Protein Evolution on Partially Correlated Landscapes

We extend an earlier model of protein evolution on a rugged landscape (Macken, C.A. & Perelson, A.S., {\it Proc. Natl. Acad. Sci. USA} {\bf 86,} 6191 (1989)) to the case in which the landscape exhibits a variable degree of correlation (i.e., smoothness). Correlation is introduced by assuming that a protein is composed of a set of independent blocks or domains, and that mutation in one block affects the contribution of that block alone to the overall fitness of the protein. We study the statistical structure of such landscapes and predict the statistical characteristics of protein evolution on a correlated landscape. Our theory is applied to the evolution of anitbody molecules by somatic hypermutation.