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. Author manuscript; available in PMC: 2007 Oct 24.
Published in final edited form as: Mol Cell. 2007 May 11;26(3):335–347. doi: 10.1016/j.molcel.2007.03.024

A Non-uniform Stepping Mechanism for E. coli UvrD Monomer Translocation along Single Stranded DNA

Eric J Tomko 1, Christopher J Fischer 1,#, Anita Niedziela-Majka 1, Timothy M Lohman 1,*
PMCID: PMC2041850  NIHMSID: NIHMS23899  PMID: 17499041

Summary

E. coli UvrD is an SF1 helicase involved in several DNA metabolic processes. Although a UvrD dimer is needed for helicase activity, a monomer can translocate with 3′ to 5′ directionality along single stranded DNA and this ATP-dependent translocation is likely involved in RecA displacement. In order to understand how the monomeric translocase functions, we have combined fluorescence stopped-flow kinetic methods with novel analysis methods to determine the kinetic mechanism, including ATP coupling stoichiometry, for UvrD monomer translocation along ssDNA. Our results suggest that the macroscopic rate of UvrD monomer translocation is not limited by each ATPase cycle, but rather by a slow step (pause) in each translocation cycle that occurs after four to five rapid one nucleotide translocation steps, with each rapid step coupled to hydrolysis of one ATP. These results suggest a non-uniform stepping mechanism that differs from either a Brownian motor or previous structure based inch-worm mechanisms.

Keywords: helicase, motor protein, fluorescence, translocase, kinetics, ATPase

Introduction

Helicases are a ubiquitous class of motor enzymes that couple nucleoside triphosphate (NTP) binding and hydrolysis to translocation along single stranded (ss) nucleic acids and unwinding of duplex DNA or RNA(Delagoutte and von Hippel, 2003; Lohman and Bjornson, 1996; Lohman et al., 2003; Patel and Donmez, 2006). Such enzymes are responsible for generating the obligate ssDNA intermediates required for DNA metabolism. A necessary feature of helicases that unwind DNA processively is that they must also translocate along ssDNA with biased directionality and some can also actively displace proteins from nucleic acids (Byrd and Raney, 2006; Eggleston et al., 1995; Fairman et al., 2004; Howard et al., 1994; Jankowsky and Bowers, 2006; Krejci et al., 2003; Mackintosh and Raney, 2006; Veaute et al., 2003, 2005).

E. coli UvrD is a superfamily 1 (SF1) DNA helicase that functions in methyl-directed mismatch repair (Modrich, 1991), DNA excision repair (Sancar, 1996), replication restart (Flores et al., 2004; Flores et al., 2005; Michel et al., 2004), and plasmid replication (Bruand and Ehrlich, 2000) and it can also dismantle RecA protein filaments formed on ssDNA (Veaute et al., 2005), presumably by displacing RecA from ssDNA. The S. cerevisiae Srs2 helicase has a similar activity towards Rad51 nucleoprotein filaments (Krejci et al., 2003; Veaute et al., 2003). In fact, mutations in UvrD and Srs2 both show hyper-recombinational phenotypes presumably due to an inability to disrupt such filaments (Krejci et al., 2003; Veaute et al., 2003). Similarly, the Pif1 helicase can displace telomerase from telomeric DNA ends (Boule et al., 2005). Although the ability to displace proteins from DNA is NTP-dependent, it may not require helicase activity per se, but only translocase activity. This is underscored by the fact that helicase activity generally requires more than an ability to simply translocate with directionality along ssDNA (Brendza et al., 2005; Fischer et al., 2004). In fact, monomers of E. coli UvrD are able to translocate with 3′ to 5′ directionality along ssDNA, although they cannot unwind DNA in vitro (Fischer et al., 2004). Although recent crystal structures of UvrD monomers bound to a ss-ds-DNA junction have assumed that a monomer is the active helicase (Lee and Yang, 2006), solution studies indicate that at least a dimer of UvrD is needed for helicase activity in vitro (Ali et al., 1999; Fischer et al., 2004; Maluf et al., 2003a,b).

In order to understand a simple molecular motor we are studying the kinetic mechanism of UvrD monomer translocation along ssDNA. This information will also be important for understanding how translocation is used within the context of the dimeric UvrD helicase (Maluf et al., 2003a,b). Several models, such as inch-worms (Lee and Yang, 2006; Soultanas and Wigley, 2001; Velankar et al., 1999; Yu et al., 2006) and Brownian motors (thermal ratchets) (Levin et al., 2005) have been proposed to explain how SF1 or SF2 monomers might translocate along a ss nucleic acid. These models all assume that the rate-limiting step in translocation is repeated within each cycle of ATP hydrolysis, yet this has not been demonstrated. Tests of these models require determinations of the basic kinetic parameters of translocation (i.e., rate, step-size, processivity and ATP coupling stoichiometry).

We previously determined a minimal kinetic mechanism for ssDNA translocation by the UvrD monomer using single turnover (with respect to the DNA) stopped-flow methods (Fischer et al., 2004). UvrD monomer translocation along ssDNA occurs with biased 3′ to 5′ directionality with an overall rate of ~190 nucleotides per second (pH 8.3, 20 mM NaCl, 20% (v/v) glycerol, 25°C). Translocation can be described by a simple sequential n-step kinetic mechanism which assumes that a series of identical rate-limiting “translocation steps” are repeated until the monomer dissociates or reaches the 5′ end of the ssDNA. This analysis suggests that at saturating ATP concentrations, a UvrD monomer moves an average of ~4 nucleotides (termed the kinetic step-size) between two successive rate-limiting “translocation steps” (Fischer et al., 2004). We emphasize that this “kinetic step size” of ~4 nucleotides is defined as the average number of nucleotides translocated between two successive rate-limiting steps, not per ATP hydrolyzed. In fact, whether one or multiple ATP molecules are hydrolyzed per 4 nucleotide “step” was not determined. Here we determine a minimal kinetic mechanism for UvrD translocation and the average number of ATP molecules hydrolyzed per nucleotide translocated (ATP coupling stoichiometry) which provide constraints to assess potential translocation mechanisms.

