High-Resolution Imaging of Two DNA Sites

We inserted the construct shown in Figure 1a into the E. coli chromosome. It contains three tandem tetO sites (tetO³) [54] and three tandem lacO^sym sites (lacO³) [55] flanking the wild-type λ lysogen sequence from O_R to O_L (including the P_R, P_RM and P_L promoters and the cI, rexA (accession number P68924) and rexB (accession number P03759) genes). In this construct, called λWT, CI is expressed from P_RM and regulates its own expression. The lacO-binding and tetO-binding proteins LacI and TetR (accession number P04483) were fused with red and yellow fluorescent proteins to generate LacI-mCherry and TetR-EYFP, and were expressed from an inducible plasmid (Figure 1b).

With the combination of strong induction, weak ribosome binding sites, and carefully controlled growth, we achieved sufficiently low LacI-mCherry and TetR-EYFP expression levels to detect distinct, diffraction-limited mCherry and EYFP spots in single cells. We then fit the fluorescence intensity profile of each individual spot with a two-dimensional Gaussian function to estimate its centroid position. The average localization precisions for individual spots of LacI-mCherry and TetR-EYFP were 17 and 14 nm, respectively (Figure S1a). Subsequently, we transformed EYFP coordinates into mCherry coordinates using fiducial data to calculate the vector between the mCherry and EYFP spots arising from LacI-mCherry and TetR-EYFP protein molecules bound to the same O_R–O_L DNA segment. We called this vector (Figure 1c). The magnitude of the vector, , is the two-dimensional projection of the distance between lacO³ and tetO³ onto the image plane; on average, it is proportional to the end-to-end distance between lacO³ and tetO³ in three dimensions. The total error for an measurement, including fitting errors in determining centroid of individual spots (Figure S1a), registration errors in aligning EYFP and mCherry two-color images (∼10 nm based upon experiments using fluorescent beads), and contributions from local fluorescent background, was on average ∼40 nm (see below). With very low TetR-EYFP and LacI-mCherry expression, it was inevitable that not all lacO³ and tetO³ sites were bound by fusion protein molecules. Furthermore, not all fusion protein molecules were fluorescent due to stochastic chromophore maturation. Figure 2a contains typical data showing that a subset of cells was successfully labeled at both sites. We analyzed all cells having distinct fluorescent spots in both emission channels to calculate . We expected to decrease when DNA between lacO³ and tetO³ looped.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 2. High-resolution imaging of lacO³ and tetO³ sites separated by 66 bp (λnull) or 2.3 kb (λΔO_L).

(a) Fluorescent images of λnull. Arrows highlight molecules that exclusively appeared in mCherry (magenta, top) and EYFP (green, middle) channels, indicating a lack of significant crosstalk between the two channels. Squares show a spot that appeared in both channels. In the overlay image (bottom), fluorescence images were bandpass filtered and background was subtracted. Only cells having both mCherry and EYFP fluorescence were used in analysis. Scale bar, 2 µm. The image order and color scheme are repeated in (b–e). (b) Fluorescent images of λΔO_L. Scale bar, 1 µm. (c–e) Timelapse images of spots acquired every 100 ms; (c) and (d) are spots in white squares in (a) and (b), respectively, and (e) shows an additional λΔO_L spot, whose apparent separation can be easily detected by eye. Top and middle rows show mCherry and EYFP channels, respectively, and bottom rows show two-color overlays on brightfield images. (f–h) Trajectory vectors from fitting fluorescence data for spots in (c–e). Coordinates are in nm. Vertices indicate the vector and subsequent time points are connected by lines that are colored to indicate elapsed time.

https://doi.org/10.1371/journal.pbio.1001591.g002

Distinguishing Between Looped and Unlooped States

To determine whether our two-color imaging method was sufficient to distinguish between looped and unlooped DNA in the crowded intracellular environment, we constructed two control strains (Table 1). In the positive control λnull, the centers of lacO³ and tetO³ sites are separated by 66 bp (Figure 1d). The outmost lacO^sym and tetO sites are separated by less than 40 nm (Figure S2a). The close proximity of lacO³ and tetO³ mimicked permanently looped DNA. In the negative control λΔO_L, we inserted the λ sequence from O_R up to but not including O_L between lacO³ and tetO³ (Figure 1e). The resulting λΔO_L DNA has comparable length as the wild-type λ DNA, but CI-mediated DNA looping between O_R and O_L is abolished.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Descriptions of strains and plasmids used in this study.

https://doi.org/10.1371/journal.pbio.1001591.t001

We first examined λnull and λΔO_L in two-color fluorescence images to determine whether we could discriminate between looped and unlooped DNA by eye. We obtained at least sixty 20-frame movies (100 ms exposures; 2 s total) for each strain in each of three independent experiments. Typical fluorescence images are shown in Figure 2a and b. Crosstalk between the two emission channels was negligible, as bright mCherry and EYFP spots only appeared in the corresponding channel but not the other.

Figure 2c and d show 1 s of typical data for individual λnull and λΔO_L spots. Representative movies for the two strains and others discussed below are included as Movies S1, S2, S3, S4, S5, S6. As expected for a permanently looped configuration, the positive control λnull exhibited overlapping EYFP and mCherry spots (Figure 2c). Generally, λΔO_L molecules did not exhibit spot separation that was easily identifiable by eye (Figure 2d). However, some λΔO_L molecules displayed large displacements between the LacI-mCherry and TetR-EYFP spots that were distinguishable by eye (Figure 2e); such images were not observed for λnull.

