Inferring the Rate-Length Law of Protein Folding

We investigate the rate-length scaling law of protein folding, a key undetermined scaling law in the analytical theory of protein folding. We demonstrate that chain length is a dominant factor determining folding times, and that the unambiguous determination of the way chain length corre- lates with folding times could provide key mechanistic insight into the folding process. Four specific proposed laws (power law, exponential, and two stretched exponentials) are tested against one an- other, and it is found that the power law best explains the data. At the same time, the fit power law results in rates that are very fast, nearly unreasonably so in a biological context. We show that any of the proposed forms are viable, conclude that more data is necessary to unequivocally infer the rate-length law, and that such data could be obtained through a small number of protein folding experiments on large protein domains.