Discovering local patterns of co - evolution: computational aspects and biological examples

<p>Abstract</p> <p>Background</p> <p>Co-evolution is the process in which two (or more) sets of orthologs exhibit a similar or correlative pattern of evolution. Co-evolution is a powerful way to learn about the functional interdependencies between sets of genes and cellular functions and to predict physical interactions. More generally, it can be used for answering fundamental questions about the evolution of biological systems.</p> <p>Orthologs that exhibit a strong signal of co-evolution in a certain part of the evolutionary tree may show a mild signal of co-evolution in other branches of the tree. The major reasons for this phenomenon are noise in the biological input, genes that gain or lose functions, and the fact that some measures of co-evolution relate to rare events such as positive selection. Previous publications in the field dealt with the problem of finding sets of genes that co-evolved along an entire underlying phylogenetic tree, without considering the fact that often co-evolution is local.</p> <p>Results</p> <p>In this work, we describe a new set of biological problems that are related to finding patterns of <it>local </it>co-evolution. We discuss their computational complexity and design algorithms for solving them. These algorithms outperform other bi-clustering methods as they are designed specifically for solving the set of problems mentioned above.</p> <p>We use our approach to trace the co-evolution of fungal, eukaryotic, and mammalian genes at high resolution across the different parts of the corresponding phylogenetic trees. Specifically, we discover regions in the fungi tree that are enriched with positive evolution. We show that metabolic genes exhibit a remarkable level of co-evolution and different patterns of co-evolution in various biological datasets.</p> <p>In addition, we find that protein complexes that are related to gene expression exhibit non-homogenous levels of co-evolution across different parts of the <it>fungi </it>evolutionary line. In the case of mammalian evolution, signaling pathways that are related to <it>neurotransmission </it>exhibit a relatively higher level of co-evolution along the <it>primate </it>subtree.</p> <p>Conclusions</p> <p>We show that finding local patterns of co-evolution is a computationally challenging task and we offer novel algorithms that allow us to solve this problem, thus opening a new approach for analyzing the evolution of biological systems.</p

Co-evolution is Incompatible with the Markov Assumption in Phylogenetics

Markov models are extensively used in the analysis of molecular evolution. A recent line of research suggests that pairs of proteins with functional and physical interactions co-evolve with each other. Here, by analyzing hundreds of orthologous sets of three fungi and their co-evolutionary relations, we demonstrate that co-evolutionary assumption may violate the Markov assumption. Our results encourage developing alternative probabilistic models for the cases of extreme co-evolution

Efficient algorithms for reconstructing gene content by co-evolution

<p>Abstract</p> <p>Background</p> <p>In a previous study we demonstrated that co-evolutionary information can be utilized for improving the accuracy of ancestral gene content reconstruction. To this end, we defined a new computational problem, the Ancestral Co-Evolutionary (ACE) problem, and developed algorithms for solving it.</p> <p>Results</p> <p>In the current paper we generalize our previous study in various ways. First, we describe new efficient computational approaches for solving the ACE problem. The new approaches are based on reductions to classical methods such as linear programming relaxation, quadratic programming, and min-cut. Second, we report new computational hardness results related to the ACE, including practical cases where it can be solved in polynomial time.</p> <p>Third, we generalize the ACE problem and demonstrate how our approach can be used for inferring parts of the genomes of <it>non-ancestral</it> organisms. To this end, we describe a heuristic for finding the portion of the genome ('dominant set’) that can be used to reconstruct the rest of the genome with the lowest error rate. This heuristic utilizes both evolutionary information and co-evolutionary information.</p> <p>We implemented these algorithms on a large input of the ACE problem (95 unicellular organisms, 4,873 protein families, and 10, 576 of co-evolutionary relations), demonstrating that some of these algorithms can outperform the algorithm used in our previous study. In addition, we show that based on our approach a ’dominant set’ cab be used reconstruct a major fraction of a genome (up to 79%) with relatively low error-rate (<it>e.g.</it> 0.11). We find that the ’dominant set’ tends to include metabolic and regulatory genes, with high evolutionary rate, and low protein abundance and number of protein-protein interactions.</p> <p>Conclusions</p> <p>The <it>ACE</it> problem can be efficiently extended for inferring the genomes of organisms that exist today. In addition, it may be solved in polynomial time in many practical cases. Metabolic and regulatory genes were found to be the most important groups of genes necessary for reconstructing gene content of an organism based on other related genomes.</p