Duygu Balcan

The Information Coded in the Yeast Response Elements Accounts for Most of the Topological Properties of Its Transcriptional Regulation Network.

The regulation of gene expression in a cell relies to a major extent on transcription factors, proteins which recognize and bind the DNA at specific binding sites (response elements) within promoter regions associated with each gene. We present an information theoretic approach to modeling transcriptional regulatory networks, in terms of a simple “sequence-matching” rule and the statistics of the occurrence of binding sequences of given specificity in random promoter regions. The crucial biological input is the distribution of the amount of information coded in these cognate response elements and the length distribution of the promoter regions. We provide an analysis of the transcriptional regulatory network of yeast Saccharomyces cerevisiae, which we extract from the available databases, with respect to the degree distributions, clustering coefficient, degree correlations, rich-club coefficient and the k-core structure. We find that these topological features are in remarkable agreement with those predicted by our model, on the basis of the amount of information coded in the interaction between the transcription factors and response elements.

Analytical solution of a stochastic content-based network model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.

Random model for RNA interference yields scale free network

Abstract.We introduce a random bit-string model of post-transcriptional genetic regulation based on sequence matching. The model spontaneously yields a scale free network with power law scaling with

Content-based networks: A pedagogical overview

\gamma = -1

Dynamics of content-based networks

and also exhibits log-periodic behaviour. The in-degree distribution is much narrower, and exhibits a pronounced peak followed by a Gaussian distribution. The network is of the smallest world type, with the average minimum path length independent of the size of the network, as long as the network consists of one giant cluster. The percolation threshold depends on the system size.

Global epidemic invasion thresholds in directed cattle subpopulation networks having source, sink, and transit nodes

Complex interactions call for the sharing of information between different entities. In a recent paper, we introduced a combinatoric model which concretizes this idea via a string-matching rule. The model was shown to lend itself to analysis regarding certain topological features of the network. In this paper, we will introduce a statistical physics description of this network in terms of a Potts model. We will give an explicit mean-field treatment of a special case that has been proposed as a model for gene regulatory networks, and derive closed-form expressions for the topological coefficients. Simulations of the hidden variable network are then compared with numerically integrated results.

Monte Carlo renormalization group for entanglement percolation

Content-based networks are introduced and their topological properties are outlined. A content-based model with Random Boolean dynamics, designed to mimic the gene regulation network, exhibits an increase in the number and complexity of attractors for increasing number of nodes. However, contrary to expectations based on Mean Field calculations for random scale-free networks, the attractors are not chaotic, even for average connectivities in excess of 2. Thus, the present model offers a promising tool for understanding complex biological networks.

Dynamical real-space renormalization group calculations with a highly connected clustering scheme on disordered networks

Through the characterization of a metapopulation cattle disease model on a directed network having source, transit, and sink nodes, we derive two global epidemic invasion thresholds. The first threshold defines the conditions necessary for an epidemic to successfully spread at the global scale. The second threshold defines the criteria that permit an epidemic to move out of the giant strongly connected component and to invade the populations of the sink nodes. As each sink node represents a final waypoint for cattle before slaughter, the existence of an epidemic among the sink nodes is a serious threat to food security. We find that the relationship between these two thresholds depends on the relative proportions of transit and sink nodes in the system and the distributions of the in-degrees of both node types. These analytic results are verified through numerical realizations of the metapopulation cattle model.

The Shift-Match Number and String Matching Probabilities for Binary Sequences

We use a large cell Monte Carlo (MC) renormalization procedure to compute the critical exponents of a system of growing linear polymers. We simulate the growth of non-intersecting chains in large MC cells. Dense regions where chains get in each others’ way, give rise to connected clusters under coarse graining. At each time step, the fraction of occupied bonds is determined in both the original and the coarse grained configurations, and averaged over many realizations. Our results for the fractal dimension on three-dimensional lattices are consistent with the percolation value.

Analytical Solution of a Stochastic Model for Gene Regulation

We have defined a type of clustering scheme preserving the connectivity of the nodes in a network, ignored by the conventional Migdal-Kadanoff bond moving process. In high dimensions, our clustering scheme performs better for correlation length and dynamical critical exponents than the conventional Migdal-Kadanoff bond moving scheme. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising model to be z=2.13 and z=2.09 , respectively, at the pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behavior of randomly bond diluted lattices in d=2 and 3 in the light of this transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law and Poissonian degree distributions.