Kinetic Mechanism for Formation of the Active, Dimeric UvrD Helicase-DNA Complex*

  • Nasib K. Maluf
    Footnotes
    Affiliations
    Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, Missouri 63110
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  • Janid A. Ali
    Footnotes
    Affiliations
    Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, Missouri 63110
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  • Timothy M. Lohman
    Correspondence
    To whom correspondence should be addressed: Dept. of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 660 S. Euclid Ave., St. Louis, MO 63110. Tel.: 314-362-4393; Fax: 314-362-7183
    Affiliations
    Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, Missouri 63110
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  • Author Footnotes
    * This work was supported in part by National Institutes of Health Grant GM45948 (to T. M. L.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
    ‡ Supported in part by National Institutes of Health Training Grant T32 GM08492. Present address: University of Colorado Health Sciences Center, School of Pharmacy, C238, 4200 East 9th Ave., Denver, CO 80262.
    § Present address: Infinity Pharmaceuticals, Inc., 780 Memorial Dr., Cambridge, MA 02139.
      Escherichia coli UvrD protein is a 3′ to 5′ SF1 helicase required for DNA repair as well as DNA replication of certain plasmids. We have shown previously that UvrD can self-associate to form dimers and tetramers in the absence of DNA, but that a UvrD dimer is required to form an active helicase-DNA complex in vitro. Here we have used pre-steady state, chemical quenched flow methods to examine the kinetic mechanism for formation of the active, dimeric helicase-DNA complex. Experiments were designed to examine the steps leading to formation of the active complex, separate from the subsequent DNA unwinding steps. The results show that the active dimeric complex can form via two pathways. The first, faster path involves direct binding to the DNA substrate of a pre-assembled UvrD dimer (dimer path), whereas the second, slower path proceeds via sequential binding to the DNA substrate of two UvrD monomers (monomer path), which then assemble on the DNA to form the dimeric helicase. The rate-limiting step within the monomer pathway involves dimer assembly on the DNA. These results show that UvrD dimers that pre-assemble in the absence of DNA are intermediates along the pathway to formation of the functional dimeric UvrD helicase.
      DNA helicases are a ubiquitous class of enzymes that catalyze the separation of double-stranded (ds)
      The abbreviations used are: ds, double-stranded; ss, single-stranded; NLLS, non-linear least squares.
      1The abbreviations used are: ds, double-stranded; ss, single-stranded; NLLS, non-linear least squares.
      DNA to form the single-stranded (ss) DNA intermediates required for DNA replication, recombination, and repair in reactions that are coupled to the binding and hydrolysis of nucleoside triphosphates (
      • Matson S.W.
      • Bean D.W.
      • George J.W.
      ,
      • Lohman T.M.
      • Bjornson K.P.
      ). The Escherichia coli UvrD helicase, also known as helicase II, plays essential roles in nucleotide excision repair and methyl-directed mismatch repair (
      • Sancar A.
      ,
      • Modrich P.
      • Lahue R.
      ) and is also required for rolling circle replication of certain plasmids (
      • Bruand C.
      • Ehrlich S.D.
      ).
      The UvrD protein (720 amino acids, molecular mass of 81,989 Da) is a member of the SF1 helicase superfamily (
      • Gorbalenya A.E.
      • Koonin E.V.
      ) and is operationally defined as a 3′ to 5′ helicase (
      • Matson S.W.
      ), based on the fact that a 3′ ssDNA tail placed adjacent to the duplex DNA stimulates the unwinding reaction in vitro. However, UvrD can also initiate DNA unwinding, albeit less efficiently, from DNA nicks and blunt-ended DNA in multiple turnover experiments in vitro (
      • Runyon G.T.
      • Lohman T.M.
      ,
      • Runyon G.T.
      • Bear D.G.
      • Lohman T.M.
      ,
      • Dao V.
      • Modrich P.
      ,
      • Mechanic L.E.
      • Frankel B.A.
      • Matson S.W.
      ). In single turnover DNA unwinding experiments (i.e. single cycle with respect to the DNA), a 3′ ssDNA tail of at least 15 nucleotides is required to observe optimal unwinding by a UvrD dimer in vitro (
      • Ali J.A.
      • Maluf N.K.
      • Lohman T.M.
      ,
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). Even though an 18-bp DNA substrate possessing a 3′ ssDNA tail of 4–10 nucleotides is sufficient to bind a single UvrD monomer with high affinity, no unwinding is observed (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). This reflects the fact that a UvrD dimer is required for helicase activity in vitro (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). In the active dimeric UvrD-DNA complex, one UvrD subunit binds tightly to the ss/dsDNA junction, whereas the second subunit binds to the 3′ ssDNA tail (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ,
      • Maluf N.K.
      • Lohman T.M.
      ). Neither the E. coli Rep helicase, which is also a 3′ to 5′ SF1 helicase (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ) with structural homology to UvrD (
      • Korolev S.
      • Hsieh J.
      • Gauss G.H.
      • Lohman T.M.
      • Waksman G.
      ), nor an ATPase-deficient UvrD mutant can substitute functionally for the second UvrD monomer (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ), indicating that the two UvrD monomers interact to form a functional helicase.
      Whereas the structurally homologous E. coli Rep protein is monomeric in the absence of DNA (
      • Chao K.L.
      • Lohman T.M.
      ), but also must oligomerize to form an active helicase in vitro (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ,
      • Ha T.
      • Rasnik I.
      • Cheng W.
      • Babcock H.P.
      • Gauss G.H.
      • Lohman T.M.
      • Chu S.
      ), UvrD protein can self-assemble to form dimers and tetramers in the absence of DNA (
      • Maluf N.K.
      • Lohman T.M.
      ,
      • Runyon G.T.
      • Wong I.
      • Lohman T.M.
      ). These UvrD self-assembly equilibria have been characterized quantitatively by analytical ultracentrifugation methods over a range of UvrD concentrations, solution conditions, and temperatures (
      • Maluf N.K.
      • Lohman T.M.
      ), including those conditions used to study UvrD-catalyzed DNA unwinding in vitro (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). Considering that a UvrD dimer is required for helicase activity in vitro, the question arises as to whether UvrD dimers that can assemble in the absence of DNA are “on the pathway” to formation of the active dimeric helicase. Alternatively, it is possible that pre-assembled UvrD dimers are not functional and thus would need to first dissociate in order to form an active dimeric helicase on the DNA.
      To address this question, we performed a series of pre-steady state kinetic studies, using chemical quenched flow methods, to examine the kinetic mechanism by which pre-assembled UvrD dimers form an active dimeric helicase on the DNA. Experiments were performed over a range of UvrD concentrations such that the initial population of UvrD monomers and pre-assembled dimers could be varied significantly. Based on the measured equilibrium constants for UvrD dimerization and tetramerization (
      • Maluf N.K.
      • Lohman T.M.
      ), we could then correlate the kinetics of formation of the active UvrD dimeric helicase-DNA complex with the population of free UvrD monomers and dimers in solution. The results of these studies show that the active, dimeric helicase can be formed either by rapid binding to the DNA substrate of pre-assembled UvrD dimers (dimer path) or by the sequential binding of two UvrD monomers followed by dimer assembly on the DNA (monomer path). The data further indicate that the rate-limiting step in the monomer pathway involves assembly of the active, dimeric UvrD complex from two UvrD monomers bound to the DNA. This rate-limiting step is not observed along the dimer pathway, suggesting that the pre-assembled UvrD dimer interface is similar to the interface involved in the active helicase dimer on the DNA. The “double-mixing” quenched flow methods described here and elsewhere (
      • Pang P.S.
      • Jankowsky E.
      • Planet P.J.
      • Pyle A.M.
      ) enable one to examine the kinetics and mechanism of formation of the active helicase complex on the DNA and should prove useful in studies of helicase-DNA assembly reactions in general.

