Workshop 1: Neuronal Dynamics

(October 7,2002 - October 18,2002 )

Organizers


Bard Ermentrout
Mathematics Department, University of Pittsburgh
David Terman
Mathematics Department, The Ohio State University

Dynamics plays an important role in neural systems at many levels from the subcellular up to the network levels. The time scales range from the submillisecond to many hours and as a consequence there are many different levels of detail reflected in the models. One of the main interests in systems and cellular neuroscience is to understand how the nonlinear properties of neurons and their connections sculpt inputs and change over time. Recent experiments have shown that the connections between neurons are not static and are influenced by the previous history of the neuron, the relative timing of spikes, and the local firing properties of the neuron. This workshop will focus on the temporal dynamics of neurons at the single cell and network levels.

The dendrites of neurons are often modeled as simple passive delay lines. However, experiments have revealed that there are many nonlinear time-dependent currents which can render the neuron sensitive to both the relative timing of inputs as well as their spatial distribution. Back propagation from the soma through the dendrites has been linked to changes in synaptic efficacy between connected neurons. One of the goals of the workshop is to consider the functional roles of these active processes.

As mentioned above, connections between neurons are dynamic even in relatively short time scales. For example, it has experimentally shown that the strength of connections between two neurons can change depending on the relative firing times of the two connected neurons. These dynamic synapses have been shown to alter the gain control in circuits.

Small networks of neurons have been shown to generate a variety of rhythms. Propagating waves appear to play a role both in development and in sensory processing while synchronous rhythms have been implicated in learning and the separation of inputs. Part of this workshop will be devoted to asking what the possible role of these rhythms is, how they are generated, and how they interact to form spatio-temporal patterns of activity such as transient synchrony and waves.

Large scale modeling of cortical networks requires certain simplifications be made in the characterization of individual neurons. One of the goals of this workshop will be to connect the biophysically detailed models of single neurons and dendrites to the simplified units required in large-scale simulations. Several mathematical approaches to this problems have been quite fruitful. These include mean-field methods (population averages), averaging methods (exploiting differences in time scales), and perturbation methods (weak coupling, neurons near a bifurcation point, etc).

The workshop will bring together computational neuroscientists, mathematicians, and experimental biologists who are all working on questions about the role of temporal dynamics in cells and networks of neurons.

The mathematical areas that are expected to be strongly involved in this workshop include dynamical systems (multiscales, bifurcations, perturbation methods), mean field methods, PDE's, integral differential equations, and stochastic equations.

Monday, October 7, 2002
Time Session
09:30 AM
10:30 AM
John Rinzel - Network oscillations in developing spinal cord

Many developing circuits show spontaneous oscillations. We study models for the slow episodic population rhythms (time scale, mins) that are seen in chick embryonic spinal cord. We use mean field models for the population firing rate in a recurrent network of excitatory-coupled cells. Geometric singular perturbation methods are used to analyze the models. The primary candidate for the slow negative feedback mechanism that sets the burst period is synaptic depression. The individual units have simple tonic firing properties. Specific predictions based on the model about how the rhythm is affected due to brief stimuli that switch the system from the quiescent to the active phase have now been confirmed in experiments. A positive correlation was found between episode duration and the preceding inter-episode interval, but not with the following interval, suggesting that episode onset is stochastic while episode termination occurs deterministically, when network excitability falls to a fixed level. We also predicted, and confirmed experimentally, that during glutamatergic blockade the interepisode interval increases and the network operates in a range of lessened depression, ie at increased network excitability. We also formulate and analyze a minimal model that demonstrates the plausibility of a specific mechanism for depression: the slow modulation of the synaptic reversal potential (for the GABA synapses, which are depolarizing at this stage of development). Preliminary results show that a cell-based network (integrate-and-fire units) with synaptic depression can also alternate between phases of active firing and quiescence. (with J Tabak, M O'Donovan, B Vladimirski)


Tabak, J., Senn, W., O'Donovan, M.J., & Rinzel, J. (2000). Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. J. Neuroscience, 20, 3041-3056.


Tabak, J., Rinzel, J., & O'Donovan, M. (2001). The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord. J. Neuroscience, 21, 8966-8976.

11:00 AM
12:00 PM
David Terman - Reduction of Neuronal Network Models Using Geometric Singular Perturbation Methods

Activity patterns in excitatory-inhibitory networks are analyzed using geometric singular perturbation methods. The networks are motivated by models for thalamic sleep rhythms and neuronal activity in the basal ganglia. The analysis is used to reduce the rather complicated neuronal models to simpler systems. Propagating patterns in two-dimensional networks are considered.

02:00 PM
02:30 PM
Xiao-Jing Wang - TBA

TBA

Tuesday, October 8, 2002
Time Session
09:00 AM
10:00 AM
Barry Conners - Functions of electrical synapses

There are two types of synapses in the nervous system: chemical synapses, which use diffusible extracellular molecules to transmit signals between one cell and another, and electrical synapses, which are comprised of intercytoplasmic channels that allow ionic current to flow between cells. Chemical synapses are ubiquitous in the mammalian brain. Electrical synapses had seemed to be quite rare, but new molecular and physiological data suggest that electrical synapses are far more widespread than suspected just a few years ago. Electrical synapses now seem to be a major feature of the neural circuitry in, among other things, the neocortex, hippocampus, thalamus, striatum, cerebellum, retina, hypothalamus, brainstem, and spinal cord. I will describe studies of electrical synapses between four distinct sets of neurons in the neocortex, the thalamus, and the inferior olive of the brainstem. The molecular and biophysical characteristics of these four sets of electrical synapses are surprisingly similar. Now that we appreciate their presence and properties, the greatest challenge is to identify the functions of electrical synapses. I will discuss some of the possibilities, namely that they serve to coordinate the subthreshold and spiking activity of specific sets of neurons, and that they play a role in the generation and synchrony of neuronal rhythms.

10:30 AM
11:30 AM
Roger Traub - Gap junctions between the axons of principal neurons, and the generation of fast oscillations in neuronal populations

In 1998, it was hypothesized that gap junctions existed between the axons of hippocampal pyramidal cells. This hypothesis was suggested by two experimental observations: the occurrence of 200 Hz population oscillations in neuronal networks in which synaptic transmission was blocked, but where the oscillations required gap junctions; and the shape of putative coupling potentials in principal neurons, which were too fast to be generated by gap junctions located on somata or dendrites. There is now electrophysiological and dye-coupling evidence that such gap junctions exist, and are located roughly 100 microns from the soma. Modeling shows that gap junctions in this location can give rise to very fast oscillations in networks of principal neurons, as well as to 200 Hz "ripples" (as seen in vivo, and consisting of IPSPs), when interneurons are also in the circuit. In addition, axonal gap junctions can underlie the generation of 40 Hz oscillations, in the presence of cholinergic agonists or of kainate. Modeling predicts, and experiments confirm, that in such conditions, the oscillation spectrum contains both 40 Hz and also very fast (>80 Hz) components.

02:00 PM
03:00 PM
Nancy Kopell - Nancy Kopell Presentation

The nervous system produces many different rhythms asociated with different behavioral contexts. This talk focuses on the different biophysical mechanisms associated with coherence of the different rhythms and transitions among them.

03:30 PM
04:30 PM
Michael Rudolph - Noisy dynamics and integrative properties of cortical neurons in vivo

Neocortical neurons recorded in vivo are subject to a considerable synaptic "noise", which reflects the activity of the network, and which may profoundly impact on the integrative properties of these cells. We examined this issue by using models based on morphological reconstructions of neocortical pyramidal neurons and biophysical representations of synapses and voltage-dependent currents. Results from intracellular recordings during active states were used to constrain models of synaptic noise caused by the presynaptic network activity. These experiments show that in vivo conditions are characterized by a stochastic intracellular activity which markedly shapes the neuronal dynamics. We analyze the integrative mode of the neurons in these conditions and examine issues such as the impact of dendritic structure on efficiency of synaptic inputs, coincidence detection and the detection of correlations in the synaptic noise. We conclude that cortical neurons function in a radically different integrative mode in vivo, which may have profound consequences on the type of information processing taking place in neocortex.

Wednesday, October 9, 2002
Time Session
09:00 AM
10:00 AM
Jeffery Smith - Cellular and Network Dynamics of the Mammalian Respiratory Oscillator

Experimental and modeling studies of the neural oscillator generating the rhythm of breathing in the mammalian brainstem are providing insights into cellular and network-level mechanisms generating rhythms in motor pattern generation networks. We have developed a hybrid pacemaker-network model of the respiratory oscillator that represents a synthesis of cellular and network mechanisms derived from experimental and modeling studies. This model incorporates a rhythm-generating neuronal kernel, located in the pre-B?tzinger complex of the ventrolateral medulla, consisting of a network of excitatory neurons with state (voltage)-dependent, oscillatory bursting/pacemaker-like properties. This kernel has been experimentally isolated in several in vitro preparations from neonatal rodents including thin brainstem slices with a functionally intact, active rhythm-generating network. We have exploited these in vitro systems for analysis of cellular biophysical mechanisms and population-level dynamics in the kernel by a combination of single-cell patch-clamp electrophysiological recording, activity-dependent neuron/population imaging and recording of population activity. Simulations with mathematical models of the pacemaker cell network are consistent with a number of features of measured cell and population rhythmic behavior that will be discussed in the talk, including the following. (1) Cellular biophysical mechanisms of oscillatory burst generation. Electrophysiological studies show that candidate rhythm-generating cells exhibit intrinsic voltage-dependent bursting behavior with burst frequencies spanning over an order of magnitude (.05 to ~1Hz), providing a mechanism for cellular-level frequency control. This behavior is mimicked by our biophysically minimal models incorporating Hodgkin-Huxley-like membrane conductances, where bursting arises via fast activation-slow inactivation of a subthreshold voltage-activating persistent sodium current (INaP) that dynamically interacts with a potassium-dominated leak current. Our voltage-clamp measurements have demonstrated INaP in bursting cells and dynamic clamp studies incorporating our modeled INaP in neurons confirm that this mechanism is sufficient for voltage-dependent oscillatory burst generation. (2) Synaptic coupling and burst synchronization. Electrophysiological and imaging studies indicate that cellular burst synchronization in the kernel arises from fast, glutamatergic excitatory synaptic coupling. Modeling studies of heterogeneous populations of synaptically-coupled bursting neurons (as described above) indicate that burst synchronization across the population is promoted by burst-generating currents and can occur to produce stable rhythms even when only a small fraction of the cells in the population are intrinsically bursting. Population bursting frequency is modulated by synaptic coupling strength. (3) Cellular/population frequency control and dynamic range. Experimentally tonic excitation regulates single cell and population bursting frequency; population bursting exhibits a wider dynamic range of frequency control by tonic excitation. Population model simulations mimic this and indicate that heterogeneity of cellular bursting parameters and excitatory coupling synergistically combine to determine dynamic range. (4) Multiple oscillatory modes and quasiperiodic dynamics. Measurements of population activity combined with nonlinear system dynamics analysis indicate that the kernel intrinsically exhibits multiple periodic states as frequency is driven experimentally by tonic excitation. Stable periodic behavior occurs with low excitation, progresses to mixed mode-oscillations, and transitions to quasiperiodic behavior at high excitation levels. Population simulations indicate that weak synaptic coupling and extreme parameter heterogeneity, leading to partial desychronization of cellular bursting, can give rise to mixed mode oscillations and quasiperiodic states.


