arXiv subjects

Peter F. Arndt

Publications and source records attributed to Peter F. Arndt.

15 recordsLinked to original sources

arXiv2016

Evolutionary dynamics of selfish DNA generates pseudo-linguistic features of genomes

Since the sequencing of large genomes, many statistical features of their sequences have been found. One intriguing feature is that certain subsequences are much more abundant than others. In fact, abundances of subsequences of a given length are distributed with a scale-free power-law tail, resembling properties of human texts, such as the Zipf's law. Despite recent efforts, the understanding of this phenomenon is still lacking. Here we find that selfish DNA elements, such as those belonging to the Alu family of repeats, dominate the power-law tail. Interestingly, for the Alu elements the power-law exponent increases with the length of the considered subsequences. Motivated by these observations, we develop a model of selfish DNA expansion. The predictions of this model qualitatively and quantitatively agree with the empirical observations. This allows us to estimate parameters for the process of selfish DNA spreading in a genome during its evolution. The obtained results shed light on how evolution of selfish DNA elements shapes non-trivial statistical properties of genomes.

q-bio.PE↗

arXiv2014

Statistical Properties of Pairwise Distances between Leaves on a Random Yule Tree

A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number of pairs separated by a certain time distance. This number turns out to follow a increasing exponential function. This property of a Yule tree can serve as a simple test for empirical data to be well described by a Yule process. We further use this recursive method to calculate the expected number of the $n$-most closely related pairs of leaves and the number of cherries separated by a certain time distance. To make our results more useful for realistic scenarios, we explicitly take into account that the leaves of a tree may be incompletely sampled and derive a criterion for poorly sampled phylogenies. We show that our result can account for empirical data, using two families of birds species.

q-bio.PE↗

arXiv2005

Universality of Long-Range Correlations in Expansion-Randomization Systems

We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion-randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent $χ$ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of $χ$, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.

q-bio.GN↗

arXiv2005

Identification and Measurement of Neighbor Dependent Nucleotide Substitution Processes

The presence of neighbor dependencies generated a specific pattern of dinucleotide frequencies in all organisms. Especially, the CpG-methylation-deamination process is the predominant substitution process in vertebrates and needs to be incorporated into a more realistic model for nucleotide substitutions. Based on a general framework of nucleotide substitutions we develop a method that is able to identify the most relevant neighbor dependent substitution processes, measure their strength, and judge their importance to be included into the modeling. Starting from a model for neighbor independent nucleotide substitution we successively add neighbor dependent substitution processes in the order of their ability to increase the likelihood of the model describing given data. The analysis of neighbor dependent nucleotide substitutions in human, zebrafish and fruit fly is presented. A web server to perform the presented analysis is publicly available.

q-bio.GN↗

arXiv2005

A Solvable Sequence Evolution Model and Genomic Correlations

We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations in the composition of letters as long as the sequence length is growing, i.e., the combined rates of duplications and insertions are higher than the deletion rate. For constant sequence length, on the other hand, all initial correlations decay exponentially. These results are obtained analytically and by simulations. They are compared with the long-range correlations observed in genomic DNA, and the implications for genome evolution are discussed.

q-bio.GN↗

arXiv2003

DNA Sequence Evolution with Neighbor-Dependent Mutation

We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of non-equilibrium models is developed by adopting well-known methods of nonlinear dynamics. Results are presented for the CpG-methylation-deamination process which dominates point substitutions in vertebrates. The dinucleotide frequencies generated by the model (using empirically obtained mutation rates) match the overall pattern observed in non-coding DNA. A web-based tool has been constructed to compute single- and dinucleotide frequencies for arbitrary neighbor-dependent mutation rates. Alsoprovided is the backward procedure to infer the mutation rates using maximum likelihood analysis given the observed single- and dinucleotide frequencies. Reasonable estimates of the mutation rates can be obtained very efficiently, using generic non-coding DNA sequences as input, after masking outlong homonucleotide subsequences. Our method is much more convenient and versatile to use than the traditional method of deducing mutation rates by counting mutation events in carefully chosen sequences. More generally, our approach provides a more realistic but still tractable description of non-coding genomic DNA, and may be used as a null model for various sequence analysis applications.

physics.bio-ph↗

arXiv2003

Distinct changes of genomic biases in nucleotide substitution at the time of mammalian radiation