Results

Experimental Design and Analysis

Approach to determine ATP coupling stoichiometry

In ensemble studies, pre-steady state transient kinetics experiments are required to obtain quantitative information on the rapid kinetic steps that occur during ssDNA translocation (Fischer and Lohman, 2004). We use two such types of experiments depicted in Figure 1. The first is a modification of a method (Dillingham et al., 2000) that uses E. coli phosphate binding protein (PBP) labeled with a fluorescent dye (MDCC) to monitor production of inorganic phosphate, Pi, resulting from ATP hydrolysis by UvrD. One modification that simplifies the analysis (Fischer and Lohman, 2004) is that we perform these experiments under “single round” conditions by including a trap (heparin) for free UvrD with the addition of ATP to eliminate rebinding to the DNA of dissociated UvrD. Heparin is a good trap for this purpose since it binds UvrD but does not stimulate ATP hydrolysis by UvrD.

Figure 1.

Figure 1

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Schematic depictions of the kinetic assays for monitoring ATP hydrolysis and UvrD translocation along ssDNA.

To obtain an accurate estimate of the ATP coupling stoichiometry for any translocase with finite processivity, the above ATPase studies need to be combined with a second set of independent experiments to obtain the kinetic parameters describing UvrD monomer translocation (Fischer and Lohman, 2004). These were determined by monitoring the time course of arrival of a translocating UvrD at the 5′ end of a ssDNA as described (Dillingham et al., 2002; Fischer et al., 2004) (Figure 1). For a 3′ to 5′ translocase such as UvrD, ssDNA ((dT)L) of defined length, L, is labeled at the 5′ end with a fluorophore (Cy3 or fluorescein) that undergoes a change in fluorescence intensity upon interaction with UvrD. From a series of “single round” stopped-flow experiments, performed as a function of L, one can determine the rate constant, kt, that limits the rate of translocation during each translocation cycle, the kinetic step size, m, (defined below), the macroscopic rate of translocation, mkt (nucleotides s−1), and the processivity (per nucleotide), P= mkt/(kd + mkt), where kd is the rate constant for UvrD dissociation from ssDNA during translocation.

Sequential “n-step” kinetic model for UvrD translocation along ssDNA

Figure 2 shows the sequential “n-step” kinetic mechanism used to analyze the time courses for UvrD monomer translocation along ssDNA and its coupling to ATP hydrolysis (Fischer and Lohman, 2004; Fischer et al., 2004). In this model, a UvrD monomer with contact size, d (nucleotides), binds randomly, but with polarity to a ssDNA, L nucleotides long. The protein is assumed to bind with equal probability to any stretch of d nucleotides (i.e., potential end effects are ignored) using its full contact size even when bound to the ends of the DNA (i.e., no dangling protein) (Fischer and Lohman, 2004). Upon addition of ATP the UvrD translocase moves with 3′ to 5′ directional bias and finite processivity along the DNA via a series of repeated translocation steps with rate constant, kt. During each translocation step UvrD moves “m” nucleotides, while hydrolyzing “c” ATP molecules and can dissociate from any internal DNA site with rate constant, kd. Therefore, “c/m” is defined as the ATP coupling stoichiometry. When UvrD reaches the end of the DNA it hydrolyzes ATP with rate constant, ka, and dissociates with rate constant, kend. Inclusion of a protein trap (heparin) with the ATP prevents any free UvrD that dissociates during translocation from rebinding ssDNA. We note that the “translocation rate constant”, kt, which is assumed to be constant for all UvrD molecules, represents the rate constant for the slowest step that occurs within each repeated translocation cycle and does not necessarily correspond to the rate constant for movement of UvrD along the DNA (Fischer and Lohman, 2004). The average number of nucleotides translocated between two successive rate-limiting steps is defined as the translocation “kinetic step-size”, m.

Figure 2.

Figure 2

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Kinetic models for ATP-dependent UvrD monomer translocation. (A)- UvrD monomers (triangle) bind randomly, but with polarity, to a ssDNA of L nucleotides, with contact size d nucleotides and translocate (3′ to 5′) in steps of m nucleotides (kinetic step-size) with rate constant, kt, hydrolyzing c ATP molecules per m nucleotides. UvrD dissociates from internal ssDNA sites with rate constant, kd, and from the 5′-end of the ssDNA with rate constant kend and is prevented from rebinding the DNA by binding to heparin (protein trap, T). Intermediate positions of UvrD along the ssDNA are shown as Ii, where In represents UvrD bound to the 3′ end of the ssDNA. (B)- Scheme 1 is used to analyze UvrD-catalyzed ATP hydrolysis during translocation monitored by phosphate production. (C)- Scheme 2 is used to analyze UvrD translocation time courses monitoring the arrival of protein at the 5′-end.

The UvrD monomer binds initially at a random position along the ssDNA, i translocation steps away from the 5′-end, with concentration, Ii. The number of translocation steps, i, needed to reach the 5′ end is constrained (1 ≤ i ≤ n), where n is the maximum number of translocation steps needed for a UvrD monomer bound at the 3′ end to move to the 5′ end of a DNA. The concentration of UvrD bound at the 5′ end is Iend and free protein, Pf, is prevented from rebinding to DNA by binding to heparin. The maximum number of translocation steps, n, for ssDNA of nucleotide length, L, is related to m and d by eq. (1).

n=L−dm (1)

Under single round conditions, Scheme 1 predicts a burst of ATP hydrolysis by UvrD, the magnitude of which increases with increasing DNA length, L as given by eq. (2),

[ADP(L)]=I(0)1+(L−dm)r[rcP(L+d(P−1)−LP+mP(PL−dm−1)m(P−1)2+ka(kd+ktr(1−PL−dm)kdkend] (2)

where P = kt/(kt +kd) is the translocation processivity (per “kinetic step”). In eq. (2), I(0) is the concentration of UvrD monomer initially bound to the DNA (at time, t =0) and r is the ratio of the probability of UvrD binding to any binding position on the DNA other than the 5′ end to the probability of UvrD binding to the 5′ end (Fischer and Lohman, 2004; Fischer et al., 2004).

