Molecular Recognition in Biomolecules Studied by Statistical-Mechanical Integral-Equation Theory of Liquids

Abstract

Recent progress in the theory of molecular recognition in biomolecules is reviewed, which has been made based on the statistical mechanics of liquids or the RISM/3D-RISM theory during the last five years in the authors' group. The method requires just the structure of protein and the potential energy parameters for the biomolecules and solutions as inputs. The calculation is carried out in two steps. The first step is to obtain the pair correlation functions for solutions consisting of water and ligands based on the RISM theory. Then, given the pair correlation functions prepared in the first step, we calculate the 3D-distribution functions of water and ligands around and inside protein based on the 3D-RISM theory. The molecular recognition of a ligand by the protein is realized by the 3D-distribution functions: if one finds some conspicuous peaks in the distribution of a ligand inside protein, then the ligand is regarded as "recognized" by the protein. Some biochemical processes are investigated, which are intimately related to the molecular recognition of small ligands including water, noble gases, and ions by a protein.

Perspective: Structural fluctuation of protein and Anfinsen’s thermodynamic hypothesis

“…The free energy surface can be obtained from the RISM (Reference Interaction Site Model) and 3D-RISM theories as a function of atomic coordinates of protein. 18,19 Therefore, the force constant of the free energy surface can be calculated from Eqs. (3) and (4).…”

“…24 The theory has been applied to a variety of the molecular recognition processes concerning functions of biomolecules and has established its position as the theory of molecular recognition. 19 Here, we briefly review the 3D-RISM/RISM theory, focusing on its physics, not its formulation. (Derivation of the RISM and 3D-RISM equations is found in Refs.…”

“…Equation (19) implies the following physics for the pressure induced structural change of protein. The pressure (∆P) first induces the displacement in the position (or structure) of an atom β of protein so as to reduce the partial molar volume (Le Chatelier's law).…”

“…Methods to calculate the free energy surface of the protein and its first derivative have been already established based on the 3D-RISM/KH theory developed by Hirata and his co-workers. 18,19,25 On the other hand, a work to calculate the second derivative is currently in progress in Hirata's group.…”

Numerical Solution of Two Dimensional Fredholm Integral Equations of the Second Kind by the Barycentric Lagrange Function*

“…Many of the mathematical physics problems and the engineering problems can be transformed into solving Fredholm integral equations [1] [2] [3]. In this paper, we pay attention to the two dimensional linear Fredholm integral equations (FIEs) of the second kind ( ) ( ) ( ) ( ) ( ( ) mensional FIEs, such as the radial basis functions method [4], Haar wavelets [5] and integral mean value method [6] [7].…”