Vijay S. Pande

Peter Eastman, Raimondas Galvelis, Raúl P. Peláez et al.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features on simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein (GFP) chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations at only a modest increase in cost.

Evan N. Feinberg, Robert Sheridan, Elizabeth Joshi et al.

The Absorption, Distribution, Metabolism, Elimination, and Toxicity (ADMET) properties of drug candidates are estimated to account for up to 50% of all clinical trial failures. Predicting ADMET properties has therefore been of great interest to the cheminformatics and medicinal chemistry communities in recent decades. Traditional cheminformatics approaches, whether the learner is a random forest or a deep neural network, leverage fixed fingerprint feature representations of molecules. In contrast, in this paper, we learn the features most relevant to each chemical task at hand by representing each molecule explicitly as a graph, where each node is an atom and each edge is a bond. By applying graph convolutions to this explicit molecular representation, we achieve, to our knowledge, unprecedented accuracy in prediction of ADMET properties. By challenging our methodology with rigorous cross-validation procedures and prospective analyses, we show that deep featurization better enables molecular predictors to not only interpolate but also extrapolate to new regions of chemical space.

Amir Barati Farimani, Joseph Gomes, Rishi Sharma et al.

Phase segregation, the process by which the components of a binary mixture spontaneously separate, is a key process in the evolution and design of many chemical, mechanical, and biological systems. In this work, we present a data-driven approach for the learning, modeling, and prediction of phase segregation. A direct mapping between an initially dispersed, immiscible binary fluid and the equilibrium concentration field is learned by conditional generative convolutional neural networks. Concentration field predictions by the deep learning model conserve phase fraction, correctly predict phase transition, and reproduce area, perimeter, and total free energy distributions up to 98% accuracy.

Hannah K. Wayment-Steele, Vijay S. Pande

As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the timescale of the latent space while inferring a reduced coordinate, which assists in finding slow processes as according to the variational approach to conformational dynamics. We additionally provide evidence that the VDE framework (Hernández et al., 2017), which uses this autocorrelation loss along with a time-lagged reconstruction loss, obtains a variationally optimized latent coordinate in comparison with related loss functions. We thus recommend leveraging the autocorrelation of the latent space while training neural network models of biomolecular simulation data to better represent slow processes.

Evan N. Feinberg, Amir Barati Farimani, Rajendra Uprety et al.

Computational chemists typically assay drug candidates by virtually screening compounds against crystal structures of a protein despite the fact that some targets, like the $μ$ Opioid Receptor and other members of the GPCR family, traverse many non-crystallographic states. We discover new conformational states of $μOR$ with molecular dynamics simulation and then machine learn ligand-structure relationships to predict opioid ligand function. These artificial intelligence models identified a novel $μ$ opioid chemotype.

Evan N. Feinberg, Debnil Sur, Zhenqin Wu et al.

The arc of drug discovery entails a multiparameter optimization problem spanning vast length scales. They key parameters range from solubility (angstroms) to protein-ligand binding (nanometers) to in vivo toxicity (meters). Through feature learning---instead of feature engineering---deep neural networks promise to outperform both traditional physics-based and knowledge-based machine learning models for predicting molecular properties pertinent to drug discovery. To this end, we present the PotentialNet family of graph convolutions. These models are specifically designed for and achieve state-of-the-art performance for protein-ligand binding affinity. We further validate these deep neural networks by setting new standards of performance in several ligand-based tasks. In parallel, we introduce a new metric, the Regression Enrichment Factor $EF_χ^{(R)}$, to measure the early enrichment of computational models for chemical data. Finally, we introduce a cross-validation strategy based on structural homology clustering that can more accurately measure model generalizability, which crucially distinguishes the aims of machine learning for drug discovery from standard machine learning tasks.

