Membrane-catalyzed Nucleotide Exchange on DnaA

DnaA is the initiator protein for chromosomal replication in bacteria; its activity plays a central role in the timing of the primary initiations within the Escherichia coli cell cycle. A controlled, reversible conversion between the active ATP-DnaA and the inactive ADP forms modulates this activity. In a DNA-dependent manner, bound ATP is hydrolyzed to ADP. Acidic phospholipids with unsaturated fatty acids are capable of reactivating ADP-DnaA by promoting the release of the tightly bound ADP. The nucleotide dissociation kinetics, measured in the present study with the fluorescent derivative 3′-O-(N-methylantraniloyl)-5′-adenosine triphosphate, was dependent on the density of DnaA on the membrane in a cooperative manner: it increased 5-fold with decreased protein density. At all surface densities the nucleotide was completely released, presumably due to protein exchange on the membrane. Distinct temperature dependences and the effect of the crowding agent Ficoll suggest that two functional states of DnaA exist at high and low membrane occupancy, ascribed to local macromolecular crowding on the membrane surface. These novel phenomena are thought to play a major role in the mechanism regulating the initiation of chromosomal replication in bacteria.

DnaA is the initiator protein for chromosomal replication in bacteria; its activity plays a central role in the timing of the primary initiations within the Escherichia coli cell cycle. A controlled, reversible conversion between the active ATP-DnaA and the inactive ADP forms modulates this activity. In a DNA-dependent manner, bound ATP is hydrolyzed to ADP. Acidic phospholipids with unsaturated fatty acids are capable of reactivating ADP-DnaA by promoting the release of the tightly bound ADP. The nucleotide dissociation kinetics, measured in the present study with the fluorescent derivative 3-O-(N-methylantraniloyl)-5-adenosine triphosphate, was dependent on the density of DnaA on the membrane in a cooperative manner: it increased 5-fold with decreased protein density. At all surface densities the nucleotide was completely released, presumably due to protein exchange on the membrane. Distinct temperature dependences and the effect of the crowding agent Ficoll suggest that two functional states of DnaA exist at high and low membrane occupancy, ascribed to local macromolecular crowding on the membrane surface. These novel phenomena are thought to play a major role in the mechanism regulating the initiation of chromosomal replication in bacteria.
Initiation of DNA replication is the central event in the bacterial cell cycle (1). To create identical daughter cells, the initiation should occur only once per cycle, synchronously at all origins of replication and at the right time (2). These requirements imply the existence of one or more precise regulatory systems that can adjust to a variety of physiological conditions (3). DnaA is the key protein in the initiation of replication in all known eubacteria species and has analogs in eukaryotes. Its overall activity cycle is driven by ATP binding and hydrolysis that "acts as a molecular switch that couples key events during initiation of replication" (4). In Escherichia coli DnaA binds to the five DnaA-boxes on oriC and promotes the replication complex assembly (5). Naturally, this first event in the multistep initiation process is the target for regulation: the initiating activity of DnaA depends on the type of the bound nucleotide, and only the ATP-DnaA form is functional (6). Immediately after the initiation, DnaA has to be inactivated to prevent untimely initiations on the newly replicated oriCs. Accordingly, the RIDA (replication inactivation of DnaA) mechanism induces ATPase activity of DnaA by converting it into the inactive ADP form (7)(8)(9). The next phase of the DnaA activity cycle is reactivation of ADP-DnaA to its ATP form. The spontaneous exchange of ADP to ATP is a very slow process even at a high ATP/ADP ratio, as under physiological conditions (6). This is perhaps the reason for the relatively low (ϳ20%) average level of ATP-DnaA found in growing cells, which is elevated at the verge of initiation time (10). Acidic phospholipids in a fluid membrane were shown to be responsible for the acceleration of the nucleotide exchange in vitro (11) and are involved in the DnaA-dependent initiation in vivo (12). Further investigations shed light on the mode of DnaA-membrane interaction (13,14) and pointed to a specific region of the protein responsible for this interaction (15-18; and for a review see Refs. 19 and 20).
How could DnaA initiating activity be dependent on the progress of the cell cycle? At least two general possibilities may be considered. First, ATP-DnaA is rapidly and continuously regenerated by the membrane, but some factors restrain its initiation activity until the proper time in the cell cycle. Second, ADP-ATP exchange does not occur continuously and is triggered at the right moment. The first possibility may be realized by (i) regulation of the DnaA concentration in the cell at the transcriptional level, (ii) modulation of the level of the free protein, e.g. through titration by multiple DnaA boxes on the chromosome (titration model (21)). These two mechanisms are considered as important for normal replication control but not crucial for exact timing (2), particularly because the continuous expression of DnaA from a plasmid had no effect on the replication control (22). Recently, the deletion of the datA site (DnaA binding) was shown not to affect the right timing of the initiation (23), thus strongly rejecting the titration model.
