Thermodynamics of Complex Systems: Computing Entropy
in Proteins and Glassy Materials

Dr. M. Scott Shell

Department of Chemical Engineering
Princeton University

Date: Thursday, February 3, 2005
Time: 4:00 p.m.
Place: Engineering II, Room 3361

ABSTRACT

A grand challenge in statistical physics, which seeks to understand complex and fluctuating systems, is the bottom-up design of novel molecules and microstructures. Traditionally, statistical mechanics has examined problems in which the individual configurations or states of a system are irrelevant at the macroscopic level. However, a number of systems of technological interest—such as proteins and glasses—cannot be understood in this way. In these cases, one must consider the role that individual states play and the mechanism by which a few come to dominate the macroscopic behavior. Such an analysis necessitates the study of an underlying entropy function since it is the dramatic range in the degeneracy of sampled configurations that makes these systems unique.

In this talk, I will discuss novel computational and theoretical techniques that we have developed to calculate entropies and free energies in such complex systems. I will first discuss our recent work on the statistical properties of sequence mutations in biomolecules. Using a powerful and general Monte Carlo algorithm [1,2], we characterize the entire distribution of possible amino acid sequences of a given structure. Our results suggest a thermodynamic interpretation for nature's use of a 20-amino acid “palette” to evolve proteins. I will then discuss theoretical approaches for understanding the glass transition, the sudden rigidifying and falling out of equilibrium experienced by a liquid when cooled sufficiently fast. We have developed a theory of glassy materials, based on the statistical properties of their energy landscapes, which describes the phase behavior of the liquid state and provides a thermodynamic basis for glass analysis and design [3,4].

[1] M. S. Shell, P. G. Debenedetti, and A. Z. Panagiotopoulos, “Generalization of the Wang-Laudau method for off-lattice simulations,” Phys. Rev. E 66, 056703 (2002).
[2] M. S. Shell, P. G. Debenedetti, and A. Z. Panagiotopoulos, “An improved Monte-Carlo method for direct calculation of the density of states,” J. Chem. Phys. 119 , 9406 (2003).
[3] M. S. Shell, P. G. Debenedetti, and A. Z. Panagiotopoulos, “Saddles in the energy landscape: extensivity and thermodynamic formalism,” Phys. Rev. Lett. 92 , 035506 (2003).
[4] M. S. Shell and P. G. Debenedetti, “Thermodynamics and the glass transition in model energy landscapes,” Phys. Rev. E 69, 051102 (2004).