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Feinberg, Evan N., Sheridan, Robert, Joshi, Elizabeth, Pande, Vijay S., and Cheng, Alan C.
 Subjects

Computer Science  Machine Learning and Statistics  Machine Learning
 Abstract

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 crossvalidation 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.
Comment: 41 pages
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Sinitskiy, Anton V. and Pande, Vijay S.
 Subjects

Physics  Chemical Physics and Physics  Computational Physics
 Abstract

Density functional theory (DFT) is one of the main methods in Quantum Chemistry that offers an attractive trade off between the cost and accuracy of quantum chemical computations. The electron density plays a key role in DFT. In this work, we explore whether machine learning  more specifically, deep neural networks (DNNs)  can be trained to predict electron densities faster than DFT. First, we choose a practically efficient combination of a DFT functional and a basis set (PBE0/pcS3) and use it to generate a database of DFT solutions for more than 133,000 organic molecules from a previously published database QM9. Next, we train a DNN to predict electron densities and energies of such molecules. The only input to the DNN is an approximate electron density computed with a cheap quantum chemical method in a small basis set (HF/ccVDZ). We demonstrate that the DNN successfully learns differences in the electron densities arising both from electron correlation and small basis set artifacts in the HF computations. All qualitative features in density differences, including local minima on lone pairs, local maxima on nuclei, toroidal shapes around CH and CC bonds, complex shapes around aromatic and cyclopropane rings and CN group, etc. are captured by the DNN. Accuracy of energy predictions by the DNN is ~ 1 kcal/mol, on par with other models reported in the literature, while those models do not predict the electron density. Computations with the DNN, including HF computations, take much less time that DFT computations (by a factor of ~2030 for most QM9 molecules in the current version, and it is clear how it could be further improved).
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Eastman, Peter and Pande, Vijay S.
 Subjects

Quantitative Biology  Genomics
 Abstract

We train a neural network to predict chemical toxicity based on gene expression data. The input to the network is a full expression profile collected either in vitro from cultured cells or in vivo from live animals. The output is a set of fine grained predictions for the presence of a variety of pathological effects in treated animals. When trained on the Open TGGATEs database it produces good results, outperforming classical models trained on the same data. This is a promising approach for efficiently screening chemicals for toxic effects, and for more accurately evaluating drug candidates based on preclinical data.
Comment: 12 pages, 2 figures, 4 tables
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4. Improved Training with Curriculum GANs [2018]

Sharma, Rishi, Barratt, Shane, Ermon, Stefano, and Pande, Vijay
 Subjects

Computer Science  Machine Learning, Computer Science  Artificial Intelligence, and Statistics  Machine Learning
 Abstract

In this paper we introduce Curriculum GANs, a curriculum learning strategy for training Generative Adversarial Networks that increases the strength of the discriminator over the course of training, thereby making the learning task progressively more difficult for the generator. We demonstrate that this strategy is key to obtaining stateoftheart results in image generation. We also show evidence that this strategy may be broadly applicable to improving GAN training in other data modalities.
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Sharma, Rishi, Farimani, Amir Barati, Gomes, Joe, Eastman, Peter, and Pande, Vijay
 Subjects

Statistics  Machine Learning and Computer Science  Machine Learning
 Abstract

In typical machine learning tasks and applications, it is necessary to obtain or create large labeled datasets in order to to achieve high performance. Unfortunately, large labeled datasets are not always available and can be expensive to source, creating a bottleneck towards more widely applicable machine learning. The paradigm of weak supervision offers an alternative that allows for integration of domainspecific knowledge by enforcing constraints that a correct solution to the learning problem will obey over the output space. In this work, we explore the application of this paradigm to 2D physical systems governed by nonlinear differential equations. We demonstrate that knowledge of the partial differential equations governing a system can be encoded into the loss function of a neural network via an appropriately chosen convolutional kernel. We demonstrate this by showing that the steadystate solution to the 2D heat equation can be learned directly from initial conditions by a convolutional neural network, in the absence of labeled training data. We also extend recent work in the progressive growing of fully convolutional networks to achieve high accuracy (< 1.5% error) at multiple scales of the heatflow problem, including at the very large scale (1024x1024). Finally, we demonstrate that this method can be used to speed up exact calculation of the solution to the differential equations via finite difference.
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6. Binding Pathway of Opiates to $\mu$ Opioid Receptors Revealed by Unsupervised Machine Learning [2018]

