Universal dynamical properties preclude standard clustering in a large class of biochemical data

Motivation: Clustering of chemical and biochemical data based on observed features is a central cognitive step in the analysis of chemical substances, in particular in combinatorial chemistry, or of complex biochemical reaction networks. Often, for reasons unknown to the researcher, this step produces disappointing results. Once the sources of the problem are known, improved clustering methods might revitalize the statistical approach of compound and reaction search and analysis. Here, we present a generic mechanism that may be at the origin of many clustering difficulties. Results: The variety of dynamical behaviors that can be exhibited by complex biochemical reactions on variation of the system parameters are fundamental system fingerprints. In parameter space, shrimp-like or swallow-tail structures separate parameter sets that lead to stable periodic dynamical behavior from those leading to irregular behavior. We work out the genericity of this phenomenon and demonstrate novel examples for their occurrence in realistic models of biophysics. Although we elucidate the phenomenon by considering the emergence of periodicity in dependence on system parameters in a low-dimensional parameter space, the conclusions from our simple setting are shown to continue to be valid for features in a higher-dimensional feature space, as long as the feature-generating mechanism is not too extreme and the dimension of this space is not too high compared with the amount of available data. Availability and implementation: For online versions of super-paramagnetic clustering see http://stoop.ini.uzh.ch/research/clustering. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Two universal physical principles shape the power-law statistics of real-world networks

The study of complex networks has pursued an understanding of macroscopic behavior by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex networks generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations.Comment: 14 pages, 7 figure

Natural data structure extracted from neighborhood-similarity graphs

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods also introduce a bias, either by starting from the assumption of a particular geometric form of the clusters, or by using iterative schemes to enhance cluster contours, with uncontrollable consequences. The goal of data analysis should, however, be to encode and detect structural data features at all scales and densities simultaneously, without assuming a parametric form of data point distances, or modifying them. We propose a novel approach that directly encodes data point neighborhood similarities as a sparse graph. Our non-iterative framework permits a transparent interpretation of data, without altering the original data dimension and metric. Several natural and synthetic data applications demonstrate the efficacy of our novel approach

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Model-driven analysis of gene expression control

