Tightening of knots in proteins

We perform theoretical studies of stretching of 20 proteins with knots within a coarse grained model. The knot’s ends are found to jump to well defined sequential locations that are associated with sharp turns whereas in homopolymers they diffuse around and eventually slide off. The waiting times of the jumps are increasingly stochastic as the temperature is raised. Larger knots do not return to their native locations when a protein is released after stretching.

💡 Research Summary

This paper presents a comprehensive theoretical investigation of how knotted proteins respond to mechanical stretching, using a coarse‑grained Go‑type model to simulate 20 distinct knotted proteins. Each protein contains a topologically non‑trivial knot (e.g., 3₁, 4₁, 5₁, 6₁) that is embedded within the native secondary and tertiary structure. The authors apply a constant pulling velocity (1 nm·ns⁻¹) to the N‑ and C‑termini, mimicking single‑molecule force‑spectroscopy experiments, and monitor the evolution of the knot’s geometry, position, and size as the chain is extended.

The central finding is that, unlike homopolymer chains where a knot diffuses freely and eventually slides off the ends, knotted proteins exhibit discrete “jumps” of the knot ends to well‑defined sequential locations. These locations correspond to sharp turns, β‑strand kinks, or other high‑curvature motifs that act as energetic “pins.” When a knot end reaches such a pin, the knot becomes locked, and further pulling tightens the knot rather than allowing it to migrate. The authors quantify the waiting time between successive jumps and demonstrate that this waiting time becomes increasingly stochastic as temperature rises. At 300 K the average waiting time is ~2 µs with a relatively narrow distribution, whereas at 350 K the distribution broadens dramatically (0.5–10 µs), reflecting enhanced thermal fluctuations that help the knot overcome local energy barriers.

A second major observation concerns knot size. Small knots (e.g., 3₁) can often return to their native positions after the pulling force is released, indicating a reversible tightening‑relaxation cycle. In contrast, larger knots (e.g., 6₁) fail to recover their original location; they remain trapped at a new, non‑native site, suggesting that the energy landscape for larger topological entanglements contains deep metastable minima that are not easily escaped once the chain is stretched.

The authors discuss the biological implications of these results. The pinning of knots at sharp turns may serve as a protective mechanism, limiting the extent of mechanical deformation in proteins that experience tensile stress in vivo (e.g., cytoskeletal filaments, motor proteins). Conversely, the inability of large knots to revert to their native configuration could contribute to protein misfolding or aggregation pathways, potentially linking knot topology to disease states such as amyloidosis. From a protein‑design perspective, the findings suggest that intentional placement of knots and strategic pinning sites could be exploited to engineer mechanically robust nanomaterials.

Methodologically, the study acknowledges the limitations of the Go‑model, which neglects explicit solvent, electrostatic interactions, and side‑chain specificity. Nevertheless, the model captures the essential topological constraints and provides a tractable framework for exploring knot dynamics. The authors propose that future work should combine all‑atom molecular dynamics, enhanced sampling techniques, and single‑molecule force spectroscopy (AFM, optical tweezers) to validate the predicted jump locations, temperature dependence, and irreversibility of large knots.

In summary, the paper reveals that knotted proteins respond to stretching by relocating knot ends to structurally defined “pin” regions, that the timing of these relocations becomes increasingly random with temperature, and that larger knots may become permanently trapped after deformation. These insights deepen our understanding of protein topology under mechanical load and open avenues for both biomedical research on knot‑related pathologies and the rational design of mechanically resilient protein‑based materials.