APPLICATION OF APPROXIMATE BAYESIAN COMPUTATION FOR THE ESTIMATION OF PARAMETERS IN A MODEL FOR THE CALCIUM DYNAMICS IN NEURONS

Resumo

Ionic transfer plays an important role in several processes in the human body, in special in the electrophysiology of neurons, where the most important ions are those of potassium, sodium and calcium. The models for the dynamics of potassium and sodium are classical and well established in the literature. On the other hand, several models were proposed for the dynamics of calcium ions, such as those of Dupont and Erneux , 1997and of Dupont and Goldbetter ,1993. In fact, none of the proposed models for calcium dynamics is widely accepted and general to represent phenomena characteristic of anomalous behaviors observed in neurons, related, for example, to epilepsy. Due to the nonlinear character of these models, the values of their parameters strongly affect the predicted responses, like the transient ion concentrations, as well as the dynamics of several state variables, including the electrical current responses in voltage clamp experiments. Approximate Bayesian Computation (ABC) methods have been conceived for inferring posterior distributions where likelihood functions are computationally intractable, too costly to evaluate or not exactly known. In this work, we apply an ABC algorithm based on the Monte Carlo method (Toni et al., 2009) for the estimation of parameters appearing in the Calcium model proposed by Dupont and Goldbetter, 1993. Simulated measurements of the concentration of calcium ions in the cytosol are used for the parameter estimation.