Size effects on the open probability of two-state ion channel system in cell membranes using microcanonical formalism based on gamma function

Abstract

Ion channel systems are a class of proteins that reside in the membranes of all biological cells and forms conduction pores that regulate the transport of ions into and out of cells. They can be investigated theoretically in the microcanonical formalism since the number of accessible states can be easily evaluated by using the Stirling approximation to deal with factorials. In this work, we have used gamma function (Gamma (n)) to solve the two-state or open-close channel model without any approximation. New values are calculated for the open probability (p(0)) and the relative error between our numerical results and the approximate one using Stirling formula is presented. This error (p(0)(app) p(0))/p(0) is significant for small channel systems.