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-Nørrelykke * 
* The Niels Bohr Institute, Copenhagen, Denmark; European Laboratory for Nonlinear Spectroscopy, Sesto Fiorentino, Italy; and Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany
Correspondence: Address reprint requests to Simon F. Toli-Nørrelykke, Max-Planck Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187 Dresden, Germany. Tel.: 0049-0351-871-1211; E-mail: simonftn{at}pks.mpg.de.
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ABSTRACT |
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INTRODUCTION |
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–3). Also, single-molecule techniques often allow the application of a mechanical force to the system and thus the introduction of a well-defined reaction coordinate (4).
The TATA-box binding protein (TBP) is a small, single-chain, saddle-shaped protein (5), the DNA-binding part of which is highly conserved throughout evolution. The inner, concave side of TBP directly contacts the DNA, whereas the outer and evolutionary more-variable side interacts with various other proteins involved in the regulation of transcription (6). With TBP bound, the DNA is bent by 
80° and locally unwound by 120° (7,8). DNA distortion is thought to play a role in transcription initiation, the distortion influencing recruitment and stabilization of RNA polymerases and associated proteins. Furthermore, this distortion may have a direct mechanical role in chromatin remodeling: Histones have been shown to slide along the DNA upon TBP binding (9). Association of TBP with promoter DNA is a slow process, but after binding the complex can support multiple rounds of transcription initiation (10).
Most DNA-binding proteins interact with DNA through the major groove, where the basepaired sequence is easily accessible. TBP, however, interacts with DNA through the minor groove (7,8) in a manner that differs also from that of other minor-groove-binding proteins (11). The TBP-DNA interaction is well studied at the ensemble level: Bending angles (7,8,12) as well as the specificity of the binding (12–18) to different DNA sequences under various conditions of pH, temperature, osmolyte, and electrolyte concentrations have been revealed using x-rays, electron microscopy, gel-retardation, DNase I footprinting, fluorescence anisotropy, and Förster resonance energy transfer. However, no previously reported studies have addressed this system at the single-molecule level.
TBP is known to bind to several consensus and nonconsensus TATA-boxes (13). The best studied TATA-box is the adenovirus major late promoter (AdMLP), which serves as a reference example of TBP-DNA interactions. When binding to the AdMLP, TBP has to overcome an activation barrier of nearly 10 kcal/mol, but once bound, the protein resides in an energetic minimum that is almost 11 kcal/mol deep (17). A careful analysis of ensemble data taken at a range of temperatures and protein concentrations led to a prediction of two intermediate states on the reaction pathway between the initial, unbound state and the final, bound state (17). The structure of the TBP-DNA complex in these intermediate states is not known, but was proposed (17) to be nearly identical to the final bound form. However, direct observation of these intermediates has not previously been reported.
We set up a tethered-particle-motion system (19,20) to study the interaction between TBP and DNA at the single-molecule level. A microsphere (i.e., bead) was tethered to a microscope coverslip by 324 bp of DNA. In the center of the DNA sequence we placed a TATA-box, the rest of the DNA contained no TATA-like sequences. Using video microscopy, we followed the Brownian motion of the bead and from this motion constructed a measure for the conformation of the DNA tether. Upon introduction of TBP, we observed a decrease in Brownian motion and interpreted this decrease as the binding of TBP to the DNA. A series of control experiments were undertaken to ensure that the observed effect was caused by active TBP, binding specifically to the TATA-sequence. We showed that TBP can be forced off the TATA-box sequence by increasing the electrolyte concentration or by mechanically pulling on the DNA using laser tweezers. The choice of a short DNA-tether and relatively large beads ensured that any change in conformation of the DNA was amplified into a larger change in the position of the tethered bead. Using this system, we studied the binding kinetics of TBP to DNA and showed by direct observation that at least one of the intermediate states is less bent than the final state. This constitutes the first direct observation of a structural intermediate on the TBP-DNA binding pathway, a finding that may have implications for our understanding of the regulation of transcription initiation.
