The Effect of Stochasticity on the Lac Operon: An Evolutionary Perspective

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Abstract
The role of stochasticity on gene expression is widely discussed. Both potential advantages and disadvantages have been revealed. In some systems, noise in gene expression has been quantified, in among others the lac operon of Escherichia coli. Whether stochastic gene expression in this system is detrimental or beneficial for the cells is, however, still unclear. We are interested in the effects of stochasticity from an evolutionary point of view. We study this question in the lac operon, taking a computational approach: using a detailed, quantitative, spatial model, we evolve through a mutation–selection process the shape of the promoter function and therewith the effective amount of stochasticity. We find that noise values for lactose, the natural inducer, are much lower than for artificial, nonmetabolizable inducers, because these artificial inducers experience a stronger positive feedback. In the evolved promoter functions, noise due to stochasticity in gene expression, when induced by lactose, only plays a very minor role in short-term physiological adaptation, because other sources of population heterogeneity dominate. Finally, promoter functions evolved in the stochastic model evolve to higher repressed transcription rates than those evolved in a deterministic version of the model. This causes these promoter functions to experience less stochasticity in gene expression. We show that a high repression rate and hence high stochasticity increases the delay in lactose uptake in a variable environment. We conclude that the lac operon evolved such that the impact of stochastic gene expression is minor in its natural environment, but happens to respond with much stronger stochasticity when confronted with artificial inducers. In this particular system, we have shown that stochasticity is detrimental. Moreover, we demonstrate that in silico evolution in a quantitative model, by mutating the parameters of interest, is a promising way to unravel the functional properties of biological systems. Gene expression is a process that is inherently stochastic because of the low number of molecules that are involved. In recent years it has become possible to measure the amount of stochasticity in gene expression, which has inspired a debate about the importance of stochasticity in gene expression. Little attention, however, has been paid to stochasticity in gene expression from an evolutionary perspective. We studied the evolutionary consequences of stochastic gene expression in one of the best-known systems of genetic regulation, the lac operon of E. coli, which regulates lactose uptake and metabolism. We used a computational approach, in which we let cells evolve their lac operon promoter function in a fluctuating, spatially explicit, environment. Cells can in this way adapt to the environment, but also change the amount of stochasticity in gene expression. We find that cells evolve their repressed transcription rates to higher values in a stochastic model than in a deterministic model. Higher repressed transcription rates means less stochasticity, and, hence, these cells appear to avoid stochastic gene expression in this particular system. We find that this can be explained by the fact that stochastic gene expression causes a larger delay in lactose uptake, compared with deterministic gene expression.