Visual inspection of the apparent separation between the LacI-mCherry and TetR-EYFP spots suggested that comparing the end-to-end separation in O_R–O_L DNAs required a more quantitative approach. We calculated for all O_R–O_L DNA molecules in the λΔO_L and λnull strains that exhibited fluorescent spots in both EYFP and mCherry images. Figure 2f–h shows calculations for movies in Figure 2c–e, respectively, and Figure S3 shows vectors for all movies lasting 0.8 s or longer. We then compiled the corresponding probability density distributions (PDF, , Figure 3a) and cumulative density distributions (CDF, , Figure 3b) of the vector magnitude, . The long-tailed PDF observed for λnull (Figure 3a) is consistent with the expected end-to-end distance distribution measured from two spots with a fixed separation when the localization of each spot is subject to Gaussian fitting error [56]. A simple numerical simulation of the end-to-end distance PDF for two sites separated by 22 nm and each subject to 22-nm localization error largely recapitulates the long-tailed distribution (Figure S2c).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 3. End-to-end distance () distributions and looping frequency fitting.

(a) Probability density distribution (PDF) of the vector magnitude for the looped (λnull, red) and unlooped (λΔO_L, blue) controls. The PDF is estimated for 10-nm bins as described in the main text. Light-colored areas indicate 1 s.e.m. calculated by bootstrapping. (b) Cumulative density (CDF) of for the looped (λnull) and unlooped (λΔO_L) controls. The CDF is estimated for 10-nm bins as described in the main text. Light-colored area indicates 1 s.e.m. calculated by bootstrapping. (c) The PDF is shown for strains λWT (green), λO_R3⁻ (orange), and λO_L3⁻ (purple), calculated as in (a), and PDFs for strains λnull and λΔO_L are shown as dashed lines for comparison. (d) CDF estimates for three strains (dots; λWT, green; λO_R3⁻, orange; λO_L3⁻, purple) were fit as linear combinations of the positive (λnull) and negative (λΔO_L) control CDFs to estimate looping frequency. Colored lines indicate CDF fits and CDFs for strains λnull and λΔO_L are shown as dashed lines for comparison.

https://doi.org/10.1371/journal.pbio.1001591.g003

We found that the distribution for λΔO_L was distinctly different from that of λnull (p<10⁻³); the difference was reproduced in three independent experiments (Figure S1b). The mean separations, , were 47 (N = 1,153) and 71 nm (N = 979) for λnull and λΔO_L respectively (results and measurement errors summarized in Table 2). Peaks in plots centered at ∼40 nm, reflecting our experimental precision in determining ; that is, O_R–O_L molecules with below 40 nm could not be distinguished from each other. Hence, it was more meaningful to compare distributions of at large values where distributions differed most prominently. The cumulative probability of being 75 nm or more was ∼40% for λΔOL and only ∼15% for λnull (Figure 3b). Furthermore, two-dimensional distributions of vectors (Figure S4) were clearly wider for λΔO_L than for λnull. Thus, by examining distributions, we could distinguish between the looped and unlooped control strains, suggesting that this approach could be used to probe CI-mediated DNA looping.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Summary of measurements and sample statistics in this study.

https://doi.org/10.1371/journal.pbio.1001591.t002

Compact Conformation of Unlooped DNA λΔO_L Does Not Depend on Transcription or Nonspecific CI Binding

We measured the mean end-to-end separation for λΔO_L at 71-nm, much shorter than the ∼200-nm distance expected for B-form DNA with a typical 50-nm in vitro persistence length [57]. While such a result is expected given the many factors known to compact prokaryotic chromosomes [58], it is possible that nonspecifically bound CI on the λΔO_L DNA and/or P_RM transcription activity could influence the distribution, as indicated by a series of recent studies in vitro and in higher eukaryotic systems [46],[59],[60].

To examine these possibilities, we first compared the distribution of the λΔO_L strain to that of a control strain λΔO_LP_RM⁻cI⁻/cI^trans (Table 1, Figure S5a and b). In this control strain, promoter P_RM was mutated to abolish transcription and the cI start codon was eliminated, but CI binding to O_R was unaffected (Figure S5c, d, and e). In addition, we expressed CI from a plasmid at ∼9 times its level in λWT (Table S8). We found that the distributions of the λΔO_L and λΔO_LP_RM⁻cI⁻/cI^trans strains were indistinguishable (Figure S5a and b), demonstrating that the compact λΔO_L distribution does not depend on P_RM transcription. Furthermore, distributions for the same λΔO_LP_RM⁻cI⁻ strain with or without the CI-expressing plasmid were indistinguishable (Figure S5a and b), suggesting that nonspecifically bound CI did not interact with specifically bound CI at O_R operator sites to condense DNA in vivo [46].

In Vivo Observations of DNA Looping

We next investigated DNA looping in the context of wild-type and mutant O_R–O_L DNAs. In λWT, the wild-type λ sequence from O_R through O_L was inserted between lacO³ and tetO³. CI could bind all O_R and O_L sites to mediate looping with both octameric and tetrameric CI complexes (Figure 1a). In λO_R3⁻ and λO_L3⁻, mutations in O_R3 and O_L3 essentially eliminated CI binding to these operators at lysogenic CI concentrations (Table 1) [35],[61].

We measured for these three strains and found that distributions differed significantly from those of the positive and negative controls λnull and λΔO_L (p<10⁻³, except p = 0.004 for λWT and λnull), with and being intermediate to those of the controls (Figure 3c and d). Mean values for the three strains also fell in between those of λnull and λΔO_L (Table 2). The wild-type strain had lower than λO_R3⁻ and λO_L3⁻, and its distribution differed from those of the mutant strains with moderate to high significance (p = 0.001 and 0.048 for λO_R3⁻ and λO_L3⁻, respectively); distributions for λO_R3⁻ and λO_L3⁻ were indistinguishable from each other (p = 0.493). The trend of λnull<λWT<λO_R3⁻≈λO_L3⁻<λΔO_L for was reproduced in three independent experiments (Figure S1b). Assuming that a DNA molecule in the λWT, λO_R3⁻, and λO_L3⁻ strains is in either a looped or unlooped state, the intermediate values of the three strains suggested that the fraction of looped DNA molecules (herein termed looping frequency) could be estimated by comparing distributions of these strains to those of the looped and unlooped controls λnull and λΔO_L.