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MATERIALS AND METHODS |
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) for details). DNA-tethers without the TATA-box (i.e., control-DNA) were produced by site-directed mutagenesis using PCR to have the XhoI recognitions sequence (underlined) 5'-TACTCGAG-3' at position 155. We screened the DNA for consensus as well as nonconsensus TBP binding sequences known from the literature (18,22–26). In the TATA-DNA, we found no high-affinity sequences other than the AdMLP TATA-box and in the control-DNA, we found no high-affinity sequences.
Beads
The beads used were streptavidin-coated polystyrene spheres of diameter d = 0.46 µm (Bangs Laboratories, Fishers, IN), as well as 1.0-µm streptavidin-coated silica spheres (Spherotech, Libertyville, IL). One end of the DNA tether was specifically attached to the avidin-coated microsphere by biotin-streptavidin binding. The other end was attached to a glass coverslip by digoxigenin/anti-digoxigenin interaction. Nuclease-free bovine serum albumin (BSA; Roche Diagnostics, Indianapolis, IN) was added to the beads to a final concentration of 1 mg/ml and incubated for >14 h at 4°C before use, to suppress sticking to the glass coverslip. Fig. 1 shows a schematic drawing of the setup.
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) and Petri et al. (27). The protein was stored at –80°C, at a concentration of 33.9 µM, in Buffer A (25 mM HEPES-KOH, 2.7 M glycerol, 1 mM EDTA, 1 mM DTT, pH 7.9) until immediately before use, at which time it was thawed, diluted in Buffer 1 (10 mM Tris-HCl, 100 mM KCl, 2.5 mM MgCl2, 1 mM CaCl2, 1 mM DTT, pH 7.4) to the working concentration of 50–678 nM, and kept on ice between experiments. The stock concentration of TBP was determined from the absorbance at 280 nm using an extinction coefficient of 12,700 M–1 cm–1 (27). TBP is monomeric under the conditions and concentrations used in the experiments described here (17,28).
Preparation of samples
Microscopy flow cells (20 µl) were prepared by placing one coverslip No. 0 on top of another, separated by spacers made from a single thickness of Parafilm (American National Can, Menasha, WI) coated with silicone vacuum grease (Dow-Corning, Midland, MI). Anti-digoxigenin was attached to the working surface by injecting the flow cell with 20 µg/ml anti-digoxigenin in PBS and incubating at 4°C for >14 h. The flow cells were then washed with 3 x 100 µl Buffer 1, incubated with DNA for 15 min, and again washed with 3 x 100 µl Buffer 1. To suppress nonspecific binding of beads and TBP to the surface, the flow cells were incubated with 2 mg/ml BSA in Buffer 1 for 15 min saturating all surfaces with BSA. Samples were mounted on a microscope for observation, and beads were flowed in at high concentrations (40–160 pM) and allowed to form tethers for 20 min before unbound beads were removed by washing with 3–5 x 100 µl Buffer 1.
Video microscopy and optical tweezers
Timelapse video images for the experiments using silica beads were acquired using a modified microscope (Model No. DM IRB, 100 x oil-immersion objective; Leica, Heerbrugg, Switzerland (29)). Bead positions were determined in each video-frame using a cross-correlation type tracking algorithm written in MatLab (The MathWorks, Natick, MA) (21). The laser tweezers experiments were also performed on this setup.
To zoom in (temporally) on the binding step, a different microscope was used (Eclipse Model No. TE300, 60x water immersion objective; Nikon, Tokyo, Japan (30)). Bead positions were determined by using a thresholded centroid-tracking method for each of the two deinterlaced videofields that comprise a videoframe, thus obtaining a time resolution of 1/50 s.
Brownian motion measure
The shortness of the DNA ensured that tethered beads stayed in the focal plane of the microscope. Motion perpendicular to the surface was not detected. Motion parallel to the surface, in the (x,y)-plane, was detected using one of the two above-mentioned tracking algorithms. Time-series of (x,y)-positions were broken into nonoverlapping segments and the variances, 
and 
, were calculated in each segment. As measure for the Brownian motion of a tethered bead, we chose the root mean-square deviation (RMSD), 
. Additional measures were applied that allowed us to distinguish between beads tethered by one, two, or more DNA-molecules (see Appendices A and B, and Fig. 6).