      EXPERIMENTAL PROCEDURES

      Buffers—Buffers were made with reagent grade chemicals using distilled water that was further deionized using a Milli-Q system (Millipore Corp., Bedford, MA). Buffer T20 is 10 mm Tris, pH 8.3, at 25 °C, 20 mm NaCl, and 20%(v/v) glycerol. Storage buffer is 20 mm Tris, pH 8.3, at 25 °C, 200 mm NaCl, 50%(v/v) glycerol, 1 mm EDTA, 0.5 mm EGTA, and 25 mm 2-mercaptoethanol. Storage minimal buffer is 20 mm Tris, pH 8.3, at 25 °C, 200 mm NaCl, and 50%(v/v) glycerol.
      UvrD Protein and DNA Substrates—UvrD protein was purified to greater than 99% homogeneity, and the protein concentration was determined spectrophotometrically using an extinction coefficient of ϵ280 = 1.06 × 105m–1 cm1, as described (
      • Runyon G.T.
      • Wong I.
      • Lohman T.M.
      ). For all experiments performed here, aliquots of UvrD were dialyzed, as needed, versus storage minimal buffer, and stored for periods up to ∼5 months at –20 °C without any loss of helicase activity. Any further dilutions of UvrD were made into storage minimal buffer for experiments performed on that same day; unused protein was discarded.
      Oligodeoxynucleotides were synthesized using an ABI model 391 DNA synthesizer (Applied Biosystems, Foster City, CA) and purified as described (
      • Wong I.
      • Chao K.L.
      • Bujalowski W.
      • Lohman T.M.
      ). The DNA substrate used here, referred to as 3′-(dT20)-ds18, consists of a 3′ ssDNA region (dT20) attached to an 18-bp duplex DNA and is the same DNA used in previous studies (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ,
      • Maluf N.K.
      • Lohman T.M.
      ). The sequence of the DNA strand without the 3′-(dT20) ssDNA tail (the top strand) is 5′-GCCTCGCTGCCGTCGCCA-3′. This top strand was radiolabeled with 32P at the 5′ end using T4 polynucleotide kinase (U. S. Biochemical Corp.) and purified as described (
      • Wong I.
      • Chao K.L.
      • Bujalowski W.
      • Lohman T.M.
      ). The radiolabeled strand was mixed with a 1.25-fold excess of bottom strand in 10 mm Tris, pH 8.3 (at 25 °C), and 50 mm NaCl, heated to 95 °C for 5 min, and then cooled slowly to room temperature. The “protein trap” was a 10-bp DNA hairpin with a 3′-(dT40) ssDNA tail (5′-GCCTCGCTGCT5GCAGCGAGGCT40-3′) and was used to prevent additional binding of free UvrD to the DNA substrate after DNA unwinding has been initiated (see below). The “DNA trap” was an 18-nucleotide ssDNA complementary to the 18-nucleotide top strand of the DNA substrate and was included to ensure that no re-annealing of the radiolabeled top strand occurred with the unwound 3′-(dT20)-ssDNA bottom strand either during unwinding or after quenching. The DNA trap anneals with the unwound 18-nucleotide top strand, but this species (a blunt ended 18-bp dsDNA) can be easily separated from the 3′-(dT20)-ds18 radiolabeled DNA substrate by non-denaturing gel electrophoresis (see below).
      Double-mixing Quenched Flow Experiments—Chemical quenched flow experiments were carried out using a three-pulsed quenched flow apparatus (KinTek RQF-3, University Park, PA) in the “double-mixing mode” maintained at 25 °C using a circulating water bath. UvrD, in Buffer T20 containing 0.2 mg/ml bovine serum albumin, was preincubated at 4 °C (on ice) for at least 20 min and then incubated in a 25 °C heat block for 15 min, after which it was loaded into one loop of the quenched flow apparatus and allowed to incubate for an additional 5 min at 25 °C before the experiment was started. Further incubation times (at 25 °C) up to 1 h had no effect on the results. The other loop was loaded with the radiolabeled 3′-(dT20)-ds18 DNA substrate in Buffer T20. The first push of the quenched flow apparatus rapidly mixed the contents of these two loops together, and the binding reaction (in the absence of ATP) was allowed to proceed for Δt 1 seconds. The second push then rapidly mixed these reaction contents with Buffer T20 containing 1 mm ATP:Mg2+, 2 μm protein trap, and 1 μm DNA trap. This second mixing event initiates unwinding of any DNA on which an active dimeric UvrD helicase has assembled within the time, Δt 1, while also preventing any further binding of UvrD to the DNA substrate after the first incubation time (Δt 1). The DNA unwinding reactions initiated after the second push of the quenched flow were allowed to proceed for Δt 2 = 20 s, after which the reaction contents were expelled into an Eppendorf tube containing 100 μlof0.4 m EDTA + 10% (v/v) glycerol to quench the reaction. A Δt 2 of 20 s is sufficient to allow any DNA unwinding reactions that were initiated by UvrD to be completed (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). The background fraction of ssDNA in the sample at t = 0 was determined by mixing the DNA substrate with Buffer T20 + 0.2 mg/ml bovine serum albumin, in the absence of UvrD. The DNA samples were analyzed by non-denaturing PAGE (10% PAGE) to separate the duplex DNA from the ssDNA, and the fraction of DNA unwound was quantitated as described (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ).
      The kinetics of dissociation of active UvrD helicase-DNA complexes were also performed using the KinTek quenched flow in the double-mixing mode. One syringe contained a mixture of 50 nm UvrD and 3 nm radiolabeled 3′-(dT20)-ds18 DNA substrate, which had been incubated for at least 5 min at 25 °C in one loop of the quenched flow. The other loop contained varying concentrations of the unlabeled 3′-(dT20)-ds18 DNA substrate. The contents of these two loops were then rapidly mixed and allowed to incubate for Δt 1 seconds, after which a second push mixed the solution with 1 mm ATP:Mg2+ to start the DNA unwinding reaction, along with 2 μm protein trap and 1 μm DNA trap, as described above.
      Analysis of Kinetic Data—The biphasic kinetic time courses for formation of the active UvrD helicase-DNA complexes were fit initially using non-linear least squares (NLLS) to the double-exponential function shown in Equation 1 to estimate the observed rates (k obs,1 and k obs,2) and amplitudes (A 1 and A 2) of both phases.
      F(t)=A1(1-e-kobs,1t)+A2(1-e-kobs,2t)
      (Eq. 1)


      For experiments performed at total initial UvrD concentrations ≥120 nm, both the monomer and pre-assembled UvrD dimer concentrations were in sufficiently large excess over the DNA substrate concentration (2 nm initial concentration) so that the reactions were pseudo-first order with respect to both the UvrD monomer and dimer concentrations.
      The software package SCIENTIST (MicroMath Software, St. Louis, MO) was used to analyze the kinetic data by numerical integration methods. The pre-steady state quenched flow experiments performed at sufficiently low total UvrD concentrations such that no UvrD dimer was present at the start of the reaction were analyzed according to Scheme 1, using the differential equations in Equations 2, 3, 4, 5, 6.
      d[Uf]dt=-k1[Uf][Df]-k2[Uf][UD]+k-1[UD]+k-2[U2D]
      (Eq. 2)


      d[Df]dt=-k1[Uf][Df]+k-1[UD]
      (Eq. 3)


      d[UD]dt=k1[Uf][Df]+k-2[U2D]-(k-1+k2)[UD]
      (Eq. 4)


      d[U2D]dt=k2[UD][Uf]+k-3[U2D*]-(k-2+k3)[U2D]
      (Eq. 5)


      d[U2D*]dt=k3[U2D]-k-3[U2D*]
      (Eq. 6)


