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arXiv2011

The Quality of Oscillations in Overdamped Networks

The second law of thermodynamics implies that no macroscopic system may oscillate indefinitely without consuming energy. The question of the number of possible oscillations and the coherent quality of these oscillations remain unanswered. This paper proves the upper-bounds on the number and quality of such oscillations when the system in question is homogeneously driven and has a discrete network of states. In a closed system, the maximum number of oscillations is bounded by the number of states in the network. In open systems, the size of the network bounds the quality factor of oscillation. This work also explores how the quality factor of macrostate oscillations, such as would be observed in chemical reactions, are bounded by the smallest equivalent loop of the network, not the size of the entire system. The consequences of this limit are explored in the context of chemical clocks and limit cycles.

cond-mat.stat-mech↗
arXiv2010

Critical properties of complex fitness landscapes

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been expended to understand the evolutionary dynamics of adapting populations, but much less is known about the structure of the landscapes. Here, we study the global and local structure of complex fitness landscapes of interacting loci that describe protein folds or sets of interacting genes forming pathways or modules. We find that in these landscapes, high peaks are more likely to be found near other high peaks, corroborating Kauffman's "Massif Central" hypothesis. We study the clusters of peaks as a function of the ruggedness of the landscape and find that this clustering allows peaks to form interconnected networks. These networks undergo a percolation phase transition as a function of minimum peak height, which indicates that evolutionary trajectories that take no more than two mutations to shift from peak to peak can span the entire genetic space. These networks have implications for evolution in rugged landscapes, allowing adaptation to proceed after a local fitness peak has been ascended.

q-bio.PE↗
arXiv2010

From statistical mechanics to information theory: understanding biophysical information-processing systems

These are notes for a set of 7 two-hour lectures given at the 2010 Summer School on Quantitative Evolutionary and Comparative Genomics at OIST, Okinawa, Japan. The emphasis is on understanding how biological systems process information. We take a physicist's approach of looking for simple phenomenological descriptions that can address the questions of biological function without necessarily modeling all (mostly unknown) microscopic details; the example that is developed throughout the notes is transcriptional regulation in genetic regulatory networks. We present tools from information theory and statistical physics that can be used to analyze noisy nonlinear biological networks, and build generative and predictive models of regulatory processes.

q-bio.MN↗
arXiv2010

Discovering Graphical Granger Causality Using the Truncating Lasso Penalty

Components of biological systems interact with each other in order to carry out vital cell functions. Such information can be used to improve estimation and inference, and to obtain better insights into the underlying cellular mechanisms. Discovering regulatory interactions among genes is therefore an important problem in systems biology. Whole-genome expression data over time provides an opportunity to determine how the expression levels of genes are affected by changes in transcription levels of other genes, and can therefore be used to discover regulatory interactions among genes. In this paper, we propose a novel penalization method, called truncating lasso, for estimation of causal relationships from time-course gene expression data. The proposed penalty can correctly determine the order of the underlying time series, and improves the performance of the lasso-type estimators. Moreover, the resulting estimate provides information on the time lag between activation of transcription factors and their effects on regulated genes. We provide an efficient algorithm for estimation of model parameters, and show that the proposed method can consistently discover causal relationships in the large $p$, small $n$ setting. The performance of the proposed model is evaluated favorably in simulated, as well as real, data examples. The proposed truncating lasso method is implemented in the R-package grangerTlasso and is available at http://www.stat.lsa.umich.edu/~shojaie.

stat.ML↗
arXiv2010

Increased entropy of signal transduction in the cancer metastasis phenotype

Studies into the statistical properties of biological networks have led to important biological insights, such as the presence of hubs and hierarchical modularity. There is also a growing interest in studying the statistical properties of networks in the context of cancer genomics. However, relatively little is known as to what network features differ between the cancer and normal cell physiologies, or between different cancer cell phenotypes. Based on the observation that frequent genomic alterations underlie a more aggressive cancer phenotype, we asked if such an effect could be detectable as an increase in the randomness of local gene expression patterns. Using a breast cancer gene expression data set and a model network of protein interactions we derive constrained weighted networks defined by a stochastic information flux matrix reflecting expression correlations between interacting proteins. Based on this stochastic matrix we propose and compute an entropy measure that quantifies the degree of randomness in the local pattern of information flux around single genes. By comparing the local entropies in the non-metastatic versus metastatic breast cancer networks, we here show that breast cancers that metastasize are characterised by a small yet significant increase in the degree of randomness of local expression patterns. We validate this result in three additional breast cancer expression data sets and demonstrate that local entropy better characterises the metastatic phenotype than other non-entropy based measures. We show that increases in entropy can be used to identify genes and signalling pathways implicated in breast cancer metastasis. Further exploration of such integrated cancer expression and protein interaction networks will therefore be a fruitful endeavour.