Jade Shi, Rhiju Das, Vijay S. Pande

Solving the RNA inverse folding problem is a critical prerequisite to RNA design, an emerging field in bioengineering with a broad range of applications from reaction catalysis to cancer therapy. Although significant progress has been made in developing machine-based inverse RNA folding algorithms, current approaches still have difficulty designing sequences for large or complex targets. On the other hand, human players of the online RNA design game EteRNA have consistently shown superior performance in this regard, being able to readily design sequences for targets that are challenging for machine algorithms. Here we present a novel approach to the RNA design problem, SentRNA, a design agent consisting of a fully-connected neural network trained end-to-end using human-designed RNA sequences. We show that through this approach, SentRNA can solve complex targets previously unsolvable by any machine-based approach and achieve state-of-the-art performance on two separate challenging test sets. Our results demonstrate that incorporating human design strategies into a design algorithm can significantly boost machine performance and suggests a new paradigm for machine-based RNA design.

Carlos X. Hernández, Mohammad M. Sultan, Vijay S. Pande

Cell counting is a ubiquitous, yet tedious task that would greatly benefit from automation. From basic biological questions to clinical trials, cell counts provide key quantitative feedback that drive research. Unfortunately, cell counting is most commonly a manual task and can be time-intensive. The task is made even more difficult due to overlapping cells, existence of multiple focal planes, and poor imaging quality, among other factors. Here, we describe a convolutional neural network approach, using a recently described feature pyramid network combined with a VGG-style neural network, for segmenting and subsequent counting of cells in a given microscopy image.

Mohammad M. Sultan, Vijay S. Pande

Selection of appropriate collective variables for enhancing sampling of molecular simulations remains an unsolved problem in computational biophysics. In particular, picking initial collective variables (CVs) is particularly challenging in higher dimensions. Which atomic coordinates or transforms there of from a list of thousands should one pick for enhanced sampling runs? How does a modeler even begin to pick starting coordinates for investigation? This remains true even in the case of simple two state systems and only increases in difficulty for multi-state systems. In this work, we solve the initial CV problem using a data-driven approach inspired by the filed of supervised machine learning. In particular, we show how the decision functions in supervised machine learning (SML) algorithms can be used as initial CVs (SML_cv) for accelerated sampling. Using solvated alanine dipeptide and Chignolin mini-protein as our test cases, we illustrate how the distance to the Support Vector Machines' decision hyperplane, the output probability estimates from Logistic Regression, the outputs from deep neural network classifiers, and other classifiers may be used to reversibly sample slow structural transitions. We discuss the utility of other SML algorithms that might be useful for identifying CVs for accelerating molecular simulations.

Mohammad M. Sultan, Hannah K. Wayment-Steele, Vijay S. Pande

Variational auto-encoder frameworks have demonstrated success in reducing complex nonlinear dynamics in molecular simulation to a single non-linear embedding. In this work, we illustrate how this non-linear latent embedding can be used as a collective variable for enhanced sampling, and present a simple modification that allows us to rapidly perform sampling in multiple related systems. We first demonstrate our method is able to describe the effects of force field changes in capped alanine dipeptide after learning a model using AMBER99. We further provide a simple extension to variational dynamics encoders that allows the model to be trained in a more efficient manner on larger systems by encoding the outputs of a linear transformation using time-structure based independent component analysis (tICA). Using this technique, we show how such a model trained for one protein, the WW domain, can efficiently be transferred to perform enhanced sampling on a related mutant protein, the GTT mutation. This method shows promise for its ability to rapidly sample related systems using a single transferable collective variable and is generally applicable to sets of related simulations, enabling us to probe the effects of variation in increasingly large systems of biophysical interest.

Brooke E. Husic, Vijay S. Pande

In this report, we present an unsupervised machine learning method for determining groups of molecular systems according to similarity in their dynamics or structures using Ward's minimum variance objective function. We first apply the minimum variance clustering to a set of simulated tripeptides using the information theoretic Jensen-Shannon divergence between Markovian transition matrices in order to gain insight into how point mutations affect protein dynamics. Then, we extend the method to partition two chemoinformatic datasets according to structural similarity to motivate a train/validation/test split for supervised learning that avoids overfitting.

Carlos X. Hernández, Hannah K. Wayment-Steele, Mohammad M. Sultan et al.

