Related papers: Emergent L\'evy behavior in single-cell stochastic…
Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene…
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
We study the spatial decay behaviour of resolvent kernels for a large class of non-local L\'evy operators and bound states of the corresponding Schr\"odinger operators. Our findings naturally lead us to proving results for L\'evy measures,…
Gene expression has a stochastic component owing to the single molecule nature of the gene and the small number of copies of individual DNA binding proteins in the cell. We show how the statistics of such systems can be mapped on to quantum…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
Investigation of protein self-assembly processes is important for the understanding of the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering…
The rampant phenomenon of overpopulation and the remarkable increase of human movements over the last decade have caused an aggressive re-emergence of dengue fever, which made it the subject of several research fields. In this regard,…
The advent of new experimental genomic technologies and the massive increase of DNA sequence information is helping researchers better understand how our genes work. Recently, experiments on mRNA abundance (gene expression) have revealed…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription factor-regulated gene expression. Recently, a mathematical model has been proposed to…
This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
In this kind of model, the main characteristic that determines population viability in the long term is the stochastic growth rate (SGR) denoted $\lambda_S$. When $\lambda_S$ is larger than one, the population grows exponentially with…
Genetically identical cells in the same population can take on phenotypically variable states, leading to differentiated responses to external signals, such as nutrients and drug-induced stress. Many models and experiments have focused on a…
A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can…
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics…