Collective Variable-Guided Engineering of the Free-Energy Surface of a Small Peptide

Abstract

Engineering the free-energy surfaces (FES) of proteins and peptides is central to controlling conformational ensembles and their responses to perturbations. However, predicting how chemical modifications such as point mutations reshape the FES and shift conformational equilibria remains challenging, particularly in data-scarce settings. Building on the Collective Variables for Free Energy Surface Tailoring (CV-FEST) framework, we develop a computational approach that leverages short, unbiased molecular dynamics trajectories to guide mutation analysis. Using the ten-residue beta-hairpin CLN025 and a systematic library of its single-point mutants, we apply Harmonic Linear Discriminant Analysis (HLDA) to extract collective variables from the conformational data. We find that the HLDA eigenvector learned solely from short wild-type trajectories provides residue-level insight into the propensity of mutations at specific positions to thermodynamically stabilize or destabilize the folded state. Extending this analysis, we show that shifts in the leading HLDA eigenvalue across mutants, a measure of changes in separability between the conformational ensembles along the HLDA coordinate, correlate strongly with mutation-induced changes in the free-energy difference between states, as reflected in melting temperatures. Benchmarked against Replica Exchange Molecular Dynamics simulations, these findings suggest a promising and computationally affordable route toward guiding the engineering of biomolecular free-energy landscapes.

Figures (7)

• Figure 1: (a) Structural model of CLN025 with inter-residue distance descriptors (black lines). (b) Absolute HLDA eigenvector weights for each distance descriptor.
• Figure 2: Comparison of WT CLN025 and two representative mutants: (a) Free-energy profiles along the RMSD CV at 340 K showing mutation-dependent changes. (b) Folded probability versus temperature from REMD simulations, with $T_m$ defined at $P_{\mathrm{folded}}=0.5$.
• Figure 3: WT HLDA eigenvector–derived residue weights versus per-residue mean changes in the peptide’s melting temperature: (a) Scatter plot summarizing the relationship between the WT residue-score computed using Eq.\ref{['eq_res_imp']} and the mean $\Delta T_m$ across mutations at each site (Pearson $r=-0.98$, $p=8.09\times10^{-5}$). (b) Per-residue WT weights shown as bars to highlight differences across positions.
• Figure 4: Mutation-level relationship between HLDA eigenvalue shifts and changes in the peptide thermodynamic conformational stability: (a) Correlation between $\Delta\lambda$ and $\Delta T_m$ (Pearson $r=0.69$, $p=3.4\times10^{-6}$; Spearman $\rho=0.64$, $p=2.3\times10^{-5}$). (b) Subsampling analysis demonstrating the robustness of the correlation upon excluding a fraction of mutants.
• Figure S1: RMSD versus time for the folded- (blue) and unfolded-start (orange) unbiased trajectories. Dashed lines denote the representative RMSD thresholds used here ($\mathrm{thr}_F=0.35~\mathrm{nm}$, $\mathrm{thr}_U=0.69~\mathrm{nm}$), corresponding to the main-text $\Delta\lambda$--$\Delta T_m$ analysis (Fig. \ref{['fig:dhlda_scatter']}).