Ramón Huerta

Fast Response and Temporal Coherent Oscillations in Small-World Networks

We have investigated the role that different connectivity regimes play in the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random topologies give rise to fast system response yet are unable to produce coherent oscillations in the average activity of the network; on the other hand, regular topologies give rise to coherent oscillations, but in a temporal scale that is not in accordance with fast signal processing. Finally, small-world topologies, which fall between random and regular ones, take advantage of the best features of both, giving rise to fast system response with coherent oscillations.

Transient Dynamics for Neural Processing

A computational view of how perception and cognition can be modeled as dynamic patterns of transient activity within neural networks.

Synchronous Behavior of Two Coupled Biological Neurons

We report experimental studies of synchronization phenomena in a pair of biological neurons that interact through naturally occurring, electrical coupling. When these neurons generate irregular bursts of spikes, the natural coupling synchronizes slow oscillations of membrane potential, but not the fast spikes. By adding artificial electrical coupling we studied transitions between synchrony and asynchrony in both slow oscillations and fast spikes. We discuss the dynamics of bursting and synchronization in living neurons with distributed functional morphology. [S0031-9007(98)08008-9] The dynamics of many neural ensembles such as central pattern generators (CPGs) or thalamo-cortical circuits pose questions related to cooperative behavior of neurons. Individual neurons may show irregular behavior [1], while ensembles of different neurons can synchronize in order to process biological information [2] or to produce regular, rhythmical activity [3]. How do the irregular neurons synchronize? How do they inhibit noise and intrinsic fluctuations? What parameters of the ensemble are responsible for such synchronization and regularization? Answers to these and similar questions may be found through experiments that enable one to follow qualitatively the cooperative dynamics of neurons as intrinsic and synaptic parameters are varied. Despite their interest, these problems have not received extensive study. Results of such an experiment for a minimal ensemble of two coupled, living neurons are reported in this communication. The experiment was carried out on two electrically coupled neurons (the pyloric dilators, PD) from the pyloric CPG of the lobster stomatogastric ganglion [3]. Individually, these neurons can generate spiking-bursting activity that is irregular and seemingly chaotic. This activity pattern can be altered by injecting dc current (I1 and I2) into the neurons; see Fig. 1. In parallel to their natural coupling, we added artificial coupling by a dynamic current clamp device [7]. Varying these control parameters (offset current and artificial coupling), we found the following regimes of cooperative behavior. Natural coupling produces state-dependent synchronization; see Fig. 2. (i) When depolarized by positive dc current, both neurons fire a continuous pattern of synchronized spikes (Fig. 2d). (ii) With little or no applied current, the neurons fire spikes in irregular bursts: now the slow oscillations are well synchronized while spikes are not (Fig. 2a). Changing the magnitude and sign of electrical coupling restructures the cooperative dynamics. (iii) Increasing the strength of coupling produces complete synchronization of both irregular slow oscillations and fast spikes (see below). (iv) Compensating the natural coupling leads to the onset

Transient Cognitive Dynamics, Metastability, and Decision Making

The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. The main problem faced when using dynamical theory to describe transient cognitive processes is the fundamental contradiction between reproducibility and flexibility of transient behavior. In this paper, we propose a theoretical description of transient cognitive dynamics based on the interaction of functionally dependent metastable cognitive states. The mathematical image of such transient activity is a stable heteroclinic channel, i.e., a set of trajectories in the vicinity of a heteroclinic skeleton that consists of saddles and unstable separatrices that connect their surroundings. We suggest a basic mathematical model, a strongly dissipative dynamical system, and formulate the conditions for the robustness and reproducibility of cognitive transients that satisfy the competing requirements for stability and flexibility. Based on this approach, we describe here an effective solution for the problem of sequential decision making, represented as a fixed time game: a player takes sequential actions in a changing noisy environment so as to maximize a cumulative reward. As we predict and verify in computer simulations, noise plays an important role in optimizing the gain.

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.

Mechanism for Hypocretin-mediated sleep-to-wake transitions

Current models of sleep/wake regulation posit that Hypocretin (Hcrt)-expressing neurons in the lateral hypothalamus promote and stabilize wakefulness by projecting to subcortical arousal centers. However, the critical downstream effectors of Hcrt neurons are unknown. Here we use optogenetic, pharmacological, and computational tools to investigate the functional connectivity between Hcrt neurons and downstream noradrenergic neurons in the locus coeruleus (LC) during nonrapid eye movement (NREM) sleep. We found that photoinhibiting LC neurons during Hcrt stimulation blocked Hcrt-mediated sleep-to-wake transitions. In contrast, when LC neurons were optically stimulated to increase membrane excitability, concomitant photostimulation of Hcrt neurons significantly increased the probability of sleep-to-wake transitions compared with Hcrt stimulation alone. We also built a conductance-based computational model of Hcrt-LC circuitry that recapitulates our behavioral results using LC neurons as the main effectors of Hcrt signaling. These results establish the Hcrt-LC connection as a critical integrator-effector circuit that regulates NREM sleep/wake behavior during the inactive period. This coupling of distinct neuronal systems can be generalized to other hypothalamic integrator nuclei with downstream effector/output populations in the brain.

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 stom-atogastric central pattern generator of lobster and earlier observations in other cells. In this paper we work with models of 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.

Learning classification in the olfactory system of insects

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 fo 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.

Contact tracing and epidemics control in social networks

A generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks is introduced which incorporates contact tracing in addition to random screening. We propose a deterministic mean-field description that yields quantitative agreement with stochastic simulations on random graphs. Both the stochastic simulations and the mean-field equations show secondary epidemics if the contact tracing is not performed with sufficient strength. We also analyze the role of contact tracing in epidemics control in small-world networks and show that its effectiveness grows as the rewiring probability is reduced.

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.