The membrane-regulated triggering may include (i) oscillation in the level of acidic phospholipids during the cell cycle and (ii) formation of membrane domains with appropriate compositions at the right time. Data on changes in the level of individual phospholipids during the cell cycle are controversial (24,25). Such changes could provide the activation signal in view of the stimulation of nucleotide dissociation from DnaA by raising the fraction of acidic phospholipids in mixed liposomes (13). However, there is an indication that clustering, rather than the concentration of acidic phospholipids, in such a membrane is essential for nucleotide dissociation (26). In the E. coli membrane, both structural and compositional heterogeneity were revealed (27,28). Domains containing cardiolipin were visualized at the cell poles (29), consistent with an enrichment of cardiolipin in minicells (30). It was shown that acidic and neutral phospholipids are sequestered into separate pre-existing domains in the bacterial membrane (31). Our working hypothesis is that such domains may provide the binding sites for integral and peripheral (amphitropic) membrane proteins and serve as spatially and temporally localized signal (32). The dynamics of such domains during the cell cycle may trigger the accessibility of the activating acidic phospholipids to DnaA. Alternatively, the membrane environment is suitable for regenerating ATP-DnaA throughout the cell cycle, but such regeneration does not occur until a specific time in the cell cycle, because an unidentified factor may restrain the regeneration process until that time. The results obtained in this work in vitro suggest that in growing bacteria both alternatives may be combined as interplay between the phospho-lipid domain size and protein concentration, wherein the protein surface density (crowding) plays the role of the restraining factor.
In this work we examined how the kinetics of membrane-induced nucleotide dissociation from DnaA depends on the phospholipid/protein ratio (PL/Pr). 3 The nucleotide binding kinetics, followed by the fluorescent derivative, 3Ј-O-(N-methylanthraniloyl)-adenosine 5Ј-triphosphate (MANT-ATP), appeared to be strongly sensitive to the protein density on the membrane. We will discuss this finding in relation to the timing of the initiation of DNA replication in the bacterial cell cycle.
Purification of His 10 -DnaA-Recombinant polyhistidine-tagged DnaA was expressed in E. coli strain BLR(DE3)pLysS from the plasmid pZL411, kindly provided by Prof. Elliott Crooke (Georgetown University, Washington, D. C.). The purification procedure was essentially as described (33) with slight modifications. A protease inhibitor, phenylmethylsulfonyl fluoride, was added prior to lysate preparation. An Ni-NTA column (3 ml of the resin volume) was used instead of a batch preparation to obtain larger amounts of protein. Nonspecifically bound proteins were washed with 40 mM imidazole and His 10 -DnaA was eluted with 0.8 M imidazole. Protein concentrations were measured by a dye-binding assay (34), using bovine serum albumin as a standard. Protein purity was determined by SDS-PAGE following Coomassie Brilliant Blue staining (35). The eluted protein was frozen in liquid nitrogen and stored at Ϫ80°C. Before each experiment, aggregated proteins were removed from the soluble fraction by centrifugation (3 ϫ 10 5 g, 10 min). Throughout this report, the tagged protein is designated as DnaA for simplicity.
Binding of MANT-ATP to DnaA-All experiments were carried out in 600 l of Buffer AC (50 mM PIPES⅐KOH (pH 7), 30 mM KCl, 2.5 mM magnesium acetate, 20% (w/v) sucrose, 0.1 mM EDTA, 2 mM dithiothreitol) containing 0.2 M ammonium sulfate at 30°C. Fluorescence intensity was measured on a LS55 fluorometer (PerkinElmer Life Sciences) at fixed wavelengths ex ϭ 352 nm and em ϭ 442 nm with both slits at 10 nm width. Vertical and horizontal polarizers were introduced for excitation and emission, respectively, to reduce the contribution of scattered light in the presence of liposomes without affecting the changes in fluorescence intensity of MANT-ATP upon binding to DnaA.
Titration of MANT-ATP (0.1 M) with DnaA (0.059 -1.89 M) was used to convert fluorescence changes into molar values by determining the relative fluorescence intensity increase per molecule of MANT-ATP bound to the protein (Q), where F i and F 0 are the fluorescence intensities of MANT-ATP in the presence and absence of DnaA, respectively, F background is the fluorescence intensity of buffer and DnaA, V i is the current volume, and V 0 is the initial volume of the sample. Changes in total MANT-ATP concen-tration because of dilution were neglected, because the maximal volume changes were Ͻ4%.
