Cooperative Mechanism of RNA Packaging Motor*

P4 is a hexameric ATPase that serves as the RNA packaging motor in double-stranded RNA bacteriophages from the Cystoviridae family. P4 shares sequence and structural similarities with hexameric helicases. A structure-based mechanism for mechano-chemical coupling has recently been proposed for P4 from bacteriophage φ12. However, coordination of ATP hydrolysis among the subunits and coupling with RNA translocation remains elusive. Here we present detailed kinetic study of nucleotide binding, hydrolysis, and product release by φ12 P4 in the presence of different RNA and DNA substrates. Whereas binding affinities for ATP and ADP are not affected by RNA binding, the hydrolysis step is accelerated and the apparent cooperativity is increased. No nucleotide binding cooperativity is observed. We propose a stochastic-sequential cooperativity model to describe the coordination of ATP hydrolysis within the hexamer. In this model the apparent cooperativity is a result of hydrolysis stimulation by ATP and RNA binding to neighboring subunits rather than cooperative nucleotide binding. The translocation step appears coupled to hydrolysis, which is coordinated among three neighboring subunits. Simultaneous interaction of neighboring subunits with RNA makes the otherwise random hydrolysis sequential and processive.

P4 is a hexameric ATPase that serves as the RNA packaging motor in double-stranded RNA bacteriophages from the Cystoviridae family. P4 shares sequence and structural similarities with hexameric helicases. A structure-based mechanism for mechano-chemical coupling has recently been proposed for P4 from bacteriophage 12. However, coordination of ATP hydrolysis among the subunits and coupling with RNA translocation remains elusive. Here we present detailed kinetic study of nucleotide binding, hydrolysis, and product release by 12 P4 in the presence of different RNA and DNA substrates. Whereas binding affinities for ATP and ADP are not affected by RNA binding, the hydrolysis step is accelerated and the apparent cooperativity is increased. No nucleotide binding cooperativity is observed. We propose a stochastic-sequential cooperativity model to describe the coordination of ATP hydrolysis within the hexamer. In this model the apparent cooperativity is a result of hydrolysis stimulation by ATP and RNA binding to neighboring subunits rather than cooperative nucleotide binding. The translocation step appears coupled to hydrolysis, which is coordinated among three neighboring subunits. Simultaneous interaction of neighboring subunits with RNA makes the otherwise random hydrolysis sequential and processive.
Genomes of many viruses are encapsulated through NTPdriven packaging motor into preformed capsids. This process requires a portal complex that operates as the molecular motor and converts chemical energy into mechanical work. Doublestranded RNA bacteriophages from the Cystoviridae family (6)(7)(8)(9)(10)(11)(12)(13)(14) package their ssRNA 1 genomic precursors using a hexameric portal complex, the packaging NTPase P4 (1). P4 proteins share sequence and structural similarities with hexameric helicases and some of them possess helicase activity (2,3). The P4 hexamer is also used as a passive pore for the exit of nascent transcripts from the viral core (4).
A power stroke mechanism was proposed on the basis of P4 structures encompassing the key states of the catalytic cycle (3). Nucleotide exchange and hydrolysis was shown to induce concerted structural changes in two regions, namely the P-loop and the L2 loop-␣6 helix segment. The P-loop (Walker A or H1a motif in hexameric helicases) interacts with ␣ and ␤ phosphates of the nucleotide bound within the catalytic site. The L2 loop (H3 motif) is directly connected to the ␣6-helix (H4 motif) and binds to RNA. In the pre-hydrolysis state (P4-MgAMP-CPP complex) the P-loop is in a "relaxed" configuration and the L2 loop/␣6 helix is in an "up" configuration. After hydrolysis (P4-MgADP complex) the P-loop is in the "strained" configuration and the L2 loop/␣6 helix is in the "down" configuration. In the absence of any nucleotide the P-loop is in the relaxed configuration and the L2 loop/␣6 helix can swivel between the up and down configurations. Thus, it was proposed that the binding of ATP locks the L2 loop/␣6 helix in the up configuration, where it engages the ssRNA. Upon ATP hydrolysis, the nucleotide binding P-loop strains, push against one end of the L2 loop, so that the rest of the L2 loop and the ␣6 helix are forced to pivot down, carrying along the engaged RNA (3).
