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Armstrong, E, Abarbanel HDI.  2016.  Model of the songbird nucleus HVC as a network of central pattern generators. Journal of Neurophysiology. 116:2405-2419.   10.1152/jn.00438.2016   AbstractWebsite

We propose a functional architecture of the adult songbird nucleus HVC in which the core element is a "functional syllable unit" (FSU). In this model, HVC is organized into FSUs, each of which provides the basis for the production of one syllable in vocalization. Within each FSU, the inhibitory neuron population takes one of two operational states: 1) simultaneous firing wherein all inhibitory neurons fire simultaneously, and 2) competitive firing of the inhibitory neurons. Switching between these basic modes of activity is accomplished via changes in the synaptic strengths among the inhibitory neurons. The inhibitory neurons connect to excitatory projection neurons such that during state 1 the activity of projection neurons is suppressed, while during state 2 patterns of sequential firing of projection neurons can occur. The latter state is stabilized by feedback from the projection to the inhibitory neurons. Song composition for specific species is distinguished by the manner in which different FSUs are functionally connected to each other. Ours is a computational model built with biophysically based neurons. We illustrate that many observations of HVC activity are explained by the dynamics of the proposed population of FSUs, and we identify aspects of the model that are currently testable experimentally. In addition, and standing apart from the core features of an FSU, we propose that the transition between modes may be governed by the biophysical mechanism of neuromodulation.

Nogaret, A, Meliza CD, Margoliash D, Abarbanel HDI.  2016.  Automatic construction of predictive neuron models through large scale assimilation of electrophysiological data. Scientific Reports. 6   10.1038/srep32749   AbstractWebsite

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20-50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight.

Nogaret, A, O'Callaghan EL, Lataro RM, Salgado HC, Meliza CD, Duncan E, Abarbanel HDI, Paton JFR.  2015.  Silicon central pattern generators for cardiac diseases. Journal of Physiology-London. 593:763-774.   10.1113/jphysiol.2014.282723   AbstractWebsite

Cardiac rhythm management devices provide therapies for both arrhythmias and resynchronisation but not heart failure, which affects millions of patients worldwide. This paper reviews recent advances in biophysics and mathematical engineering that provide a novel technological platform for addressing heart disease and enabling beat-to-beat adaptation of cardiac pacing in response to physiological feedback. The technology consists of silicon hardware central pattern generators (hCPGs) that may be trained to emulate accurately the dynamical response of biological central pattern generators (bCPGs). We discuss the limitations of present CPGs and appraise the advantages of analog over digital circuits for application in bioelectronic medicine. To test the system, we have focused on the cardio-respiratory oscillators in the medulla oblongata that modulate heart rate in phase with respiration to induce respiratory sinus arrhythmia (RSA). We describe here a novel, scalable hCPG comprising physiologically realistic (Hodgkin-Huxley type) neurones and synapses. Our hCPG comprises two neurones that antagonise each other to provide rhythmic motor drive to the vagus nerve to slow the heart. We show how recent advances in modelling allow the motor output to adapt to physiological feedback such as respiration. In rats, we report on the restoration of RSA using an hCPG that receives diaphragmatic electromyography input and use it to stimulate the vagus nerve at specific time points of the respiratory cycle to slow the heart rate. We have validated the adaptation of stimulation to alterations in respiratory rate. We demonstrate that the hCPG is tuneable in terms of the depth and timing of the RSA relative to respiratory phase. These pioneering studies will now permit an analysis of the physiological role of RSA as well as its any potential therapeutic use in cardiac disease.

Neftci, EO, Toth B, Indiveri G, Abarbanel HDI.  2012.  Dynamic State and Parameter Estimation Applied to Neuromorphic Systems. Neural Computation. 24:1669-1694. AbstractWebsite

Neuroscientists often propose detailed computational models to probe the properties of the neural systems they study. With the advent of neuromorphic engineering, there is an increasing number of hardware electronic analogs of biological neural systems being proposed as well. However, for both biological and hardware systems, it is often difficult to estimate the parameters of the model so that they are meaningful to the experimental system under study, especially when these models involve a large number of states and parameters that cannot be simultaneously measured. We have developed a procedure to solve this problem in the context of interacting neural populations using a recently developed dynamic state and parameter estimation (DSPE) technique. This technique uses synchronization as a tool for dynamically coupling experimentally measured data to its corresponding model to determine its parameters and internal state variables. Typically experimental data are obtained from the biological neural system and the model is simulated in software; here we show that this technique is also efficient in validating proposed network models for neuromorphic spike-based very large-scale integration (VLSI) chips and that it is able to systematically extract network parameters such as synaptic weights, time constants, and other variables that are not accessible by direct observation. Our results suggest that this method can become a very useful tool formodel-based identification and configuration of neuromorphic multichip VLSI systems.

