A revised worm-like chain model for elasticity of polypeptide chains

Unraveling the molecular mechanism of collagen flexibility during physiological warmup using molecular dynamics simulation and machine learning

Physiological warmup plays an important role in reducing the injury risk in different sports. In response to the associated temperature increase, the muscle and tendon soften and become easily stretched. In this study, we focused on type I collagen, the main component of the Achilles tendon, to unveil the molecular mechanism of collagen flexibility upon slight heating and to develop a model to predict the strain of collagen sequences. We used molecular dynamics approaches to simulate the molecular structures and mechanical behavior of the gap and overlap regions in type I collagen at 307 K, 310 K, and 313 K. The results showed that the molecular model in the overlap region is more sensitive to temperature increases. Upon increasing the temperature by 3 degrees Celsius, the end-to-end distance and Young's modulus of the overlap region decreased by 5% and 29.4%, respectively. The overlap region became more flexible than the gap region at higher temperatures. GAP-GPA and GNK-GSK triplets are critical for providing molecular flexibility upon heating. A machine learning model developed from the molecular dynamics simulation results showed good performance in predicting the strain of collagen sequences at a physiological warmup temperature. The strain-predictive model could be applied to future collagen designs to obtain desirable temperature-dependent mechanical properties.

Energy/entropy partition of force at DNA stretching

We compute by molecular simulation the energy/entropic partition of the force in a stretched double-stranded (ds)DNA molecule that is not yet available from the single-molecule measurements. Simulation using the coarse-grained wormlike chain (WLC) model predicts a gradual decrease in the internal (bending) energy of DNA at stretching. The ensuing negative energy contribution to force f_U is outweighed by the positive entropy contribution f_S . The ratio f_U /f, used to assess the polymer elasticity, is about -1 at the moderate extension of DNA. At the high extension, the extra energy expenses due to the contour length elongation make the ratio f_U /f less negative. The simulation findings of the hybrid energy/entropy nature of DNA elasticity at weak and moderate forces are supported by computations using the thermoelastic method mimicking the polymer experiments in bulk. It is contended that the observation of the negative energy elasticity in DNA can be generalized to other semiflexible polymers described by the WLC model.

Non-tight and tight chemomechanical couplings of biomolecular motors under hindering loads

Biomolecular motors make use of free energy released from chemical reaction (typically ATP hydrolysis) to perform mechanical motion or work. An important issue is whether a molecular motor exhibits tight or non-tight chemomechanical (CM) coupling. The tight CM coupling refers to that each ATPase activity is coupled with a mechanical step, while the non-tight CM coupling refers to that an ATPase activity is not necessarily coupled with a mechanical step. Here, we take kinesin, monomeric DNA helicase, ring-shaped hexameric DNA helicase and ribosome as examples to study this issue. Our studies indicate that some motors such as kinesin, monomeric helicase and ribosome exhibit non-tight CM coupling under hindering forces, while others such as the ring-shaped hexameric helicase exhibit tight or nearly tight CM coupling under any force. For the former, the reduction of the velocity caused by the hindering force arises mainly from the reduction of the CM coupling efficiency, while the ATPase rate is independent or nearly independent of the force. For the latter, the reduction of the velocity caused by the hindering force arises mainly from the reduction of the ATPase rate, while the CM coupling efficiency is independent or nearly independent of the force.

The hierarchical emergence of worm-like chain behaviour from globular domain polymer chains

Biological organisms make use of hierarchically organised structures to modulate mechanical behaviour across multiple lengthscales, allowing microscopic objects to generate macroscopic effects. Within these structural hierarchies, the resultant physical behaviour of the entire system is determined not only by the intrinsic mechanical properties of constituent subunits, but also by their organisation in three-dimensional space. When these subunits are polyproteins, colloidal chains or other globular domain polymers, the Kratky-Porod model is often assumed for the individual subunits. Hence, it is implicitly asserted that the polymeric object has an intrinsic parameter, the persistence length, that defines its flexibility. However, the persistence lengths extracted from experiment vary, and are often relatively small. Through a series of simulations on polymer chains formed of globular subunits, we show that the persistence length itself is a hierarchical structural property, related not only to the intrinsic mechanical properties of the underlying monomeric subunits, but emerging due to the organisation of inhomogenous geometry along the polymer contour.