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Register a new userLaplacian Spectrum and Protein-Protein Interaction Networks
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From the spectral plot of the (normalized) graph Laplacian, the essential qualitative properties of a network can be simultaneously deduced. Given a class of empirical networks, reconstruction schemes for elucidating the evolutionary dynamics leading to those particular data can then be developed. This method is exemplified for protein-protein interaction networks. Traces of their evolutionary history of duplication and divergence processes are identified. In particular, we can identify typical specific features that robustly distinguish protein-protein interaction networks from other classes of networks, in spite of possible statistical fluctuations of the underlying data.
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The determination of protein functions is one of the most challenging problems of the post-genomic era. The sequencing of entire genomes and the possibility to access genes co-expression patterns has moved the attention from the study of single proteins or small complexes to that of the entire proteome. In this context, the search for reliable methods for proteins function assignment is of uttermost importance. Previous approaches to deduce the unknown function of a class of proteins have exploited sequence similarities or clustering of co-regulated genes, phylogenetic profiles, protein-protein interactions, and protein complexes. We propose to assign functional classes to proteins from their network of physical interactions, by minimizing the number of interacting proteins with different categories. The function assignment is made on a global scale and depends on the entire connectivity pattern of the protein network. Multiple functional assignments are made possible as a consequence of the existence of multiple equivalent solutions. The method is applied to the yeast Saccharomices Cerevisiae protein-protein interaction network. Robustness is tested in presence of a high percentage of unclassified proteins and under deletion/insertion of interactions.
Aligning protein-protein interaction (PPI) networks of different species has drawn a considerable interest recently. This problem is important to investigate evolutionary conserved pathways or protein complexes across species, and to help in the identification of functional orthologs through the detection of conserved interactions. It is however a difficult combinatorial problem, for which only heuristic methods have been proposed so far. We reformulate the PPI alignment as a graph matching problem, and investigate how state-of-the-art graph matching algorithms can be used for that purpose. We differentiate between two alignment problems, depending on whether strict constraints on protein matches are given, based on sequence similarity, or whether the goal is instead to find an optimal compromise between sequence similarity and interaction conservation in the alignment. We propose new methods for both cases, and assess their performance on the alignment of the yeast and fly PPI networks. The new methods consistently outperform state-of-the-art algorithms, retrieving in particular 78% more conserved interactions than IsoRank for a given level of sequence similarity. Availability:http://cbio.ensmp.fr/proj/graphm_ppi/, additional data and codes are available upon request. Contact: [email protected]
Machine-learning models that learn from data to predict how protein sequence encodes function are emerging as a useful protein engineering tool. However, when using these models to suggest new protein designs, one must deal with the vast combinatorial complexity of protein sequences. Here, we review how to use a sequence-to-function machine-learning surrogate model to select sequences for experimental measurement. First, we discuss how to select sequences through a single round of machine-learning optimization. Then, we discuss sequential optimization, where the goal is to discover optimized sequences and improve the model across multiple rounds of training, optimization, and experimental measurement.
Potts models and variational autoencoders (VAEs) have recently gained popularity as generative protein sequence models (GPSMs) to explore fitness landscapes and predict the effect of mutations. Despite encouraging results, quantitative characterization and comparison of GPSM-generated probability distributions is still lacking. It is currently unclear whether GPSMs can faithfully reproduce the complex multi-residue mutation patterns observed in natural sequences arising due to epistasis. We develop a set of sequence statistics to assess the generative capacity of three GPSMs of recent interest: the pairwise Potts Hamiltonian, the VAE, and the site-independent model, using natural and synthetic datasets. We show that the generative capacity of the Potts Hamiltonian model is the largest, in that the higher order mutational statistics generated by the model agree with those observed for natural sequences. In contrast, we show that the VAEs generative capacity lies between the pairwise Potts and site-independent models. Importantly, our work measures GPSM generative capacity in terms of higher-order sequence covariation statistics which we have developed, and provides a new framework for evaluating and interpreting GPSM accuracy that emphasizes the role of epistasis.
We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field.
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