References.



  • Butera, R.J., Rinzel, J. & Smith, J.C. (1999). Models of respiratory rhythm generation in the pre-B?tzinger complex. I. Bursting pacemaker neurons. J. Neurophysiology, 81, 382-397.

  • Butera, R.J., Rinzel, J. & Smith, J.C. (1999). Models of respiratory rhythm generation in the pre-B?tzinger complex. II. Populations of coupled pacemaker neurons. J. Neurophysiology, 81, 398-415.

  • Del Negro, C.A., Johnson, S.M., Butera, R.J., & Smith, J.C. (2001). Models of respiratory rhythm generation in the pre-B?tzinger complex. III. Experimental tests of model predictions. J. Neurophysiology, 86, 59-74.

  • Koshiya, N., & Smith, J.C. (1999). Neuronal pacemaker for breathing visualized in vitro. Nature, 400, 360-363.

  • Del Negro, C., Butera, R.J., Wilson, C.G., & Smith, J.C. (2002). Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network. Biophysical Journal, 82, 206-214.

10:30 AM
11:30 AM
Carl van Vreeswijk - Long Term Behavior of 1 Dimensional Networks of Spiking Neurons

Over the last ten years we have gained significant insight in the role of synaptic interactions in the synchronization of neuronal networks. A crucial first in these investigations was the study of extremely simplified networks, all-to-all coupled networks of indentical neurons. The mathematical tools developed to analyse both the asynchronous and fully synchronized state in such networks were subsequently extended to study networks with more realistic architectures. However, long term behavior in spatially extended networks of synaptically coupled neurons, in which the coupling strength decreases with distance, have not yet received much attention. In this talk I will consider a network of identical integrate-and-fire neurons, positioned on a 1-D ring. I will show that strongly coupled networks of oscil- lators behave qualitatively differently from weakly coupled ones, and also differ qualitatively from rate based models. Such networks can evolve, depending on the coupling parameters, evolve to either an asynchronous state, or to a traveling wave state. I will show how the existence and stability of these states can be analyzed in this simple model. For fast excitatory synapses a third state co-exist with the travelling wave state. In this state the activity is highly complex and the symmetry is broken. So far, no analytical treatment of this state has been found for this state.

02:00 PM
03:00 PM
Philip Ulinske - Propagating Waves in Turtle Visual Cortex

Visual stimuli evoke waves of activity that propagate throughout the visual cortex of freshwater turtles. These waves have been visualized using both multielectrode recording and voltage sensitive dye methods. This talk will discuss the use of a large-scale model of turtle visual cortex to study the cellular mechanisms underlying the propagation of the wave and to suggest that information about visual stimuli is encoded in the temporal dynamics of the waves.


 


The model consists of approximately 1,000 geniculate and cortical neurons. It is based upon the anatomical distribution of neurons in turtle visual cortex and the biophysics of individual types of cortical neurons. The model suggests that waves originate near the rostrolateral pole of the cortex due to a high density of geniculocortical synapses at that point. It reproduces features of the dynamics of the wave, such as its velocity and tendency to reflect at the caudal border of visual cortex. Analysis of real and simulated waves using a principal components method (Karhunen-Loeve decomposition) indicates that information about the position of stimuli in visual space is encoded in the dynamics of the wave in the sense that stimulus position can be reliably estimated from the dynamics of the wave using Bayesian estimation methods.

03:30 PM
04:00 AM
Aurthur Sherman - The Chay-Keizer Model: Half Right or Half Wrong?

One of the first models for bursting electrical activity was developed by Chay and Keizer. It was based on the behavior of insulin secreting pancreatic beta-cells but has been extended and modified to cover a number of neural systems, including pacemaker cells of the pre-Botzinger complex (Butera et al), thalamic neurons (Hindmarsh and Rose; Rush and Rinzel), pituitary somatotrophs (Li, Van Goor, Stojilkovic), and hippocampal pyramidal cells (Pinsky and Rinzel; Wang and Kepecs). The unifying feature of these models is hysteresis of steady states. However, one of the key predictions of the model, a slowly rising and falling intracellular calcium concentration, has not held up for the very slowly bursting beta-cells. We show how the spirit of the model can be retained, but with important differences in detail, by introducing one or more additional internal calcium compartments.

04:00 PM
04:30 AM
Tim Lewis - Tim Lewis Presentation

Fast-spiking interneurons in the cortex are connected by both inhibitory synapses and electrical synapses. We are only beginning to understand how intrinsic properties and two types of coupling interact to produce network dynamics.In this talk, I will consider oscillating pairs of leaky integrate-and-fire (LIF) cells that are connected by inhibition and electrical coupling, and I will describe how phase-locked states depend on intrinsic frequency and relative coupling strengths. The phase-locking results for the integrate-and-fire model will be compared to preliminary in vitro experiments on pairs of fast-spiking cells (from the laboratory of Dr. Barry Connors). Finally, I will discuss the possible implications of the results for the function of fast-spiking interneuronal networks.

Thursday, October 10, 2002
Time Session
09:00 AM
10:00 AM
Hugh Wilson - Dynamics of perceptual oscillations and waves in vision

Visual oscillations can occur in response to certain ambiguous stimuli, and both oscillations and travelling waves occur in binocular rivalry and migraine auras. After presenting relevant data, neural models at both the individual action potential level and at the spike rate level will be developed to interpret and explain these phenomena. These models include a two-level model for binocular rivalry in which the first level can be dynamically defeated by appropriate stimulus manipulation.

10:00 AM
11:00 AM
Hugh Wilson - Dynamics of perceptual oscillations and waves in vision

Visual oscillations can occur in response to certain ambiguous stimuli, and both oscillations and travelling waves occur in binocular rivalry and migraine auras. After presenting relevant data, neural models at both the individual action potential level and at the spike rate level will be developed to interpret and explain these phenomena. These models include a two-level model for binocular rivalry in which the first level can be dynamically defeated by appropriate stimulus manipulation.

10:30 AM
11:30 AM
David Kleinfeld - Engineering principles for detection and control in the vibrissa sensorimotor system

The sensory system of animals is of limited value without the participation of the elaborate motor apparatus that moves the sensors into useful positions. I will focus on behavioral and computational aspects of the vibrissa somatosensory system in rat, and review the experimental evidence for phase-sensitive detection as a model for discriminating contact with an object and as a means to control the position of the vibrissae. A theme of the talk is that principles from communication and control engineering provide a framework to guide experiments.

02:00 PM
03:00 PM
Marla Feller - The mechanisms underlying spontaneous propagating activity in the developing mammalian retina

In the mammalian retina, highly correlated activity is present weeks before vision in the form of spontaneous waves of action potentials recorded from retinal ganglion cells. This activity is required for the normal patterning of retinal ganglion cell axon arbors in the developing thalamus. Recordings from retinal cells participating in the waves demonstrate that wave generation requires synaptic activation, indicating that the developing network consists of various cell types connected through excitatory chemical synapses. Fluorescence imaging has revealed that the propagating activity consists of spatially restricted domains of activity that form a mosaic pattern over the entire retina. The spatial properties of waves are not determined by fixed structural units within the retina, rather they are determined by the past history of wave activity. A biophysical model of the network based on known anatomical and physiological properties of the developing retina reproduces the same spatiotemporal properties measured experimentally, and that these properties are determined by a single variable which describes the local excitability of the network. Consistent with this hypothesis, pharmacological manipulations that alter local excitability also alter the spatiotemporal properties of waves. This approach to describing the developing retina provides unique insight into how the organization of a neural circuit can lead to generation of complex, correlated activity patterns required for the normal development of the nervous system.

03:00 PM
04:00 PM
Steve Coombes - Modelling Thalamic Relay Networks

In the mammalian retina, highly correlated activity is present weeks before vision in the form of spontaneous waves of action potentials recorded from retinal ganglion cells. This activity is required for the normal patterning of retinal ganglion cell axon arbors in the developing thalamus. Recordings from retinal cells participating in the waves demonstrate that wave generation requires synaptic activation, indicating that the developing network consists of various cell types connected through excitatory chemical synapses. Fluorescence imaging has revealed that the propagating activity consists of spatially restricted domains of activity that form a mosaic pattern over the entire retina. The spatial properties of waves are not determined by fixed structural units within the retina, rather they are determined by the past history of wave activity. A biophysical model of the network based on known anatomical and physiological properties of the developing retina reproduces the same spatiotemporal properties measured experimentally, and that these properties are determined by a single variable which describes the local excitability of the network. Consistent with this hypothesis, pharmacological manipulations that alter local excitability also alter the spatiotemporal properties of waves. This approach to describing the developing retina provides unique insight into how the organization of a neural circuit can lead to generation of complex, correlated activity patterns required for the normal development of the nervous system.