In eq. (2) c appears as a product with kt or P, and thus cannot be determined without independent knowledge of the translocation parameters, m, kt and kd, which can be obtained from a set of independent translocation experiments that monitor the arrival of UvrD at the 5′-end of ssDNA ((dT)L). Eq. (3), based on Scheme 2, gives the expression for the time course of UvrD arrival at the 5′ end of ssDNA and subsequent dissociation (Fischer et al., 2004).

f(t)=A1+nrℒ−1(1s+kc(1+ktrs+kd(1−kts+kt+kd)n))×(1+fend∗kcfend(s+kend))+Σi=1j(rfifend)kt+kd+s−kt(kts+kt+kd)n−i(kd+s)(kt+kd+s)) (3)

In eq. (3), ℒ−1 is the inverse Laplace transform operator, s is the Laplace variable (Lucius et al., 2003), the parameters f*end, fend, and fi are the fluorescent signals associated with UvrD bound at I*end, Iend, and “i” steps away from Iend, respectively, and “A” is the signal associated with UvrD initially bound to the ssDNA (f*I(0)). A two-step 5′-end dissociation process (Scheme 2) with rate constants kc and kend is required to describe the time courses obtained with 5′-Cy3-(dT)L and 5′-F-(dT)L substrates (Fischer et al., 2004). Time courses from translocation experiments performed with two series of (dT)L substrates, varying in length and labeled at the 5′-end with either Cy3 or fluorescein, can be analyzed using eq. (3) to obtain fluorophore independent values of kt, n and d (Fischer et al., 2004). The kinetic translocation step-size, m, is determined from a plot of the maximum number of translocation steps, n, vs. L using eq. (1).

Kinetics of ATP hydrolysis during UvrD monomer translocation along ssDNA

ATP hydrolysis during UvrD translocation was measured using a fluorescent assay that monitors the production of inorganic phosphate, Pi (Brune et al., 1994, 1998; Dillingham et al., 2000). This assay was modified (see Experimental Procedures and Supplemental Data) in that an excess of the polyanion heparin was included in the ATP solution to serve as a trap for free UvrD protein to insure that these are “single round” experiments, which simplifies the analysis (Fischer and Lohman, 2004). We showed previously (Fischer et al., 2004) that although heparin actively dissociates some fraction of the UvrD during translocation (i.e., increases the apparent dissociation rate constant, kd), heparin does not affect the translocation rate constant, kt or the kinetic step-size, m. The additional advantage of heparin is that it does not stimulate the ATPase activity of UvrD and thus heparin bound UvrD does not contribute to the production of Pi. The fluorescent assay to detect inorganic phosphate production was optimized for use with UvrD (see Supplementary Data).

All ssDNA used in these experiments was composed of deoxyribothymidylates ((dT)L or poly(dT)) to avoid intramolecular base pair formation. The concentrations of UvrD monomer, ssDNA, heparin, and PBP-MDCC reported are the final concentrations after mixing. Figure 3A shows time courses of Pi production resulting from UvrD monomer translocation for a series of (dT)L substrates, with L= 10, 15, 20, 35, 45, 54, 64, 79, 84, 97, 101, and 124 nucleotides. UvrD was pre-incubated with (dT)L in buffer T20 and then mixed with buffer T20 containing ATP, MgCl2, heparin and PBP-MDCC. Each time course shows an exponential increase in Pi production, the amplitude of which increases with increasing ssDNA length, consistent with ATP-dependent translocation of UvrD monomers along ssDNA. This is followed by a slow linear increase in Pi production which reflects a small fraction of UvrD that can rebind to the ssDNA and hydrolyze additional ATP (see below). In Figure 3B we plot the total moles of Pi produced per mole of UvrD monomer in the burst phase as a function of (dT)L length, L, determined from fitting each time course in Figure 3A to eq. (4) (see Experimental Procedures and Supplemental Data).

Figure 3.

Figure 3

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Kinetics of ATP hydrolysis during UvrD monomer translocation. UvrD (25 nM, post mix) was pre-incubated with excess (dT)L (buffer T20, 25°C) and translocation initiated by the addition of ATP, Mg2+, heparin, and PBP-MDCC to final concentrations of 500 μM, 2 mM, 4 mg/ml, and 10 μM, respectively. Time courses were corrected for contaminating phosphate (Pi) and converted to Pi/UvrD monomer (see Experimental Procedures). (A)- Time courses of Pi production during UvrD monomer translocation along (dT)L. Solid curves (L = 54–124 nts) used 300 nM (dT)L, and dashed curves (L = 10 – 45 nts) used 1.0 μM (dT)L. (B)- Dependence of the normalized burst phase amplitude (Pi/UvrD monomer) on ssDNA length, L, fit to a straight line with slope = (0.4 ± 0.01). The error bars reflect (±1) standard deviation of the average of three independent determinations. (C)- Same data as in (B) showing the best NLLS fit to the data using eq. (2) where P, m, d, r and kend were constrained to the values determined independently (Table 1) while c and ka were floated yielding c = 4.5 ± 0.1 ATP per kinetic step-size (m), ka = 40 ± 13 s−1. (D)- Simulations of the time courses of the population of translocating UvrD (smooth blue curve) and UvrD bound at the 5′-end (smooth red curve) for (dT)124 superimposed on the experimental time course of ATP hydrolysis (Pi production) with (dT)124. Dashed lines show Pi production due to translocating UvrD (dashed blue) and UvrD bound at the 5′ end (dashed red).