To further investigate whether the observed DNA looping in the λWT, λO_R3⁻, and λO_L3⁻ strains could be abolished by eliminating CI cooperative binding rather than by deleting O_L, we constructed a control strain λCI^G147D (Table 1). This strain differs from λWT by a CI mutation G147D known to be defective in pairwise cooperative interaction [62],[63]. Structural evidence suggests that cooperative binding interfaces are shared for pairwise binding to adjacent operator sites and the formation of CI tetramers or octamers via DNA loops [64]. We found that the distribution of the λCI^G147D strain was indistinguishable from that of λΔO_L (Figure S5f and g, Table S7). We note that this G147D mutant also diminishes P_RM transcription because of its weakened ability to form a CI tetramer at the O_R1 and O_R2 sites; hence its expression level is lower than that with wild-type CI (Table S8). Therefore, we constructed another control strain (λCI^G147D/cI^G147D,trans), in which the CI^G147D mutant protein was expressed constitutively at ∼11 times the CI expression level in λWT from a plasmid transformed into the λCI^G147D strain (Table S8). We found that distribution of this strain was indistinguishable from that of the λΔO_L and the λCI^G147D strains, demonstrating that DNA looping could be abolished by eliminating CI cooperative binding.

Estimating DNA Looping Frequency from

To quantitatively examine how operator mutations influence DNA looping, we estimated looping frequencies for λWT, λO_R3⁻, and λO_L3⁻ by assuming a simple model. In this model, DNA molecule can only exist in one of two states, looped or unlooped, with distributions for each state resembling those of the looped and unlooped controls, λnull and λΔO_L, respectively. Therefore, the distribution or for one of the three strains is the linear combination of that of λnull and λΔO_L, with their distributions weighted by the looping frequency, :Using this model, we found that the looping frequency was 79% for λWT, and reduced to 53% for λO_R3⁻ and 60% for λO_L3⁻ (results with errors summarized in Table 2). The results were indistinguishable within error regardless of whether cumulative or probability density distributions were used, or whether data points from all frames or only the first frame of each molecule's movie were used (Table S1). The looping frequencies for λO_R3⁻ and λO_L3⁻ were indistinguishable from each other within error, suggesting a similar role of O_R3 and O_L3 in loop formation. Reduced looping frequencies of λO_R3⁻ and λO_L3⁻ compared to λWT suggest that while a CI octamer at O_R12 and O_L12 is sufficient to loop DNA, the resulting loop can be further stabilized by an additional CI tetramer only if both O_R3 and O_L3 are intact. To our knowledge, these measurements provide the first quantitative in vivo estimates of DNA looping frequencies that are independent of gene regulation models.

Estimating DNA Looping Kinetics

In the above analyses, we only utilized , the magnitude of the vector, and discarded information about the direction of and its evolution in time. Looping frequencies estimated from distributions are analogous to equilibrium constants and lack kinetic information. While many DNA molecules only exhibited fluorescent spots in both EYFP and mCherry channels for one or two consecutive frames due to photobleaching, some molecules had fluorescent spots lasting for several consecutive frames in both channels (Figure 2c–h; also see plots from molecules with many frames in Figure S3). By analyzing how evolves in time, we can obtain additional information about DNA looping kinetics.

We calculated the autocorrelation of (the average dot product of two vectors separated by a time lag) up to 0.5 s for each strain using all movies in which fluorescent spots in both channels lasted two or more frames (Figure 4a). The autocorrelation curves of all strains showed an initial drop of ∼2,500 nm² at the first time lag, corresponding to uncorrelated errors in determining . After the initial drops, all autocorrelation curves showed positive correlation values that were approximately constant at time lags up to 0.5 s.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 4. DNA looping kinetics and CI expression levels.

(a) Vector dot-product autocorrelation for time trajectories for each strain. Plots show the average dot product of two vectors separated by a given time lag. Error bars show 1 s.e.m. calculated by bootstrapping. (b) Typical smFISH images for λnull, which has no P_RM transcripts, and for all other strains. Top, brightfield images showing a group of fixed cells for each strain. Bottom, maximum-intensity projections of fluorescence image stacks. Spots indicate one or more transcripts. (c) Distribution of P_RM transcripts per cell determined by smFISH. The average expression level in wild-type λ units (WLU) is defined as the mean number of transcripts per cell in a given strain divided by the mean transcript number in λWT cells.

https://doi.org/10.1371/journal.pbio.1001591.g004

The observation of near constant autocorrelation values after the first time lag for all the strains indicated that the conformation of each DNA molecule, characterized by both the magnitude and orientation of , persisted for at least 0.5 s. This provides a lower limit for the amount of time it takes for two DNA sites in the relaxed, unlooped state to move relative to each other and potentially form a DNA loop, and thus an upper limit of ∼2 s⁻¹ for the rate of DNA looping. The plateau values are related to the averaged mean end-to-end separations—λΔO_L has the highest autocorrelation plateau and λWT, λO_R3⁻, and λO_L3⁻ have intermediate values because they contain a mixture of looped and unlooped DNA molecules.