      At the start of the reaction (t = 0), we set [Ut] = [Uf], [Dt] = [Df], and [UD] = [U2D] = [U2D*] = 0, where [Ut] is the total UvrD monomer concentration, and [Dt] is the total DNA substrate concentration. The fraction of DNA molecules unwound as a function of time, F(t), is related to the concentration of the active helicase species (U2D* in Scheme 1), according to Equation 7,
      F(t)=AU2D*[U2D*][Dt]
      (Eq. 7)


      where we note that [U2D*] is itself a function of time. A U2D* is the probability that the [U2D*] complex will proceed to form fully unwound ssDNA upon initiation of DNA unwinding. The second step in Scheme 1 was considered to be in rapid equilibrium relative to the third step. This was constrained in the NLLS fitting by setting k 2k 3 in Equations 2, 3, 4, 5, 6 (in general, fixing k 2 = 100 s1 was sufficient to satisfy this constraint) and then allowing k 2 to float. The equilibrium constant, K 2, was then calculated from K 2 = k 2/k 2.
      Global NLLS analysis of the pre-steady state quenched flow experiments performed over the entire UvrD concentration range used, where both dimers and monomers can be present at the start of the reaction, were analyzed using Scheme 2. The differential equations describing Scheme 2 are given in Equations 8, 9, 10, 11, 12, 13.
      d[Uf]dt=-k1[Uf][Df]-k2[Uf][UD]+k-1[UD]+k-2[U2D]
      (Eq. 8)


      d[Df]dt=-k1[Uf][Df]+k-1[UD]-k5[U2][Df]+k-5[U2D*]
      (Eq. 9)


      d[U2]dt=-k5[U2][Df]+k-5[U2D*]
      (Eq. 10)


      d[UD]dt=k1[Uf][Df]+k-2[U2D]-k-1[UD]+k2[UD][Uf]
      (Eq. 11)


      d[U2D]dt=k2[UD][Uf]+k-3[U2D*]-(k-2+k3)[U2D]
      (Eq. 12)


      d[U2D*]dt=k3[U2D]+k5[U2][Df]-(k-3+k-5)[U2D*]
      (Eq. 13)


      At t = 0, the initial concentrations of UvrD monomer and dimer, immediately after mixing of the reactants, were calculated using Equations 14 and 15.
      [Uf]=0.5-1+1+8L20[Ut]4L20
      (Eq. 14)


      [U2]=0.5L20-1+1+8L20[Ut]4L202
      (Eq. 15)


      where [Ut] is the total UvrD monomer concentration before mixing. Each of these concentrations is multiplied by 0.5 because the equilibrium between monomer and dimer is established at the concentrations that exist before the reactants are mixed (diluted 2-fold) to start the reaction. We have assumed that the rates of association and dissociation of the dimer are slow relative to all other rate constants in Scheme 2. Furthermore, at t = 0, [UD] = [U2D] = [U2D*] = 0. The rapid equilibrium condition for formation of the U2D species was constrained in the analysis as described above, and F(t) is defined as in Equation 7 above.
      Uncertainties are reported at the 68% confidence limit (±1 S.D.) and were calculated using SCIENTIST. In some NLLS analyses performed here, some of the fitting parameters were fixed at their experimentally determined values, whereas other parameters were allowed to float. In order to estimate the extent to which the uncertainty associated with the fixed parameters propagates to the calculated uncertainty of the floated parameters, a Monte Carlo method was employed as described previously (
      • Maluf N.K.
      • Lohman T.M.
      ). The UvrD species fraction distributions were calculated as described (
      • Maluf N.K.
      • Lohman T.M.
      ).