The structure also revealed that nucleotides bind at the subunit-subunit interfaces (3). Half of the adenine binding pocket and so called "arginine fingers" are contributed by neighboring subunits, whereas the rest of the binding site is contributed by the catalytic subunit. This provides the structural basis for cooperativity. However, the mechanism of ATP hydrolysis coordination within the P4 hexamer and RNA-dependent stimulation of hydrolysis remains elusive (4).
Here we present detailed enzymatic study of nucleotide binding, hydrolysis, and product release by 12 P4 in the presence of different nucleic acids, nucleotides, and inhibitors. Using these data we delineate the mechanism of ATP hydrolysis coordination and cooperativity during RNA translocation.

MATERIALS AND METHODS
Protein Purification-12 P4 protein was expressed in Escherichia coli and purified as previously described (5). P4 concentrations were determined by absorption at 280 nm using an extinction coefficient of 26,930 M Ϫ1 cm Ϫ1 , which was calculated based on the amino acid composition.
Phosphate Release Measurements-Phosphate release assays were done using the EnzChek Phosphate Assay Kit (Molecular Probes, Inc.) in the standard reaction buffer (20 mM Tris-HCl, pH 7.5, containing 75 mM NaCl and 7.5 mM MgCl 2 ) as described (6). Absorbance values at 360 nm were converted to concentrations of inorganic phosphate (P i ) using calibration with KH 2 PO 4 standards. AMP was used as a background control in all experiments. Steady-state kinetics of phosphate release were measured using a Victor 2 plate reader (Wallac-PerkinElmer) with time resolution of 20 s at 28°C. ATP, ADP, and UTP were purchased from Amersham Biosciences, AMP-PNP from Fluka, poly(rC) was from Sigma (concentration expressed as mole of base per liter), and oligoribocytidines of lengths 5,7,10,15,20,30, and 60 nucleotides were custom-made by Dharmacon (concentrations expressed as mole of oligonucleotide strand per liter).
Equilibrium Competitive Binding Assay-1 M 12 P4 was mixed with 50 M 3Ј-MANT-2Ј-dATP in 20 mM Tris-HCl buffer, pH 7.5, containing 75 mM NaCl and 7.5 mM MgCl 2 (final concentrations). The solution was aliquoted. Fluorescence spectra (310 -550 nm, 10 nm slit) were recorded within seconds upon addition of appropriate concentrations of the competing nucleotide (ATP, ADP, AMP-PNP, or UTP) to the aliquots using a MOS 250 fluorometer (Bio-Logic), exc ϭ 290 nm (20 nm slit), at 28°C. where the parameter n is the Hill coefficient. P4 translocates along the RNA strand of length L and falls off the RNA after an average of x bases because of limited processivity or limited substrate length. x is related to the processivity parameter M as follows: x ϭ LM/(L ϩ M). The processivity parameter M is an intrinsic property of the enzyme and reflects the average number of translocated bases at which half of the enzymes release RNA. Taking into account release and rebinding to RNA, the rate of phosphate release v during translocation along RNA is given by, where k RNA is the rate of RNA binding (which happens once per x bases translocated) and k H is the rate of ATP hydrolysis per one base translocated (i.e. rate of ATP hydrolysis divided by the number of bases translocated per one ATP molecule). Combining these two equations gives, Taking into account the footprint of the P4 on RNA, R (RNA longer than R bases must be bound to achieve translocation), and the basal ATPase activity, k B (in the absence of RNA), the final equation for obtaining the processivity parameter M is as follows. v Fluorescence intensity traces, f, corresponding to binding of MANT-ADP, 3Ј-MANT-2Ј-dATP, and 2Ј-MANT-3Ј-dATP were approximated by a single exponential term, where a is the amplitude of fluorescence change, b is the fluorescence plateau at infinite times, k is the apparent first-order rate, and t is time.
