School
of Computing Science
Abstract
The Salk Institute for Biological Studies
Elementary neurophysiological processes are mediated by thousands of neurons. Their modeling with ordinary differential equations (e.g., Hodgkin-Huxley (HH) type models) quickly reaches the computer resource as the number of elements in the network increases. We propose to use difference equations (map-based models) for simulations of the dynamics of neurons and synapses. These map-based models can replicate the firing patterns produced by specific types of thalamic and cortical neurons (including thalamic relay and reticular cells, cortical fast spiking, regular spiking and intrinsically bursting neurons) and allow one to simulate networks containing hundreds of thousands of neurons within realistic times using a conventional workstation. Model networks built from regular spiking cells, fast-spiking interneurons, GABA-A and AMPA-mediated synapses with short-term plasticity were studied using these map-based models. (1) In a one-dimensional network, the stimulus triggered waves of activity were propagated with a constant velocity which was controlled by the synapses strength. Starting at some threshold strength of the inhibitory feedback the wave front displayed instability that resulted in periodic variation of the front velocity. This network effect was confirmed in HH-based simulations. (2) In a 2-D network, plain waves broke into rotating spirals. We found that the effect of short-term synaptic depression and a sufficiently large size of the network are critical for survivability of the spiral activity. The simulation efficiency of the map-based approach allows one to explore in detail various dynamical processes in large-scale thalamic and cortical networks, including information coding and pattern formation.
Centre
for Intelligent Systems and Complex Processes
Hawthorn,
VIC,
Recording the electrocortical activity of the human brain with the EEG has a long history of successful clinical use. But theoretical explanations of the observed features, like the alpha-rhythm at 8-13 Hz, remain elusive. The EEG model presented here is based on eight partial-differential, two-dimensional, nonlinear mean field equations, which describe the space-averaged dynamics of large populations of cortical neurons. The model's rich and complex dynamics can give rise to resonances matching those of the human EEG under physiologically plausible simulation conditions. A brief summary of numerical methods and results is provided.
Center for Complex Systems & Brain
Sciences
There is considerable evidence that cognitive function requires the large-scale coordination of multiple cortical areas. The coordinating mechanism must allow local areas to function within the large-scale anatomical structure of the cortex so as to satisfy competing requirements for stability and flexibility. Each specialized cortical area must be allowed to perform its unique role by expressing its own form of information, yet must have its performance constrained by interactions with other areas to which it is connected. In order to generate adaptive behavior within changing and not fully predictable environments, the cortex as a whole must be able to rapidly coordinate the activities of variable assemblages of areas that can collectively express consensual information that is appropriate for the functional requirements engendered by each successive stage of behavioral performance. In this talk, I will discuss the role played by phase synchronization of neuronal population activity from different cortical areas. Theoretical studies suggest that the cortex normally operates in a metastable dynamic regime in which groups of areas are able to rapidly and reversibly coordinate their activities through changes in their degree of phase synchronization. Recent experimental results from the study of phase-synchronized local field potential oscillations in distributed cortical areas indicate that coordination dynamics is an important factor in visuomotor function.
Department
of Biology
Bursting is an oscillatory behavior
consisting of intervals of repetitive spiking separated by intervals of
quiescence. Brain functions such as motor control, information processing and
memory formation frequently involve bursting behavior
of neurons. We focused on determining mechanisms underlying bursting activity
to tease apart the functional advantages for bursting of intrinsic membrane
dynamics and network interactions. Isolated neurons are capable of expressing a
variety of qualitatively different regimes, such as bursting, tonic spiking, subthreshold oscillations, plateaus and rest potentials.
The complexity of endogenous dynamics originates from dynamical diversity of
ionic currents which can be separated by different time scales and other
characteristics. Analysis in terms of fast- slow dynamical systems gives
insights into mechanisms for generation of bursting behavior.
On the other hand bursting behavior in neurons can be
generated due to interactions between neurons in a network. A half-center oscillator is the most celebrated network mechanism.
It consists of two mutually inhibitory neuronal units where a unit is either a
single neuron or a population of neurons. The heartbeat motor pattern in
leeches is based on the activity of two_mutually
inhibitory pairs of heart interneurons, which
generate alternating bursting activity. Experiments and dynamical system
analysis were combined to study bursting and other dynamic behaviors
of heart interneurons both as single cells and in the
half-center_oscillator configuration. Bicuculline methiodide (0.1 mM) has been shown to block mutual inhibition between these
interneurons (Schmidt & Calabrese, 1992).
