THE TOPOLOGY OF MULTIDIMENSIONAL POTENTIAL-ENERGY SURFACES - THEORY AND APPLICATION TO PEPTIDE STRUCTURE AND KINETICS

Topological characteristics of multidimensional potential energy surfa ces are explored and the full conformation space is mapped on the set of local minima. This map partitions conformation space into energy-de pendent or temperature-dependent ''attraction basins'' and generates ' 'disconnectivity'' graph that reflects the basin connectivity and char acterizes the shape of the multidimensional surface. The partitioning of the conformation space is used to express the temporal behavior of the system in terms of basin-to-basin kinetics instead of the usual st ate-to-state transitions. For this purpose the transition matrix of th e system is expressed in terms of basin-to-basin transitions and the c orresponding master equation is solved. As an example, the approach is applied to the tetrapeptide, isobutyryl-(ala)(3)-NH-methyl (IAN), whi ch is the shortest peptide that can form a full helical turn. A nearly complete List of minima and barriers is available for this system fro m the work of Czerminiski and Elber. The multidimensional potential en ergy surface of the peptide is shown to exhibit an overall ''funnel'' shape. The relation between connectivity and spatial proximity in dihe dral angle space is examined. It is found that, although the two are s imilar, closeness in one does not always imply closeness in the other. The basin to basin kinetics is examined using a master equation and t he results are interpreted in terms of kinetic connectivity. The confo rmation space of the peptide is divided up in terms of the surface top ography to model its ''folding'' behavior. Even in this very simple sy stem, the kinetics exhibit a ''trapping'' state which appears as a ''k inetic intermediate,'' as in the folding of proteins. The approach des cribed here can be used more generally to classify multidimensional po tential energy surface sand the time development of complex systems. ( C) 1997 American Institute of Physics.