Mechanochemistry of T7 DNA Helicase

Home , Helicase, Mechanochemistry, Molecular motor, T7 DNA Helicase

doi:10.1016/j.jmb.2005.04.051 J. Mol. Biol. (2005) 350, 452–475

Jung-Chi Liao1†, Yong-Joo Jeong2†, Dong-Eun Kim2, Smita S. Patel2* and George Oster1*

1Departments of Molecular and The bacteriophage T7 helicase is a ring-shaped hexameric motor protein Cell Biology and ESPM that unwinds double-stranded DNA during DNA replication and University of California recombination. To accomplish this it couples energy from the nucleotide Berkeley, CA 94720-3112 hydrolysis cycle to translocate along one of the DNA strands. Here, we USA combine computational biology with new biochemical measurements to infer the following properties of the T7 helicase: (1) all hexameric subunits 2Department of Biochemistry are catalytic; (2) the mechanical movement along the DNA strand is driven Robert Wood Johnson Medical by the binding transition of nucleotide into the catalytic site; (3) hydrolysis School, 675 Hoes Lane is coordinated between adjacent subunits that bind DNA; (4) the hydrolysis Piscataway, NJ 08854, USA step changes the affinity of a subunit for DNA allowing passage of DNA from one subunit to the next. We construct a numerical optimization scheme to analyze transient and steady-state biochemical measurements to determine the rate constants for the hydrolysis cycle and determine the flux distribution through the reaction network. We find that, under physiological and experimental conditions, there is no dominant pathway; rather there is a distribution of pathways that varies with the ambient conditions. Our analysis methods provide a systematic procedure to study kinetic pathways of multi-subunit, multi-state cooperative enzymes. q 2005 Elsevier Ltd. All rights reserved. *Corresponding authors Keywords: helicase; ring; ATPase; sequential; pre-steady state kinetics

Introduction DNA replication and recombination and unwinds the complementary DNA strands.1,5 Although Helicases are motor proteins that translocate crystal structures for heptameric helicases have 6 along nucleic acid chains using the energy of NTP been reported, we will focus here on the hexameric hydrolysis. The ability to translocate unidirection- species. However, our analyses can easily be ally enables them to carry out processes involving applied to the heptameric ring with some modiﬁ- nucleic acid metabolism, especially those that cations. The energy source for the T7 helicase is require the separation of duplex nucleic acids into dTTP (deoxythymidine triphosphate), whose func- their component single strands.1–3 Helicases drive tion is equivalent to that of ATP in other motor critical biological processes such as DNA replica- proteins. The chemical energy of dTTP hydrolysis is tion, repair, and recombination; hence, mutations in converted into mechanical work to move the heli- a helicase protein lead to many human diseases case unidirectionally along the DNA. dTTPs (or including cancer and/or premature aging.4 other nucleotides) also stabilize the formation of the 7 Bacteriophage T7 gene 4 helicase is a hexameric hexameric ring structure in T7 helicase. Similarly, ring helicase that translocates along DNA during we have shown that T7 helicase binds DNA tightly in the presence of dTTP or dTMPPCP but not in the presence of dTDP.7 Thus, dTTP binding and † J.-C.L. & Y.-J.J. made equal contributions to this work. hydrolysis allow DNA bind–release cycles but the Present addresses: D.-E. Kim, Department of step in the dTTPase cycle that triggers DNA release Biotechnology and Bioengineering, Dong-Eui University, is not known. Translocation of T7 helicase proceeds Busan 614-714, South Korea. Y.-J. Kim, Department of Bio at a rate of w130 nt/s along ssDNA, hydrolyzing and Nanochemistry, Kookmin University, 861-1, 8 Chongnung-dong, Songbuk-gu, Seoul 136-702, Korea. one dTTP per three-base movement. On unwind- Abbreviations used: ssDNA and dsDNA, single- ing forked duplex DNA, the movement is slower, stranded and double-stranded DNA, respectively. where strand separation catalyzed by T7 helicase 9 E-mail addresses of the corresponding authors: proceeds at an average rate w15 bp/s. [email protected]; [email protected] Figure 1(a) shows two subunits of the ring

Figure 1. Structural arrangement of T7 helicase. (a) The model of DNA strand separation by T7 helicase built from electron microscopy13 and the structures of two helicase subunits and their interaction with an ssDNA.5 Mutation experiments suggest that motif II (residues 424–439, shown in green) and motif III (residues 464–475, shown in pink) interact with DNA.5,27,28 (b) Topological diagram of the secondary structures of two adjacent subunits using the same color coding as in (a).11 A Mg-dTTP molecule is shown adjacent to subunits of the helicase. The conserved b-sheet strands are numbered in the usual order: 5,1,4,3,2. The network of hydrogen bonds and salt-bridges that anneal the C Mg2 and the nucleotide to the catalytic site are shown broken and color coded according to their donor sites. These bonds were determined using a 3.3 A˚ cutoff; a larger cutoff would reveal more, but weaker, bonds. The suspected ssDNA binding motifs reside in the loops from the b-strands adjacent to the b-strands that form the dTTP catalytic site. helicase from the crystal structure,5 and a possible To understand the mechanochemical coupling for single-stranded DNA (ssDNA) configuration in the T7 helicase, it is first necessary to determine the central channel of the ring. The structure of the kinetic pathways of dTTP hydrolysis, so that the catalytic site in each subunit belongs to the class of relationship between the kinetics and the mechan- “RecA-like” NTPases,10,11 with the highly con- ical steps can be identified. Previous studies have served five-stranded parallel b-sheet as shown in determined the dTTP hydrolysis pathway of T7 Figure 1(b). Two loops emanating from the central helicase in the absence of DNA.12 Those studies b-sheet are suggested in the crystal structure to showed that only one of the six sites in the hexamer contact DNA.5 These two loops emerge from hydrolyzed dTTP at a fast rate and not all six sites strands 3 and 4, which are adjacent to the energy- participated in the dTTPase turnover. Here, we converting P-loop (Figure 1(b)), and this arrange- investigate the pathways of dTTP hydrolysis ment may facilitate the energy transfer from the catalyzed by T7 helicase in the presence of Mg$NTP hydrogen bond network to the DNA ssDNA. We find that up to four sites in the hexamer movement. hydrolyze dTTP at a fast rate and that all six sites 454 Mechanochemistry of T7 DNA Helicase likely participate in dTTPase turnover. Under high specific steps at which DNA binds and releases dTTP concentration, both in the absence and in the from the helicase subunit; (d) the coordination of presence of the DNA, the rate-limiting step is the dTTP hydrolysis among the hexamer subunits. release of the product, Pi. The number of possible kinetic states of the six catalytic sites is extremely Pre-assembly of the helicase hexamer on DNA large, and so to analyze the kinetics of dTTP hydrolysis a numerical method is developed to DNA binds within the central channel of the T7 determine the kinetic rate constant for each step and helicase hexamer and previous studies have shown to determine the main reaction pathways. Using the that DNA binding is a slow process.16 To measure combined approach of pre-steady-state kinetics and the pre-steady-state kinetics of dTTP hydrolysis, it computational kinetic modeling, we dissect the is therefore important to pre-assemble the helicase dTTPase mechanism of T7 helicase in the presence hexamer on the DNA to assure that DNA binding or of ssDNA and propose a multi-subunit, multi-state hexamer assembly does not limit the observed kinetic model that indicates that dTTP hydrolysis dTTP hydrolysis rate. Since the T7 hexamer requires and power strokes occur sequentially around the the presence of dTTP to bind DNA,7 it was hexameric ring. This model is mechanically con- particularly challenging to set up conditions to sistent with the electron microscopy observations measure the pre-steady-state kinetics of dTTP that showed only one or two subunits bind DNA.13 hydrolysis in the presence of DNA. Our finding Also, recently Mancini et al. proposed a similar that T7 helicase can be pre-assembled on the DNA C sequential translocation mechanism for the f12 P4 with dTTP without Mg2 provided us with initial hexameric packaging motor, which is structurally conditions to pre-assemble the hexamer on the C related to T7 helicase.14 However, additional data DNA prior to reaction start. In the absence of Mg2 , K will be required to determine if the power-strokes dTTP hydrolysis is insignificant (8.5!10 3 M/M are partially or strictly sequential around the T7 per second at 25 8C; w5000-fold slower than the C helicase ring. dTTPase rate in the presence of Mg2 ).17 The pre- The methodology we use augments the steady-state dTTP hydrolysis experiments were kinematic† notion of “conformational coupling” carried out using the long circular M13 ssDNA as with the mechanical concept of stress, or force per the nucleic acid substrate.8 We determined exper- unit area. This allows us to bring to bear mechanical imentally that the optimal concentration of M13 concepts to the phenomenology of cooperativity ssDNA was 15 nM per mM of T7 helicase hexamer between different regions of a protein. (see Appendix A). The pre-steady-state kinetic set up was as follows: T7 helicase was incubated with C DNA in the presence of dTTP (without Mg2 ) for three minutes, which was determined experimen- Results tally as an optimum pre-incubation period that provides sufficient time for assembly and to load To understand the mechanisms of translocation, the pre-incubated sample in the quench-flow it is necessary to dissect the dTTPase pathway in the instrument, and reactions were initiated by C absence and in the presence of the DNA and addition of Mg2 . determine when DNA binds and releases from the subunit. In addition to dissecting the dTTPase Chase-time kinetics indicates all subunits are pathway, it is important to determine how the catalytic dTTPase cycles are coordinated among the hexamer subunits. Previously, using pre-steady-state kinetic The chase-time experiments provide information approaches, we have determined the kinetic path- 12,15 about the number of dTTPs that are tightly bound to way of dTTP hydrolysis in the absence of DNA. the helicase hexamer and competent in hydrolysis. We found that, in the absence of DNA, only one In the chase-time setting, T7 helicase was incubated subunit of the hexamer hydrolyzed dTTP at a fast with dTTP, [a-32P]dTTP, and DNA in the absence of rate and that several of the hexamer subunits 2C 12,15 Mg . After three minutes, excess non-radiolabeled appeared to be non-catalytic. The dTTPase Mg-dTTP was added as a chase and the chase-time turnover rate was much slower at the non-catalytic was varied before acid-quenching. During the subunits compared to the observed dTTPase kcat chase-time, the dTTP molecules that were bound value. Here, we use a combination of pre-steady- initially to the hexamer subunits can get hydrolyzed state kinetic methods and computational modeling or may dissociate into solution. Once the radio- to determine the dTTP hydrolysis pathway in the labeled dTTP dissociates from the helicase into presence of DNA. We use these approaches to solution, it is diluted by excess non-radiolabeled address the following issues: (a) the number of dTTP chase and hence not observed in our actively participating hexamer subunits; (b) the rate reactions. Thus, the chase-time kinetics measures limiting step(s) in the presence of DNA; (c) the the hydrolysis reaction only from the tightly bound dTTPs. In this setting, and also later in the acid- † The branch of mechanics that studies the motion of a quench experiment, the measurements included body or a system of bodies without consideration given to three different species: dTDP in solution; dTDP its mass or the forces acting on it. bound to enzyme; and dTDP-Pi bound to enzymes. Mechanochemistry of T7 DNA Helicase 455