The data in Figure 3B can be described by a straight line with slope of (0.4 ± 0.01) Pi/nucleotide. Based on a semi-quantitative analysis (Dillingham et al., 2000), this suggests an ATP coupling stoichiometry of (0.80 ± 0.02) ATP hydrolyzed per UvrD monomer per nucleotide translocated. However, as discussed (Fischer and Lohman, 2004), this analysis yields an underestimate of the ATP coupling stoichiometry since it neglects the finite processivity of the translocase. In fact, quantitative analysis of these data requires independent knowledge of the processivity of UvrD translocation, P = kt/(kt + kd), determined as described below.

Kinetic parameters for UvrD monomer translocation and dissociation

The kinetic parameters for UvrD monomer translocation and dissociation were determined under the same solution conditions, including heparin concentration, used in the ATPase experiments.

Rate constant for UvrD monomer dissociation from internal ssDNA sites

We first determined the rate constant for UvrD monomer dissociation from internal sites within ssDNA (kd) using poly(dT) since (dT)L was used for the translocation and ATPase experiments. UvrD dissociation was monitored by the increase in the intrinsic UvrD tryptophan fluorescence upon dissociation from poly(dT) (Fischer et al., 2004). We used long poly(dT) with weight average lengths of 3,500 ± 100 and 16,200 ± 500 nucleotides that was fractionated (see Experimental Procedures) to eliminate shorter lengths to insure that the rate constant reflects UvrD dissociation from internal sites (Fischer et al., 2004). UvrD was pre-bound to poly(dT) (1 monomer per 400 nucleotides of poly(dT)) in buffer T20 and dissociation was initiated by mixing with buffer T20 containing heparin, ATP and MgCl2. The resulting time courses (Figure 4A) are well described by a single exponential function yielding values of kd = 0.81 ± 0.04 s−1 for both poly(dT) samples, hence the poly(dT) was sufficiently long to eliminate end effects.

Figure 4.

Figure 4

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Kinetics of UvrD monomer dissociation from ssDNA. (A)- Dissociation from internal sites on poly(dT). Time course of UvrD monomer (25 nM, post mix) dissociation from poly(dT) (10 μM nts, post mix) (16.2 ± 0.5 kb), (buffer T20, 500 μM ATP, 2 mM MgCl2, and 4 mg/ml heparin, 25°C) fit to a single exponential decay yields kd = 0.81 ± 0.04 sec−1. (B)- Dissociation from the 5′ ends of (dT)L. Time courses of UvrD monomer (25 nM) dissociation from (dT)L (50 nM) (L = 54, 84, and 124 nucleotides) in the presence of 500 μM ATP, 2 mM MgCl2, and 4 mg/ml heparin. The continuous lines are simulations based on eq. (5) and the best fit parameters determined from NLLS analysis of time courses for (dT)L with L = 54, 79, 84, 97, 101, 104 and 124 nts (see Supplemental Data). The values of kt, kd, r, m and d were constrained (Table 1) and kend = 27.8 ± 0.8 sec−1 was determined from NLLS fit to the data.

Kinetic parameters for UvrD monomer translocation

The kinetics of UvrD monomer translocation were examined in a stopped-flow experiment as described (Fischer et al., 2004) by monitoring the arrival of UvrD monomers at the 5′-end of a series of oligodeoxythymidylates labeled at the 5′-end with Cy3 (5′-Cy3-(dT)L) or fluorescein (5′-F-(dT)L) (L = 54, 79, 84, 97, 101, 104, and 124 nts). A final heparin concentration of 4 mg/ml was sufficient to prevent rebinding of UvrD to the ssDNA (black trace, Figure 5B), thus insuring “single round” conditions.

Figure 5.

Figure 5

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Kinetics of UvrD monomer translocation monitored by the arrival of UvrD at the 5′-end of fluorescently labeled (dT)L. UvrD (25 nM, post mix) was pre-incubated with either 5′-Cy3-(dT)L or 5′-F-(dT)L (50 nM, post mix) in buffer T20 at 25° C and translocation initiated by the addition of ATP (500 μM), MgCl2 (2 mM) and heparin (4 mg/mL) (final concentrations). (A)- Time courses monitoring Cy3 fluorescence with 5′-Cy3-(dT)L. (B)- Time courses monitoring fluorescein fluorescence with 5′-F-(dT)L. The black time course shows that 4 mg/ml heparin is sufficient to prevent 25 nM UvrD from binding to 50 nM 5′-F-(dT)124. The smooth black curves are simulations using eq. (3) and the best-fit parameters determined from a combined global NLLS analysis of the time courses in (A) and (B) (Table 1, column 1). (C)- The maximum number of steps, n, obtained from analysis of the data in (A) and (B) plotted as a function of ssDNA length, L. A linear least squares fit of the data to eq. (1) yields m = 4.6 ± 0.2 nt/step and d = 8.0 ± 1.0 nts. The error bars reflect (±1) standard deviation determined from a Monte Carlo simulation of the data (see Supplemental Data).

The time courses in Figure 5A and B, resulting from experiments with 5′-Cy3-(dT)L and 5′-F-(dT)L, respectively, show the characteristic profiles indicative of translocation. Arrival of a translocating UvrD at the 5′ end enhances Cy3 fluorescence, whereas it quenches fluorescein fluorescence (Fischer et al., 2004). The time required to reach the maximum fluorescence signal change increases with increasing ssDNA length, L, reflecting the translocation process (Dillingham et al., 2002; Fischer et al., 2004). The time courses also broaden with increasing ssDNA length since the initial random distribution of UvrD bound to (dT)L broadens with increasing ssDNA length (Fischer and Lohman, 2004).