To determine the affinity and stoichiometry of MANT-ATP binding to DnaA, the measurement of fluorescence intensity was carried out at various concentrations of MANT-ATP (0.013-1.220 M) in the absence and the presence of DnaA (0.8 M). The calculations of the concentration of free ligand ([MANT-ATP] free ) and the concentration bound to DnaA ([MANT-ATP] bound ) were as follows where [MANT-ATP] total is the concentration of added MANT-ATP.
The changes in total DnaA concentration were neglected, because the maximal volume changes were Ͻ3%. The data were analyzed using a single-site binding isotherm in Equation 4.

͓MANT-ATP͔
The fluorescence method was validated by parallel determination of the affinity and stoichiometry of ATP binding to DnaA by the filter retention radioactive technique using [␣-32 P]ATP (33).
Preparation of Liposomes-Briefly, the powder of phospholipids was dissolved in chloroform, and subsequently dried under a stream of nitrogen gas and resuspended in Buffer AC. Large unilamellar vesicles were prepared with Avanti Mini Extruder by 11 passes through a Nucleopore polycarbonate membrane with a pore diameter of 100 nm at room temperature. Phospholipid concentrations were determined by the phosphomolybdate colorimetric assay (36). The size of the liposomes was estimated by dynamic light scattering on ALV/GCS-3 with the ALV/LSE-5003 correlator. The diameter of SOPG and SOPC liposomes in Buffer AC at 20°C was 124 and 140 nm, respectively (refractive index and viscosity were taken from a reference table for 20% sucrose solution (63).
Co-sedimentation of DnaA with Liposomes-The binding of DnaA to phospholipids was examined by co-sedimentation with liposomes of various compositions (37). To this end, DnaA was preincubated with 1 mM ATP on ice for an hour and then diluted 10-fold in Buffer AC and ultracentrifuged at 300,000 ϫ g (Sorvall Discovery M-120 centrifuge with a S120-AT2 rotor) for 10 min at 25°C. Protein concentration in the supernatant was determined by the Bradford assay. Afterward, DnaA (0.15-1.4 M) was incubated for 10 min with freshly prepared SOPG or SOPC liposomes (5-500 M phospholipids) in 200 l of Buffer AC in the presence of 1 mM ATP at room temperature. The samples were centrifuged for 10 min at 15,000 ϫ g, at 25°C (Sorvall M-120 with a S100-AT3 rotor), and 160 l of supernatant was carefully removed. The pellet was resuspended in the rest, 40 l.
The protein in each fraction was visualized by SDS-PAGE following Coomassie Brilliant Blue staining. Stained gels were scanned, and the protein bands were quantified using the National Institutes of Health Image program. The relative amount of sedimented DnaA (D) was calculated as follows, where P is the amount of protein (arbitrary integral band intensity) found in 20 l of the pellet fraction loaded on the gel, and S is the amount of protein found in 40 l of the supernatant fraction loaded on the gel. The amount of DnaA sedimented in the absence of liposomes was used to obtain the correct values of the co-precipitated protein.
For determining the amount of the sedimented phospholipids, liposomes were prepared with incorporated DPH-PC (DPH-PC:SOPG ϭ 1:100). After centrifugation with varying concentrations of protein as described above, the fluorescence signal of DPH-PC (excitation 350 nm, emission 430 nm) was measured in the pellet, and the supernatant fractions were dissolved in 700 l of 0.1% SDS. A relative amount of sedimented phospholipids was calculated similar to Equation 5 ([fluorescence of pellet]/[total fluorescence]).
Calculation of Membrane Occupancy-The membrane occupancy () is defined here as the ratio of the number of phospholipids in the bilayer "occupied" by bound protein molecules to the total phospholipids in the membrane.
The results of co-sedimentation experiments were fitted with a binding isotherm, where PL T is the total concentration of the phospholipids, and Pr T and Pr B are the total and bound DnaA concentrations, respectively, and K D is the apparent dissociation constant. At infinitesimal PL T , K D /Pr T approximates PL min , the minimal amount of phospholipids needed to bind one molecule of DnaA. According to the above definition, Equation 7 results.
After substitution of Pr B in Equation 7, the membrane occupancy may be calculated using Equation 8.
Measurement of Membrane Dynamics-Changes in membrane dynamics induced by the binding of DnaA were examined through alteration of the fluorescence emission spectra of laurdan and pyrene. SOPG liposomes (30 M) were labeled with 0.5 M pyrene or 0.3 M laurdan added from a stock solution in ethanol to Buffer AC with 1 mM ATP. The emission spectra of pyrene were recorded at an excitation wavelength of 337 nm with 3 nm slits at increasing concentrations of ATP-DnaA (0.01-1.5 M) (prepared as described above) at 30°C. The excimer-to-monomer ratio was calculated from the intensities of the emission peaks at 470 and 374 nm. Laurdan was excited at 354 nm, and the ratio of the emission intensities at 490 and 440 nm was calculated. All fluorescence intensity values were corrected for the background of unlabeled liposomes and protein.