$ Detection of dTDP Pi permits tracing the hydrolysis modating more than four dTTPs in the ring. Similar events. negative cooperativity in nucleotide binding has Figure 2(a) shows the chase-time kinetics of dTTP been reported for other ring-shaped hexamer hydrolysis at various dTTP concentrations. The helicases.18–21 data fit to the single-exponential equation (4), The chase-time experiments showing that the shown in Experimental Procedures, that provides average number of catalytic sites is greater than the observed amplitudes shown in Figure 2(b). The three for T7 helicase is crucial, because without this amplitude provides an estimate of the number of piece of information it is difficult to distinguish a tightly bound dTTP molecules that are hydrolyzed three catalytic site model and a six catalytic site C upon binding Mg2 . Figure 2(b) shows that the model. Based on mechanochemical considerations, amplitude increases with increasing concentration we argue as follows that it is most likely that all six of radiolabeled dTTP, reaching a maximum value of sites are catalytically active in the hexameric T7 about four dTTPs/hexamer. These chase-time helicase. Figure 3 shows the three different possi- experiments, in addition to showing the number bilities for a four catalytic site model ((a), (b) and (c)) of catalytic sites, provide information about the and the single possibility for a five catalytic site initial conditions. The amplitude in Figure 2(b) model (d). A site is considered non-catalytic only if gives an estimate of the ensemble average dTTP it remains non-catalytic at all times (at least much occupancy for all helicases in solution. Later we will longer than the time-scale of the other kinetic use this information as the initial conditions in our events). All of the cases shown in Figure 3 are kinetic simulations. Similar chase-time experiments very unlikely, according to the following reasoning. in the absence of DNA have shown that only one The only communication mechanism between site per hexamer hydrolyzes dTTP at a fast rate and subunits is via the stresses developed at the catalytic a second one at a slower rate, which is consistent sites during the hydrolysis cycle and the conse- with product release at the first site limiting quent conformational couplings. hydrolysis at the next.12 Such biphasic kinetics in As each catalytic site passes through its occu- the chase-time experiments of dTTP hydrolysis was pancy cycle, it simultaneously passes through its not observed in the presence of DNA. stress cycle as well. The reason that less than six sites appear catalytic Any site that loses its catalytic activity at all times in the chase-time experiment might be that the must do so because the stress cycles of other sites initially bound dTTP dissociates, and the chase- can bypass its nucleotide binding site. time experiment can only detect the hydrolysis We will show later that the T7 helicase translo- events of those subunits whose dTTPs do not cates DNA sequentially. Stress considerations make dissociate from the catalytic sites. However, we it very unlikely that this homo-oligomeric enzyme consider this unlikely because direct dTTP and can maintain the catalytic site arrangements shown dTMPPCP binding experiments have shown about in Figure 3 when hydrolysis cycles take place four nucleotides bound per hexamer.17,18 A more sequentially. That is, it would require very unusual likely explanation is that negative cooperativity in and asymmetric stresses to keep some sites non- dTTP binding biases the preferences of the helicase catalytic at all times while other sites cycle. to bind no more than four dTTPs in each hexamer. The five catalytic site model shown in Figure 3(d) The basis for the negative cooperativity may be is possible if there is an active open ring, where one mechanical because the binding of dTTP introduces of the sites cannot form the hydrogen bond network mechanical stress around the enzyme ring. This required for hydrolysis. However, this would circumferential stress becomes large when accom- reduce the processivity dramatically, which is not

Figure 2. Time trajectories of chase-time experiments and the steady-state amplitudes. (a) The total [dTDP] includes dTDP-Pi, dTDP inside the catalytic sites and dTDP in solution. Time trajectories of chase-time experiments (60, 110, 250, 500 mM dTTP) ﬁt approximately to equation (4). (b) The amplitudes are obtained from the steady-state values of dTDP production (A in equation (4)) in (a). This amplitude represents the lower bound of the average number of catalytic sites initially occupied by dTTP. 456 Mechanochemistry of T7 DNA Helicase

kinetics of dTTP hydrolysis in the first turnover as well as those of the subsequent ones. If the first turnover is faster than the subsequent ones, the kinetics will show a “burst” phase. The burst kinetics in our experimental setting indicates that a step after dTTP hydrolysis is rate limiting, because our initial conditions involved pre-incubating the helicase with dTTP that bypasses the dTTP binding step. Figure 4(a) shows the time trajectories of dTTP hydrolysis in the acid-quench setting at different initial [dTTP]0 that clearly shows the burst kinetics. For each dTTP concentration, the kinetics of dTDP formation was biphasic and can be fit by a single exponential followed by linear growth (cf. equation (5) in Experimental Procedures). The initial exponential phase (burst phase) reflects the fast hydrolysis step, while the linear phase is the steady-state controlled by the rate-limiting step. Figure 4(b) shows that the slope of the linear phase increases with increasing dTTP concentrations in a hyper- Figure 3. Configurations for a four or five catalytic site bolic manner. Thus, from low to high concen- model. The black ellipses represent sites that are catalytic trations of dTTP the rate-limiting step shifts from at any moment, while the white ellipses are non-catalytic dTTP binding to product release. The burst ampli- sites; the non-catalytic site in any hexamer must be non- tude, similar to the chase-time amplitude, provides catalytic at all times. (a), (b), and (c) are the three possible information about the average number of catalytic configurations for a four catalytic site model. (d) The only sites undergoing fast dTTP hydrolysis. In the possible configuration for a five catalytic site model. absence of DNA we previously observed a burst amplitude about one dTTP/hexamer; here, in the presence of DNA, about four dTTPs are hydrolyzed per hexamer at saturating dTTP. consistent with the observed high processivity 8 along single-stranded DNA. Pi release is the rate-limiting step in the Thus, the occupancy states continuously cycle hydrolysis cycle their state of stress, so no single site can remain permanently inactive while subject to the time- To investigate which product release (Pi or dTDP) varying stresses. is the rate-limiting step, a coupled assay was used 23 Thus, we conclude that in the presence of DNA, it to measure the real-time kinetics of Pi release. is most likely that all subunits are catalytic. A mixture of T7 helicase, M13 ssDNA, and dTTP C Note that in a sequential mechanism, it is possible was rapidly mixed with Mg2 and PBP-MDCC in a to have a cyclically symmetric three-site or six-site stopped-flow instrument, and the fluorescence enzyme. For a three catalytic site model, the stresses changewasmeasuredasafunctionoftime. bypass the adjacent site and affect the site two A standard curve was used to convert the magni- subunits away. Electron microscopy shows a trimer tude of fluorescence increase into Pi concentration. 22 of dimer structure for other ring-shaped helicases, Figure 4(c) shows the time trajectories of Pi release which could support a three-site proposal. The non- at different initial concentrations, [dTTP]0. Unlike catalytic sites observed previously in the absence of the acid-quench experiments there are no clear DNA may belong to this three catalytic site species. biphasic characteristics. The linear steady-state phase has approximately the same slope as in the Pre-steady-state kinetics show biphasic acid-quench experiment for each corresponding behavior in dTTP hydrolysis [dTTP]0, because the rate-limiting step is the same for both experiments. In Figure 4(d) comparison of To characterize the rate-limiting step in the dTTP the acid-quench and Pi-release experiments show a hydrolysis pathway, acid-quench pre-steady-state delay in Pi release relative to dTTP hydrolysis. kinetics experiments were performed. In the acid- These results indicate that the hexamer subunits quench setting, T7 helicase was pre-incubated with hydrolyze dTTP at a faster rate than they release the 32 M13 ssDNA, dTTP, and [a- P]dTTP and after a product Pi. The kinetics were modeled to determine three minute incubation, the reaction was initiated the rate constants and, as shown in Table 1, we find 2C by rapidly mixing with a solution of Mg . The that at high dTTP concentration Pi release is the reactions were acid-quenched at various times rate-limiting step. (milliseconds to seconds). The acid-quench setting differs from the chase-time setting in that excess $ C dTDP Pi is weakly bound to DNA non-radiolabeled dTTP is not added with the Mg2 . Thus, the acid-quench experiment exhibits the Figure 4(d) shows the delay in Pi release relative Mechanochemistry of T7 DNA Helicase 457

Figure 4. Experimental data and simulation results for [dTDP] and [Pi] time trajectories. (a) The total [dTDP] includes dTDP-Pi, dTDP inside the catalytic sites and dTDP in solution. The simulations (continuous lines) agree well with the transient and steady-state experiments for four different initial dTTP concentrations. (b) The steady-state hydrolysis rate per hexamer from slopes of the linear phases in (a). It shows a hyperbolic trend toward saturation with increasing [dTTP]. (c) [Pi] in solution is measured and simulated under the same four initial dTTP concentrations. The continuous lines represent the simulation results. (d) Comparison between dTTP hydrolysis and Pi release at 500 mM dTTP. The delay in of Pi release in the transient phase is caused by the slow Pi release compared to dTTP hydrolysis.