Global NLLS analysis of both sets of time courses (Cy3 and fluorescein) in Figure 5A and B using the sequential n-step kinetic model in Scheme 2 (eq. (3)) is used to determine the translocation kinetic parameters, kt, m, d, and n (Fischer et al., 2004) (Supplemental Data). The resulting best fit translocation kinetic parameters, kt, P and m, d, and n are fluorophore independent, whereas kc and kend are fluorophore dependent (see Table 1). The maximum number of translocation steps, n, increases linearly with increasing ssDNA length, L, as shown in Figure 5C. A linear least squares fit of the data in Figure 5C to eq. (1) yields a kinetic translocation step-size, m = (4.6 ± 0.2) nts, and a UvrD monomer contact size, d = 8 ± 1 nt. Under these conditions, UvrD monomers translocate with a stepping rate constant, kt = (42 ± 2) s−1 and macroscopic rate (mkt) = (193 ± 1) nts/sec. In the presence of 4 mg/mL heparin, UvrD monomer has a translocation processivity, P = mkt/(mkt + kd) = (0.9958 ± 0.0002) (in nucleotide units), corresponding to translocation of an average of (1-P)−1 =(239 ±1) nts before dissociation from the DNA. In the absence of heparin, UvrD monomer translocation proceeds for an average of (769 ± 1) nts due to a lower UvrD dissociation rate constant.

Table 1.

UvrD monomer ssDNA translocation kinetic parameters (buffer T20, 2 mM MgCl2, 0.5 mM ATP, 4 mg/mL heparin, 25°C)

Translocation Kinetic Parameters Translocation assayA Dissociation assayB (kd) Dissociation assayA (kend) Pi-release assayB
kt (kinetic steps sec−1) 42 ± 2 — Constrained Constrained
kd (sec−1) Constrained 0.81 ± 0.04 Constrained Constrained
Dissociation from 5′-end — 27.8 ± 0.8 Constrained
 kc (sec−1) Fluorescein 13.7 ± 0.2
  Cy3 30 ± 3
 kend (sec−1) Fluorescein 2.5 ± 0.1
  Cy3 0.5 ± 0.1
ka (ATP UvrD−1 sec−1) — — — 40 ± 13
c (ATP kinetic-step−1) — — — 4.5 ± 0.1
r 1.8 ± 0.8 — Constrained Constrained
m (nts kinetic-step−1) 4.6 ± 0.2 — Constrained Constrained
d (contact size, nts) 8 ± 1 — Constrained Constrained
c/m (ATP nt−1) — — — 0.98 ± 0.06
mkt (nts sec−1)B 193 ± 1 — Constrained Constrained
1/(1-P) (nts) (4 mg/mL heparin) 239 ± 1 — Constrained Constrained
1/(1-P) (nts) (no heparin) 769 ± 1 — — —
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A

Error is (± 1) standard deviation determined from Monte Carlo simulation (see Supplemental Data).

B

Error is (± 1) standard deviation determined from the average of three independent determinations.

constrained Kinetic parameter was constrained in the NLLS analysis to the value determined in either the translocation or dissociation assay.

Rate constant for UvrD monomer dissociation from the 5′-end of unlabeled (dT)L

Although we anticipate that the fraction of ATP hydrolyzed by UvrD bound at the 5′ end of the ssDNA is small compared to that hydrolyzed by translocating UvrD, we can determine this explicitly with knowledge of the rate constant for UvrD monomer dissociation from the 5′-end of unlabeled (dT)L (kend). Once kend is known, the apparent rate constant for ATP hydrolysis at the 5′-end, ka, can be determined from a global analysis of the amount of Pi produced as a function of ssDNA length using eq. (2).

To determine kend, we monitored UvrD dissociation kinetics from a series of defined length (dT)L substrates. With the short (dT)L molecules, each time course has contributions both from UvrD dissociation from internal sites, kd, as well as the 5′ end, kend. Time courses for UvrD dissociation were obtained for (dT)L with L= 54, 79, 84, 97, 101, 104, and 124 nts, monitoring UvrD fluorescence, although only data for (dT)54, (dT)84 and (dT)124 are shown in Figure 4B. The average time for dissociation decreases with decreasing ssDNA length reflecting the increasing contribution from UvrD monomers bound at the 5′ ends, which dissociate with a faster rate than UvrD bound at internal sites. UvrD dissociation from all seven lengths of (dT)L were analyzed using eq. (5) (Supplemental Data), by constraining all parameters to those determined above, with the exception of kend, which was allowed to float, returning kend = (27.8 ± 0.8) s−1.

ATP coupling stoichiometry during ssDNA translocation

An expression for the total amount of ATP hydrolyzed by UvrD translocating along a ssDNA of length L is given in eq. (2) (Fischer and Lohman, 2004). The first term in eq. (2) reflects ATP hydrolysis by translocating UvrD monomers, whereas the second term reflects ATP hydrolysis by UvrD monomers bound at the 5′ end of the ssDNA. Figure 3C shows a plot of the total Pi produced per UvrD monomer as a function of ssDNA length, L. The solid curve is a NLLS fit of the data to eq. (2) where kt, kd, m, d, and kend were constrained to the values determined independently (Table 1) and c and ka were determined as fitting parameters, yielding c = (4.5 ± 0.1) ATP hydrolyzed per translocation step, m, and ka = (40 ± 13) ATP molecules hydrolyzed per UvrD monomer s−1. Since the translocation kinetic step-size, m = (4.6 ± 0.2) nucleotides (Figure 5C), this yields an average ATP coupling stoichiometry of c/m = (0.98 ± 0.06) ATP molecules hydrolyzed per nucleotide translocated per UvrD monomer.

