Mechanistic picture for conformational transition of a ... - PNAS

Mechanistic picture for conformational transition of a membrane transporter at atomic resolution Mahmoud Moradi and Emad Tajkhorshid1 Center for Biophysics and Computational Biology, Department of Biochemistry, College of Medicine, and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana–Champaign, Urbana, IL 61801 Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved October 8, 2013 (received for review July 11, 2013)

During their transport cycle, ATP-binding cassette (ABC) transporters undergo large-scale conformational changes between inward- and outward-facing states. Using an approach based on designing system-specific reaction coordinates and using nonequilibrium work relations, we have performed extensive all-atom molecular dynamics simulations in the presence of explicit membrane/solvent to sample a large number of mechanistically distinct pathways for the conformational transition of MsbA, a bacterial ABC exporter whose structure has been solved in multiple functional states. The computational approach developed here is based on (i) extensive exploration of system-specific biasing protocols (e.g., using collective variables designed based on available lowresolution crystal structures) and (ii) using nonequilibrium work relations for comparing the relevance of the transition pathways. The most relevant transition pathway identified using this approach involves several distinct stages reflecting the complex nature of the structural changes associated with the function of the protein. The opening of the cytoplasmic gate during the outwardto inward-facing transition of apo MsbA is found to be disfavored when the periplasmic gate is open and facilitated by a twisting motion of the nucleotide-binding domains that involves a dramatic change in their relative orientation. These results highlight the cooperativity between the transmembrane and the nucleotidebinding domains in the conformational transition of ABC exporters. The approach introduced here provides a framework to study large-scale conformational changes of other membrane transporters whose computational investigation at an atomic resolution may not be currently feasible using conventional methods.

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positions; PDB ID codes 3B5X and 3B5W), with around 40 and 70 Å of separation between the mass centers of the two NBDs, termed IF-closed (IF-c) and IF-open (IF-o), respectively. These structures indicate the involvement of a large conformational change in the TMDs during the transport cycle of ABC exporters, an observation also supported by several other experiments (8, 9, 12–14). However, the nature of the conformational changes and the transition pathway are largely unknown. Molecular dynamics (MD) simulations have been used to study the dynamics of various ABC transporters (15–22). Because the IF ↔ OF transition is beyond the timescales presently allowed by unbiased all-atom MD simulations, the technique has been mainly used to study the individual states. To systematically study such transitions, here, we introduce an approach based on using nonequilibrium-driven simulations as a search tool for practical biasing protocols and reliable transition pathways. Nonequilibrium-driven MD simulations have been extensively used in the past, most prominently in steered (23) and targeted (24) MD simulations, where a time-dependent biasing potential is used to drive the system from one state toward another along a distance- or rmsd-based reaction coordinate, respectively. The key distinction of the approach presented here lies in the fact that we focus a major fraction of our computational effort on finding relevant system-specific reaction coordinates (such as those shown in Fig. 1) and practical biasing protocols to generate more reliable transition pathways. Particularly, we have designed several collective variables based on the formalism of “orientation quaternion” (25–27) as an effective method to induce rotational transformations in a molecular system. We have performed more than 200 nonequilibrium-driven MD simulations to generate a wide range of mechanistically distinct pathways (Fig. 2 and Significance

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TP-binding cassette (ABC) transporters constitute one of the largest and most ancient protein superfamilies that are involved in diverse cellular processes (e.g., multidrug resistance) by actively transporting a wide variety of substrates (e.g., cytotoxic agents) across the cellular membrane (1). Their general architecture is characterized as a complex with two nucleotidebinding domains (NBDs) and two transmembrane domains (TMDs) (2). The NBDs dimerize when bound to ATP and dissociate in the absence of a bound nucleotide or in response to ATP hydrolysis (3, 4). The ATP-driven dimerization/dissociation of the NBDs is coupled to the conformational changes of the TMDs that facilitate the vectorial movement of the substrates across the membrane by alternating between “inward-facing” (IF) and “outward-facing” (OF) states, open toward the cytoand periplasm, respectively. Although evidence supports an IF ↔ OF transition during the transport cycle (4, 5) (“alternatingaccess” mechanism), the conformational changes involved in this transition are not fully understood in a mechanistic context. The resolved crystal structures of ABC exporters (5–10) reveal a great structural flexibility, particularly those of the lipid flippase MsbA (7), a bacterial homolog of human multidrug resistance protein MDR1 (11), including an OF conformation [solved to 3.7 Å; Protein Data Bank (PDB) ID code 3B60] and two IF conformations (solved to 4.5 Å, only including Cα 18916–18921 | PNAS | November 19, 2013 | vol. 110 | no. 47

Membrane transporters rely on large-scale conformational changes for their function. Despite considerable effort, however, details of such structural transitions are largely unknown, leaving many fundamental questions regarding the transport mechanism in this important family of membrane proteins unanswered. Here, we present a nonequilibrium approach to characterize the conformational transition of MsbA, a member of the ATP-binding cassette exporter family, which is involved in transport of diverse substrates across the membrane. The design of the study is based on complex, system-specific reaction coordinates and protocols resulting in an unprecedented level of detail on the nature of conformational coupling and the mechanism of transport. The presented approach opens opportunities for investigating large-scale conformational changes of other membrane transporters. Author contributions: M.M. and E.T. designed research; M.M. performed research; M.M. analyzed data; and M.M. and E.T. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. Freely available online through the PNAS open access option. 1

To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1313202110/-/DCSupplemental.