Fluorescent Analog MANT-ATP Is Suitable to Assess Nucleotide-
DnaA Binding Kinetics-The binding of the fluorescent analog of ATP, MANT-ATP, to purified His 10 -DnaA was compared with that of ATP. MANT-ATP is an environmentally sensitive fluorophor, which exhibits increased fluorescence intensity upon binding to proteins (38). The addition of DnaA to MANT-ATP caused a gradual increase in fluorescence intensity, indicative of the hydrophobic environment of the nucleotide-binding site (Fig. 1). Upon the addition of an excessive amount of ATP, the fluorescence intensity was reduced to its initial level, apparently due to the competitive exchange of MANT-ATP for ATP at the binding site on DnaA (Fig. 1). The observed increase and decrease in fluorescence reflect the binding and dissociation kinetics of the fluorescent nucleotide and thus obey first-order kinetics (e.g. see Fig.  4). The corresponding fit allows estimation of the rate constant and the amplitude of changes.
To obtain both the dissociation constant and the binding stoichiometry, we first attempted to estimate the relative fluorescent intensity increase for one molecule of MANT-ATP bound to DnaA. A binding experiment fitted with a corresponding saturation function ( Fig. 2A) showed that the fluorescence intensity of MANT-ATP bound to DnaA increases 1.4-fold. Using this parameter and Equation 2 (see "Experimental Procedures"), the titration of DnaA with MANT-ATP (Fig. 2B) resulted in a K D value of 98 Ϯ 13 nM and a MANT-ATP-to-DnaA ratio of 0.13 Ϯ 0.01. The radioactive filterretention technique (Fig. 2C) enabled us to make a comparison with the native non-fluorescent ligand, which resulted in K D ϭ 20 Ϯ 4 nM and an ATP-to-DnaA ratio of 0.36 Ϯ 0.01 at 30°C, and 25 Ϯ 3 nM and 0.27 Ϯ 0.01, respectively, at 4°C. These latter results are very close to the data found in the literature (33).
Furthermore, a competition experiment was performed, in which MANT-ATP fluorescence intensity changes were measured with a constant amount of MANT-ATP and with varying concentrations of ATP (Fig. 2D). The exact competition analysis is hampered, because the DnaA concentration was close to that of ATP or MANT-ATP. It follows that 0.3 M ATP was needed to replace one half of bound MANT-ATP on DnaA (Fig. 2D), which is about three times less than the total concentration of MANT-ATP. Combining this result with the K D values obtained from fluorescent and radioactive experiments (a difference of ϳ5-fold), we arrived at an estimation that ATP binds to DnaA ϳ4-fold better than MANT-ATP. This implies that the same order of magnitude of affinity exists for both the native and fluorescent analog of ATP, rendering the latter suitable for the following studies. The advantage of using the fluorescent analog is that it enables a continuous follow up of binding kinetics.
Binding Characteristics of DnaA to the Phospholipid Membrane Determined by Co-precipitation of the Protein with Liposomes and by Changes in Membrane Dynamics-To make our results comparable and consistent with the previous data, we used the same type of phospholipids as employed in the thorough work from Crooke's laboratory (13). Binding of DnaA to liposomes composed of acidic phospholipid SOPG was measured by co-precipitation of the protein with the liposomes by centrifugation as described under "Experimental Procedures" (Fig. 3A). The technique is based on published methods (37,39) and relies on the fact that a liposome with a bound protein has a higher density and hence may be precipitated. Indeed, Fig. 3B shows that in addition to more than a half of liposomes that sediment in the absence of protein (as estimated by DPH-PC fluorescence, see "Experimental Procedures"), the relative amount of phospholipids found in the pellet fraction rises with increased protein concentrations, at a constant concentration of SOPG. Thus, after incubation of DnaA with different concentrations of phospholipids and subsequent centrifugation, the protein found in the pellet is considered as bound to liposomes. The fractions of DnaA in the pellet and the supernatant were quantified (see "Experimental Procedures," Equation 5), and the data were fitted with a binding isotherm (Fig. 3, A and C, and Equation 6) resulting in K D (SOPG) ϭ 43.4 Ϯ 15 M. No binding was observed with liposomes composed of zwitterionic SOPC (Fig. 3C).
