Application of the one- and two-dimensional Ising models to studies of cooperativity between ion channels

26Citations
Citations of this article
25Readers
Mendeley users who have this article in their library.

Abstract

The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels. © 1993, The Biophysical Society. All rights reserved.

Cite

CITATION STYLE

APA

Liu, Y., & Dilger, J. P. (1993). Application of the one- and two-dimensional Ising models to studies of cooperativity between ion channels. Biophysical Journal, 64(1), 26–35. https://doi.org/10.1016/S0006-3495(93)81337-7

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free