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# Tunability and Noise Dependence in Differentiation Dynamics

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Science  23 Mar 2007:
Vol. 315, Issue 5819, pp. 1716-1719
DOI: 10.1126/science.1137455

## Abstract

The dynamic process of differentiation depends on the architecture, quantitative parameters, and noise of underlying genetic circuits. However, it remains unclear how these elements combine to control cellular behavior. We analyzed the probabilistic and transient differentiation of Bacillus subtilis cells into the state of competence. A few key parameters independently tuned the frequency of initiation and the duration of competence episodes and allowed the circuit to access different dynamic regimes, including oscillation. Altering circuit architecture showed that the duration of competence events can be made more precise. We used an experimental method to reduce global cellular noise and showed that noise levels are correlated with frequency of differentiation events. Together, the data reveal a noise-dependent circuit that is remarkably resilient and tunable in terms of its dynamic behavior.

Three aspects of genetic circuits control dynamic cellular behaviors: the circuit architecture or pattern of regulatory interactions among genetic elements; quantitative parameter values, such as promoter strengths; and stochastic fluctuations, or “noise,” associated with the concentration of cellular components. A fundamental biological question is how these three aspects of genetic circuits combine to determine cellular behavior, its variability, and its potential to evolve (1).

Competence in B. subtilis is a stress response that allows cells to take up DNA from the environment (2, 3). Differentiation into competence is transient (Fig. 1A) (4). The genetic basis for this behavior is a circuit involving comK and comS (Fig. 1B). The transcription factor ComK is necessary and sufficient for differentiation into competence (5, 6). ComK positively autoregulates its own expression but is degraded by the ClpP-ClpC-MecA protease complex (Fig. 1B) (79). ComS competitively inhibits this degradation and is repressed in competent cells, forming a negative feedback loop (4, 10, 11). The circuit operates as an excitable system in which a relatively small perturbation induces a larger and stereotyped response, as occurs with action potentials in neurons, for example (4, 12). Competence events occur only in a fraction of cells and may be driven by noise in underlying circuit components (4, 7, 8, 13).

Two key characteristics of competence are its probability of initiation, Pinit, and the mean duration of transient competence events, τcomp (Fig. 1A). Pinit denotes the chance per cell division that an individual cell will become competent. Competence events can be quantified by automated time-lapse fluorescence microscopy using fluorescent reporter genes under the control of the ComK-specific comG promoter and the comS promoter (denoted PcomG and PcomS, respectively) (4).

Two parameters that are expected to affect the behavior of the circuit are the basal expression rates of comK and comS, denoted by αK and αS, respectively (Fig. 1B and Eq. S1). To manipulate these parameters, we chromosomally integrated an additional copy of either comS or comK under the control of an inducible promoter, denoted Phyp, generating the Hyper-αS and Hyper-αK strains, respectively [see Supporting Online Material (SOM) text]. To systematically scan a range of values for αK and αS, we made time-lapse fluorescence movies of these strains on media containing different concentrations of the inducer isopropyl-β-d-thiogalactopyranoside (IPTG) (Fig. 2, A and B).

We investigated how αK and αS combine to regulate Pinit. Without IPTG, Pinit was ∼3% in the Hyper-αK strain, unchanged from its wild-type value. Pinit increased rapidly with basal comK expression (Fig. 2C). Increased expression of comK in the Hyper-αK strain also showed a transition to an oscillatory regime, in which cells repeatedly went in and out of the competent state (Fig. 2A). At αK ∼20 times its wild-type value, α wtK, all cells entered competence (Fig. 2, A and C). ComS, like ComK, is necessary for competence. However, expression of Phyp-comS had a modest effect on initiation, increasing Pinit to ∼20% (Fig. 2C). Thus, Pinit was predominantly regulated by αK rather than αS.

