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