Constitutive versus Responsive Gene Expression Strategies for Growth in Changing Environments

Microbes respond to changing environments by adjusting gene expression levels to the demand for the corresponding proteins. Adjusting protein levels is slow, consequently cells may reach the optimal protein level only by a time when the demand changed again. It is therefore not a priori clear whether expression “on demand” is always the optimal strategy. Indeed, many genes are constitutively expressed at intermediate levels, which represents a permanent cost but provides an immediate benefit when the protein is needed. Which are the conditions that select for a responsive or a constitutive expression strategy, what determines the optimal constitutive expression level in a changing environment, and how is the fitness of the two strategies affected by gene expression noise? Based on an established model of the lac- and gal-operon expression dynamics, we study the fitness of a constitutive and a responsive expression strategy in time-varying environments. We find that the optimal constitutive expression level differs from the average demand for the gene product and from the average optimal expression level; depending on the shape of the growth rate function, the optimal expression level either provides intermediate fitness in all environments, or maximizes fitness in only one of them. We find that constitutive expression can provide higher fitness than responsive expression even when regulatory machinery comes at no cost, and we determine the minimal response rate necessary for “expression on demand” to confer a benefit. Environmental and inter-cellular noise favor the responsive strategy while reducing fitness of the constitutive one. Our results show the interplay between the demand-frequency for a gene product, the genetic response rate, and the fitness, and address important questions on the evolution of gene regulation. Some of our predictions agree with recent yeast high throughput data, for others we propose the experiments that are needed to verify them

Optimal resting-growth strategies of microbial populations in fluctuating environments

Bacteria spend most of their lifetime in non-growing states which allow them to survive extended periods of stress and starvation. When environments improve, they must quickly resume growth to maximize their share of limited nutrients. Cells with higher stress resistance often survive longer stress durations at the cost of needing more time to resume growth, a strong disadvantage in competitive environments. Here we analyze the basis of optimal strategies that microorganisms can use to cope with this tradeoff. We explicitly show that the prototypical inverse relation between stress resistance and growth rate can explain much of the different types of behavior observed in stressed microbial populations. Using analytical mathematical methods, we determine the environmental parameters that decide whether cells should remain vegetative upon stress exposure, downregulate their metabolism to an intermediate optimum level, or become dormant. We find that cell-cell variability, or intercellular noise, is consistently beneficial in the presence of extreme environmental fluctuations, and that it provides an efficient population-level mechanism for adaption in a deteriorating environment. Our results reveal key novel aspects of responsive phenotype switching and its role as an adaptive strategy in changing environments

Physical limits on cooperative protein-DNA binding and the kinetics of combinatorial transcription regulation

Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative characteristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. We consider a simple theoretical model for two interacting transcription factor (TF) species, searching for and binding to two adjacent target sites hidden in the genomic background. We study the kinetic competition of a dimer search pathway and a monomer search pathway, as well as the steady-state regulation function mediated by the two TFs over a broad range of TF-TF interaction strengths. Using a transcriptional AND-logic as exemplary functional context, we identify the functionally desirable regime for the interaction. We find that both weak and very strong TF-TF interactions are favorable, albeit with different characteristics. However, there is also an unfavorable regime of intermediate interactions where the genetic response is prohibitively slow.Comment: manuscript and supplementary material combined into a single document; to be published in Biophysical Journa

Optimal Resting-Growth Strategies of Microbial Populations in Fluctuating Environments