The kinetic fluorescence traces corresponding to MANT-ATP binding were described by two exponential terms.
In the case of a simple second-order reaction, the linear dependence of the apparent rate on substrate concentration [S] was described by, k on and k off are the true second-order association and first-order dissociation rate constants. Equilibrium dissociation constants were estimated from the fluorescence change amplitudes a (corrected for the inner filter effect as previously described (6)).
This equation describes stochiometric binding of the nucleotide analog (concentration [S]) to P4 (protein concentration [P]) with the apparent dissociation constant K app . Parameter C describes the maximum increase in quantum yield upon binding. The equilibrium competition assays against the fluorescent nucleotide analog were performed at low protein concentration and the fluorescence intensity was approximated by, where d and e are constants. The correct dissociation constant K d was calculated from the apparent dissociation constant K app as follows, where [I] is the concentration and K I is the dissociation constant of the fluorescent analog, respectively (7).

P4 Is a RNA Specific Motor with Low Translocation
Processivity-P4 12 slowly hydrolyzed ATP in the absence of any nucleic acid, whereas ssRNA but not ssDNA stimulated the activity (Fig. 1A). RNA affected both k cat (ϳ3-fold increase) and K m (2-fold decrease), and induced cooperativity in ATP hydrolysis with an apparent Hill coefficient n ϭ 2.7 Ϯ 0.3 (Table I). ATP analogs AMP-PNP and AMP-CPP were not hydrolyzed by 12 P4 (Fig. 1A, triangles). On the other hand, slow but detectable hydrolysis of AMP-PCP was observed (data not shown).
Dependence of k cat on ssRNA concentration provided an indirect measure of RNA-P4 complex formation (6). The apparent dissociation constant of the RNA-P4 complex was 0.40 Ϯ 0.06 mM in the presence of 1 mM ATP and 0.39 Ϯ 0.04 mM in the presence of 1 mM ATP and 0.5 mM ADP, respectively (Fig. 1B). Thus, the low affinity for RNA remained unaffected by ADP. Unfortunately, this method does not permit quantitative assessment of RNA affinity in the absence of ATP. However, no stable complex was detected by gel mobility shift (4) and thus we conclude that the affinity in the nucleotide free state remained low. Fig. 1C shows the dependence of the k cat on the ssRNA length. RNA as short as a pentamer stimulated P4 activity. Extrapolation of the experimental data using Equation 6 suggested that (rC) 4 would not stimulate and (rC) 5 constitutes the shortest stimulating RNA. The saturation of ATPase activity with relatively short RNAs suggested low processivity of translocation. The rate of ATP hydrolysis was roughly the same when stimulated by a 20-mer RNA or by poly(C), which has a length of several thousand bases (6). Using Equation 6 a processivity parameter (M) of 2.1 Ϯ 0.7 was obtained indicating frequent dissociation of the P4-RNA complex. This is in contrast to 8 P4 (Fig. 1C, open circles), which was stimulated by RNA longer than 8 bases and exhibited higher processivity (M ϳ 11).