      RESULTS

      Kinetics of Formation of the Active UvrD Helicase-DNA Complex under Conditions Where Both UvrD Monomers and Dimers Are Populated in the Absence of DNA—Chemical quenched flow experiments were performed to study the kinetics of formation of the active UvrD helicase-DNA complex, starting from free DNA substrate and free UvrD protein. All experiments were carried out in Buffer T20 (10 mm Tris, pH 8.3, 20 mm NaCl, 20%(v/v) glycerol) at 25 °C, which are the identical conditions used to determine the equilibrium constants describing UvrD self-association, as well as the stoichiometries of UvrD binding to the DNA substrate (
      • Maluf N.K.
      • Lohman T.M.
      ). We have shown that under these solution conditions, UvrD can self-assemble to form dimers and tetramers in the absence of DNA, with dimerization constant, L 20 = [U2]/[U]2 = (2.33 ± 0.30) μm–1 and overall tetramerization constant, L 40 = [U4]/[U]4 = (5.11 ± 0.80) μm–3 (
      • Maluf N.K.
      • Lohman T.M.
      ). By using these equilibrium constants, we show in Fig. 1 the predicted distributions of UvrD monomers, dimers, and tetramers as a function of total UvrD concentration. Under these conditions, at least 90% of the UvrD protein exists in either the monomeric or dimeric state at total UvrD monomer concentrations of ≤500 nm.
      Figure thumbnail gr1
      Fig. 1UvrD oligomeric species fraction distributions. Fraction of total UvrD (monomer units) found as free monomers (M), dimers (D), and tetramers (T), as a function of total UvrD concentration. The species fractions were calculated using the dimerization and tetramerization self-association equilibrium constants, L 20 = (2.33 ± 0.30) μm–1, and L 40 = (5.11 ± 0.80) μm3 determined in Buffer T20, at 25 °C, as described by Maluf and Lohman (
      • Maluf N.K.
      • Lohman T.M.
      ).
      In previous studies (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ) we have shown that a dimer of UvrD is required to observe helicase activity in single turnover DNA unwinding experiments in vitro. As designed, these experiments are single turnover (single round) with respect to the DNA substrate, whereas multiple ATP turnovers are required for DNA unwinding of even an 18-bp DNA substrate. However, these studies did not address whether UvrD dimers that can pre-assemble in the absence of DNA (hereafter referred to as the “free dimer”) occur on the pathway to formation of the active UvrD helicase dimer on the DNA substrate. If formation of the free UvrD dimer occurs off-pathway, it would compete with formation of the active helicase dimer and thus inhibit formation of the active helicase-DNA complex. On the other hand, if formation of the free UvrD dimer occurs on the pathway to forming the active helicase dimer, then an increase in total UvrD concentration would increase the population of the free UvrD dimer, which would increase the rate of assembly of the active helicase dimer on the DNA substrate. We therefore examined the kinetic mechanism of formation of the active dimeric helicase-DNA complex, starting with free UvrD and free DNA, over a range of UvrD concentrations to determine whether the pre-assembled UvrD dimer occurs “on” or “off” the pathway to formation of the active helicase-DNA complex. Quantitative analysis of these kinetic studies was possible only because we have determined the equilibrium constants for assembly of the free UvrD dimer and tetramer from UvrD monomers under the identical solution conditions used in the kinetic studies (
      • Maluf N.K.
      • Lohman T.M.
      ). Such information is required in order to correlate the formation of active helicase-DNA complexes with the free concentrations of UvrD monomer, free UvrD dimer, or free UvrD tetramer.
      To study the kinetics of formation of the active dimeric UvrD helicase-DNA complex, we performed chemical quenched flow experiments, using the “double-mixing” mode of the KinTek quenched flow apparatus (see “Experimental Procedures”). As diagrammed in Fig. 2, one syringe contained UvrD in Buffer T20, whereas the other syringe contained 2 nm of a radiolabeled DNA unwinding substrate, also in Buffer T20. The DNA substrate used is the same substrate that we have used in previous studies (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ,
      • Maluf N.K.
      • Lohman T.M.
      ) and consists of a 3′ (dT)20 ssDNA tail attached to an 18-bp duplex DNA (3′-dT20-ds18). The contents of these two syringes were rapidly mixed in the first “push” of the quenched flow and allowed to incubate for a period of time (Δt 1), after which the resulting sample was then rapidly mixed with a third solution of 1 mm ATP:Mg2+, along with a large excess of a “protein trap” (a DNA molecule that consists of a 3′ (dT)40 ssDNA tail attached to a 10-bp hairpin). This second mixing event serves to initiate unwinding of any DNA substrates on which an active dimeric UvrD complex has assembled during the time of the first incubation period (Δt 1), whereas the large excess of trap for free protein prevents any binding or rebinding of free UvrD to the DNA substrate. The resulting DNA unwinding reaction was allowed to proceed for a constant time of 20 s (Δt 2), which is sufficient time to allow any productively bound UvrD to complete the unwinding of the 18-bp duplex, as determined in our previous studies (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). After 20 s, the solution was then expelled into a solution containing 0.4 m EDTA which quenches the unwinding reaction. By performing a series of experiments in which we varied the time, Δt 1, between the first and second push, we obtain the kinetic time course that monitors selectively the formation of UvrD-DNA complexes that are active in DNA unwinding.
      Figure thumbnail gr2
      Fig. 2Design of double-mixing quenched flow kinetics experiment. Schematic representation of the double-mixing quenched flow experiment for measuring the kinetics of formation of the active UvrD helicase-DNA substrate complex is shown.
      The total UvrD monomer concentration that exists before mixing with the DNA substrate, i.e. before the first push of the quenched flow apparatus, was used to calculate the free UvrD monomer and dimer concentrations before the start of the UvrD-DNA binding reaction, using the known UvrD monomerdimer-tetramer equilibrium constants (
      • Maluf N.K.
      • Lohman T.M.
      ). However, since the first mixing event dilutes each sample 2-fold, the concentrations of free UvrD monomer and dimer used for analysis of the kinetics of assembly of the active helicase-DNA complex have been reduced by a factor of 2.
      In this analysis we have assumed that the monomer-dimer equilibrium relaxes slowly with respect to the rate of binding of UvrD monomers and dimers to the DNA, which is supported by simulations (see “Discussion”). However, if the concentrations of free UvrD monomer and dimer are calculated using the 2-fold lower total UvrD concentration that exists after the first push, the quantitative results are not affected significantly.
      The second mixing event, whereby DNA unwinding is initiated by any UvrD that has assembled on the DNA as an active helicase, occurs under single turnover DNA unwinding conditions (due to the inclusion of the protein trap), and thus this second dilution of the sample does not need to be considered in the analysis. Based on these considerations, we refer to the concentration of UvrD that exists in the syringe prior to the first mixing event (first push) as the “pre-mix” concentration, and we refer to the concentration of UvrD that exists subsequent to the first mixing event as the “post-mix” concentration.
      Fig. 3, A and B, shows the results of experiments in which radiolabeled 3′-(dT20)-ds18 DNA substrate (1 nm post-mix concentration) was mixed with UvrD at 15, 60, 120, and 250 nm total UvrD monomer concentrations (post-mix). The experiments performed at 60, 120, and 250 nm UvrD show biphasic time courses. Furthermore, as the total UvrD concentration is decreased, the amplitude of the rapid first phase also decreases. In fact, the experiment performed at 15 nm UvrD displays a single exponential time course with no observable rapid first phase. These results suggest that the first fast phase results from the rapid binding to the DNA of pre-formed UvrD dimers since an increase in total UvrD concentration, which will increase the concentration of free UvrD dimer, results in an increase in the first phase amplitude. Because we know that a UvrD dimer is required to observe helicase activity in vitro,it is likely that the second slower phase of the time course represents the sequential binding of two monomers to form the active UvrD dimer-DNA complex. In fact, this should be the only pathway observed at low enough UvrD concentrations where only UvrD monomers exist in solution prior to the mixing of the reactants. Because the fraction of total UvrD existing as free UvrD tetramers is low (<10% at the highest UvrD concentration used in our experiments; see Fig. 1), we do not need to consider the binding of free tetramer in our analyses.
      Figure thumbnail gr3
      Fig. 3Pre-steady state kinetics of formation of the active UvrD helicase-DNA substrate complex determined using double-mixing quenched flow experiments. A, kinetic time courses obtained at a DNA (3′-(dT20)-ds18) concentration of 1 nm (post-mix) are plotted as the fraction of DNA molecules unwound as a function of Δt 1 up to 1.5 s for the four representative UvrD concentrations indicated ([UvrD] are post-mixing). The solid lines are simulations based on the best fit values using . B, time courses for the same experiments shown in A but displayed over 50 s. C, best fit values of the first phase rate constant, k obs,1, obtained from NLLS analysis using , plotted versus the total UvrD concentration (monomer units; post-mixing). The plotted values are the averages of at least three experiments for all concentrations except at 120 nm, which is the average of two experiments. D, best fit values of the second phase rate constant, k obs,2, plotted versus the total UvrD concentration (post-mixing). These data were fit to a hyperbolic equation, the results of which are shown as the solid line. The plotted values are the averages of at least three experiments for all concentrations except at 120 nm, which is the average of two experiments.
