Biomedical subjects

Henry D I Abarbanel

Publications and source records attributed to Henry D I Abarbanel.

At least 19 recordsLinked to original sources

PubMed2006

Neural circuitry for recognizing interspike interval sequences.

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.

Action Potentials↗

PubMed2006

From crawling to cognition: analyzing the dynamical interactions among populations of neurons.

By using multi-electrode arrays or optical imaging, investigators can now record from many individual neurons in various parts of nervous systems simultaneously while an animal performs sensory, motor or cognitive tasks. Given the large multidimensional datasets that are now routinely generated, it is often not obvious how to find meaningful results within the data. The analysis of neuronal-population recordings typically involves two steps: the extraction of relevant dynamics from neural data, and then use of the dynamics to classify and discriminate features of a stimulus or behavior. We focus on the application of techniques that emphasize interactions among the recorded neurons rather than using just the correlations between individual neurons and a perception or a behavior. An understanding of modern analysis techniques is crucially important for researchers interested in the co-varying activity among populations of neurons or even brain regions.

Action Potentials↗

PubMed2005

Self-organization in the olfactory system: one shot odor recognition in insects.

We show in a model of spiking neurons that synaptic plasticity in the mushroom bodies in combination with the general fan-in, fan-out properties of the early processing layers of the olfactory system might be sufficient to account for its efficient recognition of odors. For a large variety of initial conditions the model system consistently finds a working solution without any fine-tuning, and is, therefore, inherently robust. We demonstrate that gain control through the known feedforward inhibition of lateral horn interneurons increases the capacity of the system but is not essential for its general function. We also predict an upper limit for the number of odor classes Drosophila can discriminate based on the number and connectivity of its olfactory neurons.

Animals↗

PubMed2005

Synaptic plasticity with discrete state synapses.

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.

Action Potentials↗

PubMed2005

A network of electronic neural oscillators reproduces the dynamics of the periodically forced pyloric pacemaker group.

Low-dimensional oscillators are a valuable model for the neuronal activity of isolated neurons. When coupled, the self-sustained oscillations of individual free oscillators are replaced by a collective network dynamics. Here, dynamical features of such a network, consisting of three electronic implementations of the Hindmarsh-Rose mathematical model of bursting neurons, are compared to those of a biological neural motor system, specifically the pyloric CPG of the crustacean stomatogastric nervous system. We demonstrate that the network of electronic neurons exhibits realistic synchronized bursting behavior comparable to the biological system. Dynamical properties were analyzed by injecting sinusoidal currents into one of the oscillators. The temporal bursting structure of the electronic neurons in response to periodic stimulation is shown to bear a remarkable resemblance to that observed in the corresponding biological network. These findings provide strong evidence that coupled nonlinear oscillators realistically reproduce the network dynamics experimentally observed in assemblies of several neurons.

Action Potentials↗

PubMed2005

Dopamine modulation of spike dynamics in bursting neurons.

The pyloric network of the lobster stomatogastric ganglion is a prime example of an oscillatory neural circuit. In our previous study on the firing patterns of pyloric neurons we observed characteristic temporal structures termed 'interspike interval (ISI) signatures' which were found to depend on the synaptic connectivity of the network. Dopamine, a well-known modulator of the pyloric network, is known to affect inhibitory synapses so it might also tune the fine temporal structure of intraburst spikes, a phenomenon not previously investigated. In the recent work we study the DA modulation of ISI patterns of two identified pyloric neurons in normal conditions and after blocking their glutamatergic synaptic connections. Dopamine (10-50 microM) strongly regularizes the firing of the lateral pyloric (LP) and pyloric dilator (PD) neurons by increasing the reliability of recurrent spike patterns. The most dramatic effect is observed in the LP, where precisely replicated spike multiplets appear in a normally 'noisy' neuron. The DA-induced regularization of intraburst spike patterns requires functional glutamatergic inputs to the LP neuron and this effect cannot be mimicked by simple intracellular depolarization. Inhibitory synaptic inputs arriving before the bursts are important factors in shaping the intraburst spike dynamics of both the PD and the LP neurons. Our data reveal a novel aspect of chemical neuromodulation in oscillatory neural networks. This effect sets in at concentrations lower than those affecting the overall burst pattern of the network. The sensitivity of intraburst spike dynamics to preceding synaptic inputs also suggests a novel method of temporal coding in neural bursters.

Action Potentials↗

PubMed2005

Estimating entropy rates with Bayesian confidence intervals.

The entropy rate quantifies the amount of uncertainty or disorder produced by any dynamical system. In a spiking neuron, this uncertainty translates into the amount of information potentially encoded and thus the subject of intense theoretical and experimental investigation. Estimating this quantity in observed, experimental data is difficult and requires a judicious selection of probabilistic models, balancing between two opposing biases. We use a model weighting principle originally developed for lossless data compression, following the minimum description length principle. This weighting yields a direct estimator of the entropy rate, which, compared to existing methods, exhibits significantly less bias and converges faster in simulation. With Monte Carlo techinques, we estimate a Bayesian confidence interval for the entropy rate. In related work, we apply these ideas to estimate the information rates between sensory stimuli and neural responses in experimental data (Shlens, Kennel, Abarbanel, & Chichilnisky, in preparation).

Bayes Theorem↗

PubMed2004

Dynamical model of birdsong maintenance and control.

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 approximately equal 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.

