Toyoichi Tanaka

Statistical mechanics of simple models of protein folding and design.

It is now believed that the primary equilibrium aspects of simple models of protein folding are understood theoretically. However, current theories often resort to rather heavy mathematics to overcome some technical difficulties inherent in the problem or start from a phenomenological model. To this end, we take a new approach in this pedagogical review of the statistical mechanics of protein folding. The benefit of our approach is a drastic mathematical simplification of the theory, without resort to any new approximations or phenomenological prescriptions. Indeed, the results we obtain agree precisely with previous calculations. Because of this simplification, we are able to present here a thorough and self contained treatment of the problem. Topics discussed include the statistical mechanics of the random energy model (REM), tests of the validity of REM as a model for heteropolymer freezing, freezing transition of random sequences, phase diagram of designed (minimally frustrated) sequences, and the degree to which errors in the interactions employed in simulations of either folding and design can still lead to correct folding behavior.

Molecular dynamics of multichain Coulomb polymers and the effect of salt ions

The multichain effect and that of added salt for the polymers of random charge sequences (polyampholytes) are studied by molecular dynamics simulations, i.e., non-lattice model. The periodic boundary conditions are adopted where the Coulomb force is calculated with the use of the Ewald sum method. These polymers are under thermal oscillations in a Langevin fluid, where they form a collapsed globule at low temperature, and are composed of separate and elongated coils at high temperature. The volume of latter polyampholyte is much greater than that for a single-chain one due to creation of large void space among the chains. The polyampholytes with the chains of larger molecular weight or stiff chains are less soluble to salt-free solvent. The ions of added salt screen the internal electric field among the monomers to cause swelling of the polyampholyte, if the salt density is comparable to that of the polyampholyte and if salt ions have an easy access to inside of the polyampholyte chains.