Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session B16: Nonlinear Dynamics of Neuronal and Cardiac Systems |
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Sponsoring Units: DBP Chair: John Beggs, Indiana University Room: Morial Convention Center 208 |
Monday, March 10, 2008 11:15AM - 11:27AM |
B16.00001: Quantitative universality and non-local interactions in neural pattern formation Matthias Kaschube, Michael Schnabel, Siegrid Loewel, David Coppola, Leonard White, Fred Wolf The occurrence of universal quantitative laws in a strongly interacting multi-component system indicates that its behavior can be elucidated through the identification of general mathematical principles rather than by the detailed characterization of its individual components. Here we demonstrate that universal quantitative laws govern the spatial layout of orientation selective neurons in the visual cortex in three mammalian species separated in evolution by more than 50 million years. Most suggestive of a mathematical structure underlying this universality, the average number of pinwheel centers per orientation hyper-column in all three species is statistically indistinguishable from the constant $\pi$. Mathematical models of neural pattern formation can reproduce all observed universal quantitative laws if non-local interactions are dominant, indicating that non-local interactions are constitutive in visual cortical development. The spatial layout adheres to these laws even if visual cortical organization exhibits marked overall inhomogeneities and when neuronal response properties are experimentally altered. These results demonstrate that mathematical principles can shape the organization of the brain as powerfully as an organism's genetic make-up. [Preview Abstract] |
Monday, March 10, 2008 11:27AM - 11:39AM |
B16.00002: Spike-timing dependent plasticity in integrate-and-fire networks Chun-Chung Chen, David Jasnow We study plastic integrate-and-fire networks with spike-timing dependent plasticity. Following recent experiments, the long-term potentiation (depression) for causal (anti-causal) spike pairs is assumed to be additive (multiplicative) with reference to the existing synaptic strength. Assuming realistic physiological parameters, for time scales of minutes, the synaptic strength can be assumed fixed while neural activities equilibrate. A mean-field analysis in this regime predicts a first order phase transition for the neural activity. As the constant synaptic strength is increased, the network goes from a quiescent phase with only noise triggered activities, to a phase of persistent activity. The number of synapses per neuron controls the transition point in the synaptic strength. However, the activity level of the network just above the transition point is insensitive to the synapse number and represents a neural firing rate of about 20 to 30 Hz for the set of physiological parameters we considered. Simulations on random networks with fixed connectivities agree well with the mean-field predictions for a per-neuron synapse number of 10 or larger. Applying the plasticity rules and performing simulations covering physical times of days, at fixed depression factor for anti-causal spike pairs, the networks develop a unimodal distribution of synaptic strengths at small potentiation values for causal pairs, while run-away synaptic strengths are observed at large values. [Preview Abstract] |
Monday, March 10, 2008 11:39AM - 11:51AM |
B16.00003: A Maximum Entropy Model Applied to Temporal Correlations in Cortical Networks Wei Chen, Aonan Tang, Jon Hobbs, Jodi L. Smith, Hema Patel, Anita Prieto, John Beggs, David Jackson, Dumitru Petrusca, Matthew I. Grivich, Alexander Sher, Alan M. Litke Multi-neuron firing states are often observed, yet are predicted to be rare by models that assume independent firing. To predict these states, two groups recently applied a second-order maximum entropy model that used only observed firing rates and pairwise interactions as parameters (Schneidman et al., 2006; Shlens et al., 2006). Interestingly, these models predicted 90-99{\%} of network correlations. If generally applicable, this approach could vastly simplify analyses of complex networks. However, this work did not address the temporal evolution of correlated states. We applied the model to multielectrode data from cortical slices and cultures. In 8/13 preparations the observed sequences of correlated states were significantly longer than predicted by concatenating states from the model. We found a significant relationship between strong pairwise temporal correlations and observed sequence length, suggesting that pairwise temporal correlations may allow the model to be extended into the temporal domain. [Preview Abstract] |
Monday, March 10, 2008 11:51AM - 12:03PM |
B16.00004: Effective connectivity in a network of spiking cortical neurons Aonan Tang, Jon Hobbs, Wei Chen, Dumitru Petrusca, Matthew Grivich, Alexander Sher, Alan Litke, John Beggs The average cortical neuron makes and receives about 1,000 synaptic contacts. This anatomical information suggests that local cortical networks are connected in a fairly democratic manner, with all nodes having about the same degree. But the physical connections found in the brain do not necessarily reveal how information flows through the network. We used transfer entropy (Schreiber, 2000) to assess effective connectivity in cortical slice cultures placed on a 512 electrode array system (in collaboration with Alan Litke of UC Santa Cruz). These cultures (n = 6) were active for periods exceeding 1 hr, allowing us to collect long data sets for entropy statistics. Data were binned at ~1 ms to match the width of a single neural spike. Analysis revealed wide differences in node degrees, but did not clearly point to a small-world or a scale-free structure. [Preview Abstract] |
Monday, March 10, 2008 12:03PM - 12:15PM |
