Three-state, Steady-state Ising Systems: Monte Carlo and Bragg-Williams Treatments

Overview

Journal Proc Natl Acad Sci U S A

Specialty Science

Date 1981 Jan 1

PMID 16592956

Citations 1

Authors

T L Hill

Y D Chen

Affiliations

Soon will be listed here.

Abstract

In two earlier papers, the steady-state critical and phase-transition properties of a lattice of three-state enzyme molecules were studied by using the "closed" Bragg-Williams (BW), or mean field, approximation. The "open" BW and Monte Carlo methods are applied to the same problem in this paper by using finite lattices. The open BW treatment provides a way of locating the cut across a van der Waals type of loop encountered in a phase transition in the closed BW system. Thermodynamic-like methods cannot be used for this purpose as they can with two-state, steady-state systems.

Citing Articles

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

Liu Y, Dilger J Biophys J. 1993; 64(1):26-35.

PMID: 7679298 PMC: 1262299. DOI: 10.1016/S0006-3495(93)81337-7.

References

Hill T, Stein L . Properties of some three-state, steady-state Ising systems, according to the Bragg-Williams approximation. Proc Natl Acad Sci U S A. 1980; 77(2):693-7. PMC: 348346. DOI: 10.1073/pnas.77.2.693. View

Hill T, Stein L . Approximate steady-state properties of lattices of interacting three-state enzyme molecules: a novel phase transition. Proc Natl Acad Sci U S A. 1979; 76(3):1014-7. PMC: 383177. DOI: 10.1073/pnas.76.3.1014. View

Hill T, Chen Y . Interacting enzyme systems at steady state: further Monte Carlo calculations on two-state molecules. Proc Natl Acad Sci U S A. 1978; 75(11):5260-3. PMC: 392940. DOI: 10.1073/pnas.75.11.5260. View

Hill T, Chen Y . Interacting enzyme systems at steady state: location of the phase transition in approximations of the mean field type. Proc Natl Acad Sci U S A. 1978; 75(7):3015-8. PMC: 392702. DOI: 10.1073/pnas.75.7.3015. View

Hill T . Further study of the effect of enzyme-enzyme interactions on steady-state enzyme kinetics. Proc Natl Acad Sci U S A. 1977; 74(10):4111-5. PMC: 431885. DOI: 10.1073/pnas.74.10.4111. View