simulations of nucleotide release from the circadian clock protein KaiC reveal atomic-resolution functional insights

Lu Honga, Bodhi P. Vanib, Erik H. Thiedeb, Michael J. Rustc,d,e,1, and Aaron R. Dinnerb,d,f,1

aGraduate Program in Biophysical Sciences, The University of Chicago, Chicago, IL 60637; bDepartment of Chemistry, The University of Chicago, Chicago, IL 60637; cDepartment of Molecular Genetics and Cell Biology, The University of Chicago, Chicago, IL 60637; dInstitute for Biophysical Dynamics, The University of Chicago, Chicago, IL 60637; eInstitute for Genomics and Systems Biology, The University of Chicago, Chicago, IL 60637; and fJames Franck Institute, The University of Chicago, Chicago, IL 60637

Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved October 18, 2018 (received for review July 20, 2018) The cyanobacterial clock proteins KaiA, KaiB, and KaiC form a respectively. Thus, the hexameric assembly has a two-tiered ring powerful system to study the biophysical basis of circadian rhythms, structure. Both the CI and CII domains hydrolyze ATP, and the because an in vitro mixture of the three proteins is sufficient to CII domain can also reversibly transfer phosphoryl groups be- generate a robust ∼24-h rhythm in the phosphorylation of KaiC. The tween amino acids S431 and T432 and bound nucleotides (i.e., nucleotide-bound states of KaiC critically affect both KaiB binding to from ATP and to ADP) (17–19). KaiC is a relative of the AAA+ the N-terminal domain (CI) and the phosphotransfer reactions that superfamily (15), and each KaiC globular domain shares close (de)phosphorylate the KaiC -terminal domain (CII). However, the structural similarity to F1-ATPase, part of the FOF1-ATP syn- nucleotide exchange pathways associated with transitions among thase (18). Many of the proteins that are evolutionarily related to these states are poorly understood. In this study, we integrate recent KaiC use mechanochemical coupling to do work, and it is an advances in molecular dynamics methods to elucidate the structure open question how the mechanisms of action of these ATPases · and energetics of the pathway for Mg ADP release from the CII do- relate to those of the KaiC family, which uses ATP hydrolysis for main. We find that nucleotide release is coupled to large-scale con- signal transduction and timing. BIOPHYSICS AND formational changes in the KaiC hexamer. Solvating the nucleotide Stimulation by KaiA promotes KaiC phosphorylation during requires widening the subunit interface leading to the active site, COMPUTATIONAL BIOLOGY the day (9, 20–25), and sequestration of KaiA by KaiB leads to which is linked to extension of the A-loop, a structure implicated dephosphorylation during the night (12, 26–28). However, the in KaiA binding. These results provide a molecular hypothesis for molecular mechanism of KaiA’s action is unclear. The activity of how KaiA acts as a nucleotide exchange factor. In turn, structural parallels between the CI and CII domains suggest a mechanism for KaiA was initially defined by its ability to stimulate KaiC auto- allosteric coupling between the domains. We relate our results to kinase activity (25). Kinetic studies indicate that this activity also structures observed for other hexameric ATPases, which perform inhibits the rate of dephosphorylation (20). Recent work shows diverse functions. that KaiA can act as a nucleotide exchange factor for CII, which otherwise very slowly releases ADP with an estimated rate less −1 homohexameric ATPases | allosteric regulation | enhanced sampling than 0.1 h (29). These observations, together with the fact that methods | free energy methods | conformational asymmetry CII is a reversible phosphotransferase, suggest that KaiA pro- motes phosphorylation by enabling exchange of ADP for ATP. ircadian clocks are based on biochemical oscillators found in Corganisms in all kingdoms of life. In general, a circadian Significance oscillator is characterized by its ability to generate self-sustaining oscillations with a near-24-h period in the absence of external Circadian rhythms enable organisms to adapt to the 24-h day/ environmental cues. Furthermore, the period of the oscillation is night cycle. The importance of these rhythms is evident from largely insensitive to temperature and metabolic perturbations their prevalence across the kingdoms of life and their dysre- over the physiological range (1). Circadian rhythms are impor- gulation in many diseases. The core clock of the cyanobacterium tant for maintaining regular cellular and physiological activities, Synechococcus elongatus serves as a paradigm for molecular and defects in the circadian clock can result in reduced fitness (2) studies of circadian rhythms because its oscillations can be and various health issues (3–7). reconstituted in vitro. There is evidence that the action of KaiC, The core circadian oscillator of the cyanobacterium Synecho- the central component of the oscillator, depends critically on coccus elongatus PCC 7942 presents a unique opportunity for whether its active sites bind ADP or ATP, metabolites that elucidating the biophysical basis of circadian rhythms (2, 8), function as the energy currency in cells. Here, we use molecular because its molecular oscillations can be reconstituted in vitro dynamics simulations to develop an atomic-resolution picture from purified proteins (9), and they show all of the hallmark of ADP release and, in turn, hypotheses for the regulation of properties of circadian rhythms described above. The oscillator is ADP/ATP exchange. based on periodic interactions among three soluble proteins: Author contributions: L.H., M.J.R., and A.R.D. designed research; L.H. performed research; KaiA, KaiB, and KaiC. These interactions give rise to near-24-h B.P.V. and E.H.T. contributed new reagents/analytic tools; and L.H., M.J.R., and A.R.D. oscillations in the phosphorylation pattern of KaiC, and these wrote the paper. oscillations are coupled to the external environment in part The authors declare no conflict of interest. through the relative concentrations of ATP and ADP (10–12). This article is a PNAS Direct Submission. KaiC is a homohexamer (13) (Fig. 1A) within the RecA/DnaB Published under the PNAS license. superfamily (14, 15), which includes a large variety of ATPases in 1To whom correspondence may be addressed. Email: [email protected] or dinner@ archaea, bacteria, and eukaryotes (15). Each subunit of S. uchicago.edu. elongatus KaiC has 519 residues that are organized into two do- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. mains formed by a tandem repeat of a common ATPase fold (16); 1073/pnas.1812555115/-/DCSupplemental. the N-terminal and C-terminal domains are known as CI and CII,

