Conformational changes upon binding and allostery as generic features of enzymes: implication of multiple degrees of freedom

A growing number of experimental evidence shows that it is general for an enzyme to perform a conformational change upon binding to its substrate and during the release of its product. In addition, enzymes generically have in common allosteric and evolutionary potential. O. Rivoire has recently proposed an evolutionary scenario that explains these properties as a generic byproduct of selection for exquisite discrimination between very similar targets upon binding (between the substrate and the product in enzymes). 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 is established, and a 2D spin glass model. 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, a conformational change upon binding does not require a special explanation, rather its absence indicates on special circumstances. Furthermore, the evolutionary solutions to the exquisite discrimination problem, if exist, are located near a codimension 1 subspace of an appropriate genotypical space.