arXiv subjects

Murat Tugrul

Publications and source records attributed to Murat Tugrul.

4 recordsLinked to original sources

arXiv2015

Anomalous scaling in an age-dependent branching model

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $τ$ as $τ^{-α}$. Depending on the exponent $α$, the scaling of tree depth with tree size $n$ displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition ($α=1$) tree depth grows as $(\log n)^2$. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

q-bio.PE↗

arXiv2009

Anomalies in the transcriptional regulatory network of the yeast Saccharomyces cerevisiae

We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare it with two unbiased ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first -by construction- exactly and the second approximately), degree-degree correlations and the $k$-core structure observed in Yeast. An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications in the network's degree distributions. We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. We find that the Yeast's core network has a qualitatively different behaviour, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. Finally, we investigate the robustness of the networks and find that the stability depends strongly on the used function class. The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the reference models and the Yeast's core is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network.

q-bio.MN↗

arXiv2009

Robustness of Transcriptional Regulation in Yeast-like Model Boolean Networks

We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. By means of a dynamically determinant subnetwork, we explore the robustness of transcriptional regulation as a function of the type of Boolean functions used in the model that mimic the influence of regulating agents on the transcription level of a gene. We compare the results obtained for the actual yeast network with those from two different model networks, one with similar in-degree distribution as the yeast and random otherwise, and another due to Balcan et al., where the global topology of the yeast network is reproduced faithfully. We, surprisingly, find that the first set of model networks better reproduce the results found with the actual yeast network, even though the Balcan et al. model networks are structurally more similar to that of yeast.

q-bio.MN↗

arXiv2009

Simple models for scaling in phylogenetic trees

Many processes and models --in biological, physical, social, and other contexts-- produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this motivation, we analyze numerically two branching models leading to non-logarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.

q-bio.QM↗