arXiv subjects

Ayse Erzan

Publications and source records attributed to Ayse Erzan.

At least 19 recordsLinked to original sources

arXiv2011

Spectral renormalization group theory on networks

Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second order phase transitions call for special techniques. We set up a renormalization group scheme by expanding an arbitrary scalar field living on the nodes of an arbitrary network, in terms of the eigenvectors of the normalized graph Laplacian. The renormalization transformation involves, as usual, the integration over the more "rapidly varying" components of the field, corresponding to eigenvectors with larger eigenvalues, and then rescaling. The critical exponents depend on the particular graph through the spectral density of the eigenvalues.

cond-mat.stat-mech↗

arXiv2009

Information content based model for the topological properties of the gene regulatory network of Escherichia coli

Gene regulatory networks (GRN) are being studied with increasingly precise quantitative tools and can provide a testing ground for ideas regarding the emergence and evolution of complex biological networks. We analyze the global statistical properties of the transcriptional regulatory network of the prokaryote Escherichia coli, identifying each operon with a node of the network. We propose a null model for this network using the content-based approach applied earlier to the eukaryote Saccharomyces cerevisiae. (Balcan et al., 2007) Random sequences that represent promoter regions and binding sequences are associated with the nodes. The length distributions of these sequences are extracted from the relevant databases. The network is constructed by testing for the occurrence of binding sequences within the promoter regions. The ensemble of emergent networks yields an exponentially decaying in-degree distribution and a putative power law dependence for the out-degree distribution with a flat tail, in agreement with the data. The clustering coefficient, degree-degree correlation, rich club coefficient and k-core visualization all agree qualitatively with the empirical network to an extent not yet achieved by any other computational model, to our knowledge. The significant statistical differences can point the way to further research into non-adaptive and adaptive processes in the evolution of the E. coli GRN.

q-bio.MN↗

arXiv2009

Tracking tumor evolution via the prostate marker PSA: An individual post-operative study

The progress of the prostate-specific antigen after radical prostatectomy is observed for a patient in order to extract information on the growth mode of the tumor cells. An initial fast-growth mode goes over to a slower power-law regime within two years of surgery. We argue that such studies may help determine the appropriate time window for subsequent therapies in order to increase the life expectancy of the patient.

q-bio.QM↗

arXiv2006

Spontaneous Self-Assembly of Transcription Factor Based Gene Regulation Networks

We model the transcription factor based regulation network of yeast using a content-based network model that mimicks the recognition of binding motifs on the regulatory regions of the genes. We are thereby able to faithfully reproduce many of the topological features of the gene regulatory network of yeast once the parameters of the yeast genome, in particular the distribution of information coded by the "binding sequences" within the promoter regions is provided as input. The length distribution for the promoter regions is fixed by comparing the k-core analysis of the model network with that of yeast. Our results strongly point to the possibility that the observed topological features are generic to networks formed via sequence-matching between random strings obeying certain length distributions.

q-bio.MN↗

arXiv2005

Content based network model with duplication and divergence

We construct a minimal content-based realization of the duplication and divergence model of genomic networks introduced by Wagner [A. Wagner, Proc. Natl. Acad. Sci. {\bf 91}, 4387 (1994)] and investigate the scaling properties of the directed degree distribution and clustering coefficient. We find that the content based network exhibits crossover between two scaling regimes, with log-periodic oscillations for large degrees. These features are not present in the original gene duplication model, but inherent in the content based model of Balcan and Erzan. The scaling exponents $γ_1$ and $γ_2=γ_1-1/2$ of the Balcan-Erzan model turn out to be robust under duplication and point mutations, but get modified in the presence of splitting and merging of strings. The clustering coefficient as a function of the degree, $C(d)$, is found, for the Balcan-Erzan model, to behave in a way qualitatively similar to the out-degree distribution, however with a very small exponent $α_1= 1-γ_1$ and an envelope for the oscillatory part, which is essentially flat, thus $α_2= 0$. Under duplication and mutations including splitting and merging of strings, $C(d)$ is found to decay exponentially.

q-bio.MN↗

arXiv2005

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 behavior 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 scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.

q-bio.MN↗

arXiv2004

Dynamical real-space renormalization group calculations with a new clustering scheme on random networks

We have defined a new type of clustering scheme preserving the connectivity of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving process. Our new clustering scheme performs much better for correlation length and dynamical critical exponents in high dimensions, where the conventional Migdal-Kadanoff bond moving scheme breaks down. 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 pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behaviour for randomly bond diluted lattices in d=2 and 3, in the light of this new transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law degree distributions, both in the pure and random cases.

cond-mat.stat-mech↗

arXiv2003

Random model for RNA interference yields scale free network

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 $ γ=-1$ 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.