Gibb, L, Gentner TQ, Abarbanel HDI.  2009.  Brain stem feedback in a computational model of birdsong sequencing. Journal of Neurophysiology. 102:1763-1778.   10.1152/jn.91154.2008   AbstractWebsite

Gibb L, Gentner TQ, Abarbanel HDI. Brain stem feedback in a computational model of birdsong sequencing. J Neurophysiol 102: 1763-1778, 2009. First published June 24, 2009; doi:10.1152/jn.91154.2008. Uncovering the roles of neural feedback in the brain is an active area of experimental research. In songbirds, the telencephalic premotor nucleus HVC receives neural feedback from both forebrain and brain stem areas. Here we present a computational model of birdsong sequencing that incorporates HVC and associated nuclei and builds on the model of sparse bursting presented in our preceding companion paper. Our model embodies the hypotheses that 1) different networks in HVC control different syllables or notes of birdsong, 2) interneurons in HVC not only participate in sparse bursting but also provide mutual inhibition between networks controlling syllables or notes, and 3) these syllable networks are sequentially excited by neural feedback via the brain stem and the afferent thalamic nucleus Uva, or a similar feedback pathway. We discuss the model's ability to unify physiological, behavioral, and lesion results and we use it to make novel predictions that can be tested experimentally. The model suggests a neural basis for sequence variations, shows that stimulation in the feedback pathway may have different effects depending on the balance of excitation and inhibition at the input to HVC from Uva, and predicts deviations from uniform expansion of syllables and gaps during HVC cooling.

Gibb, L, Gentner TQ, Abarbanel HDI.  2009.  Inhibition and recurrent excitation in a computational model of sparse bursting in song nucleus HVC. Journal of Neurophysiology. 102:1748-1762.   10.1152/jn.00670.2007   AbstractWebsite

Gibb L, Gentner TQ, Abarbanel HDI. Inhibition and recurrent excitation in a computational model of sparse bursting in song nucleus HVC. J Neurophysiol 102: 1748-1762, 2009. First published June 10, 2009; doi:10.1152/jn.00670.2007. The telencephalic premotor nucleus HVC is situated at a critical point in the pattern-generating premotor circuitry of oscine songbirds. A striking feature of HVC's premotor activity is that its projection neurons burst extremely sparsely. Here we present a computational model of HVC embodying several central hypotheses: 1) sparse bursting is generated in bistable groups of recurrently connected robust nucleus of the arcopallium (RA)- projecting (HVC(RA)) neurons; 2) inhibitory interneurons terminate bursts in the HVC(RA) groups; and 3) sparse sequences of bursts are generated by the propagation of waves of bursting activity along networks of HVC(RA) neurons. Our model of sparse bursting places HVC in the context of central pattern generators and cortical networks using inhibition, recurrent excitation, and bistability. Importantly, the unintuitive result that inhibitory interneurons can precisely terminate the bursts of HVC(RA) groups while showing relatively sustained activity throughout the song is made possible by a specific constraint on their connectivity. We use the model to make novel predictions that can be tested experimentally.

Haas, JS, Nowotny T, Abarbanel HDI.  2006.  Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. Journal of Neurophysiology. 96:3305-3313.   10.1152/jn.00551.2006   AbstractWebsite

Actions of inhibitory interneurons organize and modulate many neuronal processes, yet the mechanisms and consequences of plasticity of inhibitory synapses remain poorly understood. We report on spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. After pairing presynaptic stimulations at time t(pre) with evoked postsynaptic spikes at time t(post) under pharmacological blockade of excitation we found, via whole cell recordings, an asymmetrical timing rule for plasticity of the remaining inhibitory responses. Strength of response varied as a function of the time interval Delta t = t(post) - t(pre): for Delta t > 0 inhibitory responses potentiated, peaking at a delay of 10 ms. For Delta t < 0, the synaptic coupling depressed, again with a maximal effect near 10 ms of delay. We also show that changes in synaptic strength depend on changes in intracellular calcium concentrations and demonstrate that the calcium enters the postsynaptic cell through voltage-gated channels. Using network models, we demonstrate how this novel form of plasticity can sculpt network behavior efficiently and with remarkable flexibility.