q-bio.MN↗
arXiv2010

Rule-based Modeling and Simulation of Biochemical Systems with Molecular Finite Automata

We propose a theoretical formalism, molecular finite automata (MFA), to describe individual proteins as rule-based computing machines. The MFA formalism provides a framework for modeling individual protein behaviors and systems-level dynamics via construction of programmable and executable machines. Models specified within this formalism explicitly represent the context-sensitive dynamics of individual proteins driven by external inputs and represent protein-protein interactions as synchronized machine reconfigurations. Both deterministic and stochastic simulations can be applied to quantitatively compute the dynamics of MFA models. We apply the MFA formalism to model and simulate a simple example of a signal transduction system that involves a MAP kinase cascade and a scaffold protein.

q-bio.QM↗
arXiv2010

Detecting local network motifs

Studying the topology of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are built from small functional units called motifs, which can be found by looking for small subgraphs whose numbers of occurrences in the whole network are surprisingly high. In this article, we propose to define motifs through a local overrepresentation in the network and develop a statistic to detect them without relying on simulations. We then illustrate the performance of our procedure on simulated and real data, recovering already known biologically relevant motifs. Moreover, we explain how our method gives some information about the respective roles of the vertices in a motif.

stat.AP↗
arXiv2010

Complex dynamics in hard oscillators: the influence of constant inputs

Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several deterministic models based on systems of nonlinear ordinary differential equations have been proposed. Few studies have been developed to characterize how either an external input or the coupling can drive systems with different coexisting states. For the sake of simplicity, in this manuscript we focus on systems belonging to the class of radial isochron clocks that exhibits hard excitation, in order to investigate their complex dynamics, local and global bifurcations arising in presence of constant external inputs. In particular the occurrence of saddle node on limit cycle bifurcations is detected.

math.DS↗
arXiv2010

A Monte Carlo study of ligand-dependent integrin signal initiation

Integrins are allosteric cell adhesion receptors that control many important processes, including cell migration, proliferation, and apoptosis. Ligand binding activates integrins by stabilizing an integrin conformation with separated cytoplasmic tails, thus enabling the binding of proteins that mediate cytoplasmic signaling. Experiments demonstrate a high sensitivity of integrin signaling to ligand density and this has been accounted mainly to avidity effects. Based on experimental data we have developed a quantitative Monte Carlo model for integrin signal initiation. We show that within the physiological ligand density range avidity effects cannot explain the sensitivity of cellular signaling to small changes in ligand density. Src kinases are among the first proteins to be activated, possibly by trans auto-phosphorylation. We calculate the extent of integrin and ligand clustering as well as the speed and extent of Src kinase activation by trans auto-phosphorylation or direct binding at different experimentally monitored ligand densities. We find that the experimentally observed ligand density dependency can be reproduced if Src kinases are activated by trans auto-phosphorylation or some other mechanism limits integrin-dependent Src kinase activation. We propose that Src kinase and thus cell activation by trans auto-phosphorylation may provide a mechanism to enable ligand-density dependent responses at physiological ligand densities. The capacity to detect small differences in ligand density at a ligand density that is large enough to permit cell adhesion is likely to be important for haptotaxis.

q-bio.QM↗
arXiv2010

Protein abundances and interactions coevolve to promote functional complexes while suppressing non-specific binding

How do living cells achieve sufficient abundances of functional protein complexes while minimizing promiscuous non-functional interactions? Here we study this problem using a first-principle model of the cell whose phenotypic traits are directly determined from its genome through biophysical properties of protein structures and binding interactions in crowded cellular environment. The model cell includes three independent prototypical pathways, whose topologies of Protein-Protein Interaction (PPI) sub-networks are different, but whose contributions to the cell fitness are equal. Model cells evolve through genotypic mutations and phenotypic protein copy number variations. We found a strong relationship between evolved physical-chemical properties of protein interactions and their abundances due to a "frustration" effect: strengthening of functional interactions brings about hydrophobic interfaces, which make proteins prone to promiscuous binding. The balancing act is achieved by lowering concentrations of hub proteins while raising solubilities and abundances of functional monomers. Based on these principles we generated and analyzed a possible realization of the proteome-wide PPI network in yeast. In this simulation we found that high-throughput affinity capture - mass spectroscopy experiments can detect functional interactions with high fidelity only for high abundance proteins while missing most interactions for low abundance proteins.

q-bio.BM↗
arXiv2010

Networks with the Smallest Average Distance and the Largest Average Clustering

We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal.

q-bio.MN↗
arXiv2010

Protein contact networks at different length scales and role of hydrophobic, hydrophilic and charged residues in protein's structural organisation

