Empirical modeling and prediction of neuronal dynamics.

Mathematical modeling of neuronal dynamics has experienced a fast growth in the last decades thanks to the biophysical formalism introduced by Hodgkin and Huxley in the 1950s. Other types of models (for instance, integrate and fire models), although less realistic, have also contributed to understand neuronal dynamics. However, there is still a vast volume of data that have not been associated with a mathematical model, mainly because data are acquired more rapidly than they can be analyzed or because it is difficult to analyze (for instance, if the number of ionic channels involved is huge). Therefore, developing new methodologies to obtain mathematical or computational models associated with data (even without previous knowledge of the source) can be helpful to make future predictions. Here, we explore the capability of a wavelet neural network to identify neuronal (single-cell) dynamics. We present an optimized computational scheme that trains the ANN with biologically plausible input currents. We obtain successful identification for data generated from four different neuron models when using all variables as inputs of the network. We also show that the empiric model obtained is able to generalize and predict the neuronal dynamics generated by variable input currents different from those used to train the artificial network. In the more realistic situation of using only the voltage and the injected current as input data to train the network, we lose predictive ability but, for low-dimensional models, the results are still satisfactory. We understand our contribution as a first step toward obtaining empiric models from experimental voltage traces.

High-Density Exploration of Activity States in a Multi-Area Brain Model.

To simulate whole brain dynamics with only a few equations, biophysical, mesoscopic models of local neuron populations can be connected using empirical tractography data. The development of mesoscopic mean-field models of neural populations, in particular, the Adaptive Exponential (AdEx mean-field model), has successfully summarized neuron-scale phenomena leading to the emergence of global brain dynamics associated with conscious (asynchronous and rapid dynamics) and unconscious (synchronized slow-waves, with Up-and-Down state dynamics) brain states, based on biophysical mechanisms operating at cellular scales (e.g. neuromodulatory regulation of spike-frequency adaptation during sleep-wake cycles or anesthetics). Using the Virtual Brain (TVB) environment to connect mean-field AdEx models, we have previously simulated the general properties of brain states, playing on spike-frequency adaptation, but have not yet performed detailed analyses of other parameters possibly also regulating transitions in brain-scale dynamics between different brain states. We performed a dense grid parameter exploration of the TVB-AdEx model, making use of High Performance Computing. We report a remarkable robustness of the effect of adaptation to induce synchronized slow-wave activity. Moreover, the occurrence of slow waves is often paralleled with a closer relation between functional and structural connectivity. We find that hyperpolarization can also generate unconscious-like synchronized Up and Down states, which may be a mechanism underlying the action of anesthetics. We conclude that the TVB-AdEx model reveals large-scale properties identified experimentally in sleep and anesthesia.