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Fig. 1. Definitions of reaction coordinates. (A) Cartoon representation of MsbA structure in three different conformations: OF (Left), IF-c (Center) (two views), and IF-o (Right) along with the definitions of reaction coordinates α, β, and γ. NBDcis=trans is colored yellow/green, and TMD bundles B1 trans cis cis trans (TMcis helices), B2 (TMtrans 1,2 ,TM4,5 1,2 ,TM4,5 ), B3 ðTM3,6 Þ, and B4 ðTM3,6 Þ are colored blue, red, yellow, and green, respectively. In the OF conformation, the roll axes of bundles B1/B4 and B2/B3 are colored blue and red, respectively, to illustrate the definition of β. In the IF-o conformation, the roll axes of bundles B1/B3 and B2/B4 are colored blue and red, respectively, to illustrate the definition of α. The roll axes of NBDcis=trans in the OF and IF-c conformations are colored yellow/green to illustrate the definition of γ. (B) Side (Top and Middle) and top (Bottom) views of the NBDs in OF and IF-c conformations along with the definitions of dNBD (Top) and γ (Middle).

SI Appendix, Fig. S1) and identified the most relevant ones using measures such as the amount of work needed to induce the transition and the stability of the products. Collectively, more than 5 μs of unbiased and biased simulations have been performed on a system of ∼250,000 atoms, including the full-length MsbA transporter in an explicit water/lipid environment. We work in the framework of nonequilibrium work relations, mathematically robust ideas developed to study nonequilibriumdriven systems particularly to estimate equilibrium free energies (28–31). The approach introduced here, however, aims at using (in a practical manner) nonequilibrium work measurements to establish a reliable qualitative understanding of the overall trend of the transition and the intermediate structures by sampling many different pathways, without the need for accurate freeenergy calculations. The results indicate that the optimum transition pathway of apo MsbA involves several complex NBD and TMD conformational changes, which are highly cooperative in nature. The closing of the TMD periplasmic gate is facilitated by the dissociation of the NBDs, whereas twisting of the NBDs is facilitated by the closure of the TMD periplasmic gate. On the other hand, the opening of the TMD cytoplasmic gate is facilitated by both twisting of the NBDs and the closure of the TMD periplasmic gate. Results and Discussion Conventional Methods. Starting from the known OF state of

MsbA, we first performed several conventional simulations including: (i) unbiased equilibrium simulations; (ii) steered MD simulations using the distance between two NBD mass centers ðdNBD Þ as the reaction coordinate; and (iii) targeted MD simulations using the Cα rmsd from the IF-o structure as the reaction coordinate. The unbiased equilibrium simulations of the OF state do not show any significant conformational changes within the timescales of the simulations; the apo structure stays firmly close to the experimentally solved structure of the OF state (SI Appendix, Figs. S2 and S3). In the steered MD simulations, the dissociation of the NBDs can be induced, but the NBD dissociation per se does not result in the opening of the cytoplasmic gate nor the closing of the periplasmic gate, as also reported previously (32). Moreover, the NBD dissociation is transient in that once the bias is removed, the NBDs reassociate, although not fully recovering the exact predissociation dimeric configuration. Both the dissociation and the reassociation involve asymmetric behaviors. The overall assessment is that dNBD as a collective variable can be used to (transiently) separate the NBDs, but it cannot fully induce the OF → IF transition. Moradi and Tajkhorshid

In the trajectories resulting from the targeted MD protocols (Fig. 2B and SI Appendix, Fig. S4), the cytoplasmic opening occurs consistently before the closing of the periplasmic side resulting in an intermediate structure that is open to both cytoand periplasm. This clearly contradicts the required alternating access mechanism and, thus, questions the relevance of these trajectories. The nonequilibrium work required for these simulations is typically on the order of hundreds of kilocalories per moles (SI Appendix, Figs. S5 and S6). System-Specific Biasing Protocols. Conventional techniques described above clearly fail to provide a reliable framework to investigate the IF ↔ OF conformational transition of MsbA; thus, we use a more systematic approach to sample the reaction-path ensemble of this complex transition. We use different combinations of following reaction coordinates to induce the OF → IF transition; α: the relative orientation of the TMD helices describing the cytoplasmic opening; β: the relative orientation of the TMD helices describing the periplasmic opening; γ: the relative orientation of the two NBDs; and dNBD: the distance between the two NBD mass centers (Fig. 1). Note that α and β are associated with the TMD conformational changes and can be used to induce opening of the cytoplasmic side and closing of the periplasmic side, respectively. On the other hand, γ and dNBD are associated with the NBD conformational changes and can be used to induce the twisting of the NBDs and their dissociation, respectively. One can design many different biasing protocols using these reaction coordinates (Fig. 2 and SI Appendix, Fig. S1). Assuming the major changes in α, β, γ, and dNBD occur in