www.pnas.org/cgi/doi/10.1073/pnas.1812555115 PNAS Latest Articles | 1of10 Downloaded by guest on September 26, 2021 Fig. 1. The CII nucleotide release pathway involves both local and global conformational changes. (A) KaiC is a homohexamer with active sites located at the subunit interfaces. The hexamer forms a double- ring architecture; the N-terminal ring is termed the CI domain, and the C-terminal ring is termed the CII domain. The secondary structures of subunits D and E are shown as yellow and green ribbon diagrams, respectively, while the other four subunits are rep- resented by a white van der Waals surface. The CI–CII linker (residues 248–261) and the A-loop (residues 486–498) of subunits D and E are colored blue. (B)A

β-hairpin (βnt; residues 468–483) and an α-loop-α motif (αlα; residues 321–342) show the biggest dis- placements in the locally enhanced sampling simu- lations. The color represents the per-residue rmsd between initial and final protein backbone confor- mations, mapped onto the initial structure. (C)The string calculation reveals concerted motion of the six CII intersubunit angles during ADP dissociation at the subunit D–E active site. (Inset) A schematic of the CII domain, illustrating the intersubunit angle variables and the ADP–subunit distance variables employed in the simulation. (D) The nucleotide moves radially outward in the string pathway; the arrows indicate the movement of N6 and Pβ atoms in ADP. In A, B, and D, the Mg·ADP atoms are colored by element (C, cyan; N, blue; O, red; P, gold; H, white; Mg, pink).

