278391 Coupling of Gene Expression and Growth Rate Determines Selection of Transcriptional Regulation Mechanisms

Wednesday, October 31, 2012
Hall B (Convention Center )
Priya Rao, Jatin Narula and Oleg Igoshin, Rice University, Houston, TX

Coupling of Gene Expression and Growth Rate Determines Selection of Transcriptional Regulation Mechanisms

Priya Rao, Jatin Narula, Oleg Igoshin

Department of Bioengineering, Rice University, Houston, TX

Gene expression in bacterial cells can be regulated by either activators or repressors but it is not clear how evolution selects one mode of regulation over the other. From a molecular biology perspective, selection of a particular mode of regulation could be based upon optimization of functional performance if these modes differ functionally [1]. Alternatively, even functionally equivalent modes of regulation may be selected for or against based upon robustness to evolutionary forces of mutation and drift [2]. Previously, both of these approaches were applied separately to this problem to show that the mode of regulation is selected such that the regulator is active for greater part of the cell's lifetime (i.e. activators are selected to control often-needed genes and repressors to control seldom-needed genes). In reality, both types of criteria probably interact and together affect the selection of the appropriate modes of gene regulation. Here we combine mathematical modeling of gene regulation with a theoretical population biology framework to explain how evolution and functional performance together influence the choice between activator and repressor modes of control.

Methods

We modeled inducible gene regulation by activators and repressors using the typical ODE formulation. Coupling between gene expression and cell growth was modeled following the results of [3]. In this formulation, we used a system of two coupled ODEs for the concentration of the transcription factor and cell volume respectively. Cells were assumed to divide when they doubled their initial volume. Stochasticity of gene expression was included in this model by adding a Gaussian white-noise type term to set up a Langevin equation for the concentration of the transcription factor. For the population biology simulations we used a continuous-time version of the Wright-Fisher genetic drift simulation analogous to the Moran process [4]. The two coupled ODE system described above was propagated for a population of cells in this framework. We ignored the effects of mutations for the small time-scales considered in our simulations. 

Results

Activators and Repressor are functionally equivalent modes of inducible gene regulation

Inducible gene expression control can be achieved by both activators and repressors if the activity of these transcription factors is modulated by binding of a small molecule inducer. We used a mathematically controlled comparison to determine if these modes of regulation differ functionally. We show that with appropriate choice of parameters, both modes of control can result in identical gene expression over the whole range of inducer concentrations. Thus these modes of control are functionally equivalent in terms of their control over gene expression.

Feedback between cell growth and gene expression depends on mode of regulation

Several recent reports have shown that gene expression is associated with costs and benefits that couple it to cell growth [3, 5]. In an environment when the gene is needed, gene expression increases growth rate. In an environment when the gene is not needed, gene expression decreases growth rate. We show that this coupling between gene expression and growth results in a feedback loop between the concentration of transcription factors and cellular growth rate. While the increase in growth rates leads to higher effective dilution rate of stable proteins, the resulting decrease in protein concentration may either increase or decrease growth rates resulting in either negative or positive feedback loops. Specifically, when the gene of interest is needed for growth, increases in gene expression increase growth rate. In this scenario, activators increase gene expression and thus increase growth rate resulting in a negative feedback loop whereas repressors have the opposite effect on growth and are coupled to it in a positive feedback loop. The feedback signs for activators and repressor modes are reversed if the expression of the gene of interest is not essential and decreases growth. Therefore, we show that the choice between activator and repressor is a choice between negative and positive feedback coupling of the regulator and growth rate.

We found that a positive feedback loop between growth and gene expression increases the time required to dilute stochastic fluctuations in protein concentrations. This creates a greater variance in protein levels within a cell population, which then leads to a greater variance in growth rates. However, the mean growth rate is unaffected by the choice of feedback loop. As a result, if the fluctuations are not heritable, the two modes of control are functionally equivalent in their control over both gene expression and cell growth.

Heritable fluctuations in gene expression can influence the selection of activators and repressors

If the fluctuations in gene expression are heritable (dilution of the fluctuation takes longer than a single cell generation), then the resulting heritable variability in growth rates affects both the mean and variance of gene expression in a cell population. Specifically, gene expression fluctuations that increase growth rate are selected for and the population becomes biased over time. This effect is more prominent in the case of positive feedback since it takes longer to dilute out fluctuations and effectively has greater fluctuation heritability. As a result, when we set up a competition between different modes of gene regulation in a Wright-Fisher type genetic drift simulation, we found that the otherwise equivalent modes of control differed in their probability of fixation. In particular, modes of regulation that were coupled with cell growth in a positive feedback loop always had a higher probability of fixation in the population.

This result was quite surprising since it predicts that activators and repressors should control seldom-needed and often-needed genes respectively and contradicts a rule for selection of mode of regulation based on mutational robustness that has been proposed previously [2]. As a follow-up, we compared positive and negative feedback modes when fluctuations of gene expression only adversely affect growth. In this case, we found that modes of regulation coupled with cell growth in a negative feedback loop have greater probability of fixation. This result agrees with the previously proposed rules of Savageau [2] for selection of mode of regulation and predicts that activators and repressors should control often-needed and seldom-needed genes respectively.

The two scenarios regarding the effect of gene expression fluctuations on cell growth described above refer to situations where gene expression is optimized for growth and where gene expression is not optimally controlled respectively. The first scenario is relevant for the regulation of many essential metabolic enzymes and in this case activators and repressors indeed control often-needed and seldom-needed genes respectively. However we also found several stress-response related, seldom-needed, genes that are sub-optimally regulated (expressed even in the absence of stress) and controlled by activators. These examples are significant because they contradict the mode of regulation rule based on mutational robustness but can be explained by evolutionary selection based on these growth feedback effects as described here.

Conclusions

We have shown that evolutionary selection between functionally equivalent modes of regulation can be explained when the coupling between gene expression and cell growth is taken into account. Strikingly, activators and repressors differ in their feedback coupling with cell growth. We have found that this feedback can affect the heritability of fluctuations in cell growth and thereby influence the selection of the mode of regulation. These results illustrate the importance of evaluating design principles for gene regulatory networks in a population dynamics framework rather than basing them entirely upon principles of functional optimization.

[1] Shinar G, Dekel E, Tlusty T, Alon U. Rules for biological regulation based on error minimization. Proc Natl Acad Sci USA. 2006;103(11):3999-4004.

[2] Savageau M A. Design of molecular control mechanisms and the demand for gene expression. Proc Natl Acad Sci USA. 1977;74(12):5647-5651.

[3] Dekel E, Alon U. Optimality and evolutionary tuning of the expression level of a protein. Nature. 2005;436:588-592.

[4] Hamilton, M. Population Genetics. 2009.

[5] Klumpp S, Zhang Z, Hwa T. Growth Rate-Dependent Global Effects on Gene Expression in Bacteria. Cell. 2009;139(7):1366-1375.


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