Inferring the Rate-Length Law of Protein Folding

TL;DR

This paper examines how protein folding times scale with chain length, finding that a power law best fits existing data but suggests more experiments are needed for definitive conclusions.

Contribution

It compares multiple proposed rate-length laws for protein folding and highlights the need for additional data to determine the correct scaling law.

Findings

Power law best explains the data.

Folding rates predicted are very fast and possibly unrealistic.

More experimental data needed for conclusive results.

Abstract

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.