Action Potentials↗

PubMed2004

Spike timing and synaptic plasticity in the premotor pathway of birdsong.

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 approximately 40- 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 approximately 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.

Action Potentials↗

PubMed2004

Mapping neural architectures onto acoustic features of birdsong.

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.

Action Potentials↗

PubMed2003

Enhancement of synchronization in a hybrid neural circuit by spike-timing dependent plasticity.

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-Huxley-type 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.

Action Potentials↗

PubMed2003

Biophysical model of synaptic plasticity dynamics.

We discuss a biophysical model of synaptic plasticity that provides a unified view of the outcomes of synaptic modification protocols, including: (1) prescribed time courses of postsynaptic intracellular Ca(2+) release, (2) postsynaptic voltage clamping with presentation of presynaptic spike trains at various frequencies, (3) direct postsynaptic response to presynaptic spike trains at various frequencies, and (4) LTP/LTD as a response to precisely timed presynaptic and postsynaptic spikes.

Animals↗

PubMed2003

Spatial representation of temporal information through spike-timing-dependent plasticity.

We suggest a mechanism based on spike-timing-dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely connected by STDP synapses. All synapses are modified according to the so-called normal STDP rule observed in various real biological synapses. After conditioning through repeated input of a limited number of temporal sequences, the system is able to complete the temporal sequence upon receiving the input of a fraction of them. This is an example of effective unsupervised learning in a biologically realistic system. We investigate the dependence of learning success on entrainment time, system size, and presence of noise. Possible applications include learning of motor sequences, recognition and prediction of temporal sensory information in the visual as well as the auditory system, and late processing in the olfactory system of insects.

Animals↗

PubMed2003

Using distributed nonlinear dynamics for public key encryption.

We introduce a new method for asymmetric (public key/private key) encryption exploiting properties of nonlinear dynamical systems. A high-dimensional dissipative nonlinear dynamical system is distributed between transmitter and receiver, so we call the method distributed dynamics encryption (DDE). The transmitter dynamics is public, and the receiver dynamics is hidden. A message is encoded by modulation of parameters of the transmitter, and this results in a shift of the overall system attractor. An unauthorized receiver does not know the hidden dynamics in the receiver and cannot decode the message. We present an example of DDE using a coupled map lattice.

Journal Article↗

PubMed2003

Dynamical synaptic plasticity: a model and connection to some experiments.

Using a modified version of a phenomenological model for the dynamics of synaptic plasticity, we examine some recent experiments of Wu et al. [(2001) J Physiol 533:745-755]. We show that the model is quantitatively consistent with their experimental protocols producing long-term potentiation (LTP) and long-term depression (LTD) in slice preparations of rat hippocampus. We also predict the outcome of similar experiments using different frequencies and depolarization levels than reported in their results.

Action Potentials↗

PubMed2003

Synaptic modulation of the interspike interval signatures of bursting pyloric neurons.

The pyloric network of the lobster stomatogastric nervous system is one of the best described assemblies of oscillatory neurons producing bursts of action potentials. While the temporal patterns of bursts have been investigated in detail, those of spikes have received less attention. Here we analyze the intraburst firing patterns of pyloric neurons and the synaptic interactions shaping their dynamics in millisecond time scales not performed before. We find that different pyloric neurons express characteristic, cell-specific firing patterns in their bursts. Nonlinear analysis of the interspike intervals (ISIs) reveals distinctive temporal structures ('interspike interval signatures'), which are found to depend on the synaptic connectivity of the network. We compare ISI patterns of the pyloric dilator (PD), lateral pyloric (LP), and ventricular dilator (VD) neurons in 1) normal conditions, 2) after blocking glutamatergic synaptic connections, and 3) in various functional configurations of the three neurons. Manipulation of the synaptic connectivity results in characteristic changes in the ISI signatures of the postsynaptic neurons. The intraburst firing pattern of the PD neuron is regularized by the inhibitory synaptic connection from the LP neuron as revealed in current-clamp experiments and also as reconstructed with a dynamic clamp. On the other hand, mutual inhibition between the LP and VD neurons tend to produce more irregular bursts with increased spike jitter. The results show that synaptic interactions fine-tune the output of pyloric neurons. The present data also suggest a way of processing of synaptic information: bursting neurons are capable of encoding incoming signals by altering the fine structure of their intraburst spike patterns.

Action Potentials↗

PubMed2002

When are synchronization errors small?

We address the question of bounds on the synchronization error for the case of nearly identical nonlinear systems. It is pointed out that negative largest conditional Lyapunov exponents of the synchronization manifold are not sufficient to guarantee a small synchronization error and that one has to find bounds for the deformation of the manifold due to perturbations. We present an analytic bound for a simple subclass of systems, which includes the Lur'e systems, showing that the bound for the deformation grows as the largest singular value of the linearized system gets larger. Then, the Lorenz system is taken as an example to demonstrate that the phenomenon is not restricted to Lur'e systems.

Journal Article↗

PubMed2002

False neighbors and false strands: a reliable minimum embedding dimension algorithm.

The time-delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. We demonstrate a reliable method to estimate the minimum necessary embedding dimension that improves upon previous methods by correcting for systematic effects due to temporal oversampling, autocorrelation, and changing time lag. The method gives a sharp and reliable indication of the proper dimension. With little computational cost, the method also distinguish easily between infinite-dimensional colored noise-including noisy periodicity-and low-dimensional dynamics.

Journal Article↗