ATP-Induced Conformational Changes of Nucleotide-Binding

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ATP-Induced Conformational Changes of Nucleotide-Binding Domains in an ABC Transporter. Importance of the Water-Mediated Entropic Force Tomohiko Hayashi, Shuntaro Chiba, Yusuke Kaneta, Tadaomi Furuta, and Minoru Sakurai J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 10 Oct 2014 Downloaded from http://pubs.acs.org on October 11, 2014

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The Journal of Physical Chemistry

ATP-Induced Conformational Changes of Nucleotide-Binding Domains in an ABC Transporter. Importance of the WaterMediated Entropic Force Tomohiko Hayashi, † Shuntaro Chiba, † Yusuke Kaneta, † Tadaomi Furuta, † and Minoru Sakurai*† †Center for Biological Resources and Informatics, Tokyo Institute of Technology, 4259-B-62, Nagatsuta-cho, Midori-ku, Yokohama, 226-8501, Japan

ABSTRACT. ATP binding cassette (ABC) proteins belong to a superfamily of active transporters. Recent experimental and computational studies have shown that binding of ATP to the nucleotide binding domains (NBDs) of ABC proteins drives the dimerization of NBDs, which, in turn, causes large conformational changes within the transmembrane domains (TMDs). To elucidate the active substrate transport mechanism of ABC proteins, it is first necessary to understand how the NBD dimerization is driven by ATP binding. In this study, we selected MalKs (NBDs of a maltose transporter) as a representative NBD and calculated the free-energy change upon dimerization using molecular mechanics calculations combined with a statistical thermodynamic theory of liquids, as well as a method to calculate the translational, rotational and vibrational entropy change. This combined method is applied to a large number of snapshot structures obtained from molecular dynamics simulations containing explicit water molecules. 1 ACS Paragon Plus Environment


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The results suggest that the NBD dimerization proceeds with a large gain of water entropy when ATP molecules bind to the NBDs. The energetic gain arising from direct NBD-NBD interactions is canceled by the dehydration penalty and the configurational-entropy loss. ATP hydrolysis induces a loss of the shape complementarity between the NBDs, which leads to the dissociation of the dimer, due to a decrease in the water-entropy gain and an increase in the configurationalentropy loss. This interpretation of the NBD dimerization mechanism in concert with ATP, especially focused on the water-mediated entropy force, is potentially applicable to a wide variety of the ABC transporters. KEYWORDS. ABC transporter, ATP, 3D-RISM, water entropy, dehydration penalty, configurational entropy

INTRODUCTION Active transport in cells is performed by a class of integral membrane proteins, known as ATPbinding cassette (ABC) transporters. ABC transporters belong to one of the largest transporter families1 and use ATP to drive the transport of a wide range of substrates across the membranes in both prokaryotic and eukaryotic cells. These structures all have two nucleotide-binding domains (NBDs) and two transmembrane domains (TMDs). The NBDs provide the free energy necessary for transport by binding and hydrolyzing two molecules of ATP, and the TMDs form a pathway for substrate transport. Recently, several high-resolution structures of ABC transporters have been determined by Xray crystallography.2-5 Among these transporters, two ABC transporters, MalFGK2 (maltose

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transporter from Escherichia coli) and MsbA (bacterial ABC lipid flippase), have been captured in multiple states.6-8 MalFGK2 and MsbA adopt inward-facing conformations when the ATP binding pockets (ABPs) of the NBDs are unoccupied and when the two NBDs are apart from each other and the TMDs are opened toward the intracellular side. These transporters adopt outward-facing conformations when the ABPs are occupied by ATP molecules and when the NBDs are dimerized and the TMDs are opened toward the extracellular side. These conformations are consistent with an alternating access model.9 It is usually assumed that, 1) energy is required to reorient the TMDs from the inward- to an outward-facing conformation, and 2) the energy is provided by ATP hydrolysis in the NBDs. By analogy with internal combustion engines, these assumptions are often termed the ‘‘power-stroke’’ of transport.10 Because NBDs from different ABC transporters share a high degree of sequence and structural homology,11 it is generally assumed that there is a universal mechanism, at least for the NBD dimerization/dissociation. However, the details remain unclear. One hypothesis is that the binding of ATP drives the power stroke.3,12-15 Wen et al. have performed a set of molecular dynamics (MD) simulations for MalKs,16 the NBDs of MalFGK2 (Figure 1). The MD simulations started with the closed form of the MalK dimer (dimerized state of the NBDs, see Fig. 1 (b)) with possible combinations of ATP or ADP-Pi bound to the two ABPs, and the simulations suggested that the closed form of the MalK dimer can only be maintained with two bound ATP molecules.16 Newstead et al. performed MD simulations for the crystal structure of FbpCs, the NBDs of the iron transporter FbpABC from N. gonorrhoeae, and for its homologous protein MalKs, and found that NBDs in both systems open once ATP is removed.17 This observation implies that the closed structures of FbpC and MalK with bound ATP have higher free energies than their respective open states. Conversely, the closing of the 3 ACS Paragon Plus Environment


