Cell-to-cell variability in protein expression is a significant factor in driving divergent cell signaling responses to identical stimuli, and additionally, poses challenges for the design of engineered biological systems. Although protein expression variability has been extensively characterized experimentally in cell systems ranging from bacteria to mammals, how the basic mechanisms of protein expression give rise to the observed probability distributions still remains an open question. Through a combination of first-principles theoretical analysis, direct numerical simulations, empirical modeling, and comparison to experimental data, we find that over a wide range of conditions, the total protein distribution is well-modeled by the gamma distribution. The gamma distribution model is consistent with the experimentally reported scaling observations that protein expression noise (squared coefficient of variation) is inversely proportional to the mean protein abundance (43 proteins under 11 different environmental conditions in S. Cerevisiae, Bar-Even et al., 2006), and that the mean protein abundance is directly proportional to the standard deviation (Colman-Lerner et al., 2005). We find that the total protein distributions depend only on two parameters, θ, the mean number of proteins produced per expression burst, and the composite k_degt, the product of the first-order degradation rate constant (k_deg) and the mean waiting time between expression bursts (t). Our model analysis reveals that while the mean protein abundance depends on both θ and k_degt, both protein expression noise and the proportionality constant between mean protein abundance and standard deviation are uniquely determined by k_degt. Our results therefore suggest that protein expression noise can be manipulated independently of mean protein abundance. Additionally, we find that protein expression variance may be reduced by regulating the waiting times between expression bursts, but only when k_degt is small (< 1). The understanding gained here not only yields quantitative insight into the how the fundamental processes of protein expression and degradation contribute to protein expression variability, but can also be exploited in the design of engineered biological systems to tune protein expression noise.

References

Bar-Even, A. et al. Noise in protein expression scales with natural protein abundance. Nat Genet 38, 636-43 (2006).

Colman-Lerner, A. et al. Regulated cell-to-cell variation in a cell-fate decision system. Nature 437, 699-706 (2005).