2Ј-MANT-3Ј-dATP Is a Hydrolyzable Fluorescent ATP Analog-12 P4 contains three tryptophan residues that allowed for detection of nucleotide binding using FRET between the tryptophans and MANT-labeled nucleotides. MANT-ATP was hydrolyzed by 12 P4 with k cat and K m approximately 1 order of magnitude lower than those for ATP hydrolysis. However, the relative stimulation by RNA and the apparent cooperativity were identical as for the hydrolysis of unlabeled ATP ( Fig.  2A and Table I). Traces of MANT-ADP fluorescence upon mixing with P4 were single-exponential, whereas the traces corresponding to MANT-ATP binding had to be fitted by two exponential terms (Fig. 2, B and C). This suggested that MANT-ATP binding is either a two-step process or that there are two distinct classes of MANT-ATP binding sites. Alternatively, we considered the possibility that the two phases in MANT-ATP binding could arise from the two isomers of MANT-ATP present in the commercial preparation (i.e. the MANT group linked to the 2Ј-hydroxyl versus the 3Ј-hydroxyl group). Such an effect has been observed for MANT-ATP binding to the transcription termination factor Rho (8). Therefore, we investigated the interactions of P4 with two additional MANT-nucleotide derivatives, where the fluorophore was attached specifically to the 3Ј-hydroxyl (3Ј-MANT-2Ј-dATP) or the 2Ј-hydroxyl (2Ј-MANT-3Ј-dATP) of the deoxyribose ring. Both MANT-dATP analogs bound to P4 in a single kinetic phase. Only the 2Ј-MANT-3Ј-dATP was hydrolyzed by 12 P4 ( Fig. 2A and Table I). Thus, 2Ј-MANT-3Ј-dATP constitutes a suitable analog to study ATP binding, whereas 3Ј-MANT-2Ј-dATP can be used as a fluorescent ATPase inhibitor.

2Ј-MANT-3Ј-dATP Binding Is a RNA Independent, Single
Step Second-order Process-ATP binding kinetics was determined using the 2Ј-MANT-3Ј-dATP analog (Fig. 3). Rate of FRET intensity change increased linearly with the 2Ј-MANT-3Ј-dATP concentration (Fig. 3A). Thus, 2Ј-MANT-3Ј-dATP binding was a single step second-order, reaction. No significant difference in 2Ј-MANT-3Ј-dATP binding in the absence and presence of RNA was detected. Concentration dependences of the measured apparent rate constants yielded the second-order rate constants and dissociation constant:  Step Second-order Process-Although the MANT-ADP used in this study was a mixture of 2Ј-and 3Ј-isomers, single exponential binding kinetics were obtained for all concentrations. This could be the result of identical binding of the two isomers or lack of binding or FRET signal for one isomer. Fig. 4A shows the apparent rate of FRET intensity increase upon MANT-ADP mixing with P4 as a function of MANT-ADP concentration. Linearity of this dependence (up to 200 M MANT-ADP, i.e. about five times more than K d for MANT-ADP) suggests that MANT-ADP binding is a single step second-order association. Fig. 4B represents the FRET amplitude upon MANT-ADP binding to P4 as a function of MANT-ADP concentration. The apparent dissociation constants were independent of RNA (K d ϭ 36 Ϯ 5 and 41 Ϯ 8 M in the absence and presence of ssRNA, respectively). Similarly, inorganic phosphate had no effect on MANT-ADP binding (K d ϭ 43 Ϯ 9 M in the presence of ssRNA and 50 mM inorganic phosphate). AMP-PNP (nonhydrolyzable ATP analog) competed with MANT-ADP binding (K d ϭ 114 Ϯ 19 M in the presence of ssRNA and 1 mM AMP-PNP) demonstrating that MANT-ADP and ATP bind to the same set of sites.
Mg 2ϩ Inhibits Nucleotide Binding-Under typical cellular conditions more than 99% of all ATP and ADP is found in a complex with Mg 2ϩ (9). As shown previously for 6 P4 (10, 11) and more recently for 12 P4 (4), Mg 2ϩ at concentrations  Nucleotide Affinities-P4 affinity for different nucleotides was measured using competition against the non-hydrolyzable fluorescence ATP analog 3Ј-MANT-2Ј-dATP. Fig. 5B shows the FRET intensity decrease as a result of increasing competition with ATP and UTP. Dissociation constants determined for different nucleotides are listed in Table II. P4 exhibited similar affinity for ATP, ADP, and AMP-PNP. Thus, under the cellular conditions, where ATP concentration is millimolar and ADP concentration is micromolar, most of the nucleotide binding sites would be occupied by ATP. The UTP binding was approx-imately 1 order of magnitude weaker than ATP binding. This is consistent with the previously reported purine specificity of 12 P4 (4).