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two NBDs is driven by the free energy obtained from ATP binding. Recently, to confirm this hypothesis, we performed MD simulations for the inward-facing conformations of the full-length wild-type ABC transporters mouse P-glycoprotein (P-gp)18 and cystic fibrosis transmembrane conductance regulator (CFTR).19 Consequently, it was found in both systems that the NBDs are immediately dimerized by the binding of ATP. This finding strongly supports the above hypothesis that the binding of ATP drives the power stroke. However, the following questions still remain: 1) why does binding of ATP to the NBDs induce their dimerization, and 2) why does hydrolysis of ATP cause the dissociation of the NBD dimer. This can be rephrased “Why does the driving force responsible for the NBD dimerization become smaller after ATP hydrolysis”. These questions might arise because the driving force responsible for the dimerization of NBDs remains ill-defined. Clarification of the driving force for the NBD dimerization is the essential next step for understanding how the binding and hydrolysis of ATP cause a large movement of the NBDs. Here, we perform free-energy calculations for the dimerization and dissociation of MalKs to answer the above questions. Molecular mechanics (MM) calculations, combined with a statistical thermodynamic theory of liquids, referred to as the three-dimensional reference interaction site model (3D-RISM) theory,20-23 i.e., MM/3D-RISM approach, are employed in the free-energy calculations. The 3D-RISM theory is an integral equation theory based on statistical mechanics, which enables us to obtain the 3D distribution function of water molecules around a prescribed structure of a given molecule. We do not regard water as a dielectric continuum,24 but take the molecular picture of liquid water into account for the free-energy calculations. The 3D-RISM theory has successfully been applied to important problems in biological systems, such as the


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hydration properties of peptides and proteins,22,25 receptor-ligand binding processes,26,27 and the association of protein molecules.28,29 For the sampling of the large configurational space of MalKs in aqueous solution, we perform several short independent MD simulations with explicit water molecules, as proposed by Genheden and Ryde.30 We further calculate the translational and rotational entropy changes upon dimerization by applying the methods proposed by Swanson et al. to the MD simulation trajectories.31 The vibrational entropy change is also calculated by performing normal mode analysis. The free-energy change upon dimerization of MalKs is thus calculated in a quantitatively reliable manner, and the results are compatible with the corresponding experimental data. Our important findings are as follows: the dimerization of ATP-bound MalKs is driven by a large gain of water entropy. The energetic gain arising from the MalK-MalK attractive interactions is compensated by the large loss of the MalK-water interactions, plus the loss of the configurational entropy upon dimerization. The driving force for the dimerization of ADP-bound MalKs, which is a possible model of the MalKs after hydrolysis of ATP, becomes weaker than that of ATP-bound MalKs. This is because the water-entropy gain upon dimerization decreases simultaneously with an increase in the configurational-entropy loss, leading to the MalK dissociation. Our approach paves a new way for the elucidation of a substrate-transportation mechanism for all types of ABC transporters accompanied by a large movement of their subunits in concert with ATP. MODEL AND THEORY



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Free-energy function. For a solute molecule immersed in pure water, we define the Gibbs freeenergy function G as = − + ,

(1)

where EC and SC are the conformational energy and the configurational entropy of a solute molecule, respectively, T is the absolute temperature, and µH is the hydration free energy defined as the excess chemical potential of the solute. We note that µH is independent of solute insertion conditions: isochoric (constant volume) or isobaric (constant pressure) conditions. We consider here isobaric conditions that are much more comparable to standard experimental conditions. Hereafter, the subscript “H” denotes the hydration under isobaric conditions. We define µH as = − ,

(2)

where HH and SH are the hydration enthalpy and entropy, respectively. We applied the 3D-RISM theory,20-23 which is a statistical-mechanical theory for molecular liquids and hydration of solutes, to calculate the hydration free energy (µH) and its two components (HH, −TSH). EC is calculated on the basis of an MM potential and is thus able to be decomposed into components as follows: = + + ,

(3)

where Ebond is the bonded energy comprising the bond-stretching, bond-bending, and torsional terms, EvdW is the van der Waals energy, and Ees is the electrostatic energy. We employ the Amber99SB force field32 for the calculation of EC (the van der Waals energy is represented by


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the Lennard Jones (LJ) potential), where the force field parameters developed by Carlson et al.33 were used for ATP and ADP. By substituting Eqs. 2 and 3 into Eq. 1, the final form of the present Gibbs free-energy function is expressed as follows: = − − ,

(4a)

= ( + + ) + ,

(4b)

where Htotal is the total enthalpy of a given system. The Gibbs free-energy function can thus be decomposed into enthalpic and entropic parts. Free-energy change upon dimerization of MalKs. The free-energy function and its components defined above were applied to a MalK dimer and two MalK monomers. Figure 2 shows the schematic representation of the path considered for calculation of the free-energy change upon the dimerization of MalKs.Two MalK monomers in the complex were simply separated without undergoing any structural changes (i.e., ∆Ebond = 0), and the resulting structures were employed as with the two MalK monomers in the isolated state. (This is called “the single-trajectory approach” for the binding free-energy calculation34). Hereafter, the two MalK monomers are denoted by MalKa and MalKb, respectively, and the MalK homodimer is denoted by MalKa:MalKb. The binding free energy, ∆G, is expressed as follows: ∆ = (MalK : MalK ) − !(MalK ) + (MalK )} = ∆ − ∆ − ∆

(5)

