Premium
A reevaluation of the mathematical models for simulating single‐channel and whole‐cell ionic currents
Author(s) -
Millhauser Glenn L.,
Oswald Robert E.
Publication year - 1988
Publication title -
synapse
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 106
eISSN - 1098-2396
pISSN - 0887-4476
DOI - 10.1002/syn.890020113
Subject(s) - expression (computer science) , eigenvalues and eigenvectors , channel (broadcasting) , kinetic scheme , ionic bonding , markov process , simple (philosophy) , kinetic energy , master equation , computer science , statistical physics , markov chain , mathematics , process (computing) , ion , physics , classical mechanics , telecommunications , philosophy , statistics , quantum mechanics , epistemology , machine learning , quantum , programming language , operating system
We have developed a technique that allows for the simulation of both single‐channel and whole cell ionic currents given any arbitrary first‐order kinetic scheme for the conformational states of an ion channel. The procedure is based on the solution of the master equation, which, in turn, is a general expression for a Markov process. The solution is expressed in terms of the eigenvalues and eigenvectors of the kinetic system and the system's deviation from equilibrium. Our derived expression provides a general recipe for the calculation of whole‐cell currents. By further manipulation of this expression, we show how conditional probabilities are derived that can be used for the simulation of single‐channel currents. We discuss computer implementation of the results so that complicated kinetic schemes can be solved numerically. Finally, we demonstrate the procedure by providing a worked example of a simple model of activation followed by inactivation.