ATPase Inhibition Experiments Revealed Sequential Catalytic Mechanism-Considering the similar values of dissociation constants for ATP, ADP, and AMP-PNP, ADP and AMP-PNP should inhibit ATP hydrolysis. Detailed characteristics of the inhibition could shed light on the catalytic mechanism. Therefore we measured steady-state kinetics of ATP hydrolysis at different concentrations of ADP or AMP-PNP and in the absence as well as in the presence of RNA (Fig. 6). In the absence of RNA, ADP inhibited hydrolysis competitively (unchanged k cat , increased K m ), whereas AMP-PNP inhibited non-   Table II. Additional data for AMP-PNP and ADP are not shown. competitively (decreased k cat , unchanged K m ). In the presence of RNA the inhibition by ADP became a mixed type (decreased k cat , increased K m ), whereas the inhibition by AMP-PNP remained noncompetitive. These results demonstrated that some configurations of ATP and AMP-PNP within the hexamer (and some configurations of ATP and ADP in the presence of RNA) led to inactive protein. To find which configurations were inhibitory we have performed a titration experiment. Fig. 7A shows all possible configurations (microstates) of the ATP and the inhibitor within the hexamer. Abundance of a particular microstate is equal to and parameter i is the number of subunits occupied by the inhibitor (in Fig. 7A, i ϭ 0 for the first column, i ϭ 1 for the second column, etc.). As discussed above only some of the microstates would lead to hydrolysis. For example, if three neighboring subunits are required to bind ATP before one of them is hydrolyzed, then only the configurations, highlighted in gray, will be active. Fig. 7B shows the predicted inhibition curves for several model cases. In the "trimer of dimers" model ATP is hydrolyzed by every other subunit, in a fashion similar to F 1 -ATPase mechanism (12). The model "one in the row" describes ATP hydrolysis going in sequential steps around the P4 hexamer with only one of binding sites participating in ATP hydrolysis at a time (i.e. no cooperativity). "Two in the row" model requires that two neighboring subunits cooperate in ATP hydrolysis, whereas the rest of the hexamer may bind inhibitor without any loss of activity. In analogy, the "three in the row" model assumes cooperation of three neighboring subunits. An extreme case is the concerted ATP hydrolysis model of simul-taneous binding and hydrolysis of all six ATPs, which was recently proposed for the SV40 large T antigen (13).
The experimental data obtained for P4 and AMP-PNP as inhibitor compared well with the three in the row model, whereas ADP inhibition was approximated by the two in the row model (Fig. 7B). This implicates that to get a catalytically active complex three binding sites in the row need to be occupied, two of which must be ATP, whereas one can be ADP. The remaining three subunits are dispensable for hydrolysis and may bind AMP-PNP or ADP. Note that the model is a steadystate approximation and does not take into account effects of nucleotide binding kinetics. That might explain why the match between the experimental data and the model was not perfect (e.g. equilibrium dissociation constant of ATP and ADP are equal but rates of ATP association and dissociation might be different from those of ADP).

