ASCRIBING WEIGHTS TO FOLDING HISTORIES - EXPLAINING THE EXPEDIENCY OF BIOPOLYMER FOLDING

We develop a novel scheme of statistical inference whereby statistical weights are assigned to folding pathways. Evidence is presented that supports the fact that this scheme accounts for the robustness and expediency of biopolymer folding processes. The essential properties of folding are captured by showing that the weight is concentrated over a very limited domain of closely related folding pathways. To make probabilistic inferences, we constructively define a measure eta over the space of folding pathways. Such a scheme stands in contrast to traditional methods built upon a Boltzmann measure over conformation space. In order to implement and validate this new approach we combine analytical theory and computations that successfully reproduce pulse-chase kinetic experiments. We first present a rigorous analytical result by proving that an appropriate measure exists over the space of folding pathways. This existence theorem is shown to hold in two general scenarios: (i) the unbiased folding (UF) scenario, in which the complete chain starts its search in conformation space in an unbiased manner; (ii) the sequential folding (SF) scenario, in which the chain starts searching in conformation space concurrently with its own sequential assembling by progressive incorporation of monomers. A systematic coarse-graining simplification of the space of folding pathways is implemented to make the computations feasible and to validate our theory as a means of accounting for the expedient way of searching for the functionally competent conformation.