Friday, October 11, 2002
Time Session
09:00 AM
10:00 AM
David Hansel - Emergence of Synchrony in Networks of Electrically Coupled Neurons: The Role on Intrinsic Currents

The existence of electrical synapses (ES) has been recently assessed in many regions of the mammalian brain. It has been also found that the spikes fired by interneurons interconnected with ES may get tightly synchronized. Here we investigate theoretically the conditions of emergence of synchronous activity in large networks of neurons coupled with ES. We consider two models. In the first one, which is analytically tractable, the neurons are fully connected and they are modeled with the "quadratic integrate-and-fire" dynamics which is a good approximation for the subthreshold behavior of a large class of neurons. The second model consists of randomly connected conductance-based neurons in which the voltage time course and the shapeof the linear response function of the neuron to small persturbations can be controlled by potassium currents and a persistent sodium current. We investigate analytically and numerically how the stability of the asynchronous state (AS) depends on the size of the action potentials fired by the neurons, on the after-hyperpolarization which follows it and on the duration of the refractory period. We predict that potassium currents promote synchrony mediated by ES whereas sodium currents oppose it.

10:30 AM
11:30 AM
David Golomb - Propagation of pulses in cortical networks

We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory neurons. Each neuron is represented by the integrate-and-fire model, and is allowed to fire only one spike. Two types of propagating pulses are observed. During fast pulses, inhibitory neurons fire a short time before or after the excitatory neurons. During slow pulses, inhibitory cells fire well before neighboring excitatory cells, and potentials of excitatory cells become negative and then positive before they fire. Fast pulses can propagate at low levels of inhibition, are affected by fast excitation but are almost unaffected by slow excitation, and are easily elicited by stimulating groups of neurons. In contrast, slow pulses can propagate at intermediate levels of inhibition, and are difficult to evoke. They can propagate without slow excitation, but slow excitation makes their propagation substantially more robust. We suggest that the fast and slow pulses observed in our model correspond to the fast and slow propagating activity observed in experiments on neocortical slices.

Saturday, October 12, 2002
Time Session
Sunday, October 13, 2002
Time Session
Monday, October 14, 2002
Time Session
09:30 AM
10:30 AM
Larry Abbott - Larry Abbott Presentation

Larry Abbott Presentation

10:30 AM
11:30 AM
Larry Abbott - Larry Abbott Presentation

Larry Abbott Presentation

11:00 AM
12:00 PM
Henry Markrum - The Neocortical Microcircuitry: The Heart of the Brain

The Neocortical Microcircuitry: The Heart of the Brain

02:00 PM
03:00 PM
Brad Ermentrout - Plasticity and synchrony

Plasticity in neural oscillators has not been explored in much detail. In this talk I describe two different types of plasticity and its role in facilitating the synchronization of coupled oscillators. In the first part of the talk, I discuss a problem motivated by the synchronization of certain species of fireflies. Pteroptyx malaccae is known to synchronize its flash to a strobe light in such a way that the phase-lag is eventually zero. It does this by altering its intrinsic frequency through a slow process. We show the consequences of this in a large locally coupled network of oscillators with a range of intrinsic frequencies and demonstrate how this leads to global synchrony. In the second part of the talk, we show that under rather general circumstances a spike-time dependent plasticity rule acting on the connection strengths of weakly coupled oscillators can lead to global synchrony.

03:00 PM
03:30 PM
Richard Bertram - The Role of G-Proteins in Synaptic Filtering

The role of the synapse as the center of learning and memory in neuronal systems is now widely appreciated. Synaptic plasticity occurs in both presynaptic and postsynaptic regions of the synapse, and takes place over a range of time scales. This plasticity can be viewed as a means for filtering information in the form of electrical signals. At the presynaptic terminal, synaptic depression and various forms of facilitation due to plasticity in the transmitter release mechanism are well-known sources of short-term plasticity. Another form of plasticity has been the focus of a great deal of experimental work over the past few years. This involves receptor-induced activation of G-proteins in the presynaptic terminal, which regulate calcium channels and thus the release of neurotransmitters. This form of plasticity has been observed in many nerve cells, and can be induced by a wide range of neurotransmitters and neurohormones. We will discuss the mechanism of G-protein regulation of transmitter release, and demonstrate how this mechanism can be used to filter information in a neuronal circuit. Using a minimal model suitable for neural network simulations, we will demonstrate that G-protein regulation can provide synaptic depression or facilitation, and can be the mechanism for network-based bursting oscillations.

Tuesday, October 15, 2002
Time Session
09:00 AM
10:00 AM
Guogiang Bi - Spike timing-dependent synaptic plasticity

Electrophysiological experiments have shown that activity-dependent synaptic modifications may depend on the precise timing of pre- and postsynaptic action potentials (spikes). Such spike timing-dependent plasticity (STDP) represents a quantitative extension of the Hebb's rule and has profound implications in the development and function of neuronal circuits. This talk will summarize experimental studies on STDP, including the description of spike-timing windows in cell culture and other systems, as well as the most recent development on the issue of STDP temporal integration.

10:30 AM
11:30 AM
Jonathan Rubin - Why the Biological Basis for Spike-Timing-Dependent Plasticity is Computationally Relevant

From experimental data, one can attempt to extract spike-timing-dependent plasticity (STDP) "rules" that operate on synapses in various systems. One can then apply these rules in models and derive information about the rules' consequences, such as asymptotic limits for synaptic weights and neuronal firing patterns in the systems. I will discuss how different rules lead to different consequences in some cases, and to similar consequences in others. I will use these examples to argue that biological details must be understood before the computational implications of STDP can be fully appreciated.

11:00 AM
11:30 AM
Carson Chow - A Biolophysically based model of Spike-Timing-Dependent Plasticity (STDP)

Experiments show that synapses can either increase their strength (LTP), decrease their strength (LTD) or do nothing at all, depending on the temporal relation between pre- and post-synaptic spiking activity. It remains a puzzle as to how neurons are able to discriminate spike-timing so precisely if at all. Here, I will first discuss some constraints that must be satisfied by any biophysical model aiming to explain STDP. I will then present a model of neuronal ionic and molecular dynamics that seems to account for the experimental results.

11:30 AM
12:30 PM
Carson Chow - A Biolophysically based model of Spike-Timing-Dependent Plasticity (STDP)

Experiments show that synapses can either increase their strength (LTP), decrease their strength (LTD) or do nothing at all, depending on the temporal relation between pre- and post-synaptic spiking activity. It remains a puzzle as to how neurons are able to discriminate spike-timing so precisely if at all. Here, I will first discuss some constraints that must be satisfied by any biophysical model aiming to explain STDP. I will then present a model of neuronal ionic and molecular dynamics that seems to account for the experimental results.

02:00 PM
02:30 PM
Steven Baer - Background-Induced flicker enhancement in cat retinal horizontal cells

In human psychophysics, it is well known that after a brilliant desensitizing flash, cone flicker sensitivity first increases but then, paradoxically, decreases with a time course paralleling rod dark adaptations. This interaction between rods and cones is called suppressive rod-cone interaction (SRCI). Analogous physiological effects involving rod and cone signals occur in horizontal cells and bipolar cells. For example, in cat, dim backgrounds can enhance small-spot flicker responses of retinal horizontal cells. This is called background-induced flicker enhancement. We formulate a biophysically based model to simulate background-induced flicker enhancement and its spatial properties. In this model we assume that depolarized horizontal-cell dendritic terminals, in a feedback effect, decrease the entry of calcium into the cone terminal. Hyperpolarization of the horizontal cell reduces this effect, allowing calcium to enter the terminal, stimulating transmitter release by the cone presynaptic apparatus. The result is an increase in synaptic gain. This accounts for how peripheral rod-induced, horizontal-cell hyperpolarizations, conducted centripetally to the horizontal-cell dendritic terminals via gap junctions, can enhance postsynaptic cone responses. Background-induced flicker enhancement also depends on the size of the test stimulus. We explore this with a spatial model that includes the thousands of horizontal cell processes (dendritic spines) entering cone pedicles.

02:30 PM
03:00 PM
Amitabha Bose - Maintaining phase between neuronal oscillators using synaptic depression

In many neuronal networks ranging in diversity from the crustacean STG to the CA3 region of the hippocampus, neurons are capable of maintaining phase relationships despite large changes in network frequency. In this talk, we show how short-term synaptic depression may act to promote phase maintenance.Using a simple model of an oscillator coupled to a follower neuron by a depressing inhibitory synapse, we show how the time to firing of the follower is a function of synaptic strength. For a depressing synapse, synaptic strength changes as a function of frequency. As a result, we obtain a network in which phase maintenance is roughly achieved over a 4-fold change in frequency. We will contrast the ability of our network to maintain phase against those with non-depressing synapses, and also those in which intrinsic currents play a prominent role.

03:30 PM
04:30 PM
David Pinto - Theoretical and experimental analysis of seizure-like activity waves in cerebral cortex

I will present a set of integrodifferential equations, derived from known biophysical properties of cerebral cortex, and with solutions that describe activity waves that occur under some pathological conditions. One approach for establishing the existence of wave solutions uses singular perturbation analysis, which assumes that the dynamics underlying each stage of the wave is approximately independent from the others. In the laboratory, this assumption becomes an explicit experimental prediction. I will present data demonstrating that real seizure-like activity waves, measured in vitro using cortical slices, consist of three stages - initiation, propagation, and termination - each governed by a distinct set of dynamics within the underlying neural circuitry. Examining the data more closely will reveal new possible avenues of investigation for understanding the dynamics of each stage individually. I will also present several intriguing experimental results suggesting other new directions for analysis of the original system of equations.