Z to dTTP hydrolysis by the hexamer subunits. This units. For [dTTP]0 500 mM, more than two sub- also provides insight into the DNA binding afﬁnity units per hexamer are delayed in releasing Pi of the dTDP-Pi state. As subunits start hydrolysis relative to the subunits hydrolyzing dTTP. If the and produce dTDP and Pi,Pi is not immediately dTDP-Pi state has a high afﬁnity for the DNA and Pi released when dTTP is hydrolyzed in other sub- release is more than two subunits behind the

Table 1. Rate constants and corresponding valid ranges for steps in the hydrolysis cycle of T7 helicase

Step Reaction Rate constant Lower bound Upper bound K K K K K K E/T* dTTP docking 5.0!104 M 1 s 1 4.8!104 M 1 s 1 5.7!104 M 1 s 1 K K K T*/N$T* DNA binding 951 s 1 380 s 1 O1!106 s 1 K K K N$T*/N$T Power stroke 778 s 1 311 s 1 1.17!104 s 1 K K K N$T/DP dTTP hydrolysis 66 s 1 53 s 1 297 s 1 K K K DP/DPrelease 15 s 1 14 s 1 18 s 1 i K K K D/E dTDP release 159 s 1 103 s 1 O1!106 s 1 K K K K T*/E dTTP release 1.5 s 1 !1!10 5 s 1 2.5 s 1 K K K K N$T*/T* DNA release 70 s 1 !1!10 5 s 1 1.35!103 s 1 K K K K N$T/N$T* Recoil power stroke 6.2 s 1 !1!10 5 s 1 120 s 1 K K K DP/N$T dTTP synthesis 0.03 s 1 0.028 s 1 0.041 s 1 K K D/DP P binding 1.1!103 M 1 s 1 n/a n/a i K K E/D dTDP binding 1.0!106 M 1 s 1 n/a n/a The rate constants are obtained by least-squares fit to the data. The lower and upper bounds of the rate constants are found by varying one parameter at a time but keeping all others fixed so that the residual errors of the prediction are within tolerance (see the text). This tolerance is roughly equivalent to 10% prediction error, on average. Numbers in bold are those upper or lower bounds in the same order of magnitude as the best-fit rate constants. 458 Mechanochemistry of T7 DNA Helicase hydrolysis subunit, then at least three subunits must 0.02 ppm up-field compared that of the 16O species. 18 be attached to the DNA. This contradicts the protein– Figure 5(a) and (b) show that [ O]Pi to H2O DNA cross-linking experiments and electron exchange was not observed even after 12 hours of microscopy observations showing that single- reaction, with and without DNA. The absence of 18 stranded DNA interacts with only one or two medium [ O]Pi exchange indicates that dTTP subunits of the hexamer.13 Thus, we conclude that hydrolysis is almost irreversible in the helicase- the dTDP-Pi bound state must have a low affinity for active sites or that Pi binding is weak. DNA. Surprisingly, Figure 5(c) shows that when a small Mechanical considerations also suggest that the amount of dTMPPCP, a non-hydrolyzable version dTDP-Pi state should have a low affinity for DNA. If of dTTP, is included in the reaction with ssDNA, 18 three or more subunits in the dTDP-Pi state bind dTDP, and [ O]Pi,considerableexchangewas DNA, and only one of them is responsible for observed. That is, in the presence of dTMPPCP translocating DNA, then DNA will be distorted and ssDNA, Pi can rebind to the catalytic site and significantly. The bending of ssDNA at this length even participate in re-synthesis of dTTP. However, scale requires energy, not favorable for the motor to as shown in Figure 5(d), in the presence of proceed. If three or more subunits attempt to move dTMPPCP, but without ssDNA, no exchange was DNA together, all these subunits must move observed. One explanation is that the reverse step C / simultaneously about the same distance so that dTDP Pi dTTP can only take place if DNA is the DNA strand is not ruptured. Moreover, upon present in the central channel of the ring. Recall that completion of the power stroke, other subunits the dTMPPCP-bound state has a high affinity for must bind DNA to commence the next power DNA, while the dTDP-bound state has a low stroke, and this transition will bend ssDNA affinity.7 Because dTMPPCP helps recruit ssDNA considerably. Taken together, we find this scenario into the ring by its high affinity, other subunits are / / highly unlikely. accessible so that the transition dTDP dTDP. Pi Another possibility is that all subunits work dTTP is possible during the incubation. In the simultaneously. In this scenario, after one power experiment of Figure 5(b), although DNA, dTDP, stroke, all subunits must reset to their original and Pi are all added, DNA cannot be recruited to the positions so that the next power stroke can begin. central channel. Therefore, the DNA–dTDP state This reset transition requires the subunits have a cannot be achieved, and so neither can the DNA– low affinity for DNA so that DNA will not be moved dTDP-Pi or DNA–dTTP states. This scenario also back to its original position. However, this synchro- explains why exchange was not observed with nous low affinity for DNA corresponds to reducing dTMPPCP in the absence of DNA (Figure 5(d)), and the duty ratio of the motor, which would allow is consistent with the conclusion that the dTDP-Pi- DNA to diffuse away. Furthermore, if w2– bound state has low affinity for DNA. There are 3 nt/dTTP are translocated, then the power stroke other possible explanations for the results of the distance would have to be w3.6–5.4 nm, which is oxygen exchange experiments, but they require impossible given the lengths of the possible DNA more sophisticated models that include the effects binding loops, and very unlikely if all subunits go of multi-subunit interactions (see Appendix A). through a dramatic rotation synchronously along the z axis in one chemical transition. A DNA binding-deficient mutant inhibits the Taken together, we conclude that DNA will not activity of T7 helicase bind to three or more subunits simultaneously, and that the dTDP-Pi state has low affinity for DNA. To distinguish between random and sequential mechanisms of power strokes (see below), we dTMPPCP promotes synthesis of dTTP studied the activity of mixed helicase hexamers made with wild-type T7 helicase and an inactive T7 To determine if the dTTP hydrolysis step is helicase mutant protein. Previous studies have reversible at the helicase-active sites, we carried shown that mixed hexamers can be made by mixing 18 25 out the [ O]Pi medium exchange experiments mutant and wild-type T7 helicase proteins. developed by Boyer and co-workers that have Previous studies were carried out with mixed been used to analyze the reversibility of the hexamers made with a dTTPase-defective mutant hydrolysis step of many ATPases.24 Briefly, high protein, and these studies showed that both the 18 concentrations of dTDP (6 mM) and [ O]Pi dTTPase and helicase activities decreased steeply as (20 mM) were mixed with T7 helicase in the a function of mutant protein concentration.25,26 presence of M13 ssDNA. The dTDP concentration These results support a sequential power stroke used here is saturating as determined by a dTDP mechanism. However, since the dTTPase-defective w inhibition experiment (Ki value of dTDP 200 mM; mutant was able to bind ssDNA, the dramatic data not shown). The time-course of incorporation decrease in the activity of the mixed hexamer could of unlabeled oxygen from water into Pi due to be due to ssDNA binding to the mutant subunit in reversible dTTPase reactions was monitored. the hexamer, thereby blocking the rest of the 18 31 The loss of O label in Pi was monitored by P subunits in the hexamer from binding or translocat- NMR experiments, as the 18O bound to the ing ssDNA. Therefore, we chose to carry out mixed phosphorus atom shifts the 31P NMR by about hexamer studies with a DNA binding-deficient Mechanochemistry of T7 DNA Helicase 459 mutant, which would not adhere to the DNA in a hexamers, bind dTTP, and hydrolyze dTTP at the mixed hexamer. Previous studies have shown that DNA unstimulated rate.27,28 We mixed R487C and R487C mutation in T7 helicase greatly reduces the wild-type T7 helicase proteins in different ratios, DNA binding and helicase activities of T7 helicase, but the final concentration of the protein mixture but the R487C mutant still retains the ability to form was kept constant at 100 nM hexamer, and the

31 18 18 Figure 5. P NMR spectra of different species of [ O]Pi under different conditions (the shaded circles represent O 16 18 and the unshaded O). (a) T7 helicase (1 mM), 6 mM dTDP, 20 mM [ O]Pi. No synthesis event was observed with dTDP 18 and Pi. (b) T7 helicase (1 mM), 6 mM dTDP, 20 mM [ O]Pi, 15 nM M13 ssDNA. The only minimal synthesis event was 18 observed in the presence of dTDP, Pi, and ssDNA. (c) T7 helicase (1 mM), 6 mM dTDP, 20 mM [ O]Pi, 15 nM M13 ssDNA, 50 mM dTMPPCP. dTMPPCP significantly enhances the synthesis of dTTP in the presence of dTDP, Pi and ssDNA. (d) T7 18 helicase (1 mM), 6 mM dTDP, 20 mM [ O]Pi,50mM dTMPPCP. No synthesis event was observed without DNA even in the presence of dTMPPCP. Thus, it is necessary to have both ssDNA and dTMPPCP to promote synthesis of dTTP. 460 Mechanochemistry of T7 DNA Helicase dTTPase activity of the mixed hexamers was paper show that (i) at saturating dTTP concen- measured in the presence of ssM13 DNA. Figure 6 trations, up to four dTTPs are hydrolyzed in a single shows the measured hydrolysis rates under differ- exponential phase. (ii) At saturating dTTP concen- ent [R487C] versus [wild-type] ratios. trations, the rate-limiting step in a single dTTPase To test whether the power stroke mechanism is cycle is the release of the product Pi.dTTP sequential or random, we conducted simulations hydrolysis is faster at the hexamer subunits, with for both cases and compared them with the the result that more than two subunits of the experimental results. Figure 6 shows that when all hexamer lag behind in Pi release. (iii) We have subunits are made by the R487C mutant species shown that DNA binds to the hexamer in the dTTP- ð½R487C=½R487CC½wtZ1Þ under our experimen- bound state,7 and experiments described here tal conditions, hydrolysis occurred at about 20% of indicate that DNA releases immediately after the wild-type rate. If DNA translocation is carried dTTP is hydrolyzed. (iv) The mutant poisoning out by hexamer subunits randomly, then after a experiments rule out a random power stroke power stroke the probability that the next power mechanism and support a sequential power stroke stroke is performed by a wild-type subunit or a mechanism. mutant subunit depends on the ratio of the two Using the available data, we develop below a species. This assumes that both species form kinetic model that globally fits all the data, and hexamers equivalently. Thus, the overall hydrolysis construct a numerical optimization method to rate will be proportional to the average of the wild- deduce the rate constants of the individual steps. type fast rate and the mutant slow rate weighted by We also develop a computational approach to corresponding species amounts. While the ratios of identify the main pathways by which a multi-site the two species change linearly, the hydrolysis rates enzyme system such as T7 helicase coordinates the should also change linearly, as shown in Figure 6. activity at each subunit to drive translocation along This is different from the experimental observations DNA. that as [R487C] increases in the protein mixture, the ssM13-stimulated dTTP hydrolysis rate decreases The DNA translocation power stroke occurs sharply. The non-linear decrease in dTTP hydrolysis during dTTP binding rate rules out the random power stroke mechanism. We also carried out simulations for a sequential Previous studies have shown that the affinity of power stroke mechanism and it shows a non-linear DNA for helicase is high in the dTTP-bound states, decrease in dTTP hydrolysis rate as shown in but low in both the dTDP-bound state and the Figure 6. The detail of how the simulation was 7 empty state. Here, we show that the dTDP-Pi- conducted is shown below after we introduce the bound state also has low affinity for DNA. In order algorithm of the kinetic model. to translocate DNA, the subunit must be in the high- In summary, the experiments described in this affinity state for DNA. Thus, the DNA translocation step can only take place in the dTTP-bound state. In order to describe the translocation of DNA as the hydrolysis cycle proceeds in each subunit we require the following minimal kinetic steps: (1) weak dTTP binding (or “docking”); (2) strong dTTP binding; (3) dTTP hydrolysis; (4) Pi release; and (5) dTDP release. In addition, (6) DNA binding and (7) unbinding must also be considered. Here, we assume that, like many other motors (e.g. F1- ATPase, kinesin, and myosin) Pi is released before dTDP. This is because Pi has many fewer hydrogen bonds than dTDP, and additionally dTDP has hydrophobic interactions with the catalytic site, so that the energy required for Pi release is smaller than that for dTDP release. Thus, the kinetic paths in each subunit can be written in terms of the states of its catalytic site: Figure 6. Effect of the R487C mutant on the dTTPase activity of T7 helicase. The ssDNA-stimulated dTTPase rate at steady-state was measured for a mixture of R487C (1) and wild-type T7 helicase. The proteins were mixed in different ratios keeping the final protein constant at 100 nM hexamer. The plot shows the decrease in the dTTPase rate as a function of increasing [R487C]. The Here, E is the empty state, T* is the weakly bound continuous line shows the predicted behavior of a dTTP state, T is the tightly bound dTTP state, DP is sequential power stroke mechanism, while the broken the dTDP-Pi state (after hydrolysis), and D is the line shows the predicted behavior of a random power dTDP state (after Pi release). The lower row (with N stroke mechanism. prefix) corresponds to DNA-bound states. Since Mechanochemistry of T7 DNA Helicase 461