Figure 3D shows a plot of the fraction of UvrD that is either translocating at any position on a ssDNA ((dT)124) or bound at the 5′ end of (dT)124 as a function of time, along with the overall time course for ATP hydrolysis and the contributions of each species to total ATP hydrolysis, calculated from the kinetic parameters in Table 1. Clearly, the time course of ATP hydrolysis follows closely the population of UvrD monomers involved in ssDNA translocation. The slow steady-state ATPase rate occurs well after UvrD translocation is finished, further indicating that this phase reflects the small fraction of UvrD that can rebind to the ssDNA and hydrolyze additional ATP. Under the conditions used here, the contribution to ATP hydrolysis due to UvrD bound at the 5′ end of (dT)124 is less than 2% of the total ATP hydrolyzed in the burst phase. However, for (dT)10, ~40% of the total ATP hydrolyzed in the burst phase results from UvrD bound at the 5′ end (data not shown).

Discussion

E. coli UvrD is an SF1 superfamily helicase/translocase with a monomer structure (Lee and Yang, 2006) that is similar to both E. coli Rep (Korolev et al., 1997) and B. stearothermophilus PcrA (Subramanya et al., 1996; Velankar et al., 1999). Each monomer consists of two domains (1 and 2), with each domain composed of two subdomains (1A, 1B and 2A, 2B). The ssDNA binding site lies across the top of the 1A and 2A sub-domains, with one ATP binding site at the interface between these sub-domains.

In all three proteins, the 2B sub-domain can rotate about a hinge region connected to the 2A sub-domain and has been observed in both a “closed” and “open” form for Rep bound to ssDNA (Korolev et al., 1997). The 2B sub-domain is in the “closed” form in all of the UvrD monomer-ss-ds-DNA crystal structures (Lee and Yang, 2006), whereas apo UvrD crystallizes in the “open” form (S. Korolev, N. K. Maluf, G. Gauss, T. Lohman, G. Waksman, unpublished data). Single molecule studies (Rasnik et al., 2004) show that a Rep monomer bound to a ss-dsDNA junction is in the “closed” form. Whereas neither Rep (Cheng et al., 2001; Ha et al., 2002; Myong et al., 2005) nor UvrD monomers are able to unwind DNA in vitro (Fischer et al., 2004; Maluf et al., 2003b), deletion of the 2B sub-domain within Rep, to form RepΔ2B, activates monomer helicase activity in vitro, thus the 2B sub-domain inhibits Rep monomer helicase activity (Brendza et al., 2005). The RepΔ2B monomer also translocates with a ~2-fold higher rate than does the full length Rep monomer (Brendza et al., 2005). These observations suggest that the “closed” forms of these monomers are inactive for helicase activity in vitro. Thus, Rep and UvrD monomers are translocases, but oligomerization is needed in vitro to activate the helicase activity for both Rep (Brendza et al., 2005; Cheng et al., 2001; Ha et al., 2002) and UvrD (Fischer et al., 2004; Maluf et al., 2003a,b).

Implications for the mechanism of UvrD monomer translocation along ssDNA

Several mechanisms have been proposed to describe translocation of SF1 or SF2 monomers along ssDNA or RNA and these can be grouped into “stepping” and “Brownian motor” (thermal ratchet) mechanisms (Patel and Donmez, 2006). Stepping mechanisms require at least two nucleic acid binding sites and for a monomeric translocase generally have been described as inch-worm mechanisms (Hill and Tsuchiya, 1981; Lee and Yang, 2006; Soultanas and Wigley, 2001; Velankar et al., 1999; Yarranton and Gefter, 1979; Yu et al., 2006).

Based on crystal structures, inch-worm mechanisms have been proposed for translocation and unwinding by both a PcrA monomer (Soultanas and Wigley, 2001; Velankar et al., 1999; Yu et al., 2006) and a UvrD monomer (Lee and Yang, 2006). In these mechanisms, unidirectional translocation is proposed to result from relative movements between the 1A and 2A sub-domains, with one ATP hydrolyzed per nucleotide translocated (Lee and Yang, 2006; Velankar et al., 1999). In one model (Soultanas and Wigley, 2001; Velankar et al., 1999) the relative movements of the 1A and 2A sub-domains are coordinated with stacking interactions between aromatic side chains and the ssDNA bases (waves of base flipping) that are modulated through ATP binding and hydrolysis.

A Brownian motor model (Levin et al., 2003, 2005) requires only one DNA binding site but invokes two conformational states of the translocase with tight and weak affinities for the ss nucleic acid that are modulated by nucleotide cofactors (e.g., ATP, ADP) binding. In the weak affinity state, the translocase can diffuse in either direction along the nucleic acid lattice, or dissociate. If it diffuses forward, then upon reforming the high affinity state, the translocase will move forward, whereas if it diffuses backward while in the low affinity state, then upon reforming the high affinity state it will either remain in the same position or move backward. This model predicts that translocation will have low processivity and a high ATP coupling stoichiometry (multiple ATP molecules hydrolyzed per nucleotide translocated) (Levin et al., 2005).

Our findings favor a stepping mechanism for UvrD monomer translocation, since we find a high translocation processivity ((1-P)−1 = ~770 nucleotides in the absence of heparin) and a low coupling stoichiometry of (0.98 ± 0.06) ATP hydrolyzed per nucleotide translocated. We also find that biased (3′ to 5′) directional translocation of a UvrD monomer along ssDNA at saturating ATP concentrations can be described by a simple mechanism in which a rate-limiting step, occurring with rate constant kt, is repeated every ~4 to 5 nucleotides translocated. Taken together, these results suggest a non-uniform stepping mechanism (see Figure 6A), in which ~4 to 5 rapid one nucleotide translocation steps, each coupled to hydrolysis of one ATP, are followed by a slower step (pause) that limits the overall rate of translocation.

Figure 6.

