Statistical Mechanics of Secondary Structures in Proteins: Characterization of a molten globule—like state

Abstract

In order to obtain a simple characterization of the molten globule state of proteins, we re-examine a simple model for the formation and stability of secondary structures in proteins. We consider chains on a cubic lattice; each monomer can be considered to reperesent a helical turn, and we assign a Boltzmann weight exp(ε _H /T) when two monomers are aligned, and 1 when they make a turn. Here, ε _H is positive and represents the energy gain due to hydrogen bonds (H-bonds). In addition, we include an attractive nearest neighbour monomer—monomer interaction to represent the hydrophobic effect which drives the collapse of the chains. In the thermodynamic limit ( and in the mean-field approximation), the system undergoes two transitions: first, a second order collapse transition at high temperature, from random coil to globular structures, similar to the usual theta point of polymers. Then, at lower temperature, the system undergoes a first order freezing transition, from a high temperature phase where the helix-like secondary structures are present but mobile in the system, to a frozen phase where secondary structures invade the whole globule, and make their turns only on the outside surface. We have checked these results by extensive Monte Carlo simulations on finite chains, and have indeed observed the theta point at higher temperature, and the freezing transition at lower temperature. The structure factor in this frozen phase exhibits more structure than in the non-frozen phase, and the number of co—linear bonds is maximized. Above the freezing transition, the number of H-bonds drops sharply, but the system still exhibits significant secondary structure, and we observe a slight increase of the radius of gyration. The collapsed phase above the freezing point thus provides a simplified representation of the molten globule phase of real proteins.