AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems

Abstract

In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular “action at a distance” is termed allostery. Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system's underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.

The allosteric mechanism of substrate-specific transport in SLC6 is mediated by a volumetric sensor

“…1A, χ 2 angles of approximately ~75° and ~255°), whereas in the parallel state, the side chain turns approximately 90° (χ 2 angles of approximately ~ -5° and ~165°) and is aligned with the axis of the substrate. The free exchange between perpendicular and parallel states observed in our simulations is consistent with the behavior of an ideal allosteric channel in the allosteric Ising model (42).…”

Mechanism-based enzyme activating compounds

“…Computational studies of allosteric modulation 26,27 employ methods such as dynamics simulations to sample protein global degrees of freedom, including domain motions. These global degrees of freedom are conveniently represented in terms of principal components.…”

Dissipation in Non-Steady State Regulatory Circuits

“…In order to analyse the system in its natural timescale, we set , where is the inverse of the relaxation time (smallest, non-zero eigenvalue of the matrix ) and calculate . The term under the logarithm, which has been called the thermodynamic coupling function for systems with many degrees of freedom [ 75 , 76 ], describes the degree of correlation of the two variables, and is zero if the joined probability distribution factorizes. The thermodynamic coupling function has been shown to be useful to quantify the contributions of specific energy terms in binary models of allosteric systems [ 75 , 76 ].…”