Wednesday, October 16, 2002
Time Session
09:00 AM
10:00 AM
Dan Johnston - Information Processing and Storage by Neuronal Dendrites

The dendrites of hippocampal CA1 pyramidal neurons receive inputs from tens of thousands of excitatory and inhibitory synapses. The dendrites must coordinate and blend these inputs to produce an output in what is called synaptic integration. The dendrites also participate in the dynamic adjustment of the synaptic strengths of these inputs during synaptic plasticity. Dendrites were previously thought to be mostly passive structures that provided some form of algebraic summation of excitatory and inhibitory inputs. Using new techniques of dendritic patch clamp recordings and fluorescence imaging, a great deal of new information is now available concerning how dendrites perform synaptic integration and participate in synaptic plasticity. Using cell-attached patch recordings from dendrites of CA1 neurons, we have mapped the distribution and characterized the properties of voltage-gated Na+, Ca2+, and K+ channels along the apical dendrites. We found that the density of Na+ channels is approximately the same from the initial segment of the axon, through the soma, and up to at least the first 350 ?m of the apical dendrites. The total density of voltage gated Ca2+ channels is also about the same from the soma up to 350 ?m from the soma. There are at least 5 di erent types of Ca2+ channels, however, and we found that these were distributed di erentially along the soma-dendritic axis. For example, the Land N-types are at a higher density in the soma and proximal dendrites while the R- and T-types are at a higher density in the distal dendrites. We also studied dendritic K+ channels. We found that there is a fast, transient, A-type K+ channel in the dendrites. Surprisingly, the density of this channel increases dramatically with distance from the soma so that its density at 350 ?m is about 5-fold higher than that in the soma. This channel activates rapidly and limits the amplitude of back-propagating, dendritic action potentials as well as synaptic potentials. Recently, we found that this K+ channel is modulated by several protein kinases. PKA and PKC both shift the voltage range of activation of the channel to more positive potentials thereby reducing the activity of these K+ channels at any given membrane potential and increasing the amplitude of synaptic potentials and back-propagating action potentials. The actions of both of these kinases appears to be upstream of MAPK. We also found that the K+ channels can be inactivated by brief trains of synaptic input. Synaptic input can thus produce an increase in the amplitude of back-propagating action potentials on the specific branch receiving the input. If the synaptic input is appropriately timed with the dendritic action potential, long-term potentiation is induced. We thus hypothesize that these K+ channels play a role in spike-timing dependent LTP. Furthermore, we have found local increases in excitability following the induction of LTP, which may be partly responsible for the phenomenon of E-S potentiation, and we hypothesize that this increase in excitability is due to local decreases in K+ channel activity. In conclusion, dendrites are not passive structures, but contain a vast array of voltage-gated ion channels. These channels play important roles in synaptic integration and both the induction and expression of various forms of synaptic plasticity.

10:30 AM
11:30 AM
Dan Tranchina - Reproducibility of the single-photon response of retinal rods: testingtheories by detailed stochastic modeling of underlying biochemicalmechanisms

A major outstanding problem in sensory physiology is to understand how the response of a retinal rod to a single photon manages to have such little variation in amplitude and kinetics, despite the fact that it is mediated by the activity of a single molecule of activated rhodopsin (R*). In the dark, there is a circulating current across the rod membrane, which flows inward through channels in the outer segment membrane gated by cyclic-GMP, and flows outward across the inner segment membrane. The modulation of the voltage across the rod membrane in response to light is a consequence of the reduction of this dark (light-sensitive) current by the following mechanism. When rhodopsin absorbs a photon it is converted into an activated enzyme (R*) that initiates a cascade of biochemical reactions: G-protein is activated by R*; G-protein activates phosphodiesterase; phosphodiesterase hydrolyzes cyclic-GMP; the cyclic-GMP concentration drops, resulting in closure of some of the light-sensitive channels; the reduction of inward current causes the rod membrane voltage to become hyperpolarized. The sequence of events following the activation of rhodopsin continues until R* is inactivated. The regularity of the single-photon response implies that the lifetime of R* is controlled with high precision. Numerous theories have been proposed. All are based in part on known biochemical elements of the transduction cascade, and some also include additional hypothetical mechanism. Liebman and Gibson recently proposed a theory based on their biochemical experiments. The idea is that R* is partially deactivated by multiple steps of phosphorylation catalyzed by rhodopsin kinase, followed by an irreversible "capping" reaction in which R* is completely inactivated by arrestin. In this theory, three molecules, rhodopsin kinase, G-protein and arrestin, compete in a mutually exclusive manner for R*. Every time R* is phosphorylated, its affinity for G-protein (i.e. its catalytic activity) is reduced, its affinity for rhodopsin kinase is reduced, and its affinity for arrestin is increased. I will explain how some statistics of the single-photon responses can be derived analytically in this theory. I will also demonstrate by Monte Carlo simulation the extent to which the proposed mechanism reduces variability in the single-photon response. Deficiencies of the theory will be demonstrated, and alternative mechanisms will be discussed and evaluated.

02:00 PM
03:00 PM
David McLaughllin - Modeling the Primary Visual Cortex

Modeling the Primary Visual Cortex

03:00 PM
03:30 PM
Farzan Nadim - Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity

When depressing synapses are embedded in a circuit composed of a pacemaker neuron and a neuron with no autorhythmic properties, the network can show two modes of oscillation. In one mode the synapses are mostly depressed and the oscillations are dominated by the properties of the oscillating neuron. In the other mode, the synapses recover from depression and the oscillations are largely controlled by the synapses. We demonstrate the two modes of oscillation in a hybrid circuit consisting of a biological pacemaker and a model neuron, reciprocally coupled via model depressing synapses. We show that across a wide range of parameter values this network shows robust bistability of the oscillation mode, and that it is possible to switch the network from one mode to the other by injection of a brief current pulse in either neuron. The underlying mechanism for bistability may be present in many types of circuits with reciprocal connections and synaptic depression.


 


Bose, A., Manor, Y., & Nadim, F. (2001). Bistable oscillations arising from synaptic depression. SIAM Journal on Applied Mathematics, 62, 706-727.


Manor, Y., & Nadim F. (2001). Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity. J. Neuroscience, 21, 9460-9470.

Thursday, October 17, 2002
Time Session
09:00 AM
10:00 AM
Mike Shelley - The Simple and the Complex in Visual Cortex Dynamics

So-called Simple cells in the primary visual cortex (V1) respond to visual stimulation in a roughly linear way, while Complex cells do not. This longstanding classification -- the basis for the influential hierarchical model of Hubel & Wiesel -- is far from sharp; Recent experiments show that most cortical cells lie somewhere in a continuum between being Simple or Complex. I and my collaborators have posed and studied an "egalitarian" model of V1, based on the local architecture of a V1 hypercolumn, where all cortical cells are coupled nonspecifically within the network. I show that by requiring the total synaptic weight on each cell to be constant, though divided between between geniculate and network couplings, leads to broad response distributions like those found in experiment, and rationalizes several aspects of the experimental data.

10:30 AM
11:30 AM
Paul Bressloff - The crystalline-like structure of cortex

One of the major simplifying assumptions in many large-scale models of cortical tissue is that the interactions between cell populations are invariant under the action of the Euclidean group of rigid body motions in the plane. Euclidean symmetry plays a key role in determining the types of activity patterns and waves that can be generated in these cortical networks. However, the assumptions of homogeneity and isotropy are no longer valid when the detailed microstructure of cortex is taken into account. In fact, cortex has a distinctly crystalline-like structure at the mm length-scale, as exemplified by the patchy nature of long-range horizontal (and feedback) connections in primary visual cortex. These patchy connections are correlated with a number of periodically repeating feature maps, in which local populations of neurons respond preferentially to stimuli with particular properties such as orientation, spatial frequency and left/right eye (ocular) dominance. In this talk we present some recent analytical results regarding the large-scale dynamics of cortex in the presence of periodically modulated long-range interactions.

02:00 PM
03:00 PM
Robert Shapley - Neuronal and network dynamics in V1 cortex

Interesting things happen in the time evolution of visual responses of neurons in V1 cortex. V1 neurons studied individually exhibit time-dependent sensitivity and selectivity for orientation and spatial frequency. This implies an important role for inhibitory interactions in the production of selectivity. From a theory of the network dynamics, one finds that the V1 network causes neurons to be "overdamped" in a high conductance state during visual stimulation, making these neurons into coincidence detectors. Nevertheless, the time-averaged spike rate of a V1 neuron is an approximately linear function of its net synaptic input.

03:00 PM
03:30 PM
Duane Nykamp - Reconstructing the coupling of visual neurons from spike times

Reconstructing the connectivity patterns of neural networks in higher organisms has been a formidable challenge. Most neurophysiology data consist only of spike times, and current analysis methods are unable to resolve the ambiguity in connectivity patterns that could lead to such data. We present a new method that can determine the presence of a connection between two visual neurons from the spike times of the neurons in response to spatiotemporal white noise. The method successfully distinguishes such a direct connection from common input originating from other, unmeasured neurons. Although the method is based on a highly idealized linear-nonlinear approximation of neural response, we demonstrate via simulation that the approach can work with a more realistic, integrate-and-fire neuron model. We propose that the approach exemplified by this analysis may yield viable tools for econstructing visual neural networks from data gathered in neurophysiology experiments.

