We first investigate the 1D Brownian motion of T7 RNAP on λ-DNA molecules. λ-DNA does not contain any T7 promoter sequence; hence the RNAP is not expected to initiate transcription on λ-DNA. We label T7 RNAP with primary and fluorescent secondary ABs forming a RNAP–AB complex (RPAB) for direct visualization. The epitope for specific binding of T7 RNAP monoclonal AB is located on the C-terminal portion of the palm domain (residues 861–883), facing away from the catalytic core (C). The catalytic activity of this RPAB complex was examined by investigating its ability to synthesize RNA. The green fluorescent dots (left in D) indicate fluorescent UTPs incorporated into RNA transcripts formed along the contour of single combed T7 DNA (
23), and orange fluorescent dots (right in D) show the positions of RPABs on the same DNA. Since the locations of the green and red fluorescent dots coincide, we conclude that RPAB is capable of initiation and elongation.
The dye manufacturer has indicated that the molar ratio of dye to secondary antibody is 3.14. We checked this by measuring the photobleaching behavior of the protein complex measured in free solution, where to reduce noise the intensity was added over a 6 × 8 pixel array and each point integrated over 2

s. As shown in E, is the results are consistent with the presence of around 3–4 dye molecules on the protein complex (imaged while not attached to DNA), based on the number of apparent steps in the decrease of fluorescence intensity. We observe similar apparent step-wise photobleaching behavior, and similar fluorescence intensity, for the free stained secondary antibody alone, imaged under the same conditions, from which we can infer a similar number of dye molecules (3–4 dyes) on the secondary antibody alone (inset, E). We therefore expect to find a single secondary antibody in the RPAB complex. This can also be verified by estimating the size of the complex from its diffusivity. The majority of the fresh RPABs have a diameter of around 40–50

nm, as determined by following their 3D diffusion in the bulk to measure their bulk diffusivity. With a diameter of ~6

nm for T7 RNAP and ~13

nm for both the primary and secondary AB, the size of the whole complex (40–50

nm in diameter) is consistent with its containing only one, or at most a few monomers of each of the three proteins (RNAP, primary AB, secondary AB) within the experimental error.
We next observe diffusive motion of RPAB after it binds to the DNA stretched on a substrate. We arrange the flow of RPAB to be approximately perpendicular to the direction along which the DNA was stretched, so that diffusion of the protein along the DNA molecules can easily be distinguished from convection in the flow direction. Stretching of a coiled DNA molecule into a linear configuration is likely to limit our observation of protein motion to sliding and short-range hopping. The stretched configuration of the DNA molecules prevents us from observing any long-range jumping between segments of DNA that are remote to each other along the chain contour, but which could be physically close to each other if the DNA were in a coiled conformation.
As can be seen in A, the movement is bidirectional along the DNA contour. The two dots that do not move in A are presumably proteins bound to the DNA at points where the DNA is attached to the substrate. It has been shown that combing of DNA molecules onto a hydrophobic substrate at acidic conditions leads to multiple anchor points along the backbone, evidently because of local unpairing of hydrophobic bases (
26). We observed that the protein that initially binds to a free segment of the DNA between two anchor points diffuses freely without interference by the substrate. The RPABs showed no significant photobleaching on the time scale of our experiments, so that we could visualize these molecules for as long as several minutes. We also observed RPAB diffusing along YOYO-stained DNA (B). The displacements of proteins in A and B, and of another similarly diffusing protein, are plotted as a function of time in C and their distributions of relative displacements
y(
j)−
y(
j−1) in D. The distribution of displacements can be well fitted to a Gaussian centered around zero, which is a characteristic of Brownian motion.
We can obtain the 1D diffusion coefficient (
D1) by plotting the mean-square displacement (MSD) versus the time interval over which the displacement takes place and taking the slope of the linear region. The MSD is calculated using
where
xi and
yi denote centroid positions of the protein in the
ith image,
iΔ
t denotes an interval of
i time steps each of duration Δ
t (=0.2

s), and
N is the total number of positions measured.
D1 is thereby calculated to be 1.2 ± 1.0 × 10
−9
cm
2/s (mean ± SD,
n = 32) for the RPAB at [NaCl] = 0

M. Increasing the salt concentration to 0.05

M does not affect the diffusivity, suggesting that the protein maintains close contact with the DNA over the time scale of our observation. A further increase in salt concentration to 0.1