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Tethers
A concentration series of DNA showed that the number of tethered beads varied linearly with the amount of DNA, with few or no beads tethered when no DNA was present and saturation at high DNA concentrations. Flow cells prepared without anti-digoxigenin lead to a >90% decrease in the number of tethers formed, as did preblocking the streptavidin-coated beads with saturating amounts of biotin.
Effect of glycerol
The presence of osmolytes, e.g., glycerol and glucose, have been reported to dramatically increase both binding affinity and bending angle for TBP binding to DNA (12). Since our protein was stored in a glycerol-rich buffer, we decided to investigate the effect of glycerol on our single-molecule experiments. We added 226 nM TBP in 0.91 M glycerol (1/3 Buffer A and 2/3 Buffer 1) to flow cells with beads tethered by either TATA-DNA or control-DNA. Essentially all of the tethered beads showed large and instant decreases in Brownian RMSD, making it impossible to distinguish between beads tethered by TATA-DNA and beads tethered by control-DNA. To avoid this effect, all experiments reported hereafter were conducted at 4–18 mM glycerol. This is within the range of intracellular concentrations found in S. cerevesiae at different growth stages (31), and below the concentration where bend-angles are expected to be affected (12). The effect of osmolytes on the binding to nonspecific versus target DNA was recently reported in detail for the lac repressor system (32).
Protein
TBP not competent in binding DNA might interact with the bead directly by sticking to the glass and the bead simultaneously, or indirectly through entropic effects (33). Such interaction would influence the motion of the bead and hence also the conformations of the DNA. To clarify whether any such effects were present, we conducted experiments with heat-inactivated protein: TBP was incubated at 100°C for 5 min, allowed to cool to room temperature, and then added at a concentration of 226 nM to microscopy samples with either TATA-DNA tethers or control-DNA tethers. No change in the Brownian RMSD of the tethered beads was observed in samples where inactivated TBP was added.
Specificity of TBP binding
To investigate whether the interaction between TBP and DNA was confined to the TATA-box of the DNA we used the control-DNA described above. Any effect of TBP on the Brownian motion of beads tethered by control-DNA would be caused by nonspecific interactions between TBP and DNA, since no TATA-box is present in this tether. At low concentrations of TBP (<100 nM) we detected no change in the Brownian RMSD of beads tethered by control-DNA. At intermediate concentrations (226 nM), a small fraction of beads tethered by control-DNA showed brief (1 min), minor (10 nm) decreases in Brownian RMSD. At high concentrations of TBP (678 nM), beads tethered by control-DNA showed abrupt decreases in Brownian RMSD, often resulting in the bead becoming irreversibly stuck on the coverslip—this behavior was also observed for beads tethered by TATA-DNA. We interpret this latter high-concentration-behavior as the collapse of DNA induced by nonspecific action of the protein, a process also observed in the nonspecific interaction of other proteins with DNA (34,35). To collect the data summarized in Fig. 3 we used 226 nM TBP, and for the data shown in Fig. 4, we worked at 50–100 nM TBP.
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RESULTS AND DISCUSSION |
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75 nm; 200 s after addition of TBP, decreased abruptly to 50 nm; finally, after exposure to 1 M KCl and washing with Buffer 1, the Brownian RMSD returned to 75 nm. We interpret this type of behavior as the specific binding of TBP to the recognition sequence in the middle of the DNA, concurrent with a decrease in Brownian RMSD (henceforth referred to as a "binding event"). Addition of a high concentration of salt was followed by an increase in Brownian RMSD. We interpret this increase as the release of TBP from the TATA-box (henceforth referred to as a "dissociation event"). The inset in Fig. 2 shows a scatterplot of the positions visited by the DNA-tethered bead. The recorded positions visited before TBP bends the DNA-tether are shown as shaded points connected by lines. Solid dots and lines show the recorded positions visited after TBP has bound to and bent the DNA-tether. The positions visited by the bead are isotropically distributed in the (x,y)-plane, both before and after addition of TBP.
