Joaquín J. Torres

Associative memory with dynamic synapses

We have examined a role of dynamic synapses in the stochastic Hopfield-like network behavior. Our results demonstrate an appearance of a novel phase characterized by quick transitions from one memory state to another. The network is able to retrieve memorized patterns corresponding to classical ferromagnetic states but switches between memorized patterns with an intermittent type of behavior. This phenomenon might reflect the flexibility of real neural systems and their readiness to receive and respond to novel and changing external stimuli.

Entropic Origin of Disassortativity in Complex Networks

Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated? To answer this long-standing question, we define the ensemble of correlated networks and obtain the associated Shannon entropy. Maximum entropy can correspond to either assortative (correlated) or disassortative (anticorrelated) configurations, but in the case of highly heterogeneous, scale-free networks a certain disassortativity is predicted--offering a parsimonious explanation for the question above. Our approach provides a neutral model from which, in the absence of further knowledge regarding network evolution, one can obtain the expected value of correlations. When empirical observations deviate from the neutral predictions--as happens for social networks--one can then infer that there are specific correlating mechanisms at work.

Influence of topology on the performance of a neural network

Abstract We studied the computational properties of an attractor neural network (ANN) with different network topologies. Though fully connected neural networks exhibit, in general, a good performance, they are biologically unrealistic, as it is unlikely that natural evolution leads to such a large connectivity. We demonstrate that, at finite temperature, the capacity to store and retrieve binary patterns is higher for ANN with scale-free (SF) topology than for highly random-diluted Hopfield networks with the same number of synapses. We also show that, at zero temperature, the relative performance of the SF network increases with increasing values of the distribution power-law exponent. Some consequences and possible applications of our findings are discussed.

Regularization mechanisms of spiking-bursting neurons.

An essential question raised after the observation of highly variable bursting activity in individual neurons of Central Pattern Generators (CPGs) is how an assembly of such cells can cooperatively act to produce regular signals to motor systems. It is well known that some neurons in the lobster stomatogastric ganglion have a highly irregular spiking-bursting behavior when they are synaptically isolated from any connection in the CPG. Experimental recordings show that periodic stimuli on a single neuron can regulate its firing activity. Other evidence demonstrates that specific chemical and/or electrical synapses among neurons also induce the regularization of the rhythms. In this paper we present a modeling study in which a slow subcellular dynamics, the exchange of calcium between an intracellular store and the cytoplasm, is responsible for the origin and control of the irregular spiking-bursting activity. We show this in simulations of single cells under periodic driving and in minimal networks where the cooperative activity can induce regularization. While often neglected in the description of realistic neuron models, subcellular processes with slow dynamics may play an important role in information processing and short-term memory of spiking-bursting neurons.

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

Abstract. 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 polarity of the conductance between the neurons. We observed a sequence of bifurcations 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.

Competition Between Synaptic Depression and Facilitation in Attractor Neural Networks

We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network displays different behaviors, including associative memory and switching of activity between different attractors. We conclude that synaptic facilitation enhances the attractor instability in a way that (1) intensifies the system adaptability to external stimuli, which is in agreement with experiments, and (2) favors the retrieval of information with less error during short time intervals.

Maximum memory capacity on neural networks with short-term synaptic depression and facilitation

In this work, we study, analytically and employing Monte Carlo simulations, the influence of the competition between several activity-dependent synaptic processes, such as short-term synaptic facilitation and depression, on the maximum memory storage capacity in a neural network. In contrast to the case of synaptic depression, which drastically reduces the capacity of the network to store and retrieve static activity patterns, synaptic facilitation enhances the storage capacity in different contexts. In particular, we found optimal values of the relevant synaptic parameters (such as the neurotransmitter release probability or the characteristic facilitation time constant) for which the storage capacity can be maximal and similar to the one obtained with static synapses, that is, without activity-dependent processes. We conclude that depressing synapses with a certain level of facilitation allow recovering the good retrieval properties of networks with static synapses while maintaining the nonlinear characteristics of dynamic synapses, convenient for information processing and coding.

Irregular dynamics in up and down cortical states.

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a biologically motivated stochastic model of up and down transitions. The model is constituted by a simple bistable rate dynamics, where the synaptic current is modulated by short-term synaptic processes which introduce stochasticity and temporal correlations. A complete analysis of our model, both with mean-field approaches and numerical simulations, shows the appearance of complex transitions between high (up) and low (down) neural activity states, driven by the synaptic noise, with permanence times in the up state distributed according to a power-law. We show that the experimentally observed large fluctuation in up and down permanence times can be explained as the result of sufficiently noisy dynamical synapses with sufficiently large recovery times. Static synapses cannot account for this behavior, nor can dynamical synapses in the absence of noise.

Effects of Fast Presynaptic Noise in Attractor Neural Networks

We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological findings that show that synaptic strength may either increase or decrease on a short timescale depending on presynaptic activity. We thus describe a mechanism by which fast presynaptic noise enhances the neural network sensitivity to an external stimulus. The reason is that, in general, presynaptic noise induces nonequilibrium behavior and, consequently, the space of fixed points is qualitatively modified in such a way that the system can easily escape from the attractor. As a result, the model shows, in addition to pattern recognition, class identification and categorization, which may be relevant to the understanding of some of the brain complex tasks.

The role of synaptic facilitation in spike coincidence detection

Using a realistic model of activity dependent dynamical synapse, which includes both depressing and facilitating mechanisms, we study the conditions in which a postsynaptic neuron efficiently detects temporal coincidences of spikes which arrive from N different presynaptic neurons at certain frequency f. A numerical and analytical treatment of that system shows that: (1) facilitation enhances the detection of correlated signals arriving from a subset of presynaptic excitatory neurons, and (2) the presence of facilitation yields to a better detection of firing rate changes in the presynaptic activity. We also observed that facilitation determines the existence of an optimal input frequency which allows the best performance for a wide (maximum) range of the neuron firing threshold. This optimal frequency can be controlled by means of facilitation parameters. Finally, we show that these results are robust even for very noisy signals and in the presence of synaptic fluctuations produced by the stochastic release of neurotransmitters.