A linear transformation of the data from Fig. 3C resulted in an estimated minimal SOPG amount required for binding one molecule of DnaA (Fig. 3C, inset). When the SOPG concentration is infinitesimal, the ratio of SOPG/DnaA approaches 120. In other words, a minimum of 120 SOPG molecules is required to bind a single molecule of DnaA. From this ratio the minimal membrane surface area needed to bind one molecule of the protein can be estimated based on the following assumptions: (i) only half of the phospholipids of the bilayer, which is the outer leaflet, are accessible to DnaA, and (ii) the area of one SOPG on the membrane surface is ϳ70 Å 2 (40). Thus, the minimal binding area is ϳ4200 Å 2 . From the crystallographic data of a truncated homologue from a thermophilic bacterium (41), the hypothetical area of DnaA projected on the membrane surface can be roughly calculated as 2500 Å 2 . Apparently, DnaA binding to the membrane requires a surface area ϳ2-fold higher than its packed solid-state structure. This could mean that the maximal density of DnaA on the membrane is limited merely by its dynamic volume.
DnaA binding induced changes at the polar surface of the membrane as well as in its hydrophobic core, which were evaluated by changes in the fluorescence spectra of laurdan and pyrene, respectively. Pyrene forms excited-state dimers (excimers) with emission at 470 nm. The ratio of excimer (470 nm) to monomer (374 nm) emission increases with increasing rates of diffusion (42). Because pyrene is highly hydro- phobic, it reports on changes in the hydrophobic membrane core. The relatively polar nature of laurdan enables one to obtain information about changes at the polar membrane surface. Owing to its dipolar relaxation, the emission spectrum of laurdan is sensitive to the polarity and the lamellar phase domains of the bilayer (28). The ratio of emission intensities at 490 nm and 440 nm was used as a measure of the changes in membrane dynamics. Both fluorophores showed a gradual increase in membrane "microviscosity" as SOPG-liposomes were titrated by DnaA (Fig. 3D), along with the binding of the protein to the membrane (Fig.  3C). The apparent K D (SOPG/DnaA) values calculated from the laurdan and pyrene data (51.5 Ϯ 2.3 and 47.3 Ϯ 2.7, respectively) are similar to those obtained from co-precipitation experiments (K D (SOPG/DnaA) ϭ 59.5 Ϯ 13.4). Accordingly, the gradual changes in microviscosity caused by DnaA binding may be used to characterize the affinity of the protein to the membrane as a relatively easy and fast method, with no need to separate free from bound DnaA. Figs.  1 and 2). The kinetics of MANT-ATP dissociation from the MANT-ATP⅐DnaA complex caused by acidic phospholipids (SOPG), excess unlabeled ATP, or in the presence of both, is shown in Fig. 4. Neutral phospholipids (SOPC), as expected, did not cause the release of MANT-ATP. From the first order exponential decay fit, the reaction rate constant in the presence of 1 mM SOPG with and without ATP is 6.9 Ϯ 0.4 and 7.3 Ϯ 0.4 s Ϫ1 ϫ 10 Ϫ3 , respectively. The measured rate constant reflects the rate-limiting step of the complex dissociation (k Ϫ3 , Scheme 1), because the rate of protein binding to the membrane is faster as is evident from the changes observed by the membrane fluorescent probes (data not shown). This rate constant is 3-fold higher than in the presence of ATP alone, k Ϫ1 ϭ 2.5 Ϯ 0.2 s Ϫ1 ϫ 10 Ϫ3 (k Ϫ3 Ͼ k Ϫ1 ). Notably, SOPG has a dominant effect on the dissociation reaction, such that the presence of ATP does not influence it (Fig. 4). This lack of acceleration of nucleotide exchange by ATP (even at physiological concentrations) on the membrane-bound complex may indicate that the rebinding of ATP to DnaA is slower on the membrane surface as compared with the aqueous phase (k ϩ3 Ͻ k ϩ1 , see Scheme 1). This could be ascribed to a very low affinity of the nucleotide to membrane-bound DnaA.

Membrane-induced Nucleotide Dissociation from MANT-ATP⅐DnaA Depends on the Protein Density on the Membrane, Exhibiting Cooperativity-MANT-ATP is well suited for measuring binding kinetics (
We examined the dependence of the dissociation of the MANT-ATP⅐DnaA complex on the ratio of SOPG/DnaA (Fig. 5, A and B). The dissociation rate constant rose sigmoidally from 2.0 Ϯ 0.1 to 5.9 Ϯ 1.2 s Ϫ1 ϫ 10 Ϫ3 with increasing phospholipid-to-protein ratios (Fig. 5A). Applying the Hill equation to this data revealed an average cooperativity coefficient of 3.0; among the various repeats even a coefficient of 7.0 was observed. This is strikingly different from the hyperbolic saturation curve observed with DnaA binding to the membrane (Fig. 3, C and D). Identical results were obtained even in the presence of physiological (1 mM) concentrations of ATP at all SOPG/DnaA values (data not shown). Moreover, there was no difference in the maximal fluorescence intensity changes at any SOPG concentration (Fig. 5B), indicating a complete release of MANT-ATP from the MANT-ATP⅐DnaA complex. This complete release, even at a low phospholipid-to-protein ratio at which only a small steady-state fraction of protein is membrane-bound (Fig.  3B), led us to suggest the existence of a fast continuous dynamic exchange of the protein on the surface of the membrane. The net result of the latter is that all DnaA molecules, in due time, may undergo a membrane-catalyzed nucleotide release/exchange process.
