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In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The origin of heredity is studied as a recursive state in a replicating proto-cell consisting of many molecule species in mutually catalyzing reaction networks. Protocells divide when the number of molecules, increasing due to replication,…
The production processes of proteins in prokaryotic cells are investigated. Most of the mathematical models in the literature study the production of {\em one} fixed type of proteins. When several classes of proteins are considered, an…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
Gene expression and its regulation is a nonequilibrium stochastic process. Different molecules are involved in several biochemical steps in this process with low copies. It is observed that the stochasticity in biochemical processes is…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Genome-wide patterns of genetic divergence reveal mechanisms of adaptation under gene flow. Empirical data show that divergence is mostly concentrated in narrow genomic regions. This pattern may arise because differentiated loci protect…
Tomasetti and Vogelstein recently proposed that the majority of variation in cancer risk among tissues is due to "bad luck," that is, random mutations arising during DNA replication in normal noncancerous stem cells. They generalize this…
Proteins are macromolecules that mediate a significant fraction of the cellular processes that underlie life. An important task in bioengineering is designing proteins with specific 3D structures and chemical properties which enable…
Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression. A quantitative understanding of…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
The bacterium Escherichia coli initiates replication once per cell cycle at a precise volume per origin and adds an on average constant volume between successive initiation events, independent of the initiation size. Yet, a molecular model…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We consider diffusion under stochastic resetting to the origin in one dimension and compute the mean time to find both of two targets placed either side of the origin. A surprising result is that increasing the distance between two targets…
We consider the simple random walk (or P\'olya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability $r$ at each time step. The focus is on the joint statistics of the numbers…
We consider a stochastic model for a pathogen population in the presence of an immune response, in which pathogen types are partially ordered by ancestry and the immune system must eliminate ancestor types before it can eliminate their…
Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…