Farimani, Amir Barati, Feinberg, Evan N., and Pande, Vijay S.
 Subjects

Quantitative Biology  Biomolecules and Quantitative Biology  Quantitative Methods
 Abstract

Many important analgesics relieve pain by binding to the $\mu$Opioid Receptor ($\mu$OR), which makes the $\mu$OR among the most clinically relevant proteins of the G Protein Coupled Receptor (GPCR) family. Despite previous studies on the activation pathways of the GPCRs, the mechanism of opiate binding and the selectivity of $\mu$OR are largely unknown. We performed extensive molecular dynamics (MD) simulation and analysis to find the selective allosteric binding sites of the $\mu$OR and the path opiates take to bind to the orthosteric site. In this study, we predicted that the allosteric site is responsible for the attraction and selection of opiates. Using Markov state models and machine learning, we traced the pathway of opiates in binding to the orthosteric site, the main binding pocket. Our results have important implications in designing novel analgesics.
Comment: 25 pages, 8 figures
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7. Deep Learning Phase Segregation [2018]

Farimani, Amir Barati, Gomes, Joseph, Sharma, Rishi, Lee, Franklin L., and Pande, Vijay S.
 Subjects

Computer Science  Learning, Physics  Computational Physics, and Statistics  Machine Learning
 Abstract

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 datadriven 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.
Comment: arXiv admin note: text overlap with arXiv:1709.02432
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8. Note: Variational Encoding of Protein Dynamics Benefits from Maximizing Latent Autocorrelation [2018]

WaymentSteele, Hannah K. and Pande, Vijay S.
 Subjects

Physics  Chemical Physics, Computer Science  Learning, Physics  Biological Physics, and Statistics  Machine Learning
 Abstract

As deep Variational AutoEncoder (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 (Hern\'andez et al., 2017), which uses this autocorrelation loss along with a timelagged 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.
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Feinberg, Evan N., Farimani, Amir Barati, Uprety, Rajendra, Hunkele, Amanda, Pasternak, Gavril W., Majumdar, Susruta, and Pande, Vijay S.
 Subjects

Quantitative Biology  Biomolecules and Statistics  Machine Learning
 Abstract

Computational chemists typically assay drug candidates by virtually screening compounds against crystal structures of a protein despite the fact that some targets, like the $\mu$ Opioid Receptor and other members of the GPCR family, traverse many noncrystallographic states. We discover new conformational states of $\mu OR$ with molecular dynamics simulation and then machine learn ligandstructure relationships to predict opioid ligand function. These artificial intelligence models identified a novel $\mu$ opioid chemotype.
Comment: 28 pages, machine learning, computational biology, GPCRs, molecular dynamics, molecular docking, molecular simulation
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Feinberg, Evan N., Sur, Debnil, Wu, Zhenqin, Husic, Brooke E., Mai, Huanghao, Li, Yang, Sun, Saisai, Yang, Jianyi, Ramsundar, Bharath, and Pande, Vijay S.
 Subjects

Computer Science  Machine Learning
 Abstract

The arc of drug discovery entails a multiparameter optimization problem spanning vast length scales. They key parameters range from solubility (angstroms) to proteinligand binding (nanometers) to in vivo toxicity (meters). Through feature learninginstead of feature engineeringdeep neural networks promise to outperform both traditional physicsbased and knowledgebased 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 stateoftheart performance for proteinligand binding affinity. We further validate these deep neural networks by setting new standards of performance in several ligandbased tasks. In parallel, we introduce a new metric, the Regression Enrichment Factor $EF_\chi^{(R)}$, to measure the early enrichment of computational models for chemical data. Finally, we introduce a crossvalidation 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.
Comment: 13 pages, 5 figures, 8 tables
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Hernández, Carlos X., Sultan, Mohammad M., and Pande, Vijay S.
 Subjects

Computer Science  Computer Vision and Pattern Recognition, Computer Science  Learning, and Quantitative Biology  Quantitative Methods
 Abstract

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 timeintensive. 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 VGGstyle neural network, for segmenting and subsequent counting of cells in a given microscopy image.
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Sultan, Mohammad M. and Pande, Vijay S.
 Subjects

Statistics  Machine Learning, Computer Science  Computational Engineering, Finance, and Science, and Quantitative Biology  Biomolecules
 Abstract

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 multistate systems. In this work, we solve the initial CV problem using a datadriven 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 miniprotein 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.
Comment: 26 pages, 11 figures
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Wagoner, Jason A. and Pande, Vijay S.
 Subjects