Since ATP cannot be used as a phosphotransfer acceptor in the S431 (pS431) form of CII allow ADP accumulation in CI? In dephosphorylation reaction, the ability of KaiA to regulate the principle, molecular dynamics (MD) simulations can provide nucleotide-bound state in CII provides a unifying hypothesis that atomic-resolution answers to these questions. However, the size could explain both stimulation of phoshorylation and inhibition of the system and the timescale of nucleotide exchange prohibit of dephosphorylation. direct treatment by conventional methods. To overcome this Thus, the mechanism of nucleotide exchange in CII is key to challenge, we implemented a pipeline of methods for enhancing understanding the regulation of KaiC phosphorylation. Indeed, the sampling of rare events. The results of our simulations pro- control of nucleotide exchange is likely used throughout the vide a detailed characterization of the structure and energetics of clock cycle. The binding of KaiB to the homologous CI domain the ADP release pathway in CII and give insight into how KaiC requires the ability of CI to go through a catalytic cycle (12, 30), conformational changes during nucleotide release are coupled to and structural studies of the KaiB·KaiC complex show that ADP KaiA binding. Implications for other homohexameric ATPases is retained in the CI active site when KaiB is bound (28, 31). are discussed. However, accessing this binding-competent state in CI requires S431 phosphorylation in the distal CII domain (20, 32, 33). Results Taken together, these results suggest that the CII ring influences Nucleotide Release in CII Involves both Local and Intersubunit nucleotide exchange in the CI ring, just as KaiA influences nu- Conformational Changes. Our goal was to simulate nucleotide cleotide exchange in CII. release and to understand how it is coupled to changes in KaiC To the best of our knowledge, a nucleotide exchange pathway structure. In KaiC, the central channel is sufficiently large to has not been previously characterized for any homohexameric accommodate a free nucleotide, so it is not immediately obvious ATPase in the RecA/DnaB or AAA+ superfamilies. However, from the structure whether the nucleotide exits radially structures of these proteins in certain nucleotide-bound states inward or outward. We thus performed the simulation in stages show that they can take on conformations that lack C6 symmetry. that progressed from exploratory and qualitative to physically Examples include the staggered conformation of ClpX resulting well-controlled and quantitative, as follows. We first determined from a rigid-body rotation of the small α and large αβ domains the general direction of release using a method known as locally (34), the split washer conformation at the apo interface of NSF enhanced sampling (40–42), which floods the protein with non- (35), or the staircase-like DNA-binding hairpin structures of the interacting copies of Mg·ADP that weakly interact with the E1 helicase (36, 37). These structures have been interpreted to protein and activate local conformational dynamics to accelerate mean that hydrolysis proceeds sequentially or stochastically, the release. Given the general direction of release, we then rather than concertedly, around the rings of these proteins (38). sought to identify a manageable number of collective variables Although there are subtly asymmetric structures of the CI do- (CVs) that could be used to characterize and control sampling main of KaiC with both ATP- and ADP-bound active sites (39), along the pathway. We used these CVs to generate an initial it is not clear whether the full molecule functions in a symmetric guess for the release pathway with steered MD (SMD) (43), (i.e., concerted) or asymmetric fashion and, if the latter, how its which introduces an artificial force to drive the release. We then structures relate to those of other homohexameric ATPases. used the string method (44, 45) to refine this guess to a minimum What is the molecular mechanism of nucleotide exchange, and free energy path without artificial driving forces. Finally, the free how is it influenced by KaiA? How does the phosphorylated energy of the release pathway was characterized using umbrella

2of10 | www.pnas.org/cgi/doi/10.1073/pnas.1812555115 Hong et al. Downloaded by guest on September 26, 2021 sampling (46). While our conclusions are based only on these The Energetics of Mg·ADP Release Are Dominated by Salt-Bridge final simulations, to explain the CVs that we use to analyze the Interactions. We used umbrella sampling to characterize the dynamics, we briefly review the findings of the full series of free energy in the (extended) neighborhood of the string pathway. calculations (further detailed in Methods) in the remainder of In this method, copies of the system are restrained to different this section and the following one. values of the CVs to enforce sampling, and the contributions from In both CI and CII, the active sites are located at the subunit different copies are then reweighted to obtain the correct equi- interfaces, for a total of 12 sites per hexamer. Our calculations librium statistics (Methods). Because the computational cost of are based on a KaiC crystal structure [Protein Data Bank (PDB) umbrella sampling grows exponentially with the number of CVs, ID code 3DVL] (47), which we modified to be in the phos- we again focused on the 2D space defined by the ADP–subunit D phorylated T432-only (pT432) form in all six subunits and with distance and the subunit D–E angle. Care was taken to ensure all bound ATPs replaced by ADPs in the CII domain. Because convergence, as discussed in Methods. the structure has almost perfect C6 symmetry, we arbitrarily The free energy as a function of these CVs is shown in Fig. 2A. chose the active site at the interface of subunits D and E for the As the ADP–subunit D distance increases from 10 to 13 Å, there release simulations. The locally enhanced sampling simulations is a steep rise in the free energy to a plateau that is about 10 kcal/mol show that Mg·ADP is released radially outward (Fig. 1 and SI above the bound state, consistent with the fact that nucleo- Appendix, Fig. S1); this is consistent with further analyses of the tide binding is required for the hexamerization of KaiC (13). alternative possibility of inward release, which appears highly This rise coincides with the disruption of electrostatic interac- unfavorable (SI Appendix, Supplementary Results and Fig. S2). tions in the active site: The side chains of T295, E319, and D378 directly and indirectly determine the coordination of the For steric reasons the outward release requires an increase in 2+ the distance between the β-hairpin at residues 468–483 (which Mg ion, and the side chain of K294 makes a salt bridge to the terminal phosphate group of the ADP (Fig. 2B). Among these we denote βnt)andanα-loop-α motif (αlα)atresidues321–342, both of which are located near the exit point of the release residues, K294 and T295 are Walker A residues, D378 is a pathway (Fig. 1B and SI Appendix,Fig.S3). It is worth noting Walker B residue, and E319 is a catalytic glutamate (18); the that β is directly connected to the A-loop (residues 486–498), importance of such conserved residues for nucleotide binding nt and catalysis is well-established for many AAA+ and RecA-like which is implicated in KaiA binding. For these reasons, we – included the distance between the β and αlα centers of mass as ATPases (38). The free energy plateau for ADP subunit D nt distances greater than 10 Å is centered on subunit D–E angle aCV. BIOPHYSICS AND values of about 64°, compared with 60° observed in the crystal

