DiAMoNDBack: Diffusion-Denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces.

Coarse-grained molecular models of proteins permit access to length and time scales unattainable by all-atom models and the simulation of processes that occur on long time scales, such as aggregation and folding. The reduced resolution realizes computational accelerations, but an atomistic representation can be vital for a complete understanding of mechanistic details. Backmapping is the process of restoring all-atom resolution to coarse-grained molecular models. In this work, we report DiAMoNDBack (Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping) as an autoregressive denoising diffusion probability model to restore all-atom details to coarse-grained protein representations retaining only Cα coordinates. The autoregressive generation process proceeds from the protein N-terminus to C-terminus in a residue-by-residue fashion conditioned on the Cα trace and previously backmapped backbone and side-chain atoms within the local neighborhood. The local and autoregressive nature of our model makes it transferable between proteins. The stochastic nature of the denoising diffusion process means that the model generates a realistic ensemble of backbone and side-chain all-atom configurations consistent with the coarse-grained Cα trace. We train DiAMoNDBack over 65k+ structures from the Protein Data Bank (PDB) and validate it in applications to a hold-out PDB test set, intrinsically disordered protein structures from the Protein Ensemble Database (PED), molecular dynamics simulations of fast-folding mini-proteins from DE Shaw Research, and coarse-grained simulation data. We achieve state-of-the-art reconstruction performance in terms of correct bond formation, avoidance of side-chain clashes, and the diversity of the generated side-chain configurational states. We make the DiAMoNDBack model publicly available as a free and open-source Python package.

DEL-Dock: Molecular Docking-Enabled Modeling of DNA-Encoded Libraries.

DNA-encoded library (DEL) technology has enabled significant advances in hit identification by enabling efficient testing of combinatorially generated molecular libraries. DEL screens measure protein binding affinity though sequencing reads of molecules tagged with unique DNA barcodes that survive a series of selection experiments. Computational models have been deployed to learn the latent binding affinities that are correlated to the sequenced count data; however, this correlation is often obfuscated by various sources of noise introduced in its complicated data-generation process. In order to denoise DEL count data and screen for molecules with good binding affinity, computational models require the correct assumptions in their modeling structure to capture the correct signals underlying the data. Recent advances in DEL models have focused on probabilistic formulations of count data, but existing approaches have thus far been limited to only utilizing 2-D molecule-level representations. We introduce a new paradigm, DEL-Dock, that combines ligand-based descriptors with 3-D spatial information from docked protein-ligand complexes. 3-D spatial information allows our model to learn over the actual binding modality rather than using only structure-based information of the ligand. We show that our model is capable of effectively denoising DEL count data to predict molecule enrichment scores that are better correlated with experimental binding affinity measurements compared to prior works. Moreover, by learning over a collection of docked poses we demonstrate that our model, trained only on DEL data, implicitly learns to perform good docking pose selection without requiring external supervision from expensive-to-source protein crystal structures.

Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-Fly Data-Driven Discovery of and Enhanced Sampling in Slow Collective Variables.

Molecular dynamics simulations of microscopic phenomena are limited by the short integration time steps which are required for numerical stability but which limit the practically achievable simulation time scales. Collective variable (CV) enhanced sampling techniques apply biases to predefined collective coordinates to promote barrier crossing, phase space exploration, and sampling of rare events. The efficacy of these techniques is contingent on the selection of good CVs correlated with the molecular motions governing the long-time dynamical evolution of the system. In this work, we introduce Girsanov Reweighting Enhanced Sampling Technique (GREST) as an adaptive sampling scheme that interleaves rounds of data-driven slow CV discovery and enhanced sampling along these coordinates. Since slow CVs are inherently dynamical quantities, a key ingredient in our approach is the use of both thermodynamic and dynamical Girsanov reweighting corrections for rigorous estimation of slow CVs from biased simulation data. We demonstrate our approach on a toy 1D 4-well potential, a simple biomolecular system alanine dipeptide, and the Trp-Leu-Ala-Leu-Leu (WLALL) pentapeptide. In each case GREST learns appropriate slow CVs and drives sampling of all thermally accessible metastable states starting from zero prior knowledge of the system. We make GREST accessible to the community via a publicly available open source Python package.

Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution.

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data.

Orbital Mixer: Using Atomic Orbital Features for Basis-Dependent Prediction of Molecular Wavefunctions.

