Figure 2. A stochastic model of gene expression.
A) Left, the central dogma of molecular biology – DNA to RNA to protein – is shown with rate constants of production and degradation: the rate of transcription ν0, the rate of RNA degradation d0, the rate of translation ν1, and the rate of protein decay d1. Once degradation, the RNA and protein are Right, a model of gene induction known as the telegraph model. The gene transitions between an inactive off state and an active on state (red line). From the active state, transcripts initiation events (vertical green lines) are separated by an average time interval ν0−1. B) The probability distributions (Px) for each step of MDN1 expression, from left to right: nascent RNA at a transcription site (Pm, m = number of nascent chains), total cellular mRNA (Pr, r = number of mRNA), proteins/mRNA (Pn, n = number of proteins/mRNA), and total protein/cell (PN, N = number of proteins/cell). The gray symbols are published data; the red lines are theoretical fits using the equations shown below each panel. The data for nascent transcripts and total mRNA is from 3. There is no experimental data for proteins/mRNA for MDN1. The data for total protein/cell was reported as a mean and variance (σ2) 5,6, shown here as a Gaussian distribution. The parameters in the probability distributions are shown in panel A. τ is the time to synthesize an MDN1 transcript. Γ denotes the gamma function. Upon degradation, neither the RNA nor the protein is considered in the probability distribution, so the state of degraded RNA and degraded protein is indicated by the symbol ϕ. Two additional symbols are used for simplicity: a is the ratio of transcription rate/protein degradation rate (ν0/d1); b is the translation rate/RNA decay (ν1/d0), also known as the protein burst size. For MDN1, a=19, b=29.