Temperature Dependences and a Crowding Agent Indicate Two Functional States of DnaA at High and Low Membrane Occupancy-The extent of surface density of bound DnaA, termed membrane occupancy (calculated as detailed under "Experimental Procedures"), at various phospholipid-to-protein ratios, is shown in Fig. 5A. The differences in the dissociation rates between high and low SOPG/protein ratios are apparently due to different levels of membrane occupancy. An open question is what could be the effect of protein-membrane occupancy on protein structure. In an attempt to address this question, we first examined the temperature dependence of the nucleotide dissociation rate constant at low and high membrane occupancy as well as in an aqueous, membrane-free phase. Corresponding Arrhenius plots are shown in Fig.  5C. The temperature range studied is well above the transition temperature for SOPG membrane (ϳϪ10°C), so that the observed linear dependences, devoid of any abrupt breaks, were expected. The activa-

AQUEOUS PHASE
Ficoll SCHEME 1. Proposed equilibrium states of the MANT-ATP⅐DnaA complex in aqueous phase and at different membrane occupancies (protein surface densities). Relative to the aqueous phase, at a high membrane occupancy, only the association rate constant is decreased with the unchanged dissociation constant (conformation MANT-ATP⅐DnaA I). At low occupancy, the association rate constant is decreased and the dissociation rate constant is increased (conformation MANT-ATP⅐DnaA II). The relations between the relevant rate constants are shown in the box. The crowding, imposed by added Ficoll, shifts DnaA from conformation II to I. See text for explanations.
tion energy and the pre-exponential factor for aqueous (with excess ATP) and for high occupancy states were found to be very similar (Table  1). In contrast, at low membrane occupancy, both the observed activation energy and the pre-exponential factor were significantly higher (Fig. 5C, closed circles, and Table 1). Owing to the high pre-exponential factor, despite the higher activation energy, at 30°C k Ϫ3 is 3-fold higher than that observed at high occupancy (k Ϫ2 ) or in the aqueous phase (k Ϫ1 ). This led us to suggest that MANT-ATP release at the high, 0.66 (at 50 M SOPG, Fig. 5A) and low, 0.09 (at 1000 M SOPG, Fig. 5A) membrane occupancies occurs at two distinct protein states. At high occupancy, the dissociation rate values on the membrane are similar to the membrane-free form of DnaA with excess ATP at all temperatures. This implies an unaffected dissociation rate constant (k Ϫ2 ϭ k Ϫ1 ) and a reduced association rate constant (k ϩ2 Ͻ k ϩ1 ) for the protein on the membrane. As a result, there is no re-association between the nucleo-tide and DnaA on the membrane surface (Fig. 5B). On the contrary, at low membrane occupancy, yet another DnaA state is suggested, characterized by a relatively higher MANT-ATP dissociation rate k Ϫ3 . At high membrane occupancy, the local macromolecular (DnaA) concentration on the membrane surface is extremely high (tightly packed). In other words, high protein density on the membrane surface may correspond to high local molecular crowding. Molecular crowding, specifically on the membrane surface, was proposed to account for stabilization of certain protein conformations or for protein clustering, often expressed as cooperativity in protein binding kinetics (43,44). To test whether this hypothesis holds in our case, we used a high molecular weight co-solvent, Ficoll 70, as a crowding agent, which has minimal effects on the dielectric and water activities of the solution (45). The k Ϫ values obtained at varied Ficoll concentrations are shown in Fig. 5D. At a high SOPG/protein ratio, k Ϫ decreases ϳ4-fold at Ͼ10% Ficoll, approaching the values obtained at low SOPG/protein ratios. The latter, nevertheless, changes only slightly (a decrease of ϳ25%) at the same range of Ficoll concentrations. Ficoll has no effect on membrane viscosity as determined by DPH anisotropy (data not shown). In the water phase, the rate of the ATP/MANT-ATP exchange declined 4-fold, presumably because of the expected effect of increased viscosity on this bi-molecular reaction (46).

DISCUSSION
This study proposes the existence of two functional states of membrane-bound DnaA with fast and slow membrane-induced nucleo-  tide dissociation. Most intriguing, the interconversion between these two states is highly cooperative with respect to membrane protein density. These novel phenomena are thought to play a major role in the mechanism regulating the initiation of chromosomal replication in bacteria.
