Biomedical subjects

H D Abarbanel

Publications and source records attributed to H D Abarbanel.

At least 19 recordsLinked to original sources

PubMed2001

Dynamical encoding by networks of competing neuron groups: winnerless competition.

Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e(N-1)!, i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output.

Action Potentials↗

PubMed2001

Extended dynamic clamp: controlling up to four neurons using a single desktop computer and interface.

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 < or =2 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 < or =8 Hodgkin-Huxley-type conductances and < or =18 (chemical and/or electrical) synapses in < or =4 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.

Algorithms↗

PubMed2001

Topology selection by chaotic neurons of a pyloric central pattern generator.

The pyloric Central Pattern Generator (CPG) in the lobster has an architecture in which every neuron receives at least one connection from another member of the CPG. We call this a "non-open" network topology. An "open" topology, where at least one neuron does not receive synapses from any other CPG member, is found neither in the pyloric nor in the gastric mill CPG. Here we investigate a possible reason for this topological structure using the ability to perform a biologically functional task as a measure of the efficacy of the network. When the CPG is composed of model neurons that exhibit regular membrane voltage oscillations, open topologies are as able to maximize this functionality as non-open topologies. When we replace these models by neurons which exhibit chaotic membrane voltage oscillations, the functional criterion selects non-open topologies. As isolated neurons from invertebrate CPGs are known in some cases to undergo chaotic oscillations, this suggests that there is a biological basis for the class of non-open network topologies that we observe.

Animals↗

PubMed2001

Dynamics of two electrically coupled chaotic neurons: experimental observations and model analysis.

Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process calcium exchange and storage in the endoplasmic reticulum as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polar-of the conductance between the neurons. We observed a sequence of bifarctions that took the neurons from strongly synchronized in-phase behavior. through uncorrelated chaotic oscillations to strongly synchronized and now regular out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities.

Animals↗

PubMed2001

Model of transient oscillatory synchronization in the locust antennal lobe.

Transient pairwise synchronization of locust antennal lobe (AL) projection neurons (PNs) occurs during odor responses. In a Hodgkin-Huxley-type model of the AL, interactions between excitatory PNs and inhibitory local neurons (LNs) created coherent network oscillations during odor stimulation. GABAergic interconnections between LNs led to competition among them such that different groups of LNs oscillated with periodic Ca(2+) spikes during different 50-250 ms temporal epochs, similar to those recorded in vivo. During these epochs, LN-evoked IPSPs caused phase-locked, population oscillations in sets of postsynaptic PNs. The model shows how alternations of the inhibitory drive can temporally encode sensory information in networks of neurons without precisely tuned intrinsic oscillatory properties.

Animals↗

PubMed2001

Model of cellular and network mechanisms for odor-evoked temporal patterning in the locust antennal lobe.

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.

Animals↗

PubMed2001

Neurodynamics: nonlinear dynamics and neurobiology.

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.

Animals↗

PubMed2001

Odor encoding as an active, dynamical process: experiments, computation, and theory.

We examine early olfactory processing in the vertebrate and insect olfactory systems, using a computational perspective. What transformations occur between the first and second olfactory processing stages? What are the causes and consequences of these transformations? To answer these questions, we focus on the functions of olfactory circuit structure and on the role of time in odor-evoked integrative processes. We argue that early olfactory relays are active and dynamical networks, whose actions change the format of odor-related information in very specific ways, so as to refine stimulus identification. Finally, we introduce a new theoretical framework ("winnerless competition") for the interpretation of these data.

Animals↗

PubMed2001

Nonlinear behavior of sinusoidally forced pyloric pacemaker neurons.