= ∆( + + ) − ∆ − ∆ , 7 ACS Paragon Plus Environment


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G(MalKa:MalKb), for example, is the free-energy function applied to the MalK homodimer. ∆EvdW and ∆Ees originate from the van der Waals and electrostatic interactions between MalKa and MalKb, respectively. ∆HH is the hydration-enthalpy change upon dimerization of the MalKs. ∆SC and ∆SH represent the configurational-entropy change and the water-entropy change upon MalKa-MalKb dimerization, respectively. Eq. 5 thus corresponds to the free-energy change upon dimerization of the MalKs Path I in Figure 2 is a model pathway for the MalK dimerization before ATP hydrolysis. In Path I, the ABP in each MalK monomer is occupied by one ATP molecule and one magnesium ion (Mg2+). ∆GI thus represents the free-energy gain upon dimerization of MalKs induced by binding of two ATP molecules (∆GI < 0). Path II in Figure 2 is a model pathway for the dissociation of the MalK dimer after ATP hydrolysis. ∆GII thus represents the free-energy loss upon the dimerization of the MalK dimer (∆GII > 0). Unlike Path I, in Path II the nature of the ATP hydrolysates that occupy the ABPs when the MalK dimer dissociates is still controversial. Direct experimental evidence that answers this question has not been obtained. In the present study, we employ the Path II (dissociation) model, in which the ABP on each of the MalK monomers is occupied with one ADP molecule and one Mg2+. This finding is observed because, unlike other possible models, the experimental data for MalK dimerization corresponding to Path II are available for the ADP-bound state. Lu et al. have shown that when MalK becomes solvated with water, and together with ADP and MgCl2 were injected onto a size-exclusion column, the MalK eluted as a monomer.35 Therefore, ADP-bound MalKs are not dimerized, which implies that the calculated ∆GII for the ADP-bound MalKs must have a positive value (∆GII > 0). By comparing ∆GII with ∆GI, we would obtain an insight into the reason why the driving force responsible for the MalK dimerization becomes smaller after ATP hydrolysis. 8 ACS Paragon Plus Environment

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The validity of our theoretical methods is evaluated further in the following manner. The dissociation constant KD for the MalK dimer is calculated by considering a reaction as KD

MalK:MalK ⇔ MalK+ MalK. KD is then defined by

$% =

[MalK]( , [MalK: MalK])°

(6)

where [MalK:MalK], [MalK], and C° are the mole concentrations of the MalK dimer, the MalK monomer, and the standard concentration, i.e., 1 M in the present study, respectively. We estimated the dissociation constant KD for the dimerization of ATP-bound MalKs based on the experimental data of Lu et al.35 When a 1 µM solution of MalK was solvated with 0.5 mM ATP and water and injected onto a size-exclusion column, the elution peak contained the dimerized MalK at a concentration of ≈ 0.1 µM. Using this approximate concentration rate, we can obtain the KD (6.4 µM) and hence estimate an approximate experimental value of the binding free energy corresponding to ∆GI as RTln(KD), hereafter denoted as ∆GExp (R is the gas constant and T = 295.15 K). The value obtained for ∆GExp was –7.01 kcal/mol, which can be compared with the theoretical ∆GI in Path I (∆GI < 0). Calculation of hydration enthalpy HH and entropy SH using the 3D-RISM theory. The hydration enthalpy HH and the contribution of hydration entropy –TSH in Eq. 2 were calculated by applying the 3D-RISM theory20-23 to MalK monomers and their dimer structures. The 3DRISM theory is an integral equation theory based on statistical mechanics, which enables us to obtain the 3D distribution functions, gγ(r) of site γ, for oxygen and hydrogen of water molecules around a prescribed structure of a given molecule.21 Thermodynamic properties, such as the 9 ACS Paragon Plus Environment


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hydration free energy µH, the hydration entropy SH, and the hydration enthalpy HH, can be calculated from gγ(r). A description of the 3D-RISM theory and its calculations are provided in Sec. A in the Supporting Information. The 3D-RISM theory coupled with the Kovalenko-Hirata (KH) closure equation21 was applied to the snapshot structures of the MalKa:MalKb dimer and those of the two MalK monomers extracted from the dimer trajectory. The dimer structures were generated by several independent MD simulations described in “Structural sampling” below. The transferable intermolecular potential three point (TIP3P) model36 was employed for water molecules with corrections in terms of the LJ potential parameters for the hydrogen sites (σ = 1.2363 Å, ε = 0.0152 kcal/mol). All calculations were carried out using the AMBER 12 molecular simulation package37 with the Amber99SB force field32. Calculation of configurational entropy SC. The configurational entropy, SC, of the solute molecules (MalK monomers and their dimer) was calculated in the following manner. First, we would assume that A solute molecule can exist in N conformational states, each of which can be treated as a disjoint multidimensional harmonic well on the free-energy landscape. The configurational entropy, SC, is thus defined as /

/

-

-

= − + ,- ln ,- + + ,- ,- ,

(7)

where pj represents the probability that a structure of a solute molecule belongs to a well j. SC,j corresponds to the configurational entropy of the molecule in a local well j, including translational, rotational, and vibrational entropies. The conformational part of the configurational entropy (the first term on the right-hand side of Eq. 7) was not considered here for the following reasons: i) the conformational-entropy 10 ACS Paragon Plus Environment

