# Allostery and conformational changes upon binding as generic features of proteins: a high-dimension geometrical approach

## TL;DR

This paper demonstrates that proteins' ability to undergo conformational changes and allosteric regulation upon ligand binding is a generic feature arising from evolutionary pressures for ligand discrimination, supported by a high-dimensional geometric analysis.

## Contribution

It extends previous models to high-dimensional smooth systems, showing that allostery and conformational changes are generic outcomes of evolutionary selection for ligand discrimination.

## Key findings

- Allosteric regulation and conformational changes are generic features of proteins.
- High-dimensional geometric analysis supports the universality of these features.
- Evolutionary solutions are near a codimension-1 subspace in genotypical space.

## Abstract

A growing number of experimental evidence shows that it is general for a ligand binding protein to have a potential for allosteric regulation and for further evolution. In addition, such proteins generically change their conformation upon binding. O. Rivoire has recently proposed an evolutionary scenario that explains these properties as a generic byproduct of selection for exquisite discrimination between very similar ligands. The initial claim was supported by two classes of basic examples: continuous protein models with small numbers of degrees of freedom, on which the development of a conformational switch was established, and a 2-dimensional spin glass model supporting the rest of the statement. This work aimed to clarify the implication of the exquisite discrimination for smooth models with large number of degrees of freedom, the situation closer to real biological systems. With the help of differential geometry, jet-space analysis, and transversality theorems, it is shown that the claim holds true for any generic flexible system that can be described in terms of smooth manifolds. The result suggests that, indeed, evolutionary solutions to the exquisite discrimination problem, if exist, are located near a codimension-1 subspace of the appropriate genotypical space. This constraint, in turn, gives rise to a potential for the allosteric regulation of the discrimination via generic conformational changes upon binding.