Differences in the regional substitution patterns in the human genome created patterns of large-scale variation of base composition known as genomic isochores. To gain insight into the origin of the genomic isochores we develop a maximum likelihood approach to determine the history of substitution patterns in the human genome. This approach utilizes the vast amount of repetitive sequence deposited in the human genome over the past ~250 MYR. Using this approach we estimate the frequencies of seven types of substitutions: the four transversions, two transitions, and the methyl-assisted transition of cytosine in CpG. Comparing substitutional patterns in repetitive elements of various ages, we reconstruct the history of the base-substitutional process in the different isochores for the past 250 Myr. At around 90 Myr ago (around the time of the mammalian radiation), we find an abrupt 4- to 8-fold increase of the cytosine transition rate in CpG pairs compared to that of the reptilian ancestor. Further analysis of nucleotide substitutions in regions with different GC-content reveals concurrent changes in the substitutional patterns. While the substitutional pattern was dependent on the regional GC-content in such ways that it preserved the regional GC-content before the mammalian radiation, it lost this dependence afterwards. The substitutional pattern changed from an isochore-preserving to an isochore-degrading one. We conclude that isochores have been established before the radiation of the eutherian mammals and have been subject to the process of homogenization since then.

cond-mat.stat-mech↗

arXiv2001

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: II. The Charged System and the Two-component Burgers Equations

We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. We extend the analysis of this model to the case when the densities of the charged particles are not the same. The mean-field equations describing the model are coupled nonlinear differential equations that we call the two-component Burgers equations. We find roundabout weak solutions of these equations. These solutions are used to describe the properties of the stationary states of the stochastic model. The values of the currents and of various two-point correlation functions obtained from Monte-Carlo simulations are compared with the mean-field results. Like in the case of equal densities, one finds a pure phase, a mixed phase and a disordered phase.

cond-mat.stat-mech↗

arXiv2000

A New Criterion for Crack Formation in Disordered Materials

Crack formation is conventionally described as a nucleation phenomenon despite the fact that the temperatures necessary to overcome the nucleation barrier are far too high. In this paper we consider the possibility that cracks are created due to the presence of frozen disorder (e.g. heterogeneities or frozen dislocations). In particular we calculate the probability for the occurrence of a critical crack in a quasi two-dimensional disordered elastic system. It turns out that this probability takes the form of an Arrhenius law (as for thermal nucleation) but with the temperature T replaced by an effective disorder temperature T_eff which depends on the strength of the disorder. The extension of these results to d=3 dimensions is briefly discussed.

cond-mat.stat-mech↗

arXiv2000

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System

We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. The model depends on two parameters. Analytic calculations using quadratic algebras, inhomogeneous solutions of the mean-field equations and Monte-Carlo simulations suggest that the model has three phases. A pure phase in which one has three pinned blocks of only positive, negative particles and vacancies and in which translational invariance is broken. A mixed phase in which the current has a linear dependence on one parameter but is independent of the other one and of the density of the charged particles. In this phase one has a bump and a fluid. The bump (condensate) contains positive and negative particles only, the fluid contains charged particles and vacancies uniformly distributed. The mixed phase is separated from the disordered phase by a second-order phase-transition which has many properties of the Bose-Einstein phase-transition observed in equilibrium. Various critical exponents are found.

cond-mat.stat-mech↗

arXiv2000

Yang-Lee Theory for a Nonequilibrium Phase Transition

To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can identified with two different phases. In a region of the parameter space both of these phases coexist. The condensation point can be computed with high accuracy.

cond-mat.stat-mech↗

arXiv1997

Metastability and spinodal points for a random walker on a triangle

We investigate time-dependent properties of a single particle model in which a random walker moves on a triangle and is subjected to non-local boundary conditions. This model exhibits spontaneous breaking of a Z_2 symmetry. The reduced size of the configuration space (compared to related many-particle models that also show spontaneous symmetry breaking) allows us to study the spectrum of the time-evolution operator. We break the symmetry explicitly and find a stable phase, and a meta-stable phase which vanishes at a spinodal point. At this point, the spectrum of the time evolution operator has a gapless and universal band of excitations with a dynamical critical exponent z=1. Surprisingly, the imaginary parts of the eigenvalues E_j(L) are equally spaced, following the rule Im E_j(L)\propto j/L. Away from the spinodal point, we find two time scales in the spectrum. These results are related to scaling functions for the mean path of the random walker and to first passage times. For the spinodal point, we find universal scaling behavior. A simplified version of the model which can be handled analytically is also presented.

cond-mat.stat-mech↗

arXiv1997

Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.

cond-mat.stat-mech↗

arXiv1997

First-order phase transitions in one-dimensional steady states

The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function but looks like a standard Ginzburg-Landau picture. If a symmetry breaking term is introduced in the boundaries the Ginzburg-Landau picture remains and one obtains spinodal points. The spectrum of the hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the first-order phase transition line with a dynamical critical exponent z=2 as expected from the existence of shocks and at the spinodal points where we find $z=1$. It is for the first time that this value which characterizes conformal invariant equilibrium problems appears in stochastic processes.

cond-mat.stat-mech↗

arXiv1997

Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras.

cond-mat.stat-mech↗