Sami El Boustani

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin–Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.

A master equation formalism for macroscopic modeling of asynchronous irregular activity states

Many efforts have been devoted to modeling asynchronous irregular (AI) activity states, which resemble the complex activity states seen in the cerebral cortex of awake animals. Most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which AI states are sustained through recurrent sparse connectivity, with or without external input. In this letter we propose a mesoscopic description of such AI states. Using master equation formalism, we derive a second-order mean-field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks. This formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized. We compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces. Considering the randomly connected network as a unit, this approach could be used to build large-scale networks of such connected units, with an aim to model activity states constrained by macroscopic measurements, such as voltage-sensitive dye imaging.

Network-state modulation of power-law frequency-scaling in visual cortical neurons.

Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of Vm activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the Vm reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the “effective” connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI.

Correlated input reveals coexisting coding schemes in a sensory cortex

As in other sensory modalities, one function of the somatosensory system is to detect coherence and contrast in the environment. To investigate the neural bases of these computations, we applied different spatiotemporal patterns of stimuli to rat whiskers while recording multiple neurons in the barrel cortex. Model-based analysis of the responses revealed different coding schemes according to the level of input correlation. With uncorrelated stimuli on 24 whiskers, we identified two distinct functional categories of neurons, analogous in the temporal domain to simple and complex cells of the primary visual cortex. With correlated stimuli, however, a complementary coding scheme emerged: two distinct cell populations, similar to reinforcing and antagonist neurons described in the higher visual area MT, responded specifically to correlations. We suggest that similar context-dependent coexisting coding strategies may be present in other sensory systems to adapt sensory integration to specific stimulus statistics.

Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons

The relationship between the dynamics of neural networks and their patterns of connectivity is far from clear, despite its importance for understanding functional properties. Here, we have studied sparsely-connected networks of conductance-based integrate-and-fire (IF) neurons with balanced excitatory and inhibitory connections and with finite axonal propagation speed. We focused on the genesis of states with highly irregular spiking activity and synchronous firing patterns at low rates, called slow Synchronous Irregular (SI) states. In such balanced networks, we examined the “macroscopic” properties of the spiking activity, such as ensemble correlations and mean firing rates, for different intracortical connectivity profiles ranging from randomly connected networks to networks with Gaussian-distributed local connectivity. We systematically computed the distance-dependent correlations at the extracellular (spiking) and intracellular (membrane potential) levels between randomly assigned pairs of neurons. The main finding is that such properties, when they are averaged at a macroscopic scale, are invariant with respect to the different connectivity patterns, provided the excitatory-inhibitory balance is the same. In particular, the same correlation structure holds for different connectivity profiles. In addition, we examined the response of such networks to external input, and found that the correlation landscape can be modulated by the mean level of synchrony imposed by the external drive. This modulation was found again to be independent of the external connectivity profile. We conclude that first and second-order “mean-field” statistics of such networks do not depend on the details of the connectivity at a microscopic scale. This study is an encouraging step toward a mean-field description of topological neuronal networks.

Stable Learning in Stochastic Network States

The mammalian cerebral cortex is characterized in vivo by irregular spontaneous activity, but how this ongoing dynamics affects signal processing and learning remains unknown. The associative plasticity rules demonstrated in vitro, mostly in silent networks, are based on the detection of correlations between presynaptic and postsynaptic activity and hence are sensitive to spontaneous activity and spurious correlations. Therefore, they cannot operate in realistic network states. Here, we present a new class of spike-timing-dependent plasticity learning rules with local floating plasticity thresholds, the slow dynamics of which account for metaplasticity. This novel algorithm is shown to both correctly predict homeostasis in synaptic weights and solve the problem of asymptotic stable learning in noisy states. It is shown to naturally encompass many other known types of learning rule, unifying them into a single coherent framework. The mixed presynaptic and postsynaptic dependency of the floating plasticity threshold is justified by a cascade of known molecular pathways, which leads to experimentally testable predictions.

Spatial organization of evoked neuronal dynamics in 2D recurrent networks, with or without structured stimulation

Neuronal dynamics in the awake mammalian cortex are known to display highly irregular spiking activity and asynchronous firing patterns at the population level (AI regime). Many computational models have proposed simplified benchmarks to investigate information propagation in such regimes [1]. However, to allow explicit analytical analysis, most of them assume random connectivity within the network, no propagation delays and unstructured Poisson external input [2]. In particular, for AI regimes, these models do not exhibit any substantial spatial correlations [3]. In contrast, in biological V1, it has been observed that the large-scale dynamics produced by ongoing reverberation correspond to spatially structured activity maps characterized by distance-dependent correlations [4,5]. A realistic model of sensory neocortex should thus take into account the presence of intrinsic spatial correlation in order to study how this may interfere with structured correlation evoked by the sensory drive.

Mesoscopic model of balanced neuron networks using a Master equation formalism

Cortical activity in awake animals manifests highly complex behaviour [1]. It is during this regime that the main computational tasks are performed and no model is yet able to explain how this complex dynamics is exploited to provide a fast and accurate information processing. However, many efforts have been devoted to the study of how such activity emerges. Balanced networks have been introduced as a possible model to generate dynamical states similar to the biological ones [2]. The stability of such states was studied for current-based Integrate-And-Fire (IAF) neurons with respect to external input and excitatory-inhibitory synaptic strength ratio [3]. In particular, stable asynchronous irregular (AI) states with a relatively low level of activity have been obtained. Recently, AI states have been observed in balanced networks of conductance-based IAF neurons with self-sustained activity [4]. However, no simple description of the network activity dynamics has been developed yet. First-order mean-field approximation fails to describe these networks because of their inherent dynamics which rely dramatically on activity fluctuations. Moreover, the thermodynamic limit is usually performed for randomly connected networks despite the lack of biological relevance. We introduce here a new framework in which network dynamics as well as inherent neuron behaviour is taken into account. We aim to obtain a reduced description of mesoscopic balanced networks where finite size effects are not neglected. The model is intended to describe AI states far from critical boundaries where long-term behaviours appear. Furthermore, we set the spatial and temporal scales of the model by using biological data. Using the master equation formalism, we derive a second-order mean-field set of ordinary differential equations. The transition matrix necessary in the master equation context is computed based on the Fokker-Plank approach. Conductance-based as well as current-based IAF neurons are constructed. The kernel of this formalism lays in the way activity micro-fluctuations are modelled. We discuss different possibilities and considerations in regard to this question. This model provides at the same time an extracellular and a sub-threshold description of finite size neuron networks. Once the couplings will be adjusted, it will be possible to build a large-scale model of cortical area with specific architectures, where the fundamental unit is the randomly connected network. We further discuss the possibility to compare large-scale behaviour observed in voltage-sensitive dyes experiments with our model.