Friday, October 18, 2002
Time Session
Name Email Affiliation
Abbott, Larry Volen Center, Brandeis University
Baer, Steven Mathematics Department, Arizona State University
Bell, Jonathan jbell@math.umbc.edu Department of Mathematics & Statistics, University of Maryland Baltimore County
Bertram, Richard bertram@sb.fsu.edu Mathematics Department, Florida State University
Bi, Guogiang Neurobiology Department, University of Pittsburgh
Bibbig, Andrea Brooklyn Health Sciences Center, City University of New York (CUNY)
Bibbig, Andrea Brooklyn Health Sciences Center, City University of New York (CUNY)
Booth, Victoria vbooth@umich.edu Mathematics Department, New Jersey Institute of Technology
Borisyuk, Alla borisyuk@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Bose, Amitabha Mathematics Department, New Jersey Institute of Technology
Bressloff, Paul bressloff@math.utah.edu Mathematics Department, University of Utah
Brown, Eric Applied & Computational Mathematics, Princeton University
Brunel, Nicolas CNRS - Neurophysique et Physiologie du Sys. M, France
Butera, Robert School of Electrical & Computer Engineering, Georgia Institute of Technology
Chow, Carson carsonc@mail.nih.gov Department of Mathematics, University of Pittsburgh
Conners, Barry Department Neuroscience, Brown University
Coombes, Stephen stephen.coombes@nottingham.ac.uk Department of Mathematics, Loughborough University
Cowan, Jack Mathematics Department, University of Chicago
Cowen, Carl cowen@mbi.osu.edu Department of Mathematics, The Ohio State University
Cox, Steven Department of Computational & Applied Mathematics, Rice University
Cracium, Gheorghe Mathematical Biosciecnces Institute, The Ohio State University
Curtu, Rodica Rodica-Curtu@uiowa.edu Mathematics Department, University of Pittsburgh
Danthi, Sanjay danthi.1@osu.edu Mathematical Biosciences Institute, The Ohio State University
Deng, Bo Mathematics & Statistics Department, University of Nebraska
Dodla, Ramana ramana.dodla@utsa.edu Center for Neural Science, New York University
Dougherty, Daniel dpdoughe@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Ermentrout, Bard brad@math.pitt.edu Mathematics Department, University of Pittsburgh
Fall, Chris fall@uic.edu Center for Neural Science, New York University
Feller, Marla Biology Department, University of California, San Diego
French, Donald french@math.uc.edu Department of Mathematics, University of Cincinnati
Goel, Pranay goelpra@helix.nih.gov Mathematics Department, University of Pittsburgh
Golomb, David golomb@bgumail.bgu.ac.il Mathematical Biosciences Institute, The Ohio State University
Golubitsky, Marty mg@uh.edu Mathematics Department, University of Houston
Guckenheimer, John gucken@cam.cornell.edu; Department of Mathematics, Cornell University
Guo, Yixin yixin@math.drexel.edu Mathematics Department, University of Pittsburgh
Hansel, David david.hansel@biomedicale.univ-paris5.fr CNRS - Neurophysique et Physiologie de Sys. Moteur, France
Hayot, Fernand hayot@mps.ohio-state.edu Department of Physics, The Ohio State University
Herrera-Valdez, Marco ARL Division of Neurobiology, University of Arizona
Holmes, Phil pholmes@Math.Princeton.EDU Mechanical & Aerospace Engineering, Princeton University
Hoogendoorn, Stephanie Mathematics Department, University of Pittsburgh
Jazayeri, Mehrdad Center for Neural Science, New York University
Johnston, Dan Bayor College of Medicine
Jones, Stephanie NMR Center, Massachusetts General Hospital
Kleinfeld, David Physics Department, University of California, San Diego
Kopell, Nancy nk@math.bu.edu Mathematics Department, Boston University
Lee, Euiwoo ewlee@ssu.ac.kr Mathematics Department, The Ohio State University
Lewis, Tim tim.lewis@nyu.edu Center for Neural Science, New York University
Lou, Yuan lou@math.ohio-state.edu Mathematics Department, The Ohio State University
Markrum, Henry Department of Neurology, Weizmann Institute of Science
Matveev, Victor matveev@njit.edu Laboratory of Biological Modeling, National Institutes of Health
McLaughllin, David Courant Institute, New York University
Mischaikow , Konstantin mischaik@math.rutgers.edu Center for Dynamical Systems & Nonlinear Studies, Georgia Institute of Technology
Moehlis, Jeff Applied & Computational mathematics, Princeton University
Nadim, Farzan Biological Sciences, Rutgers University
Nadim, Farzan Department of Biological Sciences, New Jersey Institute of Technology
Ndim, Farzan Department of BiologicalScience, Rutgers University
Nykamp, Duane nykamp@math.ucla.edu School of Mathematics, University of Minnesota
Pinto, David BioMed Neuroscience Department, Brown University
Plesser, Hans Mathematical Biosciences Institute, The Ohio State University
Pugh, Mary mpugh@math.toronto.edu Department of Mathematics, University of Toronto
Rejniak, Katarzyna rejniak@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Riecke, Hermann Applied Mathematics Department, J. L. Kellogg Graduate School of Management
Rinzel, John rinzel@cns.nyu.edu Center for Neural Science & Courant Institute, New York University
Roper, Peter National Institutes of Health
Rubin, Jonathan rubin@euler.math.pitt.edu Mathematics Department, University of Pittsburgh
Rudolph, Michael CNRS/UNIC, France
Sandstede, Bjorn sandsted@math.ohio-state.edu Mathematics Department, The Ohio State University
Shapley , Robert shapley@cns.nyu.edu Center for Neural Science, New York University
Shelley, Mike Courant Institute, New York University
Sherman, Aurthur National Institutes of Health
Smith, Jeffery Laboratory of Neural Control, National Institutes of Health
Su, Jianzhong su@uta.edu Department of Mathematics, University of Texas
Tao, Louis tao@njit.edu Center for Neural Science, New York University
Terman, David terman@math.ohio-state.edu Mathematics Department, The Ohio State University
Terry, John Department of Mathematics, University of Queensland
Tranchina, Dan dt2@nyu.edu Courant Institute, New York University
Traub, Roger Brooklyn Health Sciences Center, New York University
Ulinske, Philip Department of Organismal Biology & Anatomy, University of Chicago
van Vreeswijk, Carl carl.van-vreeswijk@biomedicale.univ-paris5.fr CNRS - Neurophysique et Physiologie du Sys. nmoteur, France
Wang, DeLiang dwang@cis.ohio-state.edu Department of Computer Science, The Ohio State University
Wang, Xiao-Jing Computational Neuroscience, Brandeis University
Wechselberger, Martin wm@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
White, John john.white@utah.edu Engineering Research, Boston University
Wilson, Hugh Spatial and Computational Vision, York University
Wong, Kong-Fatt Brandeis University
Wright, Geraldine wright.572@osu.edu Mathematical Biosciences Institute, The Ohio State University
Wu, Jian-Young Department of Physiology and Biophysics, Georgetown University
Yew, Alice yew@math.ohio-state.edu Mathematics Department, The Ohio State University
Yixin, Guo yigst@pitt.edu Mathematics Department, University of Pittsburgh
Zhang, Linghai liz5@lehigh.edu School of Mathematics, University of Minnesota
Larry Abbott Presentation

Larry Abbott Presentation

TBA

TBA

Background-Induced flicker enhancement in cat retinal horizontal cells

In human psychophysics, it is well known that after a brilliant desensitizing flash, cone flicker sensitivity first increases but then, paradoxically, decreases with a time course paralleling rod dark adaptations. This interaction between rods and cones is called suppressive rod-cone interaction (SRCI). Analogous physiological effects involving rod and cone signals occur in horizontal cells and bipolar cells. For example, in cat, dim backgrounds can enhance small-spot flicker responses of retinal horizontal cells. This is called background-induced flicker enhancement. We formulate a biophysically based model to simulate background-induced flicker enhancement and its spatial properties. In this model we assume that depolarized horizontal-cell dendritic terminals, in a feedback effect, decrease the entry of calcium into the cone terminal. Hyperpolarization of the horizontal cell reduces this effect, allowing calcium to enter the terminal, stimulating transmitter release by the cone presynaptic apparatus. The result is an increase in synaptic gain. This accounts for how peripheral rod-induced, horizontal-cell hyperpolarizations, conducted centripetally to the horizontal-cell dendritic terminals via gap junctions, can enhance postsynaptic cone responses. Background-induced flicker enhancement also depends on the size of the test stimulus. We explore this with a spatial model that includes the thousands of horizontal cell processes (dendritic spines) entering cone pedicles.

The Role of G-Proteins in Synaptic Filtering

The role of the synapse as the center of learning and memory in neuronal systems is now widely appreciated. Synaptic plasticity occurs in both presynaptic and postsynaptic regions of the synapse, and takes place over a range of time scales. This plasticity can be viewed as a means for filtering information in the form of electrical signals. At the presynaptic terminal, synaptic depression and various forms of facilitation due to plasticity in the transmitter release mechanism are well-known sources of short-term plasticity. Another form of plasticity has been the focus of a great deal of experimental work over the past few years. This involves receptor-induced activation of G-proteins in the presynaptic terminal, which regulate calcium channels and thus the release of neurotransmitters. This form of plasticity has been observed in many nerve cells, and can be induced by a wide range of neurotransmitters and neurohormones. We will discuss the mechanism of G-protein regulation of transmitter release, and demonstrate how this mechanism can be used to filter information in a neuronal circuit. Using a minimal model suitable for neural network simulations, we will demonstrate that G-protein regulation can provide synaptic depression or facilitation, and can be the mechanism for network-based bursting oscillations.

Spike timing-dependent synaptic plasticity

Electrophysiological experiments have shown that activity-dependent synaptic modifications may depend on the precise timing of pre- and postsynaptic action potentials (spikes). Such spike timing-dependent plasticity (STDP) represents a quantitative extension of the Hebb's rule and has profound implications in the development and function of neuronal circuits. This talk will summarize experimental studies on STDP, including the description of spike-timing windows in cell culture and other systems, as well as the most recent development on the issue of STDP temporal integration.

Maintaining phase between neuronal oscillators using synaptic depression

In many neuronal networks ranging in diversity from the crustacean STG to the CA3 region of the hippocampus, neurons are capable of maintaining phase relationships despite large changes in network frequency. In this talk, we show how short-term synaptic depression may act to promote phase maintenance.Using a simple model of an oscillator coupled to a follower neuron by a depressing inhibitory synapse, we show how the time to firing of the follower is a function of synaptic strength. For a depressing synapse, synaptic strength changes as a function of frequency. As a result, we obtain a network in which phase maintenance is roughly achieved over a 4-fold change in frequency. We will contrast the ability of our network to maintain phase against those with non-depressing synapses, and also those in which intrinsic currents play a prominent role.

The crystalline-like structure of cortex

One of the major simplifying assumptions in many large-scale models of cortical tissue is that the interactions between cell populations are invariant under the action of the Euclidean group of rigid body motions in the plane. Euclidean symmetry plays a key role in determining the types of activity patterns and waves that can be generated in these cortical networks. However, the assumptions of homogeneity and isotropy are no longer valid when the detailed microstructure of cortex is taken into account. In fact, cortex has a distinctly crystalline-like structure at the mm length-scale, as exemplified by the patchy nature of long-range horizontal (and feedback) connections in primary visual cortex. These patchy connections are correlated with a number of periodically repeating feature maps, in which local populations of neurons respond preferentially to stimuli with particular properties such as orientation, spatial frequency and left/right eye (ocular) dominance. In this talk we present some recent analytical results regarding the large-scale dynamics of cortex in the presence of periodically modulated long-range interactions.