Abarbanel, HDI, Talathi SS.  2006.  Neural circuitry for recognizing interspike interval sequences. Physical Review Letters. 96   10.1103/PhysRevLett.96.148104   AbstractWebsite

Sensory systems present environmental information to central nervous system as sequences of action potentials or spikes. How do animals recognize these sequences carrying information about their world? We present a biologically inspired neural circuit designed to enable spike pattern recognition. This circuit is capable of training itself on a given interspike interval (ISI) sequence and is then able to respond to presentations of the same sequence. The essential ingredients of the recognition circuit are (a) a tunable time delay circuit, (b) a spike selection unit, and (c) a tuning mechanism using spike timing dependent plasticity of inhibitory synapses. We have investigated this circuit using Hodgkin-Huxley neuron models connected by realistic excitatory and inhibitory synapses. It is robust in the presence of noise represented as jitter in the spike times of the ISI sequence.

Abarbanel, HDI, Talathi SS, Gibb L, Rabinovich MI.  2005.  Synaptic plasticity with discrete state synapses. Physical Review E. 72   10.1103/PhysRevE.72.031914   AbstractWebsite

Experimental observations on synaptic plasticity at individual glutamatergic synapses from the CA3 Shaffer collateral pathway onto CA1 pyramidal cells in the hippocampus suggest that the transitions in synaptic strength occur among discrete levels at individual synapses [C. C. H. Petersen , Proc. Natl. Acad. Sci. USA 85, 4732 (1998); O'Connor, Wittenberg, and Wang, D. H. O'Connor , Proc. Natl. Acad. Sci. USA (to be published); J. M. Montgomery and D. V. Madison, Trends Neurosci. 27, 744 (2004)]. This happens for both long term potentiation (LTP) and long term depression (LTD) induction protocols. O'Connor, Wittenberg, and Wang have argued that three states would account for their observations on individual synapses in the CA3-CA1 pathway. We develop a quantitative model of this three-state system with transitions among the states determined by a competition between kinases and phosphatases shown by D. H. O'Connor , to be determinant of LTP and LTD, respectively. Specific predictions for various plasticity protocols are given by coupling this description of discrete synaptic alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor ligand gated ion channel conductance changes to a model of postsynaptic membrane potential and associated intracellular calcium fluxes to yield the transition rates among the states. We then present various LTP and LTD induction protocols to the model system and report the resulting whole cell changes in AMPA conductance. We also examine the effect of our discrete state synaptic plasticity model on the synchronization of realistic oscillating neurons. We show that one-to-one synchronization is enhanced by the plasticity we discuss here and the presynaptic and postsynaptic oscillations are in phase. Synaptic strength saturates naturally in this model and does not require artificial upper or lower cutoffs, in contrast to earlier models of plasticity.See correction: 10.1103/PhysRevE.72.069903

Abarbanel, HDI, Gibb L, Mindlin GB, Rabinovich MI, Talathi S.  2004.  Spike timing and synaptic plasticity in the premotor pathway of birdsong. Biological Cybernetics. 91:159-167.   10.1007/s00422-004-0495-1   AbstractWebsite

The neural circuits of birdsong appear to utilize specific time delays in their operation. In particular, the anterior forebrain pathway (AFP) is implicated in an approximately 40- to 50- ms time delay, DeltaT, playing a role in the relative timing of premotor signals from the nucleus HVc to the nucleus robust nucleus of the archistratium (RA) and control/learning signals from the nucleus lateral magnocellular nucleus of the anterior neostratium (lMAN) to RA. Using a biophysical model of synaptic plasticity based on experiments on mammalian hippocampal and neocortical pyramidal neurons, we propose an understanding of this approximate to40- to 50- ms delay. The biophysical model describes the influence of Ca2+ influx into the postsynaptic RA cells through NMDA and AMPA receptors and the induction of LTP and LTD through complex metabolic pathways. The delay, DeltaT, between HVc --> RA premotor signals and lMAN --> RA control/learning signals plays an essential role in determining if synaptic plasticity is induced by signaling from each pathway into RA. If DeltaT is substantially larger than 40 ms, no plasticity is induced. If DeltaT is much less than 40 ms, only potentiation is expected. If DeltaT approximate to 40 ms, the sign of synaptic plasticity is sensitive to DeltaT. Our results suggest that changes in DeltaT may influence learning and maintenance of birdsong. We investigate the robustness of this result to noise and to the removal of the Ca2+ contribution from lMAN --> RA NMDA receptors.