To enable global structural changes, we also selected as CVs COMPUTATIONAL BIOLOGY the six angles formed by each pair of adjacent subunits in the CII structure. Although this opening permits additional water mol- ecules into the active site, maximum solvation is not achieved ring (Fig. 1C, Inset). This choice of CVs is motivated by two – observations. First, small-angle X-ray scattering experiments in- until after loss of the protein nucleotide interactions (SI Ap- pendix dicate that the radius of gyration of KaiC changes depending on , Fig. S7). In addition to the interactions listed above, two arginine resi- the phosphorylation state of the protein, and the variations in dues on the periphery of the active site also exhibit strong elec- this parameter are attributed to contraction and expansion of the trostatic interactions with Mg·ADP for ADP–subunit D distances CII ring (48). Second, other multimeric nucleotide-binding up to 16 Å (Fig. 2C). R451 forms salt bridges to each phosphate proteins have been shown to exhibit changes in solvent accessi- group in turn as the ADP makes its way out of the protein. The bility upon nucleotide binding at subunit interfaces (34, 35, 49– interaction of Mg·ADP with R459 from subunit E contrasts with 56). Two final CVs that we used to parameterize the release those discussed so far in that it is net-repulsive. Both R451A and pathway were the distances between the center of mass of the R459A abolish oscillation in vivo (57), confirming the importance ADP and the centers of mass of the active-site residues of the D of these two residues. In particular, R459 is an arginine finger, a and E subunits, respectively. We note that the two adjacent common motif required for sensing the presence of γ-phosphate subunits do not contribute equally to the active site; specifically, groups during ATP hydrolysis (38, 57). the nucleotide makes more extensive contact with subunit D In all of the nucleotide release simulations that we performed, + (Fig. 1D and SI Appendix, Fig. S4). A summary of the CVs is the Mg2 ion and ADP dissociated from the active site together, given in SI Appendix, Table S1. even though no restraint was applied to enforce either the Mg– Among the nine CVs that we identified, we found that the ADP or Mg–active site distance. However, it has been suggested subunit D–EangleandADP–subunit D distance provided the 2+ for F1-ATPase that the Mg ion leaves before ADP dissociation best control in SMD, and we used them to construct an ini- (58), so we also considered such a two-step release mechanism. tial guess for the release pathway. Specifically, we opened the To test this possibility, we ran a free energy calculation to de- · + intersubunit angle, moved the Mg ADP to increase the distance, termine the standard binding free energy of the Mg2 ion to a and then closed the angle in a stepwise manner. This pathway CII active site with bound ADP using the double annihilation was then refined using the string method in the full nine- method (59) (Methods and SI Appendix, Figs. S8 and S9). The dimensional CV space (SI Appendix, Fig. S5). In the refined result of the calculation suggests that the standard binding free · + pathway, the intersubunit angle opens and the Mg ADP disso- energy of Mg2 is at least –34 kcal/mol, which is very strong. We ciates in a concerted fashion (Fig. 1C). With the exception of the thus disfavor the two-step release mechanism. subunit A–B angle, which is diametrically opposed to the vacated active site, the angles between the rest of the subunits are Mg·ADP Release Is Regulated by Tryptophan Residues. Two trypto- compressed, especially the subunit E–F angle. This implies that phan residues close to the protein surface also make extensive ADP release in CII does not occur concurrently around the ring. contact with the adenine base throughout the release process No clear trends are observed for the CI intersubunit angles (SI (Fig. 2 B and C). The side chain of W331 forms hydrogen bond Appendix, Fig. S6). interactions first with the adenine base and then with the phos- In summary, our simulations show that Mg·ADP dissociation phate groups as ADP moves out of the active site. The geometry from CII is coupled to global conformational changes in that in proximity of W462 is suggestive of π-stacking, although the domain, which involves an asymmetric opening of the subunit does not explicitly include such effects. Previous ex- angles. Below, we further analyze the pathway from the string periments point to the importance of these residues; the muta- method to understand the energetics of nucleotide release. tions W331F and W462F lead to abnormal oscillations in vitro