Single-Molecule Measurements of CI Expression Levels

Next, we measured average CI expression levels, , in all strains in order to understand to what different extent DNA looping influences P_RM regulation. We used single-molecule fluorescence in situ hybridization (smFISH, [2],[65],[66]), in which multiple fluorescently labeled oligonucleotides probe targeted nonoverlapping regions of cI mRNA, to count the number of P_RM transcripts in individual cells (Figure 4b and c). Given the assumption that the average number of CI molecules translated per P_RM transcript is the same in all strains and the observation of indistinguishable cell growth rates (Figure S6a and b), we expected average mRNA expression levels proportional to . The λnull strain does not contain the cI gene and was used as a negative control. All other strains were transcriptionally active. Under our experimental conditions, the false positive rate using the λnull strain was ∼1 transcript per 50 cells, two orders of magnitude below the levels of all other strains; false positives arise when nonspecifically bound probes occasionally co-localize to create a fluorescent spot above the detection threshold. Typical smFISH images of the five strains are shown in Figure 4b. We quantified the number of transcripts in each individual cell by dividing the total intensity of fluorescent spots in each cell by the average intensity of a single-transcript spot (Figure 4c). We then determined in wild-type λ units (WLU) by dividing the average number of transcripts in cells of a given strain by the average number of transcripts in λWT cells. We found that deleting O_L increased to ∼1.4 WLU (Table 2), indicating that the DNA loop formed between O_L and O_R in λWT enhances P_RM repression. Mutating either O_R3 or O_L3 further increased to ∼2.5 WLU. These observations are consistent with previous observations that although O_L3 is 2.3 kb away from the P_RM promoter, it has as important a role as O_R3 in repressing P_RM at lysogenic CI concentrations [13]. This suggests that P_RM was not strongly repressed by CI binding to O_R3 in the absence of a tetrameric interaction with an additional dimer at O_L3. Finally, elevated in λO_L3⁻ relative to λΔO_L indicated that DNA looping could also activate P_RM, which was likely mediated by the binding of a CI octamer at O_L12 and O_R12, and was consistent with recent in vivo [49],[51] and in vitro [53] experiments.

Evaluating Looping Free Energies and Transcription Activation Using a Thermodynamic Model

We have shown that reduced looping frequencies in λO_L3⁻ and λO_R3⁻ compared to that in λWT corresponded to increased expression levels of CI in the two strains, and that unlooped λΔO_L has a higher expression level than the λWT strain. To establish a quantitative framework that explains all observed relationships between looping and CI expression levels, we refined a thermodynamic model, with which we estimated looping free energies and the degree to which DNA looping changes the activity of P_RM. These parameters are important because free energies describe the likelihood of interaction between two distal DNA sites, and changes in promoter activity directly reflect the influence of DNA looping on gene regulation.

The thermodynamic approach was first applied to model repression and activation of P_RM by CI bound to O_R [52] and recently modified to address looping [35],[44],[49],[51]. Our modeling approach is unique in that we used two independent, in vivo measurements, looping frequencies, and corresponding CI expression levels, to refine parameters for DNA-looping free energies and transcription activities. In previous modeling work, DNA-looping free energies were either inferred from P_RM and P_R expression-level measurements [35],[49],[51] or estimated using in vitro data [44].

The thermodynamic model and fixed physical parameters from previous reports we used to estimate P_RM expression levels and DNA looping frequencies are essentially identical to the one used to analyze in vivo gene expression experiments [35]. Briefly, we assume that DNA states can be enumerated, that steady-state, in vitro DNA-binding measurements are applicable in vivo, and that mean expression rate, , equals the sum of all products , where is the transcription rate in a particular state and is the probability of the state at a given concentration of free CI dimers :Each state is defined by its free energy, , the number of bound CI dimers, , and the degeneracy, , which is the number of states with the same , , and . The model is described in greater detail in the Materials and Methods section; all states considered are listed in Table S2. is normalized by the partition function, , so that the sum of all state probabilities is 1. Following earlier work [49] and considering that the CI-mediated loop is relatively long, we assumed looping free energies to be independent of parallel or antiparallel orientation. Note that loop orientation is important in shorter DNA loops such as those mediated by Gal repressor [67]. We approximated the average CI concentration, , as the concentration at which the degradation rate equaled the production rate.

We refined our model to fit seven experimental observables: CI expression levels for λΔO_L, λWT, λO_R3⁻, and λO_L3⁻, and the looping frequencies for λWT, λO_R3⁻, and λO_L3⁻. We varied four free parameters: the free energies of forming a CI octamer and tetramer in the DNA loop as defined by Dodd et al. [35], , and , and the P_RM expression rates when O_R12 is bound by CI and DNA is either looped () or unlooped (). is the free energy of bringing together O_R and O_L when both are bound by two adjacent CI dimers to form a CI octamer, resulting in a looped conformation. is the free energy of adding a CI tetramer to a loop already secured by a CI octamer. All other free energies and parameters such as specific and nonspecific DNA binding of CI were fixed at the values used by Dodd et al. [35]. The wild-type CI concentration was fixed to 220 nM (∼150 molecules/cell) based upon our previous experiment in which CI molecules were counted at the single-molecule level in a similar strain at similar growth conditions [3]. The CI degradation rate was fixed to give a half-life equal to the observed 2-h doubling time in our experiments.

The four free parameters were adjusted to best fit our experimental measurements of looping frequencies and CI expression levels. Modeled looping frequencies and CI expression rates at different CI concentrations are shown in Figure 5a and b. The best fit estimated and at 0.3 and −3.2 ^kcal/_mol, respectively, and the CI expression rates at 1.9 nM/s and 4.5 nM/s for unlooped () and looped () DNA when CI binds O_R12. These results suggest that the DNA looping mediated by only a CI octamer is not strongly favored, while looping mediated by both an octamer and tetramer is the dominant configuration if all six binding sites are bound by CI dimers. Note that a small, positive is consistent with measured looping frequencies greater than 50% for ΔλO_L3⁻ and ΔλO_R3⁻, as one unlooped configuration could lead to multiple looped configurations (Table S2). The higher CI expression rate from the looped configuration suggests that, in the absence of O_R3 binding, bringing the distal O_L and O_R sites together to form a DNA loop activates P_RM to 2.4 times the unlooped level.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 5. Thermodynamic modeling of P_RM autoregulation by CI.