Moreover, simultaneous intracellular recording with sharp microelectrode showed
that the heart interneurons, which burst in
alternation in normal saline, spike tonically when
pharmacologically isolated by bicuculline. Using extracellular recording techniques, we have shown that
oscillator heart interneurons continue to burst when
pharmacologically isolated with bicuculline (Cymbalyuk et al., 2002). Most likely, sharp microelectrode
penetration prevents the endogenous bursting by shifts in Eleak
and gleak. To explore this hypothesis, we constructed
a two-parameter bifurcation diagram (Eleak vs gleak) of model activities. We
used a mathematical model (Hill et al., 2001) developed and thoroughly tested
in our previous studies (Hill et al., 2001, Nadim et
al., 1995; Olsen et al., 1995). Analysis of the single neuron model reveals
that bursting behavior is sensitive to variation of
the parameters Eleak and gleak.
The bifurcation diagram (Eleak vs
gleak) shows a narrow stripe of parameter values
where bursting behavior occurs, separating large
zones of tonic spiking and silent behaviors. In
addition, it shows regions of multistability. In
contrast to a single cell, similar analysis performed for a half-center oscillator model outlines a rather large area of
bursting. The half- center oscillator model is
considerably less sensitive to variation of the maximal conductances
of the voltage-gated currents as it is with leak current parameters. This study
indicates that the half-center configuration enhances
robustness of oscillations thereby making them less susceptible to changes in
membrane parameters, while endogenous bursting behavior
limits the minimum period of the half-center
oscillator and ensures bursting even when the strength of mutual inhibition is
weakened. Basic mechanisms underlying different dynamical regimes can be
understood by using the methods of the qualitative theory of slow-fast
dynamical systems (Rinzel, Lee, 1987; Hoppensteadt, Izhikevich, 1997;
de Vries, 1998; Belykh
et al., 2000; Izhikevich, 2000; Golubitsky
et al., 2001). These methods can be supported by experiments, e.g. blockade of
certain groups of currents can simplify neuronal dynamics, and elicit
characteristic behaviors. One of the experimental
tests commonly used in studies of endogenous bursting regimes is to test
whether a neuron produces oscillatory activity under a blockade of fast sodium current.
Unfortunately, we do not have specific blocker for fast sodium current in the
leech neurons. However, a gedanken experiment
performed in the single neuron model shows that if the fast sodium current is
blocked, slow oscillations with a period 1.5 times larger than the original
period and membrane potential trajectory during the interburst
interval follows closely that of the original model. The interburst
intervals of the two models remain very close and constant as Eleak and gleak are co-varied to
follow the midline of the bursting region of the full model. These oscillations
are observed in the area of parameters close to the area where the bursting
regime is observed in the full model. The area of this oscillatory regime has
borders with areas supporting stationary states so that the state with a
depolarized rest potential roughly corresponds to tonic spiking area in the
full model and the state with the hyperpolarized rest potential corresponds to
the stationary state. The no-INa model is similar to
the full model in its responses and robustness to parameter variation. Thus in
the depolarized phase of bursting fast currents significantly alter neuronal
dynamics while in the hyperpolarized phase as may be expected, they have little
effect. Acknowledgements: This work was supported by
Brain
Research Laboratory
Department
of Information and Communication Sciences
Recent discovery of the massive presence of gap junction couplings among neocortical FS (and LTS) interneurons poses serious questions about their collective dynamical behavior, and their possible cognitive roles. Through theoretical studies, we present the possibility that gap junction-coupled interneuron systems may possess chaotic behavior which is itinerant among quasi-attractors of Milnor's sense, which in turn organizes synchronous cell groups transiently. Some physiological observations from the neocortex, e.g., local field potential (LFP) data exhibiting transient synchrony may provide evidence. We discuss also possible role in the so-called binding problem.
Tel
The dynamic neural filter (DNF) is a binary
recurrent network that serves as generator of complex spatio-temporal
patterns. This will be demonstrated on some examples, including reconstruction
of a teacher-DNF by a student network learning a spatiotemporal sequence. The
DNF can be used to model results form locust olfaction. We define a
'data-model', generated by a DNF, and proceed to investigate it using SVD as a
processing tool. We discuss the question to what extent are the results spatial
or spatio-temporal, and to what extent can synaptic
dynamics modify the complexity of the model.
Institute
for Nonlinear Science
It is well known that the first relay station of the
olfactory system generates stimulus dependent spatio-temporal
activity. The question is: Does this spatio-temporal
code have any function? We will address this question in the context of the
problem of discrimination and association of odors.