A Biolophysically based model of Spike-Timing-Dependent Plasticity (STDP)

Experiments show that synapses can either increase their strength (LTP), decrease their strength (LTD) or do nothing at all, depending on the temporal relation between pre- and post-synaptic spiking activity. It remains a puzzle as to how neurons are able to discriminate spike-timing so precisely if at all. Here, I will first discuss some constraints that must be satisfied by any biophysical model aiming to explain STDP. I will then present a model of neuronal ionic and molecular dynamics that seems to account for the experimental results.

A Biolophysically based model of Spike-Timing-Dependent Plasticity (STDP)

Experiments show that synapses can either increase their strength (LTP), decrease their strength (LTD) or do nothing at all, depending on the temporal relation between pre- and post-synaptic spiking activity. It remains a puzzle as to how neurons are able to discriminate spike-timing so precisely if at all. Here, I will first discuss some constraints that must be satisfied by any biophysical model aiming to explain STDP. I will then present a model of neuronal ionic and molecular dynamics that seems to account for the experimental results.

Functions of electrical synapses

There are two types of synapses in the nervous system: chemical synapses, which use diffusible extracellular molecules to transmit signals between one cell and another, and electrical synapses, which are comprised of intercytoplasmic channels that allow ionic current to flow between cells. Chemical synapses are ubiquitous in the mammalian brain. Electrical synapses had seemed to be quite rare, but new molecular and physiological data suggest that electrical synapses are far more widespread than suspected just a few years ago. Electrical synapses now seem to be a major feature of the neural circuitry in, among other things, the neocortex, hippocampus, thalamus, striatum, cerebellum, retina, hypothalamus, brainstem, and spinal cord. I will describe studies of electrical synapses between four distinct sets of neurons in the neocortex, the thalamus, and the inferior olive of the brainstem. The molecular and biophysical characteristics of these four sets of electrical synapses are surprisingly similar. Now that we appreciate their presence and properties, the greatest challenge is to identify the functions of electrical synapses. I will discuss some of the possibilities, namely that they serve to coordinate the subthreshold and spiking activity of specific sets of neurons, and that they play a role in the generation and synchrony of neuronal rhythms.

Modelling Thalamic Relay Networks

In the mammalian retina, highly correlated activity is present weeks before vision in the form of spontaneous waves of action potentials recorded from retinal ganglion cells. This activity is required for the normal patterning of retinal ganglion cell axon arbors in the developing thalamus. Recordings from retinal cells participating in the waves demonstrate that wave generation requires synaptic activation, indicating that the developing network consists of various cell types connected through excitatory chemical synapses. Fluorescence imaging has revealed that the propagating activity consists of spatially restricted domains of activity that form a mosaic pattern over the entire retina. The spatial properties of waves are not determined by fixed structural units within the retina, rather they are determined by the past history of wave activity. A biophysical model of the network based on known anatomical and physiological properties of the developing retina reproduces the same spatiotemporal properties measured experimentally, and that these properties are determined by a single variable which describes the local excitability of the network. Consistent with this hypothesis, pharmacological manipulations that alter local excitability also alter the spatiotemporal properties of waves. This approach to describing the developing retina provides unique insight into how the organization of a neural circuit can lead to generation of complex, correlated activity patterns required for the normal development of the nervous system.

Plasticity and synchrony

Plasticity in neural oscillators has not been explored in much detail. In this talk I describe two different types of plasticity and its role in facilitating the synchronization of coupled oscillators. In the first part of the talk, I discuss a problem motivated by the synchronization of certain species of fireflies. Pteroptyx malaccae is known to synchronize its flash to a strobe light in such a way that the phase-lag is eventually zero. It does this by altering its intrinsic frequency through a slow process. We show the consequences of this in a large locally coupled network of oscillators with a range of intrinsic frequencies and demonstrate how this leads to global synchrony. In the second part of the talk, we show that under rather general circumstances a spike-time dependent plasticity rule acting on the connection strengths of weakly coupled oscillators can lead to global synchrony.

The mechanisms underlying spontaneous propagating activity in the developing mammalian retina

In the mammalian retina, highly correlated activity is present weeks before vision in the form of spontaneous waves of action potentials recorded from retinal ganglion cells. This activity is required for the normal patterning of retinal ganglion cell axon arbors in the developing thalamus. Recordings from retinal cells participating in the waves demonstrate that wave generation requires synaptic activation, indicating that the developing network consists of various cell types connected through excitatory chemical synapses. Fluorescence imaging has revealed that the propagating activity consists of spatially restricted domains of activity that form a mosaic pattern over the entire retina. The spatial properties of waves are not determined by fixed structural units within the retina, rather they are determined by the past history of wave activity. A biophysical model of the network based on known anatomical and physiological properties of the developing retina reproduces the same spatiotemporal properties measured experimentally, and that these properties are determined by a single variable which describes the local excitability of the network. Consistent with this hypothesis, pharmacological manipulations that alter local excitability also alter the spatiotemporal properties of waves. This approach to describing the developing retina provides unique insight into how the organization of a neural circuit can lead to generation of complex, correlated activity patterns required for the normal development of the nervous system.

Propagation of pulses in cortical networks

We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory neurons. Each neuron is represented by the integrate-and-fire model, and is allowed to fire only one spike. Two types of propagating pulses are observed. During fast pulses, inhibitory neurons fire a short time before or after the excitatory neurons. During slow pulses, inhibitory cells fire well before neighboring excitatory cells, and potentials of excitatory cells become negative and then positive before they fire. Fast pulses can propagate at low levels of inhibition, are affected by fast excitation but are almost unaffected by slow excitation, and are easily elicited by stimulating groups of neurons. In contrast, slow pulses can propagate at intermediate levels of inhibition, and are difficult to evoke. They can propagate without slow excitation, but slow excitation makes their propagation substantially more robust. We suggest that the fast and slow pulses observed in our model correspond to the fast and slow propagating activity observed in experiments on neocortical slices.

Emergence of Synchrony in Networks of Electrically Coupled Neurons: The Role on Intrinsic Currents

The existence of electrical synapses (ES) has been recently assessed in many regions of the mammalian brain. It has been also found that the spikes fired by interneurons interconnected with ES may get tightly synchronized. Here we investigate theoretically the conditions of emergence of synchronous activity in large networks of neurons coupled with ES. We consider two models. In the first one, which is analytically tractable, the neurons are fully connected and they are modeled with the "quadratic integrate-and-fire" dynamics which is a good approximation for the subthreshold behavior of a large class of neurons. The second model consists of randomly connected conductance-based neurons in which the voltage time course and the shapeof the linear response function of the neuron to small persturbations can be controlled by potassium currents and a persistent sodium current. We investigate analytically and numerically how the stability of the asynchronous state (AS) depends on the size of the action potentials fired by the neurons, on the after-hyperpolarization which follows it and on the duration of the refractory period. We predict that potassium currents promote synchrony mediated by ES whereas sodium currents oppose it.

Information Processing and Storage by Neuronal Dendrites

The dendrites of hippocampal CA1 pyramidal neurons receive inputs from tens of thousands of excitatory and inhibitory synapses. The dendrites must coordinate and blend these inputs to produce an output in what is called synaptic integration. The dendrites also participate in the dynamic adjustment of the synaptic strengths of these inputs during synaptic plasticity. Dendrites were previously thought to be mostly passive structures that provided some form of algebraic summation of excitatory and inhibitory inputs. Using new techniques of dendritic patch clamp recordings and fluorescence imaging, a great deal of new information is now available concerning how dendrites perform synaptic integration and participate in synaptic plasticity. Using cell-attached patch recordings from dendrites of CA1 neurons, we have mapped the distribution and characterized the properties of voltage-gated Na+, Ca2+, and K+ channels along the apical dendrites. We found that the density of Na+ channels is approximately the same from the initial segment of the axon, through the soma, and up to at least the first 350 ?m of the apical dendrites. The total density of voltage gated Ca2+ channels is also about the same from the soma up to 350 ?m from the soma. There are at least 5 di erent types of Ca2+ channels, however, and we found that these were distributed di erentially along the soma-dendritic axis. For example, the Land N-types are at a higher density in the soma and proximal dendrites while the R- and T-types are at a higher density in the distal dendrites. We also studied dendritic K+ channels. We found that there is a fast, transient, A-type K+ channel in the dendrites. Surprisingly, the density of this channel increases dramatically with distance from the soma so that its density at 350 ?m is about 5-fold higher than that in the soma. This channel activates rapidly and limits the amplitude of back-propagating, dendritic action potentials as well as synaptic potentials. Recently, we found that this K+ channel is modulated by several protein kinases. PKA and PKC both shift the voltage range of activation of the channel to more positive potentials thereby reducing the activity of these K+ channels at any given membrane potential and increasing the amplitude of synaptic potentials and back-propagating action potentials. The actions of both of these kinases appears to be upstream of MAPK. We also found that the K+ channels can be inactivated by brief trains of synaptic input. Synaptic input can thus produce an increase in the amplitude of back-propagating action potentials on the specific branch receiving the input. If the synaptic input is appropriately timed with the dendritic action potential, long-term potentiation is induced. We thus hypothesize that these K+ channels play a role in spike-timing dependent LTP. Furthermore, we have found local increases in excitability following the induction of LTP, which may be partly responsible for the phenomenon of E-S potentiation, and we hypothesize that this increase in excitability is due to local decreases in K+ channel activity. In conclusion, dendrites are not passive structures, but contain a vast array of voltage-gated ion channels. These channels play important roles in synaptic integration and both the induction and expression of various forms of synaptic plasticity.

Engineering principles for detection and control in the vibrissa sensorimotor system

The sensory system of animals is of limited value without the participation of the elaborate motor apparatus that moves the sensors into useful positions. I will focus on behavioral and computational aspects of the vibrissa somatosensory system in rat, and review the experimental evidence for phase-sensitive detection as a model for discriminating contact with an object and as a means to control the position of the vibrissae. A theme of the talk is that principles from communication and control engineering provide a framework to guide experiments.

Nancy Kopell Presentation

The nervous system produces many different rhythms asociated with different behavioral contexts. This talk focuses on the different biophysical mechanisms associated with coherence of the different rhythms and transitions among them.