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Fig. 2. Three-dimensional reaction coordinate space (α, β, γ). (A) Projection of 20 select trajectories (out of ∼250) onto the (α, β, γ) space along with their projections onto the 2D spaces (α, β), (α, γ), and (β, γ) (all trajectories are shown in SI Appendix, Fig. S1). (B) The smoothed trace of the 160-ns optimized pathway (black) compared with the 160-ns targeted MD (red) pathway. OF (cube), IF-c (sphere), and IF-o (pyramid) crystal structures are also shown in the (α, β, γ) space whose 2D projections are given by square, circle, and triangle, respectively.

PNAS | November 19, 2013 | vol. 110 | no. 47 | 18917

BIOPHYSICS AND COMPUTATIONAL BIOLOGY

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discrete stages, we designed 14 distinct classes of protocols (Fig. 3A and SI Appendix, Fig. S5) that include all possibilities (SI Appendix). To validate our discrete-protocol assumption, we have also explored certain nondiscrete protocols as shown and discussed in SI Appendix, Fig. S7. Work-Based Analysis. It has been shown that the relative importance of competing transition paths involved in a transition can be estimated using nonequilibrium work measurements (33). Ideally, the protocols can be designed to focus on one “explanatory” variable at a time to avoid complications in the workbased comparison (SI Appendix). Here, the presumptive explanatory variable is the order of events associated with α, β, γ, and dNBD . To simplify our work-based analysis, we classify all of the used protocols into three mechanistically distinct classes: (i) the cytoplasmic opening occurs before the periplasmic closing (denoted as α → β); (ii) the periplasmic closure occurs before the cytoplasmic opening [unlike i], and the NBDs twist after this opening (denoted as β → α → γ); and (iii) both the periplasmic closure [unlike i] and the NBD twist [unlike ii] occur before the cytoplasmic opening [denoted as (β, γ) → α]. This mechanistic classification correlates well with the trend of work (Fig. 3A). Comparing the trajectories generated by these protocols, we find that the α → β and the (β, γ) → α classes of transitions require the most and the least amount of work, respectively. Note that because of the nonequilibrium feature of the simulations, these work profiles are associated with a dissipative term that is stochastic in nature; thus, one cannot make reliable statements based on single trajectories. To address this issue, we emphasize that instead of comparing these work profiles individually, we are looking for a general pattern in the trend of work in different classes. We also repeated these simulations using different simulation times and/or different initial structures to ensure the validity of our statements. We derived our 18918 | www.pnas.org/cgi/doi/10.1073/pnas.1313202110

conclusions based on the common trends observed in all sets (SI Appendix, Table S2 and Fig. S6). Based on the trend of work shown in Fig. 3A, one can argue that the α → β class—which requires opening of the cytoplasmic gate before the closing of the periplasmic gate—is energetically disfavored. Similar to the targeted MD trajectories, the α → β protocols generate intermediate structures that are open to both cyto- and periplasmic sides (i.e., inconsistent with the alternating access mechanism). One can conclude that among the studied protocols, the (β, γ) → α class generates the most relevant pathways in which both periplasmic closure and NBD twist occur before the cytoplasmic opening. Note that the β → α → γ trajectories along which the cytoplasmic opening occurs before the NBD twist, although in line with the alternating access mechanism, are not favored energetically (Fig. 3A and SI Appendix, Fig. S6). The picture that emerges is that the opening of the cytoplasmic gate is facilitated not only by the periplasmic closure of the TMDs but also by the twisting of the NBDs. As an alternative work-based analysis, one can construct the work profiles of individual stages (i.e., cytoplasmic opening, NBD twist, periplasmic closure, and NBD dissociation) in 1D reaction coordinate spaces (i.e., α, γ, β, and dNBD ) (Fig. 3 B–E). Fig. 3B indicates that opening of the cytoplasmic gate (associated with α) is disfavored energetically if not preceded by both the periplasmic closure of the TMDs (associated with β) and the twisting of the NBDs (associated with γ). Interestingly, the dissociation of the NBDs (associated with dNBD ) does not seem to lower the barrier associated with the opening of the cytoplasmic gate considerably, unless accompanied by a twist in the NBDs. Once the periplasmic gate is closed and the NBDs are twisted, the opening of the cytoplasmic gate becomes favorable energetically (indicated by a negative slope in the initial segment of the black curve in Fig. 3B). The work profiles in Fig. 3A are plotted against time, whereas the work profiles in Figs. 3 B–E are constructed along the reaction coordinates using certain reweighting and integration discussed in SI Appendix. Note that (unlike time) the reaction coordinates fluctuate along the trajectories. The Optimum Protocol. Among all of the biasing protocols used,

one that consistently requires less work than others is (dNBD → β → γ → α) (Fig. 4 and Movie S1; also see the black curves in Figs. 2 and 3). One feature distinguishing this protocol from the others in the (β, γ) → α class is its highly cooperative NBD-TMD interaction. Note that change in α or β describes a TMD conformational change, whereas change in γ or dNBD describes an NBD conformational change. In our optimum pathway, each TMD conformational change is followed and preceded by an NBD conformational change and vise versa (Fig. 4). Fig. 3 C and D highlights

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Fig. 4. Transition pathway of MsbA from the optimum protocol. Snapshots of MsbA structure (in surface representation) along the optimized OF → IF transition pathway (two perpendicular side views). The reaction coordinates and NBD/TMD conformational changes associated with each stage are given. Also see Movie S1 and SI Appendix, Table S4.

