Related papers: Global Constraint Principle for Microbial Growth L…
In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…
One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…
This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth. The mathematical challenge is due to the fact that the…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading…
Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random…
The dynamics governing the evolution of a many body system is constrained by a nonabelian local symmetry. We obtain a general form of the global macroscopic conditions assuring that at the microscopic level the evolution respects the…
Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell…
When bacteria are grown on a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that…
The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. First, the chemical abundances measured over many cells are found to obey a log-normal distribution and second, the relationship between…
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive…
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a…
It is natural to ask how bacteria coordinate metabolism when depletion of an essential nutrient limits their growth, and they must slow their entire rate of biosynthesis. A major nutrient with a fluctuating abundance is nitrogen. The growth…
Given a monoidal category C, an ordinary category M, and a monad T in M, the lifts in a strict sense of a fixed action of C on M to an action of C on the Eilenberg-Moore category of T-modules in M are in a bijective correspondence with…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve…
The solution space of genome-scale models of cellular metabolism provides a map between physically viable flux configurations and cellular metabolic phenotypes described, at the most basic level, by the corresponding growth rates. By…
Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…