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Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes

Fig 2

Stochastic models of gene expression with cell division.

Arrows denote stochastic events that change the protein level by discrete jumps as shown in Eqs (1) and (4). The differential equation within the circle represents the time evolution of x(t) in between events. A) Model with all the different sources of noise: proteins are expressed in stochastic bursts, cell division occurs at random times, and molecules are partitioned between the two daughter cells based on Eq (5). The trivial dynamics signifies that the protein level is constant in-between stochastic events. B) Hybrid model where randomness in cell-division events is the only source of noise. Protein production is modeled deterministic through a differential equation and partitioning errors are absent, i.e., α = 0 in Eq (5). C) Hybrid model where noise comes from both cell-division events and partitioning errors. Protein production is considered to be deterministic as in Fig 2B. Since x(t) is continuous here, x₊(t_s) has a positively-valued continuous distribution with same mean and variance as in Eq (5)

doi: https://doi.org/10.1371/journal.pcbi.1004972.g002