N$DP is a short-lived state, the energy well for this random, or sequential? Four power stroke state is not very deep and so we omit this state. sequences must be considered. Mathematically, it is always possible to lump two states together into one state and use rate constants Simultaneous equivalent to the collective jump probabilities of the original states. Experiments indicate that the helicase trans- Thus, we can write the principal pathway for a locates an average of 3 nt/dTTP hydrolyzed.8 subunit as: Since nucleotides in DNA are separated by w0.3 nm, the distance translocated per dTTP is E4T*4N,T*4N,T4DP4D4E (2) w Power 0.9 nm. If all six subunits work simultaneously Stroke (i.e. the power strokes act in parallel), then the Structural considerations suggest two possible translocation distance for each subunit would have mechanisms for the translocation power stroke. to be 6!0.9Z5.4 nm. Since the channel height of the First, the crystal structure suggests that the relative T7 hexamer is only w5 nm, this is very unlikely. rotational angles of adjacent subunits of the Furthermore, we have mentioned that the reset hexamer are different for the empty state and the transition requires the subunits have a low affinity dTTP-bound state. In this “subunit rotation” model, for DNA, and this synchronous low affinity for when dTTP binds to the catalytic site, it triggers the DNA corresponds to reducing the duty ratio of the alignment of the positive charge groups constitut- motor, which would allow DNA to diffuse away. ing the “arginine finger” with the negatively Therefore, we discard this possibility. charged g-phosphate of dTTP.29 This alignment drives the relative rotation between neighboring subunits, and so the DNA contact residues rotate Paired sequential with it to translocate the DNA. A second possibility Based on the “dimer of trimers” arrangement in the is that dTTP binding directly deforms the local b- crystal structure, Singleton et al. suggested that the 30,31 sheet structure, as in F1-ATPase. In this “direct power strokes progress sequentially around the ring, drive” model, the deformation induced in the b- but with diametrically opposing subunits in the same sheet propagates to the DNA binding loop that also state.5 For example, subunit 4 is opposite subunit 1 emanates from the b-sheet, and thence to DNA and so the two pass through the hydrolysis cycle contact residues to translocate the DNA strand. synchronously. In this scheme, two dTTPs are Recent crystal structures of the f12 P4 hexameric consumed during each translocation step, and so packaging motor show its RNA contact residues the translocation step should be w1.8 nm. This is undergo a large conformational change from an inconsistent with the 0.6–0.7 nm distance of subunit 14 ATP-bound state to an ADP-bound state. The rotation in the possible DNA contact regions deter- translocation stroke is coupled to a different kinetic mined from the crystal structure.5 Thus, we consider step from the helicase studied here, presumably the paired power stroke sequence unlikely; indeed, due to the difference in the high-affinity state to the Singleton et al.5 pointed out that, in the presence of substrate RNA or DNA. However, the idea being DNA, asymmetry may occur and the paired sequen- that subunit deformation induced by nucleotide tial mechanism could be invalid. binding and release is the same. These two mechanisms differ in how stress radiates outward from the catalytic site to drive the translocation Random power stroke. Both mechanisms begin with the There are two possible random power stroke dTTP binding site undergoing the “binding zipper” mechanisms. (1) Random in time: the power stroke transition: the formation of the hydrogen bond of each subunit starts and finishes at random times 32,33 network during dTTP binding. In both cases, independent of other subunits. This mechanism is the power stroke of each subunit is driven by the not consistent with the very high processivity binding zipper transition of dTTP from its weakly observed in experiments because there is an bound to the tightly bound state, N$T*/N$T. The appreciable probability that none of the subunits conformational changes accompanying NTP binding bind DNA at the same time. Thus, we can discard 32,33 34 have been shown for F1-ATPase and myosin. this mechanism. (2) Random in sequence: the power strokes are sequential in time (i.e. each subunit can The translocation power strokes take place only commence after another subunit finishes), but sequentially around the ring the order of the power strokes around the ring is random. That is, the sequence of the power strokes One of the most important questions that relate to is not 1-2-3-4-5-6, but random, as in rolling a die. the mechanism of the ring helicases is the sequence After subunit 1 binds and moves the DNA strand, of the power strokes that drive the movement of the subunits 2–6 have equal probabilities of binding ring along the DNA strand. Knowing the order of DNA and moving it. In terms of binding DNA, it is the power strokes helps clarify how the hexamer still sequential (one after the other), but in terms of subunits communicate with each other. We address the power stroke order, it is random. The mutant the following questions: are the translocation power poisoning experiment does not support the random strokes in the hexamer subunits simultaneous, mechanisms. 462 Mechanochemistry of T7 DNA Helicase

