Proving the Role of Entropic Elasticity in Protein Folding

Abstract

Force-spectroscopy has been an essential tool for understanding how proteins fold and unfold, and their involvement in regulating cell responses to mechanical stimuli. Hence, it is of significance to establish an accurate free energy model of proteins under force capable of describing the mechanisms of protein folding. Even though numerous models have been proposed, the role of polymer physics and the changes in entropy involved in protein elasticity are still controversial. We have developed a model to construct the free energy of elastic proteins under force based on protein folding and polymer physics. The model is constructed by combining Morse and Gaussian potentials describing the enthalpic interactions in the folded state, and the freely jointed-chain (FJC) energy model accounting for the entropic changes during unfolding and stretching. The free parameters of each component are dependent on the protein and thus regulate its mechanical properties [J. Valle-Orero et al, BBRC 460 (2015)]. Here we aim to prove the accuracy of the model by reproducing force-spectroscopy data of a model protein, protein L (B1 domain from Peptostreptococcus magnus). We experimentally fit the force dependent extension of unfolded domains with the FJC using a contour length of 16.3 nm and a Kuhn length of 1.1 nm. The Morse depth of 2 kBT was established by measuring the probability that a domain folds at a given force. A Gaussian barrier of 10.5 kBT was chosen by comparing the experimental unfolding kinetics to those obtained using Brownian dynamics on our energy model. The excellent agreement of our model with experimental data validates and reinforces the theoretical foundations of our physics model. Furthermore, we demonstrate that changes in entropy during extending or collapsing a protein results in departure from simple Bell-like models.