Tim Lewis Presentation

Fast-spiking interneurons in the cortex are connected by both inhibitory synapses and electrical synapses. We are only beginning to understand how intrinsic properties and two types of coupling interact to produce network dynamics.In this talk, I will consider oscillating pairs of leaky integrate-and-fire (LIF) cells that are connected by inhibition and electrical coupling, and I will describe how phase-locked states depend on intrinsic frequency and relative coupling strengths. The phase-locking results for the integrate-and-fire model will be compared to preliminary in vitro experiments on pairs of fast-spiking cells (from the laboratory of Dr. Barry Connors). Finally, I will discuss the possible implications of the results for the function of fast-spiking interneuronal networks.

The Neocortical Microcircuitry: The Heart of the Brain

The Neocortical Microcircuitry: The Heart of the Brain

Modeling the Primary Visual Cortex

Modeling the Primary Visual Cortex

Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity

When depressing synapses are embedded in a circuit composed of a pacemaker neuron and a neuron with no autorhythmic properties, the network can show two modes of oscillation. In one mode the synapses are mostly depressed and the oscillations are dominated by the properties of the oscillating neuron. In the other mode, the synapses recover from depression and the oscillations are largely controlled by the synapses. We demonstrate the two modes of oscillation in a hybrid circuit consisting of a biological pacemaker and a model neuron, reciprocally coupled via model depressing synapses. We show that across a wide range of parameter values this network shows robust bistability of the oscillation mode, and that it is possible to switch the network from one mode to the other by injection of a brief current pulse in either neuron. The underlying mechanism for bistability may be present in many types of circuits with reciprocal connections and synaptic depression.


 


Bose, A., Manor, Y., & Nadim, F. (2001). Bistable oscillations arising from synaptic depression. SIAM Journal on Applied Mathematics, 62, 706-727.


Manor, Y., & Nadim F. (2001). Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity. J. Neuroscience, 21, 9460-9470.

Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity

When depressing synapses are embedded in a circuit composed of a pacemaker neuron and a neuron with no autorhythmic properties, the network can show two modes of oscillation. In one mode the synapses are mostly depressed and the oscillations are dominated by the properties of the oscillating neuron. In the other mode, the synapses recover from depression and the oscillations are largely controlled by the synapses. We demonstrate the two modes of oscillation in a hybrid circuit consisting of a biological pacemaker and a model neuron, reciprocally coupled via model depressing synapses. We show that across a wide range of parameter values this network shows robust bistability of the oscillation mode, and that it is possible to switch the network from one mode to the other by injection of a brief current pulse in either neuron. The underlying mechanism for bistability may be present in many types of circuits with reciprocal connections and synaptic depression.


 


Bose, A., Manor, Y., & Nadim, F. (2001). Bistable oscillations arising from synaptic depression. SIAM Journal on Applied Mathematics, 62, 706-727.


Manor, Y., & Nadim F. (2001). Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity. J. Neuroscience, 21, 9460-9470.

Reconstructing the coupling of visual neurons from spike times

Reconstructing the connectivity patterns of neural networks in higher organisms has been a formidable challenge. Most neurophysiology data consist only of spike times, and current analysis methods are unable to resolve the ambiguity in connectivity patterns that could lead to such data. We present a new method that can determine the presence of a connection between two visual neurons from the spike times of the neurons in response to spatiotemporal white noise. The method successfully distinguishes such a direct connection from common input originating from other, unmeasured neurons. Although the method is based on a highly idealized linear-nonlinear approximation of neural response, we demonstrate via simulation that the approach can work with a more realistic, integrate-and-fire neuron model. We propose that the approach exemplified by this analysis may yield viable tools for econstructing visual neural networks from data gathered in neurophysiology experiments.

Theoretical and experimental analysis of seizure-like activity waves in cerebral cortex

I will present a set of integrodifferential equations, derived from known biophysical properties of cerebral cortex, and with solutions that describe activity waves that occur under some pathological conditions. One approach for establishing the existence of wave solutions uses singular perturbation analysis, which assumes that the dynamics underlying each stage of the wave is approximately independent from the others. In the laboratory, this assumption becomes an explicit experimental prediction. I will present data demonstrating that real seizure-like activity waves, measured in vitro using cortical slices, consist of three stages - initiation, propagation, and termination - each governed by a distinct set of dynamics within the underlying neural circuitry. Examining the data more closely will reveal new possible avenues of investigation for understanding the dynamics of each stage individually. I will also present several intriguing experimental results suggesting other new directions for analysis of the original system of equations.

Network oscillations in developing spinal cord

Many developing circuits show spontaneous oscillations. We study models for the slow episodic population rhythms (time scale, mins) that are seen in chick embryonic spinal cord. We use mean field models for the population firing rate in a recurrent network of excitatory-coupled cells. Geometric singular perturbation methods are used to analyze the models. The primary candidate for the slow negative feedback mechanism that sets the burst period is synaptic depression. The individual units have simple tonic firing properties. Specific predictions based on the model about how the rhythm is affected due to brief stimuli that switch the system from the quiescent to the active phase have now been confirmed in experiments. A positive correlation was found between episode duration and the preceding inter-episode interval, but not with the following interval, suggesting that episode onset is stochastic while episode termination occurs deterministically, when network excitability falls to a fixed level. We also predicted, and confirmed experimentally, that during glutamatergic blockade the interepisode interval increases and the network operates in a range of lessened depression, ie at increased network excitability. We also formulate and analyze a minimal model that demonstrates the plausibility of a specific mechanism for depression: the slow modulation of the synaptic reversal potential (for the GABA synapses, which are depolarizing at this stage of development). Preliminary results show that a cell-based network (integrate-and-fire units) with synaptic depression can also alternate between phases of active firing and quiescence. (with J Tabak, M O'Donovan, B Vladimirski)


Tabak, J., Senn, W., O'Donovan, M.J., & Rinzel, J. (2000). Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. J. Neuroscience, 20, 3041-3056.


Tabak, J., Rinzel, J., & O'Donovan, M. (2001). The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord. J. Neuroscience, 21, 8966-8976.

Why the Biological Basis for Spike-Timing-Dependent Plasticity is Computationally Relevant

From experimental data, one can attempt to extract spike-timing-dependent plasticity (STDP) "rules" that operate on synapses in various systems. One can then apply these rules in models and derive information about the rules' consequences, such as asymptotic limits for synaptic weights and neuronal firing patterns in the systems. I will discuss how different rules lead to different consequences in some cases, and to similar consequences in others. I will use these examples to argue that biological details must be understood before the computational implications of STDP can be fully appreciated.

Noisy dynamics and integrative properties of cortical neurons in vivo

Neocortical neurons recorded in vivo are subject to a considerable synaptic "noise", which reflects the activity of the network, and which may profoundly impact on the integrative properties of these cells. We examined this issue by using models based on morphological reconstructions of neocortical pyramidal neurons and biophysical representations of synapses and voltage-dependent currents. Results from intracellular recordings during active states were used to constrain models of synaptic noise caused by the presynaptic network activity. These experiments show that in vivo conditions are characterized by a stochastic intracellular activity which markedly shapes the neuronal dynamics. We analyze the integrative mode of the neurons in these conditions and examine issues such as the impact of dendritic structure on efficiency of synaptic inputs, coincidence detection and the detection of correlations in the synaptic noise. We conclude that cortical neurons function in a radically different integrative mode in vivo, which may have profound consequences on the type of information processing taking place in neocortex.

Neuronal and network dynamics in V1 cortex

Interesting things happen in the time evolution of visual responses of neurons in V1 cortex. V1 neurons studied individually exhibit time-dependent sensitivity and selectivity for orientation and spatial frequency. This implies an important role for inhibitory interactions in the production of selectivity. From a theory of the network dynamics, one finds that the V1 network causes neurons to be "overdamped" in a high conductance state during visual stimulation, making these neurons into coincidence detectors. Nevertheless, the time-averaged spike rate of a V1 neuron is an approximately linear function of its net synaptic input.

The Simple and the Complex in Visual Cortex Dynamics

So-called Simple cells in the primary visual cortex (V1) respond to visual stimulation in a roughly linear way, while Complex cells do not. This longstanding classification -- the basis for the influential hierarchical model of Hubel & Wiesel -- is far from sharp; Recent experiments show that most cortical cells lie somewhere in a continuum between being Simple or Complex. I and my collaborators have posed and studied an "egalitarian" model of V1, based on the local architecture of a V1 hypercolumn, where all cortical cells are coupled nonspecifically within the network. I show that by requiring the total synaptic weight on each cell to be constant, though divided between between geniculate and network couplings, leads to broad response distributions like those found in experiment, and rationalizes several aspects of the experimental data.

The Chay-Keizer Model: Half Right or Half Wrong?

One of the first models for bursting electrical activity was developed by Chay and Keizer. It was based on the behavior of insulin secreting pancreatic beta-cells but has been extended and modified to cover a number of neural systems, including pacemaker cells of the pre-Botzinger complex (Butera et al), thalamic neurons (Hindmarsh and Rose; Rush and Rinzel), pituitary somatotrophs (Li, Van Goor, Stojilkovic), and hippocampal pyramidal cells (Pinsky and Rinzel; Wang and Kepecs). The unifying feature of these models is hysteresis of steady states. However, one of the key predictions of the model, a slowly rising and falling intracellular calcium concentration, has not held up for the very slowly bursting beta-cells. We show how the spirit of the model can be retained, but with important differences in detail, by introducing one or more additional internal calcium compartments.