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calculation is an extravagant and formidable task, and ii) usually the conformational entropy decreases upon dimerization and thereby it should contribute to an increase of the free-energy, in other words, not a driving force for dimerization. However, MalK-MalK binding also gives rise to a loss of the configurational entropy arising from the loss of translational and rotational freedom. The contributions from the translational and rotational entropy losses are considerably large regardless of the solute conformational change. Fortunately, we can calculate the translational and rotational entropy changes upon dimerization, ∆SCtrans,

rot

, by applying the

elegant and affordable method proposed by Swanson et al. to a large number of snapshot structures generated by MD simulations.31,38 The method uses a standard binding free-energy calculation, where the total volume available to the translational and rotational displacement of one MalK relative to the other is explicitly taken into account. The volume, which was estimated using principal component analysis applied to a merged MD trajectory (25 runs), described in “Structural sampling” below, was used to calculate losses of ∆SCtrans, rot in a standard state, i.e., 1 M in this study, which enables us to compare directly the calculated and experimental values. The calculations were carried out using our in-house program. Because the volume is estimated using the merged MD trajectory as mentioned above, the calculated ∆SCtrans, rot does not have a standard error value. Moreover, a change of the vibrational part of configurational entropy upon MalK-MalK binding would also arise, and it is known as a key factor that governs the binding affinity.39 Thus, the vibrational entropy change, ∆SCvib, was also calculated by performing the normal mode analysis, which was applied to a large number of snapshot structures of the MalKa:MalKb dimer (SCvib (MalKa:MalKb)) and structures of the two MalK monomers (SCvib (MalKa), SCvib (MalKb)) extracted from the dimer trajectory (the dimer structures were generated by several independent MD simulations described in “Structural sampling” below). The reported



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final value was obtained by averaging those values of ∆SCvib (= SCvib (MalKa:MalKb) − SCvib (MalKa) − SCvib (MalKb)). The normal mode analysis was conducted using the NAB module of the AMBER 12 package.37 Initial structure modeling. The initial structures of NBDs were modeled from ATP analog (adenosine-5’-(β,γ-imido) triphosphate; AMP-PNP)-bound MalK dimer40 in the following manner. First, AMP-PNP-bound MalK dimer was taken from the structure of the full-length MalFGK2 (the structure also contains a maltose-binding protein (MalE)) (Protein Data Bank (PDB) code: 3RLF). We here emphasize again that the dimerization of NBDs is focused in this study, because NBDs from different ABC transporters share a high degree of sequence and structural homology, suggesting that they share a universal mechanism (or driving force). We thus removed the TMDs and the MalE, and the unique C-terminal domain of each MalK (residues 236-372) and capped the resulting C-terminus with an N-methyl amide group. In the above structure 3RLF, the ABPs of both the MalK monomers are occupied with one AMP-PNP and one Mg2+ ion. The two AMP-PNPs were modified to ATPs by replacing the nitrogen atom located between the β phosphate and the γ phosphate groups with an oxygen atom, while the Mg2+ ions were maintained in their initial positions. The missing residue, Met1, was also added to the N-terminal end. Next, based on the finally obtained structure of the ATP-bound MalK dimer, the ADP-bound MalK dimer was modeled in the following manner. The structure of ADP (and Pi and sodium ion (Na+))-bound MJ0796 dimer (PDB code: 3TIF), which has good similarity with the MalK dimer in both sequence and structure, has been reported.41 Because the conformation of ADP is perturbed along with the bound protein (i.e., the conformation of the “ADP moiety” of ATP bound to MalK is different from that of ADP bound to MalK), we thus superimposed ADPs from MJ0796 onto the modeled ATP-bound MalK dimer in the following 12 ACS Paragon Plus Environment

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manner. First, the amino acid sequence of MalK was aligned with that of MJ0796, and then the 3D-structure alignment was performed. Then, ATPs and Mg2+ ions of MalK were replaced with ADPs and Na+ ions from MJ0796 at the aligned position, and then Na+ ions were changed to Mg2+ ions (with no further structural modification in this process). The sequence and structure alignments were performed using the Discovery Studio 3.1 program package.42,43 The protonation states of all the charged residues were determined by calculations of pKa using the algorithms implemented on the PDB2PQR web server.44 In the case of His192, the protonation state would be significantly affected by the charged state of the nearby nucleotide ATP or ADP, that have −4 and −3 charges, respectively. Furthermore, we assumed that both δ and ε nitrogen atoms of the imidazole ring in His192 are protonated (i.e., net charge of His192 is +1) in the ATP-bound MalKs. On the other hand, only the δ nitrogen in His192 was assumed to be protonated (i.e., the net charge of His192 is 0) in the ADP-bound MalKs. Structure sampling. MD simulations using the Amber99SB force field32 were employed for the structure sampling of the MalK dimer. Genheden et al. reported that for the binding freeenergy calculations, the structure sampling of the ligand-receptor complex from several short independent simulations provides a “well-converged result (i.e., a mean value of the calculated binding free energies for the sampled structures with a small standard error)” compared with that from a single long simulation.30 They also suggested that before executing a set of sampling simulations, it is important to perform a single pre-sampling simulation, which is long enough to attain equilibration in the system. We employed their approach for the structure sampling of both the ATP-bound and ADP-bound MalK dimers in this study. Next, we explain the procedure for a pre-sampling equilibrium MD simulation. The MalK dimer modeled above was solvated in the TIP3P model36 with water molecules using a 13 ACS Paragon Plus Environment