q-bio.GN↗

arXiv2003

A Thermodynamic Model for Prebiotic Protein Function

We propose a scenario for the prebiotic co-evolution of RNA and of fast folding proteins with large entropy gaps as observed today. We show from very general principles that the folding and unfolding of the proteins synthesized by RNA can function as a heat pump. Rock surfaces can facilitate the folding of amino acid chains having polar and hydrophobic residues, with an accompanying heat loss to the surrounding rock. These chains then absorb heat from the soup as they unfold. This opens the way to the enhancement of RNA replication rates, by the enzymatic action of folded proteins present in greater numbers at reduced temperatures. This gives an evolutionary advantage to those RNA coding amino acid sequences with non-degenerate folded states which would provide the most efficient refrigeration.

cond-mat.soft↗

arXiv2002

Statistics of a hydrophobic chain near a hydrophobic boundary

We study the behaviour of a hydrophobic chain near a hydrophobic boundary in two dimensions, using the decorated lattice model of Berkema and Widom [G.T. Barkema and B. Widom, J. Chem. Phys. 113, 2349 (2000)] to obtain effective, temperature dependent intrachain and chain-boundary interactions. We use these interactions to construct two model hamiltonians which can be solved exactly. Our results compare favorably with preliminary Monte Carlo computations, using the same effective interactions. At relatively low temperatures and at high temperatures, we find that the chain is randomly configured in the ambient water, and detached from the wall, whereas at intermediate temperatures it adsorbs onto the wall in a stretched or partially folded state, again depending upon the temperature, and the energy of solvation.

cond-mat.stat-mech↗

arXiv2002

Monte Carlo Renormalization Group for Entanglement Percolation

We use a large cell Monte Carlo 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.

cond-mat.stat-mech↗

arXiv2002

Hamiltonian model for multidimensional epistasis

We propose and solve a Hamiltonian model for multidimensional epistastatic interactions between beneficial mutations. The model is able to give rise either to a phase transition between two equilibrium states, without any coexistence, or exhibits a state where hybrid species can coexist, with gradual passage from one wild type to another. The transition takes place as a function of the "tolerance" of the environment, which we define as the amount of noise in the system.

physics.bio-ph↗

arXiv2001

Evolutionary route to diploidy and sex

Using a bit-string model of evolution, we find a successful route to diploidy and sex in simple organisms. Allowing the sexually reproducing diploid individuals to also perform mitosis, as they do in a haploid-diploid cycle, leads to the complete takeover of the population by sexual diploids. This mechanism is so robust, that even the accidental conversion and pairing of only two diploids give rise to a sexual population.

cond-mat.soft↗

arXiv2001

Strategies for the evolution of sex

We find that the hypothesis made by Jan, Stauffer and Moseley [Theory in Biosc., 119, 166 (2000)] for the evolution of sex, namely a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multi-stable regime. On the other hand, in the limit of extremely slow drive, another transition takes place to a different steady state distribution, with fewer deleterious mutations within the asexual population.

cond-mat.soft↗

arXiv2000

Temporal and spatial correlations in a visco-elastic model of heterogeneous faults

We study the temporal and spatial correlations in a one-dimensional model of a heterogeneous fault zone, in the presence of visco-elastic effects. As a function of dynamical weakening and of dissipation, the system exhibits three different "phases" : one in which there are no time correlations between the events, a second, in which there are ``Omori's law'' type temporal correlations, and a third, runaway phase with quasiperiodic system size events.

cond-mat.stat-mech↗

arXiv2000

Testing a hypothesis for the evolution of sex

An asexual set of primitive bacteria is simulated with a bit-string Penna model with a Fermi function for survival. A recent hypothesis by Jan, Stauffer and Moseley on the evolution of sex from asexual cells as a strategy for trying to escape the effects of deleterious mutations is checked. This strategy is found to provide a successful scenario for the evolution of a stable macroscopic sexual population.

cond-mat.soft↗

arXiv1999

Dissipative Dynamics and the Statistics of Energy States of a Hookean Model for Protein Folding

A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process and giving rise to the so called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.

cond-mat.soft↗

arXiv1999

Glassy Dynamics of Protein Folding

A coarse grained model of a random polypeptide chain, with only discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues is shown to display stretched exponential relaxation under Metropolis dynamics at low temperatures with the exponent $β\simeq 1/4$, in agreement with the best experimental results. The time dependent correlation functions for fluctuations about the native state, computed in the Gaussian approximation for real proteins, have also been found to have the same functional form. Our results indicate that the energy landscape exhibits universal features over a very large range of energies and is relatively independent of the specific dynamics.

cond-mat.soft↗