Abarbanel, HDI, Talathi SS, Mindlin G, Rabinovich M, Gibb L.  2004.  Dynamical model of birdsong maintenance and control. Physical Review E. 70   10.1103/PhysRevE.70.051911   AbstractWebsite

The neuroethology of song learning, production, and maintenance in songbirds presents interesting similarities to human speech. We have developed a biophysical model of the manner in which song could be maintained in adult songbirds. This model may inform us about the human counterpart to these processes. In songbirds, signals generated in nucleus High Vocal center (HVc) follow a direct route along a premotor pathway to the robust nucleus of the archistriatum (RA) as well as an indirect route to RA through the anterior forebrain pathway (AFP): the neurons of RA are innervated from both sources. HVc expresses very sparse bursts of spikes having interspike intervals of about 2 ms. The expressions of these bursts arrive at the RA with a time difference DeltaT approximate to 50 +/- 10 ms between the two pathways. The observed combination of AMPA and NMDA receptors at RA projection neurons suggests that long-term potentiation and long-term depression can both be induced by spike timing plasticity through the pairing of the HVc and AFP signals. We present a dynamical model that stabilizes this synaptic plasticity through a feedback from the RA to the AFP using known connections. The stabilization occurs dynamically and is absent when the RA --> AFP connection is removed. This requires a dynamical selection of DeltaT. The model does this, and DeltaT lies within the observed range. Our model represents an illustration of a functional consequence of activity-dependent plasticity directly connected with neuroethological observations. Within the model the parameters of the AFP, and thus the magnitude of DeltaT, can also be tuned to an unstable regime. This means that destabilization might be induced by neuromodulation of the AFP.

Abarbanel, HDI, Gibb L, Mindlin GB, Talathi S.  2004.  Mapping neural architectures onto acoustic features of birdsong. Journal of Neurophysiology. 92:96-110.   10.1152/jn.01146.2003   AbstractWebsite

The motor pathway responsible for the complex vocalizations of songbirds has been extensively characterized, both in terms of intrinsic and synaptic physiology in vitro and in terms of the spatiotemporal patterns of neural activity in vivo. However, the relationship between the neural architecture of the song motor pathway and the acoustic features of birdsong is not well understood. Using a computational model of the song motor pathway and the songbird vocal organ, we investigate the relationship between song production and the neural connectivity of nucleus HVc ( used as a proper name) and the robust nucleus of the archistriatum ( RA). Drawing on recent experimental observations, our neural model contains a population of sequentially bursting HVc neurons driving the activity of a population of RA neurons. An important focus of our investigations is the contribution of intrinsic circuitry within RA to the acoustic output of the model. We find that the inclusion of inhibitory interneurons in the model can substantially influence the features of song syllables, and we illustrate the potential for subharmonic behavior in RA in response to forcing by HVc neurons. Our results demonstrate the association of specific acoustic features with specific neural connectivities and support the view that intrinsic circuitry within RA may play a critical role in generating the features of birdsong.

Huerta, R, Nowotny T, Garcia-Sanchez M, Abarbanel HDI, Rabinovich MI.  2004.  Learning classification in the olfactory system of insects. Neural Computation. 16:1601-1640.   10.1162/089976604774201613   AbstractWebsite

We propose a theoretical framework for odor classification in the olfactory system of insects. The classification task is accomplished in two steps. The first is a transformation from the antennal lobe to the intrinsic Kenyon cells in the mushroom body. This transformation into a higher-dimensional space is an injective function and can be implemented without any type of learning at the synaptic connections. In the second step, the encoded odors in the intrinsic Kenyon cells are linearly classified in the mushroom body lobes. The neurons that perform this linear classification are equivalent to hyperplanes whose connections are tuned by local Hebbian learning and by competition due to mutual inhibition. We calculate the range of values of activity and size of the network required to achieve efficient classification within this scheme in insect olfaction. We are able to demonstrate that biologically plausible control mechanisms can accomplish efficient classification of odors.