(a) Measured and modeled CI expression rates as a function of CI expression levels in wild-type λ units (WLU; the concentration of CI molecules in the λWT strain). Colored curves indicate the modeled dependence of CI expression rates on CI expression levels and dashed black curve indicates the CI degradation rate. Modeled, steady-state CI expression levels are indicated by white circles where the degradation curve intersects CI-expression-level curves. Vertical dashed lines indicate measured CI expression levels (Table 2). (b) Measured and modeled looping frequencies as a function of CI expression levels. Curves show the dependence of looping frequencies on CI expression levels; white circles indicate modeled CI expression levels and measured looping frequencies for λWT, λO_R3⁻, and λO_L3⁻ with vertical lines indicating error in looping frequency estimates. (c, d) Fitting residual plots showing the uniqueness of best-fit model parameters. In each plot a parameter pair ( and in c; and in d) is fixed, while the other parameter pair is varied and the corresponding minimum of the sum of squares of the difference between modeled and experimental parameters for all possible pairs was calculated. Parameter grids are colored according to the logarithm of the minimum sum of squares; well-defined minima indicate uniquely determined parameters.

https://doi.org/10.1371/journal.pbio.1001591.g005

To test how sensitive the fitting results were to two fixed parameters that are poorly defined in previous work, we varied CI expression levels and nonspecific DNA binding affinity. We found that across the examined ranges, octameric looping energies, , were consistently near 0 and tetrameric looping energies, , were strongly favorable between −2.8 to −4.6 ^kcal/_mol (Table S3). Similarly, CI expression rates and remained close to the original fit values, giving activation ratios between 1.7 and 2.5 (Table S3). We also verified that our fit parameters were unique—as shown in Figure 5c and d, the values of fit parameters corresponded to a well-defined minimum in the sum of squared residuals in the four-dimensional (two free energies and two expression rates) parameter space (Figure 5c and d). Hence we conclude that the four fit parameters resulted from the model were robust and well defined.

Differences with in Vitro Looping Measurements

Our estimated looping frequencies of 79% for λWT and greater than 50% for λO_R3⁻ and λO_L3⁻ are larger than those observed in vitro by TPM and AFM, where looping frequencies at lysogenic CI concentrations were approximately 60% with wild-type operators and 10%–40% in the absence of O_R3 and O_L3 [42],[44],[46]. As looping frequency is directly linked to looping free energy, comparison of values showed the same trend: values estimated in these in vitro experiments were similar to our estimate of −3.2 ^kcal/_mol, while in vitro values were 1–2 ^kcal/_mol higher than ours [44],[46].

Significantly different values likely resulted from differences between naked DNA in an in vitro environment and the compact, protein-decorated E. coli chromosome in the crowded cellular environment. Factors such as supercoiling and nonspecific, “histone-like” DNA-binding proteins could compact DNA and lead to more frequent encounters between O_R and O_L. Our observation that the unlooped λΔO_L DNA was extremely compact (discussed in more detail below) was consistent with this view; this level of compaction (comparable to a polymer with a 3-nm rather than a 50-nm persistence length) could lead to a 50-fold increase in the rate at which O_R and O_L encounter each other [68]. The relatively unchanged values could reflect the fact that the entropic and energetic costs of bringing O_R and O_L together are included in . Our looping frequency estimates confirm what were predicted by in vivo gene expression experiments—DNA was estimated to loop ∼72% of the time for wild-type O_R–O_L DNA and ∼69% for DNAs similar to our λO_R3⁻ and λO_L3⁻ constructs [35]. Correspondingly, the and estimated in the in vivo work (−0.5 and −3.0 ^kcal/_mol) [35] compared well to ours (0.3 and −3.2 ^kcal/_mol).

One important assumption we employed in calculating looping frequencies is that that looped and unlooped λWT, λO_R3⁻, and λO_L3⁻ DNA molecules had similar distributions to those of the looped control λnull and unlooped control λΔO_L, respectively. It is possible that the unlooped states in the λWT, λO_R3⁻, and λO_L3⁻ strains were more compact than that in λΔO_L if after a DNA loop breaks O_R–O_L DNA does not always completely relax before it reforms again. In such a case, looping frequencies estimated using the linear-combination model would be upper limits on the true looping frequencies. Nevertheless, as we show above, our looping frequency estimates broadly agree with expectations from previous studies. Since this simple model only requires one free parameter and gives reasonable results, it is unnecessary to invoke more complicated models.

Effects of DNA Looping on Transcription Regulation

By comparing looping frequencies and corresponding CI expression levels in λWT, λΔO_L, λO_R3⁻, and λO_L3⁻, we showed that loop stabilization by the CI tetramer between O_R3 and O_L3 is important for efficient P_RM repression, and that looping mediated by a CI octamer at O_R1 and O_R2 is important for P_RM activation. We note that while it is possible that the presence of tetO³ and lacO³ binding sites flanking O_R–O_L DNA may influence CI binding and/or transcription, this influence is negligible. This is because CI expression levels in these strains measured using smFISH are comparable to that of a wild-type λ lysogen (Table S8), and our results are consistent with previous observations [13],[49],[51],[53]. Furthermore, results are directly comparable as all strains used in this study are identical with respect to the presence and positioning of these binding sites.

Combining these results in our thermodynamic model, we estimated that CI-mediated DNA looping activates P_RM to 2.4 times its level when the DNA does not loop. This compares well to earlier estimates of 2–4 fold [49], and 1.6-fold for a high-expression P_RM mutant [53]. Another study did not find looping activates transcription, modeling CI-concentration-dependent P_R and P_RM activities without invoking activation via looping (by assuming ) [35]. A later study indicated that this discrepancy may have resulted from different constructs used in the earlier study [49].

The molecular basis for DNA loop-enhanced P_RM activation is unclear. One possibility is that a CI dimer bound to O_R2 interacts with RNA polymerase to a greater extent if it is part of a higher-order CI octamer [53]. Alternatively, a recent work showed that a DNA UP element proximal to O_L [49],[69] enhances CI expression from P_RM in looped DNA by contacting the α-C-terminal domain of RNA polymerase [51]. The activation mechanism could be clarified in future experiments measuring both looping frequency and P_RM activity while varying operator and UP element sequences and introducing CI mutations affecting operator binding, oligomerization, and RNA polymerase interaction.

