Maurizio Mattia

Efficient Event-Driven Simulation of Large Networks of Spiking Neurons and Dynamical Synapses

A simulation procedure is described for making feasible large-scale simulations of recurrent neural networks of spiking neurons and plastic synapses. The procedure is applicable if the dynamic variables of both neurons and synapses evolve deterministically between any two successive spikes. Spikes introduce jumps in these variables, and since spike trains are typically noisy, spikes introduce stochasticity into both dynamics. Since all events in the simulation are guided by the arrival of spikes, at neurons or synapses, we name this procedure event-driven. The procedure is described in detail, and its logic and performance are compared with conventional (synchronous) simulations. The main impact of the new approach is a drastic reduction of the computational load incurred upon introduction of dynamic synaptic efficacies, which vary organically as a function of the activities of the pre- and postsynaptic neurons. In fact, the computational load per neuron in the presence of the synaptic dynamics grows linearly with the number of neurons and is only about 6 more than the load with fixed synapses. Even the latter is handled quite efficiently by the algorithm. We illustrate the operation of the algorithm in a specific case with integrate-and-fire neurons and specific spike-driven synaptic dynamics. Both dynamical elements have been found to be naturally implementable in VLSI. This network is simulated to show the effects on the synaptic structure of the presentation of stimuli, as well as the stability of the generated matrix to the neural activity it induces.

Collective behavior of networks with linear (VLSI) integrate-and-fire neurons

We analyze in detail the statistical properties of the spike emission process of a canonical integrate-and-fire neuron, with a linear integrator and a lower bound for the depolarization, as often used in VLSI implementations (Mead, 1989). The spike statistics of such neurons appear to be qualitatively similar to conventional (exponential) integrate-and-fire neurons, which exhibit a wide variety of characteristics observed in cortical recordings. We also show that, contrary to current opinion, the dynamics of a network composed of such neurons has two stable fixed points, even in the purely excitatory network, corresponding to two different states of reverberating activity. The analytical results are compared with numerical simulations and are found to be in good agreement.

Inhibitory Modulation of Cortical Up States

The balance between excitation and inhibition is critical in the physiology of the cerebral cortex. To understand the influence of inhibitory control on the emergent activity of the cortical network, inhibition was progressively blocked in a slice preparation that generates spontaneous rhythmic up states at a similar frequency to those occurring in vivo during slow-wave sleep or anesthesia. Progressive removal of inhibition induced a parametric shortening of up state duration and elongation of the down states, the frequency of oscillations decaying. Concurrently, a gradual increase in the network firing rate during up states occurred. The slope of transitions between up and down states was quantified for different levels of inhibition. The slope of upward transitions reflects the recruitment of the local network and was progressively increased when inhibition was decreased, whereas the speed of activity propagation became faster. Removal of inhibition eventually resulted in epileptiform activity. Whereas gradual reduction of inhibition induced linear changes in up/down states and their propagation, epileptiform activity was the result of a nonlinear transformation. A computational network model showed that strong recurrence plus activity-dependent hyperpolarizing currents were sufficient to account for the observed up state modulations and predicted an increase in activity-dependent hyperpolarization following up states when inhibition was decreased, which was confirmed experimentally.

Bistable perception modeled as competing stochastic integrations at two levels.

We propose a novel explanation for bistable perception, namely, the collective dynamics of multiple neural populations that are individually meta-stable. Distributed representations of sensory input and of perceptual state build gradually through noise-driven transitions in these populations, until the competition between alternative representations is resolved by a threshold mechanism. The perpetual repetition of this collective race to threshold renders perception bistable. This collective dynamics – which is largely uncoupled from the time-scales that govern individual populations or neurons – explains many hitherto puzzling observations about bistable perception: the wide range of mean alternation rates exhibited by bistable phenomena, the consistent variability of successive dominance periods, and the stabilizing effect of past perceptual states. It also predicts a number of previously unsuspected relationships between observable quantities characterizing bistable perception. We conclude that bistable perception reflects the collective nature of neural decision making rather than properties of individual populations or neurons.

