Explaining LD1’s γ sensitivity to bias-deposition time

Ascertain the mechanistic reason why the collective-variable biasing efficiency γ for the Linear Discriminant Analysis coordinate (LD1) exhibits pronounced sensitivity to bias-deposition time compared to other collective variables in the protein G unfolding system, despite LD1 effectively separating folded and unfolded states.

Background

The study benchmarks multiple collective variables (CVs) for unfolding of protein G and extracts rates and CV biasing efficiencies (γ) using KTR and EATR. For most CVs, γ increases with slower biasing and aligns with intuitive CV quality, but LD1 shows a particularly strong dependence: large γ at slow biasing and small γ at fast biasing.

The authors explicitly acknowledge that the cause of LD1’s heightened γ sensitivity remains unresolved, even though LD1 is otherwise a good CV for distinguishing folded and unfolded states. Understanding this behavior would clarify how γ reflects CV quality and guide the choice of biasing coordinates.

References

The CV obtained from linear discriminant analysis (LD1, Ref.~\citenum{posLDA2023}) appears to have a large value of γ for slow biasing and a small value of γ for fast biasing. A similar trend appears for all CVs tested, but this is most prominent in LD1, and we are still investigating the reason γ for LD1 is so much more sensitive than the other CVs here, while still serving as a very good CV for distinguishing folded and unfolded states (as proposed in our previous study ).

— Good rates from bad coordinates: the exponential average time-dependent rate approach  (2403.10668 - Mazzaferro et al., 2024) in Results and Discussion — Protein G unfolding