Cellular and Network Dynamics of the Mammalian Respiratory Oscillator

Experimental and modeling studies of the neural oscillator generating the rhythm of breathing in the mammalian brainstem are providing insights into cellular and network-level mechanisms generating rhythms in motor pattern generation networks. We have developed a hybrid pacemaker-network model of the respiratory oscillator that represents a synthesis of cellular and network mechanisms derived from experimental and modeling studies. This model incorporates a rhythm-generating neuronal kernel, located in the pre-B?tzinger complex of the ventrolateral medulla, consisting of a network of excitatory neurons with state (voltage)-dependent, oscillatory bursting/pacemaker-like properties. This kernel has been experimentally isolated in several in vitro preparations from neonatal rodents including thin brainstem slices with a functionally intact, active rhythm-generating network. We have exploited these in vitro systems for analysis of cellular biophysical mechanisms and population-level dynamics in the kernel by a combination of single-cell patch-clamp electrophysiological recording, activity-dependent neuron/population imaging and recording of population activity. Simulations with mathematical models of the pacemaker cell network are consistent with a number of features of measured cell and population rhythmic behavior that will be discussed in the talk, including the following. (1) Cellular biophysical mechanisms of oscillatory burst generation. Electrophysiological studies show that candidate rhythm-generating cells exhibit intrinsic voltage-dependent bursting behavior with burst frequencies spanning over an order of magnitude (.05 to ~1Hz), providing a mechanism for cellular-level frequency control. This behavior is mimicked by our biophysically minimal models incorporating Hodgkin-Huxley-like membrane conductances, where bursting arises via fast activation-slow inactivation of a subthreshold voltage-activating persistent sodium current (INaP) that dynamically interacts with a potassium-dominated leak current. Our voltage-clamp measurements have demonstrated INaP in bursting cells and dynamic clamp studies incorporating our modeled INaP in neurons confirm that this mechanism is sufficient for voltage-dependent oscillatory burst generation. (2) Synaptic coupling and burst synchronization. Electrophysiological and imaging studies indicate that cellular burst synchronization in the kernel arises from fast, glutamatergic excitatory synaptic coupling. Modeling studies of heterogeneous populations of synaptically-coupled bursting neurons (as described above) indicate that burst synchronization across the population is promoted by burst-generating currents and can occur to produce stable rhythms even when only a small fraction of the cells in the population are intrinsically bursting. Population bursting frequency is modulated by synaptic coupling strength. (3) Cellular/population frequency control and dynamic range. Experimentally tonic excitation regulates single cell and population bursting frequency; population bursting exhibits a wider dynamic range of frequency control by tonic excitation. Population model simulations mimic this and indicate that heterogeneity of cellular bursting parameters and excitatory coupling synergistically combine to determine dynamic range. (4) Multiple oscillatory modes and quasiperiodic dynamics. Measurements of population activity combined with nonlinear system dynamics analysis indicate that the kernel intrinsically exhibits multiple periodic states as frequency is driven experimentally by tonic excitation. Stable periodic behavior occurs with low excitation, progresses to mixed mode-oscillations, and transitions to quasiperiodic behavior at high excitation levels. Population simulations indicate that weak synaptic coupling and extreme parameter heterogeneity, leading to partial desychronization of cellular bursting, can give rise to mixed mode oscillations and quasiperiodic states.


References.



  • Butera, R.J., Rinzel, J. & Smith, J.C. (1999). Models of respiratory rhythm generation in the pre-B?tzinger complex. I. Bursting pacemaker neurons. J. Neurophysiology, 81, 382-397.

  • Butera, R.J., Rinzel, J. & Smith, J.C. (1999). Models of respiratory rhythm generation in the pre-B?tzinger complex. II. Populations of coupled pacemaker neurons. J. Neurophysiology, 81, 398-415.

  • Del Negro, C.A., Johnson, S.M., Butera, R.J., & Smith, J.C. (2001). Models of respiratory rhythm generation in the pre-B?tzinger complex. III. Experimental tests of model predictions. J. Neurophysiology, 86, 59-74.

  • Koshiya, N., & Smith, J.C. (1999). Neuronal pacemaker for breathing visualized in vitro. Nature, 400, 360-363.

  • Del Negro, C., Butera, R.J., Wilson, C.G., & Smith, J.C. (2002). Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network. Biophysical Journal, 82, 206-214.

Reduction of Neuronal Network Models Using Geometric Singular Perturbation Methods

Activity patterns in excitatory-inhibitory networks are analyzed using geometric singular perturbation methods. The networks are motivated by models for thalamic sleep rhythms and neuronal activity in the basal ganglia. The analysis is used to reduce the rather complicated neuronal models to simpler systems. Propagating patterns in two-dimensional networks are considered.

Reproducibility of the single-photon response of retinal rods: testingtheories by detailed stochastic modeling of underlying biochemicalmechanisms

A major outstanding problem in sensory physiology is to understand how the response of a retinal rod to a single photon manages to have such little variation in amplitude and kinetics, despite the fact that it is mediated by the activity of a single molecule of activated rhodopsin (R*). In the dark, there is a circulating current across the rod membrane, which flows inward through channels in the outer segment membrane gated by cyclic-GMP, and flows outward across the inner segment membrane. The modulation of the voltage across the rod membrane in response to light is a consequence of the reduction of this dark (light-sensitive) current by the following mechanism. When rhodopsin absorbs a photon it is converted into an activated enzyme (R*) that initiates a cascade of biochemical reactions: G-protein is activated by R*; G-protein activates phosphodiesterase; phosphodiesterase hydrolyzes cyclic-GMP; the cyclic-GMP concentration drops, resulting in closure of some of the light-sensitive channels; the reduction of inward current causes the rod membrane voltage to become hyperpolarized. The sequence of events following the activation of rhodopsin continues until R* is inactivated. The regularity of the single-photon response implies that the lifetime of R* is controlled with high precision. Numerous theories have been proposed. All are based in part on known biochemical elements of the transduction cascade, and some also include additional hypothetical mechanism. Liebman and Gibson recently proposed a theory based on their biochemical experiments. The idea is that R* is partially deactivated by multiple steps of phosphorylation catalyzed by rhodopsin kinase, followed by an irreversible "capping" reaction in which R* is completely inactivated by arrestin. In this theory, three molecules, rhodopsin kinase, G-protein and arrestin, compete in a mutually exclusive manner for R*. Every time R* is phosphorylated, its affinity for G-protein (i.e. its catalytic activity) is reduced, its affinity for rhodopsin kinase is reduced, and its affinity for arrestin is increased. I will explain how some statistics of the single-photon responses can be derived analytically in this theory. I will also demonstrate by Monte Carlo simulation the extent to which the proposed mechanism reduces variability in the single-photon response. Deficiencies of the theory will be demonstrated, and alternative mechanisms will be discussed and evaluated.

Gap junctions between the axons of principal neurons, and the generation of fast oscillations in neuronal populations

In 1998, it was hypothesized that gap junctions existed between the axons of hippocampal pyramidal cells. This hypothesis was suggested by two experimental observations: the occurrence of 200 Hz population oscillations in neuronal networks in which synaptic transmission was blocked, but where the oscillations required gap junctions; and the shape of putative coupling potentials in principal neurons, which were too fast to be generated by gap junctions located on somata or dendrites. There is now electrophysiological and dye-coupling evidence that such gap junctions exist, and are located roughly 100 microns from the soma. Modeling shows that gap junctions in this location can give rise to very fast oscillations in networks of principal neurons, as well as to 200 Hz "ripples" (as seen in vivo, and consisting of IPSPs), when interneurons are also in the circuit. In addition, axonal gap junctions can underlie the generation of 40 Hz oscillations, in the presence of cholinergic agonists or of kainate. Modeling predicts, and experiments confirm, that in such conditions, the oscillation spectrum contains both 40 Hz and also very fast (>80 Hz) components.

Propagating Waves in Turtle Visual Cortex

Visual stimuli evoke waves of activity that propagate throughout the visual cortex of freshwater turtles. These waves have been visualized using both multielectrode recording and voltage sensitive dye methods. This talk will discuss the use of a large-scale model of turtle visual cortex to study the cellular mechanisms underlying the propagation of the wave and to suggest that information about visual stimuli is encoded in the temporal dynamics of the waves.


 


The model consists of approximately 1,000 geniculate and cortical neurons. It is based upon the anatomical distribution of neurons in turtle visual cortex and the biophysics of individual types of cortical neurons. The model suggests that waves originate near the rostrolateral pole of the cortex due to a high density of geniculocortical synapses at that point. It reproduces features of the dynamics of the wave, such as its velocity and tendency to reflect at the caudal border of visual cortex. Analysis of real and simulated waves using a principal components method (Karhunen-Loeve decomposition) indicates that information about the position of stimuli in visual space is encoded in the dynamics of the wave in the sense that stimulus position can be reliably estimated from the dynamics of the wave using Bayesian estimation methods.

Long Term Behavior of 1 Dimensional Networks of Spiking Neurons

Over the last ten years we have gained significant insight in the role of synaptic interactions in the synchronization of neuronal networks. A crucial first in these investigations was the study of extremely simplified networks, all-to-all coupled networks of indentical neurons. The mathematical tools developed to analyse both the asynchronous and fully synchronized state in such networks were subsequently extended to study networks with more realistic architectures. However, long term behavior in spatially extended networks of synaptically coupled neurons, in which the coupling strength decreases with distance, have not yet received much attention. In this talk I will consider a network of identical integrate-and-fire neurons, positioned on a 1-D ring. I will show that strongly coupled networks of oscil- lators behave qualitatively differently from weakly coupled ones, and also differ qualitatively from rate based models. Such networks can evolve, depending on the coupling parameters, evolve to either an asynchronous state, or to a traveling wave state. I will show how the existence and stability of these states can be analyzed in this simple model. For fast excitatory synapses a third state co-exist with the travelling wave state. In this state the activity is highly complex and the symmetry is broken. So far, no analytical treatment of this state has been found for this state.

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Dynamics of perceptual oscillations and waves in vision

Visual oscillations can occur in response to certain ambiguous stimuli, and both oscillations and travelling waves occur in binocular rivalry and migraine auras. After presenting relevant data, neural models at both the individual action potential level and at the spike rate level will be developed to interpret and explain these phenomena. These models include a two-level model for binocular rivalry in which the first level can be dynamically defeated by appropriate stimulus manipulation.

Dynamics of Perceptual Oscillations and Waves in Vision

Visual oscillations can occur in response to certain ambiguous stimuli, and both oscillations and travelling waves occur in binocular rivalry and migraine auras. After presenting relevant data, neural models at both the individual action potential level and at the spike rate level will be developed to interpret and explain these phenomena. These models include a two-level model for binocular rivalry in which the first level can be dynamically defeated by appropriate stimulus manipulation.