Statistical analysis of channel current from a membrane patch. I. Some stochastic properties of ion channels or molecular systems in equilibrium

The stochastic behavior of single-channel current in a steady-state has been interpreted as the channel's state transitions between several open and shut states, and these transitions have been regarded as a homogeneous Markov process. When a channel is in equilibrium, the principle of detailed balance holds for every step in the state transition scheme. Here we show two stochastic properties of a channel, or any molecule obeying a reversible state transition scheme, under the constraint of detailed balance. First, the distribution functions and the probability density functions of shut or open dwell-time are expressed by the sum of exponential terms with positive coefficients. The same holds for the time-dependent open (or shut) frequency after the shut (or open) transition. Second, the time course of state transition from the state SI to SJ (PI,J(t] is proportional to its reverse transition time course (PJ,I(t], even if SI and SJ are widely separated. The same relation holds also for a transition scheme having transition pathways to the absorbing states. If analysis of a channel current record shows it to be incompatible with either of these two properties, the channel is not in equilibrium but in a steady-state with an energy-consuming cyclic flow. These two properties are also useful for the analysis of any molecular process obeying a homogeneous Markov process or a network of first-order chemical reactions.