Sequential (see Figure A1 in Appendix A).5,29 The effect of this transmitted stress is to ensure the catalytic residues This mechanism carries out power strokes in and the catalytic water molecules are constrained in strict sequential order: 1-2-3-4-5-6. After one sub- the right configurations to form the transition state unit finishes a power stroke, the adjacent subunit for hydrolysis. binds DNA and executes the next power stroke. To summarize, three cooperative steps are This scheme requires cooperativity between adja- required for sequential DNA bind–release cycles cent subunits to coordinate the sequence. We that also assure processivity of translocation (they consider this mechanism most likely, for it is are shown in Figure 8): consistent with the structural features that permit adjacent subunit coupling discussed below. (1) The power stroke, N$T*/N$T, takes place It is also possible that the power strokes are when the DNA is bound to one subunit. partially sequential; that is, sequential but with (2) The transition T*/N$T* requires the previous some random variation. For example, after trans- subunit to be in the N$T state. location by subunit 1, there is a probability of (3) The transition N$T/DP requires the next continuing the next translocation in subunit 2 and subunit to be in the N$T* state. another probability to continue in subunit 3. Currently, there is no evidence that can unequi- We also examined the necessity of each of these vocally demonstrate that the order of translocation three steps, and the simulations showed that these power strokes is strictly sequential or mixed. The three steps are essential (see Appendix A). only thing known is that power strokes cannot take In order to model the three cooperative steps, we place simultaneously. Here, we use the purely applied a rate enhancement factor to each of the sequential mechanism to illustrate how “one after above steps. For all other transitions the rate the other” power strokes can work. This sequential constant is independent of the states of other mechanism is consistent with the electron subunits. To ensure a detailed balance, which is microscopy observations and the mechanism 13,14 necessary for the kinetic scheme to obey the Second shown for the P4 packaging motor. We will see Law of Thermodynamics, if a forward rate is that this fits all of the experimental observations enhanced then the same enhancement must be satisfactorily. applied to the reverse rate constant. The standard free energy of 12.5 kBT is used for the hydrolysis Mechanical stress coordinates the hydrolysis cycle,sooneofthereverserateconstantsis cycles between subunits predefined by this energy relationship. This simple model with cooperativity only in the above three Based on experimental data and structural transitions reduces the total number of fitting considerations we develop a set of rules that govern parameters to six forward rate constants, five sequential hydrolysis of dTTP and processive DNA reverse constants, and three enhancement factors, translocation. If the power strokes are sequential, for a total of 14 unknown parameters. The forward the translocation step N$T*/N$T can take place rate constants are kE/T*, kT*/NT*, kNT*/NT, kNT/DP, only when the DNA is bound to only one subunit. kDP/D*, and kD/E. The backward rate constants, Otherwise, each translocation step would be including the one obtained from the free energy impeded by the DNA being tethered to an adjacent constraint, are kT*/E, kNT*/T*, kNT/NT*, kDP/NT, subunit. After completing one power stroke, the kD/DP, and kE/D. The three enhancement factors next subunit must bind DNA to continue transloca- are fNT*/NT, fT*/NT*, fNT/DP*, corresponding to the tion. Using the kinetic notation in equation (2), the three enhancement rules stated above. With these DNA binding step in the next subunit, T*/N$T*, parameters, we can construct the rate equations and commences when the previous subunit in the solve them. sequence has completed its power stroke and is in the N$T state. Geometrically, this is possible if the power stroke of the previous subunit brings the Kinetic pathways DNA strand into a position where it can quickly fluctuate to the next subunit. As shown above in equation (2), there are six Since hydrolysis enables release of the DNA nucleotide ligation states in each subunit of the 6Z strand, in order to ensure high processivity the hexamer, so that the total number of states is 6 unbinding of DNA in one subunit must take place 46,656. Each hexamer state can be denoted by after the binding of DNA to the next subunit. Thus, EEEEEE (all sites empty), EEDDDD (four sites the transition N$T/DP in one catalytic site must occupied by dTDP), etc. The rate equation for all follow the binding of nucleotide to the next site, i.e. states can be written as pseudo-first-order state T*/N$T*. (Recall: N$DP is omitted from the equations: kinetics in equation (2) because it is a short-lived dc state.) The most likely explanation for this is that Z K,c (3) efficient hydrolysis is greatly enhanced when the dt two subunits that are bound to DNA form a where c(t) is a concentration vector of all the mechanical stress loop through the arginine finger possible kinetic states. Thus, c(t) is a concentration Mechanochemistry of T7 DNA Helicase 463 vector with 46,656 elements, and K is the 46,656! 46,656 rate matrix. For example, k12 is the rate Box 1. Sketch of the computational algorithm constant for the change of state [EEEEEE] (i.e. the The solution to equation (3) determines the rate concentration of state EEEEEE) as a function of constants for the pre-steady-state kinetic data shown [EEEEET*]:kEEEEET*/EEEEEE.Equation(3)corre- in Figure 4. The flow chart for the computational sponds to the experimental conditions where the algorithm is shown in Figure 10 in Appendix A, concentrations of dTTP, dTDP, and Pi do not vary where more details can be found. The underlying too much over the course of an experiment, so that principle is to first solve the rate equations with a their concentrations can be incorporated into the trial set of rate constants, and then to use the rate matrix, K. (However, the algorithm we use is optimization algorithm to find a set of best-fit rate not confined by the linear approximation.) constants. The best fit is defined as the least-squares Notice that the complexity of this large system of error of the prediction compared with the experimental data. First, a set of 14 estimated parameters equations is purely computational: the underlying (11 rate constants and three enhancement factors) are chemistry includes only the three cooperative steps, assigned to the corresponding kinetic steps as similar to the classical treatment of subunit inter- elements of the rate matrix K. For example, the 35–37 actions. These three cooperative steps devel- element in the matrix K is the rate constant, since it oped from structural and mechanochemical corresponds to the transition T*/E in the last considerations impose constraints on the system subunit. Another example: the element is assigned such that many of the 46,656 states are either totally to, since it corresponds to the mechanical coupling inaccessible or have very low probability. The enhancement for the hydrolysis step, with the next computational results will report these inaccessible subunit ready to take over the next power stroke. states as well as the time-dependent concentrations Once the matrix is constructed, the rate equation dc/dtZK$c can be solved using an iterative method of those accessible states. The purpose of the (the quasi-minimal residual method in algorithm is to find the main pathway(s) by fitting MATLABe).38 Simply guessing the set of initial this equation to the data. The difficulty arises from parameters gives a poor fit, so we used the simplex the large number of coupled differential equations. optimization method.39 An initial 14 dimensional However, the rate matrix, K, while large, is sparse, simplex is constructed consisting of 14C1 vertices. so that an efficient numerical method can be used to Each vertex contains a set of 14 fitting parameters. integrate the equations.38 For each vertex (i.e. each set of rate constants), a rate The initial conditions can be inferred from the matrix K is constructed and the rate equation is chase-time experiments. The optimization algor- solved. To compare the predictions with the ithm is used to obtain 14 parameters needed for the measurements, the computed concentrations must be converted to the corresponding experimental computation. The details of obtaining initial con- concentrations. For each vertex, we obtain the sum of ditions and defining the necessary parameters are the square of the difference between predictions and given in Appendix A. measurements:, where cp is the predicted concen- The results of the calculations are shown in trations and cm is the measured concentrations. The Figure 4, and the computed rate constants are given prediction error, E, is to be minimized. After in Table 1. The fit to the data is quite good in both prediction errors are obtained for all vertices, the the transient and steady-state phases. The free vertices of the simplex are moved according to the energy diagram calculated from these best-fit rate Nelder–Mead method so that the size of the simplex gradually shrinks corresponding to convergence to a constants is given in Appendix A. 39 A sensitivity test was conducted to find the valid minimum. The best-fit parameters are obtained when the size of the simplex is smaller than a ranges of the rate constants obtained from the fitting predetermined cutoff. algorithm. To determine the range of one rate constant, we varied that constant while keeping all other constants fixed, and then computed the the same order of magnitude. For example, our time trajectories and the corresponding residual experiments can determine the dTTP docking rate, error of the new parameters. The residual error is the Pi release rate, and the dTTP synthesis rate. K 2 Scase i St DtðCðtÞi;compute CðtÞi;measureÞ ,summing Some rates have well-defined lower bounds while the concentration differences of all cases and all others have well-defined upper bounds. A sensi- time steps. When that constant is different from the tivity test of the Pi and dTDP binding rates is not best-fit rate constant, the residual error is greater possible because dTDP and Pi concentration- than the best-fit residual error. We chose a tolerance dependent experiments are not available. residual error roughly equivalent to 10% prediction With the best-fit rate constants and their corre- error on average. The upper and lower bounds of sponding ranges being considered, Table 1 shows each rate constant reported in Table 1 are identified that when the initial concentration, [dTTP]0, is low, / when the corresponding residual error equals the the E T* step is rate-limiting. When [dTTP]0 is tolerance residual error. The Table shows that some high, the E/T* step and the DP/D steps are of the rate constants are sensitive while others are not. same order, and a combined effect must be Thus, our experiments can determine some rate considered. Changing [dTTP]0 shifts the rate limit- constants with good accuracy, leaving other con- ing step. The slow DP/D step is consistent with stants underdetermined. The bold-face numbers in the phase delay between hydrolysis and Pi release. Table 1 are those whose best-fit rate constants are of The mechanical power stroke step, N$T*/N$T, is 464 Mechanochemistry of T7 DNA Helicase fast compared to other kinetic steps. A mechanical to compute, but follows the partially sequential step is generally not equivalent to a kinetic step. If a mechanism we describe above. mechanical step is rate limiting, the dynamics of the system is dominated by spatial motion. A kinetic What is the “main” kinetic pathway? process is an instantaneous jump transition with a distribution of waiting times in the source state; One goal of the calculation is to find the “main therefore, it is generally not a good model for a pathway(s)” amongst the very large number of mechanical step. On the other hand, if the mechan- possible pathways. One quantitative definition of a ical step is fast compared to other kinetic steps, the main pathway is that, at steady-state, it carries the dynamics of the system are dominated by the maximum kinetic flux. Using the best fit rate kinetic process. In this case, it is appropriate to use a constants, the steady-state concentrations of all kinetic step to approximate the mechanical step, states can be determined, and the fluxes of all with equivalent mean passage time chosen for the kinetic steps computed (see, e.g. Hill40). Many kinetic approximation. pathways transmit negligible flux and can be We used the same approach for simulations of the ignored. Those kinetic pathways with a flux DNA binding-deficient mutant, as illustrated in threshold above 3% of the total flux were identified. Figure 6. First, we assume the mutant species have Figure 7 shows the steady-state kinetic flux network the same property as the wild-type species in under two different concentration conditions. The forming hexamers. Thus, different proportions of thickness of the connections between any two states wild-type versus mutant species give different is proportional to the kinetic flux between them. distributions of various mixed hexamers, such as Figure 7 shows that the distribution of pathways WWWWWW, WWWWWM, etc., where W rep- depends on the initial conditions. For physiological resents the wild-type subunit while M represents conditions (assumed to be [dTTP]Z100 mM, Z Z the mutant subunit. There are a total of 64 species of [dTDP] 10 mM, and [Pi] 1 mM), the flux passes mixed hexamers and their initial distributions can mostly through one or two pathways with low be computed from the [R487C] versus [wild-type] occupancy, while under experimental conditions of Z ratio. For each species, the kinetic equations are [dTTP]0 500 mM, the kinetics spread over many formulated and the steady-state hydrolysis rate can pathways. In the latter case, it is not possible to be obtained. Different species have a different rate define a single principal pathway. With a 3% flux matrix. For a mutant subunit, because it is unable to threshold, the net flux in the partial network shown bind DNA, the states N$T* and N$T are not in Figure 7(a) is about 91% of the total flux, while in reachable. This subunit, however, is still able to Figure 7(b) the net flux is only about two-thirds of hydrolyze dTTP as observed in the all mutant the total flux. Figure 7(b) also shows the shifting of hexamers. Thus, we assign a detour state for mutant kinetic fluxes toward high-occupancy states com- subunits: E4T*4T4DP4D4E. We also make a pared to Figure 7(a), and this is consistent with the preliminary assumption that all rate constants, experiments where increasing [dTTP]0 corresponds except the one of the hydrolysis step, are the same to increasing average occupancy. The calculation of as those for the wild-type subunits. The power the kinetic flux network shown here can be applied stroke here T*/T has the same rate constants as to any cooperative multiple-protein kinetics. NT*/NT. The hydrolysis step T/DP, however, becomes the rate-limiting step because of the lack of Translocation along single-stranded DNA the subunit–subunit coordination as described involves multiple kinetic pathways above. This slow hydrolysis rate can be easily found by fitting to the data of all mutant species Here, we summarize how the subunits of the (MMMMMM) shown on the right in Figure 6. With hexamer coordinate their actions to translocate this rate constant and all others known, we along DNA. The three required cooperative steps construct the rate matrix for each species and obtain in the reaction network are shown schematically in its corresponding steady-state hydrolysis rate. Figure 8(a). Previous results have shown that T7 Knowing the distributions of all species under a helicase translocates on an average 3 nt per dTTP certain [R487C] versus [wild-type] ratio, we then hydrolyzed; therefore, we can assume that after one weight them accordingly and obtain the average dTTP hydrolysis cycle, the ssDNA is translocated hydrolysis rate for each case. The simulated results by 3 nt. Figure 8(b) shows the pathways that were for this sequential power stroke mechanism are extracted from the high-flux pathways shown in shown as the continuous line in Figure 6. The trend Figure 7(b). Within this subset, the translocation can of the simulation is similar to the trend of the take place by several pathways. For example, the experimental data, while in the middle range of first step in Figure 8(a) is the hydrolysis step; this mixing the simulation underestimates the rate. One step occurs when DNA is bound to two subunits possible explanation for this discrepancy is that the and, as shown in Figure 8(b), one in which the third mixing of the mutant and the wild-type species may subunit is E (in step 1a) and the other where the not be uniform, so that it may have a higher third subunit is DP (in step 1b). After dTTP probability to form homogeneous wild-type rings hydrolysis the DNA dissociates from that subunit than calculated. Another possibility is that the and the N$T* state goes to N$T, which is the power sequential power stroke is not as strict as we use stroke step that translocates the DNA. Depending Mechanochemistry of T7 DNA Helicase 465