The major results were obtained using a continuous follow up of nucleotide exchange on DnaA, based on changes in fluorescence intensity of MANT-ATP upon binding to DnaA. The reversible binding of this fluorescent nucleotide to DnaA is remarkably slow (Fig. 1). The kinetic characteristics obtained by MANT-ATP are comparable with those found for radioactive nucleotides (6). Accordingly, the application of MANT-ATP is pertinent despite its 4-fold lower affinity to DnaA as compared with its native analogue (Fig. 2).
When an excess of ATP is added to MANT-ATP⅐DnaA in solution, the apparent dissociation rate of the fluorescent nucleotide reflects the dissociation rate constant of the complex (Figs. 1 and 4, k Ϫ1 in Scheme 1). DnaA, as was previously shown (Ref. 13, and see Ref. 19, for a review), binds preferentially to acidic phospholipids (Fig. 3C) that induce MANT-ATP dissociation from the protein (Fig. 4). At low PL/Pr the dissociation rate constant is the same as the ATP-induced one in solution (k Ϫ2 ϭ k Ϫ1 , see Scheme 1); an excess of ATP cannot further accelerate it, and the two constants display identical temperature dependences (Fig. 5C). These observations suggest that the stability of the complex on the membrane is changed primarily due to a decreased association constant (k ϩ2 Ͻ k ϩ1 ). The putative protein conformation (MANT-ATP⅐DnaA I, Scheme 1) on the membrane under these conditions is such that the interaction with the bound ligand is not changed, but its binding is hindered. At high PL/Pr, the remarkably different temperature dependence with higher activation energy suggests yet another protein conformation (MANT-ATP⅐DnaA II, Scheme 1) characterized by a weaker interaction with the nucleotide (k Ϫ3 Ͼ k Ϫ1 ; k ϩ3 Ͻ k ϩ1 ).
Noteworthy, the dissociation equilibrium levels are similar, almost 100%, at each PL/Pr (Fig. 5B), resulting in essentially a complete dissociation of the nucleotide despite the fact that only a fraction of the DnaA is membrane-bound (Fig. 3C). This may be accounted for by a continuous exchange of free with membrane-bound DnaA, followed by membrane-catalyzed nucleotide dissociation. The relatively slow rate of nucleotide re-association, together with the rapid binding of the protein to the membrane, ensures the observed complete dissociation of the MANT-ATP⅐DnaA complex. This result is contrary to the previously reported concentration dependence of nucleotide dissociation on PL/Pr (see for example Refs. 11,18,and 47). The relatively higher nucleotide concentration used by these authors (1 M ATP versus 0.045 M MANT-ATP in the present study), together with the lower affinity of MANT-ATP, may account for the difference in the dissociation characteristics; at the higher ATP concentration its re-association rate with the free DnaA is apparently higher than the rate of DnaA exchange on the membrane.
Based on the co-sedimentation of DnaA with liposomes (Fig. 3), we determined the apparent dissociation constant, K D (SOPG) ϭ 43.4 Ϯ 15 M, essential for estimating the minimal membrane surface area required for binding a single DnaA molecule. This parameter was used to calculate the membrane occupancy, necessary to assess the degree of protein crowding, alluded to below. The obtained apparent K D values were confirmed by independent measurements based on the accompanying changes in the fluorescence characteristics of either pyrene or laurdan inserted into the membrane (Fig. 3D). These probes report on changes in membrane microviscosity, supposedly induced by DnaA binding.