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rectangular solvent box whose edges were 10 Å from the closest protein atoms. Chloride ions (Cl–) were also added to neutralize the net charge of the system. The total number of water molecules was 22708 in the system with the ATP-bound MalK and 20918 in the system with the ADP-bound MalK, respectively. Each system was first refined with 500 steps of steepest-descent energy minimization, followed by 1500 steps of conjugated-gradient energy minimization. Then, we performed a 100-ps MD simulation, in which the system temperature T was increased from 0 to 300 K at a constant-volume condition. In the minimization and heating simulations, 2 kcal/(mol Å2) of the positional restraints using a harmonic potential were added to all the heavy atoms in the MalKs, ATPs or ADPs, Mg2+ ions, and co-crystalized water molecules. We then switched the condition to a constant temperature and pressure condition (T = 300 K, P = 1 bar) and performed a 200-ps MD simulation. For the first 100 ps in this simulation, the same positional restraints, except for the co-crystalized water molecules, were used to equilibrate the solvent-water density, followed by a 100 ps- MD simulation with the same restraints added to only the heavy atoms of the backbone to relax the side-chain atoms in the MalKs, ATPs or ADPs and Mg2+ ions. Then, a 15-ns pre-sampling MD simulation was performed without any restraints Finally, starting from the final snapshot of a single pre-sampling simulation, we performed 25 short independent MD simulations, each with 1.2 ns duration, for the structure sampling. The MD starting velocities for all of the 25 simulations were different from each other. For the calculation of free-energy change, we picked the set of structures, each of which consists of the MalKs, ATPs or ADPs, and Mg2+ ions, from every 10 ps after 600 ps of each short simulation. We thus obtained 60 structures per simulation, and calculated the free-energy change and its components as defined in Eq. 5 for the structures obtained. We performed the prerequisite energy minimization before the normal mode analysis by applying the conjugate gradient method 14 ACS Paragon Plus Environment

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followed by the Newton-Raphson method with a final convergence criterion of 1 × 10–8 kcal/(mol Å) of the root-mean-square gradient. Some energetic terms of dimer or monomer structures did not reach the criterion adopted. We thus excluded such structures and continued the free-energy calculations until we obtained 40 structures per one simulation (except for one sampling simulation for ADP-bound MalK, where only 39 structures were converged). The final total numbers for the MalK structures for the free-energy calculations were 1000 for the ATPbound MalK and 999 for the ADP-bound MalK. The pre-sampling and sampling simulations were performed using Langevin thermostat45 (the collision frequency γ was set to 2 ps–1) and Berendsen barostat.46 The SHAKE algorithm47 was employed to constrain all the bonds connected with hydrogen atoms. The simulation time step was set to 2 fs under the periodic boundary condition. The particle-mesh Ewald method48,49 was employed for calculating the electrostatic interactions, and the cut-off distance for the interactions between non-bonded atoms was set to 8.0 Å. All of the simulations were carried out using the AMBER 12 molecular simulation package.37 RESULTS AND DISCUSSION Driving force for MalK dimerization: importance of water entropy gain. Table 1 summarizes the calculated free-energy change (∆G) upon dimerization of the MalKs and its decomposition into the total enthalpy change (∆Htotal = ∆(EvdW + Ees + HH)), the configurational-entropy change (–T∆SC), and water-entropy change (–T∆SH) components. First, we discuss the dimerization of the ATP-bound MalKs in terms of the changes in the thermodynamic quantities (∆GI and its components). Discussions of the dimerization of ADP-bound MalK will be provided in later sections. The calculated ∆GI for the ATP-bound MalKs is −4.11 ± 0.41 kcal/mol. The 15 ACS Paragon Plus Environment


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contribution from the water-entropy change is a large negative value (−53.71 ± 0.06 kcal/mol). The MalK-MalK dimerization is accompanied by a large increase in the water entropy. On the other hand, the total enthalpy change is positive (+16.55 ± 0.13 kcal/mol). The configurationalentropy change upon dimerization is also positive (+33.06 ± 0.32 kcal/mol), which implies that the dimerization is accompanied by a decrease in the configurational entropy. Next, we compare the calculated ∆GI with the experimentally determined value, ∆GExp. ∆GExp can be obtained from RTln(KD), where KD is the dissociation constant for MalK-MalK dimerization in aqueous solution in the ATP-bound state. The value obtained for ∆GExp was – 7.01 kcal/mol (see Sec. A in the Supporting Information).35 In a strict sense, the theoretical ∆GI cannot be in complete agreement with ∆GExp. This is because the standard state is at infinite dilution in the 3D-RISM calculation, while for ∆GExp the standard state is 1 M, and the activity coefficient is set at unity.50 In addition, the removal of the unique C-terminal domain of each MalK might be responsible for the deviation between the experimental and calculated values. Given these factors, it should be noted that the calculated value is in fairly good agreement (an error of only +2.90 kcal/mol) with the experimental value. In summary, upon dimerization of the ATP-bound MalKs, the decrease in free energy due to the water-entropy gain (∆SH > 0, −T∆SH < 0) surpasses the free-energy increase due to the totalenthalpy loss (∆HH > 0) and the configurational-entropy loss (∆SC < 0, −T∆SC > 0). Since we employed the “single trajectory approach (see MODEL AND THEORY)”, the conformational part of the configurational entropy (the first term on the right-hand side of Eq. 7) was not considered in this study. However, this would not exert an unfavorable influence on our final conclusion because the conformation entropy should decrease upon dimerization and cause an increase of the dimerization free-energy. Thus, the conformation entropy cannot be a driving 16 ACS Paragon Plus Environment

