Inferring network dynamics and neuron properties from population recordings

Grid Cells, Border Cells and Discrete Complex Analysis

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity towards the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

Attractor competition enriches cortical dynamics during awakening from anesthesia

Slow oscillations (≲ 1 Hz), a hallmark of slow-wave sleep and deep anesthesia across species, arise from spatiotemporal patterns of activity whose complexity increases as wakefulness is approached and cognitive functions emerge. The arousal process constitutes an open window to the unknown mechanisms underlying the emergence of such dynamical richness in awake cortical networks. Here, we investigate the changes in network dynamics as anesthesia fades out in the rat visual cortex. Starting from deep anesthesia, slow oscillations gradually increase their frequency, eventually expressing maximum regularity. This stage is followed by the abrupt onset of an infra-slow (~0.2 Hz) alternation between sleep-like oscillations and activated states. A population rate model reproduces this transition driven by an increased excitability that brings it to periodically cross a critical point. Based on our model, dynamical richness emerges as a competition between two metastable attractor states, a conclusion strongly supported by the data.

Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed 'quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.

Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.

The neuronal response at extended timescales: a linearized spiking input-output relation

Many biological systems are modulated by unknown slow processes. This can severely hinder analysis – especially in excitable neurons, which are highly non-linear and stochastic systems. We show the analysis simplifies considerably if the input matches the sparse “spiky” nature of the output. In this case, a linearized spiking Input–Output (I/O) relation can be derived semi-analytically, relating input spike trains to output spikes based on known biophysical properties. Using this I/O relation we obtain closed-form expressions for all second order statistics (input – internal state – output correlations and spectra), construct optimal linear estimators for the neuronal response and internal state and perform parameter identification. These results are guaranteed to hold, for a general stochastic biophysical neuron model, with only a few assumptions (mainly, timescale separation). We numerically test the resulting expressions for various models, and show that they hold well, even in cases where our assumptions fail to hold. In a companion paper we demonstrate how this approach enables us to fit a biophysical neuron model so it reproduces experimentally observed temporal firing statistics on days-long experiments.

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.