How sequence determines elasticity of disordered proteins

Abstract

How nature tunes sequences of disordered protein to yield the desired coiling properties is not yet well understood. To shed light on the relationship between protein sequence and elasticity, we here investigate four different natural disordered proteins with elastomeric function, namely: FG repeats in the nucleoporins; resilin in the wing tendon of dragonfly; PPAK in the muscle protein titin; and spider silk. We obtain force-extension curves for these proteins from extensive explicit solvent molecular dynamics simulations, which we compare to purely entropic coiling by modeling the four proteins as entropic chains. Although proline and glycine content are in general indicators for the entropic elasticity as expected, divergence from simple additivity is observed. Namely, coiling propensities correlate with polyproline II content more strongly than with proline content, and given a preponderance of glycines for sufficient backbone flexibility, nonlocal interactions such as electrostatic forces can result in strongly enhanced coiling, which results for the case of resilin in a distinct hump in the force-extension curve. Our results, which are directly testable by force spectroscopy experiments, shed light on how evolution has designed unfolded elastomeric proteins for different functions.

Figure 1

Chain entropy of the four disordered proteins. (A) Force extension curves of FG (cyan), resilin (brown), PPAK (orange), and silk (violet) obtained from entropic chain simulations and weighted histogram analysis method (WHAM). (Inset) Semilogarithmic plot of panel A. (B) Force extension curves for individual disordered protein from entropic chain simulations (colored lines as in panel A), wormlike chain (WLC) fit to all data (black dashed line), and WLC fit to data with F < 60 pN (red solid line), WLC fit to all data (black dashed lines), and WLC fit to only the data with forces <60 pN (red solid lines). Average forces with standard error of the mean in umbrella sampling windows (blue circles). (C) Snapshots of FG, resilin, PPAK, and silk from left to right with an extension-per-bond of 0.25 nm. Highlighted are particular sequence features in each structure, namely Phe and Gly (FG), Gly (resilin), Pro (PPAK), and Gly (silk).

Figure 2

Influence of glycine and proline on entropic chain elasticity. (A) PPII content as a function of persistence length. (Inset) Glycine content (square) and proline content (triangle) versus persistence length. Persistence lengths are obtained from WLC fits (red curves in Fig. 1B). A high correlation is found for the PPII content and glycine content. (B) PPII content of FG (diamond), resilin (star), PPAK (triangle), and silk (circle) as a function of extension-per-bond.

Figure 3

Force extension curves for FG (A), resilin (B), PPAK (C), and silk (D) from umbrella sampling and WHAM using standard MD simulations including electrostatic and solvent effects (red). For comparison, the force-extension curves of the respective entropic chains are shown (black). Sample conformations of resilin at extensions of ∼3.0 nm, ∼3.5 nm, and ∼4.0 nm are shown in panel B. Charged residues of D6 (magentas) and R18 (orange) are shown in sticks.

Figure 4

Electrostatic energy per residue (E, black) and solvent-accessible surface area per residue (SASA, red) for FG (A), resilin (B), PPAK (C), and silk (D) as a function of extension-per-bond.