^{1}and Philippe H. Hünenberger

^{1,a)}

### Abstract

Estimating the relative stabilities of different conformational states of a (bio-)molecule using molecular dynamics simulations involves two challenging problems: the conceptual problem of how to define the states of interest and the technical problem of how to properly sample these states, along with achieving a sufficient number of interconversion transitions. In this study, the two issues are addressed in the context of a decaalanine peptide in water, by considering the 310-, α-, and π-helical states. The simulations rely on the ball-and-stick local-elevation umbrella-sampling (B&S-LEUS) method. In this scheme, the states are defined as hyperspheres (balls) in a (possibly high dimensional) collective-coordinate space and connected by hypercylinders (sticks) to ensure transitions. A new object, the pipe, is also introduced here to handle curvilinear pathways. Optimal sampling within the so-defined space is ensured by confinement and (one-dimensional) memory-based biasing potentials associated with the three different kinds of objects. The simulation results are then analysed in terms of free energies using reweighting, possibly relying on two distinct sets of collective coordinates for the state definition and analysis. The four possible choices considered for these sets are Cartesian coordinates, hydrogen-bond distances, backbone dihedral angles, or pairwise sums of successive backbone dihedral angles. The results concerning decaalanine underline that the concept of conformational state may be extremely ambiguous, and that its tentative absolute definition as a free-energy basin remains subordinated to the choice of a specific analysis space. For example, within the force-field employed and depending on the analysis coordinates selected, the 310-helical state may refer to weakly overlapping collections of conformations, differing by as much as 25 kJ mol^{−1} in terms of free energy. As another example, the π-helical state appears to correspond to a free-energy basin for three choices of analysis coordinates, but to be unstable with the fourth one. The problem of conformational-state definition may become even more intricate when comparison with experiment is involved, where the state definition relies on spectroscopic or functional observables.

Financial support from the Swiss National Science Foundation (Grant Nos. 21-132739 and 21-138020) is gratefully acknowledged.

I. INTRODUCTION II. THEORY III. COMPUTATIONAL DETAILS IV. RESULTS AND DISCUSSION V. CONCLUSIONS

### Key Topics

- Free energy
- 57.0
- Molecular conformation
- 21.0
- Special unitary groups
- 18.0
- Conformational dynamics
- 14.0
- Peptides
- 13.0