Relationship between the Mechanical Properties and Topology of Cross-Linked Polymer Molecules:  Parallel Strands Maximize the Strength of Model Polymers and Protein Domains

Abstract

Proteins that perform mechanical functions in living organisms often exhibit exceptionally high strength and elasticity. Recent studies of the unfolding of single protein molecules under mechanical loading showed that their strength is mostly determined by their native topology rather than by thermodynamic stability. To identify the topologies of polymer molecules that maximize their resistance to unfolding, we have simulated the response of cross-linked polymer chains under tensile loading and have found that chain configurations that maximize the unfolding work and force involve parallel strands. Chains with such optimal topologies tend to unfold in an all-or-none fashion, in contrast to randomly cross-linked chains, most of which exhibit low mechanical resistance and tend to unfold sequentially. These findings are consistent with AFM studies and molecular mechanics simulations of the unfolding of β-sheet proteins. In particular, parallel strands give rise to the high strength of the immunoglobulin-like domains in the muscle protein titin.

Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single-molecule pulling experiments

“…While providing results that are qualitatively consistent wi th atomistic scale studies, our model 13 entirely ignored stochastic and rate-dependent aspects of unfolding.…”

“…In the first model, to which we refer as Model I, a cross-link ruptures deterministically once its internal force reaches a critical value f c . This model has been studied previously 13 but we include it here for comparisons. In the second model, to which we refer as Model II, rupture of a cross-link is a stochastic process described by first-order kinetics.…”

“…A single cross-link, {i, i+l}, creates a loop of length l in the chain. The optimal configurations in this case can be found analytically 13 . In particular, F m = f c for all i and l, and W ∆ depends on l only: Following the analysis in Section 3.2, it is straightforward to obtain the probability density function for the dimensionless rupture time τ ,…”

“…This case has been studied in detail in ref. 13 The key result is that the same optimal configurations maximize both F m and ∆W. Those configurations involve "parallel strands " of the form C N ={{i 1 ,…”

Molecular and Nanostructural Mechanisms of Deformation, Strength and Toughness of Spider Silk Fibrils

“…Similar to their role in other mechanical proteins [15][16][17][18][19][20][21], it has been hypothesized that H-bond arrays in beta-sheet nanocrystals reinforce the polymeric network under mechanical stretch, by forming interlocking regions that transfer the load between chains [13,22]. In particular, Termonia's pioneering empirical two-phase model based on experimental data has been instrumental in explaining the importance of the ratio and size of crystalline and semi-amorphous domains, at a time when large-scale atomistic simulations of spider silk constituents were impossible due to the lack of suitable force fields and computational resources [22].…”