Related papers: Modeling gene's length distribution in genomes
Cells actively regulate their size during the cell cycle to maintain volume homeostasis across generations. While various mathematical models of cell size regulation have been proposed to explain how this is achieved, relating these models…
Although mechanical properties of DNA are well characterized at the kilo base-pair range, a number of recent experiments have suggested that DNA is more flexible at shorter length scales, which correspond to the regime that is crucial for…
In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded in gene-frequency trajectories. We determine…
We propose and study a class-expansion/innovation/loss model of genome evolution taking into account biological roles of genes and their constituent domains. In our model numbers of genes in different functional categories are coupled to…
A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will…
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…
Genes are not located randomly along genomes. Synteny, the conservation of their relative positions in genomes of different species, reflects fundamental constraints on natural evolution. We present approaches to infer pairs of co-localized…
Gene gains and losses have shaped the gene repertoire of species since the universal last common ancestor to species today. Genes in extant species were gained at different historical times via de novo creation of new genes, duplication of…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman,…
Some genes can change their relative locations in a genome. Thus for different individuals of the same species, the orders of genes might be different. Such jumping genes are called transposons. A practical problem is to determine…
Using the Hamilton-Jacobi equation approach to study genomes of length $L$, we obtain 1/L corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model, as well as for the diploid…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
In this paper, we review the literature on statistical long-range correlation in DNA sequences. We examine the current evidence for these correlations, and conclude that a mixture of many length scales (including some relatively long ones)…
This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set $S$ with asymptotic density $\sigma$ and, on the other hand, permutations selected…
The time taken for gene expression varies not least because proteins vary in length considerably. This paper uses an abstract, tuneable Boolean regulatory network model to explore gene expression time variation. In particular, it is shown…
Unraveling the evolutionary forces shaping bacterial diversity can today be tackled using a growing amount of genomic data. While the genome of eukaryotes is highly stable, bacterial genomes from cells of the same species highly vary in…
We analyze the geometry of the species- and genotype-size distribution in evolving and adapting populations of single-stranded self-replicating genomes: here programs in the Avida world. We find that a scale-free distribution (power law)…