Partitioning of RNA polymerase activity in live Escherichia coli from analysis of single-molecule diffusive trajectories

Abstract

Superresolution fluorescence microscopy is used to locate single copies of RNA polymerase (RNAP) in live Escherichia coli and track their diffusive motion. On a timescale of 0.1-1 s, most copies separate remarkably cleanly into two diffusive states. The "slow" RNAPs, which move indistinguishably from DNA loci, are assigned to specifically bound copies (with fractional population ftrxn) that are initiating transcription, elongating, pausing, or awaiting termination. The "mixed-state" RNAP copies, with effective diffusion constant Dmixed = 0.21 μm(2) s(-1), are assigned as a rapidly exchanging mixture of nonspecifically bound copies (fns) and copies undergoing free, three-dimensional diffusion within the nucleoids (ffree). Longer trajectories of 7-s duration reveal transitions between the slow and mixed states, corroborating the assignments. Short trajectories of 20-ms duration enable direct observation of the freely diffusing RNAP copies, yielding Dfree = 0.7 μm(2) s(-1). Analysis of single-particle trajectories provides quantitative estimates of the partitioning of RNAP into different states of activity: ftrxn = 0.54 ± 0.07, fns = 0.28 ± 0.05, ffree = 0.12 ± 0.03, and fnb = 0.06 ± 0.05 (fraction unable to bind to DNA on a 1-s timescale). These fractions disagree with earlier estimates.

Figure 1

(A) Examples of RNAP trajectories from 10-Hz movies displayed atop the phase contrast image. Scale bar = 1 μm. (B) Distribution of single molecule diffusion constants D_i (Eq. 2) from 5996 trajectories truncated to six steps for the lag time τ = 300 ms. (Red and green lines) The two components of a two-state model that mimics the peak and the tail of the distribution closely. (Inset) Expanded view of long tail of the distribution. (Green line) Result of a model of free diffusion with D_mixed = 0.21 μm² s⁻¹ including confinement within one nucleoid sublobe. (C) Scatter plot of maximum excursions ε_y versus ε_x for single trajectories (ten steps at 100 ms/frame) along the x (long axis) and y (short axis) directions. (Red dots) D_i < 0.03 μm² s⁻¹; (green dots) D_i > 0.03 μm² s⁻¹. (D) Ensemble-averaged MSD_r(τ) from trajectories truncated at nine steps (Eq. 1). (Orange) All RNAP copies; (dashed line) linear fit to first three points, yielding 〈D_RNAP〉 = 0.03 μm² s⁻¹. (Green) Mixed-state RNAP population only (defined as D_i > 0.03 μm²/s). (Circles) Data taken at 10 Hz; (triangles) at 33 Hz. (Black solid line) Monte Carlo model for the mixed-state trajectories with D_mixed = 0.21 μm² s⁻¹, including confinement in one nucleoid sublobe. (Red) Slow RNAP population only (defined as D_i < 0.03 μm²/s).

Figure 2

(A) Positions of the DNA loci NSL-2 and Left-1 on the chromosome. (B) Example 1-s-long trajectories for Left-1 taken at 10 Hz and displayed atop the phase-contrast image. (C) Ensemble-averaged MSD_r(τ) plots from 10-Hz trajectories truncated to 12 steps for the slow RNAP population (D_i < 0. 03 μm²/s, 985 trajectories), for Left-1 (725 trajectories), and NSL2 (968 trajectories). MSD_r data for RNAP in cells fixed with formaldehyde is shown for comparison. To see this figure in color, go online.

Figure 3

(A) For all detected RNAP copies, scatter plot of maximum excursion ε_y versus ε_x for nine-step trajectories taken at 33 Hz (300-ms trajectory length). (Red dots) Slow RNAP trajectories (D_i < 0.03 μm² s⁻¹); (green dots) mixed-state trajectories (D_i > 0.03 μm² s⁻¹). (B) MSD(τ) plots for the mixed-state RNAP molecules (D_e > 0.03 μm²/s) along the short axis y, the long axis x, and for r = (x² + y²)^1/2. MSD_r(τ) is divided by 2 to place it on same scale as x and y. (Solid lines) Simulated MSD plots from Monte Carlo model with D_mixed = 0.21 μm² s⁻¹ and confinement within cylinder of R = 380 nm and L = 1.1 μm, as shown. To see this figure in color, go online.

Figure 4

Examples of 14-step, 7-s long RNAP trajectories obtained at 2 Hz (0.5 s/frame) with advancing time color-coded. Note examples of go-stop and stop-go trajectories.

Figure 5

(A) Examples of 10-step, 20-ms-long RNAP trajectories obtained at 500 Hz (2 ms/frame). (Dark blue) Beginning and (dark red) end of each trajectory. (B) D_i distribution for 4551 trajectories obtained at 500 Hz; lag time is τ = 3 steps = 6 ms. (Solid lines) Model calculations for two noninteracting populations, one with D_DNA-bound = 0.005 mm² s⁻¹ and F_DNA-bound = 0.81 (red curve) and the other with D_unbound = D_free = 0.7 μm² s⁻¹ and F_unbound = 0.19 (green curve). Their sum (blue curve) fits the overall distribution well, indicating the model is adequate. (C) For 10-step trajectories obtained at 500 Hz, scatter plot of ε_y versus ε_x. (Dashed circle) Value of ε_rms = 0.27, which most cleanly separates the DNA-bound from the unbound copies. See Section S8 in the Supporting Material for details. (D) Ensemble-averaged MSD_r(τ) plots for the DNA-bound and unbound fractions from 10-step, 500-Hz trajectories of 20-ms duration. The initial slope of the unbound MSD plot yields the best estimate D_free = 0.69 μm² s⁻¹.

Figure 6

Comparison of estimates of RNAP partitioning fractions from this work with earlier model results from Bremer et al. (10) and Klumpp and Hwa (9). We show our raw, uncorrected fractions and also our fractions corrected for depth of detection effects. (Labels: nb, RNAP fractions that do not bind to DNA; free, RNAP fractions that are freely diffusing within the nucleoid; ns, RNAP fractions that are binding nonspecifically to DNA; trxn, RNAP fractions that are transcribing; and Int denotes assembly intermediates.) Bremer et al. (10) interpreted their minicell fractions in terms of what we call the sum of free plus nonspecific binding. They postulated a paused state that stores a large number of nonelongating, specifically bound copies. Klumpp and Hwa (9) reinterpreted those copies as nonspecifically bound. See text and Section S9 in the Supporting Material for details. To see this figure in color, go online.