Nowotny, T, Zhigulin VP, Selverston AI, Abarbanel HDI, Rabinovich MI.  2003.  Enhancement of synchronization in a hybrid neural circuit by spike-timing dependent plasticity. Journal of Neuroscience. 23:9776-9785. AbstractWebsite

Synchronization of neural activity is fundamental for many functions of the brain. We demonstrate that spike-timing dependent plasticity (STDP) enhances synchronization ( entrainment) in a hybrid circuit composed of a spike generator, a dynamic clamp emulating an excitatory plastic synapse, and a chemically isolated neuron from the Aplysia abdominal ganglion. Fixed-phase entrainment of the Aplysia neuron to the spike generator is possible for a much wider range of frequency ratios and is more precise and more robust with the plastic synapse than with a nonplastic synapse of comparable strength. Further analysis in a computational model of Hodgkin - Huxleytype neurons reveals the mechanism behind this significant enhancement in synchronization. The experimentally observed STDP plasticity curve appears to be designed to adjust synaptic strength to a value suitable for stable entrainment of the postsynaptic neuron. One functional role of STDP might therefore be to facilitate synchronization or entrainment of nonidentical neurons.

Zhigulin, VP, Rabinovich MI, Huerta R, Abarbanel HDI.  2003.  Robustness and enhancement of neural synchronization by activity-dependent coupling. Physical Review E. 67   10.1103/PhysRevE.67.021901   AbstractWebsite

We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of spike-timing dependent plasticity. We show that this plasticity of the coupling between neurons produces enlarged frequency-locking zones and results in synchronization that is more rapid and much more robust against noise than classical synchronization arising from connections with constant strength. We also present a simple discrete map model that demonstrates the generality of the phenomenon.

Rabinovich, MI, Pinto RD, Abarbanel HDI, Tumer E, Stiesberg G, Huerta R, Selverston AI.  2002.  Recovery of hidden information through synaptic dynamics. Network-Computation in Neural Systems. 13:487-501.   10.1088/0954-898x/13/4/304   AbstractWebsite

The role of synaptic dynamics in processing neural information is investigated in a neural information channel with realistic model neurons having chaotic intrinsic dynamics. Our neuron models are realized in simple analogue circuits, and Our synaptic connections are realized both in analogue circuits and through a dynamic clamp program. The information which is input to the first chaotic neuron in the channel emerges partially absent and partially 'hidden'. Part is absent because of the dynamical effects of the chaotic oscillation that effectively acts as a noisy channel. The 'hidden' part is recoverable. We show that synaptic parameters, most significantly receptor binding time constants, can be tuned to enhance the information transmission by the combination of a neuron plus a synapse. We discuss how the dynamics of the synapse can be used to recover 'hidden' information using average mutual information as a measure of the quality of information transport.

Bazhenov, M, Stopfer M, Rabinovich M, Abarbanel HDI, Sejnowski TJ, Laurent G.  2001.  Model of cellular and network mechanisms for odor-evoked temporal patterning in the locust antennal lobe. Neuron. 30:569-581.   10.1016/s0896-6273(01)00286-0   AbstractWebsite

Locust antennal lobe (AL) projection neurons (PNs) respond to olfactory stimuli with sequences of depolarizing and hyperpolarizing epochs, each lasting hundreds of milliseconds. A computer simulation of an AL network was used to test the hypothesis that slow inhibitory connections between local neurons (LNs) and PNs are responsible for temporal patterning. Activation of slow inhibitory receptors on PNs by the same GABAergic synapses that underlie fast oscillatory synchronization of PNs was sufficient to shape slow response modulations. This slow stimulus- and neuron-specific patterning of AL activity was resistant to blockade of fast inhibition. Fast and slow inhibitory mechanisms at synapses between LNs and PNs can thus form dynamical PN assemblies whose elements synchronize transiently and oscillate collectively, as observed not only in the locust AL, but also in the vertebrate olfactory bulb.

