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A common challenge in drug design pertains to finding chemical modifications to a ligand that increases its affinity to the target protein. An underutilized advance is the increase in structural biology throughput, which has progressed from an artisanal endeavor to a monthly throughput of hundreds of different ligands against a protein in modern synchrotrons. However, the missing piece is a framework that turns high-throughput crystallography data into predictive models for ligand design. Here, we designed a simple machine learning approach that predicts protein-ligand affinity from experimental structures of diverse ligands against a single protein paired with biochemical measurements. Our key insight is using physics-based energy descriptors to represent protein-ligand complexes and a learning-to-rank approach that infers the relevant differences between binding modes. We ran a high-throughput crystallography campaign against the SARS-CoV-2 main protease (M Pro ), obtaining parallel measurements of over 200 protein-ligand complexes and their binding activities. This allows us to design one-step library syntheses which improved the potency of two distinct micromolar hits by over 10-fold, arriving at a noncovalent and nonpeptidomimetic inhibitor with 120 nM antiviral efficacy. Crucially, our approach successfully extends ligands to unexplored regions of the binding pocket, executing large and fruitful moves in chemical space with simple chemistry.

Here, we present detailed kinetic analyses of a panel of soluble lipid kinases and phosphatases, as well as Ras activating proteins, acting on their respective membrane surface substrates. The results reveal that the mean catalytic rate of such interfacial enzymes can exhibit a strong dependence on the size of the reaction system-in this case membrane area. Experimental measurements and kinetic modeling reveal how stochastic effects stemming from low molecular copy numbers of the enzymes alter reaction kinetics based on mechanistic characteristics of the enzyme, such as positive feedback. For the competitive enzymatic cycles studied here, the final product-consisting of a specific lipid composition or Ras activity state-depends on the size of the reaction system. Furthermore, we demonstrate how these reaction size dependencies can be controlled by engineering feedback mechanisms into the enzymes., Competing Interests: The authors declare no competing interest.

Intracellular phase separation of proteins into biomolecular condensates is increasingly recognized as a process with a key role in cellular compartmentalization and regulation. Different hypotheses about the parameters that determine the tendency of proteins to form condensates have been proposed, with some of them probed experimentally through the use of constructs generated by sequence alterations. To broaden the scope of these observations, we established an in silico strategy for understanding on a global level the associations between protein sequence and phase behavior and further constructed machine-learning models for predicting protein liquid-liquid phase separation (LLPS). Our analysis highlighted that LLPS-prone proteins are more disordered, less hydrophobic, and of lower Shannon entropy than sequences in the Protein Data Bank or the Swiss-Prot database and that they show a fine balance in their relative content of polar and hydrophobic residues. To further learn in a hypothesis-free manner the sequence features underpinning LLPS, we trained a neural network-based language model and found that a classifier constructed on such embeddings learned the underlying principles of phase behavior at a comparable accuracy to a classifier that used knowledge-based features. By combining knowledge-based features with unsupervised embeddings, we generated an integrated model that distinguished LLPS-prone sequences both from structured proteins and from unstructured proteins with a lower LLPS propensity and further identified such sequences from the human proteome at a high accuracy. These results provide a platform rooted in molecular principles for understanding protein phase behavior. The predictor, termed DeePhase, is accessible from https://deephase.ch.cam.ac.uk/., Competing Interests: Competing interest statement: Parts of this work have been the subject of a patent application filed by Cambridge Enterprise Limited, a fully owned subsidiary of the University of Cambridge., (Copyright © 2021 the Author(s). Published by PNAS.)

The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions., Competing Interests: The authors declare no competing interest.

Predicting ligand biological activity is a key challenge in drug discovery. Ligand-based statistical approaches are often hampered by noise due to undersampling: The number of molecules known to be active or inactive is vastly less than the number of possible chemical features that might determine binding. We derive a statistical framework inspired by random matrix theory and combine the framework with high-quality negative data to discover important chemical differences between active and inactive molecules by disentangling undersampling noise. Our model outperforms standard benchmarks when tested against a set of challenging retrospective tests. We prospectively apply our model to the human muscarinic acetylcholine receptor M1, finding four experimentally confirmed agonists that are chemically dissimilar to all known ligands. The hit rate of our model is significantly higher than the state of the art. Our model can be interpreted and visualized to offer chemical insights about the molecular motifs that are synergistic or antagonistic to M1 agonism, which we have prospectively experimentally verified., Competing Interests: Conflict of interest statement: Q.Y., A.B., C.R.B., X.H., S.J., and D.A.P. are current employees of Pfizer. The structure highlighted in red in Fig. 3A is exemplified in Patent WO/2013/072705.

Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The nonequilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that, for a narrow, unimodal spectrum, the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important nonequilibrium interactions are encoded within the fluctuation spectrum. In this sense, the noise becomes the signal., Competing Interests: The authors declare no conflict of interest.

Rapid determination of whether a candidate compound will bind to a particular target receptor remains a stumbling block in drug discovery. We use an approach inspired by random matrix theory to decompose the known ligand set of a target in terms of orthogonal "signals" of salient chemical features, and distinguish these from the much larger set of ligand chemical features that are not relevant for binding to that particular target receptor. After removing the noise caused by finite sampling, we show that the similarity of an unknown ligand to the remaining, cleaned chemical features is a robust predictor of ligand-target affinity, performing as well or better than any algorithm in the published literature. We interpret our algorithm as deriving a model for the binding energy between a target receptor and the set of known ligands, where the underlying binding energy model is related to the classic Ising model in statistical physics., Competing Interests: The authors declare no conflict of interest.