol
Rowat, Peter	University of California, San Diego
Saal, Hannes P	University of Edinburgh
Schultz, Simon	Imperial College London
Shahid, Shahjahan	University of Stirling
Skene, Nathan	University of Reading
Stocks, Nigel	University of Warwick
Suffczynski, Piotr	University of Warsaw
Svensson, Carl-Magnus	University of Nottingham
Taxidis, Ioannis	Nottingham University
Teriakidis, Adrianna	University of Edinburgh
Terman, David	Ohio State University
Terry, John	University of Bristol
Thul, Ruediger	University of Nottingham
Timofeeva, Yulia	University of Warwick
Touboul, Jonathan	INRIA
Tuckwell, Henry	Max Planck Institute for Mathematics in the Sciences
van Rossum, Mark	University of Edinburgh
Veltz, Romain	INRIA
Waddington, Amelia	University of Leeds
Wainrib, Gilles	Ecole Polytechnique
Willshaw, David	Institute for Adaptive and Neural Computation, School of Informatics