B16.00005: Inhibition is Needed to Learn Precise Multimodal Integration J. Leo van Hemmen Multimodal neuronal maps, combining input from two or more sensory systems, e.g., vision and audition, play a key role in processing and transforming sensory to motor information. For such maps to be of any use, the input from all participating modalities must be calibrated so that a stimulus at a specific spatial location is represented at an unambiguous position in the multimodal map. Here we discuss a method based on supervised spike-timing-dependent plasticity (STDP) to gauge input from different sensory modalities so as to ensure proper map alignment. We therefore analyze \emph{excitation-} and \emph{inhibition-mediated learning} in conjunction with the problem of how perfect a teacher should be. Analytical calculations and numerical simulations show on the one hand that inhibitory teacher input is essential if high-quality multimodal integration must be learnt rapidly. On the other hand, the quality of the resulting map is not limited by the quality of the teacher signal alone but rather by the accuracy of the input from other sensory modalities. [Preview Abstract] |
Monday, March 10, 2008 12:15PM - 12:27PM |
B16.00006: Distinguishing Similar Odor Stimuli in Nonlinear Recurrent Networks Stuart Wick, Martin Wiechert, Rainer Friedrich, Hermann Riecke The olfactory bulb (OB) is the first processing stage for olfactory information and receives input in the form of activity patterns across an array of discrete input channels (glomeruli). Experiments show that the OB decorrelates similar olfactory inputs: the output patterns are more distinct than the input patterns, which is likely to be important for downstream computations. The high dimensionality of odor space implies a fractured representation of odors on the two-dimensional array of glomeruli. The neural circuits achieving the decorrelation must therefore be non-trivial; their connectivity is, however, poorly known. We investigate what connectivities are optimally suited for this task. For neural networks with linear dynamics the connectivity can be given explicitly. Experiments indicate, however, that the bulbar dynamics are strongly nonlinear and must be minimally modeled by a piece-wise linear rectifier. We investigate the impact of the rectifier on two types of connectivities which are optimal for linear networks, but only one of which accomodates the rectifier. We test the performance of both types of networks by adapting them to an ensemble of odors and assessing their ability to decorrelate these and related odors at the same and other concentrations. [Preview Abstract] |
Monday, March 10, 2008 12:27PM - 12:39PM |
B16.00007: A low dimensional description of globally coupled heterogeneous neural networks of excitatory and inhibitory neurons Roxana A. Stefanescu, Viktor K. Jirsa Neural networks consisting of globally coupled excitatory and inhibitory non-identical neurons may exhibit a complex dynamic behavior including synchronization, multi-clustered solutions in phase space and oscillator death. We investigate the conditions under which these behaviors occur in a multidimensional parametric space defined by the connectivity strengths and dispersion of the neuronal membrane excitability. Using mode decomposition techniques, we further derive analytically a low dimensional description of the neural population dynamics and show that the dynamics of the entire network can be very well reproduced by this reduced system. Examples of networks of FitzHugh-Nagumo and Hindmarsh-Rose neurons are discussed in detail. [Preview Abstract] |
Monday, March 10, 2008 12:39PM - 12:51PM |
B16.00008: A Neuron-Based Model of Sleep-Wake Cycles Svetlana Postnova, Achim Peters, Hans Braun In recent years it was discovered that a neuropeptide orexin/hypocretin plays a main role in sleep processes. This peptide is produced by the neurons in the lateral hypothalamus, which project to almost all brain areas. We present a computational model of sleep-wake cycles, which is based on the Hodgkin-Huxley type neurons and considers reciprocal glutaminergic projections between the lateral hypothalamus and the prefrontal cortex. Orexin is released as a neuromodulator and is required to keep the neurons firing, which corresponds to the wake state. When orexin is depleted the neurons are getting silent as observed in the sleep state. They can be reactivated by the circadian signal from the suprachiasmatic nucleus and/or external stimuli (alarm clock). Orexin projections to the thalamocortical neurons also can account for their transition from tonic firing activity during wakefulness to synchronized burst discharges during sleep. [Preview Abstract] |
Monday, March 10, 2008 12:51PM - 1:03PM |
B16.00009: Interdependencies of Neural Impulse Pattern and Synchronization Hans Braun, Svetlana Postnova, Horst Schneider Neuronal synchronization plays a crucial role in many physiological functions such as information binding and wake-sleep transitions as well as in pathophysiological processes like Parkinson's disease and epileptic seizures. The occurrence of synchronized activity is often associated with significant alterations of the neuronal impulse pattern, mostly with a transition from tonic firing to burst discharges. We have used Hodgkin-Huxley type simulations to study how alterations of individual neurons' dynamics influence the synchronization in electrotonic coupled networks. The individual neurons have been tuned from tonic firing to bursting with chaotic dynamics in between. Our results demonstrate that these transitions have significant impact on the neurons' synchronization. Vice versa, the synchronization state can essentially modify the impulse pattern. The most remarkably effects appear when the individual neurons operate in a periodically tonic firing regime close to the transition to chaos. [Preview Abstract] |
