Unravelling the Mechanism of RNA-Polymerase Forward Motion by Using Mechanical Force

Polymerases form a class of enzymes that act as molecular motors as they move along their nucleic acid substrate during catalysis, incorporating nucleotide triphosphates at the end of the growing chain and consuming chemical energy. A debated issue is how the enzyme converts chemical energy into motion [J. Gelles and R. Landick, Cell 93, 13 (1998)]. In a single molecule assay, we studied how an opposing mechanical force affects the translocation rate of T7 RNA polymerase. Our measurements show that force acts as a competitive inhibitor of nucleotide binding. This result is interpreted in the context of possible models, and with respect to published crystal structures of T7 RNA polymerase. The transcribing complex appears to utilize only a small fraction of the energy of hydrolysis to perform mechanical work, with the remainder being converted to heat.

Figure 1

Experimental configuration: the DNA template is lambda phage DNA (48502 base pairs, about $16\mu \mathrm{m}$ in length) in which a T7 promoter is introduced at one end [20]. The other end of the DNA carries a digoxygenin and is attached to a microscopic bead coated with an antibody directed against digoxygenin. The transcribing polymerase is biotinylated at its N terminus [21] and binds to a streptavidin coated solid surface. To detect tethered beads a flow is created. After selecting a tethered bead under the microscope, the four types of nucleotides are added to the sample. The enzyme pulls the bead as it transcribes the DNA, thereby shortening the tether. The bead is held in an optical tweezers equipped with force measurement [15]. Measurements are performed in a feedback mode where a constant force can be maintained on the DNA: the voltage corresponding to the measured force is fed back to a piezoelectric translation stage that laterally displaces the sample while the trap position is fixed. In this mode, the translocation of the enzyme along DNA is reflected by the displacement of the sample. The electronic time constant of the force feedback loop is 20 ms. The position and force data are filtered through an antialiasing filter at 44 Hz, sampled with a 16 bit analog to digital conversion at a rate of 100 Hz and are stored onto a hard disk. The buffer, the sample holder, and the objective are temperature regulated at 27 °C. In order to avoid potential photodamage of the polymerase by the optical tweezers, we have taken the precaution of preventing the laser from impinging on the enzyme. This is possible because of the length of the DNA template.

Figure 2

Examples of experimental recordings: the measurements were performed at forces near 5 pN. Extension (Ex), i.e., the distance between the polymerase and the bead, is plotted vs time. Transcription is revealed by the decrease of Ex. For each curve, extension and time have been shifted for comparison. Each curve corresponds to a different polymerase; the NTP concentrations are indicated in the figure. As a control we plot two Ex($t$) curves obtained with a simple DNA construction attached between the surface and the bead. The average velocity of the enzyme (over at least 8 sec) is extracted from those curves.

Figure 3

Lineweaver-Burke plot of the experimental data: the inverse of the average velocity $1/⟨V⟩$ is plotted as a function of $1/C_0$ for three forces: $5\pm 1\mathrm{p}\mathrm{N}$ (squares), $11\pm 0.7\mathrm{p}\mathrm{N}$ (circles) and $15.5\pm 1.5\mathrm{p}\mathrm{N}$ (triangles). The error bar displayed is the “error of the mean”, i.e. $(\mathrm{\text{standard deviation}})\times (N{)}^{-1/2}$, where $N$ is the number of data points taken to obtain the average value. Restricting to $1/C_0\le 0.02\mu {\mathrm{M}}^{-1}$, we have plotted linear fits to the data [10]. We obtained $V_{\max }=129\pm 8\mathrm{b}/\mathrm{s}\mathrm{e}\mathrm{c}$, and $K_M(5\mathrm{p}\mathrm{N})=174\pm 17\mu \mathrm{M}$, $K_M(11\mathrm{p}\mathrm{N})=213\pm 22\mu \mathrm{M}$, and $K_M(15.5\mathrm{p}\mathrm{N})=243\pm 27\mu \mathrm{M}$; these results are consistent with previous bulk measurements [22]. Number of points, 395; number of enzymes, 96; time of transcription, 1 h 50 min (1 h 10 min at 5 pN, 30 min at 11 pN, and 10 min at 15.5 pN). Inset: Experimental apparent $K_M$ vs force: the $K_M$ values are deduced from linear fits. The data is fit by the following expression (see text): $K_M(F)=K_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{s}}(1+K\exp [F\delta /\mathrm{k}\mathrm{T}])$, where $\delta$ is enzyme step size, a fixed parameter equal to one base pair. The solid line is the best fit: one gets $K=0.27$ and $K_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{s}}=124\mu \mathrm{M}$. To show the effect of a change in the parameter $K$, the other lines are fits obtained when imposing respectively $\ln (K)=0$ and $\ln (K)=-5$, situations where $E_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}$ would either have the same free energy as $E_{\mathrm{p}\mathrm{r}\mathrm{e}}$, or be more stable by 5 kT.

Figure 4

Reaction cycles. (a) model inspired by Guajardo and Sousa [11]; $E_{\mathrm{p}\mathrm{r}\mathrm{e}}$: pretranslocated enzyme after hydrolysis and PPi release, unable to bind NTP; $E_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}$: posttranslocated enzyme waiting for NTP binding; $E:{\mathrm{N}\mathrm{T}\mathrm{P}}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d}}$: enzyme with NTP bound in proper position in the catalytic pocket; PPi: pyrophosphate [14]. (b) states identified from published crystal structures; $E_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}$ [1, 2] and $E:{\mathrm{N}\mathrm{T}\mathrm{P}}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d}}$ [3] designate the same states as in (a); $E:{\mathrm{N}\mathrm{T}\mathrm{P}}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d}}$: posttranslocated complex with NTP preloaded [4]; $E_{\mathrm{p}\mathrm{r}\mathrm{e}}:\mathrm{P}\mathrm{P}\mathrm{i}$: enzyme after nucleotide hydrolysis, but before PPi release [3]. $E_{\mathrm{p}\mathrm{r}\mathrm{e}}$, corresponds to a pretranslocated transient state [without corresponding crystal structure (see text)].