Pinto, RD, Elson RC, Szucs A, Rabinovich MI, Selverston AI, Abarbanel HDI.  2001.  Extended dynamic clamp: controlling up to four neurons using a single desktop computer and interface. Journal of Neuroscience Methods. 108:39-48.   10.1016/s0165-0270(01)00368-5   AbstractWebsite

The dynamic clamp protocol allows an experimenter to simulate the presence of membrane conductances in, and synaptic connections between, biological neurons. Existing protocols and commercial ADC/DAC boards provide ready control in and between less than or equal to2 neurons. Control at >2 sites is desirable when studying neural circuits with serial or ring connectivity. Here, we describe how to extend dynamic clamp control to four neurons and their associated synaptic interactions, using a single IBM-compatible PC, an ADC/DAC interface with two analog outputs, and an additional demultiplexing circuit. A specific C++ program, DYNCLAMP4, implements these procedures in a Windows environment, allowing one to change parameters while the dynamic clamp is running. Computational efficiency is increased by varying the duration of the input-output cycle. The program simulates less than or equal to8 Hodgkin-Huxley-type conductances and less than or equal to 18 (chemical and/or electrical) synapses in less than or equal to4 neurons and runs at a minimum update rate of 5 kHz on a 450 MHz CPU. (Increased speed is possible in a two-neuron version that does not need auxiliary circuitry). Using identified neurons of the crustacean stomatogastric ganglion, we illustrate on-line parameter modification and the construction of three-member synaptic rings. (C) 2001 Elsevier Science B.V. All rights reserved.

Abarbanel, HD, Rabinovich MI.  2001.  Neurodynamics: nonlinear dynamics and neurobiology. Current Opinion in Neurobiology. 11:423-430.   10.1016/s0959-4388(00)00229-4   AbstractWebsite

The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited. Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.

Selverston, AI, Rabinovich MI, Abarbanel HDI, Elson R, Szucs A, Pinto RD, Huerta R, Varona P.  2000.  Reliable circuits from irregular neurons: A dynamical approach to understanding central pattern generators. Journal of Physiology-Paris. 94:357-374.   10.1016/s0928-4257(00)01101-3   AbstractWebsite

Central pattern generating neurons from the lobster stomatogastric ganglion were analyzed using new nonlinear methods. The LP neuron was found to have only four or five degrees of freedom in the isolated condition and displayed chaotic behavior. We show that this chaotic behavior could be regularized by periodic pulses of negative current injected into the neuron or by coupling it to another neuron via inhibitory connections. We used both a modified Hindmarsh-Rose model to simulate the neurons behavior phenomenologically and a more realistic conductance-based model so that the modeling could be linked to the experimental observations. Both models were able to capture the dynamics of the neuron behavior better than previous models. We used the Hindmarsh-Rose model as the basis for building electronic neurons which could then be integrated into the biological circuitry. Such neurons were able to rescue patterns which had been disabled by removing key biological neurons from the circuit. (C) 2000 Elsevier Science Ltd. Published by Editions scientifiques et medicales Elsevier SAS.

Eguia, MC, Rabinovich MI, Abarbanel HDI.  2000.  Information transmission and recovery in neural communications channels. Physical Review E. 62:7111-7122.   10.1103/PhysRevE.62.7111   AbstractWebsite

Biological neural communications channels transport environmental information from sensors through chains of active dynamical neurons to neural centers for decisions and actions to achieve required functions. These kinds of communications channels are able to create information and to transfer information from one time scale to the other because of the intrinsic nonlinear dynamics of the component neurons. We discuss a very simple neural information channel composed of sensory input in the form of a spike train that arrives at a model neuron, then moves through a realistic synapse to a second neuron where the information in the initial sensory signal is read. Our model neurons are four-dimensional generalizations of the Hindmarsh-Rose neuron, and we use a model of chemical synapse derived from first-order kinetics. The four-dimensional model neuron has a rich variety of dynamical behaviors, including periodic bursting, chaotic bursting, continuous spiking, and multistability. We show that, for many of these regimes, the parameters of the chemical synapse can be tuned so that information about the stimulus that is unreadable at the first neuron in the channel can be recovered by the dynamical activity of the synapse and the second neuron. Information creation by nonlinear dynamical systems that allow chaotic oscillations is familiar in their autonomous oscillations. It is associated with the instabilities that lead to positive Lyapunov exponents in their dynamical behavior. Our results indicate how nonlinear neurons acting as input/output systems along a communications channel can recover information apparently "lost" in earlier junctions on the channel. Our measure of information transmission is the average mutual information between elements, and because the channel is active and nonlinear, the average mutual information between the sensory source and the final neuron may be greater than the average mutual information at an earlier neuron in the channel. This behavior is strikingly different than the passive role communications channels usually play, and the "data processing theorem" of conventional communications theory is violated by these neural channels. Our calculations indicate that neurons can reinforce reliable transmission along a chain even when the synapses and the neurons are not completely reliable components. This phenomenon is generic in parameter space, robust in the presence of noise, and independent of the discretization process. Our results suggest a framework in which one might understand the apparent design complexity of neural information transduction networks. If networks with many dynamical neurons can recover information not apparent at various way stations in the communications channel, such networks may be more robust to noisy signals, may be more capable of communicating many types of encoded sensory neural information, and may be the appropriate design for components, neurons and synapses, which can be individually imprecise, inaccurate "devices.".