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous studies focuses on generating predictions for only a fixed set of properties. Recent lines of research instead aim to explicitly learn the electronic structure via molecular wavefunctions, from which other quantum chemical properties can be directly derived. While previous methods generate predictions as a function of only the atomic configuration, in this work we present an alternate approach that directly purposes basis-dependent information to predict molecular electronic structure. Our model, Orbital Mixer, is composed entirely of multi-layer perceptrons (MLPs) using MLP-Mixer layers within a simple, intuitive, and scalable architecture that achieves competitive Hamiltonian and molecular orbital energy and coefficient prediction accuracies compared to the state-of-the-art.

Data-driven discovery of cardiolipin-selective small molecules by computational active learning.

Subtle variations in the lipid composition of mitochondrial membranes can have a profound impact on mitochondrial function. The inner mitochondrial membrane contains the phospholipid cardiolipin, which has been demonstrated to act as a biomarker for a number of diverse pathologies. Small molecule dyes capable of selectively partitioning into cardiolipin membranes enable visualization and quantification of the cardiolipin content. Here we present a data-driven approach that combines a deep learning-enabled active learning workflow with coarse-grained molecular dynamics simulations and alchemical free energy calculations to discover small organic compounds able to selectively permeate cardiolipin-containing membranes. By employing transferable coarse-grained models we efficiently navigate the all-atom design space corresponding to small organic molecules with molecular weight less than ≈500 Da. After direct simulation of only 0.42% of our coarse-grained search space we identify molecules with considerably increased levels of cardiolipin selectivity compared to a widely used cardiolipin probe 10-N-nonyl acridine orange. Our accumulated simulation data enables us to derive interpretable design rules linking coarse-grained structure to cardiolipin selectivity. The findings are corroborated by fluorescence anisotropy measurements of two compounds conforming to our defined design rules. Our findings highlight the potential of coarse-grained representations and multiscale modelling for materials discovery and design.

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.

Computationally Guided Tuning of Amino Acid Configuration Influences the Chiroptical Properties of Supramolecular Peptide-π-Peptide Nanostructures.

Self-assembled supramolecular materials derived from peptidic macromolecules with π-conjugated building blocks are of enormous interest because of their aqueous solubility and biocompatibility. The design rules to achieve tailored optoelectronic properties from these types of materials can be guided by computation and virtual screening rather than intuition-based experimental trial-and-error. Using machine learning, we reported previously that the supramolecular chirality in self-assembled aggregates from VEVAG-π-GAVEV type peptidic materials was most strongly influenced by hydrogen bonding and hydrophobic packing of the alanine and valine residues. Herein, we build upon this idea to demonstrate through molecular-level experimental characterization and all-atom molecular modeling that varying the stereogenic centers of these residues has a profound impact on the optoelectronic properties of the supramolecular aggregates, whereas the variation of stereogenic centers of other residues has only nominal influence on these properties. This study highlights the synergy between computational and experimental insight relevant to the control of chiroptical or other electronic properties associated with supramolecular materials.

Effect of Core Oligomer Length on the Phase Behavior and Assembly of π-Conjugated Peptides.

Biohybrid molecules are a versatile class of materials for controlling the assembly behavior and functional properties of electronically active organics. In this work, we study the effect of the size of the π-conjugated core on the assembly and phase behavior for a series of π-conjugated peptides consisting of oligothiophene cores of defined lengths flanked by sequence-defined peptides (OTX, where X = 4, 5, 6 is the number of thiophene core units). Interestingly, we find that π-conjugated peptides with relatively short OT4 cores assemble into ordered, high aspect ratio, one-dimensional (1D) structures, whereas π-conjugated peptides with longer OT5 and OT6 cores assemble into disordered structures or lower aspect ratio 1D structures depending on assembly conditions. Phase diagrams for assembled materials are experimentally determined as a function of ionic strength, pH, temperature, and peptide concentration, revealing the impact of molecular sequence and π-conjugated core length on assembled morphologies. Molecular dynamics (MD) simulations are further used to probe the origins of microscale differences in assembly that arise from subtle changes in molecular identity. Broadly, our work elucidates the mechanisms governing the assembly of π-conjugated peptides, which will aid in efficient materials processing for soft electronic applications. Overall, these results highlight the complex phase behavior of biohybrid materials, including the impact of molecular sequence on assembly behavior and morphology.

Discovery of Self-Assembling π-Conjugated Peptides by Active Learning-Directed Coarse-Grained Molecular Simulation.

