Statistical Mechanics of Monod–Wyman–Changeux (MWC) Models

Abstract

The 50th anniversary of the classic Monod–Wyman–Changeux (MWC) model provides an opportunity to survey the broader conceptual and quantitative implications of this quintessential biophysical model. With the use of statistical mechanics, the mathematical implementation of the MWC concept links problems that seem otherwise to have no ostensible biological connection including ligand–receptor binding, ligand-gated ion channels, chemotaxis, chromatin structure and gene regulation. Hence, a thorough mathematical analysis of the MWC model can illuminate the performance limits of a number of unrelated biological systems in one stroke. The goal of our review is twofold. First, we describe in detail the general physical principles that are used to derive the activity of MWC molecules as a function of their regulatory ligands. Second, we illustrate the power of ideas from information theory and dynamical systems for quantifying how well the output of MWC molecules tracks their sensory input, giving a sense of the “design” constraints faced by these receptors.

From conformational spread to allosteric and cooperative models of E. coli flagellar motor

“…The notation and the general scheme has been borrowed from [7]. On the right, the coupling energy: the "ferromagnetic" coupling (independent of ) accounts for the high sensitivity of the response of the ring upon binding.…”

“…The net effect of the fast coarsening dynamics is included in an effective way into rates, denoted by K c , which provide the description of the dynamics at the nucleation time scale: a concerted transition between the two coherent configurations I (all protomers inactive, σ i = −1) and A (all active, σ i = 1), besides slow binding processes. In this model, the N -protomer complex can be in 2 different activity states, each of which present in 2 N binding configurations (2 for each protomer): therefore, the model contains 2 × 2 N states, and corresponds to the concerted allosteric model of Monod, Wyman and Changeux (MWC) [6,7]. The structure of the state diagram of the MWC model with its rates K c is depicted in Fig.…”

The role of DNA sequence in nucleosome breathing

“…Therefore, we restrict ourselves in this study to comparison with the older results. Moreover, various computational models for site exposure exist [45,[49][50][51][52][53][54][55][56] but cannot be used for the current study because they do not account for sequence effects. There are two exceptions: the first exception is ref.…”

On the capacity of diffusion-based molecular communications with SiNW FET-based receiver

“…In this paper, we develop an information theoretical model for a memoryless MC system equipped with the proposed SiNW FET-based MC receiver. We derive analytical closed-form expressions for the MC capacity and capacity-achieving input distribution, following the methodology of [8]. The resulting expressions incorporate the effect of transmitter, channel and receiver parameters, and could be used for optimizing the information flow in MC systems including nanobioelectronic receivers.…”