Kinetics of DNA Looping

We estimated the time scale a DNA molecule stays in a particular state by calculating the autocorrelation function of the vector (Figure 4a). The vector was strongly correlated for at least 0.5 s, suggesting that a particular DNA conformational state, either compact or extended, persisted for at least 0.5 s. This implies an upper limit of 2 s⁻¹ for the rate of loop formation from the extended state. This upper bound of transition rate is in the range of what was observed in a previous TPM experiment, in which looped and unlooped states lasted for tens of seconds [44], and argues against a significantly faster rate used in a recent computer simulation (∼60 s⁻¹) [50]. We note that although it is possible that transient CI unbinding does not necessarily lead to immediate and complete DNA conformational relaxation at our measurement time scale, the autocorrelation analysis puts an upper limit for the true transition rate between the looped and unlooped states. The same concern also applies to in vivo 3C and in vitro TPM experiments.

Slow transitions between looped and unlooped states imply that low or high expression states resulting from a particular DNA conformation could be long-lived, potentially committing a cell to a particular fate. Supporting this is a recent study that suggested that a single unlooping event could trigger induction of the lac operon [5]. We were unable to obtain time trajectories long enough to clearly identify looped/unlooped transitions for single DNA molecules. Development of brighter, faster maturing, and more photostable fluorescent proteins or in vivo labeling with synthetic fluorophores [70],[71] will help in increasing the number of measurements made on one DNA molecule, possibly enabling accurate measurement of DNA looping kinetics in vivo.

The Short End-to-End Separation of λΔO_L Reflects the High Compactness of Chromosomal DNA

We observed very small end-to-end separation for the unlooped control ( = 71 nm). This distance was shorter than expected from modeling the unlooped DNA as a noninteracting worm-chain with an in vitro persistence length of 50 nm [72], but consistent with the recently observed extreme bendability of short DNA molecules [73]. A noninteracting chain with an equivalent to that of λΔO_L would have a persistence length of only 3 nm, which is physically infeasible. Our measurements of indistinguishable conformational distributions in the absence of P_RM transcription and the presence of CI overexpression suggest that neither transcription nor nonspecifically bound CI played a major DNA-compacting role in our experiments. Furthermore, C. crescentus chromosomal DNA segments of ∼5 kb were found to be similarly compact and consistent with Brownian dynamics simulations of supercoiled DNA [74].

We attribute the small end-to-end separation observed for λΔO_L to the high compaction of the E. coli chromosome in the crowded cellular environment. While the exact molecular mechanisms responsible for compaction remain unclear, previous studies found that in vitro binding of the histone-like HU proteins [75] (accession numbers P0ACF0, P0ACF4) and in vivo mammalian chromatin packing [76] reduced the apparent persistence length of DNA. Hence, it is possible that nucleoid-associated proteins such as HU may bring distal DNA sites together by protein–protein interactions and/or affect local DNA conformations by introducing bends and relieving torsional strain [77]. Another important factor could be negative supercoiling, which has been shown to compact the chromosomal DNA globally [78]. However, the exact effect of negative supercoiling on a 2.3-kb DNA segment is difficult to predict, because negative supercoiling could also introduce extended, plectonemic structures that promote large separations between DNA sites on relatively short length scales [78].

Potential Applications

Our two-color, high-resolution method can be applied to examine how chromosomal location, DNA length, genetic background, and growth conditions affect the distance between any two DNA sites on the E. coli chromosome. Furthermore, the spatial organization of the E. coli chromosome can be determined by systematically measuring distributions between DNA sites throughout the chromosome. This method is similar to how chromosome conformation capture was used to generate a 3D model of the C. crescentus chromosome [79], but with significantly improved spatial resolution and without potential artifacts from fixation.

Strain and Plasmid Construction

A plasmid, pS2391, containing lacO³ and tetO³ (the tetO₂ sequence [54] was used for each repeat in tetO³) sites was synthesized by Genewiz, Inc. Segments of λ DNA (O_R through O_L for λWT, O_R up to but not including O_L for λΔO_L) from the wild-type lysogen JL5392 (a gift from John Little, University of Arizona) were amplified by PCR. This DNA was sequenced and inserted between lacO³ and tetO³ using the In-Fusion PCR cloning system (Clontech). A kanamycin-resistance cassette flanked by BamHI sites was amplified by PCR and inserted after lacO³. For strains with mutated operators, mutations r1 [80], O_L3–4 [13], and cI^G147D [62] were introduced to the λWT template via QuikChange (Agilent). A plasmid carrying the P_RM⁻cI⁻ mutations (Figure S5c) (λΔO_LP_RM⁻cI⁻) was constructed by overlapping PCR mutagenesis using complementary primers carrying the desired mutations, flanked by a forward primer that sits at the EcoRI site on the upstream end of the operon and a reverse primer at the ClaI site in the rexA gene downstream of cI. The 1.13 kb PCR product was introduced to the λΔO_L plasmid by restriction ligation.

This procedure resulted in seven plasmids that were used as templates in subsequent chromosome insertion: pZH105 (λnull), pZH016 (λΔO_L), pZH107 (λWT), pZH107r1 (λO_R3⁻), pZH107O_L3–4 (λO_L3⁻), pACL006 (λWT^G147D), and pACL007 (λΔO_LP_RM⁻cI⁻). Note that we use shorthand names such as λnull here for clarity; corresponding names used in our laboratory are listed in Table S4. The DNA sequence including lacO³, the λ DNA segment, tetO³, and the kanamycin resistance cassette was inserted into the chromosome of E. coli strain MG1655 by λ Red recombination [81], excising the lac operon, lacI, and all lacO sites.

To express the CI protein in trans from a plasmid, we constructed the plasmid pACL18 in which the wild-type cI ORF is driven by a constitutive promoter, P_RM^c, which has the wild-type −35 (TAGATA) and −10 (TAGATT) sequences, lacks O_R2, and has a mutated O_R1 sequence (CGCCTCGTGAGACCA) that eliminates binding by CI. The pRM^c–cI fragment was then cloned to the ClaI site of the low-copy vector pACYC184. The plasmid pACL17 was generated similarly using a template containing the CI^G147D mutation.