We next considered the effects of the same perturbations on τcomp. Increasing αK up to ∼4.5 × α wtK caused no increase in τcomp (Fig. 2D). On the other hand, in the Hyper-αS strain, τcomp increased with increasing expression of Phyp-comS (Fig. 2D). Thus, τcomp was predominantly regulated by αS rather than αK. Together, these results show that Pinit and τcomp can be tuned independently by αK and αS, respectively (Fig. 2E).

To better understand the effect of comS expression on τcomp, we constructed a “6×S” strain in which PcomS-comS was expressed from a low–copy number plasmid, effectively increasing the activated production rate, βS, by a factor of 6 over its wild-type value, β wtS. Unlike Phyp-comS, this construct retains the regulation found in the wild-type PcomS promoter, including its negligible basal expression rate, α wtS. Despite this increase in βS, excitable behavior was maintained, as 53 ± 5% (n = 79/151) of competent cells successfully exited the competent state, compared with 61% ± 7% (n = 83/136) of wild-type cells. By contrast, increasing αS to ∼3 × β wtS in the Hyper-αS strain prevented the majority of competent cells from exiting [21.3 ± 5% (n = 26/122) of competent cells exited (table S4)]. The repressibility of the natural PcomS promoter is thus critical for maintaining excitability (4). These results show that excitability can be reliably maintained over a broad range of βS values.

To better understand independent tuning of Pinit and τcomp, as well as reliable maintenance of excitability, we developed a model of the core interactions in the competence regulation circuitry (Fig. 1B and SOM text). We used stochastic simulations to account for intrinsic noise of biochemical reactions (14). We also analyzed the corresponding continuous model to determine parameter dependence and to identify a biologically reasonable parameter regime in which the discrete model produced results consistent with experiments. We required the continuous model to remain in the excitable regime as the βS value was varied by a factor of 6 and we required its stochastic counterpart to generate the observed independent tunability of Pinit and τcomp. We identified a parameter set that accounts for both maintenance of excitability at high βS and independent tunability by αS and αK. Analysis of the model is described in detail in the SOM text (15).

Within the model, increasing αK increased the probability that vegetative cells reach the minimum concentration of ComK necessary to initiate competence, explaining the strong effect of αK on Pinit (Fig. S5). Increasing αS, on the other hand, did not raise Pinit arbitrarily high because initiation of competence is limited by fluctuations in ComK expression (Fig. 2E and fig. S6).

In the model, we also analyzed τcomp. Exit from competence requires ComS to be degraded. When the basal production rate of ComK is less than its activated production rate (αK < βK), ComS degradation, and thus τcomp, is unaffected. On the other hand, as αS is increased from zero, production of ComS offsets its degradation, prolonging competence duration.

Consistent with experimental results, in the model increasing αK switches the system from excitable to oscillatory dynamics, further distinguishing αK from αS (fig. S3). Increasing αS takes the system directly from excitability to a bistable regime in which Pinit < 1, but, once initiated, most cells remain trapped in the competent state. This behavior was also observed in experiments where no oscillatory behavior was seen at intermediate αS values (Fig. 2B).

As in the experiments, cells in the model can become stuck in competence. When the basal production rate of ComK exceeds its activated production rate (αK > βK), ComK levels cannot be reduced in competence, and cells become trapped in the competent state. A similar effect occurs at high αS values, because a new stable state arises at competence-maintaining concentrations of ComK (Fig. S7). However, in this case, exit of competence remained possible as a result of noise, which destabilizes the newly formed competent state (see Section S1.4 of SOM text). This is consistent with experimental observations showing that, even at the highest induction levels in the Hyper-αS strain, ∼20% of cells successfully exited competence.