Figure 6

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Non-uniform stepping of a UvrD monomer translocating along ssDNA. (A)- Kinetic scheme for UvrD monomer translocation assuming ATP hydrolysis is tightly coupled to translocation. One translocation cycle consists of 4 rapid one nucleotide (nt) translocation steps, each coupled to hydrolysis of one ATP, followed by a slow step (pause), with rate constant, kt, yielding m = 4 nts/step, with c/m = 1 ATP/nt translocated. (B)- One possible non-uniform stepping model. The leading (blue) and trailing (red) domain bind to ssDNA (black line with perpendicular lines representing individual nt) with a contact size of ~ 8 nt. Each round of ATP hydrolysis translocates the leading domain by one nt, while the trailing domain remains stationary. This process is repeated three more times resulting in the leading domain moving by 4 nt with 4 nt being “scrunched” between the leading and trailing domains. This is followed by a rate-limiting release of the four ssDNA nt behind the trailing domain, completing one translocation cycle.

Use of single round kinetic methods to probe translocation kinetics

Determination of the kinetic parameters and ATP coupling stoichiometry for ssDNA translocation of UvrD required two pre-steady state kinetic methods. Pre-steady state methods are needed in ensemble studies since steady state methods provide information only on the slowest step that limits the rate of turnover, which generally is a slow process (binding, dissociation or enzyme assembly) that is unrelated to the kinetic steps of translocation which are much more rapid. The first method monitors protein translocation indirectly by detecting the arrival of the translocase at one end of the ssDNA (Dillingham et al., 2002; Fischer et al., 2004). The second method measures the kinetics of ATP hydrolysis by monitoring binding of Pi to a fluorescently labeled phosphate binding protein (PBP-MDCC) (Brune et al., 1994; Dillingham et al., 2000). Both methods are needed for an accurate determination of the ATP coupling stoichiometry for any translocase with finite processivity, P, since the extent of ATP hydrolysis is a function of both the coupling stoichiometry and processivity (Fischer and Lohman, 2004). Two important modifications facilitated these studies. The first was to perform experiments under “single-round” conditions by including a trap (heparin) for free UvrD protein that prevents rebinding of UvrD to ssDNA (Fischer et al., 2004). The second involved analysis using a sequential n-step kinetic model and non-linear least squares methods (Fischer and Lohman, 2004) to determine the translocation kinetic parameters (kt, kd, kend, P, and step-size, m) and ATP coupling stoichiometry. Such an analysis is needed to obtain individual values of m and kt, rather than only their product, the macroscopic rate of translocation, mkt. This model assumes that all UvrD monomers in the population translocate with the same average rate (i.e., the same value of kt).

Previous studies of the monomeric PcrA translocase also estimated the ATP coupling stoichiometry to be ~1 ATP per nucleotide translocated (Dillingham et al., 2000). The semi-quantitative analysis used in that study assumed that the PcrA monomer does not dissociate from the ssDNA until it reaches the 5′ end (i.e., that the processivity, P=1). Application of the semi-quantitative analysis to the UvrD data reported here yields an ATP coupling stoichiometry of (0.80 ± 0.02) ATP molecules hydrolyzed per nucleotide translocated, compared with our determination of (0.98 ± 0.06) based on the same data. The semi-quantitative analysis also yields an apparent translocation rate of ~330 nucleotides s−1, compared to our determination of mkt = (193 ± 1) nt/sec. Thus, significant differences in these estimates can result in the absence of independent knowledge of the kinetic parameters for translocation, especially when translocation processivity is low (e.g., at higher salt concentrations or lower [ATP]).

Non-uniform stepping models for UvrD translocation

One possible non-uniform stepping mechanism suggested by our results is shown in Figure 6B. In this mechanism, which assumes that ATP hydrolysis is tightly coupled to translocation, four ssDNA nucleotides are rapidly “reeled” into the leading sub-domain (2A) of the translocase, with each nucleotide translocation step coupled to hydrolysis of one ATP, followed by a rate-limiting release of the four nucleotide stretch of ssDNA through the trailing sub-domain (1A). This could occur either by an inch-worm mechanism in which the leading domain moves relative to the trailing domain (Velankar et al., 1999; Yu et al., 2006) or by a “scrunching” mechanism in which the four ssDNA nucleotides translocate into the leading domain with no relative movement between the two protein domains as recently suggested for RNA polymerase (Kapanidis et al., 2006). Alternatively, a slow four nucleotide movement of the leading domain could be followed by four rapid one nucleotide movements of the trailing domain. Since rotation of the 2B sub-domain of Rep (Korolev et al., 1997; Rasnik et al., 2004) has been observed during ssDNA translocation (Myong et al., 2005), it is also possible that the rate limiting step in the translocation mechanism may be coupled to rotation of the 2B sub-domain.

If ATP hydrolysis is “weakly” coupled to UvrD translocation, then translocation could occur in one four nucleotide step, hydrolyzing only one ATP, followed by an average of 3–4 rounds of futile ATP hydrolysis. Additional experiments as a function of [ATP] will be required to determine how tightly ATP hydrolysis is coupled to UvrD translocation and to address the nature of the slow step that limits the overall rate of translocation.

The results reported here suggest a non-uniform mechanism for ssDNA translocation. Such mechanisms have been proposed for DNA unwinding by the RecBC (Bianco and Kowalczykowski, 2000; Lucius and Lohman, 2002, 2004), and T4 Dda DNA helicases (Eoff and Raney, 2006) and RNA unwinding by the Hepatitis C NS3 helicase (Dumont et al., 2006). For RecBC helicase, a quantum inch-worm mechanism was proposed for translocation in which a large translocation step, equivalent to ~22 bp (Bianco and Kowalczykowski, 2000) is followed by several smaller (4 bp) steps (Lucius and Lohman, 2002, 2004). For Hepatitis C NS3 RNA helicase (Dumont et al., 2006), RNA unwinding occurs via three rapid steps of 3.6 ± 1.3 bp, followed by a slower process occurring every 11 ± 3 bp.