      The values of k obs,1 and k obs,2, which are the observed rate constants for the first rapid phase and the second slower phase, were determined for each experiment using Equation 1 and are plotted as a function of total UvrD concentration (post-mix) in Fig. 3, C and D. Each experiment was performed at least three times (except for the experiment performed at a pre-mix concentration of 240 nm UvrD, which was performed only twice). The values of k obs,1 for UvrD concentrations ≤40 nm (concentration post mixing) are not plotted since the uncertainties associated with these data were large due to the small amplitude of the first phase at these low UvrD concentrations. Fig. 3C shows that k obs,1 increases with increasing UvrD concentration, presumably reflecting the increase in concentration of free UvrD dimers.
      Fig. 3D shows that k obs,2 increases hyperbolically with UvrD concentration, reaching a maximum value of (0.35 ± 0.01) s1. As described above, the quenched flow assay used here detects the formation of functional UvrD helicase-DNA complexes that remain after the addition of a large excess of protein trap. Therefore, this hyperbolic dependence of k obs,2 shows that the rate of formation of the active UvrD-DNA substrate complex, starting from free UvrD monomers, is limited at high [UvrD] by at least one first order process whose forward and reverse rate constants (k 3 + k 3 in Scheme 1) sum to (0.35 ± 0.01) s1.
      Fig. 4 shows the fraction of the first phase amplitude (A 1/(A 1 + A 2); filled circles) plotted as a function of the total UvrD monomer concentration (pre-mix). Overlaid on these data are the species fractions for the UvrD monomer, dimer, and tetramer predicted to be present in solution before mixing with the DNA substrate (
      • Maluf N.K.
      • Lohman T.M.
      ) (see Fig. 1). These data show that the amplitude of the first rapid phase is well correlated with the fraction of free UvrD dimers pre-assembled in solution, suggesting strongly that this phase reflects the rapid binding to the DNA of free UvrD dimers.
      Figure thumbnail gr4
      Fig. 4The fraction of the first phase amplitude of the kinetic time courses correlates with the fraction of UvrD present as free dimers. The fraction of the first phase amplitude, A 1/(A 1 + A 2) (filled circles), obtained from the kinetic traces in , is plotted versus the total UvrD concentration (pre-mixing). Also shown are the calculated species fraction distributions for the UvrD monomers, dimers, and tetramers, in the absence of DNA substrate, calculated using the known equilibrium association constants for the UvrD dimerization and tetramerization, L 20 = (2.33 ± 0.30) μm1 and L 40 = (5.11 ± 0.80) μm3, respectively. Pre-inc, preincubated.
      Kinetic Mechanism of Formation of the Functional Dimeric UvrD Helicase-DNA Complex from Free UvrD Monomers—We next performed double-mixing quenched flow experiments over a range of total UvrD concentrations that were low enough (≤10 nm UvrD monomer; pre-mixing concentrations) to ensure that >95% of the free UvrD was monomeric before addition of the DNA. These experiments were performed as described above, except that the final DNA substrate concentration (postmix) was reduced to 0.5 nm. The kinetic time courses for these reactions are shown in Fig. 5A. Each time course can be described by a single exponential phase up to the highest UvrD concentration examined (5 nm UvrD monomer, post-mix). The observed rate constant (k obs,2) and amplitude of the reaction both increase with increasing UvrD concentration. The rapid phase (with rate constant k obs,1) that is observed at higher UvrD concentrations is not observed at these low UvrD concentrations since free UvrD dimers are not present before mixing with DNA.
      Figure thumbnail gr5
      Fig. 5Kinetics of formation of the active, dimeric helicase-DNA substrate complex starting from free UvrD monomers. A, pre-steady state kinetics of formation of the active helicase-DNA substrate complex determined using double-mixing quenched flow experiments, at the sufficiently low UvrD concentrations indicated (total UvrD monomer concentrations obtained post-mixing), such that no UvrD dimers were present before the addition of DNA. The solid lines are simulations according to (Equations , , , , , ), using the best fit parameters listed in that were obtained from the global NLLS analysis of the data. B, the observed rate constant for the second slow phase of the kinetic time course, k obs,2, plotted versus the free UvrD monomer concentration (post-mix), calculated using . These data were included in the global NLLS analysis shown in A. The solid line is a simulation using and the best fit parameters given in .
      Based on these data, we propose the minimal kinetic mechanism shown in Scheme 1. Because we have shown (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ) that the active form of the UvrD helicase is a dimer in vitro, we designate the functional dimeric helicase-DNA complex as U2D* in Scheme 1. The first step in Scheme 1, with rate constants, k 1 and k 1, is the binding of a UvrD monomer, U, to the DNA substrate to form a monomer-DNA complex, UD. The second step, with rate constants k 2 and k 2, represents the binding to DNA of a second UvrD monomer to form a U2D complex, which is not yet active as a helicase. The third step in Scheme 1, with rate constants k 3 and k 3, is an isomerization step to form the active dimeric UvrD-DNA complex, U2D*. Evidence for the final isomerization step in Scheme 1 is based on the fact that we observe a hyperbolic dependence of k obs,2 on UvrD concentration, thus indicating a unimolecular step that limits the rate of formation of the active U2D* helicase at high [UvrD].
      The observation of a plateau in k obs,2 at high [UvrD] (Figs. 3D and 5B) also indicates that the U2D species in Scheme 1 is not protected from the protein trap and thus is not a tightly bound complex, whereas the U2D* species is not susceptible to the protein trap. Specifically, the species U2D in Scheme 1 must have a sufficiently short lifetime so that some part of it (presumably one UvrD monomer) will dissociate from the DNA and become bound by the protein trap. If this were not the case, then k obs,2 would not be predicted to reach a plateau value at high [UvrD] but rather would continue increasing with increasing [UvrD]. Thus, any U2D species present upon addition of a protein trap will not proceed to form the active U2D* helicase. The assumption that only the U2D* species in Scheme 1 has helicase activity results in two important predictions. The first is that the binding of the second UvrD monomer, to form the U2D species, must equilibrate rapidly with respect to the rate of formation of the U2D* species (i.e. k 2k 3). If this were not the case, computer simulations for Scheme 1 indicate that a significant lag phase would occur in the time courses, which we do not observe experimentally (Fig. 5A). As a result, information about the values of the individual rate constants, k 2 or k 2, cannot be obtained from these data, although we can obtain a lower limit estimate for k 2. As such, we describe this step by the equilibrium constant, K 2 = k 2/k 2.
      The second prediction is that the rate of formation of the UD species occurs rapidly enough on the time scale of formation of the U2D* species that it can be assumed to form instantaneously upon mixing. Again, if this were not the case, computer simulations indicate that a significant lag phase would be present in the time courses. Preliminary stopped flow experiments also support this conclusion and indicate that the rate constant k 1 in Scheme 1 is on the order of 1.2 × 108m–1 s1.
      N. K. Maluf, unpublished experiments.
      Our NLLS analysis of the data in Fig. 5A (discussed below) also yields a lower limit estimate for k 1 ∼ 1 × 108m–1 s1. Furthermore, based on our previous studies (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ,
      • Maluf N.K.
      • Lohman T.M.
      ), the equilibrium association constant for monomer binding to the DNA substrate to form the UD species (K 1 = k 1/k 1) is greater than 1 × 109m–1, which yields an upper limit estimate for k 1 = k 1/K 1 = 0.12 s1. In our NLLS analysis of the data shown in Fig. 5A,we therefore constrained k 1 = 1 × 109m–1 s1 and k 1 = 0 in order to estimate the parameters K 2 (K 2 = k 2/k 2), k 3, k 3, and A U2D*. Varying k 1 from 0 to 0.12 s1 did not affect the values of the other fitted parameters. By fixing k 1 = 1 × 109m–1 s1 and k 1 = 0, we can treat Scheme 1 as beginning with the second step, since the formation of the UD species occurs essentially instantaneously with respect to the U2D* species.
      In order to estimate the kinetic parameters for Scheme 1, we performed a global NLLS analysis using two data sets. The first data set corresponds to the full time courses shown in Fig. 5A, which were obtained at low enough [UvrD] (1, 2, 3.5, and 5 nm UvrD monomer concentration (post-mix)) so that only UvrD monomers are present before the start of the reaction. These time courses were analyzed using Equations 2, 3, 4, 5, 6, 7. We also analyzed the observed dependence of k obs,2 on the free UvrD monomer concentration (post-mix) shown in Fig. 5B. These data were obtained from the experiments performed at higher [UvrD] (Fig. 3D), where biphasic kinetics are observed due to the presence of both free UvrD dimers and UvrD monomers before the start of the binding reaction. These data were originally plotted versus the total UvrD monomer concentration in Fig. 3D and are re-plotted in Fig. 5B versus the free UvrD monomer concentration (see Equation 14 under “Experimental Procedures” for details on the calculation of the free UvrD monomer concentration that exists post-mixing).
      Based on the assumptions stated above, namely that 1) a unimolecular step is rate-limiting for formation of U2D* from free UvrD monomers, 2) formation of the UD species is much faster than formation of U2D*, and 3) the U2D species equilibrates rapidly with respect to U2D*, Scheme 1 predicts Equation 16 for the dependence of k obs,2 on the free UvrD monomer concentration ([Uf]) (
      • Johnson K.A.
      ),
      kobs,2=K2k3[Uf]1+K2[Uf]+k-3
      (Eq. 16)