DISCUSSION
Comparison of 12 P4 and 8 P4-The packaging motor from a related bacteriophage 8 has been characterized previously (6) and allows for detailed comparison. Similarly to 8 P4, the 12 P4 has comparable affinity for ATP and ADP and exhibits RNA-induced cooperativity. Thus, both molecular motors are driven by the difference in cellular concentrations of ATP and ADP. In contrast to 8 P4, RNA binding to 12 P4 has no effect on the kinetics of nucleotide binding and release. ATP hydrolysis is the only step affected by the presence of RNA. Thus, the translocation step seems coupled to hydrolysis in 12. This is in agreement with the translocation mechanism inferred from the crystal structures, in which the largest changes were observed between the pre-hydrolysis (P4-AMP-CPP-Mg complex) and post-hydrolysis state (P4-ADP-Mg) (3). Energetic considerations for ATP-driven motors have demonstrated that most of the free energy available throughout the catalytic cycle is released during ATP binding (14,15). Thus, the translocation must be energetically coupled to ATP binding. Given that the power stroke of P4 is mechanistically coupled to the hydrolysis step the ATP binding energy is either stored in a strained conformation of the enzyme or the energy is relayed between neighboring subunits using the cooperative mechanism proposed below.
An RNA pentanucleotide was able to stimulate 12 P4 activity, whereas the RNA nonamer was required for 8 P4 stimulation (Fig. 1C). 12 P4 exhibits much lower RNA affinity and translocation processivity than 8 P4 (Fig. 1, B and C). We suggest that these differences can be explained by the lower stability of the 12 P4 ring, which in turn leads to spontaneous opening during translocation. Similar low processivity because of ring opening was observed for the bacteriophage T7 gp4 helicase (16). The spontaneous ring opening will also allow direct binding of short RNA oligonucleotides to the RNA bind-ing site. On the other hand, 8 P4 employs a ring opening mechanism for RNA loading (17). Consequently, this mechanism requires longer RNA oligonucleotides that bind simultaneously to the primary and secondary binding sites (18). Note that this difference applies only for P4 hexamers in solution. After attachment to the viral procapsid the ring is stabilized and the catalytic activity is regulated (2,4).
The Origin of Cooperativity and ATP Hydrolysis Coordination-The most striking finding is that P4 exhibits steady-state hydrolysis cooperativity without ATP binding cooperativity. In other words, RNA binding, which induces cooperativity, has no FIG. 8. Model of ATP hydrolysis cooperativity. A, mechanism of ATP hydrolysis in the absence of RNA. Blue squares represent P4 subunits of the hexamer unraveled in the plane. The red symbols designate the nucleotide-binding sites occupied by ATP. The doubleheaded arrows indicate independent stochastic binding to the nucleotide sites. The lower line shows the randomly attained, three in the row, configuration that permits hydrolysis at the middle site (orange). Note that hydrolysis also requires a correct conformation of the key side chains from the neighboring subunits (e.g. arginine fingers, Gln-278, Tyr-288). Arrows depict the proposed communication of strain between subunits. B, ATP hydrolysis in the presence of RNA. Triangular appendages correspond to the L2 loops. Green symbols mark the bound ADP, whereas the red symbols designate the required ATP molecules. Pink symbols designate the binding sites that may be occupied by ATP, inhibitor, or may be empty. The yellow line and circles represent the RNA sugar phosphate backbone. Arrows depict the proposed communication of strain between subunits. effect on nucleotide binding kinetics and affinity. On the other hand, RNA binding substantially increases the catalytic efficiency by lowering the apparent K m and increasing the k cat . Hence, P4 exhibits a special type of kinetic cooperativity (19). To explain the RNA-induced cooperativity we propose a "stochastic-sequential" model. The key feature of this model is that nucleotide and RNA binding to neighboring subunits facilitates formation of the transition state. This does not lead to a change in nucleotide affinity but increases the probability of ATP hydrolysis. Thus, nucleotide binding remains independent and stochastic under all conditions, whereas the hydrolysis step becomes sequential in the presence of RNA.