Figure 7. The steady-state kinetic flux networks for hexameric T7 helicase. The mechanism behind part of these flux networks is illustrated in Figure 8(b). Here, each hexagon represents a kinetic state of the hexamer. Each subunit of the hexamer is colored with the corresponding occupancy state shown in the key: white, empty state (E); cyan, dTTP docking (weakly bound) state (T*); pink, dTTP docking with DNA bound (N$T*); red, dTTP tightly bound to DNA $ (N T); yellow, the dTDP-Pi state (DP); and green, dTDP bound (D). The reaction cycle proceeds across the columns with the possible reaction pathways linked by lines whose thickness reflect the fractions of the total flux carried through that reaction branch. Thus, the magnitude of the flux (line thickness) illustrates the relative probabilities of each pathway. The rightmost column is the same state as the first column but shifted one subunit to form a repeated kinetic cycle. Lines representing the power stroke driving DNA translocation are colored red; all other transitions are colored blue. The lower rows have higher occupancy (increasing ligand concentration). The pattern of flux pathways depends on the Z Z Z solution concentrations. For physiological conditions ([dTTP]0 100 mM, [dTDP]0 10 mM, [Pi]0 1 mM), there is a Z dominant kinetic pathway with low occupancy, while for [dTTP]0 500 mM, the kinetics spread over many pathways. In the latter case, the concept of a “principal pathway” is not well-defined. Along different pathways the order of the reaction steps is different. The states shown here are only the most populous of the 66Z46,656 possible states, i.e. those above a threshold flux of 3% of the total flux. on what is bound to the third subunit, the power forming a reaction network to accomplish the stroke step result in (DP, N$T, E) or (DP, N$T, DP) sequential translocation task processively. states, shown as states after step 2a and step 2b, respectively. In order to pass the DNA to the third subunit for the next power stroke, the third subunit Discussion must be in the T* state. The (DP, N$T, E) state can reach this state via two pathways: through steps 3a, Based on a combination of experimental obser- 4a, and 5a to (E, N$T, T*) state, or through steps 4b vations and computational methods, we propose a and 5b to (DP, N$T, T*). The cycle is then reset after consistent mechanochemical model for ssDNA the subunit in the T* state binds DNA to become the translocation by the hexameric T7 helicase. We N$T* state through steps 6a or 6b, where two analyzed data from (i) DNA and nucleotide binding subunits once again bind DNA. In this simplified affinities, (ii) pre-steady-state dTTP hydrolysis network, (DP, N$T, E) is the bottleneck that every kinetics in the presence and absence of DNA, (iii) pathway must pass through. If the network medium oxygen exchange, and (iv) a mutant includes all six subunits there are many more poisoning experiment. We combined these obser- pathways and the bottleneck may not exist for vations with the structural arrangement of the there are multiple kinetic pathways for T7 helicase catalytic sites to deduce a cooperative mechanism 466 Mechanochemistry of T7 DNA Helicase

Figure 8. Cooperative steps and multiple pathways of the T7 helicase kinetic network. (a) Schematic plot of the sequential steps in a typical translocation cycle. The vertical bars represent ssDNAwith the red intervals representing the binding phosphate groups three nucleotides apart. The orientations of DNA contacting loops are illustrated on both sides of DNA by the “lever arms” (see Figure 1). The contacts between these loops emanating from subunits 1, 2, and 3 (number in the upper left corner) are shown on both sides of the ssDNA. DNA is translocated downward in this reference frame by power strokes driven by dTTP binding to the catalytic site. Only three steps are necessary to assure a highly processive sequential mechanism. First, hydrolysis takes place when the next subunit binds to DNA ensuring that DNA will not diffuse away. When only one subunit binds to DNA, the power stroke can proceed without constraint. After each power stroke, the next subunit must proceed to the N$T* state (weak binding to DNA) in order for the whole cycle to repeat. (b) Multiple pathways extracted from the high-flux pathways shown in Figure 7(b) with matching colors of states. The helicase is shown “unwrapped” to form a band of subunits, and the position of each nucleotide binding site is shown. The diagonal orange line represents phosphate groups of ssDNA which are translocated downward. The blue dots represent the positions of ssDNA binding residues. Only three out of six subunits adjacent to the DNA binding subunit are shown; the other three subunits can be in several possible states (E, T*, DP, or D). The network shown here is meant only to represent a typical sequence amongst multiple pathways. Some kinetic steps are projected onto the corresponding steps shown in (a). that translocates ssDNA sequentially. In the absence behavior and support the view that all subunits of of DNA, we observed several sites that turned over the T7 helicase hexamer are catalytic. Although we dTTP slowly. The studies and analyses in the observed that less than six sites are hydrolytic at presence of DNA presented here show different any one time, this is likely due to the negative Mechanochemistry of T7 DNA Helicase 467 cooperativity in NTP binding that has been observed in the crystal structures. Although, the observed in other hexameric helicases.18–21 The concerted mechanism cannot be ruled out, it is not experimental data show that the rate-limiting step easy to see how all subunits can reset in concert changes from dTTP binding to Pi release as the without losing contact with DNA. If the motor does dTTP concentration increases. The hydrolysis of not hold DNA most of the time (high duty ratio), dTTP constitutes an important step in inter-subunit DNA will diffuse away or at least slip several base- communication and in modulating the DNA bind- pairs. ing affinity. The dTTP bound state has a high affinity We developed a computational algorithm to for DNA, whereas the dTDP-Pi, dTDP, and empty determine the rate constants for the NTP hydrolysis states have low affinity for DNA. This information cycle and to determine the kinetic fluxes through allowed us to isolate the mechanochemical coupling the reaction network, which is a priori quite large. step that transduces dTTP binding energy to DNA This allowed us to deduce a reduced set of states to translocation. DNA binds to a subunit when that characterize the helicase. The results reveal that subunit binds dTTP; the power stroke that drives dTTP hydrolysis can occur by multiple pathways, DNA translocation must occur as the dTTP anneals particularly at saturating dTTP concentrations. into a tight binding configuration in the catalytic Multiple pathways provide more degrees of free- site. Fast dTTP hydrolysis dissociates the DNA dom for the system to find the “low impedance” from the driving loop, but allows the next subunit sequence, as shown in Figure 8(a). Parallel kinetic in the dTTP bound state to bind DNA and continue pathways also exist in other multi-subunit motors the cycle of DNA translocation. such as myosin V.45 In multimeric proteins the Sequential mechanisms in which subunits of the existence of multiple pathways reduces the neces- protein bind and release DNA successively have sity for strict cooperativity among subunits at each been proposed for ring-shaped5,15,20,21 and non- kinetic step. For some required sequential steps the ring-shaped helicases3 as well as proteins such as cooperativity must be strong enough to ensure that the f12 P4 hexameric packaging motor.14 These the motor proteins can work processively, but for models explain processive translocation of these other kinetic steps many pathways are possible. The motor proteins along nucleic acids. The models presence of both high and low cooperative inter- based on crystal structure data for ring-shaped actions ensure robustness of these processive motor helicases are based on structures in the absence of proteins. the nucleic acid bound in the central channel.5,41,42 The elucidation of the kinetic pathways described Only two ring helicases, Rho protein and T7 here has been influenced by reasoning about helicase, have been characterized by detailed mechanical stresses to identify and quantify poss- biochemical and kinetic studies in the presence of ible cooperative interactions and to eliminate nucleic acid. Sequential hydrolysis of ATP and RNA unacceptable ones. We still do not have a complete binding and release around the hexamer ring has knowledge of the detailed interactions between the been proposed for the Rho protein where three sites subunits and how these interactions change as the have been invoked in the mechanism,20,43 which is helicase moves along the DNA. However, because different from the six-site mechanism that we theonlypossiblemechanismforcooperative propose here for T7 helicase in the presence of interactions is via mechanical stress, the number of DNA. possible coupling mechanisms is limited. We tried Recently, Gai et al.44 have suggested that the several possible mechanisms and the one shown hexameric helicase of simian virus 40 (SV40) large T here is the only one we found that could explain the antigen works by a concerted mechanism. This data. There may be other complicated mechanical model is also based on structural data obtained in interactions that we did not consider, and our the absence of DNA. The structures of SV40 large T methods cannot rule out those possibilities. The antigen in the absence of nucleic acid demonstrate detailed distributions of the kinetic pathways may many important aspects of the protein function. require revision as future studies reveal more They show conformational changes inside a subunit detailed information about conformational changes and between adjacent subunits when in different in the protein. nucleotide binding states and these conformational The large matrix analysis we have employed here changes are proposed to move DNA. It is possible to model the data has several advantages over the that when DNA is present the resulting asymmetric usual Michaelis–Menten analysis. Michaelis–Men- forces will induce only part of all subunits to change ten analysis may provide insights into the individ- conformations and to move DNA. The shapes and ual steps, including the binding events, inhibition the charge distributions are highly asymmetric, not effects, and a lumped rate for steps other than the surprising considering the major and minor binding step. However, it is based on the assump- grooves of DNA, as well as the base and the tions that the system is in the steady-state and there phosphate backbone in any cross-section of ssDNA is only a single kinetic pathway, which is almost and dsDNA. These asymmetric properties of the never the case. Departure from these assumptions DNA when bound in the central channel introduce produces non-hyperbolic enzyme kinetics and asymmetric forces on the surrounding subunits. requires more complicated kinetic equations, Without the imposition of these asymmetric forces, especially when considering the effects of subunit the ring will show symmetric arrangements, as interactions. The method we have employed to 468 Mechanochemistry of T7 DNA Helicase analyze our experiments is a modification of Pre-steady-state chase-time kinetics of dTTP classical models for subunit interactions, including hydrolysis the Monod–Wyman–Changeaux (MWC) and the Koshland–Nemethy–Filmer (KNF)-type models.35,46 The experiments were conducted using a rapid quench- Since these methods were proposed, computational flow instrument at 25 8C. T7 helicase was mixed with C a 32 power has advanced to the point that we could dTTP [ - P]dTTP, M13 ssDNA, and EDTA in the helicase buffer and immediately loaded into one syringe include all six subunits in the simulation. This large of the quench-flow instrument. After three minutes, 24 ml matrix simulation allows us to identify the distri- of the enzyme complex was rapidly mixed with an equal bution of pathways for the T7 helicase (see Figure volume of unlabeled dTTP and MgCl2 from a second 7), and enables fitting to both transient and steady- syringe of the instrument. The final concentrations after state phases of the data. Because the matrix is large, mixing were as follows: T7 helicase (1 mM hexamer), it might appear that the results are not reliable. radiolabeled dTTP (60 mM–500 mM), chase dTTP (5 mM), However, the situation is simpler than the dimen- MgCl2 (20 mM) and M13 ssDNA (15 nM). After various chase-times, the reactions were quenched with 4 M sionality might suggest, since all six subunits have 12 exactly the same kinetic cycle, and there are only formic acid and products were analyzed as described. three cooperative steps. Our method is similar to The chase-time kinetics were fit to equation (5) and the linear phase of dTTP hydrolysis due to inefficient chase the free energy of activation treatment proposed by 36,37 was subtracted. The resulting chase-time kinetics was fit Ricard et al. The complexity lies only in to a single exponential: computation, not in the underlying physics; that K is, our method provides a way, based on simple DðtÞ Z Að1 Ke k1tÞ (4) physics, to attack multimeric time-dependent kin- where D(t) is dTDP at time t, A is the burst amplitude, and etics problems. k1 is the exponential rate constant. The algorithm developed here for T7 helicase can be applied to any multimeric, multi-state enzyme, Pre-steady-state acid-quench kinetics of dTTP including ring-shape enzymes such as the virus hydrolysis portal protein, helicases, GroEL, and F1 ATP synthase. It is also easy to implement for walking The experiments were conducted at 25 8C using a rapid motors such as kinesins or double-headed myosins, chemical quench-flow instrument (KinTek RQF3 soft- although the total number of states for these motors ware, State College, PA). T7 helicase was mixed with is within the purview of the analytical method of dTTPC[a-32P]dTTP, M13 ssDNA, and EDTA in the Fisher & Kolomeisky.47–49 Our method is not helicase buffer and immediately loaded into one syringe restricted to steady-state kinetics; indeed, pre- of the quench-flow instrument. After three minutes, 24 ml steady-state kinetics and mechanical measurements of the enzyme complex was rapidly mixed with an equal (e.g. force–velocity curves) can be incorporated, so volume of MgCl2 from a second syringe of the instrument. The final concentrations after mixing were as follows: T7 long as the power stroke step can be modeled as a helicase (1 mM hexamer), dTTP (60–500 mM), MgCl2 thermally activated event. In a subsequent publi- (20 mM) and M13 ssDNA (15 nM). The mixed reactions cation this restriction will be lifted so that the power were quenched after millisecond to second intervals with stroke can be described by an arbitrary mechano- 4 M formic acid and products analyzed as described.12 chemical potential. Within its limitations, this The acid-quench kinetics were fit to the burst equation: algorithm provides a systematic procedure to K Z K k1t C study the multiple pathways of cooperative, allo- DðtÞ Að1 e Þ mt (5) steric enzymes. where D(t) is dTDP at time t, A is the burst amplitude, k1 is the exponential rate constant, and m is the slope of the linear phase.

