A Stochastic Single-Molecule Event Triggers Phenotype Switching of a Bacterial Cell

Genetically identical cells in the same environment can exhibit different phenotypes, and a single cell can switch between distinct phenotypes in a stochastic manner (1–4). In the classic example of lactose metabolism in Escherichia coli, the lac genes are fully expressed for every cell in a population under high extracellular concentrations of inducers, such as the lactose analog methyl-β-d-thiogalactoside (TMG). However, at moderate inducer concentrations, the lac genes are highly expressed in only a fraction of a population, which may confer a fitness advantage for the entire population (5). We studied the molecular mechanism that controls the stochastic phenotype switching of a single cell.

Lactose metabolism is controlled by the lac operon (6, 7), which consists of the lacZ, lacY, and lacA genes encoding β-galactosidase, lactose permease, and transacetylase, respectively. Expression of the operon is regulated by a transcription factor, the lac repressor (8), which dissociates from its specific binding sequences of DNA, the lac operators, in the presence of an inducer to allow transcription (Fig. 1A). The production of the permease increases inducer influx (9), which results in positive feedback on the permease expression level. Above a certain threshold of permease numbers, a cell will remain in a phenotype that is capable of lactose metabolism, and below this threshold, a cell will remain in a phenotype that is incapable of lactose metabolism (10, 11). The former has high fluorescence from the cell membrane when the permease is labeled with a yellow fluorescent protein (YFP), whereas the latter has low fluorescence. The image in Fig. 1B shows the coexistence of both phenotypes in a cell population at intermediate inducer concentrations, characterized by the bimodal distributions of fluorescence intensity in Fig. 1C.

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Although it is known that the bistability in the lac operon arises from positive feedback (12, 13), the molecular mechanism underlying the initiation of switching between two phenotypes remains unclear. Novick and Weiner deduced that switching from the uninduced state to the induced state occurs through a single rate-limiting molecular process (12) rather than a multistep process. They further hypothesized that the random expression of one molecule of permease was enough to trigger induction. However, this has never been observed experimentally because of insufficient sensitivity.

Our group has previously shown that a single fluorescent protein molecule can be visualized in a living bacterial cell by using the method of detection by localization (14–16). Because a permease molecule is a membrane protein with slow diffusion, its fluorescence label is highly localized as compared with a fluorescent protein in the cytoplasm, which allows for its detection above the background of cellular autofluorescence. Thus, we generated strain SX700, which possesses intact lac promoter elements and expresses a functional LacY-YFP fusion protein (fig. S1) from lacY's native chromosomal position (fig. S2). Figure 1B shows a fluorescence image of SX700 cells that allows us to directly count the number of single LacY-YFP molecules present in a cell.

Figure 1D shows the histogram of permease copy numbers in the uninduced fraction of cells, free from the complication of autofluorescence background in the lower peak of Fig. 1C. Evidently, the uninduced cells have 0 to 10 LacY molecules with significant probability, independent of the inducer concentration. Had one permease been enough to trigger induction, all cells in the uninduced subpopulation would have contained zero LacY molecules. Thus, we conclude that a single copy of LacY is not sufficient to induce switching of the phenotype, and the threshold for induction must be much higher than several molecules per cell.

We then set out to determine the threshold of permease molecules for induction. It is experimentally difficult to capture the rare events of phenotype switching in real time. To overcome this difficulty, we prepared cells covering a broad range of permease copy numbers by first fully inducing the cells and subsequently washing out the inducer. We then allowed the cells to divide for one to six generations, during which the initial permeases were partitioned into daughter cells (17). Figure 2A shows fluorescence time traces of the cells, normalized by cell size, upon the reintroduction of 40 μM TMG. Although the fluorescence in cells with low permease numbers continued to decay because of cell division and photobleaching, cells with more than 300 initial permease molecules induced again within 3 hours and showed increased fluorescence. Figure 2B shows the probability of induction as a function of initial permease number, which is well fit by a Hill equation with a Hill coefficient of 4.5 and a threshold of ∼375 molecules. The large value of the threshold indicates that hundreds of permease molecules are necessary to switch the phenotype.

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If the induction is due to a single rate-limiting event as Novick and Weiner argued, there must be a single large burst of permease expression to reach this high threshold. However, only small bursts have been observed in previous studies of the repressed lac promoter (14, 18). Large bursts, if any, would be infrequent and insufficiently sampled in the previous work. To explain why both small and large bursts may occur from the lac promoter, we considered the tetrameric repressor that is doubly bound to two operators, forming a DNA loop (19, 20). We hypothesized that more frequent partial dissociations of the tetrameric repressor from one operator lead to single transcripts and small bursts of protein expression, whereas rare complete dissociations from all operators lead to multiple transcripts and large bursts of expression. In this model, the complete dissociation of the tetrameric repressor would be the molecular event that causes a change in phenotype.

To test this model experimentally, we first removed the auxiliary operators from SX700 to generate SX702 (fig. S2), which cannot form DNA loops. As a result, every dissociation event of LacI from the remaining O1 operator results in a complete dissociation event that would generate a large burst of expression. In this case, we predicted frequent and large bursts of expression with a faster rate of phenotype switching. Indeed, Fig. 2C shows that without DNA looping, SX702 induces rapidly upon the addition of inducer, even though the initial permease numbers are much smaller than the threshold in Fig. 2, A and B [see supporting online material (SOM) text]. The removal of DNA looping eliminated bistability. This was manifested by the unimodal distributions of an inducing population in Fig. 2D at 20 μMTMG.