The two-color reporter plasmid pLau53, which expresses LacI-ECFP and TetR-EYFP polycistronically under the control of the P_BAD promoter [82], was obtained from the Yale Coli Genetic Stock Center. Because the autofluorescence spectrum of live cells is generally strongest at wavelengths around 500 nm [83], single-molecule imaging of blue-shifted fluorescent proteins such as ECFP is difficult. The red fluorescent protein mCherry, which further benefits from a large Stokes shift, fast chromophore maturation rate, and high brightness relative to other monomeric RFPs [84], was inserted in place of ECFP. We also created a tandem LacI-mCherry-EYFP reporter, which was used as a fiducial marker, by inserting the linker sequence from the tandem-dimer fluorescent protein tdTomato [84] in between mCherry and EYFP.

To accurately localize a fluorescent spot arising from only a few fluorescent protein molecules above the background of unbound molecules within a cell, we reduced the reporter expression level by weakening the ribosome binding sites (RBSs). Weakened RBS sequences were designed using an online RBS calculator [85]. For example, the RBS for TetR-EYFP translation was the consensus AGGAGG Shine-Delgarno sequence in the parent plasmid pLau53. Our reporter plasmid had an ACCAGG Shine-Delgarno sequence, with a predicted ∼300-fold decrease in the TetR-EYFP translation rate. All sequences including chromosome insertions were verified by sequencing (Genewiz Inc). Reporter plasmids are described in Table 1.

Growth Condition

For all experiments reported in this study, cells were grown and imaged at room temperature (∼25°C) in M9 minimal media supplemented with MEM amino acids (Sigma). Cells were grown overnight with 0.4% glucose and 50 µg/ml carbenicillin to an optical density (OD₆₀₀) of 0.4. After centrifugation at room temperature, cells were resuspended at OD600≈0.2 with 0.4% glycerol plus 0.2% L-arabinose and grown for 2 h (∼1 cell cycle) to induce LacI-mCherry and TetR-EYFP expression. Cells were again resuspended at OD₆₀₀≈0.2 with 0.4% glucose and grown for another 2 h before immediate observation to allow time for fluorescent protein chromophores to mature.

We compared growth rates for the parent strain MG1655 to the experimental strain λnull to determine whether inserting the lacO³ and tetO³ construct into the chromosome and/or inducing expression from the reporter plasmid introduced a significant growth defect. Under induction growth conditions (∼27°C, M9 media with 0.4% glycerol and 1× MEM amino acids) starting at OD₆₀₀≈0.1 and observing 8 h of growth, we measured doubling times of 2.7 h for MG1655 and 3.4 and 3.3 h for λnull harboring the reporter plasmid (in the absence and presence of 0.3% L-arabinose, respectively), indicating that there is no large growth defect associated with the insertion of the tandem operator sites into the chromosome and/or the expression of TetR-EYFP and LacI-mCherry fluorescent fusion proteins (Figure S6c).

Imaging Conditions

In each experiment, samples of all strains were placed on separate gel pads in the same growth chamber. Two sets of at least 30 movies were acquired for each strain, with the second set acquired in the reverse order to minimize any bias possibly introduced by observing some strains in a particular order. All images were acquired within less than one cell doubling time.

Cells were put on a gel pad made of 3% low-melting-temperature SeaPlaque agarose (Lonza) in M9 with glucose and imaged on an Olympus IX-81 inverted microscope with a 100× oil immersion objective (Olympus, PlanApo 100× NA 1.45) and additional 1.6× amplification. Images were split into red and yellow channels using an Optosplit II adaptor (Andor) and captured with an Ixon DU-895 (Andor) EM-CCD with a 13-µm pixel width using MetaMorph software (Molecular Devices). Laser illumination was provided at 514 nm by an argon ion laser (Coherent I-308), which also pumped a rhodamine dye laser (Coherent 599) tuned to ∼570 nm. A quarter-wave plate (Thorlabs) was used to circularly polarize excitation light. Emitted light was split by a long-pass filter, and the red and yellow images were filtered using HQ630/60 and ET540/30 bandpass filters (Chroma).

Measuring and Analyzing

Images were inspected manually using a custom MATLAB script to identify spots that appeared in both EYFP and mCherry images. Images from all strains were displayed in random order without knowing the strain identify to avoid bias in spot selection. Pixel intensities within 3 pixels of the initial spot location were fitted with a symmetric, two-dimensional Gaussian distribution to estimate spot coordinates. The variance of the fit distribution was constrained to be less than 2 pixels. Spot-fitting error was estimated by scrambling residuals from a fit to the fluorescence data in 10 random permutations, adding them to the data, and fitting the resulting images; the reported error for a spot is the standard deviation of the distances between these fits and the initial fit to the raw data. Fitting error distributions are shown in Figure S1a.

The LacI-mCherry-EYFP tandem dimer (Figure S2b) in which the two fluorescent proteins were directly fused together was used to acquire fiducial control points to transform between the mCherry and EYFP coordinate systems. A projective transform was calculated from the control points using the cp2tform function in MATLAB. We found that relatively simple, global transformations were sufficient to transform coordinates of fluorescent beads (Tetraspeck, Invitrogen) with ∼10-nm registration error in our microscope setup, and did not see any further improvement with a locally weighted transformation used in in vitro two-color experiments [21]. This transformation was also used to generate the overlay images in Figure 2, Figure 3, and all supplemental movies. Fluorescent beads were not used as fiducial markers because the beads' emission spectra were different from those of the fluorescent proteins. Analysis was restricted to molecules in which mCherry and transformed EYFP coordinates were separated by less than 200 nm. Separations beyond this threshold were rare (∼1% of data, see two-dimensional distributions in Figure S4) and did not correlate with strain identity in any reasonable way. They possibly arose from data in which cells contained two labeled copies of O_R–O_L DNA.