Experimental Procedures dTTPase activity of mixed wild-type and mutant T7 helicase hexamers

Protein, nucleotides, and buffer R487C and wild-type T7 helicase proteins in different ratios (final concentration of protein mixture, 100 nM 0 hexamer) were mixed in helicase buffer for 30 minutes T7 gp4A protein (referred to as the T7 helicase) is a 2C M64L mutant of T7 helicase–primase protein and and the dTTPase reaction was initiated by adding Mg , a 32 R487C were over-expressed and purified as 2 mM dTTP spiked with [ - P]dTTP, and 2 nM ssM13 described.18,50 The protein concentration was deter- DNA. The reactions were stopped after 15, 30, 45, 60, 120, mined both by absorbance measurements at 280 nm in 180, 240 seconds with 4 M formic acid, and dTTP and K K 8 M urea (the extinction coefficient is 76,100 M 1 cm 1)and dTDP were quantified as described above. The steady- by the Bradford assay using bovine serum albumin as a state dTTPase rate was calculated from the time-course standard. Both methods provided similar concentrations. (slope) and plotted as a function of [R487C]. The M13 ssDNA (M13mp18) was purified as described.51 dTTP and dTDP were purchased from Sigma Chemicals, Stopped-flow kinetics of inorganic phosphate release and [g-32P]dTTP was obtained from Amersham Pharmacia Biotech. Helicase buffer (50 mM Tris–HCl (pH 7.6), 40 mM The A197C phosphate-binding protein (PBP) was NaCl, and 10% (v/v) glycerol) was used throughout the purified and labeled with MDCC as described.23 experiments unless specified otherwise. Inorganic phosphate release reactions were performed Mechanochemistry of T7 DNA Helicase 469 at 25 8C using a stopped-flow instrument manufactured GM55310 and J.-C.L. and G.O. were supported by by KinTek Corp. (State College, PA). The instrument NIH grant GM59875-02. The authors thank Dale syringes were treated with the phosphate mop (0.5 unit/ Wigley, Oleg Igoshin, Jianhua Xing, Michael Grabe, ml of PNPase and 300 mM 7-methylguanosine) to remove and Joshua Adelman for valuable discussions. contaminating Pi. A phosphate calibration curve was created as follows. To obtain a baseline value of fluorescence intensity, C0, PBP-MDCC (10 mM) from one syringe of the stopped-flow Appendix A instrument was mixed with the helicase buffer from a second syringe. The fluorescence intensity, which Determination of the optimal concentration of remained unchanged with time for at least 300 ms, was M13 ssDNA measured using a 450 nm long pass filter (Corion LL-450 F) after excitation at 425 nm to obtain the C0 value. This T7 helicase (2 mM, hexamer) was incubated with baseline fluorescence intensity value was determined M13 ssDNA (0–50 nM, molecules) in the helicase before each Pi standard reaction. Immediately after C0 buffer containing 5 mM EDTA and 1 mM dTTP. determination, PBP-MDCC (10 mM) from one syringe was m After 15 minutes, radiolabeled 76-mer ssDNA (final mixed with a known concentration of Pi (0.1–0.8 M) from m a second syringe. The fluorescence intensity increased 6 M) was added and the samples were filtered through a NC-DEAE membrane assembly. The with time due to Pi binding to the PBP-MDCC protein, and the maximum fluorescence intensity provided Ci. The membranes were washed before and after filtration value Ci–C0 was plotted against the final Pi concentration of samples with the membrane wash buffer (50 mM to generate the phosphate calibration curve. Tris–HCl (pH 7.5), 5 mM NaCl). After the samples The Pi-release kinetics were measured in the stopped- were filtered, radioactivity on both NC and DEAE flow instrument by reacting 40 ml of solution A with filters was quantified using a Phosphoimager solution B. Solution A consisted of T7 helicase (0.2 mM, (Molecular Dynamics). The molar amount of T7 hexamer), EDTA (5 mM), Pi -mop (0.5 unit/ml of PNPase helicase–76-mer complex was calculated from the m with 300 M 7-MEG), M13 ssDNA (3 nM), and dTTP ratio of radioactivity on NC over the sum of (200–3200 mM), and solution B consisted of MgCl2 (45.2– 7 48.2 mM), P -mop, and 10 mM PBP-MDCC. A total of four radioactivity on both membranes, as described. i In the absence of M13 ssDNA, a large amount of or five kinetic traces were averaged and the fluorescence 0 intensity time-courses were converted to the kinetics of Pi radiolabeled 76-mer–gp4A complex was observed. release using the phosphate calibration curve. We ensured As the concentration of M13 ssDNA molecules was that the phosphate mop did not compete with PBP-MDCC increased in the reaction, the amount of helicase–76- for phosphate (k /K for the PNPase reaction with P is K Kcat m i mer complex decreased, and beyond 20 nM M13 3.2!106 M 1 s 1).52 A control experiment was carried ssDNA, no helicase–76-mer complex was observed, out for each dTTP concentration by mixing solution A C indicating that no free helicase was present in the with solution B lacking Mg2 . The control experiment 2C reaction to bind radiolabeled 76-mer. These experi- was subtracted from the experiment with Mg . ments indicate that for each mmol of T7 helicase hexamer, we need at least 10 nmol of M13 ssDNA Phosphate–water oxygen exchange experiments molecule to saturate the binding of protein to DNA. We therefore used a ratio of 15 nM M13 ssDNA per 18 [ O]Pi was prepared by reacting PCl5 (Sigma) with mM T7 helicase hexamer in all our experiments. In a 18 99% H2 O (Aldrich Chemical) followed by ion-exchange 53 separate experiment, we varied the time of incu- chromatography (Bio-Rad; AG1-X4). The resulting bation of the helicase with DNA and dTTP. No free inorganic phosphate had an enrichment of 96% 18O. 18 protein was detectable even after a short (two The concentration of [ O]Pi was determined by the molybdate method.54 T7 helicase (1 mM hexamer) was minutes) period of incubation (data not shown). Based on this experiment, we chose a three minute incubated with 10 mM MgCl2, 0.5 mM EDTA, 6 mM 18 dTDP, 20 mM [ O]Pi, M13 ssDNA (15 nM), and 60% pre-incubation period for all experiments, which 2 (v/v) H2O in 0.5 ml of helicase buffer at 22 8C for 2–12 also gives us enough time to load the pre-incubated hours. The reactions were quenched by vortexing with sample in the quench-flow instrument. chloroform to denature the enzyme, and aqueous phase was extracted for 31P NMR analysis. The distribution of The effect of adding Mg2C in the kinetic steps 18 16 % % P Oj O4Kj species, where 0 j 4, was determined by 31P NMR.55 The spectra were obtained with JEOL GX-400 2C In quench, chase, or Pi release experiments, Mg instrument at a frequency of 162 MHz for phosphorus. is added after dTTP and the helicase is allowed to Five hundred scans were accumulated and then Fourier 18 16 reach equilibrium. That is, an extra state should be transformed. The P Oj O4Kj peaks were each separated by 55 18 included to distinguish the states with and without shifts of 0.02 ppm. Fractional contribution of each [ O]Pi C Mg2 in the catalytic site. Experiments show that species to the spectrum was evaluated directly from the C the hydrolysis rate is negligible before Mg2 is peak area. C added to the solution.17 Therefore, before Mg2 is added, the subunits can only be in E, T**, NE, NT** states, where T** represents the dTTP docking state C C C without Mg2 . After adding Mg2 ,Mg2 can Acknowledgements diffuse into the catalytic site to become the T* or NT* state, or Mg–dTTP can be formed in solution S.S.P. and Y.-J. J. were supported by NIH grant and directly dock to the catalytic site. In the latter 470 Mechanochemistry of T7 DNA Helicase

case, the E (NE) state can directly go to the T* (NT*) kinetic steps following dTDP-Pi (DP) or dTDP (D) at state without passing through the T** (NT**) state. the adjoining site, increasing the probability of the 2C / Since Mg is much smaller than dTTP, its reverse step dTDP-Pi dTTP. For example, if dTTP diffusion to the catalytic site is very fast. Therefore, hydrolysis at one site affects Pi release at an adjacent T**/T* is very fast and so is NT**/NT*. Under site, then non-hydrolyzable dTMPPCP will prevent / this assumption, the T** and NT** states can be release of Pi, giving time for dTDP–Pi dTTP. omitted. The assumption may break down if, after Mechanically, hydrolysis in one subunit can induce 2C Mg diffuses into the catalytic site, Mg–dTTP stress in adjacent subunits facilitating Pi release. takes a long time to rearrange its coordination so DNA provides coordination between these sub- that the correct conﬁguration of T* state is achieved. units through an additional stress loop shown in In this case, the rate of E to T** is not equivalent to E Figure A1(c), so in Figure 5(d) when DNA is absent, to T*, and states T** and NT** must be retained in synthesis events are not observed. Under this the model. In the main text, we lump states T** and hypothesis, in the presence of DNA, Pi is stuck in T* as one state, T*. the catalytic site unless dTTP hydrolyzes in another site. Alternative explanations for oxygen exchange Another possibility is that DNA binding, T*/ experiments NT*, in one site triggers the release of Pi in the adjacent site. Notice that the binding of DNA Considering multi-subunit interactions provides requires the subunit to be in its weakly bound alternate explanations for the oxygen exchange dTTP state. When dTMPPCP is trapped in a observations. dTMPPCP is a non-hydrolyzable catalytic site, that subunit is in its tightly bound version of dTTP. When dTTP is replaced by state and the corresponding DNA binding residues dTMPPCP at one site, it may delay, or block, the are not in position to bind DNA. Therefore, Pi is

