Related papers: Stochastic Gene Expression in Cells: A Point Proce…
We analyze three simple genetic circuits which involve transcriptional regulation and feedback: the autorepressor, the switch and the repressilator, that consist of one, two and three genes, respectively. Such systems are commonly simulated…
A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large…
Signal-processing molecules inside cells are often present at low copy number, which necessitates probabilistic models to account for intrinsic noise. Probability distributions have traditionally been found using simulation-based approaches…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…
The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many…
Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined…
In this work, we study a protein synthesis degradation process by defining a general mathematical model. Using generating function technique we present a method that allows exact calculation of joint probability distribution of protein…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a…
The stochastic simulation algorithm commonly known as Gillespie's algorithm is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular…
Recent experiments at the level of a single cell have shown that gene expression occurs in abrupt stochastic bursts. Further, in an ensemble of cells, the levels of proteins produced have a bimodal distribution. In a large fraction of…
This paper considers the behavior of discrete and continuous mathematical models for gene expression in the presence of transcriptional/translational bursting. We treat this problem in generality with respect to the distribution of the…
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to…
The intrinsic stochasticity of gene expression can lead to large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in…
This paper considers adiabatic reduction in both discrete and continuous models of stochastic gene expression. In gene expression models, the concept of bursting is a production of several molecules simultaneously and is generally…
Inferring protein production kinetics for dividing cells is complicated due to protein inheritance from the mother cell. For instance, fluorescence measurements -- commonly used to assess gene activation -- may reflect not only newly…
Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
An important occurrence in many cellular contexts is the crossing of a prescribed threshold by a regulatory protein. The timing of such events is stochastic as a consequence of the innate randomness in gene expression. A question of…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…