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged co-variate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of variational autoencoders (VAE), which are able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.

Amir Barati Farimani, Joseph Gomes, Vijay S. Pande

We have developed a new data-driven paradigm for the rapid inference, modeling and simulation of the physics of transport phenomena by deep learning. Using conditional generative adversarial networks (cGAN), we train models for the direct generation of solutions to steady state heat conduction and incompressible fluid flow purely on observation without knowledge of the underlying governing equations. Rather than using iterative numerical methods to approximate the solution of the constitutive equations, cGANs learn to directly generate the solutions to these phenomena, given arbitrary boundary conditions and domain, with high test accuracy (MAE$<$1\%) and state-of-the-art computational performance. The cGAN framework can be used to learn causal models directly from experimental observations where the underlying physical model is complex or unknown.

Joseph Gomes, Bharath Ramsundar, Evan N. Feinberg et al.

Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a drug-like molecule to a given target. These models require expert-level knowledge of physical chemistry and biology to be encoded as hand-tuned parameters or features rather than allowing the underlying model to select features in a data-driven procedure. Here, we develop a general 3-dimensional spatial convolution operation for learning atomic-level chemical interactions directly from atomic coordinates and demonstrate its application to structure-based bioactivity prediction. The atomic convolutional neural network is trained to predict the experimentally determined binding affinity of a protein-ligand complex by direct calculation of the energy associated with the complex, protein, and ligand given the crystal structure of the binding pose. Non-covalent interactions present in the complex that are absent in the protein-ligand sub-structures are identified and the model learns the interaction strength associated with these features. We test our model by predicting the binding free energy of a subset of protein-ligand complexes found in the PDBBind dataset and compare with state-of-the-art cheminformatics and machine learning-based approaches. We find that all methods achieve experimental accuracy and that atomic convolutional networks either outperform or perform competitively with the cheminformatics based methods. Unlike all previous protein-ligand prediction systems, atomic convolutional networks are end-to-end and fully-differentiable. They represent a new data-driven, physics-based deep learning model paradigm that offers a strong foundation for future improvements in structure-based bioactivity prediction.

Bharath Ramsundar, Vijay S. Pande

We introduce a machine learning approach for extracting fine-grained representations of protein evolution from molecular dynamics datasets. Metastable switching linear dynamical systems extend standard switching models with a physically-inspired stability constraint. This constraint enables the learning of nuanced representations of protein dynamics that closely match physical reality. We derive an EM algorithm for learning, where the E-step extends the forward-backward algorithm for HMMs and the M-step requires the solution of large biconvex optimization problems. We construct an approximate semidefinite program solver based on the Frank-Wolfe algorithm and use it to solve the M-step. We apply our EM algorithm to learn accurate dynamics from large simulation datasets for the opioid peptide met-enkephalin and the proto-oncogene Src-kinase. Our learned models demonstrate significant improvements in temporal coherence over HMMs and standard switching models for met-enkephalin, and sample transition paths (possibly useful in rational drug design) for Src-kinase.

Robert T. McGibbon, Bharath Ramsundar, Mohammad M. Sultan et al.

We present a machine learning framework for modeling protein dynamics. Our approach uses L1-regularized, reversible hidden Markov models to understand large protein datasets generated via molecular dynamics simulations. Our model is motivated by three design principles: (1) the requirement of massive scalability; (2) the need to adhere to relevant physical law; and (3) the necessity of providing accessible interpretations, critical for both cellular biology and rational drug design. We present an EM algorithm for learning and introduce a model selection criteria based on the physical notion of convergence in relaxation timescales. We contrast our model with standard methods in biophysics and demonstrate improved robustness. We implement our algorithm on GPUs and apply the method to two large protein simulation datasets generated respectively on the NCSA Bluewaters supercomputer and the Folding@Home distributed computing network. Our analysis identifies the conformational dynamics of the ubiquitin protein critical to cellular signaling, and elucidates the stepwise activation mechanism of the c-Src kinase protein.