Moradi and Tajkhorshid

Alternating-Access Mechanism. The structural analysis of the trajectories provides clues on the OF → IF conformational changes of MsbA in a reduced reaction coordinate space defined solely based on the protein structure. An alternative way to assess the conformation of MsbA, particularly in the context of substrate accessibility and the alternating access mechanism is to monitor the water content of the lumen. We constructed the linear water density ρwater along the pore based on either unbiased MD or restrained MD (RMD) trajectories (SI Appendix, Fig. S9) rather than nonequilibrium trajectories to ensure the reliability of the statistics. The cyto- and periplasmic gates are never open simultaneously in our optimum transition pathway. Indeed all of the trajectories except those generated using protocols from the α → β class—which are classified as disfavored given the large work values associated with them—follow the alternating access mechanism. Monitoring the water density around the cyto- and periplasmic gates for the unbiased OF trajectory (SI Appendix, Fig. S9), one can observe a significant fluctuation in the periplasmic gate indicating the possibility of a spontaneous closure if the simulation is extended. However, this is a relatively slow process and the periplasmic gate never completely closes within the timescales of the simulations. Equilibration of the IF Conformations. Equilibrating the IF-o and IF-c conformations resulting from our carefully designed nonequilibrium simulations (the optimum protocol) show that the periplasmic/cytoplasmic gates of apo MsbA stay closed/open along 150-ns unbiased trajectories (SI Appendix, Fig. S10). Interestingly, the IF conformation resulted from the targeted MD does not seem to be stable in that the periplasmic gate quickly opens once the bias is removed. This highlights the importance of the biasing protocol for generating reliable/stable conformations. Monitoring the collective variables α, β, γ, and dNBD along the unbiased equilibrium trajectories of IF conformations resulted from the optimum protocol reveals that the IF-o (IF-c) structure seems to move toward a conformation that is less (more) open than the IF-o (IF-c) crystal structure. Unlike the IF-c trajectory, the relative orientation of NBDs (γ) in the IF-o trajectory goes back to the “untwisted” state. Comparing the rootmean-square fluctuation (RMSF) of the Cα atoms along both IF-c Moradi and Tajkhorshid

Resting State of apo MsbA. To more accurately characterize the degree of cytoplasmic opening of the nucleotide-free apo MsbA in its IF state, we performed bias-exchange umbrella sampling (BEUS) free-energy calculations along α reaction coordinate using 22 replicas with different degrees of opening. The umbrellas were centered (in the α space) between 13° and 49° (SI Appendix, Fig. S12 and Table S7). Fig. 5 shows the reconstructed potential of mean force (PMF) along α. There exists a local minimum around α ≈ 16° (the value associated with the IF-c crystal structure), whereas no free-energy basin is discernible around α ≈ 47° (the value associated with the IF-o structure). There is, however, a free-energy basin around 43° that is not too far from the IF-o crystal structure. Thus, the IF-c conformation seems to be associated with a relatively deep minimum and the IF-o–like conformations are also thermally accessible (see PMF in terms of RMSDIF−c and RMSDIF−o in SI Appendix, Fig. S13). However, the deepest minima in the α space are in the 26–32° range, forming a basin that is associated with an IF conformation resembling the crystal structures of P-glycoprotein (P-gp) (8–10), which are obtained at higher resolutions. The overall picture emerging from the PMF calculations is that MsbA is fairly flexible in its resting state in the absence of nucleotides and substrates. Doorknob Mechanism. Based on the present work-based analysis, we argue that during the OF → IF transition of MsbA, the cytoplasmic opening is disfavored before the NBD twist. In addition, we show that the TMD periplasmic closure and the NBD dissociation—which are both necessary for the OF → IF transition—cannot be sustainably achieved without a twist in the NBDs. Based on these arguments, we propose that the twisting motion of the NBDs facilitates the opening of the cytoplasmic gate during the OF → IF transition of apo MsbA. In this mechanism, the NBDs seem to act as a “doorknob” that needs to be twisted before the door (i.e., the cytoplasmic gate) can be opened. This is in agreement with—and to some extent may explain—the relative orientation of the NBDs in the crystal structures of MsbA in the IF conformations, which differs dramatically from that of the nucleotide-bound conformation. As pointed out by Ward et al. (7), the P-loops of opposing NBD monomers (∼30 Å apart in the OF state) are positioned next to

