Empirical modeling and prediction of neuronal dynamics

Abstract

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.

DA has been funded by the Collaboration in University Departments AGAUR Grant (COLAB 2020). AG and EF have been partially funded by the MINECO-FEDER-UE-MTM Grant RTI2018-093860-B-C21, the Generalitat de Catalunya-AGAUR projects 2021SGR01039 (AG) and 2021SGR00376 (EF), the Grants PID-2021-122954NB-I00 and PID2022-137708NB-I00 funded by MCIN/ AEI/ 10.13039/ 501100011033 and by ERDF ‘A way of making Europe’ (AG) and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R &D (CEX2020-001084-M) (AG). We are grateful to the Institut d’Organització i Control (IOC-UPC) for the access to its high-performance computing facilities to perform all the computations of this work.

Postprint (published version)