M dramatically reduces the binding affinity of the protein. We note that staining DNA with intercalating dye does not influence the diffusivity of protein at the staining ratio we used (dye:bp = 1:20). We define the diffusion length as the maximum distance covered by the protein over the time scale of our observation (~20

s) and it is thereby calculated to be 1640 ± 830

nm.
D1 and the diffusion length vary from protein to protein over a large range of 6.1 × 10
−11
cm
2/s–4.3 × 10
−9
cm
2/s, and 480–3630

nm, respectively as shown in E (the ‘diffusion length’ is just set by the time we ran the experiments, since we rarely saw proteins escape from the DNA along which they diffused).
Here we discuss whether this large variance in
D1 is statistically meaningful by investigating the error in the MSD for a single protein. The variance in MSD increases as
i in Equation (
2) increases from 1 to
N because the number of statistically independent data points of displacement decreases with increasing
i (F). It has been shown that the variance in MSD can be expressed as (
21,
27)
The relative SD in
D1 can thereby be estimated as [(2
i2 + 1)/3
i(
N -
i + 1)]
1/2. With
N
~
100 in our experiments and
i ~ 5 for an upper bound of the linear region in the MSD versus time plot (F), we estimate the SD of
D1 due to statistical error to be around 20%. In order to check the validity of our estimation of the error in
D1, we followed the 1D Brownian motion of a single protein for a time period of 80

s (
N = 400), which is four times longer than that of our measurements with different proteins, and obtained
D1 for each of four subsets of the data, each containing 100 measurement points. Using the same method to determine MSD, we found that
D1 for a single protein varied from a minimum of 4.4 × 10
−10
cm
2/s in one of the four time intervals to 7.9 × 10
−10
cm
2/s in another interval, giving a mean value of 6.3 × 10
−10
cm
2/s and a relative SD of 20%. We also simulated 30 sets of 1D random walks each with
N = 100 steps and obtained a relative SD of 17%, which is in good agreement with our estimated error in
D1. We thereby conclude that the relative SD of
D1 due to uncertainly associated with determination of MSD is around 20%. The much larger variance in
D1 we obtained for different proteins, yielding a relative SD of 83%, far exceeds our estimation of statistical error, suggesting that the individual RPABs have distinct intrinsic diffusivities.
We also note that the variability in 1D diffusivities that we have observed does not correlate with the light intensity of these proteins. The fluorescence intensity of a protein with a ‘high’ 1D diffusion coefficient of 3.0 × 10
−9
cm
2/s was measured to be ~1800 (arbitrary unit), and that of a protein with a ‘low’ 1D diffusion coefficient of 1.8 × 10
−10
cm
2/s was ~1000 (arbitrary unit). Intensities both higher than 1800 and lower than 1000 were also measured for proteins with 1D diffusion coefficients in between the above two values. We therefore conclude that the brightness of proteins does not correlate with the 1D diffusivity. In addition, the fairly modest variation in light intensity compared to the large variation in 1D diffusivity, is consistent with the rather tight range of particle sizes inferred from the 3D diffusivity (i.e. 40–50

nm). Also, the fluorescence intensity of the free dyed secondary antibody was measured to be 1000–2000 (arbitrary unit) under the same imaging condition we used to measure the intensity of the RNAP complex, where we measured intensity in the range of 1000–1800 (arbitrary unit). (These values differs from the intensities in E where to reduce noise the intensity was added over a 6 × 8 pixel array and each point integrated over a longer time period; i.e. 2