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Stability of the Products. The work analysis described above clearly suggests an important mechanistic role for the NBD twist. Here, we provide an additional argument based on the stability of the products to highlight the significance of this role in the IF ↔ OF transition of MsbA. Although one can induce a conformational change (e.g., the NBD dissociation or the TMD periplasmic closure) by varying certain reaction coordinates (e.g., dNBD or β), the stability of the products resulting from these simulations may depend on other degrees of freedom as well. By equilibrating the resulting structures, we find that neither the NBD dissociation nor the TMD periplasmic closure results in a stable conformation unless accompanied by a twist in the NBDs [i.e., change in γ (SI Appendix, Fig. S8)]. If the NBDs dissociate, the structure will be stable only if they also undergo the twisting motion (regardless of the order). Similarly if the periplasmic gate closes, the resulting structure will be stable as long as the NBDs twist as well (regardless of the order).

and IF-o trajectories indicate both IF conformations are associated with a larger fluctuation relative to the OF state (compare SI Appendix, Figs. S3 and S11) both in TMDs and NBDs. In TMDs, ICL2, which had the lowest RMSF in the OF conformation, is associated with one of the largest RMSF peaks in the IF-o conformation.

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the cooperativity between the TMD and NBD conformational changes more clearly; twisting of the NBDs is facilitated by the TMD periplasmic closure (Fig. 3C) and the TMD periplasmic closure is facilitated by the NBD twist and/or dissociation (Fig. 3D). Fig. 3 B–E also suggests that the dissociation of NBDs may well represent the first major stage of the OF → IF transition; NBD dissociation (induced using dNBD collective variable) can facilitate both the NBD twist (Fig. 3C) and the extracellular closure (Fig. 3D); however, the extracellular closure (induced using β collective variable) does not seem to facilitate the NBD dissociation (Fig. 3E). This is consistent with the fact that the first stage of the optimum protocol is associated with the NBD dissociation.

one another in the IF-c state, an observation also consistent with cross-linking studies of MDR1 (34, 35). Although we provide several arguments to support our proposed doorknob mechanism, one remaining question is how this mechanism facilitates the OF → IF transition. An insightful clue on the role of the NBD twist is provided by monitoring the NBDNBD interactions. The NBD monomers are associated through a complex NBD-NBD interface with several charged side chains (SI Appendix, Fig. S14A) and a complex surface charge distribution (SI Appendix, Fig. S14B). The relative orientation of the two NBD monomers, therefore, determines the pattern of the interaction which is predominantly electrostatic (SI Appendix, Fig. S14C). NBD separation without a change of their relative orientation and without the opening of the cytoplasmic gate cannot result in a stable conformation because the NBDs can easily reassociate and (at least loosely) dimerize. Here, the inward-closed conformation of the TMDs (forming a closed cytoplasmic gate) plays a crucial role in favoring the reassociation of the NBDs. In return, the association of the NBDs helps to keep the cytoplasmic gate intact, thus forming a cooperative interaction between the two. However, twisting of the NBDs may linger the reassociation of the NBDs by promoting a repulsive interaction between them (at least occasionally) and facilitate the rest of the conformational changes necessary for the opening of the cytoplasmic gate and inducing the OF → IF transition. The picture that emerges from these observations is that the charged residues present in the NBD-NBD interface play an important role in the NBD twist/separation. Interestingly, double electron–electron resonance spectroscopy has demonstrated the E506Q mutation shifts the distribution of apo MsbA from an IF-o– like conformation to a closed dimer conformation (36). This could be attributable to the disruption of the NBD twist mechanism that is driven by complex electrostatic interactions in the NBD-NBD interface. Another example is the D512G mutant which both binds and hydrolyzes ATP approximately at the wild-type rate (or even faster) but is dysfunctional because of its deficiency in undergoing conformational changes, as revealed by electron paramagnetic spin resonance (EPR) experiments (37). Similar to E506, D512 could be essential for the NBD twist as both residues are charged and located at the NBD-NBD interface. Although the NBDs stay twisted along a 150-ns unbiased trajectory starting from the IF-c conformation, the relative orientation of NBDs in the IF-o conformation eventually goes back to the untwisted state. One may conclude that the twisting of NBDs is only necessary to induce the OF → IF transition, but once the NBDs are dissociated and far apart, they are more or less free to go back to the untwisted conformation, although the γ collective variable is associated with fluctuations whose extent can be determined more reliably in longer equilibrium simulations. Interestingly, the untwisted NBD conformation in our relaxed IF-o structure is in good agreement with the crystal structures of P-gp transporter (8–10). Furthermore, the extent to which the relaxed IF-o conformation of apo MsbA is open closely resembles that of the recent P-gp crystal structure (9). We note, however, that the binding of the transport substrate could change this extent of opening, as suggested by recent crosslinking experiments (38). Generally, the IF-o state is associated with a larger fluctuation relative to both IF-c and OF conformations. One of the largest fluctuation regions of the IF-o conformation is associated with the coupling helix ICL2, a region that fluctuates only minimally in the OF conformation. This is in good agreement with a recent experimental study on ABC exporter BmrA (14) reporting a much greater ICL2 fluctuation in the IF state than in the OF state. Concluding Remarks. Nonequilibrium work relations (28–31) have been used to numerically estimate the free energies associated with various processes (39, 40). The use of nonequilibrium work measurements have recently been extended to setting up exchange criteria in a replica-exchange scheme (41) and designing adaptive biasing potentials in an adaptive-bias scheme (42). In 18920 | www.pnas.org/cgi/doi/10.1073/pnas.1313202110