To explore the effects of perturbing the circuit architecture, we reengineered the competence circuit using Rok, a protein that binds to PcomK and represses its expression (16). We inserted a copy of rok under the control of PcomG, creating an additional negative feedback loop onto comK (Fig. 3A). In this “CompRok” strain, as expected, Pinit remained unchanged from its wild-type values (∼3%). The mean value of τcomp, on the other hand, was reduced, as was its cell-cell variability. In CompRok, τcomp = 13.9 ± 3.4 hours (mean ± SD, n = 30), compared with τcomp = 20.2 ± 9.9 hours (mean ± SD, n = 31) in wild type (Fig. 3B). This reduction in cell-cell variability showed that the precision of τcomp can be improved over its wild-type value. In the model (Fig. 3B, insets), this result can be explained as follows: Exit from competence occurs when the absolute number of ComS molecules is very low and the relative size of stochastic fluctuations therefore increases. These effects increase the variability in τcomp. In the CompRok strain, however, the additional negative feedback allows exit from competence to occur at higher ComS and Rok concentrations, reducing the sensitivity of τcomp to stochastic fluctuations (fig. S10).

It is not known whether competence initiation is controlled by noise, as in the model. To test the impact of noise on competence initiation, we set out to globally modulate the amount of noise in the cell. We used a B. subtilis strain in which the ftsW gene, which is necessary for septation, was replaced by an inducible copy. In the absence of inducer, septation was inhibited, resulting in elongated filamentous cells. Each filament was composed of multiple cell units, all sharing cytoplasm. Within a filament, diffusion is expected to effectively average cell contents, reducing noise in gene expression, without affecting mean concentrations of cellular components (Fig. 4A) (17). In some bacterial mutants that have elongated filamentous morphologies, cellular growth, nucleoid density, protein expression, and other physiological characteristics appear normal, even though cellular volume is greatly increased (fig. S12) (1820). We integrated an inducible Phyp-yfp construct and measured the effect of cell length on cell-cell fluctuations in yellow fluorescent protein (YFP) expression (Fig. 4B). We found that noise does indeed decrease with increasing length (Fig. 4B, inset). A simple model of transcription and translation (2124) that incorporates the continuity of filamentous cell growth produced qualitatively similar results (Fig. 4B, inset, and SOM text). Thus, cell size can in this case be used to modulate gene expression noise.

How does noise affect the probability of initiation of competence? To answer this question, we induced filamentation in the conditional ftsW strain at the beginning of, or before, movie acquisition and quantified Pinit as a function of cell length. We determined length distributions of cells at the moment they initiated competence, as detected by PcomG expression (Fig. 4C). As a comparison, we also measured length distributions for noncompetent cells at a similar distribution of times. We plotted the relative fraction of cells that initiated competence at a given length, compared with the total number of cells at that length. The results showed that Pinit decreased as cells elongated (Fig. 4D and SOM text). A similar decrease in Pinit was observed in corresponding simulations (Fig. 4D). To test if the reduction in Pinit could be due to factors other than diminished noise, we examined two promoters, PcomS and Pspo0A, both strongly regulated under these conditions. Spo0A is a master regulator of sporulation, a competing starvation response, and high concentrations of Spo0A inhibit competence (3). Conversely, PcomS expression is necessary for competence. Mean expression of both PcomS and Pspo0A was unaffected by cell length (fig. S17). This supports the idea that gene expression levels are independent of cell length under these conditions and that Pinit depends on noise.

Noise may play at least three different functional roles in competence. First, noise could be responsible for the observed variability in duration. Second, noise may be necessary to maintain excitability over a wide parameter range, by inducing escape from states of high ComK concentration. Third, noise appears to have a pivotal role in competence initiation (Fig. 4D) and thus should be considered alongside genetic parameters and circuit architecture to comprehensively understand differentiation at the single-cell level.

Quantitative analysis of a genetic system beyond its normal operating regime, including gene expression strengths, circuit architecture, and noise levels, strongly constrains dynamical models. The competence regulation system maintains excitable behavior over a broad range of parameter values. Experimentally, αK and αS enable Pinit and τcomp to be tuned independently, allowing the system, in theory, to adapt to independent selective pressures during evolution. The circuit can also access different dynamic regimes, such as oscillation and bistability, indicating its potential to evolve alternative qualitative behaviors.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S17

Tables S1 to S4

References

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