Peptide-Cation Systems: Conformational Search, Benchmark Evaluation, and Force Field Parameter Adjustment Using Regularized Linear Regression

Metal cations often play an important role in shaping the three-dimensional structure of peptides. As an example, the model system AcPheAla5LysH+ is investigated in order to fully understand the forces that stabilize its helical structure. In particular, the question of whether the local fixation of the positive charge at the peptide's C-terminus is a prerequisite for forming helices is addressed by replacing the protonated lysine residue by alanine and a sodium cation. The combination of gas-phase cold-ion vibrational spectroscopy with molecular simulations based on density-functional theory (DFT) revealed that the charge localization at the C-terminus is imperative for helix formation in the gas phase as this stabilizes the structure through a cation-helix dipole interaction. For sodiated AcPheAla6, globular rather than helical structures were found caused by the strong cation-backbone and cation-pi interactions. Interestingly, the global minimum-energy structure from simulation is not present in the experiment where the system remains kinetically trapped in a solution-state structure.

Thereby calculated energies and IR spectra that are sufficiently accurate relied on DFT with computationally costly hybrid functionals, while for the structure search low-computational-cost force field (FF) models are crucial. This inspired a study where the goodness of commonly applied levels of theory, i.e. FFs, semi-empirical methods, density-functional approximations, composite methods, and wavefunction-based methods are being evaluated with respect to benchmark-grade coupled-cluster calculations. Acetylhistidine - either bare or in presence of a zinc cation - thereby serves as a molecular benchmark system. Neither FFs nor semi-empirical methods are reliable enough for a description of these systems within "chemical accuracy" of 1 kcal/mol. Accurate energetic description within chemical accuracy is achieved for all systems using the meta-GGA SCAN or computationally more demanding hybrid functionals. The double-hybrid functional B3LYP+XYG3 is best resembling the benchmark method DLPNO-CCSD(T).

Despite poor energetic performances of conventional FFs for peptides in the gas phase, their low computational costs still render them appealing tools for large-scale structure searches. Consequently, a machine learning approach is presented where the torsional parameters and (if desired) van der Waals parameters in the potential-energy function of a particular FF are adjusted by fitting it against DFT energies using regularized regression models like LASSO or Ridge regression. For the peptide AcAla2NMe, this resulted in a significant improvement when comparing to standard OPLS-AA parameters. For more challenging peptide-cation systems, e.g. AcAla2NMe + Na+, this approach does not give satisfying results, which is caused by the formulation of the potential energy of the FF itself: While derived empirical partial charges using Hirshfeld partitioning or the electrostatic potential (ESP) decrease the accuracy, part of the energetic discrepancy can be "compensated" due to the flexibility of the torsional contributions in terms of the energetic description.