To directly observe large bursts, we replaced the lacY gene of the E. coli chromosome with a membrane-localized protein, Tsr, fused to YFP, which generated strain SX701 (fig. S2). Eliminating LacY's positive feedback served two purposes: to allow the resolution of distinct large bursts and to prove that large bursts do not require permease activity. The Tsr-YFP fusion functioned as a surrogate reporter for protein production with single-molecule sensitivity.

When we acquired time-lapse fluorescence microscopy movies of SX701 cells with 200 μM TMG, we observed that Tsr-YFP was produced mostly in small bursts, but occasionally in a large burst (Fig. 3A). The distribution of burst sizes (Fig. 3B) taken from these real-time traces shows both the frequent exponentially distributed small bursts and the rare unusually large bursts.

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We next analyzed the inducer concentration dependence of burst frequency and size by using population distributions. Figure 3C shows that SX701 has a protein copy number distribution in a cell population very similar to the distributions of uninduced cells in Fig. 1D within the range of 0 to 10 molecules. We have shown that these copy-number distributions manifest the stochasticity in gene expression characterized by two parameters, transcription rate (a) and the burst size of proteins per mRNA (b), and can be well fit with a gamma distribution p(n) = b^–an^a–1e^–n/b/Γ(a) (18, 21). The inset in Fig. 3C shows a and b determined in this fashion for cells with fewer than 10 molecules for different TMG concentrations. The small burst size is independent of the inducer concentration, whereas the small burst frequency has only a weak concentration dependence. In fact, within the range of 0 to 50 μM TMG, the small burst frequency does not change appreciably, suggesting that the partial repressor dissociation is predominantly spontaneous at low inducer concentrations.

Because characterization of the rare, large bursts is difficult for the wild-type operators, we generated strain SX703, in which the permease gene was replaced with Tsr-YFP and the O2 and O3 operators were removed to eliminate DNA looping. Every dissociation event in the SX703 should be a complete dissociation, and hence should lead to a large burst. Because there is a 20- to 100-fold difference in the inducer-binding affinity to the repressor in DNA-bound form (∼1 mM) relative to the free form (∼10 μM) (22, 23), we expected to observe the stochastic dissociation of the repressor from the sole operator site and sequestration of the free repressor by the inducers at the concentrations we used (0 to 50 μM) rather than inducer-driven dissociation events.

Consequently, we expected the frequency of dissociation to remain constant as the inducer concentration increased but expected the length of the dissociation time to increase. When we analyzed the steady-state protein distributions at different inducer concentrations (Fig. 4C) by applying a generalized interpretation of the a-b model, which estimates the number of proteins per expression bursts (SOM text), we found that inducer concentration affects the size of large bursts but not the frequency. This observation supports our model that the inducer sequesters the repressor after it stochastically dissociates from the operator and prolongs its lifetime in the non–DNA-bound state, leading to larger burst sizes (SOM Text).

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Figure 4 summarizes the model of induction in the lac operon. In the case of high inducer concentration (Fig. 4A), the repressor is actively pulled off both operator sites by the inducer, as described in Monod and Jacob's model (6). Under low or intermediate TMG concentrations, however, the repressor can stochastically dissociate from one operator independently of the inducer, as shown in Fig. 4B. When the repressor partially dissociates from one operator, a small protein burst from a single copy of mRNA is generated (14) before the repressor rapidly rebinds to the vacant operator. When the repressor completely dissociates from both operators, multiple mRNAs are transcribed, which leads to a large protein burst that surpasses the LacY threshold, initiates positive feedback, and maintains a switch in phenotype.

Why do complete dissociation events give rise to large bursts? Our group has recently shown that if a repressor dissociates from DNA, it takes a time scale of minutes for the repressor to rebind to the operator because the repressor spends most of its time binding to nonspecific sequences and searching through the chromosomal DNA (15). In addition, there are only a few copies of the tetrameric repressors (8). Such a slow repressor rebinding time, relative to transcript-initiation frequencies (24), would allow multiple copies of lacY mRNA to be made following a complete repressor dissociation event. Furthermore, in the presence of inducer, the nonspecific binding constant remains unchanged (25), but the affinity of the inducer-bound repressor to the operator is substantially reduced, rendering specific rebinding unlikely. The large burst that results from slow repressor rebinding is an example of how a single-molecule fluctuation under out-of-equilibrium conditions can have considerable biological consequences, which has been discussed theoretically in the context of cell signaling (26) and gene expression (27) but has not previously been experimentally observed.

Because the binding affinity of inducers for operator-bound repressors is weaker than for free repressors by a factor of 20 to 100 (22, 23), the inducer's role under low concentrations is not to force a dissociation event but to simply sequester repressors that stochastically dissociated from their operators in order to aid in creating a large burst (SOM text) (Fig. 3D). When the inducer concentration increases, the size of the large bursts increases because the duration of complete dissociations increases, improving the probability that a large burst can cross the positive-feedback threshold. Consequently, it is this higher probability of successful switch-on events that shifts the bimodal population toward the fully induced state as inducer concentration increases.

The biological importance of DNA looping has been discussed in the literature in terms of facilitating interactions between distance sequences and enhancing the local concentration (19, 20). Here, we show that DNA looping allows the control of gene regulation on multiple time scales through different kinds of dissociation events. The presence of DNA looping allows the use of rare complete dissociation events to control a bistable genetic switch.

We have shown that a stochastic single-molecule event can cause a change in phenotype. It is not difficult to imagine that similar molecular events might determine more complicated phenotypes of other cells or organisms. The ability to observe and probe the properties of genetic switches at the molecular level is crucial for understanding how cells make decisions.