During this PhD, I worked on three different aspects in the broad field of experimental and theoretical analysis of gene regulation. The first part, "Quantifying the strength of miRNA-target interactions", addresses the problem of predicting mRNA targets of miRNAs. I show that biochemical measurements of miRNA-mRNA interactions can be used to optimise the parameter inference of a pre-existing model of miRNA target prediction. This model named MIRZA, predicts miRNA-mRNA binding using 25 energy parameters that describe the miRNA-mRNA hybrid structure, with 2 base pairing parameters for the AU and GC pairs, 3 configuration parameters for the symmetric and asymmetric loops, and 21 positional parameters for the 21 nucleotides of the miRNA sequence. MIRZA was built to infer these parameters from Argonaute protein CLIP data, which captures potential targets of miRNAs. Upon the publication of precise measurements of chemical kinetic constants of miRNA-mRNA binding interactions between a mRNA target and a set of systematically mutated miRNA sequences, we reasoned that such data could be used to improve the parameters inference of the MIRZA model. After showing that the prediction of the existing model on the set of measured miRNA-mRNA pairs shows high correlation with the binding energy calculated from the measurements, I used simulations as a proof of principle of the inference procedure and to design measurements that would be needed to infer the parameters of the MIRZA model. Staying in the field of miRNA, in "Single cell mRNA profiling reveals the hierarchical response of miRNA targets to miRNA induction", I developed an approach to infer miRNA targets based on scRNA-seq data from cells that express the miRNA at different levels. A miRNA can target several hundreds of different mRNAs and is present in the cell in limited quantities, implying that the interaction of a target mRNA with a specific miRNA depends on its concentration and on the interactions of the miRNA with its other targets. In other words, since miRNA binding is exclusive, mRNA targets compete for the same miRNA pool. Therefore, the concentrations of the thereby coupled mRNAs depend not only on the miRNA concentration but also on the concentration of every competing mRNA that is targeted by the same miRNA. To study this, HEK 293 cell lines were constructed to inducibly express a miRNA (hsa-miR-199a) as well as the mRNA encoding a green fluorescent protein. Express from the same promoter as the miRNA, this mRNA allows the monitoring of the miRNA concentration. The study aimed not only to determine the parameters of individual mRNA-mRNA interactions, but also to assess the degree to which mRNAs act in a competitive manner to influence each other's expression. scRNA-seq was chosen to bring the resolution needed to reach these goals. The effect of the miRNA on a bound target is to increase its decay rate, hence the expression levels of the targets depends on the miRNA concentration and their binding energy. To gain insight into the target binding energy, we constructed a model considering mRNA transcription rate, the miRNA-mRNA binding/unbinding rate, the mRNA decay rates in the bound and unbound state, and the free/bound concentration of miRNA. We showed that the model can be factored in terms of the miRNA concentrations in individual cells and the miRNA-mRNA target interaction parameters and we solved the model to obtain estimates of miRNA-mRNA interaction parameters, which we showed explain the mRNA levels in cells more accurately than the sequence-based computationally predicted interaction energies. Finally, in "Bayesian inference of the gene expression states from single-cell RNA-seq data" I carried out fundamental technical work on the normalisation of count data obtained in scRNA-seq experiments. As introduced above, multiple strategies have been developed with the aim of reducing the high level of noise present on such data, and estimating a 'true' biological state of expression for each gene in each cell. While the project aimed to reconstruct the Waddington landscape of regulator activity based on the single cell gene expression measurements, at the start of the project we realised that there is no satisfactory solution to gene expression normalisation in single cells in the literature. Thus, we tackled this problem with a Bayesian model, considering each gene independently and inferring a posterior probability of gene expression in each cell. Our model assumes a log-normal distribution of gene expression across cells and additional Poisson noise caused by the stochastic process of gene expression and the sampling process introduced by the mRNA capture in experimental protocols. These normalised gene expression values are the basis of a motif-activity response based approach for inferring the activity of TFs and miRNAs in individual cells, and for reconstructing the underlying landscape. The application of this normalisation algorithm to reconstruct a landscape is presented in the last part, "Realizing Waddington’s metaphor: Inferring regulatory landscapes from single-cell gene expression data". There I present the mathematical principles needed to formally define a landscape following the idea of Waddington from 1957, and I propose two applications of the landscape. First I show that it defines cell types as local minima, and secondly, in the case of cells undergoing differentiation, I show how the landscape can be used to find developmental path and the transcription factors associated with the differentiation process

Statistical Analysis of Protein Sequences: A Coevolutionary Study of Molecular Chaperones

Recent advances in DNA sequencing technologies led to the accumulation of enormous quantities of genetic information available in public databases. This rapid growth of available biological datasets calls for quantitative analysis tools and concomitantly opens the doors for new analysis paradigms. Particularly, the analysis of correlated mutations and their structural interpretation have witnessed a second youth in the last years. A natural formulation for such approaches is provided by the statistical physics of disordered systems. This thesis is articulated around different projects aimed at studying particular biological systems of interests, the Hsp70 molecular chaperones, through the lens provided by methods rooted in statistical physics. In a first project, we focus on correlated mutations within the Hsp70 family. Our analysis reveals the existence of a biologically important macro-molecular arrangement of these chaperones and we investigate its phylogenetic origin. A second project investigates the interactions between the Hsp70 chaperones and one of their main co-chaperones, J-proteins. Through the combined use of coevolutionary analysis and molecular simulations at both coarse-grained and atomistic levels, we construct a structural and dynamical model of this interaction which rationalizes previous experimental evidence. In a subsequent study, we specifically focus on the J-protein co-chaperones. Through phylogenetic and coevolutionary methods, we investigate the origin of recently discovered interactions which form the basis of the disaggregation machinery in higher eukaryotes. Finally, in a fourth project, we shift our attention to the analysis of proteins involved in the iron-sulfur cluster assembly pathway. Analysis of residue coevolution in the different proteins composing this pathway reveals multiple structural insights at several scales