Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables.

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

Computationally Guided Tuning of Peptide-Conjugated Perylene Diimide Self-Assembly.

Peptide-π-conjugated materials are important for biointerfacing charge-transporting applications due to their aqueous compatibility and formation of long-range π-electron networks. Perylene diimides (PDIs), well-established charge-transporting π systems, can self-assemble in aqueous solutions when conjugated with amino acids. In this work, we leveraged computational guidance from our previous work to access two different self-assembled architectures from PDI-amino acid conjugates. Furthermore, we expanded the design rule to other sequences to learn that the closest amino acids to the π core have a significant effect on the photophysical properties of the resulting assemblies. By simply altering glycine to alanine at the closest residue position, we observed significantly different electronic properties as revealed through UV-vis, photoluminescence, and circular dichroism spectroscopies. Accompanying molecular dynamics simulations revealed two distinct types of self-assembled architectures: cofacial structures when the smaller glycine residue is at the closest residue position to the π core versus rotationally shifted structures when glycine is substituted for the larger alanine. This study illustrates the use of tandem computations and experiments to unearth and understand new design rules for supramolecular materials and exposes a modest amino acid substitution as a means to predictably modulate the supramolecular organization and engineer the photophysical properties of π-conjugated peptidic materials.