Tripeptide-Dynamics from Empirical and Machine-Learned Energy Functions

TL;DR

The study demonstrates that neural-network PESs trained on MP2-level data enable nanosecond MP2-accurate MD of tripeptides AAA and AMA, linking conformational sampling to vibrational spectroscopy. For AAA in solution, the PhysNet-based ML-PES reproduces the amide-I doublet with a $25\, \mathrm{cm^{-1}}$ splitting and shows a $\beta$-sheet/$PPII$-dominated ensemble alongside altered hydration shells. For AMA in the gas phase, REMD-enabled training and a PES that encompasses zwitterionic and neutral forms reveal distinct low-energy basins in the $[\Phi,\Psi]$ space, with neutral AMA displaying two wells at $[\Phi=-90,\Psi=-60]^{\circ}$ and $[\Phi=100,\Psi=-50]^{\circ}$, and a pronounced red shift of NH/OH stretches below $3000\, \mathrm{cm^{-1}}$. The work confirms that high-level ML-PESs can deliver chemically meaningful MD trajectories and spectroscopic predictions on multi-nanosecond timescales, providing a scalable route to interrogate short peptide dynamics, with data available at https://github.com/MMunibas/aaa. AMA.

Abstract

Molecular dynamics simulations for tripeptides in the gas phase and in solution using empirical and machine-learned energy functions are presented. For cationic AAA a machine-learned potential energy surface (ML-PES) trained on MP2 reference data yields quantitative agreement with measured splittings of the amide-I vibrations. Experimental spectroscopy in solution reports a splitting of 25 cm-1 which compares with 20 cm-1 from ML/MM-MD simulations of AAA in explicit solvent. For the AMA tripeptide a ML-PES describing both, the zwitterionic and neutral form is trained and used to map out the accessible conformational space. Due to cyclization and H-bonding between the termini in neutral AMA the NH- and OH-stretch spectra are strongly red-shifted below 3000 cm-1. The present work demonstrates that meaningful MD simulations on the nanosecond time scale are feasible and provides insight into experiments.

Figures (15)

• Figure 1: Top: The structure of cationic AAA with ALA1, ALA2, and ALA3 labelled. The $\Phi$ (red, 1) and $\Psi$ (lila, 2) angles are indicated and the three -CO groups for which the IR spectra were determined are highlighted (blue, red, green). Panel A: $[\Phi,\Psi]-$angle (Ramachandran) plot for AAA simulations using CGenFF. Panel B: $[\Phi,\Psi]-$angles from simulations using the PhysNet model in ML/MM-MD simulations. The total simulation time was 1.5 ns and the histogram was generated from $250 \ 250$ bins.
• Figure 2: The radial distribution functions, $g(r)$, as a function of the distance between the water oxygen atoms, O$_{\rm W}$, and O$_{\rm CO}$ atoms for ALA1, ALA2, and ALA3, from top to bottom, see Figure \ref{['fig:ramachandran_aaa']}. Results from simulations using CGenFF and the ML/MM energy functions are shown as dashed and solid lines. The line colors correspond to the respective selected oxygen atoms, see Figure \ref{['fig:ramachandran_aaa']}.
• Figure 3: Relaxed pseudo-free energy surface for cationic AAA in terms of $\Phi$ and $\Psi$ dihedrals. The underlying probability distribution $P(\Phi,\Psi)$ was calculated after relaxation of the angles by sampling structures at 1 ns from simulations using the CGenFF energy function. This is not an equilibrium free energy surface but rather informs about possible low-energy regions sampled on the 1 ns time scale.
• Figure 4: Comparison of computed IR and power spectra (PS) for the cationic AAA and measurements.woutersen:2000 Panel A: IR spectra from ML/MM-MD (red trace) and simulations using CGenFF (black trace). Panel B: IR spectrum from ML/MM-MD simulations together with corresponding power spectra for --C=O group in ALA1, ALA2, and ALA3 (blue, orange, green). Panels C to E: Power spectra and IR spectra for the isotopically substituted $^{13}$C=O at ALA1 (C), ALA2 (D), and ALA3 (E), illustrating the spectral shifts induced by the isotopic substitution for each residue in ML/MM-MD simulations. The two arrows on top of Panel A indicate the experimentally measured line positions at 1650 and 1675 cm$^{-1}$, split by 25 cm$^{-1}$.woutersen:2000 The dashed vertical lines are shifted to best overlap with the doublet-structure at 1780, 1800 and 1839 cm$^{-1}$ which leads to a splitting of 20 cm$^{-1}$ from the ML/MM-MD simulations. For simulations using the CGenFF, see Figure \ref{['sifig:aaa-cgenff']}.
• Figure 5: Top: structure of zwitterionic AMA with labelled and dihedral angles $[\Phi,\Psi]$ indicated. Panel A: Dihedral distribution for zwitterionic AMA in the gas phase obtained from relaxed dynamics after releasing constraints using the CGenFF energy function. Darker regions indicate more populated conformations. Panel B: Two-dimensional free energy surface at 300 K as a function of the $[\Phi,\Psi]$ dihedral angles obtained from REMD simulation for zwitterionic AMA using CGenFF. A single minimum near the PPII structure is found (black). Panel C: As for panel B but using softened XH-bond potentials for generating training data for the ML-PES. Panel D: Dihedral angle distribution from pyCHARMM MD simulations, 200 ps in length at 300 K, using the ML-PES for AMA in the gas phase. This simulations started from extended, zwitterionic AMA but ring-closure and neutralization already occurred during minimization. Hence, this landscape is for neutral AMA. Two wells centered at $[\Phi=-90,\Psi=-60]^\circ$ and $[\Phi=100,\Psi=-50]^\circ$ are found.