Physics  Computational Physics and Condensed Matter  Statistical Mechanics
 Abstract

Combinedresolution simulations are an effective way to study molecular properties across a range of length and timescales. These simulations can benefit from adaptive boundaries that allow the highresolution region to adapt (change size and/or shape) as the simulation progresses. The number of degrees of freedom required to accurately represent even a simple molecular process can vary by several orders of magnitude throughout the course of a simulation, and adaptive boundaries react to these changes to include an appropriate but not excessive amount of detail. Here, we derive the Hamiltonian and distribution function for such a molecular simulation. We also design an algorithm that can efficiently sample the boundary as a new coordinate of the system. We apply this framework to a mixed explicit/continuum representation of a peptide in solvent. We use this example to discuss the conditions necessary for a successful implementation of adaptive boundaries that is both efficient and accurate in reproducing molecular properties.
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You, Jiaxuan, Liu, Bowen, Ying, Rex, Pande, Vijay, and Leskovec, Jure
 Subjects

Computer Science  Machine Learning, Computer Science  Artificial Intelligence, and Statistics  Machine Learning
 Abstract

Generating novel graph structures that optimize given objectives while obeying some given underlying rules is fundamental for chemistry, biology and social science research. This is especially important in the task of molecular graph generation, whose goal is to discover novel molecules with desired properties such as druglikeness and synthetic accessibility, while obeying physical laws such as chemical valency. However, designing models to find molecules that optimize desired properties while incorporating highly complex and nondifferentiable rules remains to be a challenging task. Here we propose Graph Convolutional Policy Network (GCPN), a general graph convolutional network based model for goaldirected graph generation through reinforcement learning. The model is trained to optimize domainspecific rewards and adversarial loss through policy gradient, and acts in an environment that incorporates domainspecific rules. Experimental results show that GCPN can achieve 61% improvement on chemical property optimization over stateoftheart baselines while resembling known molecules, and achieve 184% improvement on the constrained property optimization task.
Comment: NeurIPS 2018, spotlight presentation
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Husic, Brooke E. and Pande, Vijay S.
 Subjects

Physics  Biological Physics, Quantitative Biology  Biomolecules, Quantitative Biology  Quantitative Methods, and Statistics  Machine Learning
 Abstract

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 JensenShannon 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.
Comment: NIPS 2017 Workshop on Machine Learning for Molecules and Materials
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16. Variational Encoding of Complex Dynamics [2017]

Hernández, Carlos X., WaymentSteele, Hannah K., Sultan, Mohammad M., Husic, Brooke E., and Pande, Vijay S.
 Phys. Rev. E 97, 062412 (2018)
 Subjects

Statistics  Machine Learning, Physics  Biological Physics, Physics  Chemical Physics, Physics  Computational Physics, and Quantitative Biology  Biomolecules
 Abstract

Often the analysis of timedependent chemical and biophysical systems produces highdimensional timeseries 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 timelagged covariate 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 timelagged 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.
Comment: Fixed typos and added references
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17. SentRNA: Improving computational RNA design by incorporating a prior of human design strategies [2018]

Shi, Jade, Das, Rhiju, and Pande, Vijay S.
 Subjects

Quantitative Biology  Quantitative Methods, Computer Science  Artificial Intelligence, and Statistics  Machine Learning
 Abstract

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 machinebased 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 fullyconnected neural network trained endtoend using humandesigned RNA sequences. We show that through this approach, SentRNA can solve complex targets previously unsolvable by any machinebased approach and achieve stateoftheart 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 machinebased RNA design.
Comment: 27 pages (not including Supplementary Information), 9 figures, 7 tables
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Farimani, Amir Barati, Gomes, Joseph, and Pande, Vijay S.
 Subjects

Computer Science  Learning and Physics  Computational Physics
 Abstract

We have developed a new datadriven 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 stateoftheart 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.
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Husic, Brooke E. and Pande, Vijay S.
 Subjects

Quantitative Biology  Biomolecules, Physics  Biological Physics, and Physics  Chemical Physics
 Abstract

The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note we discuss why lag time of the operator being approximated must be held constant in the variational approach.
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Sinitskiy, Anton V. and Pande, Vijay S.
 Subjects

Quantitative Biology  Biomolecules, Physics  Biological Physics, and Physics  Computational Physics
 Abstract

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit timescale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule have never been formally proved. In this work, we present analytical results for the slowest timescale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit timescale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit timescale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit timescale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest timescales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.
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