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Register a new userSparse generative modeling via parameter-reduction of Boltzmann machines: application to protein-sequence families
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Boltzmann machines (BM) are widely used as generative models. For example, pairwise Potts models (PM), which are instances of the BM class, provide accurate statistical models of families of evolutionarily related protein sequences. Their parameters are the local fields, which describe site-specific patterns of amino-acid conservation, and the two-site couplings, which mirror the coevolution between pairs of sites. This coevolution reflects structural and functional constraints acting on protein sequences during evolution. The most conservative choice to describe the coevolution signal is to include all possible two-site couplings into the PM. This choice, typical of what is known as Direct Coupling Analysis, has been successful for predicting residue contacts in the three-dimensional structure, mutational effects, and in generating new functional sequences. However, the resulting PM suffers from important over-fitting effects: many couplings are small, noisy and hardly interpretable; the PM is close to a critical point, meaning that it is highly sensitive to small parameter perturbations. In this work, we introduce a general parameter-reduction procedure for BMs, via a controlled iterative decimation of the less statistically significant couplings, identified by an information-based criterion that selects either weak or statistically unsupported couplings. For several protein families, our procedure allows one to remove more than $90%$ of the PM couplings, while preserving the predictive and generative properties of the original dense PM, and the resulting model is far away from criticality, hence more robust to noise.
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Proteins are essential components of living systems, capable of performing a huge variety of tasks at the molecular level, such as recognition, signalling, copy, transport, ... The protein sequences realizing a given function may largely vary across organisms, giving rise to a protein family. Here, we estimate the entropy of those families based on different approaches, including Hidden Markov Models used for protein databases and inferred statistical models reproducing the low-order (1-and 2-point) statistics of multi-sequence alignments. We also compute the entropic cost, that is, the loss in entropy resulting from a constraint acting on the protein, such as the fixation of one particular amino-acid on a specific site, and relate this notion to the escape probability of the HIV virus. The case of lattice proteins, for which the entropy can be computed exactly, allows us to provide another illustration of the concept of cost, due to the competition of different folds. The relevance of the entropy in relation to directed evolution experiments is stressed.
Background: Typically, proteins perform key biological functions by interacting with each other. As a consequence, predicting which protein pairs interact is a fundamental problem. Experimental methods are slow, expensive, and may be error prone. Many computational methods have been proposed to identify candidate interacting pairs. When accurate, they can serve as an inexpensive, preliminary filtering stage, to be followed by downstream experimental validation. Among such methods, sequence-based ones are very promising. Results: We present MPS(T&B) (Maximum Protein Similarity Topological and Biological), a new algorithm that leverages both topological and biological information to predict protein-protein interactions. We comprehensively compare MPS(T) and MPS(T&B) with state-of-the-art approaches on reliable PPIs datasets, showing that they have competitive or higher accuracy on biologically validated test sets. Conclusion: MPS(T) and MPS(T&B) are topological only and topological plus sequence-based computational methods that can effectively predict the entire human interactome.
Determining which proteins interact together is crucial to a systems-level understanding of the cell. Recently, algorithms based on Direct Coupling Analysis (DCA) pairwise maximum-entropy models have allowed to identify interaction partners among paralogous proteins from sequence data. This success of DCA at predicting protein-protein interactions could be mainly based on its known ability to identify pairs of residues that are in contact in the three-dimensional structure of protein complexes and that coevolve to remain physicochemically complementary. However, interacting proteins possess similar evolutionary histories. What is the role of purely phylogenetic correlations in the performance of DCA-based methods to infer interaction partners? To address this question, we employ controlled synthetic data that only involve phylogeny and no interactions or contacts. We find that DCA accurately identifies the pairs of synthetic sequences that share evolutionary history. While phylogenetic correlations confound the identification of contacting residues by DCA, they are thus useful to predict interacting partners among paralogs. We find that DCA performs as well as phylogenetic methods to this end, and slightly better than them with large and accurate training sets. Employing DCA or phylogenetic methods within an Iterative Pairing Algorithm (IPA) allows to predict pairs of evolutionary partners without a training set. We demonstrate the ability of these various methods to correctly predict pairings among real paralogous proteins with genome proximity but no known physical interaction, illustrating the importance of phylogenetic correlations in natural data. However, for physically interacting and strongly coevolving proteins, DCA and mutual information outperform phylogenetic methods. We discuss how to distinguish physically interacting proteins from those only sharing evolutionary history.
Significant progress in computer hardware and software have enabled molecular dynamics (MD) simulations to model complex biological phenomena such as protein folding. However, enabling MD simulations to access biologically relevant timescales (e.g., beyond milliseconds) still remains challenging. These limitations include (1) quantifying which set of states have already been (sufficiently) sampled in an ensemble of MD runs, and (2) identifying novel states from which simulations can be initiated to sample rare events (e.g., sampling folding events). With the recent success of deep learning and artificial intelligence techniques in analyzing large datasets, we posit that these techniques can also be used to adaptively guide MD simulations to model such complex biological phenomena. Leveraging our recently developed unsupervised deep learning technique to cluster protein folding trajectories into partially folded intermediates, we build an iterative workflow that enables our generative model to be coupled with all-atom MD simulations to fold small protein systems on emerging high performance computing platforms. We demonstrate our approach in folding Fs-peptide and the $betabetaalpha$ (BBA) fold, FSD-EY. Our adaptive workflow enables us to achieve an overall root-mean squared deviation (RMSD) to the native state of 1.6$~AA$ and 4.4~$AA$ respectively for Fs-peptide and FSD-EY. We also highlight some emerging challenges in the context of designing scalable workflows when data intensive deep learning techniques are coupled to compute intensive MD simulations.
Generative modeling for protein engineering is key to solving fundamental problems in synthetic biology, medicine, and material science. We pose protein engineering as an unsupervised sequence generation problem in order to leverage the exponentially growing set of proteins that lack costly, structural annotations. We train a 1.2B-parameter language model, ProGen, on ~280M protein sequences conditioned on taxonomic and keyword tags such as molecular function and cellular component. This provides ProGen with an unprecedented range of evolutionary sequence diversity and allows it to generate with fine-grained control as demonstrated by metrics based on primary sequence similarity, secondary structure accuracy, and conformational energy.
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