Transcending Markov: Non-Markovian Rate Processes of Thermosensitive TRP Ion Channels

Abstract

The Markov state model (MSM) is a popular theoretical tool for describing the hierarchy of time scales involved in the function of many proteins especially ion channel gating. A MSM is a particular case of the general non-Markovian model, where the rate of transition from one state to another does not depend on the history of state occupancy within the system, i.e., it only includes reversible, non-dissipative processes. However, this requires knowledge of the precise conformational state of the protein and is not predictive when those details are not known. In the case of ion channels, this simple description fails in real (non-equilibrium) situations, for example when local temperature changes, or when energy losses occur during channel gating. Here, we show it is possible to use non-Markovian equations (i.e. offer a general description that includes the MSM as a particular case) to develop a relatively simple analytical model that describes the non-equilibrium behavior of the temperature-sensitive TRP ion channels, TRPV1 and TRPM8. This model accurately predicts asymmetrical opening and closing rates, infinite processes, and the creation of new states, as well as the effect of temperature changes throughout the process. This approach therefore overcomes the limitations of the MSM and allows us to go beyond a mere phenomenological description of the dynamics of ion channel gating towards a better understanding of the physics underlying these processes. Significance StatementModeling ion channel processes has long relied on the Markovian assumption. However, Markov theory cannot translate situations in which the physical state of an ion channel changes during its gating process. By using a non-Markovian approach, we develop a simple analytical model that describes the non-equilibrium behavior of two temperature-sensitive TRP channels, TRPV1 and TRPM8. This model accurately describes and predicts their biophysical behavior as well as their temperature dependence. This approach therefore provides a better understanding of the physics underlying dynamic conformational changes such as those that occur during ion channel gating.