In the absence of RNA, the higher K m than K d (Table I) can be explained by the necessity for simultaneous but independent binding of three ATP molecules before one of them is hydrolyzed (Fig. 8A). Inhibitor titration experiments in the absence of RNA (not shown) showed results similar to those shown in Fig. 7, suggesting that three subunits in a row need to bind ATP before one is hydrolyzed. This is also consistent with AMP-PNP being a noncompetitive inhibitor (Fig. 6), presumably acting via binding to the subunits neighboring the catalytic one. The low hydrolysis rate reflects the stochastic nature of attaining the required configuration of ATP molecules within the hexamer. In addition, this configuration must also coincide with the subunit conformations to progress toward the transition state. When, randomly, three neighboring ATP-binding subunits reach the right configuration the middle ATP molecule is hydrolyzed (Fig. 8A). This mechanism is purely stochastic with little coordination between subunits and thus the apparent cooperativity is low.
Stimulation of catalytic activity (k cat increase) in the presence of RNA indicates that RNA binding facilitates transition state formation. According to the structural model the RNA pentamer, which is the shortest oligonucleotide stimulating the activity, could interact with three neighboring subunits in the hexamer (3). Thus, we assume transient interaction of three neighboring P4 subunits with RNA (designated S1, S2, and S3 in Fig. 8B). In the crystal structures only two distinct conformations of RNA binding loop L2 were resolved (3). Based on the geometry of RNA and the fact that RNA is transiently bound by three neighboring subunits we propose that a third distinct conformation is attained during the transition state. For example, the L2-loop could assume a middle configuration between the two limiting positions seen in the crystal.
In agreement with the inhibition experiments (Fig. 7B), S1 subunit contains ADP (just after hydrolysis), whereas S2 and S3 bind ATP. The other subunits (S4, S5, and S6) may be empty or could be occupied by AMP-PNP or ADP without any effect on hydrolysis. However, under physiological conditions (high ATP concentration) inside the cell, all these sites would be occupied by ATP with the L2 loop up, i.e. poised to engage the incoming RNA (Fig. 8B). According to the crystallographic results, hydrolysis by the S1 subunit is accompanied by the down movement of its L2 loop. This motion is transmitted via the bound RNA strand to S2 and S3 L2 loops. Because these two loops are stabilized in the up position by ATP binding the forced movement causes stress accumulation. The stress is then used to reach the transition state and subsequently is relieved during hydrolysis at S2. There is evidence for stress accumulation in the 8 P4, in which the tightly bound RNA is stretched during the stroke (6). In analogy to the F 1 -ATPase (20 -22) we envision the energy from ATP binding to a neighboring subunit is stored in a stress loop of which RNA is an integral part (Fig. 8B).
The downward movement of the RNA during hydrolysis at S2 detaches RNA from the S1 subunit and brings the RNA to a suitable position for interaction with the S4 subunit (Fig. 8B). The hydrolysis cycle then repeats at the S3 subunit. Note that the hydrolysis step modulates RNA binding affinity (association at the S4, detachment from S1), whereas it does not change the nucleotide binding affinities. The ADP for ATP exchange at S1 remains stochastic as in the absence of RNA. The sequentially coordinated hydrolysis in the presence of RNA causes lowering of K m to a value comparable with K d (Table I). This is because each hydrolysis cycle requires on average binding of only one additional ATP molecule. The stochastic binding mode dominates the k cat at low ATP concentrations ([ATP] Ͻ K d ) and hence the activity is low. At higher ATP concentrations the sequential coupling is efficient. Gradual switching between the two limiting modes leads to the apparent cooperativity.
Kinetic study of hexameric packaging motor P4 from bacteriophage 12 revealed RNA-induced ATPase cooperativity. We propose a stochastic-sequential cooperativity model to describe the coordination of ATP hydrolysis within the hexamer in the absence of nucleotide binding cooperativity. In this model the apparent cooperativity is a result of hydrolysis stimulation by ATP and RNA binding to the neighboring subunits rather than of cooperative nucleotide binding. The translocation step is coupled to ATP hydrolysis. Simultaneous interaction of neighboring subunits with RNA makes the otherwise random hydrolysis sequential and processive. Given the structural and sequence similarity between P4 and hexameric helicases this mechanism may apply to other members within this large family of molecular motors.