Franck Grammont

Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time.

Abstract. We studied the dynamics of precise spike synchronization and rate modulation in a population of neurons recorded in monkey motor cortex during performance of a delayed multidirectional pointing task and determined their relation to behavior. We showed that at the population level neurons coherently synchronized their activity at various moments during the trial in relation to relevant task events. The comparison of the time course of the modulation of synchronous activity with that of the firing rate of the same neurons revealed a considerable difference. Indeed, when synchronous activity was highest, at the end of the preparatory period, firing rate was low, and, conversely, when the firing rate was highest, at movement onset, synchronous activity was almost absent. There was a clear tendency for synchrony to precede firing rate, suggesting that the coherent activation of cell assemblies may trigger the increase in firing rate in large groups of neurons, although it appeared that there was no simple parallel shifting in time of these two activity measures. Interestingly, there was a systematic relationship between the amount of significant synchronous activity within the population of neurons and movement direction at the end of the preparatory period. Furthermore, about 400 ms later, at movement onset, the mean firing rate of the same population was also significantly tuned to movement direction, having roughly the same preferred direction as synchronous activity. Finally, reaction time measurements revealed a directional preference of the monkey with, once again, the same preferred direction as synchronous activity and firing rate. These results lead us to speculate that synchronous activity and firing rate are cooperative neuronal processes and that the directional matching of our three measures – firing rate, synchronicity, and reaction times – might be an effect of behaviorally induced network cooperativity acquired during learning.

Precise spike synchronization in monkey motor cortex involved in preparation for movement

Abstract It is commonly accepted that perceptually and behaviorally relevant events are reflected in changes of activity in largely distributed neuronal populations. However, it is much less clear how these populations organize dynamically to cope with momentary computational demands. In order to decipher the dynamic organization of cortical ensembles, the activities of up to seven neurons of the primary motor cortex were recorded simultaneously. A monkey was trained to perform a pointing task in six directions. During each trial, two signals were presented consecutively. The first signal provided prior information about the movement direction, whereas the second called for the execution of that movement. Dynamic interactions between the activity of simultaneously recorded neurons were studied by analyzing individual epochs of synchronized firing (”unitary events”). Unitary events were defined as synchronizations which occur significantly more often than expected by chance on the basis of the neurons’ firing rates. The aim of the study was to describe the relationships between synchronization dynamics and changes in activity of the same neurons during the preparation and execution of voluntary movements. The data show that even neurons which were classified, on the basis of the change in their firing rate, to be functionally involved in different processes (e.g., preparation or execution related, different directional tuning) synchronized their spiking activity significantly. These findings indicate that the synchronization of individual action potentials and the modulation of the firing rate may serve different and complementary functions underlying the cortical organization of cognitive motor processes.

Multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count

The unitary events (UE) method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (Grün, 1996), which is known to be subject to loss in synchrony detection (Grün, Diesmann, Grammont, Riehle, & Aertsen, 1999). This defect has been corrected by the multiple shift coincidence count (Grün et al., 1999). The statistical properties of this count have not been further investigated until this work, the formula being more difficult to deal with than the original binned count. First, we propose a new notion of coincidence count, the delayed coincidence count, which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains. Moreover, it generalizes this notion to nondiscretized point processes, allowing us to propose a new gaussian approximation of the count. Since unknown parameters are involved in the approximation, we perform a plug-in step, where unknown parameters are replaced by estimated ones, leading to a modification of the approximating distribution. Finally the method takes the multiplicity of the tests into account via a Benjamini and Hochberg approach (Benjamini & Hochberg, 1995), to guarantee a prescribed control of the false discovery rate. We compare our new method, MTGAUE (multiple tests based on a gaussian approximation of the unitary events) and the UE method proposed in Grün et al. (1999) over various simulations, showing that MTGAUE extends the validity of the previous method. In particular, MTGAUE is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model. Furthermore MTGAUE is applied on real data.

Verification of Temporal Properties of Neuronal Archetypes Modeled as Synchronous Reactive Systems

There exists many ways to connect two, three or more neurons together to form different graphs. We call archetypes only the graphs whose properties can be associated with specific classes of biologically relevant structures and behaviors. These archetypes are supposed to be the basis of typical instances of neuronal information processing. To model different representative archetypes and express their temporal properties, we use a synchronous programming language dedicated to reactive systems (Lustre). The properties are then automatically validated thanks to several model checkers supporting data types. The respective results are compared and depend on their underlying abstraction methods.

Computer-aided Formal Proofs about Dendritic Integration within a Neuron

This article is threefold: (i) we define the first formal framework able to model dendritic integration within biological neurons, (ii) we show how we can turn continuous time into discrete time consistently and (iii) we show how a Lustre model checker can automatically perform proofs about neuron input/output behaviours owing to our framework. Our innovative formal framework is a carefully defined trade-off between abstraction and biological relevance in order to facilitate proofs. This framework is hybrid: inputs entering the synapses as well as the soma output are discrete signals made of spikes but, inside the dendrites, we combine signals quantitatively using real numbers. The soma potential is inevitably specified as a differential equation to keep a biologically accurate modelling of signal accumulation. This prevents from performing simple formal proofs. This has been our motivation to discretize time. Owing to this discretization, we are able to encode our neuron models in Lustre. Lustre is a particularly well suited flow-based language for our purpose. We also encode in Lustre a property of input/output equivalence between neurons in such a way that the model checker Kind2 is able to automatically handle the proof.

Modelling and Formal Verification of Neuronal Archetypes Coupling

In the literature, neuronal networks are often represented as graphs where each node symbolizes a neuron and each arc stands for a synaptic connection. Some specific neuronal graphs have biologically relevant structures and behaviors and we call them archetypes. Six of them have already been characterized and validated using formal methods. In this work, we tackle the next logical step and proceed to the study of the properties of their couplings. For this purpose, we rely on Leaky Integrate and Fire neuron modeling and we use the synchronous programming language Lustre to implement the neuronal archetypes and to formalize their expected properties. Then, we exploit an associated model checker called kind2 to automatically validate these behaviors. We show that, when the archetypes are coupled, either these behaviors are slightly modulated or they give way to a brand new behavior. We can also observe that different archetype couplings can give rise to strictly identical behaviors. Our results show that time coding modeling is more suited than rate coding modeling for this kind of studies.

Parallel and pseudorandom discrete event system specification vs. networks of spiking neurons: Formalization and preliminary implementation results

Usual Parallel Discrete Event System Specification (P-DEVS) allows specifying systems from modeling to simulation. However, the framework does not incorporate parallel and stochastic simulations. This work intends to extend P-DEVS to parallel simulations and pseudorandom number generators in the context of a spiking neural network. The discrete event specification presented here makes explicit and centralized the parallel computation of events as well as their routing, making further implementations easier. It is then expected to dispose of a well defined mathematical and computational framework to deal with networks of spiking neurons.