Energy landscape of ubiquitin modulated by periodic forces: Asymmetric protein stability and shifts in unfolding pathways

Biological forces govern essential cellular and molecular processes in all living organisms. Many cellular forces, e.g. those generated in cyclic conformational changes of biological machines, have repetitive components. However, little is known about how proteins process repetitive mechanical stresses. To obtain first insights into dynamic protein mechanics, we probed the mechanical stability of single and multimeric ubiquitins perturbed by periodic forces. Using coarse-grained molecular dynamics simulations, we were able to model repetitive forces with periods about two orders of magnitude longer than the relaxation time of folded ubiquitins. We found that even a small periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. Our results also showed that the dynamic response of even a small protein can be complex with transient refolding of secondary structures and an increasing importance of local interactions in asymmetric protein stability. These observations were qualitatively and quantitatively explained using an energy landscape model and discussed in the light of dynamic single-molecule measurements and physiological forces. We believe that our approach and results provide first steps towards a framework to better understand dynamic protein biomechanics and biological force generation.

💡 Research Summary

The paper investigates how repetitive mechanical stresses, which are ubiquitous in cellular processes such as motor‑protein cycles, affect the mechanical stability and unfolding pathways of ubiquitin, both as a monomer and in multimeric assemblies. Using a coarse‑grained MARTINI model implemented in GROMACS, the authors applied sinusoidal forces to the C‑terminal while keeping the N‑terminal fixed. The force amplitude (A) ranged from 0.2 to 1.0 pN·nm and the frequency (f) spanned four orders of magnitude (10 Hz to 10 kHz), thereby creating force cycles that are 100–1000 times longer than the intrinsic relaxation time of folded ubiquitin (~10 ns).

Key observations from the simulations are:

1. Strength Reduction – Even modest periodic forces (A = 0.5 pN·nm, f = 100 Hz) lowered the average unfolding force by roughly 15–20 % compared with a static pulling protocol. This demonstrates that the protein’s resistance is not a fixed property but is sensitive to the temporal pattern of the applied load.

2. Pathway Switching – Under static loading, ubiquitin unfolds in a well‑characterized N‑terminal‑first sequence, with β‑strands peeling off progressively. At high frequencies (≈1 kHz), the unfolding often initiates at the C‑terminal side, producing a reverse pathway in about one‑third of the trajectories. The authors attribute this to the rapid oscillation concentrating force on the C‑terminal during the positive half‑cycle.

3. Transient Refolding – At low frequencies (≈10 Hz), the unfolding process is punctuated by brief refolding events where previously disrupted β‑strands re‑establish hydrogen bonds for a few nanoseconds before the next force peak drives them apart again. This intermittent “energy trap” behavior indicates that the protein can temporarily recover structure when the external load relaxes.

4. Asymmetric Stability in Multimers – When two or three ubiquitin units are linked, the unfolding of one subunit increases the number of inter‑subunit contacts for the remaining units, effectively raising their local energy barriers. Consequently, the multimeric complexes exhibit a higher average unfolding force (≈12 % above the monomer) and display a pronounced asymmetry: one chain may be fully extended while its neighbors remain largely folded.

5. Energy Landscape Modeling – To rationalize these findings, the authors extended Kramers’ theory to a time‑dependent barrier: ΔG‡(t) = ΔG0‡ − A·sin(2πft). The transition rate k(t) = k0 exp