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When flowing in 1 M KCl we consistently, after a brief waiting time, saw return to the value it had before the addition of TBP. We interpret this as the release of individual molecules of TBP from single DNA-tethers. Any nonspecific, as well as specific, interaction keeping the TBP in contact with the DNA under normal conditions is suppressed at this concentration of salt because the electrostatic interactions are screened. Thus, once no longer bound to the TATA-box, the protein is expected to diffuse away from the DNA-tether.
Another way to force TBP off DNA is by stretching the tether using an externally applied mechanical force (36). As a proof of principle, experiments were performed using laser tweezers to pull on the bead, thereby stretching the DNA and forcing the protein off. These experiments are described in Appendix C. Our observations are in accordance with previously published results, showing that proteins do not stay as readily attached to stretched DNA as to relaxed DNA (37,38).
Binding kinetics
We investigated the binding kinetics by measuring the time elapsed between the addition of TBP and the first detected decrease in Brownian RMSD. In Fig. 3, a histogram of these waiting times is shown. If the binding of protein to DNA has a constant probability of success per time interval it is a Poisson process. The waiting times are then exponentially distributed. A fit of a single exponential to the data returned a time-constant of 143 s. The corresponding second-order association rate constant is ka = [TBP]–1
–1 = (3.1 ± 0.5) x 104 M–1 s–1 (mean ± SE, n = 45). This value is in rough agreement with values determined in ensemble experiments performed under similar buffer conditions and temperature (ka = 8–14 x 104 M–1 s–1 (17,25)). The difference, if any, could be caused by a lower than assumed concentration of binding-competent TBP in our experiments—the presence of surfaces is expected to diminish the amount of TBP through adsorption and denaturation (39,40). Furthermore, the protein is very sensitive to repeated freeze/thaw cycles: We kept these to a minimum, but the experimental protocol meant that a few cycles of freeze/thaw could not be avoided. Finally, the proximity of the tethered bead to the coverslip gives rise to a force on the DNA-tether due to excluded volume effects (41). This force is expected to suppress the rate of association by 25–50% (see Appendix D).
Dissociation kinetics
Characteristic times for the single-exponential decay of the TBP-AdMLP complex have been reported in the range from 10 to 170 min (14,15,17,26,42). The existence of an additional, fast phase in the dissociation, nearly two orders-of-magnitude faster than the dominant slow phase, was revealed only by detailed kinetic studies (17).
We did not determine the kinetics of spontaneous dissociation in our experiments. An experiment was typically ended after 15–20 min by exchanging the assay-buffer with 1 M KCl, and then looking for dissociation events. We did this to confirm that any observed change in Brownian RMSD was caused by TBP-DNA interactions. Furthermore, tethered beads had a tendency to get stuck on the coverslip after extended observation, thus terminating any further observation.
Intermediate states
To further investigate the binding kinetics, we modified the experimental setup. By using polystyrene beads of a smaller diameter (0.46 µm instead of 1.0 µm) as well as separately analyzing each of the two videofields that constitute a videoframe, the temporal resolution was increased. The TBP concentration was 50–100 nM, i.e., lower than in the experiments described above. At these protein concentrations 50% of the tethers showed binding events. The expected equilibrium dissociation constant for the TBP-DNA interaction is 16 nM, with the buffer and temperature conditions used here (17). However, due to the previously mentioned effects of surfaces, freeze/thaw cycles, and tension in the DNA, the observed single-molecule dissociation constant is expected to be higher. During 10 out of 11 observed binding events, the Brownian RMSD was observed to decrease and sometimes increase in a stepwise manner in the presence of TBP (see Fig. 4). The kinetic scheme suggested in Parkhurst et al. (17) (with boxes added by us):
 , |
).
In an experiment where only the first and the last state is resolved, the forward reaction can be described by a second-order association rate constant ka that depends on the microscopic rate constants ki, i = 1...6 (17). This rate-constant ka is the one cited above, because we were not able to discern intermediates using the silica beads (chosen for their high optical trapping efficiency, see Appendix C). In the following, we distinguish between the observed classes of Brownian motion, and their interpretation in terms of different underlying states of the TBP-DNA complex.
