Mechanics of allostery: contrasting the induced fit and population shift scenarios

Abstract

In allosteric proteins, binding a ligand can affect function at a distant location, for example by changing the binding affinity of a substrate at the active site. The induced fit and population shift models, which differ by the assumed number of stable configurations, explain such cooperative binding from a thermodynamic viewpoint. Yet, understanding what mechanical principles constrain these models remains a challenge. Here we provide an empirical study on 34 proteins supporting the idea that allosteric conformational change generally occurs along a soft elastic mode presenting extended regions of high shear. We argue, based on a detailed analysis of how the energy profile along such a mode depends on binding, that in the induced fit scenario there is an optimal stiffness k * a ∼ 1/N for cooperative binding, where N is the number of residues involved in the allosteric response. We find that the population shift scenario is more robust to mutation affecting stiffness, as binding becomes more and more cooperative with stiffness up to the same characteristic value k * a , beyond which cooperativity saturates instead of decaying. We confirm numerically these findings in a non-linear mechanical model. Dynamical considerations suggest that a stiffness of order k * a is favorable in that scenario as well, supporting that for proper function proteins must evolve a functional elastic mode that is softer as their size increases. In consistency with this view, we find a significant anticorrelation between the stiffness of the allosteric response and protein size in our data set.Many proteins are allosteric: binding a ligand at one or several allosteric sites can regulate function at a distant site, a long-range communication often accompanied by large conformational changes [1,2]. There is a considerable interest in predicting the amino acids involved in this communication, or "allosteric pathway", from structure or sequence data [3,4], since they can be used as targets for drug design [5]. Yet, understanding the physical principles underlying such action at a distance in proteins remains a challenge [6,7]. From a thermodynamic standpoint, two distinct views have been proposed. In the induced fit scenario, exemplified by the Koshland-Némethy-Filmer (KNF) model [8], the protein essentially lies in one single state. The latter changes as binding occurs, leading to a conformational change. In an energy landscape picture such as that of Fig.1B, it corresponds to a displacement of the energy minimum upon binding. By contrast, in the population shift model, exemplified by the Monod-Wyman-Changeux (MWC) model [9], two states are always present. Their relative stability can change sign upon binding, leading to an average conformational change. Although each of these models presumably applies to various proteins, they do not specify which designs allow for efficient action at a distance, and how robust these designs are to mutations [10].In several proteins -see below for a systematic study -it has been observed that the allosteri...

Crowding-induced opening of the mechanosensitive Piezo1 channel in silico

“…Further studies are needed to understand the complex effect of PIP 2 on Piezo channel activity. It is also possible that PIP 2 amplifies mechanical coupling, which may reduce the entropic cost associated with the conformational rearrangement of the arms, an effect explained by the population-shift theory of allostery 42,43 .…”

A Piezo1 Open State Reveals a Multi-fenestrated Ion Permeation Pathway

“…On the other hand, PIP 2 s may help anchor the intracellular side of the arms to the inner leaflet, allowing a better mechanical coupling upon membrane deformation. Such mechanical coupling may reduce the entropic cost associated with the conformational rearrangement of the arms, an effect explained by the population-shift theory of allostery ( 33, 34 ). Finally, in addition to the change in the thermodynamic quantity, PIP 2 may also affect the kinetic aspect by reducing the free energy barrier for Piezo1 activation, enabling spontaneous opening in our microsecond MD simulation.…”

Dynamic Order in Allosteric Interactions

“…In this sense they are macroscopic from the point of view of the cell since they can impart work on the cell by cutting, pushing etc. It has also been demonstrated in many cases that slow modes are related to the motion a protein exhibits when it switches from apo to holo conformation or vice versa upon allosteric activation [15,23]. The set of modes after the few rst slowest should become important when one wants to understand how smaller parts of the protein communicate with each other (these modes as microscopic from the point of view of the cell but macroscopic from the point of view of the protein).…”