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force of dimerization. Taken together, it can safely be concluded that water-entropy gain is a main driving force for the dimerization of the ATP-bound MalK. Physical origin of the water-entropy gain upon MalK dimerization. Dimerization of the two MalKs gives rise to a large gain in water entropy. Its physicochemical origin can be interpreted from a statistical thermodynamic viewpoint of hydration. As shown in Figure 3, each MalK molecule generates an excluded space where water molecules cannot enter. The volume of the excluded space is referred to as the excluded volume (EV). Upon MalK-MalK dimerization, the two excluded spaces overlap and the total EV decreases by the overlapped volume, which implies a corresponding increase in the total volume available for the translational displacement of water molecules in the system. Hence, the dimerization leads to a large increase in the configurational degrees of freedom for the water molecules (i.e., a large gain of the water entropy). It has been shown that such a water-entropy gain, which can be referred to as an “entropic EV effect”, plays a significant role in a variety of biological self-assembly processes.5155

Thus, water entropy governs the MalK-MalK association through the entropic EV effect. Conventionally, the origin of the water-entropy gain upon protein-protein binding has been

interpreted in the area of protein science as follows. The water adjacent to a nonpolar group is entropically unstable (mainly it is unstable in terms of the rotational entropy), and protein binding is driven by the release of such unfavorable water to the bulk through the burial of nonpolar groups.56 In this view, only the water molecules adjacent to nonpolar groups are considered. On the other hand, in the revised view based on the EV effect (Figure 3), the water molecules in the system, even far from the protein, can also make a significant contribution to the water-entropy gain upon binding.57



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Decomposition of the total enthalpy change: dehydration surpasses MalK-MalK interactions. The calculated total enthalpy change upon dimerization of the ATP-bound MalKs has a positive value (+16.55 ± 0.13 kcal/mol) and opposes the dimerization. To examine the physicochemical origin of such an enthalpy loss, the total enthalpy change is decomposed into ∆EvdW, ∆Ees, and ∆HH, as shown in Table 2. In Path I, both ∆EvdW and ∆Ees have large negative values (−126.31 ± 0.11, −235.27 ± 0.41 kcal/mol, respectively), whereas ∆HH has a large positive value (+378.14 ± 1.36 kcal/mol). Hence, ∆EvdW + ∆Ees and ∆HH compensate each other. In other words, the dimerization is accompanied by an energetic gain arising from van der Waals and electrostatic interactions between the MalK monomers, but this gain is cancelled out by the loss in hydration enthalpy. The latter is slightly larger than the former, and the total enthalpy change ∆(EvdW + Ees + HH) has a positive value. The physicochemical origin of the hydration-enthalpy loss induced by dimerization of the MalKs can be interpreted as follows. Before binding, each surface of the two MalK monomers is hydrated. When a solute region is hydrated, unless the region is predominantly nonpolar, the water structure near the region is significantly perturbed, due to solute-water electrostatic and van der Waals attractive interactions. Upon dimerization, the regions that become unexposed to water undergo dehydrations (i.e., a loss of MalK-water attractive interactions). The loss of MalKwater attractive interactions upon dehydration gives rise to a large decrease of the hydration enthalpy, in other words, a dehydration penalty. In reality, the energy decrease due to the loss of MalK-water attractive interactions is much larger, but about half of it is cancelled out by the water reorganization energy (i.e., the energy decrease accompanied by the structural reorganization of water upon dimerization).58,59 Thus, the net loss of hydration enthalpy is


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comparable to the energetic advantage due to the gain of the attractive interactions between the MalKs. Decomposition of configurational-entropy change: loss of mobility and flexibility. The configurational-entropy change upon dimerization of the MalKs has a positive value (+33.06 ± 0.32 kcal/mol). Table 3 lists the contributions from the configurational-entropy change and its two components, that is, the translational plus rotational entropy (denoted by −T∆SCtrans, rot) and the vibrational-entropy change (denoted by −T∆SCvib). Upon dimerization of the ATP-bound MalKs, both −T∆SCtrans, rot and −T∆SCvib have positive values, which are +14.84 and +18.22 ± 0.32 kcal/mol, respectively. Thus, the increase in the free energy upon dimerization partially originates from the loss of the translational, rotational, and vibrational entropy of the solute molecules. The loss of the translational and rotational entropy is inevitable for dimerization of the two solutes. This is because the dimerization of two solutes essentially accompanies one solute’s loss of mobility, that is, the translational and rotational degrees of freedom from the standard state.31 On the other hand, the vibrational-entropy loss upon dimerization of the two solutes does not necessarily occur (Some theoretical examples have been reported that, due to the coupling of protein-ligand motion, SCvib increase upon binding).60-62 In the case of the MalK-MalK dimerization, the process accompanies the net loss of the vibrational entropy. This might be because dimerization leads to a loss of the side-chain flexibility between the interface regions of each MalK. A possible mechanism of MalK dissociation after ATP hydrolysis. In this section, we discuss which factors are crucial for the dissociation of MalKs after ATP hydrolysis. In the present study, 19 ACS Paragon Plus Environment


