FRACTAL DIMENSIONS OF PROTEINS - WHAT ARE WE LEARNING

Proteins are compact polymers that form well defined, folded structure s. Since distant subunits along the chain can be in close proximity, p roteins can have long-range interactions and complicated connectivitie s. Because of the complexity of these structures, attempts have been m ade to apply the fractal formalism to characterize them. The emphasis of most work to date has been on two fractal properties, the fractal d imension of the polymer backbone and the fractal surface dimension, Fr om a large data set, it is seen that globular proteins show similar fr actal behavior. The fractal dimension of the backbone has values sligh tly less than 3, indicating that proteins are collapsed polymers, Prot eins typically have values for the fractal surface dimension in the ra nge 2.1-2.2: this indicates a relatively smooth surface. It is seen th at these fractal properties are more than quantitative descriptors of gross morphology. Rather, they provide insights into the nature of the folded state of a protein and how it interacts with its surrounding a queous environment, Measurements of the backbone dimension reveal that proteins behave as Hamiltonian walks, compact structures with identic al local and global scaling laws. Such a Hamiltonian walk structure ha s profound implications for the thermodynamics of protein folding. The fractal surface dimension can be used in a quantitative fashion to pr edict the kinetics of interactions of proteins with small molecules in solution. It has been successfully applied in a predictive model of h ydrogen isotope exchange kinetics.