Stochastic Modeling and and Optimization of Phage Display

Phage display, SELEX, and other methods of combinatorial chemistry have become very popular means of finding ligands with high affinities to given targets. Despite their success, they suffer from numerous sources of error and bias, such as very low initial concentrations of species, nonspecific binding, and the sampling of only a tiny fraction of the library at the end of an experiment. To understand the interaction of these errors and to better devise molecular search strategies that take the errors into account, we devise and analyze a highly detailed model of phage display. The model is specifically designed to study the influence of the stochastic nature of each laboratory step. The model includes phage multivalency, multiple classes of targets, and solid-phase equilibrium and washing, yet it is amenable to analytic results and rapid computer simulation. With both analytic and simulation approaches, we (1) describe the effects of target concentration, phage valency, degree of background binding and other laboratory parameters on the probablilities of phage binding and of being selected; (2) show the effects of an increasing selection stringency strategy and how it results in a tradeoff between rapid library enrichment and high probability of sampling the best ligands; (3) show how the number of phage sampled for detailed study at the end of a search alters search success and suggests how many generations to perform.