Monday, March 10, 2008 1:03PM - 1:15PM |
B16.00010: Mosaics of retinal cells that transmit maximal information Tatyana Sharpee In the nervous system, visual signals are encoded by retinal ganglion cells into sequences of discrete electrical pulses termed spikes. Response regions of different ganglion cells tile the visual field and are arranged on approximately hexagonal lattice. Here we consider the optimal arrangement of response regions that would collectively allow for maximal information transmitted about the location of a point light source. We find that maximal information can be transmitted when at most three neighboring regions overlap and the average radius of response field is $\sim $0.67 of the distance between response field centers. This finding was obtained with no adjustable parameters and agrees with experimental measurements of retinal mosaics [1, 2]. \newline [1] D.M. Dacey and S. Brace, Visual Neuroscience 9:279-90 (1992). \newline [2] S.H. Devries and D.A. Baylor, J Neurophysiol. 78:2048-60 (1997). [Preview Abstract] |
Monday, March 10, 2008 1:15PM - 1:27PM |
B16.00011: Phase synchronization analysis of voltage-sensitive dye imaging during drug-induced epileptic seizures. Daisuke Takeshita, Vassiliy Tsytsarev, Sonya Bahar Epileptic seizures are generally held to result from excess and synchronized neural activity. However, recent studies have suggested that this is not necessarily the case. We investigate how the spatiotemporal pattern of synchronization changes during drug-induced in vivo neocortical seizures in rats. Epileptic seizures are caused by the potassium channel blocker 4-aminopyridine, which is often used in experiments to induce epileptic seizures. In our experiments, the neocortex is stained with the voltage-sensitive dye RH-1691. The intensity changes in dye fluorescence are measured by a CCD camera and are consistent with the signal from local field potential recording. We apply phase synchronization analysis to the voltage-sensitive dye signals from pairs of pixels in order to investigate the degree to which synchronization occurs, and how spatial patterns of synchrony may change, during the course of the seizure. Our preliminary results show that two distant pixels are well synchronized during a seizure event. [Preview Abstract] |
Monday, March 10, 2008 1:27PM - 1:39PM |
B16.00012: Information transfer in ampullary electroreceptors Alexander Neiman, Tatiana Engel Many neurons in central nervous system and in sensory periphery are characterized by significant correlations between consequent interspike intervals of their stochastic spontaneous activity. Such non-renewal stochastic dynamics can result from internal properties of a neuron, such as spike-frequency adaptation, as well as from external perturbations or both. We consider one example of such system, peripheral ampullary electroreceptors in paddlefish. Spontaneous dynamics of electroreceptors is characterized by extended serial correlations of interspike intervals resulting from nonlinear interaction of two stochastic oscillators embedded into the system. Using computational modeling and approaches from information theory we show that these correlations significantly improve information transfer of weak external stimuli. [Preview Abstract] |
Monday, March 10, 2008 1:39PM - 1:51PM |
B16.00013: Spike-time-variability in stochastic Hodgkin-Huxley type neural models Peter Rowat When the classical Hodgkin-Huxley equations are simulated with Na- and K-channel noise and fixed applied current, the distribution of inter-spike intervals is bi-modal: one part is an exponential tail, as often assumed, while the other is a narrow gaussian peak centered at a short ISI value. The gaussian arises from bursts of spikes in the gamma-frequency range, the tail from the inter-burst-intervals, giving overall a very highcoefficient of variation: upto 2.5 for 180,000 Na-channels. Since neurons with a bimodal inter-spike interval distribution are common, it may be a useful model for any neuron with class 2 firing. The underlying mechanism is due to a sub-critical Hopf bifurcation together with a switching region in phase-space where a fixed point is very close to a system limit cycle. This mechanism may contribute to highly irregular spike times in cortex. Other mechanisms underlying neural variability will also be presented. [Preview Abstract] |
Monday, March 10, 2008 1:51PM - 2:03PM |
B16.00014: Ca$^{2+}$ Dynamics and Propagating Waves in Neural Networks with Excitatory and Inhibitory Neurons. Vladimir E. Bondarenko Dynamics of neural spikes, intracellular Ca$^{2+}$, and Ca$^{2+}$ in intracellular stores was investigated both in isolated Chay's neurons and in the neurons coupled in networks. Three types of neural networks were studied: a purely excitatory neural network, with only excitatory (AMPA) synapses; a purely inhibitory neural network with only inhibitory (GABA) synapses; and a hybrid neural network, with both AMPA and GABA synapses. In the hybrid neural network, the ratio of excitatory to inhibitory neurons was 4:1. For each case, we considered two types of connections, ``all-with-all" and 20 connections per neuron. Each neural network contained 100 neurons with randomly distributed connection strengths. In the neural networks with ``all-with-all" connections and AMPA/GABA synapses an increase in average synaptic strength yielded bursting activity with increased/decreased number of spikes per burst. The neural bursts and Ca$^{2+}$ transients were synchronous at relatively large connection strengths despite random connection strengths. Simulations of the neural networks with 20 connections per neuron and with only AMPA synapses showed synchronous oscillations, while the neural networks with GABA or hybrid synapses generated propagating waves of membrane potential and Ca$^{2+}$ transients. [Preview Abstract] |
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