After transformation into a uniform coordinate system, was calculated from the mCherry and EYFP coordinates and multiplied by an 81-nm pixel size (resulting from 160× magnification on a CCD with a 13-µm pixel width). Probability and cumulative distributions and were calculated for 10-nm bins using the kernel smoothing probability density estimation (ksdensity) function in MATLAB, restricting the density to positive values and employing a uniform kernel width small enough to follow empirical cumulative density distributions without any systematic errors. Significant differences between distributions were determined using a two-sample Kolmogorov–Smirnov test; two-tailed Student's t tests of sample means returned smaller, more significant p values. Errors in and were determined by calculating the means of 1,000 bootstrapped samples; the reported error is the standard deviation of the calculated means. Looping frequencies were estimated by least squares fitting of 1,000 bootstrapped distributions (control distributions were also randomized on each iteration) and their error was calculated similarly.

Single-Molecule Fluorescence in Situ Hybridization (smFISH)

Concentration measurements by smFISH followed a previously described protocol [66]. Transcripts from P_RM were labeled with a mixture of 42 oligonucleotides labeled with CAL Fluor Red 610 (Biosearch Technologies), 31 of which hybridized to cI (11 targeted sequences not found in E. coli and did not cause a problematic level of false positives). Table S5 lists all 42 oligonucleotides. Labeled cells were imaged with 561-nm excitation at six imaging planes separated by 200 nm z-depth with negligible photobleaching. For each frame, fluorescent spots were automatically detected and fit to a Gaussian using a custom MATLAB routine. Nearly all molecules appeared in multiple image slices; the slice with the largest fit amplitude was kept. The integrated fluorescence of spots was observed to be quantized with one or a few molecules localized within one diffraction-limited spot. The intensity of one transcript was estimated from the distribution of spot intensities, and the number of molecules contributing to each spot was estimated from this quantization. The number of transcripts in each cell was estimated from the sum of the number of molecules in each spot within that cell. Alternatively, the number of molecules in one cell is proportional to its integrated fluorescence; this measurement provided the same average expression levels within error. The experiment was repeated to ensure that differences in labeling efficiency between samples were not responsible for differences in the number of detected molecules; combined data from both experiments were used for analysis.

Simulation of

To generate simulated distributions, we first generated 10,000 random radial distances for a chain with a contour length and persistence length from a worm-like, noninteracting chain model using a Gaussian distribution with Daniels' approximation, which is accurate in the regime [72]:Each simulated was projected onto the plane at a random angle to give a distance . Simulated spots were placed at coordinates and . The MATLAB function mvnrnd was then used to simulate normally distributed measurement error with a standard deviation of 22 nm to the coordinates of each simulated spot. This procedure was sufficient to simulate the λnull distribution (Figure S2c) using a fixed end-to-end distance of 22-nm (approximate distance between the centers of the lacO³ and lacO³ sites; Figure S2a). Note here that the simulation is simplified in that it assumes that each spot has the same 22-nm localization error. In reality, localization error varies between different spots (Figure S1a) and there are other sources of measurement error. These differences may explain the slight deviation of the simulated distribution from the experimental distribution. The same procedure was used to estimate the expected for 2.3-kb, B-form DNA with a 50-nm persistence (∼200 nm) as well as the apparently persistence length (3 nm) implied by the 71-nm observed for λΔO_L.

Thermodynamic Modeling

Additional descriptions of thermodynamic states are listed in Table S3. Parameter values were determined by first scoring a wide range of parameter values and iteratively searching narrower and more finely grained parameter ranges to manually minimize the sum of the squares of the differences between experimental and modeled values for looping frequency and CI expression level. We then refined this fit by least-squares minimization using MATLAB. This was done using a minimized model that only accounted for states likely to be populated near or above lysogenic CI concentrations (e.g., disregarding states in which O_R1 and O_R2 are unbound by CI). Using the same parameters and accounting for all 176 possible states (122 unique states accounting for degeneracy) did not significantly change the fit results. Fitting with this much more complex model gave octameric and tetrameric looping free energies of 0.6 and −3.3 ^kcal/_mol and unlooped and looped expression rates of 2.1 and 5.3 nM/min. When determining parameters, rates were expressed in terms of changes in concentration per unit time; we followed earlier work in assuming that in a typical E. coli cell, a single molecule is at a concentration of ∼1.47 nM [35].

We do not report any estimate of fitting error; instead, we present only the parameters most consistent with our data and assumptions. Figure 5c and d shows that fit parameters were well-determined at a given combination of wild-type CI concentration and nonspecific binding parameters. As noted in the main text, varying these two parameters changed the absolute best-fit parameters, but did not dramatically change our conclusions. Furthermore, fixed parameters of previous studies were determined in a number of separate experiments employing different methods at temperatures other than 25°C; a rigorous estimate of modeling error would require knowing the error in the measurements of fixed parameters in our experimental conditions.

The basal CI expression rate, , was arbitrarily fixed at ; this did not have any significant impact on determining other parameters, as our measurements were all at or above lysogenic , where O_R2 is almost always bound by a CI dimer. Additionally, the fraction of free CI dimers was fixed at its value for 150 CI molecules per cell at a given concentration of nonspecific binding sites and nonspecific binding affinity. Fixing the concentration of free CI dimers is a reasonable approximation if (1) nearly all CI molecules are in dimers and (2) the number of free nonspecific binding sites is not significantly changed by nonspecifically bound CI dimers.

Image Representation in Figures

Figure 2a–e, Figure 4b, and Movies S1, S2, S3, S4, S5, S6 were prepared using NIH ImageJ [86]. Raw fluorescence image intensities were scaled linearly from the lowest to highest values in region shown. For EYFP/mCherry overlay images, brightfield images were inverted and converted to 8-bit RGB. Fluorescence images were bandpass filtered and background subtracted before being used to generate magenta (mCherry) and green (EYFP) 8-bit RGB images that were added to the brightfield image. The EYFP images were first transformed in MATLAB using the imtransform function and the same fiducial data that were used to transform EYFP spot locations into mCherry coordinates. For smFISH images (Figure 4b), the value of each pixel is the maximum value of that pixel in six images collected at different z-axis positions. Intensities for all images were scaled linearly from the minimum to the maximum of all pictures (117–4,840 counts in 16-bit images).