Possible forms for dwell-time histograms from single-channel current records

Time-irreversible subconductance gating associated with Ba2+ block of large conductance Ca2+-activated K+ channels

Ba2+ block of large conductance Ca2+-activated K+ channels was studied in patches of membrane excised from cultures of rat skeletal muscle using the patch clamp technique. Under conditions in which a blocking Ba2+ ion would dissociate to the external solution (150 mM N-methyl-D-glucamine+o, 500 mM K+i, 10 microM Ba2+i, +30 mV, and 100 microM Ca2+i to fully activate the channel), Ba2+ blocks with a mean duration of approximately 2 s occurred, on average, once every approximately 100 ms of channel open time. Of these Ba2+ blocks, 78% terminated with a single step in the current to the fully open level and 22% terminated with a transition to a subconductance level at approximately 0.26 of the fully open level (preopening) before stepping to the fully open level. Only one apparent preclosing was observed in approximately 10,000 Ba2+ blocks. Thus, the preopenings represent Ba2+-induced time-irreversible subconductance gating. The fraction of Ba2+ blocks terminating with a preopening and the duration of preopenings (exponentially distributed, mean = 0.75 ms) appeared independent of changes in [Ba2+]i or membrane potential. The fractional conductance of the preopenings increased from 0.24 at +10 mV to 0.39 at +90 mV. In contrast, the average subconductance level during normal gating in the absence of Ba2+ was independent of membrane potential, suggesting different mechanisms for preopenings and normal subconductance levels. Preopenings were also observed with 10 mM Ba2+o and no added Ba2+i. Adding K+, Rb+, or Na+ to the external solution decreased the fraction of Ba2+ blocks with preopenings, with K+ and Rb+ being more effective than Na+. These results are consistent with models in which the blocking Ba2+ ion either induces a preopening gate, and then dissociates to the external solution, or moves to a site located on the external side of the Ba2+ blocking site and acts directly as the preopening gate.

Testing for microscopic reversibility in the gating of maxi K+ channels using two-dimensional dwell-time distributions

An assumption usually made when developing kinetic models for the gating of ion channels is that the transitions among the various states involved in the gating obey microscopic reversibility. If this assumption is incorrect, then the models and estimated rate constants made with the assumption would be in error. This paper examines whether the gating of a large conductance Ca-activated K+ channel in skeletal muscle is consistent with microscopic reversibility. If microscopic reversibility is obeyed, then the number of forward and backward transitions per unit time for each individual reaction step will, on average, be identical and, consequently, the gating must show time reversibility. To look for time reversibility, two-dimensional dwell-time distributions of the durations of open and closed intervals were obtained from single-channel current records analyzed in the forward and in the backward directions. Two-dimensional dwell-time distributions of pairs of open intervals and of pairs of closed intervals were also analyzed to extend the resolution of the method to special circumstances in which intervals from different closed (or open) states might have similar durations. No significant differences were observed between the forward and backward analysis of the two-dimensional dwell-time distributions, suggesting time reversibility. Thus, we find no evidence to indicate that the gating of the maxi K+ channel violates microscopic reversibility.

Stochastic models for ion channels: introduction and bibliography

This paper provides an introduction to and overview of the use of stochastic models and statistical analysis in the study of ion channels in cell membranes. An extensive bibliography is included.

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.