this study, we used the work along different transition pathways, not for a quantitative description of the energetics of the system but rather to compare the feasibility and relevance of different pathways obtained from nonequilibrium simulations (43, 44). According to nonequilibrium work relations, the work measured along the energetically favored transition tube (i.e., the minimum free-energy path and its nearby paths) shows a different trend compared with the other “hypothetical,” energetically disfavored transition tubes (33). To simplify the search within the transition path ensemble, one may define a set of relevant reaction coordinates to reduce the phase space to a reaction coordinate space with a clear distinction between different states of the system, including initial, final, and different hypothetical intermediate states. A careful design of system-specific collective variables (e.g., based on the crystal structures and other available experimental data) is a key part of the approach proposed here. The use of nonequilibrium work measurements, along with the knowledge-based design of biasing protocols, is the core idea behind the present study. Although the majority of simulations described here are far from equilibrium, and the nonequilibrium work measured along these trajectories should not be mistaken for reversible work (i.e., free energy), the work along our optimum trajectory is significantly lower than that of the other nonequilibrium trajectories. To convert the work profiles into free energies (along optimum pathway), one needs to either repeat the simulations until the dissipative term in work vanishes [when integrated, for example, according to the Jarzynski scheme (28)] or perform other types of free-energy calculations. Here, we have performed one such calculation for one of the four stages of the optimized path, namely, along α. Comparison of the black curves in Figs. 3B and 5 reveals that the work profiles are dominated by the dissipative term attributable to nonequilibrium effects. Thus, it is important to distinguish between the irreversible work—and how it can be used to compare certain pathways qualitatively if they show dramatically distinct behaviors—and reversible work, which is much more informative but often difficult to obtain. Naturally, the conclusions drawn in this study are based on the sampled transition pathways. We can neither claim to have identified the minimum free-energy path nor rule out the possibility of designing an even better biasing protocol. However, we can safely state that, through substantially improving the sampling of the transition path ensemble, our computational approach provides a more efficient and advantageous way of investigating large-scale conformational transitions, compared with methods such as targeted MD. We note that the low-resolution IF crystal structures of MsbA whose relevance (particularly in the open state) has been debated (45) were not used here to model any of the simulation systems. We simply used these structures as a guide to design our reaction coordinates α, β, γ, and dNBD , the explored ranges of which were roughly based on these crystal structures. This is substantially different from conventional targeted MD in which rmsd with respect to a target structure is needed to bias the system, and, therefore, a low-resolution target structure can undermine the reliability of the resulting transition paths. The present study not only sheds light on the mechanistic features of the IF ↔ OF transition of MsbA but also introduces a fresh framework for studying membrane transporters in general, which undergo large-scale conformational changes. For example, the collective variables defined here can be readily adopted for other ABC exporters or for studying different conditions (e.g., after the explicit involvement of the nucleotides/substrates) to provide a more complete mechanistic picture of the transport cycle. We note that the transport mechanism of MsbA can only be understood fully within the context of the transport cycle, which involves other processes such as ATP binding, hydrolysis, and release, as well as substrate binding, translocation, and release, in addition to MsbA conformational changes. However, this study specifically addresses the conformational changes of apo MsbA from an OF state to its resting IF state upon Moradi and Tajkhorshid

an initial relaxation of the OF MsbA in an explicit lipid/solvent environment (SI Appendix), we performed a 150-ns unbiased equilibrium simulation. We used three structures from t = 0, t = 75, and t = 150 ns of this equilibrium trajectory to initiate several nonequilibrium-driven MD simulations that were carried out using different time-dependent biasing protocols in which the system was driven away from the initial OF state toward an IF state. A select number of these nonequilibrium simulations were followed by RMD simulations in which the system is subject to a time-independent biasing potential centered at the final target. A select number of the conformations resulted from the biased simulations were further equilibrated with no bias. We also performed BEUS [also known as window-exchange (46) or replica-exchange (47) umbrella sampling] simulations to quantify the free energies associated with different IF conformations. For a complete list of these simulations, see SI Appendix, Tables S1– S7. These simulations include both conventional (here, unbiased and targeted MD, as well as steered MD, along a distance) and nonconventional (BEUS and driven simulations along quaternion-based reaction coordinates). For a detailed description of the methods, see SI Appendix.