Periodic current forcing was used to investigate the intrinsic dynamics of a small group of electrically coupled neurons in the pyloric central pattern generator (CPG) of the lobster. This group contains three neurons, namely the two pyloric dilator (PD) motoneurons and the anterior burster (AB) interneuron. Intracellular current injection, using sinusoidal waveforms of varying amplitude and frequency, was applied in three configurations of the pacemaker neurons: 1) the complete pacemaker group, 2) the two PDs without the AB, and 3) the AB neuron isolated from the PDs. Depending on the frequency and amplitude of the injected current, the intact pacemaker group exhibited a wide variety of nonlinear behaviors, including synchronization to the forcing, quasiperiodicity, and complex dynamics. In contrast, a single, broad 1:1 entrainment zone characterized the response of the PD neurons when isolated from the main pacemaker neuron AB. The isolated AB responded to periodic forcing in a manner similar to the complete pacemaker group, but with wider zones of synchronization. We have built an analog electronic circuit as an implementation of a modified Hindmarsh-Rose model for simulating the membrane potential activity of pyloric neurons. We subjected this electronic model neuron to the same periodic forcing as used in the biological experiments. This four-dimensional electronic model neuron reproduced the autonomous oscillatory firing patterns of biological pyloric pacemaker neurons, and it expressed the same stationary nonlinear responses to periodic forcing as its biological counterparts. This adds to our confidence in the model. These results strongly support the idea that the intact pyloric pacemaker group acts as a uniform low-dimensional deterministic nonlinear oscillator, and the regular pyloric oscillation is the outcome of cooperative behavior of strongly coupled neurons, having different dynamical and biophysical properties when isolated.

Action Potentials↗

PubMed2000

Synchronization of chaotic oscillations in doped fiber ring lasers.

The synchronization of chaotic rare-earth-doped fiber ring lasers is analyzed. The lasers are first coupled by transmitting a fraction c of the circulating electric field in the transmitter and injecting it into the optical cavity of the receiver. A coupling strategy which relies on modulation of the intensity of the light alone is also examined. Synchronization is studied as a function of the coupling strength, and we see excellent synchronization, even with very small c. We prove that in an open loop configuration (c=1) synchronization is guaranteed due to the particular structure of our equations and of the injection method we use. The generalized synchronization of these model lasers is examined when there is parameter mismatch between the transmitter and receiver lasers. The synchronization is found to be insensitive to a wide range of mismatch in laser parameters, but it is sensitive to other parameters, in particular those associated with the phase and the polarization of the circulating electric field. Communicating information between the transmitter and receiver lasers is also addressed. We investigate a scheme for modulating information onto the chaotic electric field and then demodulating and detecting the information embedded in the chaotic signal passed down the communications channel. We show full recovery with very low error for a wide range of coupling strengths.

Journal Article↗

PubMed2000

Interacting biological and electronic neurons generate realistic oscillatory rhythms.

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.

Action Potentials↗

PubMed2000

Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP3.

Chaotic bursting has been recorded in synaptically isolated neurons of the pyloric central pattern generating (CPG) circuit in the lobster stomatogastric ganglion. Conductance-based models of pyloric neurons typically fail to reproduce the observed irregular behavior in either voltage time series or state-space trajectories. Recent suggestions of Chay [Biol Cybern 75: 419-431] indicate that chaotic bursting patterns can be generated by model neurons that couple membrane currents to the nonlinear dynamics of intracellular calcium storage and release. Accordingly, we have built a two-compartment model of a pyloric CPG neuron incorporating previously described membrane conductances together with intracellular Ca2+ dynamics involving the endoplasmic reticulum and the inositol 1,4,5-trisphosphate receptor IP3R. As judged by qualitative inspection and quantitative, nonlinear analysis, the irregular voltage oscillations of the model neuron resemble those seen in the biological neurons. Chaotic bursting arises from the interaction of fast membrane voltage dynamics with slower intracellular Ca2+ dynamics and, hence, depends on the concentration of IP3. Despite the presence of 12 independent dynamical variables, the model neuron bursts chaotically in a subspace characterized by 3-4 active degrees of freedom. The critical aspect of this model is that chaotic oscillations arise when membrane voltage processes are coupled to another slow dynamic. Here we suggest this slow dynamic to be intracellular Ca2+ handling.

Action Potentials↗

PubMed2000

Synchronous behavior of two coupled electronic neurons.

We report on experimental studies of synchronization phenomena in a pair of analog electronic neurons (ENs). The ENs were designed to reproduce the observed membrane voltage oscillations of isolated biological neurons from the stomatogastric ganglion of the California spiny lobster Panulirus interruptus. The ENs are simple analog circuits which integrate four-dimensional differential equations representing fast and slow subcellular mechanisms that produce the characteristic regular/chaotic spiking-bursting behavior of these cells. In this paper we study their dynamical behavior as we couple them in the same configurations as we have done for their counterpart biological neurons. The interconnections we use for these neural oscillators are both direct electrical connections and excitatory and inhibitory chemical connections: each realized by analog circuitry and suggested by biological examples. We provide here quantitative evidence that the ENs and the biological neurons behave similarly when coupled in the same manner. They each display well defined bifurcations in their mutual synchronization and regularization. We report briefly on an experiment on coupled biological neurons and four-dimensional ENs, which provides further ground for testing the validity of our numerical and electronic models of individual neural behavior. Our experiments as a whole present interesting new examples of regularization and synchronization in coupled nonlinear oscillators.