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we consider the dissociation of the ADP-bound MalKs as illustrated in Path II of Figure 2. Based on the calculated results, we propose a possible explanation why the driving force responsible for the dimerization becomes weaker after hydrolysis of ATPs in the MalK dimer. The calculated ∆GII for the ADP-bound MalKs is +3.79 ± 0.16 kcal/mol (Table 1). We verified the validity of this result by comparing it with the corresponding experimental data. According to the experimental data from the dimerization assay by Lu et al.,35 ADP-bound MalK does not dimerize (a more detailed description is given in MODEL AND THEORY), and thus ∆GII should have a positive value. Thus, our present result is consistent with the experimental observations. This is also consistent with the MD-simulation result for the complete MalFGK2 by Oliveira et al; the simulation of the ADP bound state resulted in dimer dissociation of MalKs. This implies that the MalK-dissociation mechanism presented below could also be applicable to the MalKs in the full-length transporter.63 We now explore the reason why the driving force responsible for dimerization of the ADPbound MalKs is weaker than that for the ATP-bound MalKs. Upon dimerization of the ADPbound MalKs, the contribution from the water-entropy change has a negative value (−49.07 ± 0.09 kcal/mol), and its absolute value is smaller than that for the ATP-bound MalKs (−53.71 ± 0.06 kcal/mol). By contrast, the contribution from configurational-entropy changes (+39.04 ± 0.23 kcal/mol) is larger than that for the ATP-bound MalKs (+33.06 ± 0.32 kcal/mol). As shown in Table 3, the increase in the configurational-entropy loss in Path II originates from the increase in the vibrational-entropy loss by +6.98 (= +25.20 – (+18.22)) kcal/mol relative to that in Path I. Although the total enthalpy loss is reduced by +16.55 ± 0.13 to +13.82 ± 0.13, the water-entropy gain

is

surpassed

by

the

configurational-entropy

loss

and

total

enthalpy

loss

(−49.07+39.04+13.82 = +3.79. Note that the value for ∆GII in Table 1 is not equal to the sum 20 ACS Paragon Plus Environment

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value of corresponding components due to rounding-off errors), and therefore ∆GII has a positive value. Taken together, the water-entropy gain upon binding after hydrolysis is still large, but becomes smaller and is transcended by the total enthalpy loss and the configurational-entropy loss, leading to the dissociation of the dimer. Significance of precise packing between the solutes. The calculated water-entropy gain upon dimerization of the ATP-bound MalKs is quite large. This result might arise from the construction of a closely packed structure between the interface regions of each MalK (see Figure 3). The precise packing (i.e., shape complementarity) between the solute molecules at the atomic level provides a large decrease in the total EV (−1725.63 Å3) upon ATP-bound MalK dimerization, and provides a remarkably large contribution to the water-entropy gain.53 In the case of the ADP-bound MalKs, on the other hand, such a better shape complementarity between the interface regions of each MalK might be partially collapsed, as schematically illustrated in Figure 4. In other words, the loss of two inorganic phosphates (Pi) might induce a reduction of the shape complementarity between the interface regions of the two MalKs. Such a decrease of the precise packing can lead to a loss in the overlap of the EV (−35.5 Å3), resulting in the loss of the water-entropy gain upon dimerization. Another unfavorable result due to the loss of precise packing is the decrease of the energetic gain arising from the attractive van der Waals’ interactions in the ADP-bound MalKs by −19.29 (= −126.31 – (–107.02)) kcal/mol relative to the ATP-bound MalKs (see Table 2). CONCLUSIONS We investigated the thermodynamics of the dimerization/dissociation of MalKs induced by the binding of ATP and its hydrolysis. These processes correspond to the dimerization/dissociation of 21 ACS Paragon Plus Environment


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NBDs observed in most ABC transporters. To clarify the driving force responsible for the MalKMalK dimerization, we evaluated the changes in relevant thermodynamic quantities upon dimerization of MalKs. We found that water-entropy plays an essential role in the MalK dimerization process. Water-entropy gain upon dimerization of the ATP-bound MalKs originates primarily from an increase in the total volume available to the translational displacement of water molecules in the system. The hydration-enthalpy loss arising from the loss of the MalKwater attractive interactions upon dimerization is slightly larger than the energetic gain due to the MalK-MalK direct interactions. Configurational entropy also contributes to the weakening of the dimerization, due to the loss of one MalK’s mobility and the side-chain flexibility between the interface regions of each MalK. Taken together, the water-entropy gain surpasses the enthalpic and configurational-entropic loss, leading to dimerization. When ATP in the MalK dimer is hydrolyzed, a change in the balance between the water-entropy gain and the hydration enthalpy plus the configurational-entropy loss occurs, that is, from {−T∆ISH > (∆IHTotal −T∆ISC)} to {−T∆IISH < (∆IIHTotal −T∆IISC)}, leading to the dissociation of the MalKs. These proposals for the NBD dimerization/dissociation mechanism, which are focused on the water- and configurationalentropy-mediated forces, differ from conventional proposals in that they are focused primarily on the direct interactions between the NBDs. Because the NBDs from different ABC transporters share a high degree of sequence and structural homology,11 the present results could be applicable to all types of ABC transporters and may pave the way for the elucidation of their substrate-transportation mechanisms accompanied by a large structural changes in concert with ATP.

ASSOCIATED CONTENTS


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Supporting Information. A. Calculation of Hydration Free Energy by the Three-Dimensional Reference Interaction Site Model Theory. This material is available free of charge via Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author [email protected]. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The computer program for the excluded volume calculations was developed with H. Oshima and M. Kinoshita. This work was supported in part by Grants-in-Aid for Scientific Research on Innovative Areas (No. 20118006 and 26104511) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. REFERENCES 1. Linton, K. J.; Higgins, C. F. The Escherichia coli ATP-Binding Cassette (ABC) Proteins. Mol. Microbiol. 1998, 28, 5-13. 2. Hollenstein, K.; Frei, D. C.; Locher, K. P. Structure of an ABC Transporter in Complex with Its Binding Protein. Nature 2007, 446, 213-216. 3. Oldham, M. L.; Davidson, A. L.; Chen, J. Structural Insights into ABC Transporter Mechanism. Curr. Opin. Struct. Biol. 2008, 18, 726-733.