We prepared the nucleotide-free, apo MsbA in the OF state by removing the nucleotides from the crystal structure of MsbA (PDB ID code 3B60) (7). After

ACKNOWLEDGMENTS. Simulations in this study have been performed using supercomputing facilities provided through Extreme Science and Engineering Discovery Environment Grant MCA06N060 and the Taub cluster of the Computational Science and Engineering Program at the University of Illinois at Urbana–Champaign. This research is supported by National Institutes of Health Grants U54-GM087519, R01-GM086749, and P41-GM104601.

1. Jones MK, et al. (2009) Thermal stability of apolipoprotein A-I in high-density lipoproteins by molecular dynamics. Biophys J 96(2):354–371. 2. Davidson AL, Dassa E, Orelle C, Chen J (2008) Structure, function, and evolution of bacterial ATP-binding cassette systems. Microbiol Mol Biol Rev 72(2):317–364. 3. Hollenstein K, Dawson RJ, Locher KP (2007) Structure and mechanism of ABC transporter proteins. Curr Opin Struct Biol 17(4):412–418. 4. Oldham ML, Davidson AL, Chen J (2008) Structural insights into ABC transporter mechanism. Curr Opin Struct Biol 18(6):726–733. 5. Dawson RJ, Locher KP (2006) Structure of a bacterial multidrug ABC transporter. Nature 443(7108):180–185. 6. Dawson RJ, Locher KP (2007) Structure of the multidrug ABC transporter Sav1866 from Staphylococcus aureus in complex with AMP-PNP. FEBS Lett 581(5):935–938. 7. Ward A, Reyes CL, Yu J, Roth CB, Chang G (2007) Flexibility in the ABC transporter MsbA: Alternating access with a twist. Proc Natl Acad Sci USA 104(48):19005–19010. 8. Aller SG, et al. (2009) Structure of P-glycoprotein reveals a molecular basis for polyspecific drug binding. Science 323(5922):1718–1722. 9. Jin MS, Oldham ML, Zhang Q, Chen J (2012) Crystal structure of the multidrug transporter P-glycoprotein from Caenorhabditis elegans. Nature 490(7421):566–569. 10. Ward AB, et al. (2013) Structures of P-glycoprotein reveal its conformational flexibility and an epitope on the nucleotide-binding domain. Proc Natl Acad Sci USA 110(33):13386–13391. 11. van Veen HW, et al. (1998) A bacterial antibiotic-resistance gene that complements the human multidrug-resistance P-glycoprotein gene. Nature 391(6664):291–295. 12. Dong J, Yang G, McHaourab HS (2005) Structural basis of energy transduction in the transport cycle of MsbA. Science 308(5724):1023–1028. 13. Zou P, Bortolus M, McHaourab HS (2009) Conformational cycle of the ABC transporter MsbA in liposomes: Detailed analysis using double electron-electron resonance spectroscopy. J Mol Biol 393(3):586–597. 14. Mehmood S, Domene C, Forest E, Jault JM (2012) Dynamics of a bacterial multidrug ABC transporter in the inward- and outward-facing conformations. Proc Natl Acad Sci USA 109(27):10832–10836. 15. Jones PM, George AM (2002) Mechanism of ABC transporters: A molecular dynamics simulation of a well characterized nucleotide-binding subunit. Proc Natl Acad Sci USA 99(20):12639–12644. 16. Wen PC, Tajkhorshid E (2008) Dimer opening of the nucleotide binding domains of ABC transporters after ATP hydrolysis. Biophys J 95(11):5100–5110. 17. Wen PC, Tajkhorshid E (2011) Conformational coupling of the nucleotide-binding and the transmembrane domains in ABC transporters. Biophys J 101(3):680–690. 18. Aittoniemi J, de Wet H, Ashcroft FM, Sansom MSP (2010) Asymmetric switching in a homodimeric ABC transporter: A simulation study. PLOS Comput Biol 6(4):e1000762. 19. Oliveira AS, Baptista AM, Soares CM (2011) Conformational changes induced by ATPhydrolysis in an ABC transporter: A molecular dynamics study of the SAV1866 exporter. Proteins 79(6):1977–1990. 20. Becker JP, Van Bambeke F, Tulkens PM, Prévost M (2010) Dynamics and structural changes induced by ATP binding in SAV1866, a bacterial ABC exporter. J Phys Chem B 114(48):15948–15957. 21. Jones PM, George AM (2011) Molecular-dynamics simulations of the ATP/apo state of a multidrug ATP-binding cassette transporter provide a structural and mechanistic basis for the asymmetric occluded state. Biophys J 100(12):3025–3034. 22. Wen PC, Verhalen B, Wilkens S, Mchaourab HS, Tajkhorshid E (2013) On the origin of large flexibility of P-glycoprotein in the inward-facing state. J Biol Chem 288(26):19211–19220. 23. Izrailev S, Stepaniants S, Balsera M, Oono Y, Schulten K (1997) Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys J 72(4):1568–1581.