      where K 2 is the equilibrium association constant for step 2 in Scheme 1. In fact, Equation 16 is the expression for the rate of formation of the active dimeric UvrD-DNA helicase complex (U2D*), starting from the UD species in Scheme 1. The experimental hyperbolic dependence of k obs,2 on free UvrD concentration observed in Fig. 5B is predicted by Equation 16.
      The best fit parameters resulting from the global NLLS analysis of both sets of data in Fig. 5 are given in Table I. The smooth curves shown in Fig. 5A are simulations using Equations 2, 3, 4, 5, 6, 7 and the best fit parameters from the NLLS analysis (Table I). The smooth curve shown in Fig. 5B is a simulation using Equation 16 and the best fit parameters in Table I. As seen in Fig. 5, A and B, Scheme 1 describes these data quite well over a wide range of UvrD concentrations.
      Table IKinetic parameters for Scheme 1 from global NLLS analysis
      k1k-1K2
      a Defined as a rapid equilibrium step.
      k3k-3K3K 2,ov = K 2(1 + K 3)A U2D**
      m-1 s-1s-1m-1s-1m-1
      1 × 109
      b Values are fixed.
      0
      b Values are fixed.
      (4.9 ± 0.7) × 1070.337 ± 0.0160.030 ± 0.00611.2 ± 2.3(6.0 ± 1.4) × 1080.59 ± 0.06
      a Defined as a rapid equilibrium step.
      b Values are fixed.
      As discussed above, since a plateau in k obs,2 is observed with increasing UvrD concentrations, we reasoned that the U2D species could not have significant helicase activity under the single turnover DNA unwinding conditions used here. To test this further, we also analyzed the data in Fig. 5 by allowing both the U2D and the U2D* species to have some helicase activity. This was done by assigning an amplitude term to the U2D species (A U2D), in addition to the U2D* species (A U2D*). The best fit value returned for A U2D was 0.02 ± 0.03, which is zero within the uncertainty, whereas the best fit value for A U2D* was 0.56 ± 0.08. This result indicates that all helicase activity, within error, is associated with the U2D* species.
      We also attempted to analyze the kinetic time courses using a model that assumes some of the UvrD monomer exists in equilibrium between a “competent” and “incompetent” conformation, with the latter form being unable to bind the DNA substrate (data not shown). According to such a model, the hyperbolic dependence of k obs,2 on UvrD concentration might result if the rate of formation of the active, dimeric helicase complex is limited by the rate of a conformational change from the incompetent monomer to the competent monomer, after which the sequential binding of two monomers would still be required to form the active complex. However, this model was not able to describe the data quantitatively since it overestimated the plateau value of k obs,2 at high [UvrD] by ∼30% and resulted in a higher sum of the squared residuals.
      Rate Constant for Dissociation of the Active UvrD Helicase Complex from DNA—The NLLS analysis described above yields an estimate of k 3 = (0.030 ± 0.006) s1 for the rate constant for formation of the inactive U2D complex from the active U2D* helicase-DNA complex (see Scheme 1). As a further test of this mechanism and our analysis, we performed experiments to obtain an independent estimate of k 3. The design of these experiments is shown schematically in Fig. 6A, and they were performed using the double-mixing mode of the KinTek quenched flow apparatus. One syringe of the quenched flow contained a mixture of 50 nm UvrD with 3 nm of the radiolabeled 3′-(dT20)-ds18, whereas the other syringe contained an excess of unlabeled 3′-(dT20)-ds18. The contents of the two syringes were rapidly mixed, and the solution was allowed to incubate for Δt 1 seconds, after which the second push mixed the solution with 1 mm ATP:Mg2+ along with an excess of the 3′-(dT40)-ds10HP protein trap. The resulting solution was incubated for Δt 2 = 20 s and then quenched with excess EDTA. This second mixing event serves to initiate DNA unwinding by any UvrD that is both active as a helicase and remains bound to the DNA substrate after the first Δt 1 seconds. By varying Δt 1 in a series of experiments, we can measure the time-dependent loss of active helicase-DNA complexes, since the observed amplitude of DNA unwinding is proportional to the population of active, dimeric UvrD helicase-DNA complexes remaining after time Δt 1.
      Figure thumbnail gr8
      Fig. 6Double-mixing quenched flow experiments designed to measure the net dissociation rate of the active helicase-DNA complex (U2D* species). A, schematic of the experimental design used to measure the rate of dissociation of the U2D* species upon mixing with excess trap. B, representative experiment in which 50 nm UvrD was preincubated with 3 nm radiolabeled 3′-(dT20)-ds18 DNA substrate, and then mixed with 1 μm unlabeled DNA substrate. The experiment monitors the amount of active complex remaining after Δt 1 seconds. The solid line shows the NLLS fit of the data to a single exponential function, from which we estimate the observed dissociation rate constant, k d, of the U2D* species (see ). C, values of kd were measured using a range of trap concentrations (unlabeled 3′-(dT20)-ds18 DNA substrate, from 75 nm to 5 μm, concentrations post-mixing). k d is independent of trap concentration, with an average value of (0.038 ± 0.003) s1.
      These experiments were performed using a range of protein trap (unlabeled 3′-dT20-ds18 DNA) concentrations, and the time course of a representative experiment is shown in Fig. 6B. All kinetic traces were well described by a single exponential phase, and as shown in Fig. 6C, the value for the observed dissociation rate constant, k d, is independent of trap concentration, with an average value of (0.038 ± 0.003) s1. In general, this value reflects the sum of all rate constants for all pathways leading to loss of the U2D* species. However, this value is the same, within our uncertainty, as the value of k 3 (0.030 ± 0.006) s1 determined from the global NLLS analysis of the data in Fig. 5. Hence, the net rate of loss of the U2D* species is dominated by the rate constant k 3 in Scheme 1. However, this does not rule out the presence of other slower pathways for loss of the U2D* species.
      Minimal Kinetic Mechanism for Formation of a Functional UvrD Helicase-DNA Complex under Conditions Where Free UvrD Monomers and Dimers Are Both Populated—In the experiments described above that were performed at pre-mix UvrD concentrations ≥80 nm, we interpreted the biphasic kinetic time courses observed for formation of the active, dimeric helicase-DNA complex (U2D*) as indicating that the active helicase can be formed via two pathways. The faster phase reflects formation of U2D* via the binding of free UvrD dimers to the DNA substrate, whereas the slower pathway reflects formation of U2D* via the sequential binding of two UvrD monomers to the DNA. Therefore, analysis of the UvrD concentration dependence of the time courses, at UvrD concentrations where both monomers and dimers are initially populated, should provide a further test of this model since the competition for binding to the DNA substrate between free UvrD monomers and free UvrD dimers will dictate the flux through each pathway (monomer versus dimer).
      Fig. 7 shows the results of a series of quenched flow experiments performed at UvrD concentrations of 10, 15, 40, 60, 90, 120, and 250 nm, at a DNA substrate concentration of 1 nm (post-mixing concentrations). Each time course within the data set that was analyzed consists of an average of two independent experiments collected over the course of 4 days, in which the data points were obtained using identical time intervals, except for the experiments performed at the two lowest UvrD concentrations (10 and 15 nm), each of which consisted of only a single time course.
      Figure thumbnail gr9
      Fig. 7Global NLLS analysis of the kinetics of formation of the active, dimeric helicase-DNA substrate complex under conditions where the free UvrD exists as a mixture of monomers and dimers. A, time courses for formation of the active, dimeric UvrD helicase-DNA complex obtained from double-mixing quenched flow experiments performed at UvrD concentrations (post-mixing) from 10 to 250 nm, and a 3′-(dT20)-ds18 DNA substrate concentration (post-mixing) of 1 nm. The smooth curves are simulations using the best fit values listed in Tables and and obtained from the global NLLS fitting of the data to (Equations , , , , , , , , ). Filled circles, 250 nm UvrD; filled squares, 120 nm UvrD; filled diamonds, 90 nm UvrD; filled triangles, 60 nm UvrD; filled inverted triangles, 40 nm UvrD; open circles, 15 nm UvrD; open squares, 10 nm UvrD. B, time courses in A are shown over 50 s.
      The simplest mechanism that describes the biphasic kinetic time courses (Fig. 7) is given in Scheme 2. This scheme includes the kinetic pathway already described for the sequential binding of two UvrD monomers (Scheme 1) but also incorporates a kinetic path for direct binding of free UvrD dimer to the DNA. In our analysis of the kinetic data using Scheme 2, we assumed that the rate constants for the formation and dissociation of the free UvrD dimer are slow relative to the other rate constants in Scheme 2, such that the distribution of monomers and dimers can be described by the equilibrium constant, L 20 = k 4/k 4, and that this distribution does not change significantly upon initiation of the reaction. However, use of the UvrD monomer and dimer concentrations calculated from the total UvrD concentration present after mixing does not affect the results within the reported uncertainties. For each experiment performed at each total UvrD concentration, the total free UvrD monomer concentration was sufficiently large to ensure pseudo-first order conditions (i.e. [Uf] ≫ [Dt] at a DNA substrate concentration of 1 nm (post-mix)). However, for experiments performed at total UvrD concentrations <60 nm (post-mixing), the free UvrD dimer concentration was not large enough to satisfy pseudo-first order conditions. As a result, these data were analyzed using numerical integration methods so that all the data shown in Fig. 7 could be included in the global NLLS analysis using Equations 7, 8, 9, 10, 11, 12, 13, 14, 15.
      In our NLLS analysis of these data, we constrained K 2, k 3, and k 3 to have the values given in Table I that were determined from analysis of the data at low UvrD concentration (data in Fig. 5), using Scheme 1. We also made use of two further constraints. In our previous study (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ), we determined that K 1/K 2,ov = 10 ± 3 from studies of the binding of UvrD to the 3′-(dT20)-ds18 substrate under identical solution conditions and temperature. The equilibrium constant, K 2,ov = K 2(1 + K 3), describes the equilibrium for formation of the sum of the U2D and the U2D* species from the binding of U to the UD species. Based on Scheme 1, analysis of the experiments in Fig. 5 yields a value of K 2,ov = (6.0 ± 1.4) × 108m–1 (see Table I). From this we calculate K 1 = (6.0 ± 2.3) × 109m–1 (see Table I), which we used to constrain the value of k 1 = k 1/K 1 in the NLLS analysis. Furthermore, based on the thermodynamic linkage in Scheme 2, K 5 = K 1 K 2 K 3/L 20, from which we calculate K 5 = (1.4 ± 0.7) × 1012m–1 (see Table II). This value was then used to constrain the value of k 5 (=k 5/K 5) in the NLLS analysis.
      Table IIKinetic parameters for Scheme 2 from global NLLS analysis
      K1k1k -1 = k 1/K1K 5 = K 1 K 2 K 3/L20k5k -5 = k 5/K5A U2D**
      m-1m-1 s-1s-1m-1m-1 s-1s-1
      (6.0 ± 2.3) × 109
      a Values are fixed.
      (1.5 ± 0.2) × 1080.025 ± 0.005(1.4 ± 0.7) × 1012
      a Values are fixed.
      (1.1 ± 0.2) × 108(8 ± 4) × 10-50.62 ± 0.02
      a Values are fixed.
      With these constraints, the data in Fig. 7 were analyzed based on Scheme 2 (Equations 7, 8, 9, 10, 11, 12, 13, 14, 15; see under “Experimental Procedures”), floating k 1, k 5, and the amplitude terms for each time course, whereas constraining K 2, k 3, k 3, k 1, and k 5 as described above (see Table I). The smooth curves shown in Fig. 7, A and B, are simulations based on the best fit parameters obtained from this global NLLS analysis (see Table II). These simulations show that Scheme 2 describes the data well, predicting both the decrease in the first phase amplitude and rate constant with decreasing total UvrD concentration. This analysis also provided estimates of the rate constants for the binding of the first monomer to the DNA substrate, k 1 = (1.5 ± 0.2) × 108m–1 s1 and the binding of the dimer to the DNA substrate, k 5 = (1.1 ± 0.2) × 108m–1 s1. These parameters were well constrained in the global analysis since both the amplitude and the rate of the first phase are functions of k 1[Uf] and k 5[U2].
      We also considered more complicated schemes that included additional steps after the binding of the dimer to the DNA substrate but before the formation of the final active complex. These models did not provide any better description of the data, indicating that if additional steps are present, these steps must be rapid enough so as to not influence the analysis of the experiments performed here.