Szucs, A, Varona P, Volkovskii AR, Abarbanel HDI, Rabinovich MI, Selverston AI.  2000.  Interacting biological and electronic neurons generate realistic oscillatory rhythms. Neuroreport. 11:563-569. AbstractWebsite

Small assemblies of neurons such as central pattern generators (CPG) are known to express regular oscillatory firing patterns comprising bursts of action potentials. In contrast, individual CPG neurons isolated from the remainder of the network can generate irregular firing patterns. In our study of cooperative behavior in CPGs we developed an analog electronic neuron (EN) that reproduces firing patterns observed in lobster pyloric CPG neurons. Using a tuneable artificial synapse we connected the EN bidirectionally to neurons of this CPG. We found that the periodic bursting oscillation of this mixed assembly depends on the strength and sign of the electrical coupling. Working with identified, isolated pyloric CPG neurons whose network rhythms were impaired, the EN/biological network restored the characteristic CPG rhythm both when the EN oscillations are regular and when they are irregular. NeuroReport 11:563-569 (C) 2000 Lippincon Williams & Wilkins.

La Rosa, M, Rabinovich MI, Huerta R, Abarbanel HDI, Fortuna L.  2000.  Slow regularization through chaotic oscillation transfer in an unidirectional chain of Hindmarsh-Rose models. Physics Letters A. 266:88-93.   10.1016/s0375-9601(00)00015-3   AbstractWebsite

We observed the arising of a new slow regular rhythm along the chain of unidirectional coupled neurons whose individual dynamics is periodic spiking, In this study we use the Hindmarsh-Rose type neurons which are potentially able to produce several modes of behavior: periodic spiking, periodic spiking-bursting and chaotic spiking-bursting activities. Several spatial bifurcations take place along the chain: the bifurcation from periodic spiking regime to chaotic spiking-bursting, transformation corresponding to the developing chaos, and finally, the transition from a irregular spiking-bursting regime to a regime with regular bursts, The calculation of the Kolmogorov-Sinai entropy indicates that the periodic oscillations of some neurons at the beginning of the chain are transformed into spiking-bursting chaos that is localized along the network becoming later regular slow oscillations in spite of the chaoticity of the spiking pulsations. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Rabinovich, MI, Abarbanel HDI.  1998.  The role of chaos in neural systems. Neuroscience. 87:5-14.   10.1016/s0306-4522(98)00091-8   AbstractWebsite

The ideas of dynamical chaos have altered our understanding of the origin of random appearing behavior in man fields of physics and engineering. In the 1980s and 1990s these new viewpoints about apparent random oscillations arising in deterministic systems were investigated in neurophysiology and have led to quite successful reports of chaos in experimental and theoretical investigations. This paper is a "view" paper addressing the role of chaos in living systems, not just reviewing the evidence for its existence, and in particular we ask about the utility of chaotic behavior in nervous systems. From our point of view chaotic oscillations of individual neurons may nor be essential for the observed activity of neuronal assemblies bur may, instead, be responsible for the multitude of regular regimes of operation that can be accomplished by elements which are chaotic. The organization of chaotic elements in assemblies where their synchronization can result in organized adaptive and reliable activities may lead to general principles used by nature in accomplishing critical functional goals. (C) 1998 IBRO. Published by Elsevier Science Ltd.