The three dimensional structure of a protein is an outcome of the interactions of its constituent amino acids in 3D space. Considering the amino acids as nodes and the interactions among them as edges we have constructed and analyzed protein contact networks at different length scales, long and short-range. While long and short-range interactions are determined by the positions of amino acids in primary chain, the contact networks are constructed based on the 3D spatial distances of amino acids. We have further divided these networks into sub-networks of hydrophobic, hydrophilic and charged residues. Our analysis reveals that a significantly higher percentage of assortative sub-clusters of long-range hydrophobic networks helps a protein in communicating the necessary information for protein folding in one hand; on the other hand the higher values of clustering coefficients of hydrophobic sub-clusters play a major role in slowing down the process so that necessary local and global stability can be achieved through intra connectivities of the amino acid residues. Further, higher degrees of hydrophobic long-range interactions suggest their greater role in protein folding and stability. The small-range all amino acids networks have signature of hierarchy. The present analysis with other evidences suggest that in a protein's 3D conformational space, the growth of connectivity is not evolved either through preferential attachment or through random connections; rather, it follows a specific structural necessity based guiding principle - where some of the interactions are primary while the others, generated as a consequence of these primary interactions are secondary.

q-bio.BM↗
arXiv2010

An Algebraic Approach to Signaling Cascades with n Layers

Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles, such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable, and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes. We demonstrate that many steady state concentrations are related through rational functions, which can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration and how the steady state changes in response to changes in the total amount of substrates. Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.

q-bio.QM↗
arXiv2010

Network-based confidence scoring system for genome-scale metabolic reconstructions

Reliability on complex biological networks reconstructions remains a concern. Although observations are getting more and more precise, the data collection process is yet error prone and the proofs display uneven certitude. In the case of metabolic networks, the currently employed confidence scoring system rates reactions according to a discretized small set of labels denoting different levels of experimental evidence or model-based likelihood. Here, we propose a computational network-based system of reaction scoring that exploits the complex hierarchical structure and the statistical regularities of the metabolic network as a bipartite graph. We use the example of Escherichia coli metabolism to illustrate our methodology. Our model is adjusted to the observations in order to derive connection probabilities between individual metabolite-reaction pairs and, after validation, we integrate individual link information to assess the reliability of each reaction in probabilistic terms. This network-based scoring system breaks the degeneracy of currently employed scores, enables further confirmation of modeling results, uncovers very specific reactions that could be functionally or evolutionary important, and identifies prominent experimental targets for further verification. We foresee a wide range of potential applications of our approach given the natural network bipartivity of many biological interactions.

q-bio.MN↗
arXiv2010

Finding attractors in asynchronous Boolean dynamics

We present a computational method for finding attractors (ergodic sets of states) of Boolean networks under asynchronous update. The approach is based on a systematic removal of state transitions to render the state transition graph acyclic. In this reduced state transition graph, all attractors are fixed points that can be enumerated with little effort in most instances. This attractor set is then extended to the attractor set of the original dynamics. Our numerical tests on standard Kauffman networks indicate that the method is efficient in the sense that the total number of state vectors visited grows moderately with the number of states contained in attractors.

cond-mat.dis-nn↗
arXiv2011

Dynamics on networks I. Combinatorial categories of modular continuous-time systems

We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky, Stewart and their collaborators. Our approach uses the tools and --- more importantly ---the stance of category theory. This enables us to put the groupoid formalism in a coordinate-free setting and to extend it from ordinary differential equations to vector fields on manifolds. In particular, we construct combinatorial models for categories of modular continuous time dynamical systems. Each such model, as a category, is a fibration over an appropriate category of labeled directed graphs. This makes precise the relation between dynamical systems living on networks and the combinatorial structure of the underlying directed graphs, allowing us to exploit the relation in new and interesting ways.

math.DS↗
arXiv2010

How can we kill cancer cells: insights from the computational models of apoptosis

Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to confer such resistance. Development of new experimental strategies, such as in silico modeling of biological pathways, can increase our understanding of how abnormal regulation of apoptotic pathway in cancer cells can lead to tumour chemoresistance. Monte Carlo simulations are in particular well suited to study inherent variability, such as spatial heterogeneity and cell-to-cell variations in signaling reactions. Using this approach, often in combination with experimental validation of the computational model, we observed that large cell-to-cell variability could explain the kinetics of apoptosis, which depends on the type of pathway and the strength of stress stimuli. Most importantly, Monte Carlo simulations of apoptotic signaling provides unexpected insights into the mechanisms of fractional cell killing induced by apoptosis-inducing agents, showing that not only variation in protein levels, but also inherent stochastic variability in signaling reactions, can lead to survival of a fraction of treated cancer cells.

q-bio.MN↗