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KONSTANTIN KOSTOV |
Statistical Analysis of the Topography and Dynamics of the Potential Energy Surfaces of Proteins and their Relation to Protein Folding |
Multi-dimensional potential energy surfaces (PES) of proteins are so complex
that interpreting their topographies and dynamics requires statistical analysis
of their minima and saddles. Sequences of linked minimum-saddle-minimum points,
monotonic in the energies of the lower minima, provide the necessary database to
characterize the topographies of such surfaces. The topographies are then
related to the dynamics on the surfaces thorough a master equation. The approach
has proved very successful in the interpretation of the glass-forming vs.
structure-forming characteristics of the PES of clusters. We propose to apply
these methods to protein potential energy surfaces with emphasis on how general
characteristics of the topography determine the tendency of proteins to fold.
Such an application requires addressing the following fundamental questions:
| What is the size and character of the statistical sample of minima and saddle points that is adequate and robust enough to describe the PES surfaces of
proteins with useful accuracy? How adequate is the master equation as a mathematical description of the intrawell dynamics in proteins and the RRKM theory for estimation and transition rates? How does the topography of the surface arise from the fundamental interatomic forces? Which regions of the PES in proteins are most important for the protein folding process and therefore
require more extensive sampling and more accurate modeling of the dynamics? What mathematical methods can be devised to evaluate the area of the multidimensional lakes on the surface, i.e., the microcanonical entropies crucial to estimating the free energies of different conformations.
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Initial understanding of these questions will be obtained from consideration of a simple
protein model. However, the statistical nature of the theory makes is easily
extendable to treat systems modeled with realistic, all-atom, potentials and
explicit solvent. Subsequent applications will include met-enkephalin and a 33
residue ìminiproteinî derived from staphylococcal protein A. |
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