We have studied the mechanism of ssDNA translocation by the monomeric UvrD translocase; however, a UvrD monomer does not function as a processive helicase in vitro, rather helicase activity requires an oligomer (Ali et al., 1999; Fischer et al., 2004; Maluf et al., 2003b). Hence, although some helicases are monomeric (Brendza et al., 2005; Morris et al., 2001; Sikora et al., 2006), the ability of an enzyme to translocate with biased directionality along ssDNA is not generally sufficient to make it a helicase. On the other hand, the ability of a UvrD monomer to translocate must play a role in the helicase activity of the oligomer. Furthermore, translocation by the UvrD monomer may be the essential activity needed to displace RecA protein from ssDNA (Veaute et al., 2005). In fact, the use of two different forms of UvrD (monomer vs. dimer) for its translocase and helicase activities may provide a mechanism to regulate the use of these activities in different metabolic processes.

Experimental Procedures

Buffers and Reagents

Buffers were prepared with reagent grade chemicals using distilled water, further deionized with a Milli-Q purification system (Millipore Corp., Bedford, MA) and were filtered through 0.2 micron filters. Buffer T20 is 10 mM Tris-HCl (pH 8.3 at 25°C), 20 mM NaCl, and 20 % (v/v) glycerol (enzyme grade). Other buffers are described in Supplemental Data.

Enzymes and DNA

E. coli UvrD was purified and its concentration determined as described (Runyon et al., 1993)and was stored at −20°C in minimal storage buffer for up to six months without loss of translocation activity. E. coli phosphate binding protein A197C (PBP) was purified (>96% purity) as described (Brune et al., 1994), and its concentration determined in PBP buffer (ε280 nm = 6.16(± 0.12) × 104 M−1cm−1). PBP was labeled with a coumarin derivative, MDCC, and purified (Brune et al., 1994) with modifications described in Supplemental Data.

(dT)L and (dT)L labeled with fluorescein or Cy3, were synthesized and purified as described (Kozlov and Lohman, 2002), dialyzed vs. 10 mM Tris-HCl, pH 8.3, and stored at –20°C and concentrations determined spectrophotometrically (Fischer et al., 2004). Poly(dT) (Midland Certified Reagents, Inc., Midland, TX) was fractionated by size-exclusion chromatography as described (Fischer et al., 2004), dialyzed into ssDNA buffer and stored at −20°C. The average lengths of poly(dT) were estimated from weight average sedimentation coefficients determined in 10 mM KPO4, pH 7.4, 1 M NaCl, 20°C, as described (Fischer et al., 2004).

Stopped-flow Experiments

Experiments were performed in buffer T20 at 25°C using an SX18MV stopped-flow (Applied Photophysics Ltd., Leatherhead, UK). In translocation experiments UvrD was pre-incubated with ssDNA in one syringe and reactions initiated by 1:1 mixing with buffer T20 plus 0.5 mM ATP, 2 mM MgCl2, and 4 mg/mL heparin. All concentrations given are the final concentrations after mixing in the stopped-flow.

Kinetics of inorganic phosphate production

The time course of ATP hydrolysis was monitored in the stopped-flow as an increase in PBP-MDCC fluorescence due to binding of phosphate (Pi)(Dillingham et al., 2000) (λex =430 nm, λem > 450 nm) (see Supplemental Data for details). Prior to each experiment, the stopped-flow syringes and flow lines were treated with a Pi-MOP (10 mM Tris-HCl, pH 8.0, 300 μM 7-MEG, and 0.2 units/mL PNPase) for 15 min to remove contaminating Pi (Brune et al., 1994) and then rinsed with buffer T20. The MOP was not included in the experiments. UvrD-(dT)L complexes in buffer T20 were pre-incubated on ice for 5 min, loaded into one syringe and incubated for 5 min at 25°C. A solution of PBP-MDCC, ATP, heparin, and MgCl2 in buffer T20 was loaded into the other syringe and incubated for 15 min at 25°C. A control time course, conducted without ssDNA, was subtracted from each time course to correct for the presence of contaminating phosphate. PBP-MDCC fluorescence enhancement was converted to [Pi] after calibration in the stopped-flow using [NaH2PO4] standards whose concentrations were determined by refractive index. The amount of [Pi] produced per UvrD monomer in the burst, A, was determined by fitting each time course to eq. (4) (see also Supplementary Data).

PiUvrD=A(1−exp−kobst)+ksst (4)

Kinetics of UvrD monomer translocation

UvrD monomer translocation kinetics were measured under single round conditions (no rebinding of UvrD to ssDNA) using a fluorescent stopped-flow assay to monitor the arrival of UvrD at the 5′-end of the DNA using both 5′-Cy3-(dT)L and 5-F-(dT)L as described(Fischer et al., 2004). Fluorescein fluorescence was excited at 492 nm and emission monitored at >520 nm. Cy3 fluorescence was excited at 515 nm and emission monitored at >570 nm.

UvrD monomer-ssDNA dissociation kinetics

Dissociation kinetics were monitored by the increase in UvrD tryptophan fluorescence (Fischer et al., 2004) (λex = 280 nm, λem >350 nm). The dissociation rate constant from internal ssDNA sites, kd, during UvrD translocation was measured using poly(dT) (average length 3.5–16 kb). The rate constant for UvrD dissociation from the 5′ end, kend, was measured using a series of lengths of (dT)L.

Supplementary Material

01

Acknowledgments

We thank N. Baker, P. Burgers, J. Majors, K. Maluf, A. Lucius and T. Ha for discussions, M. Webb for the phosphate binding protein expression vector. This research was supported by NIH grant (GM45948) to T.M.L. and NIH postdoctoral fellowship (GM56105) to C.J.F.

Footnotes

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