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60. Fischer, S.; Verma, C. S. Binding of Buried Structural Water Increases the Flexibility of Proteins. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 9613-9615. 61. Fischer, S.; Smith, J. C.; Verma, C. S. Dissecting the Vibrational Entropy Change on Protein/Ligand Binding: Burial of a Water Molecule in Bovine Pancreatic Trypsin Inhibitor. J. Phys. Chem. B 2001, 105, 8050-8055. 62. Moritsugu, K. B.; Njunda, M.; Smith, J. C. Theory and Normal-Mode Analysis of Change in Protein Vibrational Dynamics on Ligand Binding. J. Phys. Chem. B 2010, 114, 14791485. 63. Oliveira, A. S. F.; Baptista, A. M.; Soares, C. M. Inter-domain Communication Mechanisms in an ABC Importer: A Molecular Dynamics Study of the MalFGK2E Complex. PLOS Comput. Biol. 2011, 7, e1002128(1-12).



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Table 1. Free-energy change and its enthalpic and entropic components with standard error (in kcal/mol) upon dimerization of the MalKs Patha

∆G b

∆Htotalc

−T∆SCd

−T∆SHe

Path I (∆GI)

−4.11 ± 0.41

+16.55 ± 0.13

+33.06 ± 0.32

−53.71 ± 0.06

Path II (∆GII)

+3.79 ± 0.16

+13.82 ± 0.13

+39.04 ± 0.23

−49.07 ± 0.09

a

Path I and II correspond to the dimerization of ATP-bound and ADP-bound MalKs, respectively, as illustrated in Figure 2. b Binding free energy, ∆G = G(MalKa:MalKb) – { G(MalKa) + G(MalKb) } =∆Htotal – T∆SC – T∆SH. Note that ∆GII value in the table is not equal to the sum value of corresponding components due to the round-off error. c Total-enthalpy change, ∆Htotal =∆(EvdW + Ees + HH). d Contribution from the configurational-entropy change, −T∆SC. e Contribution from the water-entropy change, −T∆SH.


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Table 2. Total-enthalpy change with standard error (in kcal/mol) and its components upon dimerization of the MalKs Patha

∆Htotal b

∆EvdWc

∆Eesd

∆HH e

Path I (∆GI)

+16.55 ± 0.13

−126.31 ± 0.11

−235.27 ± 1.41

+378.14 ± 1.36

Path II (∆GII)

+13.82 ± 0.13

−107.02 ± 0.12

−302.05 ± 1.17

+422.89 ± 1.05

a

Path I and II correspond to the dimerization of ATP-bound and ADP-bound MalKs, respectively, as illustrated in Figure 2. b Total-enthalpy change, ∆Htotal = ∆(EvdW + Ees + HH). Note that the ∆Htotal value for Path I in the table is not equal to the sum of the values of the corresponding components due to a rounding-off error. c The MalKa-MalKb van der Waals interaction energy, ∆EvdW, represented by Lennard-Jones potential. d The MalKa-MalKb electrostatic interaction energy, ∆Ees. e Hydration-enthalpy change upon dimerization of MalKs, ∆HH. The change originates from the loss of the attractive MalKa-water and MalKb-water interactions upon MalK dimerization.



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Table 3. Configurational-entropy change with standard error (in kcal/mol) and its components upon dimerization of the MalKs Modela

−T∆SCb

−T∆SCtrans, rot c

−T∆SCvib d

Path I (∆GI)

+33.06 ± 0.32

+14.84

+18.22 ± 0.32

Path II (∆GII)

+39.04 ± 0.14

+13.84

+25.20 ± 0.23

a

Path I and II correspond to the dimerization of ATP-bound and ADP-bound MalKs, respectively, as illustrated in Figure 2. b Contribution from the configurational-entropy change, −T∆SC. Note that ∆SC values in the table are not equal to the sum of the values of the corresponding components due to a rounding-off error. c The sum value of the contributions from the translational and rotational entropy gain, −T∆SCtrans, rot. Note that the value, which is estimated by the methods proposed by Swanson et al., does not have a standard error value in principle. d Contribution from the vibrational-entropy change, −T∆SCvib.


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Figure Captions Figure 1. Structure of the MalFGK2 complex. MalFGK2 is depicted by a ribbon representation. The parts of MalK monomers corresponding to NBDs are shown in green and cyan, respectively. (a) ATP-free form (PDB code: 3FH6). (b) ATP-bound form (PDB code: 2R6G). The structure was stabilized by a mutation that prevents ATP hydrolysis. ATP molecules are represented by licorice models. Figure 2. Schematic representation of the paths considered for calculation of the free-energy change upon dimerization of MalKs. MalK monomers (NBD parts only), indicated by MalKa and MalKb are shown in green and cyan, respectively, using the ribbon model. The MalK dimer indicated by MalKa:MalKb is a snapshot of MD simulations as described in “Structure modeling”. ATPs, ADPs, and Mg2+ ions bound to MalKs are represented by the licorice models. ∆GI and ∆GII denote changes in the free-energy function along Paths I and II, respectively. Figure 3. Cartoon illustration showing the overlap of the excluded spaces caused by the binding of two MalK monomers. Figure 4. Cartoon illustration showing the decrease in the overlap of the excluded volumes after the hydrolysis of ATPs.



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Figure 1


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Figure 2



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Figure 3


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Figure 4.



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SYNOPSIS.


ATP-Induced Conformational Changes of Nucleotide-Binding

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