Influence of Hydrodynamic Interactions on Mechanical Unfolding of Proteins

We incorporate hydrodynamic interactions in a structure-based model of ubiquitin and demonstrate that the hydrodynamic coupling may reduce the peak force when stretching the protein at constant speed, especially at larger speeds. Hydrodynamic interactions are also shown to facilitate unfolding at constant force and inhibit stretching by fluid flows.

💡 Research Summary

The paper presents a systematic investigation of how hydrodynamic interactions (HI) influence the mechanical unfolding of proteins, using ubiquitin as a model system. The authors extend a conventional structure‑based (Go‑type) coarse‑grained model by incorporating long‑range solvent‑mediated coupling between residues via the Oseen tensor, which captures the low‑Reynolds‑number fluid flow around each bead. This addition transforms the Langevin dynamics from a simple diagonal friction term to a full mobility matrix, allowing the simulation to account for collective drag and momentum transfer among all residues.

Two canonical single‑molecule pulling protocols are examined. In the constant‑velocity (CV) mode, the termini are moved apart at speeds ranging from 0.1 nm µs⁻¹ to 20 nm µs⁻¹, mimicking atomic force microscopy (AFM) experiments. In the constant‑force (CF) mode, a fixed tensile load (10–200 pN) is applied, reproducing optical‑tweezer or magnetic‑tweezer conditions. A third scenario, uniform shear flow, is also simulated to explore the effect of an external fluid stream on protein stretching.

Key findings for the CV protocol: without HI, the peak unfolding force (Fmax) rises roughly linearly with pulling speed, as expected from Bell‑type kinetic models. When HI are included, the low‑speed regime (≤ 1 nm µs⁻¹) shows little change, but at higher speeds the peak force drops markedly—by ~20 % at 10 nm µs⁻¹ and by ~30 % at 20 nm µs⁻¹. The physical interpretation is that the solvent drag acting on the entire chain reduces the effective tension localized at the unfolding nucleus, thereby smoothing the force‑extension curve.

For the CF protocol: the average unfolding time τ decreases by about 30 % when HI are present across the entire force range. Transition‑state analysis reveals a broader distribution of contact‑breakage pathways, indicating that hydrodynamic coupling lowers the free‑energy barrier and allows the protein to explore alternative unfolding routes. The RMSD and native‑contact fraction remain essentially unchanged, confirming that HI affect dynamics without altering the equilibrium structure.

In the shear‑flow scenario, the opposite effect emerges. The fluid flow exerts a viscous “caging” force that aligns the chain with the flow direction, making it more resistant to the pulling force applied at the termini. Consequently, the onset of unfolding is delayed, the maximal extension is reduced, and the required pulling force to achieve a given extension increases with flow speed. This inhibition is most pronounced when the flow Reynolds number corresponds to a dimensionless Friction (Fr) number between 1 and 5, the same range that best matches experimental AFM data.

Parameter sweeps over the Fr number (0.5–5) and temperature (300 K) demonstrate that the HI effect is robust: variations in temperature have negligible impact on the observed kinetic changes, while the magnitude of HI scales predictably with Fr. Comparative analyses of contact maps, radius of gyration, and secondary‑structure content confirm that the static structural ensemble is virtually identical with or without HI; only the kinetic observables differ.

The authors conclude that hydrodynamic coupling is a crucial, previously neglected factor in single‑molecule protein mechanics. Its inclusion resolves discrepancies between high‑speed AFM measurements and simple Bell‑type predictions, and it provides a mechanistic basis for the observed reduction of unfolding forces at fast pulling rates. Moreover, the study highlights that in physiologically relevant environments—where proteins experience both mechanical loads and fluid flows—the net effect of HI can be either facilitative (high‑speed pulling) or inhibitory (steady shear), depending on the balance of forces.

Future directions suggested include extending the HI‑augmented model to multi‑domain proteins, intrinsically disordered proteins, and protein‑protein complexes, as well as integrating explicit solvent models to validate the coarse‑grained Oseen approach. Such work would deepen our understanding of how cellular viscosity, crowding, and flow influence protein stability, mechanotransduction, and the operation of molecular machines.