Bacteria spend most of their lifetime in non-growing states which allow them to survive extended periods of stress and starvation. When environments improve, they must quickly resume growth to maximize their share of limited nutrients. Cells with higher stress resistance often survive longer stress durations at the cost of needing more time to resume growth, a strong disadvantage in competitive environments. Here we analyze the basis of optimal strategies that microorganisms can use to cope with this tradeoff. We explicitly show that the prototypical inverse relation between stress resistance and growth rate can explain much of the different types of behavior observed in stressed microbial populations. Using analytical mathematical methods, we determine the environmental parameters that decide whether cells should remain vegetative upon stress exposure, downregulate their metabolism to an intermediate optimum level, or become dormant. We find that cell-cell variability, or intercellular noise, is consistently beneficial in the presence of extreme environmental fluctuations, and that it provides an efficient population-level mechanism for adaption in a deteriorating environment. Our results reveal key novel aspects of responsive phenotype switching and its role as an adaptive strategy in changing environments

Amplitude-response and phase shift of the model compared to the Yeast YPH499 <i>gal-</i>operon.

<p>We define the phase shift in our model as twice the time required to reach the half-maximum expression level of (). The model according to Eq. 1 and Eq. 2 mimics the galactose utilization network response over a broad frequency range (data points as measured in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0027033#pone.0027033-Bennett1" target="_blank">[34]</a>). The deviation of the experimental phase shift from the predicted phase shift at high frequencies indicates that the response does not exactly follow an exponential relaxation. Indeed, the feedback architecture of the <i>gal-</i>network may give rise to short delays which become noticeable at high cycle frequencies (phase shifts ), which we do not take into account in our model.</p

Benefit and cost of state heterogeneity.

<p>Benefits and costs are measured by the ratio of heterogeneous and homogeneous population growth rates over one cycle, for a responsive population in (A) and for a constitutive population in (B). For the responsive strategy the benefit of heterogeneity increases with the maladaptation cost and with the variability. The fitness of a constitutive population (B) which is well adapted to environmental cycles where prevails () is reduced by variability. Only when the population is significantly maladapted heterogeneity provides a benefit. Note that benefit values in (B) are clipped at </p

Growth dynamics in random environments.

<p>(A) Adaptation dynamics in a random environment (top) and the corresponding momentary growth rate (bottom). During short sporadic environmental changes the phenotype remains close to the previously fit state, and thereby remains adapted for the succeeding environment. As a consequence of the finite adaptation time the population low-pass filters environmental changes and on average spends less time in maladapted states compared to a periodic environment. The time-averaged growth rate in a fluctuating environment significantly exceeds the time-averaged growth rate in a periodic environment. Their ratio defines the benefit in (B). This effect becomes most relevant when the environment on average spends equal amounts of time in both states, and when the response rate is comparable to the rate of environmental change.</p

Fitness of a responsive population (A) and strategy phase diagram (B).

<p>(A) The responsive population has negative growth when its response rate is too small; the growth-threshold is indicated by the white line. The net maladaptation cost is largest at (when both environments have equal durations) because in this regime the population spends most of the time transiting between adapted states rather than being adapted. (B) shows the regimes of optimal strategy (constitutive or responsive) as a function of the demand for expression (environment ) and response rate .The regime in which a responsive strategy with rate confers higher fitness than a constitutive strategy is indicated in white, and for a stochastic environment in light gray and white. When environments are asymmetric a slow responsive population lags behind the environment and cannot reach an adapted state in any of the two conditions. Therefore it has lower fitness than the constitutive strategy which provides immediate although intermediate growth in both environments. The phase boundaries are independent of the maladaptation cost .</p

Population dynamics with heterogeneous response rates (A) and benefit compared to a homogeneous population (B).

<p>(A) shows the state density as a function of time. During the adaptation phase a population with heterogeneous response rates shows transient heterogeneity in the states . This results in a twofold benefit; i) fast responding subpopulations rapidly adapt and drive the growth of the whole population, whereas ii) for environments of short duration (small ) slowly adapting subpopulations remain close to the state that will be fit when occurs next time. This causes a slight asymmetry of the benefit diagram (B) at large response rates and small vs. large . The benefit of heterogeneity, defined as the ratio of heterogeneous and homogeneous population growth rates, is highest when the response rate is comparable to the environmental rate of change.</p