Related papers: Multiplicative noise underlies Taylor's law in pro…
Taylor's power law states that the variance function decays as a power law. It is observed for population densities of species in ecology. For random networks another power law, that is, the power law degree distribution is widely studied.…
A prominent feature of gene transcription regulatory networks is the presence in large numbers of motifs, i.e, patterns of interconnection, in the networks. One such motif is the feed forward loop (FFL) consisting of three genes X, Y and Z.…
A collection of $N$-diffusing interacting particles where each particle belongs to one of $K$ different populations is considered. Evolution equation for a particle from population $k$ depends on the $K$ empirical measures of particle…
Investigations of natural variation in cell mechanics within a cell population are essential to understand the stochastic nature of soft-network deformation. Striking commonalities have been found concerning the average values and…
The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level,…
Several recent experiments, including our own in the fission yeast, S. pombe, have characterized the motions of gene loci within living nuclei by measuring the locus position over time, then proceeding to obtain the statistical properties…
Earlier we showed that the fine structure of the spectrum of amplitude variations in the results of measurements of the processes of different nature (in other words, the fine structure of the dispersion of results or the pattern of the…
The variability in cell size of an isogenic population of Escherichia coli has been widely reported in experiment. The probability density function (PDF) of cell lengths has been variously described by exponential and lognormal functions.…
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…
In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a…
We explore the joint effect of the intrinsic noise and time delay on the spatial pattern formation within a multi-scale mobile lattice model of the epithelium. The protein fluctuations are driven by transcription/translation processes in…
Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate…
We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlations at the simulation start between the…
We consider a three-state model comprising tumor cells, effector cells and tumor detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress…
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance $\sigma^{2}>0$ of a random variable (rv) $X$ with expectation $\mu >0$ as a powerof $\mu$: $\sigma…
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…
Brownian motion occurs in a variety of fluids, from rare gases to liquids. The Langevin equation, describing friction and agitation forces in statistical balance, is one of the most successful ways to treat the phenomenon. In rare gases, it…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…
The actomyosin cortex is an active material that provides animal cells with a strong but flexible exterior, whose mechanics, including non-Gaussian fluctuations and occasional large displacements or cytoquakes, have defied explanation. We…
Cell systems consist of a huge number of various molecules that display specific patterns of interactions, which have a determining influence on the cell's functioning. In general, such complexity is seen to increase with the complexity of…