An exact steady-state solution of the stochastic equations governing the behavior of a gene
regulated by a self-generated proteomic atmosphere is presented. The solutions depend on …

… It is composed of (n × n)-matrices g which are orthogonal, that is, satisfy g T g = 1 (where g
T denotes the transpose of g), and have determinant 1. The concrete form of such a matrix in …

The exact time-dependent solution for the stochastic equations governing the behavior of a
binary self-regulating gene is presented. Using the generating function technique to …

Intrinsic transcriptional noise induced by operator fluctuations is investigated with a simple
spin-like stochastic model. The effects of transcriptional fluctuations in protein synthesis are …

We consider a general class of mathematical models for stochastic gene expression where
the transcription rate is allowed to depend on a promoter state variable that can take an …

… where F and G are arbitrary functions that must be determined from the initial conditions, …
In order to determine F and G we will use matrix and vector notation to rewrite the solutions of Eq…

… When XD = 1, proteins are produced with rate g and degraded with rate kn. When XD = 0,
production falls to χg,χ < 1. The transition between active and inactive states is commanded by …

We discuss piecewise-deterministic approximations of gene networks dynamics. These
approximations capture in a simple way the stochasticity of gene expression and the …

… In fact, they present an exact general solution for one of the generating functions named
G 1 (z), but they fail to get G 0 (z) in closed form, as they explicitly recognize. Therefore, the …

We consider Markov chains with random transition probabilities which, moreover, fluctuate
randomly with time. We describe such a system by a product of stochastic matrices,, with the …