s versus 0.2

s). The similarity in the brightness of the free dyed secondary antibody and the protein complex under two different imaging conditions suggests that a single secondary antibody may be found per RPAB complex, thus the variation in 1D diffusivity can hardly be due to protein aggregation.
The residence time of RPAB on the DNA in our experiments is much longer than that of other proteins in previous reports, which typically are on the order of a tenth of second (
6,
20), while in our experiments, we almost never see the protein detach from the DNA, even after many tens of seconds. In order to verify whether using combed DNA increases the lifetime, we alternatively stretched DNA molecules using a laminar shear flow after attaching DNA molecules to the substrate at one end via a biotin–neutravidin link. As can be seen in kymograph in A, the protein displays somewhat jerky unidirectional motion on DNA due to the shear flow, and we do not observe the 1D Brownian motion seen with combed DNA. The MSD's as functions of time for protein moving along flow-stretched DNA and along combed DNA are shown in B. The quadratic relationship seen in the MSD curve for a protein moving along flow-stretched DNA is a characteristic of convection rather than diffusion, the latter of which produces a linear relationship, such as seen when a protein diffuses along combed DNA in A. It is of interest that Blainey
et al. using a DNA molecule similarly bound at just one end and stretched by flow at the same velocity, saw only diffusive motion of the protein hOgg 1 (
20). However, convective motion of proteins in stretched DNA has been observed by Granéli
et al. and Kabata
et al. with human Rad51 (
28) and EcoRI (
29), respectively. In the experiments by Granéli
et al., Rad51 molecules were observed to move in the direction of flow along λ -DNA, stretched using a hydrodynamic force as depicted in B. In the absence of buffer flow, the 1D Brownian motion of Rad51 was observed on λ -DNA tethered at both ends. In the experiments by Kabata
et al., convective motion along the DNA could be distinguished from simple convection in the flow by a change in direction of the motion of the stained proteins when they encountered the DNA molecules, which were oriented diagonally to the flow direction.
Although we do not observe 1D Brownian motion of RPAB on flow-stretched DNA, the lifetime of the protein on the DNA is very long, as is it on combed DNA. This shows that the long residence time of proteins on combed DNA does not result from the influence of the substrate to which the combed DNA is bound. The majority of RPABs do not dissociate from either combed or flow-stretched DNA within the time scale of our observation. It is possible that the antibody binding that we use for staining represses the protein's dissociation from the DNA after a repetitive search. However, the amino acids involved in antibody binding do not directly participate in the catalytic activity which is well preserved since the protein is fully capable of binding to the DNA, initiating transcription and elongating the RNA chain, as will be discussed more in detail below. The prolonged lifetime of RPAB on the DNA and its resistance to photobleaching, however, enable us to observe both the 1D Brownian motion and transcription over a time scale that is longer than previous experiments, offering opportunities to obtain long-time trajectories for a single protein and observing protein-to-protein variations in diffusivity.
Next, we investigate the real-time dynamics of transcription by T7 RNAP beginning with the kinetics of association of T7 RNAP to individual combed T7 DNA molecules. We vary the protein concentration over the range 50–200

nM and measure the time elapsed between two consecutive binding events, yielding the results shown in histograms in A and B. The time distributions can be fitted to a single exponential, giving a decay time of 3.1

s for 200

nM T7 RNAP (A), 5.9

s at 100

nM T7 RNAP (B), and 11.2

s for 50

nM T7 RNAP (not shown). The association rate can be estimated by taking the reciprocal of the decay time and plotting it as a function of protein concentration. We thereby obtain an association rate constant of 1.6

μM
−1s
−1, which is an order of magnitude lower than reported in previous bulk studies (
4). Similar reduction in the association rate was observed for the Lac repressor when the rate was measured using a surface plasmon resonance biosensor (
30). In this biosensor, as in our experimental scheme (A), the protein must diffuse through a stagnant boundary layer, in which the velocity of fluid past the surface is reduced due to no-slip condition, to reach the surface on which it binds, and this probably affects the apparent binding-rate constant. Obtaining the true binding-rate constant will therefore require accounting for the diffusion of the protein through the stagnant boundary layer.
We then investigated the real-time dynamics of transcription by T7 RNAP on single combed DNA molecules. In similar experiments performed previously (
23), fluorescently stained uridine triphosphate (UTP) was used in the reaction mixture, where it was incorporated into the growing RNA transcripts and appeared as visible spots along combed DNA, as we also observe in A. The previous work successfully demonstrated that sequence-specific protein-DNA interactions can be observed on combed DNA, but it provided no information on the dynamics of the process because of the high background fluorescence of the free UTP. In ordinary epi-fluorescence microscopy this background fluorescence obscures the view of the RNA transcripts, which can only be observed after stopping the reaction and washing out the free UTP's, as we also did to obtain A. However, we were able to overcome this problem by using TIRF microscopy which only illuminates fluorophores very close to the substrate. This allows one to follow in real-time the trajectory of T7 RNAP both by visualizing the RNAP-RNA transcript elongation complex (RPT-EC) as it is synthesized from fluorescently labeled UTP's during transcription elongation and by directly visualizing the RPAB elongation complex (RPAB-EC).
The sequence of images in B and C shows examples of the RPT-EC moving along a single combed T7 DNA molecule incorporating fluorescent UTP into RNA. In C, a new fluorescent spot appears at
t = 76