Three classes of Brownian motion were observed in the histograms
Fig. 4 shows three examples of the time-development of as well as histograms of . Each histogram shows a distribution of the Brownian RMSD with three separate peaks. Based on such histograms we divided the Brownian motion into three classes. Each of these three classes must correspond to a different conformation of the TBP-DNA complex:
-class is defined from the Brownian RMSD observed before addition of TBP. Thus, the -class corresponds to DNA that is not bound by TBP, but includes also the transient encounter complex that is implicit in all bimolecular reactions. 
-class is defined from the Brownian RMSD observed several minutes after addition of TBP. We identify this class with a superposition of the final bound state and the second intermediate state I2 (see discussion below). 
-class was a surprise. It is defined from the Brownian RMSD that was of a magnitude midway between the - and -classes. We interpret this class as corresponding to the first intermediate state I1.
Each of these three classes is indicated by a box in the kinetic scheme shown above. The observed Brownian RMSD in each class was: 71 ± 7 nm (-class), 56 ± 7 nm (-class), and 46 ± 10 nm (-class), respectively (means ± SDs, n = 10 individual tethers). The three classes differ from each other with statistical significance: = with P = 8.3 x 10–5, = with P = 6.3 x 10–4, and = with P = 1.6 x 10–5 using right-tailed t-tests.
A fourth class of Brownian motion was observed in the time-series
The histograms do not show a second intermediate with a Brownian RMSD different from that of the three classes already mentioned. Assuming the existence of a second intermediate state I2, this lack of its observation suggests that the I2 state is structurally similar to the final-bound state and for that reason does not show up as a separate peak in the histograms of . However, there is valuable extra information in the time-series of compared to the histograms of : The temporal development of in Fig. 4 shows an initial period of multiple transitions to and from the lower class (e.g., Fig. 4 A, t 
[100:325]), followed by a quiescent period with no transitions (Fig. 4 A, t [325:650]). That is, we observed two classes of with the same Brownian RMSD but with different stability. We interpret this as the existence of two states of the TBP-DNA complex with equally bent DNA, but with different stabilities. We identify the first period (fast dynamics) with the second intermediate state I2, and the second period (slow dynamics) with the final-bound state. The rate constants determined in Parkhurst et al. (17) indicate that the second intermediate should indeed be populated for only very short periods of time (mean-occupancy-time = (k4 + k5)–1 = 1.2 s), whereas the final state is populated for a much longer time (1/k6 = 282 s). Without a second intermediate, we cannot explain the observed rapid transitions from the -class.
Comparison of rate constants to ensemble values
From manual inspection of 10 time-series of , we estimated the two microscopic rate-constants k1 and k3, and the macroscopic rate-constant ka. From the time spent in the -class, after addition of TBP and until a transition to the -class, we found k1 = 1.6 ± 0.5 µM–1s–1 (mean ± SE, n = 10), in agreement with the ensemble value (1.59 µM–1 s–1, (17)). From the -class we measured transitions to the -class and found k3 = 0.054 ± 0.016 s–1 (mean ± SE, n = 11) again in reasonable agreement with the ensemble value (0.030 s–1, (17)). Finally, from the waiting time between addition of TBP and until reaching the final-bound state we found ka = (9 ± 3) x 104 M–1 s–1 (mean ± SE, n = 8), in agreement with reported ensemble values (17,25) and with the value we found using silica beads. The remaining microscopic rate-constants could not be determined with sufficient accuracy, due to the finite time-resolution and sample size, to allow comparison with ensemble data.
What are the structures of the intermediates?
Co-crystal structures of TBP bound to the AdMLP TATA-box show two sharp kinks in the DNA (7,11). The first kink occurs where two phenylalanine residues intercalate between the first two basepairs. The second kink occurs where another pair of phenylalanine residues is inserted between the last two basepairs (5' – T
ATAAAAG – 3', triangles indicate intercalations). Both sets of intercalations produce DNA-kinks of 45° (7,11). Based on the crystal structure, the most straightforward interpretation of our data assigns one pair of intercalations to the -class and another pair to the -class. The high flexibility of the 5'-end of the TATA-box implies that this is where the first pair of intercalations is most likely to take place (43), whereas the more rigid 3'-end (A-tract) is expected to delay the second set of intercalations. We therefore propose the following sequence of events:
), as well as the formation of van der Waals' contacts between the minor groove of the DNA and the concave surface of the TBP, leading to the stable structure known from crystallography (7,11).
