Related papers: Equilibrium state of molecular breeding
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
The search for high-affinity aptamers for targets such as proteins, small molecules, or cancer cells remains a formidable endeavor. Systematic Evolution of Ligands by EXponential Enrichment (SELEX) offers an iterative process to discover…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…
Starting from common assumptions, we build a rate equation model for multi-strain disease dynamics in terms of immune repertoire classes. We then move to a strain-level description where a low-order closure reminiscent of a pair…
This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to…
In this Letter, we extend the semiconservative quasispecies equations to incorporate imperfect DNA lesion repair. We study the equilibrium behavior of this model in the limit of infinite sequence length and population size, using a…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset $\Omega$ of Euclidean space. The approximation is good when a large number of…
This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a…
We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…
The fuel-driven process of replication in living systems generates distributions of copied entities with varying degrees of copying accuracy. Here we introduce a thermodynamically consistent ensemble for investigating universal population…
We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…
We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is…
In this paper we analyze the equilibrium properties of a large class of stochastic processes describing the fundamental biological process within bacterial cells, {\em the production process of proteins}. Stochastic models classically used…