      DISCUSSION

      Our previous studies have shown that a dimer of UvrD is the active form of the helicase in vitro (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ,
      • Maluf N.K.
      • Lohman T.M.
      ). One subunit of the active dimer interacts tightly with the 3′ ss/dsDNA junction, whereas the second subunit interacts with the distal 3′ ssDNA tail, and interactions between the two subunits of the dimer are required for helicase activity (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ). Because UvrD can self-associate to form dimers in the absence of DNA, we wished to examine whether the free UvrD dimer is on the pathway to forming the functional helicase on the DNA or whether it is “off the pathway” and thus inhibitory to formation of the active helicase. Transient kinetic studies are required to determine the pathways by which UvrD binds to the DNA substrate and subsequently forms the active helicase-DNA complex.
      To measure the kinetic time course for formation of the active UvrD helicase-DNA complex, we performed a series of pre-steady state quenched flow kinetic experiments over a range of UvrD concentrations. These experiments were carried out using the double-mixing mode of the KinTek quenched flow apparatus, and the experimental design described here and elsewhere (
      • Pang P.S.
      • Jankowsky E.
      • Planet P.J.
      • Pyle A.M.
      ) provides a means to examine the kinetics and mechanism of formation of the active helicase complex on the DNA separately from the subsequent kinetics of helicase-catalyzed DNA unwinding (
      • Pang P.S.
      • Jankowsky E.
      • Planet P.J.
      • Pyle A.M.
      ). Such double-mixing experiments should be generally useful for studies of the mechanism of assembly of helicase-DNA complexes. These assays have the distinct advantage that they can monitor directly the formation of the active helicase complex, yet avoid the complication of having to consider the kinetics of the actual DNA unwinding reaction.
      Quantitative analysis of the kinetic experiments reported here required quantitative information about the distribution of assembly states of the UvrD protein in the absence of DNA. Such information was available from our previous studies of the equilibrium constants for UvrD dimerization and tetramerization that were performed under the same solution conditions used in the kinetic studies described here. Knowledge of these equilibrium constants was essential for this analysis since it was necessary to know the free UvrD monomer and dimer concentrations at the start of the reaction (Δt 1 = 0). To simplify the interpretation of these experiments, we restricted our experiments to total UvrD monomer concentrations ≤500 nm, since at higher concentrations UvrD can form tetramers in the absence of DNA (
      • Maluf N.K.
      • Lohman T.M.
      ) (see Fig. 1). Our previous sedimentation equilibrium studies of UvrD binding to the 3′-(dT20)-ds18 DNA substrate, which is the same DNA substrate used in the current studies, did not show any evidence for an equilibrium species consisting of a UvrD tetramer bound to the DNA substrate; therefore, we have focused on studying the monomer and dimer species in the experiments reported here.
      Our studies have shown that the active dimeric UvrD-DNA complex can be formed via two pathways in vitro. One pathway involves the direct binding to the DNA of a self-assembled UvrD dimer, which can then proceed to initiate DNA unwinding rapidly (dimer path). The second, slower pathway involves the sequential binding of two UvrD monomers to the DNA substrate which then assemble on the DNA to form the active helicase complex (monomer path). The relative flux through either pathway depends on the initial concentrations of the free UvrD monomer and dimer.
      The fact that pre-assembled UvrD dimers are competent to bind DNA rapidly to form a functional helicase on the DNA indicates that the pre-assembled UvrD dimer occurs on the pathway to formation of the functional helicase. We find no evidence that a pre-assembled UvrD dimer must first dissociate to form monomers and re-assemble to form the active, dimeric complex bound to the DNA substrate. These results suggest that the protein-protein interface of the pre-assembled UvrD dimer is similar to that found in the functional UvrD helicase bound to the DNA substrate. Any structural rearrangements of the UvrD dimer that might be required for helicase function, upon binding the DNA substrate, are not rate-limiting. In contrast, the rate of formation of the active dimeric UvrD helicase from UvrD monomers is limited by steps involving assembly of the functional helicase dimer on the DNA.
      Minimal Kinetic Mechanism for the Formation of the Active UvrD Helicase-DNA Complex—Based on the global NLLS analysis of the series of quenched flow experiments performed as a function of UvrD concentration, we propose the minimal kinetic mechanism in Scheme 2 and have estimated the rate constants describing this scheme. In Scheme 2, the monomer pathway starts with the rapid binding of a monomer to the DNA substrate to form a UD species. Even though we know that the highest affinity site on the DNA substrate is at the ss/dsDNA junction, it is likely that a UvrD monomer first binds to the 3′ ssDNA tail and then diffuses to the ss/dsDNA junction. After this first binding event, a second UvrD monomer binds, forming the first doubly ligated complex (U2D). The kinetic data indicate that this step equilibrates rapidly with respect to the next slower step and thus can be described by equilibrium constant K 2 = (4.9 ± 0.7) × 107m–1. By systematically lowering the rate constant k 2 in Scheme 1 to observe the effect on the NLLS fit of the data in Fig. 5, we determined a lower limit for k 2 of ∼3 s1. This then provides a lower limit for the association rate constant for this step of k 2 > ∼1.5 × 108m–1 s1, which is similar to the value of (1.5 ± 0.2) × 108m–1 s–1 determined for k 1 from the final global fit of the data in Fig. 7 to Scheme 2.
      The final step in the monomer pathway is an isomerization to form the “trap-protected” U2D* species, which is the species that displays helicase activity. This step occurs with rate constant k 3 = (0.337 ± 0.016) s1 and k 3 = (0.030 ± 0.006) s1 (K 3 = 11.2 ± 2.3). Our experiments further indicate that the U2D species cannot be an active helicase, since upon addition of trap it dissociates rather than proceeds to form the active U2D* species.
      A consequence of the mechanisms shown in Schemes 1 and 2 is that at equilibrium there always will be a mixed population of both the U2D and U2D* complexes on the DNA. As a result, even at UvrD concentrations that saturate the DNA substrate, some fraction of the DNA substrate will not be unwound since some fraction of the UvrD dimers will be present as the inactive, trappable U2D species. Therefore, the total unwinding amplitude (A tot) obtained from a single turnover DNA unwinding experiment performed at saturating UvrD concentrations will always be smaller than A U2D* by the fraction K 3/(1 + K 3), i.e. A tot = A U2D*(K 3/(1 + K 3)). In fact, we have never observed complete unwinding of any DNA substrate by UvrD under single turnover conditions (i.e. in the presence of a protein trap) (
      • Maluf N.K.
      • Fischer C.J.
      • Lohman T.M.
      ), and this can be partly explained by the finite equilibrium between the U2D and U2D* species. However, the finite processivity of UvrD unwinding (
      • Ali J.A.
      • Lohman T.M.
      ) will also contribute to this lower observed extent of unwinding.
      Our experiments indicate that pre-assembled UvrD dimers bind rapidly to the DNA substrate to form a functional helicase complex without proceeding through the same rate-limiting steps observed along the monomer pathway. In fact, we can rule out the possibility that the pre-assembled UvrD dimer binds to the DNA substrate first to form the U2D intermediate (step 6 of Scheme 2 (dashed arrows)). If this pathway were used, then the first rapid phase would not be observed in the double-mixing quenched flow experiments, since formation of the active helicase complex would now also have to proceed through the same rate-limiting step, k 3, that is present in the monomer pathway.