24. Schlitter J, Engels M, Krüger P, Jacoby E, Wollmer A (1993) Targeted molecular dynamics simulation of conformational change — application to the T ↔ R transition in insulin. Mol Simul 10(2-6):291–308. 25. Coutsias EA, Seok C, Dill KA (2004) Using quaternions to calculate RMSD. J Comput Chem 25(15):1849–1857. 26. Horn BKP (1987) Closed-form solution of absolute orientation using unit quaternions. J Opt Soc Am A 4(4):629–642. 27. Fiorin G, Klein ML, Hénin J (2013) Using collective variables to drive molecular dynamics simulations. Mol Phys, 10.1080/00268976.2013.813594. 28. Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78(14):2690–2693. 29. Crooks GE (2000) Path-ensemble averages in systems driven far from equilibrium. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 61(3):2361–2366. 30. Hummer G, Szabo A (2001) Free energy reconstruction from nonequilibrium singlemolecule pulling experiments. Proc Natl Acad Sci USA 98(7):3658–3661. 31. Jarzynski C (2001) How does a system respond when driven away from thermal equilibrium? Proc Natl Acad Sci USA 98(7):3636–3638. 32. St-Pierre JF, Bunker A, Róg T, Karttunen M, Mousseau N (2012) Molecular dynamics simulations of the bacterial ABC transporter SAV1866 in the closed form. J Phys Chem B 116(9):2934–2942. 33. Moradi M, Sagui C, Roland C (2011) Calculating relative transition rates with driven nonequilibrium simulations. Chem Phys Lett 518(0):109–113. 34. Loo TW, Clarke DM (2000) The packing of the transmembrane segments of human multidrug resistance P-glycoprotein is revealed by disulfide cross-linking analysis. J Biol Chem 275(8):5253–5256. 35. Urbatsch IL, et al. (2001) Cysteines 431 and 1074 are responsible for inhibitory disulfide cross-linking between the two nucleotide-binding sites in human P-glycoprotein. J Biol Chem 276(29):26980–26987. 36. Schultz KM, Merten JA, Klug CS (2011) Characterization of the E506Q and H537A dysfunctional mutants in the E. coli ABC transporter MsbA. Biochemistry 50(18):3599–3608. 37. Schultz KM, Merten JA, Klug CS (2011) Effects of the L511P and D512G mutations on the Escherichia coli ABC transporter MsbA. Biochemistry 50(13):2594–2602. 38. Verhalen B, Wilkens S (2011) P-glycoprotein retains drug-stimulated ATPase activity upon covalent linkage of the two nucleotide binding domains at their C-terminal ends. J Biol Chem 286(12):10476–10482. 39. Jensen MØ, Park S, Tajkhorshid E, Schulten K (2002) Energetics of glycerol conduction through aquaglyceroporin GlpF. Proc Natl Acad Sci USA 99(10):6731–6736. 40. Moradi M, Babin V, Roland C, Sagui C (2010) A classical molecular dynamics investigation of the free energy and structure of short polyproline conformers. J Chem Phys 133(12):125104. 41. Ballard AJ, Jarzynski C (2009) Replica exchange with nonequilibrium switches. Proc Natl Acad Sci USA 106(30):12224–12229. 42. Moradi M, Tajkhorshid E (2013) Driven metadynamics: Reconstructing equilibrium free energies from driven adaptive-bias simulations. J Phys Chem Lett 4(11):1882–1887. 43. Moradi M, Babin V, Roland C, Darden TA, Sagui C (2009) Conformations and free energy landscapes of polyproline peptides. Proc Natl Acad Sci USA 106(49):20746–20751. 44. Moradi M, Babin V, Roland C, Sagui C (2013) Reaction path ensemble of the B-Z-DNA transition: A comprehensive atomistic study. Nucleic Acids Res 41(1):33–43. 45. Gyimesi G, et al. (2011) ATP hydrolysis at one of the two sites in ABC transporters initiates transport related conformational transitions. Biochim Biophys Acta 1808(12):2954–2964. 46. Park S, Kim T, Im W (2012) Transmembrane helix assembly by window exchange umbrella sampling. Phys Rev Lett 108(10):108102–108105. 47. Sugita Y, Kitao A, Okamoto Y (2000) Multidimensional replica-exchange method for free-energy calculations. J Chem Phys 113(15):6042–6051.

Methods

Moradi and Tajkhorshid



ATP hydrolysis. We aim to investigate the structural preferences of MsbA along its transition path with only an implicit consideration of the ATP hydrolysis (by applying forces to the NBDs). Neither the ATP hydrolysis nor the substrate translocation is explicitly simulated; however, the framework established here may be used in future studies to investigate the effect of the nucleotide/substrate on the conformational transition of MsbA in an explicit manner. In summary, we used an approach to investigate the reactionpath ensemble of apo MsbA. Using nonequilibrium work measurements, we show the most relevant pathway is associated with a highly cooperative NBD-TMD interaction, follows alternating access mechanism, and uses a twist in the NBDs to facilitate the opening of the cytoplasmic gate (doorknob mechanism). This study highlights the importance of the relative orientation of the NBDs in their dissociation/dimerization phenomena in ABC exporters. More generally, our approach opens opportunities for studying large-scale conformational changes of other membrane transporters whose computational investigation may not be currently feasible using conventional methods.