Slow and fast rhythms generated in the cerebral cortex of the anesthetized mouse

A characterization of the oscillatory activity in the cerebral cortex of the mouse was realized under ketamine anesthesia. Bilateral recordings were obtained from deep layers of primary visual, somatosensory, motor, and medial prefrontal cortex. A slow oscillatory activity consisting of up and down states was detected, the average frequency being 0.97 Hz in all areas. Different parameters of the oscillation were estimated across cortical areas, including duration of up and down states and their variability, speed of state transitions, and population firing rate. Similar values were obtained for all areas except for prefrontal cortex, which showed significant faster down-to-up state transitions, higher firing rate during up states, and more regular cycles. The wave propagation patterns in the anteroposterior axis in motor cortex and the mediolateral axis in visual cortex were studied with multielectrode recordings, yielding speed values between 8 and 93 mm/s. The firing of single units was analyzed with respect to the population activity. The most common pattern was that of neurons firing in >90% of the up states with 1-6 spikes. Finally, fast rhythms (beta, low gamma, and high gamma) were analyzed, all of them showing significantly larger power during up states than in down states. Prefrontal cortex exhibited significantly larger power in both beta and gamma bands (up to 1 order of magnitude larger in the case of high gamma) than the rest of the cortical areas. This study allows us to carry out interareal comparisons and provides a baseline to compare against cortical emerging activity from genetically altered animals.

Temperature modulation of slow and fast cortical rhythms.

In the local cortical network, spontaneous emergent activity self-organizes in rhythmic patterns. These rhythms include a slow one (<1 Hz), consisting in alternation of up and down states, and also faster rhythms (10-80 Hz) generated during up states. Varying the temperature in the bath between 26 and 41 degrees C resulted in a strong modulation of the emergent network activity. Up states became shorter for warmer temperatures and longer with cooling, whereas down states were shortest at physiological (36-37 degrees C) temperature. The firing rate during up states was robustly modulated by temperature, increasing with higher temperatures. The sparse firing rate during down states hardly varied with temperature, thus resulting in a progressive merging of up and down states for temperatures around 30 degrees C. Below 30 degrees C and down to 26 degrees C the firing lost rhythmicity, becoming progressively continuous. The slope of the down-to-up transitions, which reflects the speed of recruitment of the local network, was progressively steeper for higher temperatures, whereas wave-propagation speed exhibited only a moderate increase. Fast rhythms were particularly sensitive to temperature. Broadband high-frequency fluctuations in the local field potential were maximal for recordings at 36-38 degrees C. Overall, we found that maintaining cortical slices at physiological temperature is critical for the generated activity to be analogous to that in vivo. We also demonstrate that changes in activity with temperature were not secondary to oxygenation changes. Temperature variation sets the in vitro cortical network at different functional regimes, allowing the exploration of network activity generation and control mechanisms.

Stop-event-related potentials from intracranial electrodes reveal a key role of premotor and motor cortices in stopping ongoing movements

In humans, the ability to withhold manual motor responses seems to rely on a right-lateralized frontal–basal ganglia–thalamic network, including the pre-supplementary motor area and the inferior frontal gyrus (IFG). These areas should drive subthalamic nuclei to implement movement inhibition via the hyperdirect pathway. The output of this network is expected to influence those cortical areas underlying limb movement preparation and initiation, i.e., premotor (PMA) and primary motor (M1) cortices. Electroencephalographic (EEG) studies have shown an enhancement of the N200/P300 complex in the event-related potentials (ERPs) when a planned reaching movement is successfully stopped after the presentation of an infrequent stop-signal. PMA and M1 have been suggested as possible neural sources of this ERP complex but, due to the limited spatial resolution of scalp EEG, it is not yet clear which cortical areas contribute to its generation. To elucidate the role of motor cortices, we recorded epicortical ERPs from the lateral surface of the fronto-temporal lobes of five pharmacoresistant epileptic patients performing a reaching version of the countermanding task while undergoing presurgical monitoring. We consistently found a stereotyped ERP complex on a single-trial level when a movement was successfully cancelled. These ERPs were selectively expressed in M1, PMA, and Brodmanns area (BA) 9 and their onsets preceded the end of the stop process, suggesting a causal involvement in this executive function. Such ERPs also occurred in unsuccessful-stop (US) trials, that is, when subjects moved despite the occurrence of a stop-signal, mostly when they had long reaction times (RTs). These findings support the hypothesis that motor cortices are the final target of the inhibitory command elaborated by the frontal–basal ganglia–thalamic network.

