EigenFold: Generative Protein Structure Prediction with Diffusion Models

Protein structure prediction has reached revolutionary levels of accuracy on single structures, yet distributional modeling paradigms are needed to capture the conformational ensembles and flexibility that underlie biological function. Towards this goal, we develop EigenFold, a diffusion generative modeling framework for sampling a distribution of structures from a given protein sequence. We define a diffusion process that models the structure as a system of harmonic oscillators and which naturally induces a cascading-resolution generative process along the eigenmodes of the system. On recent CAMEO targets, EigenFold achieves a median TMScore of 0.84, while providing a more comprehensive picture of model uncertainty via the ensemble of sampled structures relative to existing methods. We then assess EigenFold's ability to model and predict conformational heterogeneity for fold-switching proteins and ligand-induced conformational change. Code is available at https://github.com/bjing2016/EigenFold.Comment: ICLR MLDD workshop 202

Towards Joint Sequence-Structure Generation of Nucleic Acid and Protein Complexes with SE(3)-Discrete Diffusion

Generative models of macromolecules carry abundant and impactful implications for industrial and biomedical efforts in protein engineering. However, existing methods are currently limited to modeling protein structures or sequences, independently or jointly, without regard to the interactions that commonly occur between proteins and other macromolecules. In this work, we introduce MMDiff, a generative model that jointly designs sequences and structures of nucleic acid and protein complexes, independently or in complex, using joint SE(3)-discrete diffusion noise. Such a model has important implications for emerging areas of macromolecular design including structure-based transcription factor design and design of noncoding RNA sequences. We demonstrate the utility of MMDiff through a rigorous new design benchmark for macromolecular complex generation that we introduce in this work. Our results demonstrate that MMDiff is able to successfully generate micro-RNA and single-stranded DNA molecules while being modestly capable of joint modeling DNA and RNA molecules in interaction with multi-chain protein complexes. Source code: https://github.com/Profluent-Internships/MMDiff.Comment: 15 pages, 11 figures, presented at the NeurIPS 2023 Machine Learning in Structural Biology (MLSB) workshop. Code available at https://github.com/Profluent-Internships/MMDif

Growing ecosystem of deep learning methods for modeling protein\unicode{x2013}protein interactions

Numerous cellular functions rely on protein\unicode{x2013}protein interactions. Efforts to comprehensively characterize them remain challenged however by the diversity of molecular recognition mechanisms employed within the proteome. Deep learning has emerged as a promising approach for tackling this problem by exploiting both experimental data and basic biophysical knowledge about protein interactions. Here, we review the growing ecosystem of deep learning methods for modeling protein interactions, highlighting the diversity of these biophysically-informed models and their respective trade-offs. We discuss recent successes in using representation learning to capture complex features pertinent to predicting protein interactions and interaction sites, geometric deep learning to reason over protein structures and predict complex structures, and generative modeling to design de novo protein assemblies. We also outline some of the outstanding challenges and promising new directions. Opportunities abound to discover novel interactions, elucidate their physical mechanisms, and engineer binders to modulate their functions using deep learning and, ultimately, unravel how protein interactions orchestrate complex cellular behaviors.Comment: 19 pages, added model names to discussio

Accelerating Inference in Molecular Diffusion Models with Latent Representations of Protein Structure

Diffusion generative models have emerged as a powerful framework for addressing problems in structural biology and structure-based drug design. These models operate directly on 3D molecular structures. Due to the unfavorable scaling of graph neural networks (GNNs) with graph size as well as the relatively slow inference speeds inherent to diffusion models, many existing molecular diffusion models rely on coarse-grained representations of protein structure to make training and inference feasible. However, such coarse-grained representations discard essential information for modeling molecular interactions and impair the quality of generated structures. In this work, we present a novel GNN-based architecture for learning latent representations of molecular structure. When trained end-to-end with a diffusion model for de novo ligand design, our model achieves comparable performance to one with an all-atom protein representation while exhibiting a 3-fold reduction in inference time.Comment: This paper appeared as a spotlight paper at the NeurIPS 2023 Generative AI and Biology Worksho

Machine learning-guided directed evolution for protein engineering

Machine learning (ML)-guided directed evolution is a new paradigm for biological design that enables optimization of complex functions. ML methods use data to predict how sequence maps to function without requiring a detailed model of the underlying physics or biological pathways. To demonstrate ML-guided directed evolution, we introduce the steps required to build ML sequence-function models and use them to guide engineering, making recommendations at each stage. This review covers basic concepts relevant to using ML for protein engineering as well as the current literature and applications of this new engineering paradigm. ML methods accelerate directed evolution by learning from information contained in all measured variants and using that information to select sequences that are likely to be improved. We then provide two case studies that demonstrate the ML-guided directed evolution process. We also look to future opportunities where ML will enable discovery of new protein functions and uncover the relationship between protein sequence and function.Comment: Made significant revisions to focus on aspects most relevant to applying machine learning to speed up directed evolutio

A generative model for protein contact networks

In this paper we present a generative model for protein contact networks. The soundness of the proposed model is investigated by focusing primarily on mesoscopic properties elaborated from the spectra of the graph Laplacian. To complement the analysis, we study also classical topological descriptors, such as statistics of the shortest paths and the important feature of modularity. Our experiments show that the proposed model results in a considerable improvement with respect to two suitably chosen generative mechanisms, mimicking with better approximation real protein contact networks in terms of diffusion properties elaborated from the Laplacian spectra. However, as well as the other considered models, it does not reproduce with sufficient accuracy the shortest paths structure. To compensate this drawback, we designed a second step involving a targeted edge reconfiguration process. The ensemble of reconfigured networks denotes improvements that are statistically significant. As a byproduct of our study, we demonstrate that modularity, a well-known property of proteins, does not entirely explain the actual network architecture characterizing protein contact networks. In fact, we conclude that modularity, intended as a quantification of an underlying community structure, should be considered as an emergent property of the structural organization of proteins. Interestingly, such a property is suitably optimized in protein contact networks together with the feature of path efficiency.Comment: 18 pages, 67 reference

Selection of sequence motifs and generative Hopfield-Potts models for protein familiesilies

Statistical models for families of evolutionary related proteins have recently gained interest: in particular pairwise Potts models, as those inferred by the Direct-Coupling Analysis, have been able to extract information about the three-dimensional structure of folded proteins, and about the effect of amino-acid substitutions in proteins. These models are typically requested to reproduce the one- and two-point statistics of the amino-acid usage in a protein family, {\em i.e.}~to capture the so-called residue conservation and covariation statistics of proteins of common evolutionary origin. Pairwise Potts models are the maximum-entropy models achieving this. While being successful, these models depend on huge numbers of {\em ad hoc} introduced parameters, which have to be estimated from finite amount of data and whose biophysical interpretation remains unclear. Here we propose an approach to parameter reduction, which is based on selecting collective sequence motifs. It naturally leads to the formulation of statistical sequence models in terms of Hopfield-Potts models. These models can be accurately inferred using a mapping to restricted Boltzmann machines and persistent contrastive divergence. We show that, when applied to protein data, even 20-40 patterns are sufficient to obtain statistically close-to-generative models. The Hopfield patterns form interpretable sequence motifs and may be used to clusterize amino-acid sequences into functional sub-families. However, the distributed collective nature of these motifs intrinsically limits the ability of Hopfield-Potts models in predicting contact maps, showing the necessity of developing models going beyond the Hopfield-Potts models discussed here.Comment: 26 pages, 16 figures, to app. in PR