      According to Scheme 2, the U2D* species can dissociate via two pathways. One path involves disruption of the functional dimer interface to form the U2D species. The rate constant for this step, k 3, is (0.030 ± 0.006) s1 and is the same as the observed dissociation rate constant, k d = (0.038 ± 0.003) s1, that we measured for the overall dissociation of the U2D* species. The other pathway involves direct dissociation of the active UvrD dimer from the DNA substrate, with the dimer remaining intact. The rate constant for this step, k 5 = (8 ± 4) × 105 s1, is 375-fold slower than k 3. Therefore, the functional UvrD dimer (U2D*) rarely dissociates directly from the DNA substrate, rather it decays primarily via the k 3 pathway.
      Additional evidence that the monomer pathway involves assembly of DNA-bound UvrD monomers to form the proper UvrD dimer interface comes from consideration of the magnitude of the association rate constant for binding of the second monomer to the UD species (k 2). The lower limit of 1.5 × 108m–1 s1 that we estimate for k 2 is ∼50–100-fold faster than association rate constants generally observed for protein-protein association reactions (
      • Northrup S.H.
      • Erickson H.P.
      ). This suggests that the process described by rate constant k 2 does not represent a protein-protein association. Rather, the lower limit for k 2 is similar to the association rate constant for the first monomer binding to the DNA substrate, k 1, suggesting that k 2 reflects the binding of the second monomer directly to the 3′ ssDNA tail of the DNA substrate. If this is the case, then the next step toward forming the active complex likely involves association of the two monomers to form a dimer on the DNA substrate.
      Comparisons with the Mechanism of Initiation of DNA Unwinding by E. coli Rep Helicase in Vitro—A previous study (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ) examined the kinetics of initiation of DNA unwinding by the E. coli Rep helicase in vitro. Rep is also a 3′ to 5′ SF1 helicase that is structurally homologous (
      • Korolev S.
      • Hsieh J.
      • Gauss G.H.
      • Lohman T.M.
      • Waksman G.
      ) to both UvrD and Bacillus stearothermophilus PcrA (
      • Subramanya H.S.
      • Bird L.E.
      • Brannigan J.A.
      • Wigley D.B.
      ). In contrast to UvrD, the Rep protein remains monomeric and does not self-associate in the absence of DNA (
      • Chao K.L.
      • Lohman T.M.
      ). Furthermore, Rep monomers are also not able to initiate DNA unwinding, and a Rep oligomer is required to unwind a DNA substrate in vitro (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ,
      • Ha T.
      • Rasnik I.
      • Cheng W.
      • Babcock H.P.
      • Gauss G.H.
      • Lohman T.M.
      • Chu S.
      ). Hence the kinetics of assembly of the active Rep helicase are similar to those reported here for the UvrD monomer pathway. However, the Rep experiments were performed in the presence of 1.5 mm ATP, in contrast to the double-mixing experiments performed here with UvrD, which measure formation of the active UvrD helicase in the absence of ATP. Cheng et al. (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ) showed that a Rep monomer first binds to the DNA substrate with an association rate constant of (5 ± 1) × 107m–1 s1 and then undergoes an isomerization reaction to form a complex that is competent to bind a second Rep monomer. A second Rep monomer can then bind with an association rate constant of (2.1 ± 0.3) × 105m–1 s1 to form a dimeric complex that is capable of unwinding the DNA substrate. The rate constant for binding of the second Rep monomer is ∼240-fold smaller than that for binding of the first Rep monomer. The differences observed for the kinetics of DNA binding and assembly of the active helicase-DNA complexes from Rep monomers versus UvrD monomers may be due to the fact that ATP was present during the steps leading to formation of the active Rep helicase complex (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ), whereas ATP is absent in the UvrD experiments reported here. However, the differences may also reflect protein-specific effects. Recent single molecule fluorescence experiments have also shown that a Rep helicase can stall or pause during the course of DNA unwinding (
      • Ha T.
      • Rasnik I.
      • Cheng W.
      • Babcock H.P.
      • Gauss G.H.
      • Lohman T.M.
      • Chu S.
      ). These stalled complexes appear to result from partial dissociation of the active oligomeric Rep complex, leaving behind an inactive Rep monomer still bound to the DNA substrate (
      • Ha T.
      • Rasnik I.
      • Cheng W.
      • Babcock H.P.
      • Gauss G.H.
      • Lohman T.M.
      • Chu S.
      ). Addition of Rep to a stalled complex allows the re-formation of the active oligomeric complex, which can then continue DNA unwinding.
      What Is the Protein-Protein Interface in the Functional UvrD Dimer?—The model that emerges from these studies is that the protein-protein interface of the free UvrD dimer that can form in the absence of DNA is the same, or very similar to the interface of the functional dimeric UvrD helicase on the DNA substrate. A major question that remains involves identification of the dimerization interface. Mechanic et al. (
      • Mechanic L.E.
      • Hall M.C.
      • Matson S.W.
      ) previously examined the effect on UvrD self-association of deleting 40 amino acids from its C terminus to form UvrDΔ40. Sedimentation equilibrium experiments did not detect any self-assembly of UvrDΔ40 in buffer containing 200 mm NaCl, 20%(v/v) glycerol, pH 8.3, at 20 °C, even though full-length wild type UvrD forms dimers under these same conditions (
      • Mechanic L.E.
      • Hall M.C.
      • Matson S.W.
      ). We have also performed sedimentation equilibrium experiments with a similar UvrD deletion mutant in which 73 amino acids were deleted from the C terminus of UvrD to form UvrDΔ73. These experiments were performed in the same buffer as reported for UvrDΔ40 (
      • Mechanic L.E.
      • Hall M.C.
      • Matson S.W.
      ), except at 25 rather than 20 °C.
      N. K. Maluf and T. M. Lohman, unpublished data.
      We found that UvrDΔ73 also failed to dimerize under these conditions at μm loading concentrations, even though the wild type UvrD can dimerize under these same conditions. However, upon lowering the [NaCl] to 20 mm (25 °C), UvrDΔ73 does undergo self-association to form both dimers and tetramers, although the equilibrium association constants for dimerization (L 20) and tetramerization (L 40) are reduced by 25- and ∼1800-fold, respectively, compared with wild type UvrD protein under the same conditions. These data indicate that the C-terminal region of UvrD stabilizes dimerization and tetramerization, although it does not appear to be essential for oligomerization since UvrDΔ73 can still form dimers and tetramers. The C-terminal region of Rep is much shorter than that of UvrD (by ∼42% based on sequence alignment (
      • Korolev S.
      • Hsieh J.
      • Gauss G.H.
      • Lohman T.M.
      • Waksman G.
      )), and Rep does not undergo detectable self-association in the absence of DNA (
      • Chao K.L.
      • Lohman T.M.
      ). However, like UvrD, at least a dimer of Rep is also required for helicase activity in vitro (
      • Cheng W.
      • Hsieh J.
      • Brendza K.M.
      • Lohman T.M.
      ). Therefore, one role of the C-terminal region of UvrD may be to stabilize the UvrD dimer, which in turn is likely to increase its processivity during unwinding.

      Acknowledgments

      We thank Anita Niedziela-Majka, Aaron Lucius, Chris Fischer, and Kathy Brendza for discussions and comments on the manuscript and Thang Ho for synthesis and purification of the DNA.

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