Mathematical Modeling

RISM integral equation theory in study of thermodynamics of self-assembling ionic peptides

E. V. Sobolev^a, A. V. Danilkovich^bc, D. A. Tikhonov<sup>a

a</sup> Institute of Mathematical Problems of Biology of the Russian Academy of Sciences, Pushchino 142290, Russia
^b Branch of M. M. Shemyakin and Yu. A. Ovchinnikov Institute of Bioorganic Chemistry of the Russian Academy of Sciences, Pushchino 142290, Russia
^c State Life-Sciences Institute at Pushchino, Centre for Education at BIBC RAS, Pushchino 142290, Russia

Abstract: A new modification of the Reference Interaction Site Model was used to evaluate thermodynamic characteristics of self-organizing peptide complexes. The modified variant allows one to use average matrix of intramolecular correlation functions. This approach is effective for analyzing Gibbs free energy and the structure of the first solvate shield of a macromolecule, which has many configurational states. To calculate Gibbs energy we used both approximate formulas and the method of numerical thermodynamic integration. Comparison of the results of free energy values calculated by other commonly used methods demonstrates that thermodynamic integration yields the most adequate values of interaction energies for a panel of peptide nanostructures and protofilaments. Conclusions were made on the applicability of the compared methods to the study of complex polar peptide structures.

Key words: integral equations, theory of liquids, RISM, average matrix, Gibbs energy, self-organized structure, ion peptide.

UDC: 577.3, 51-76

Received 02.07.2012, Published 20.08.2012