Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

By Carlo Baldassi, M. Zamparo, Christoph Feinauer, Andrea Procaccini, Riccardo Zecchina, Martin Weigt, Andrea Pagnani. 2014

137 citations recorded by the source corpus.

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code.

Subfields: Genetics, Molecular Biology, Computational Biology & Bioinformatics

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Citations in the corpus

Distance-based protein folding powered by deep learning (2018, background): “255, respectively, much larger than GaussDCA (41) (the only DCA method blindly tested in CASP13), which has entropy score 0.”
Revealing evolutionary constraints on proteins through sequence analysis (2018, background): “For instance, in the DCA literature, the zero-sum (or Ising) gauge is often employed [61,62].”
Coevolutionary Landscape Inference and the Context-Dependence of Mutations in Beta-Lactamase TEM-1 (2015, background): “Estimating parameters from aligned sequences is a computationally hard task, but over the last years a number of accurate and computationally efficient approximate algorithms have been developed (Baldassi et al., 2014; Ekeberg et al., 2013; Morcos et al., 2011; Weigt et al., 2009).”
Accurate contact predictions for thousands of protein families using PconsC3 (2016, methodology): “Contact prediction Julia implementations have been used for both plmDCA and GaussDCA, which are available on GitHub at https://github.com/pagnani/plmDCA and https://github.com/carlobaldassi/GaussDCA.jl, respectively.”
Synthetic protein alignments by CCMgen quantify noise in residue-residue contact prediction (2018, background): “…most often used score for residue contact prediction simply takes the L 2 norm of the 20 × 20-dimensional vector w ij with components w ij ( a, b ) [3, 10, 11, 31, 50], 505 Recap: Average Product Correction The APC subtracts from each score c ij the product of the average score c i • for row i…”
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity (2016, unknown): “We start from the multiple sequence alignment of the heavy chain variable region sequences belonging to the hypermutated cluster and define a summary statistics of the data set in terms of the single residue frequency counts (means)~ x and the covariance matrixC calculated after pseudo-count correct”
Deep learning techniques have significantly impacted protein structure prediction and protein design. (2021, background): “…likelihood function is computationally intractable due to the need to calculate the partition function, various approximations have been developed including those based on message passing [23], Gaussian approximation [25], mean-ﬁeld approximation [24], and pseudo-likelihood maximization [26].”
Inferring interaction partners from protein sequences using mutual information (2018, methodology): “DCA-based methods have been used to predict interacting partners of “orphan” HKs and RRs involved in prokaryotic twocomponent signaling systems [14, 15].”
Unified framework for modeling multivariate distributions in biological sequences (2019, methodology): “To capture additional two-body interaction terms, i.e. coevolving positions, MRFs and MGs have emerged, speciﬁcally in the context of protein structure contact prediction (Balakrishnan et al., 2011; Kamisetty et al., 2013; Ekeberg et al., 2013; Morcos et al., 2011; Baldassi et al., 2014).”
Inferring interaction partners from protein sequences (2016, background): “In a well-trained model, the residue pairs with the largest couplings have been shown to correspond to contacts in the protein complex (7, 16, 31).”
Toward the solution of the protein structure prediction problem (2021, methodology): “A widely used DCA method is to ﬁ t a Markov random ﬁ eld (MRF), or more speci ﬁ cally a Potts model, to an MSA using message passing (142), Gaussian approximation (144), mean-ﬁ eld approximation (143), or pseudo-likelihood maximization (145 – 147).”
Applications of sequence coevolution in membrane protein biochemistry (2017, unknown): “coupling parameters [8], including susceptibility propagation [9], mean-field approximation (mfDCA and in the original EVFold) [10–12], multivariate Gaussian modeling [13], pseudolikelihood maximization (implemented in plmDCA, CCMpred, the new EVFold, and GREMLIN) [14–17], Boltzmann network formalis”
Simultaneous identification of specifically interacting paralogs and interprotein contacts by direct coupling analysis (2016, methodology): “Within Gaussian DCA (28), the total log-likelihood of an arbitraryMSAX depends only on its regularized covariance matrix CðXÞ and reads LðXÞ=−1=2 log det CðXÞ (SI Appendix).”