Assuming a three-step pathway, there are two other possible assignments for the two pairs of intercalation events, both of which have previously been proposed: The first set of intercalations takes place in Step 2 and the second set in Step 3 (17). Alternatively, the first set of intercalations take place in Step 1 and the second set in Step 3 (25). Based on the data presented in this article, we favor the first model over the latter two. However, we emphasize that it is not possible to make any definitive distinction between these three models based on the existing data—all assignments of structures to states are speculation, so far.
What are the biological implications of the intermediates?
From in vitro experiments, a picture of the assembly of the transcription preinitiation complex (PIC) has emerged (44). In this picture, assembly takes place in steps: TBP binds to DNA, followed by the binding of TFIIB, after which a preformed complex that includes the polymerase is recruited. Later yet, additional factors bind to the complex. It is possible for TFIIA to enter the PIC at any point after TBP. Now, assume that the I1-state exists and has a single kink in the upstream part of the TATA-box. This will allow TFIIA to bind stably to the complex, since this factor makes contacts only with upstream DNA-sequences and TBP (45,46). On the other hand, TFIIB makes contacts with both upstream and downstream DNA, as well as the TBP (47). In the one-kink I1-state, geometry dictates that proximal to the TBP, upstream and downstream DNA is further apart than in the two-kink I2-state. In the I1-state therefore, the formation of a stable association between TFIIB and DNA will presumably be suppressed. In the I2-state both pairs of phenylalanine intercalations are in place, the DNA is fully bent, and TFIIB can form the contacts known from its crystal structure (47). Thus, we arrive at a picture in which assembly of the PIC can proceed already from the I1-state, and in which the structural conformation of I1 suggests an ordering of events with TFIIA binding before TFIIB (see Fig. 5). The kinetics of the I1-state may facilitate the correct orientation of DNA-bound TBP, as discussed in Parkhurst et al. (17).
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CONCLUSIONS |
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Intriguingly, changes in Brownian motion during a binding event revealed the existence of two intermediate states on the binding pathway. This constitutes the first direct experimental corroboration of a model suggested in Parkhurst et al. (17), in which the kinetic pathway of the TBP-DNA interaction has two such intermediates. By direct observation of individual departures and their time of occurrence, we measured kinetic constants describing rates to and from the intermediate states. These rates were in agreement with the model-dependent rates derived in Parkhurst et al. (17) and thus support the kinetic scheme given there. However, contrary to what is speculated in Parkhurst et al. (17) and Powell et al. (25), we found that the DNA is less bent in the first intermediate than in the final complex. This, in turn, might have implications for the order of the assembly of the transcription preinitiation complex, favoring the association of TFIIA before TFIIB.
The results presented here prove that it is possible to make time-resolved observations of single binding and dissociation events of TBP to promoter DNA. This shows that DNA-distortions that are much less dramatic than, e.g., the looping induced by the lac repressor (48), can be reliably detected using well-established single-molecule techniques. Furthermore, the work presented here opens the door to a number of studies of the system, such as quantitative measurements of the force and torque dependence of rate-constants describing the TBP-DNA interaction.
