(593b) Coupling of Gene Expression and Growth Rate Determines Selection of Transcriptional Regulation Mechanisms

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.