RESUMEN
In a series of previous studies, we provided a stochastic description of a theory of synaptic plasticity. This theory, called BCM from the names of the three authors, has been formulated in two ways: the original formulation, where the plasticity threshold is defined as the square of the time-averaged neuronal activity, and a newer formulation, where the plasticity threshold is defined as the time average of the square of the neuronal activity. The newest formulation of the BCM rule of synaptic activity has interesting statistical properties, derived from a risk (or energy) function, the minimization of which leads to seeking of interesting projections in high-dimensional space. Moreover, these two rules, if implemented by a chemical master equation approach, show another interesting difference: the original rule satisfies the detailed balance, whereas the other not. Based on this different behavior, we found a continuous parameterization between these two rules. This parameterization shows a minimum that corresponds to maximum negative eigenvalues of the Jacobian matrix. In addition, the newest rule, due to the fact that it is in a nonequilibrium steady state (NESS), shows a higher level of plasticity than the original rule. This higher level of plasticity has to be interpreted in the framework of open thermodynamical systems and we show that entropy production and energy consumption in the newest rule are both less than in the original BCM rule.
Asunto(s)
Plasticidad Neuronal/fisiología , Neuronas/fisiología , Entropía , TermodinámicaRESUMEN
We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their "far from equilibrium behavior," hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative "external vector field" whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the "plasticity property" of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.