A strong cooperative effect of the SOPG/protein ratio on the nucle-otide dissociation rate constant was observed for the first time (Fig. 5A). Interestingly, it cannot be accounted for either by the binding kinetics (Fig. 3C) or by the accompanying changes in membrane dynamics (Fig.  3D), both of which exhibit a monotonous dependence on PL/Pr with no cooperativity. Extrapolation to the physiological 37°C yields a sharp increase, ϳa 5-fold acceleration of nucleotide dissociation (Fig. 5C), upon a decrease in the membrane occupancy from 0.6 to 0.2. Such a change in membrane occupancy reflects an increase in the average minimal distance between two adjacent proteins from almost a real contact and close, two-dimensional-surface packing (30 Å), to a loose, independent free protein that lacks any contact with its neighbors, i.e. 90 Å away. These calculations are based on an assumed 50 Å average rotational diameter of the protein and a 4200 Å 2 minimal surface area occupied by the protein (see Fig. 3C, inset). At low occupancy the protein presumably attains an "open" conformation (MANT-ATP⅐DnaA II, Scheme 1), characterized by a faster dissociation of the bound nucleotide from the DnaA. Despite the elevated activation energy, the fast dissociation of ATP emerges from the high value of the pre-exponential factor in the Arrhenius equation (Table 1). Macromolecular crowding on a membrane surface presumably accounts for the unusual, highly cooperative, sharp transformation from a relatively slow to a rapid rate of nucleotide exchange on the membranebound DnaA. This is supported by the effect of Ficoll on the kinetic properties of DnaA bound to the membrane (Fig. 5D). The notion of a solution crowding effect of Ficoll, a water-soluble polysaccharide, in "pushing" protein molecules onto the surface of the membrane, based on the models proposed by Minton (44,48), is unlikely to occur in our case. Under conditions of high PL/Pr, where Ficoll is effective in reversing DnaA to slow kinetics (Fig. 5D), most of the protein is already membrane-bound (Fig. 3). The crowding effect may still be induced at the aqueous layer adjacent to the membrane surface where the DnaA molecules are situated. Thus, conditions attained at a high Ficoll concentration may mimic the high surface density of DnaA at a low PL/Pr. At least two outcomes of macromolecular crowding could be invoked (49): 1) stabilization of a compact protein conformation, rendering it less amenable to conformational relaxation upon binding to the membrane, and 2) enhancement of protein clusterization (oligomerization) on the surface of the membrane, when such a tendency for intermolecular attraction naturally exists. This is presumably the case with DnaA, a member of the superfamily class of ATPases associated with a variety of cellular activities (AAAϩ) known to assemble into hexamers (50). Oligomers of DnaA were suggested from its structural studies (41) and were experimentally demonstrated recently (51). The existence of a hexameric form may also explain the low nucleotide binding stoichiometry of DnaA reported before and found in the present study, because the putative hexamer may contain two or three unliganded (nucleotide-free) units (50). Both a conformational relaxation and/or oligomerization state could be a prerequisite to a membrane-accelerated nucleotide exchange. Additional experiments are needed to differentiate between these alternatives.
A comparison between the amount of DnaA molecules (1200 (52)) and that of acidic phospholipids (ϳ3 ϫ 10 6 (53)) per E. coli cell, could suggest that there is a considerable excess of acidic phospholipids, thus ensuring rapid activation of DnaA (well above the saturation in Fig. 5A). However, the actual intracellular concentrations of both the protein and phospholipids accessible for interaction are unknown. For example, although it was shown that most DnaA is adjacent to the membrane surface (54), there are numerous competing sites for its binding on the chromosome (55). On the other hand, numerous membrane integral and peripheral proteins show specific preferences to acidic phospholipids (e.g. Ref. 56, and see Ref. 57, for a review) so that the availability of potential binding sites for acidic phospholipid-seeking proteins on the membrane could be limited (58). Moreover, phospholipid clustering i.e. domain organization rather than a total concentration of acidic phospholipids in the membrane is essential for DnaA activation (26). Therefore, the PL/Pr range (200 -500) for the activation of the nucleotide exchange on DnaA reported here (Fig. 5A) could be of physiological relevance.
In the present work we studied the kinetics of the nucleotide dissociation stage in the DnaA reactivation process and its dependence on the DnaA density on the membrane. How the membrane-bound nucleotide-free DnaA is converted to the ATP form in solution remains to be determined. In their work, Crooke et al. (59) show that oriC DNA facilitates the high affinity binding of ATP to DnaA during treatment with phospholipids. In our future studies we will address this problem using the three-component model system, membrane-DnaA-oriC.
In conclusion, the present work shows that the kinetics of the nucleotide exchange on DnaA depends primarily on the specific character of the phospholipid constituents, on the one hand, and on the macromolecular arrangement of the protein on the surface of the membrane, on the other hand. The results reveal that macromolecular crowding on the membrane surface accounts for the unusual, highly cooperative, sharp transformation from a relatively slow to a rapid rate of nucleotide exchange on membrane-bound DnaA. This is relevant to the major question that we addressed, namely, what is the spatial-temporal control of the bacterial cell cycle, i.e. what controls the precise timing of the initiation of DNA replication? We propose that the specific membrane domain, unique in its acidic phospholipid composition, serves as a catalyst in activating DnaA at the right time, which is when the size of the continuously growing bacterial membrane domain (during the cell cycle) reaches a critical protein (DnaA)-to-phospholipid (PG or cardiolipin) ratio, switching on (due to cooperativity) the rejuvenation of DnaA, which in turn initiates replication. In a cell, macromolecular crowding of DnaA on the membrane surface may involve specific interactions with other proteins, e.g. the directly binding DiaA with yet unclear function (60), or membrane-located Hda (61) that was recently proved as predominant in inactivation of DnaA (62).