Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels

Abstract

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems.

Multiscale Modeling Indicates That Temperature Dependent [Ca2+]iSpiking in Astrocytes Is Quantitatively Consistent with Modulated SERCA Activity

“…Our modeling strategy for this coupled system is based on separation of the two involved length scales. On the microscopic scale we use a detailed model for the channels [ 25 ]. Those will be open and close in a stochastic manner due to stochastic binding of the signaling molecules IP 3 and Ca 2+ .…”

“…The activating binding sites for Ca 2+ have a higher affinity compared to the dominant inhibiting site. This is a minimal choice to generate the nonlinearity in Ca 2+ , which is the source of the bell shaped open probability ( Figure 2(b) ) and the basis of CICR [ 25 ].…”

“…From the cytosol Ca 2+ is pumped back into the ER by SERCA that decreases diffusion. (b) From the Markov chain model of a single subunit the non-Markovian stationary open probability P o of a channel can be calculated in dependence on Ca 2+ and IP 3 concentration [ 25 ].…”