Electronically active organic molecules have demonstrated great promise as novel soft materials for energy harvesting and transport. Self-assembled nanoaggregates formed from π-conjugated oligopeptides composed of an aromatic core flanked by oligopeptide wings offer emergent optoelectronic properties within a water-soluble and biocompatible substrate. Nanoaggregate properties can be controlled by tuning core chemistry and peptide composition, but the sequence-structure-function relations remain poorly characterized. In this work, we employ coarse-grained molecular dynamics simulations within an active learning protocol employing deep representational learning and Bayesian optimization to efficiently identify molecules capable of assembling pseudo-1D nanoaggregates with good stacking of the electronically active π-cores. We consider the DXXX-OPV3-XXXD oligopeptide family, where D is an Asp residue and OPV3 is an oligophenylenevinylene oligomer (1,4-distyrylbenzene), to identify the top performing XXX tripeptides within all 203 = 8000 possible sequences. By direct simulation of only 2.3% of this space, we identify molecules predicted to exhibit superior assembly relative to those reported in prior work. Spectral clustering of the top candidates reveals new design rules governing assembly. This work establishes new understanding of DXXX-OPV3-XXXD assembly, identifies promising new candidates for experimental testing, and presents a computational design platform that can be generically extended to other peptide-based and peptide-like systems.

Controlling Supramolecular Chirality in Peptide-π-Peptide Networks by Variation of the Alkyl Spacer Length.

Self-assembled supramolecular organic materials with π-functionalities are of great interest because of their applications as biocompatible nanoelectronics. A detailed understanding of molecular parameters to modulate the formation of hierarchical structures can inform design principles for materials with engineered optical and electronic properties. In this work, we combine molecular-level characterization techniques with all-atom molecular simulations to investigate the subtle relationship between the chemical structure of peptide-π-peptide molecules and the emergent supramolecular chirality of their spontaneously self-assembled nanoaggregates. We demonstrate through circular dichroism measurements that we can modulate the chirality by incorporating alkyl spacers of various lengths in between the peptides and thienylene-phenylene π-system chromophores: even numbers of alkyl carbons in the spacer units (0, 2) induce M-type helical character whereas odd numbers (1, 3) induce P-type. Corroborating molecular dynamics simulations and explicating machine learning analysis techniques identify hydrogen bonding and hydrophobic packing to be the principal discriminants of the observed chirality switches. Our results present a molecular-level design rule to engineer chirality into optically and electronically active nanoaggregates of these peptidic building blocks by exploiting systematic variations in the alkyl spacer length.

Modeling Protein-Based Hydrogels under Force.

Hydrogels made from structured polyprotein domains combine the properties of cross-linked polymers with the unfolding phase transition. The use of protein hydrogels as an ensemble approach to study the physics of domain unfolding is limited by the lack of scaling tools and by the complexity of the system. Here we propose a model to describe the biomechanical response of protein hydrogels based on the unfolding and extension of protein domains under force. Our model considers the contributions of the network dynamics of the molecules inside the gels, which have random cross-linking points and random topology. This model reproduces reported macroscopic viscoelastic effects and constitutes an important step toward using rheometry on protein hydrogels to scale down to the average mechanical response of protein molecules.

Force-Clamp Rheometry for Characterizing Protein-based Hydrogels.

Here, we describe a force-clamp rheometry method to characterize the biomechanical properties of protein-based hydrogels. This method uses an analog proportional-integral-derivative (PID) system to apply controlled-force protocols on cylindrical protein-based hydrogel samples, which are tethered between a linear voice-coil motor and a force transducer. During operation, the PID system adjusts the extension of the hydrogel sample to follow a predefined force protocol by minimizing the difference between the measured and set-point forces. This unique approach to protein-based hydrogels enables the tethering of extremely low-volume hydrogel samples (< 5 µL) with different protein concentrations. Under force-ramp protocols, where the applied stress increases and decreases linearly with time, the system enables the study of the elasticity and hysteresis behaviors associated with the (un)folding of proteins and the measurement of standard elastic and viscoelastic parameters. Under constant-force, where the force pulse has a step-like shape, the elastic response, due to the change in force, is decoupled from the viscoelastic response, which comes from protein domain unfolding and refolding. Due to its low-volume sample and versatility in applying various mechanical perturbations, force-clamp rheometry is optimized to investigate the mechanical response of proteins under force using a bulk approach.