Figure 2.

Maintenance of autoregulated gene expression is sensitive to copy number in a stochastic manner. (A) The model of Fig. 1 was modified to simulate simultaneous binding (with affinity Kp) of two P molecules to a receptor that activates gene expression, and the expression deactivation rate was decreased 10-fold (Td = 10Tp/4) to simulate a relatively stable gene with infrequent expression lapses. The expression rate, Jp, was decreased to 12.2 to maintain an average product level of ≈0.5 uP. Setting Kp = 0.2 of the full-scale value of P = 1.0 established an all-or-none activation/deactivation threshold at a value Pth = 0.05. (B) When two genes were active (upper trace and histogram), P levels were maintained well above the threshold, and the genes were expressed indefinitely. However, when one gene was inactivated, random lapses of expression allowed P levels to fall below the threshold level (lower trace continued as a second line, and lower histogram). (C) Histogram of survival times for 100 trials of a one-gene model starting with active expression and an initial P of 0.25 (the steady-state level of P for persistent expression). As expected for a stochastic process, survival times were distributed exponentially where ≈63% of trials lasted less than the average survival time of ≈23 Tp.