We will show that in order to be able to discriminate and associate odors we need a coding machine that is able to translate a
spatial code into a spatio-temporal one before the
discrimination and association of odors takes place.
Division
of Computer Science
Department
of Mathematical Sciences
Abstract
Department of Biophysics
KFKI Research Institute for Particle
and Nuclear Physics
Conventional neuropharmacology
hardly uses neurophysiologial techniques, while
conventional computational neuroscience generaly
neglects the detailed neurochemical mechanisms. The
integration of the neurochemical/pharmacological
perspective into the these models seems to be neccessary to understand normal and pathological neural
processes and to offer therapeutic strategies. Sepcifically,
septo-hippocampal theta activity maight
have a controversial role: it is known
to be strongly involved in enhancing cognitive functions, but might be
correlated to anxiety. The 'optimal performance' of the system might be the
result of a finely tuned control system. To make a step into the direction of
understanding this control mechanism a skeleton model for the mechanism of the
generation and pharmacological modulation of the septo-hippocampal
theta activity is given. Combined pharmacological and computational studies
explain the effects of certain pharmacological agents, which supress, enhances or induced hippocampal
activity on a path-dependent way. Such kinds of selective modulation of
neurotransmission might contribute to reduce the cognitive dysfunction related
to a set of psychiatric disorder
Center for Biodynamics
Department
of Mathematics
It has been shown the existence of
atropine-resistant theta frequency oscillations in slices of the CA1 hippocampal area in the
presence of metabotropic glutamate agonists and
total blockade of AMPA receptors. We present a biophysically-inspired
mathematical model that successfully reproduces the experimental findings. This
model focuses on the activity of O-LM (O), cells producing slow IPSPs, and other inhibitory neurons (I), each modeled as a single compartment. In addition to standard
Hodgkin-Huxley currents, persistent Na and a hyperpolarization-activated
(Ih) current were used for the O cells; blockade of Ih has been shown to destroy the rhythmicity
both experimentally and in simulations. We explain by means of numerical and
analytical techniques the mechanism by which coherent theta oscillations are
created, due to the interaction of the I and O cells via the fast and slow
inhibition; we emphasize the effect that I cells exert on O cells due to the
presence of Ih. We show that for a single O cell
the interspike interval may be divided in
subintervals inside which the dynamics can be described by lower dimensional
systems with slower currents as modulators; we exploit this in order to explain
the synchronization properties in larger networks.
Department of Physics
The talk discuss the effects of white noise on spontaneous activity of a cortical network model. We model a cortical network using Excitatory-Inhibitory (EI) Cowan-Wilson-like stochastic equations. Both all-to-all connection matrices (mean field) and more realistic finite-range connections are analyzed. Analytically, different regimes can be distinguished depending on the network parameters (i.e. on the connection matrices' eigenvalues) and noise level. Using analytical results as a guide line, we perform numerical simulations of the nonlinear stochastic model in the different regimes. The Power Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI) distributions are computed, to be compared with experimental results. In regime called B noise induces synchronous oscillations and Stochastic Resonance effects. Activity induced by noise is highly spatially correlated (synchrony), and it's temporally correlated only on short time scales (not perfectly periodic). The IEI shows a slow decay at long times, resembling the experimental results of Segev et al (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002). At zero noise the oscillatory activity vanishes in this regime. In regime C the model shows spontaneous synchronous periodic activity, both in presence and absence of noise, that mimic activity observed at 1 mM Ca concentration by R. Segev et al.. Due to interplay between noise and nonlinearity, the PSD shows a broad band at low frequency in presence of noise, that is in agreement with experiments (but cannot be accounted for by the Segev et al. IF model). Changing the connectivity structures of the model, phase-locked oscillations arise; then in regime of parameters called B the noise induces phase-locked oscillations, while in regime C phase-locked oscillations arise spontaneously (with and without noise).
Department
of Organismal Biology and Anatomy
Committee
on Computational Neuroscience
The
Visual stimuli elicit waves of activity that propagate across the visual cortex of turtles. These waves can be studied using multielectrode arrays and voltage-sensitive dye methods. In addition, we have constructed a large scale model of turtle visual cortex that accurately simulates cortical responses to visual stimuli. Since the waves are complex phenomena, a principal component analysis has been used to reduce the dimensionality of the waves and represent them in low dimensional phase spaces. Analysis of both real and simulated waves demonstrates that the waves encode information about the position of stimuli in visual space. It also provides a method of characterizing the underlying dynamics of the waves.