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APPENDIX A: BROWNIAN MOTION MEASURE |
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 | (1) |
The principal moments are the entries of the diagonalized matrix, and we denote them Imin and Imax in order of increasing magnitude. They are
 | (2) |
 |
 |
 |
and 
are averages calculated from the N positions in each segment. The sum of the principal moments equals the sum of the variances along the x- and y-axes: Imin + Imax = + . As a measure for the amplitude of the Brownian motion of a tethered bead we used 
and as a measure for the isotropy of the bead-motion we used the ratio 
Thus, is the RMSD for the positions visited by a tethered bead. The isotropy-measure was 50–100% for a bead with only a single DNA tether. If r was consistently smaller than 50% we interpreted this as a bead tethered by two DNA molecules, a polystyrene link, or some other, nonspecific interaction, and discarded the data. An example of nonisotropic motion is shown in Fig. 6. |
APPENDIX B: MULTIPLE TETHERS |
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An example is shown in Fig. 6: This scatter-plot of bead positions indicates that two DNA-molecules tethered the bead. Addition of restriction enzyme lead to a stepwise change in Brownian motion, with interpretation: Initially the bead was tethered by two DNA molecules. The presence of two tethers broke the rotational symmetry of the setup and forced the bead to move in a quasi-one-dimensional fashion. After 120 s, an enzyme cut one of the DNA tethers and rotational symmetry was restored. After an additional 40 s, the other DNA tether was also cut, and the bead diffused away (see movie in Supplementary Material).
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APPENDIX C: LASER TWEEZERS STRETCHING EXPERIMENTS |
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The Brownian motion of the tether was measured before and after each of these steps. Tension was applied by moving the laser back and forth over the tethered bead six times: The peak-to-peak distance of the motion was 5 µm and the speed was kept constant at 0.1 µm/s, i.e., this procedure lasted 5 min. The maximum force exerted on the silica bead by the laser tweezers was estimated to be 38 ± 4 pN by an escape-method calibration (49).
Fig. 7 shows how the Brownian motion changed during the laser tweezers experiment. Before TBP was flowed in (at t = 0 s), was equal to the length of a normal, unbent tether. After TBP was flowed in, it bound to DNA. Unbound TBP was washed out 20 min after it was flowed in, the Brownian motion was measured, and the laser tweezers were applied for the 5-min stretching procedure. After application of the laser tweezers, returned to the value of an unbent DNA tether. We interpret this length-change as the dissociation of TBP from DNA. Due to irreversible sticking of the bead to the coverslip, the Brownian motion of the tethered bead was determined in only four cases after application of the laser tweezers. Results similar to those shown in Fig. 7 were found in all cases.
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APPENDIX D: WEAK ENTROPIC FORCES TENSE THE DNA-TETHER |
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 | (3) |
g(l) 
e–E(l)/kBT is the Boltzmann weight-factor, and E(l) is the energy associated with the tether extension (see Fig. 8). Integrating over 
, ß, 
, and 
, we are left with
 | (4) |
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 | (5) |
,
 | (6) |
If the tether is a stiff rod of length , g(l) 
(l – ), where is Dirac's -function. In this case, the tension is given by the simple expression
 | (7) |
Because work is done against a force when DNA is bent by TBP, the rate of association is expected to be reduced. Making the approximation that the association rate-constant decreases as
 | (8) |
): In bulk, the end-to-end distance of 300 bp dsDNA is 15% shorter than its contour length (51). Thus, when no external force is applied, the end-to-end distance of a 324-bp DNA is expected to be 94 nm, assuming a 0.34 nm axial rise per bp (52). If we model the DNA as a stiff rod of length = 94 nm, an 80° kink in the middle of the rod, decreases the end-to-end distance of the rod by 
= 22 nm. The actual change in end-to-end distance is likely to be somewhat smaller due to the flexibility of the DNA and the presence of the force FDNA. A lower limit of 
7.3 nm is set by Förster resonance energy transfer experiments (18). |
SUPPLEMENTARY MATERIAL |
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ACKNOWLEDGEMENTS |
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-Nørrelykke for comments on the manuscript. This work was supported by the Danish Research Councils and the Carlsberg Foundation.
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FOOTNOTES |
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Submitted on September 23, 2005; accepted for publication February 6, 2006.
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ABSTRACT
INTRODUCTION
and 
are shown in shaded and solid representations, respectively. During the first 120 s, the motion of the bead was highly anisotropic (isotropy measure, r = 39%). After 120 s, the motion of the bead was isotropic (r = 94%); the bead released from the surface after 160 s.
60 s (indicated by vertical dashed line). We proceeded by excluding from further analysis all events in the first 60 s (n =3). A maximum likelihood, single-exponential fit returned a characteristic time of 
. The value 
and the surface normal, and 
around the surface normal through P. Rotation of the sphere around