Animals↗

PubMed2000

Information transmission and recovery in neural communications channels.

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 waystations 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."

Action Potentials↗

PubMed1999

Dynamic control of irregular bursting in an identified neuron of an oscillatory circuit.

In the oscillatory circuits known as central pattern generators (CPGs), most synaptic connections are inhibitory. We have assessed the effects of inhibitory synaptic input on the dynamic behavior of a component neuron of the pyloric CPG in the lobster stomatogastric ganglion. Experimental perturbations were applied to the single, lateral pyloric neuron (LP), and the resulting voltage time series were analyzed using an entropy measure obtained from power spectra. When isolated from phasic inhibitory input, LP generates irregular spiking-bursting activity. Each burst begins in a relatively stereotyped manner but then evolves with exponentially increasing variability. Periodic, depolarizing current pulses are poor regulators of this activity, whereas hyperpolarizing pulses exert a strong, frequency-dependent regularizing action. Rhythmic inhibitory inputs from presynaptic pacemaker neurons also regularize the bursting. These inputs 1) reset LP to a similar state at each cycle, 2) extend and further stabilize the initial, quasi-stable phase of its bursts, and 3) at sufficiently high frequencies terminate ongoing bursts before they become unstable. The dynamic time frame for stabilization overlaps the normal frequency range of oscillations of the pyloric CPG. Thus, in this oscillatory circuit, the interaction of rhythmic inhibitory input with intrinsic burst properties affects not only the phasing, but also the dynamic stability of neural activity.

Animals↗

PubMed1998

Nonlinear analysis of epileptic activity in rabbit neocortex.

We report on the nonlinear analysis of electroencephalogram (EEG) recordings in the rabbit visual cortex. Epileptic seizures were induced by local penicillin application and triggered by visual stimulation. The analysis procedures for nonlinear signals have been developed over the past few years and applied primarily to physical systems. This is an early application to biological systems and the first to EEG data. We find that during epileptic activity, both global and local embedding dimensions are reduced with respect to nonepileptic activity. Interestingly, these values are very low (dE approximately equal to 3) and do not change between preictal and tonic stages of epileptic activity, also the Lyapunov dimension remains constant. However, between these two stages the manifestations of the local dynamics change quite drastically, as can be seen, e.g., from the shape of the attractors. Furthermore, the largest Lyapunov exponent is reduced by a factor of about two in the second stage and characterizes the difference in dynamics. Thus, the occurrence of clinical symptoms associated with the tonic seizure activity seems to be mainly related to the local dynamics of the nonlinear system. These results thus seem to give a strong indication that the dynamics remains much the same in these stages of behavior, and changes are due to alterations in model parameters and consequent bifurcations of the observed orbits.

Animals↗

PubMed1998

The role of chaos in neural systems.

The ideas of dynamical chaos have altered our understanding of the origin of random appearing behavior in many 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 not be essential for the observed activity of neuronal assemblies but 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.

Animals↗

PubMed1996

Synchronized action of synaptically coupled chaotic model neurons.

Experimental observations of the intracellular recorded electrical activity in individual neurons show that the temporal behavior is often chaotic. We discuss both our own observations on a cell from the stomatogastric central pattern generator of lobster and earlier observations in other cells. In this paper we work with models with chaotic neurons, building on models by Hindmarsh and Rose for bursting, spiking activity in neurons. The key feature of these simplified models of neurons is the presence of coupled slow and fast subsystems. We analyze the model neurons using the same tools employed in the analysis of our experimental data. We couple two model neurons both electrotonically and electrochemically in inhibitory and excitatory fashions. In each of these cases, we demonstrate that the model neurons can synchronize in phase and out of phase depending on the strength of the coupling. For normal synaptic coupling, we have a time delay between the action of one neuron and the response of the other. We also analyze how the synchronization depends on this delay. A rich spectrum of synchronized behaviors is possible for electrically coupled neurons and for inhibitory coupling between neurons. In synchronous neurons one typically sees chaotic motion of the coupled neurons. Excitatory coupling produces essentially periodic voltage trajectories, which are also synchronized. We display and discuss these synchronized behaviors using two "distance" measures of the synchronization.

Action Potentials↗