A Fluctuation-Driven Mechanism for Slow Decision Processes in Reverberant Networks

The spike activity of cells in some cortical areas has been found to be correlated with reaction times and behavioral responses during two-choice decision tasks. These experimental findings have motivated the study of biologically plausible winner-take-all network models, in which strong recurrent excitation and feedback inhibition allow the network to form a categorical choice upon stimulation. Choice formation corresponds in these models to the transition from the spontaneous state of the network to a state where neurons selective for one of the choices fire at a high rate and inhibit the activity of the other neurons. This transition has been traditionally induced by an increase in the external input that destabilizes the spontaneous state of the network and forces its relaxation to a decision state. Here we explore a different mechanism by which the system can undergo such transitions while keeping the spontaneous state stable, based on an escape induced by finite-size noise from the spontaneous state. This decision mechanism naturally arises for low stimulus strengths and leads to exponentially distributed decision times when the amount of noise in the system is small. Furthermore, we show using numerical simulations that mean decision times follow in this regime an exponential dependence on the amplitude of noise. The escape mechanism provides thus a dynamical basis for the wide range and variability of decision times observed experimentally.

Heterogeneous Attractor Cell Assemblies for Motor Planning in Premotor Cortex

Cognitive functions like motor planning rely on the concerted activity of multiple neuronal assemblies underlying still elusive computational strategies. During reaching tasks, we observed stereotyped sudden transitions (STs) between low and high multiunit activity of monkey dorsal premotor cortex (PMd) predicting forthcoming actions on a single-trial basis. Occurrence of STs was observed even when movement was delayed or successfully canceled after a stop signal, excluding a mere substrate of the motor execution. An attractor model accounts for upward STs and high-frequency modulations of field potentials, indicative of local synaptic reverberation. We found in vivo compelling evidence that motor plans in PMd emerge from the coactivation of such attractor modules, heterogeneous in the strength of local synaptic self-excitation. Modules with strong coupling early reacted with variable times to weak inputs, priming a chain reaction of both upward and downward STs in other modules. Such web of “flip-flops” rapidly converged to a stereotyped distributed representation of the motor program, as prescribed by the long-standing theory of associative networks.

Robust Working Memory in an Asynchronously Spiking Neural Network Realized with Neuromorphic VLSI

We demonstrate bistable attractor dynamics in a spiking neural network implemented with neuromorphic VLSI hardware. The on-chip network consists of three interacting populations (two excitatory, one inhibitory) of leaky integrate-and-fire (LIF) neurons. One excitatory population is distinguished by strong synaptic self-excitation, which sustains meta-stable states of “high” and “low”-firing activity. Depending on the overall excitability, transitions to the “high” state may be evoked by external stimulation, or may occur spontaneously due to random activity fluctuations. In the former case, the “high” state retains a “working memory” of a stimulus until well after its release. In the latter case, “high” states remain stable for seconds, three orders of magnitude longer than the largest time-scale implemented in the circuitry. Evoked and spontaneous transitions form a continuum and may exhibit a wide range of latencies, depending on the strength of external stimulation and of recurrent synaptic excitation. In addition, we investigated “corrupted” “high” states comprising neurons of both excitatory populations. Within a “basin of attraction,” the network dynamics “corrects” such states and re-establishes the prototypical “high” state. We conclude that, with effective theoretical guidance, full-fledged attractor dynamics can be realized with comparatively small populations of neuromorphic hardware neurons.