Figure A1. Stress paths between subunits in the T7 helicase. (a) Stereo view of the T7 hexamer showing (in red) the main-chain connections between adjacent catalytic sites. (b) Detail showing the main stress pathways between adjacent catalytic sites, assuming motif III is the DNA contact residues. (c) Cartoon illustrating the circumferential stress path and the stress loop passing through the nucleotide in the (N$T, N$T*) state. The springs represent the b-sheet and the continuous red lines represent the loops emanating from them. Mechanochemistry of T7 DNA Helicase 471 trapped in its site waiting for dTMPPCP to dTTP binding events probably occur in almost all dissociate. This waiting time can be sufficient for subunits. Therefore, to obtain the initial concen- some synthesis events. trations of all states we modeled a random dTTP These hypotheses rest on cooperativity between binding process with binding probability given by the hexamer subunits for dTTP hydrolysis. The the chase occupancy. 18 absenceofmedium[O]Pi exchange with dTMPPCP without DNA indicates that regulation or cooperativity among subunits occurs via DNA, Alternative optimization methods but not because dTTP and dTMPPCP have different binding affinities. We used the downhill simplex method for the optimization to obtain rate constants that fit the The complete simulation experimental data well. Several other optimization methods have been devised, including those We have presented alternate explanations for the specifically designed for least-squares fitting,56 results of the oxygen exchange experiments. In maximum likelihood methods,57,58 and genetic order to distinguish one explanation from the other, algorithms.59,60 However, because the function to acompletekineticcyclemustbeconsidered be minimized is highly non-linear, none of these explicitly, including both D/DP and N$D/ methods guarantee finding a global minimum. We N$DP steps. Also, the effect of non-hydrolyzable have compared the simplex method with several dTMPPCP binding must be included. The other non-linear solvers and none has provided minimal kinetics required to describe each subunit any compelling advantage over the simplest is: approach. T^ 4 T^ 4 E 4 T 4 T 4 DP 4 D 4 E hhhhhh hh(A1)

N,T^ 4 N,T^ 4 N,E 4 N,T 4 N,T 4 N,DP 4 N,D 4 N,E where T^ represents the dTMPPCP-bound state. Flux methods Because dTMPPCP is not hydrolyzable, the states in the left side are terminated before the hydrolysis The flux diagram method developed by T. Hill events. The complete kinetic network has 146Z has been successful in computing states and fluxes 7,529,536 states. Although our method applies in for small kinetic networks.40 However, the network principle, this system is too large to be addressed for the T7 helicase is too large for the diagram computationally within current computer power method, and so a numerical scheme such as we and memory limits. developed here is required. Recently, Fisher & Kolomeisky developed kinetic models with Initial conditions sequences and branches applied to motor proteins.47–49 In these models, analytical solutions for The concentrations of all states at the initial time any number of sequential states with branches and are required to solve the kinetic equations. Chase jumps were obtained and used to fit data for myosin experiments provide information to deduce the and kinesin dimers with two catalytic sites. Rajen- initial conditions. For this, a simulation was carried dran et al. used the analytical solution of a out by considering only three possible states before sequential kinetic model for another ring helicase C Mg2 is added (i.e. hydrolysis has not yet DnaB.19 However, it is difficult to extend these occurred): E, T*, and NT*. Using these states, the models to the large kinetic network that character- initial occupancy can be inferred from the chase izes the T7 helicase, so the problem is better experiments. In order for sequential translocation to approached by numerical schemes rather than proceed, only one subunit can bind tightly to DNA analytical solutions. The mechanical considerations at a time. That is, at most one subunit can be in state we used to prune the possible kinetic pathways are NT*; all other subunits are in states E or T*. The acid also an important element in distinguishing our quench data show the transient phase takes about method from others. four or five hydrolysis cycles to reach the steady- state slope. The hydrolysis speed (slope) in this Three cooperative steps are necessary transient phase is greater than the steady-state speed. This is because some subunits are already in The fitting is based on the three required the T* state, ready to hydrolyze. The [dTTP]0 cooperative steps involving multi-subunit inter- dependence of steady-state slopes indicates dTTP actions. To examine the necessity of each of these binding is the rate-limiting step. Because dTTP three steps, we also carried out simulations relaxing binding is rate limiting, the subunits, which already one required step at a time. In each case either the have dTTP bound, bypass this slow step. The four power strokes are not sequential, or DNA loses or five startup hydrolysis cycles imply that initial contact to all subunits of the helicase, thus 472 Mechanochemistry of T7 DNA Helicase

Figure A2. Flow chart illustrating the computational scheme used to obtain the best-fit rate constants to the kinetic experiments. losing tight coupling between hydrolysis and estimate how this protein might function under a translocation. mechanical load. Assume a single molecule force– To further test the model, extra requirements velocity measurement can be accomplished for T7 were also imposed in addition to the three required helicase, analogous to the DNA pulling experiment 61 cooperative steps. For example, in F1 ATP synthase carried out for the f29 portal protein. As the force ADP release is enhanced by ATP binding on opposing translocation increases, the translocation another subunit.31 Therefore, an additional require- power stroke, NT*/NT, becomes the rate-limiting ment was imposed that dTDP release is triggered by step as the hydrolysis cycle slows. Because the dTTP binding at adjacent sites. Simulation based on hydrolysis cycle is tightly coupled to translocation, this additional cooperative requirement shows that as the stall force is approached, the rate of the dTDP is released too slowly so that the occupancy hydrolysis cycle becomes too small to be measured. does not correspond to the measurements.18 Since The prediction of force dependence is shown in the data also show Pi release has a phase delay after Figure A3 based on the assumption that the power hydrolysis, we also simulated the situation that Pi stroke can be modeled as a thermally activated release is triggered by dTTP binding or the power event, with the forward rate modified by a K stroke. In both cases Pi release becomes the rate- Boltzmann factor, exp( Fd/2kBT), and the back- limiting step under all initial [dTTP]0, and fitting for ward rate modified by exp(Fd/2kBT). Here, F is the different slopes under different [dTTP]0 is impos- external load force and d is the power stroke w sible. We conclude that the phase delay of Pi release displacement, d 0.9 nm. The initial conditions are results simply because the rate is intrinsically slow, the same as those shown in Figure 4. Physiological not because this step is affected by multi-subunit conditions are assumed to be [dTTP]Z100 mM, Z Z interactions. [dTDP] 10 mM, and [Pi] 1 mM, as for Figure 7. For low initial [dTTP]0, a force less than 5 pN does Predictions for single molecule force–velocity not have a large effect on the hydrolysis rate. This is experiments because dTTP binding, rather than the power stroke, is the rate-limiting step at low load. As the Based on the computed rate constants, we can load force increases, the hydrolysis rates for all Mechanochemistry of T7 DNA Helicase 473

Figure A3. Force and free energies of translocation. (a) Predicted force dependence for the steady-state dTTP hydrolysis rate under different initial conditions assuming a Boltzmann force dependence; i.e. the power stroke is a thermally activated step. Since N$T*/N$T is the power stroke, this step is affected by the load force. When the load force is large, this step becomes rate limiting and the hydrolysis cycle slows. The values at FZ0 correspond to the steady-state Z Z Z slopes in Figure 4. The prediction for physiological conditions is also shown ([dTTP] 100 mM, [dTDP] 10 mM, [Pi] 1 mM). The stall force is estimated to be about 30 pN. (b) The free energy levels for physiological conditions under different load forces. The corresponding hydrolysis rates under these four different forces are marked in (a). The load force only changes the free energy of the power stroke step, N$T*/N$T. As the load force increases, this step eventually becomes endothermic, and the corresponding hydrolysis rate decreases. curves drop until, around 30 pN, the hydrolysis rate References is very small, and can be considered an estimate of the stall force. An actual mechanical potential 1. Patel, S. S. & Picha, K. M. (2000). Structure and model, rather than the exponential Boltzmann function of hexameric helicases. Annu. Rev. Biochem. model used here, can be implemented to obtain a 69, 651–697. different force–velocity relationship, especially near 2. Eggleston, A. K. & West, S. C. (1996). Exchanging the stall force.31,33 partners–recombination in E. coli. Trends Genet. 12, 20– As shown in Figure A3(a), under physiological 26. conditions the hydrolysis rate at zero force is about 3. Lohman, T. M. & Bjornson, K. P. (1996). Mechanisms K 13.5 s 1. The hydrolysis rate also decreases with of helicase-catalyzed DNA unwinding. Annu. Rev. Biochem. 65, 169–214. increasing load force; values of four different load 4. Bachrati, C. Z. & Hickson, I. D. (2003). RecQ helicases: forces are shown: 0 pN, 10 pN, 20 pN, and 30 pN. suppressors of tumorigenesis and premature aging. For each of these forces, the computed free energy Biochem. J. 374, 577–606. level of each chemical state is plotted in Figure 5. Singleton, M., Sawaya, M., Ellenberger, T. & Wigley, A3(b), illustrating the free energy drop in each D. (2000). Crystal structure of T7 gene 4 ring helicase kinetic step. Of course, there is an activation free indicates a mechanism for sequential hydrolysis of energy barrier in each kinetic step; however, since nucleotides. Cell, 101, 589–600. the barrier heights are not determined (i.e. the 6. Toth, E. A., Li, Y., Sawaya, M. R., Cheng, Y. & frequency factor of each step is not known), we link Ellenberger, T. (2003). The crystal structure of the the free energy levels by broken lines. Note that bifunctional primase–helicase of bacteriophage T7. only the power stroke step is affected by the load Mol. Cell. 12, 1113–1123. force, the free energy differences of all other steps 7. Hingorani, M. M. & Patel, S. S. (1993). Interactions of remain unaltered. At physiological conditions, the bacteriophage-T7 DNA primase helicase protein with concentration of P is high, and so the P release step single-stranded and double-stranded DNAs. Biochem- i i 32 is endothermic. This is consistent with the exper- istry, , 12478–12487. 8. Kim, D. E., Narayan, M. & Patel, S. S. (2002). T7 DNA imental observation that Pi release is slow. Brow- helicase: a molecular motor that processively and nian ﬂuctuations drive the system through this unidirectionally translocates along single-stranded unfavorable kinetic step, which will be rectiﬁed by 321 / / DNA. J. Mol. Biol. , 807–819. the subsequent steps (D E, E T*, etc) with large 9. Jeong, Y. J., Levin, M. K. & Patel, S. S. (2004). The free energy drops. As the load force increases, the DNA-unwinding mechanism of the ring helicase of power stroke step becomes endothermic, and this bacteriophage T7. Proc. Natl Acad. Sci. USA, 101, 7264– step becomes rate limiting. 7269. 474 Mechanochemistry of T7 DNA Helicase

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Edited by R. Ebright

(Received 24 January 2005; received in revised form 22 April 2005; accepted 22 April 2005)