s as fluorescent UTP is incorporated into the location (topmost bright dot). The transcription rate of RPT-EC can be obtained by tracking pixel positions in each frame and assuming 0.34

nm rise/bp for a B-form DNA (since transcription does not occur along overstretched DNA) as shown in D. The RPT-EC stalls when it encounters a point at which the DNA is attached to the surface. At an attachment point, RPT-EC halts presumably due to lack of space for the complex to rotate around the helix (
11,
31). The mean transcription rate is found to be 42 ± 8

nt/s (
n = 16) for 0.2

mM NTPs, which agrees well with recent single molecule measurement under similar conditions (43 ± 3.2

nt/s for 0.25

mM NTP) (
15), obtained using a DNA molecule anchored both ends to beads held in optical traps. This transcription rate is faster than that of
E. coli RNAP (4–7

nt/s for 0.2

mM NTP
12 and 5–15

nt/s for 0.1

mM NTP) (
8,
9).
The sequence of images in A shows one of the examples of RPAB-EC translocating along a single combed T7 DNA. Using RPAB enables us to study transcription rates as a function of NTP concentration, which is difficult to achieve with RPT-EC, since at higher concentrations of fluorescent UTP there is excessive background light even when TIRF is used. The transcription rates at different NTP concentrations, inferred from RPAB-EC imaging, are shown in B. The transcription rate is observed to be 30 ± 8

nt/s (
n = 11) for 0.1

mM NTP, 49 ± 4

nt/s (
n = 9) for 0.2

mM NTP, 72 ± 13

nt/s (
n = 12) for 0.4

mM NTP, and 95 ± 15

nt/s (
n = 12) for 0.6

mM NTP. Transcriptional pausing and arrest that have been observed for
E. coli RNAP were not detected in RPT-EC and RAB-EC imaging within our optical resolution. We also estimate from the Lineweaver–Burke plot in C the maximum transcription rate
Vmax and the Michaelis constant
KM, which is the NTP concentration at which the reaction rate is half maximal. We obtain
Vmax = 149

nt/s and
KM = 0.4

mM from linear relationship of the plot. Thomen
et al. previously obtained the following expression for
KM by measuring transcription rates on the DNA under varying tensions imposed using an optical trap (
15)
where
δ is enzyme step size (= 1

bp) and
Kdiss is the dissociation constant for NTP binding. Using their values for
Kdiss = 0.124

mM, and
K = 0.27, and fitting the above formula to our data in , we obtain an average force of
F = 25 pN applied on our combed DNA molecules capable of interacting with proteins. At this force, the DNA is fully stretched (
32,
33), but not overstretched (i.e. stretched beyond the B-form contour length, which does occur for some DNA molecules are at the pH condition we used for combing) (
26).
In summary, we have investigated the real-time dynamics of the 1D diffusion of fluorescently labeled T7 RNAP along a combed DNA, the association kinetics of promoter binding, and the rate of transcription as a function of NTP concentration. We have fluorescently labeled T7 RNAP with primary and secondary antibodies, yielding a protein complex fully capable of binding to the DNA, initiating transcription and elongating the RNA molecule. We have visualized for the first time that T7 RNAP, upon encountering DNA molecules, diffuses one-dimensionally along the contour of the DNA molecule, which we had aligned orthogonally to the bulk flow. The 1D diffusion coefficient and diffusion length vary over a large range, almost two decades, suggesting inhomogeneity in the molecular properties revealed by single-molecule analysis. We note that a previous study of 1D diffusion of LacI repressor labeled by green fluorescent protein by Wang
et al. yielded an even larger molecule-to-molecule variation in 1D diffusivity, namely over three decades (
21). The apparent association rate obtained in our experiment is in good agreement with previous reported value for Lac repressor binding to the target on a surface, although the diffusion through a stagnant boundary layer should be accounted for when comparing with bulk values. We have also visualized the transcriptional motion of RPT-EC and RPAB-EC along individual combed T7 DNA molecules. The transcription rates of RPT-EC and RPAB-EC seem to agree well with previous single-molecule measurements, when the tension on the combed DNA molecules is accounted for. These results indicate that both diffusive and processive motion as well as enzymatic activity of proteins can be observed on DNA that has been deposited onto a surface, for example by molecular combing.