Hong et al. PNAS Latest Articles | 3of10 Downloaded by guest on September 26, 2021 Fig. 2. Electrostatic interactions dominate the en- ergetics of nucleotide release. (A) The free energy profile of the release process, calculated using um- brella sampling. B and C show the interaction be- tween Mg∙ADP and key active-site residues. The solid lines show the coordination of the Mg2+ ion, and the dotted lines represent hydrogen-bond in- teractions. Colors are the same as in Fig. 1D.(B)A representative nucleotide-bound structure, from (8.5 Å, 60.2°) in A.(C) A representative structure from the region of rapid increase in free energy, specifically (10.4 Å, 64.0°) in A.(D) Alternative pro- jection of the umbrella sampling data in A. The CVs are the subunit D–E angle and the electrostatic in- teraction energy between solvent and active-site residues K294, T295, E319, and D378.

(33), and W331A traps KaiC in a constitutively phosphorylated ponent analysis (PCA) to the Cα atoms in the structures obtained state (23). from umbrella sampling, without reweighting, after aligning all Evolutionarily, W331 and W462 are highly conserved among structures with respect to the CII domain of subunit D. The first KaiC proteins found in KaiABC clusters in the cyanobacterial two principal components, PC1 and PC2, account for most of the phylum, a clade known as KaiC1 (SI Appendix, Table S2) (60). variance (43% and 28%, respectively) (SI Appendix,Fig.S10A). W331 is also conserved among the KaiC3 clade, proteins which Structures representative of the extremes of these two PCs are have not been functionally characterized (61). Because of the shown in Fig. 3 A and B. PC1 represents the formation of a split proposed role of KaiA as a nucleotide exchange factor (29) and washer structure with a helical pitch up to about 11 Å (Fig. 3C)in the observation that KaiA-mediated phosphorylation has only the CII domain, and a concomitant rigid-body tilt in the CI been found among KaiC1 homologs (60), the simulation results domain. The split in the CII ring is located at the subunit D–E are consistent with the notion that the tryptophan residues, in interface, the site of Mg·ADP dissociation in the simulation. particular W462, may play a role in KaiA-regulated nucleotide PC2 represents a concerted, circular compression motion in exchange in the CII domain. both domains in response to the angle-widening motion at the subunit D–Einterface. Subunit Angle Motion Is Coupled to Quaternary Conformational Given that the PCs are correlated with the subunit D–E angle, Changes. In the crystal structure of the KaiC protein employed which possesses at least two metastable states in the nucleotide- in the present study, all six CII intersubunit angles assume bound state (Fig. 2A), we hypothesized that motions in the di- equilibrium values around 60° (the difference between the larg- rection of the PCs are accessible even without nucleotide release. est and smallest angle is no more than 0.3°). The umbrella To test this hypothesis, we measured motion along the afore- sampling calculation, however, reveals an additional asymmetric mentioned PCs in a 100-ns SMD simulation of the bound state, metastable state where the subunit interface from which the with the artificial force in the direction of subunit D–E angle nucleotide is released opens to ∼64°, while the nucleotide re- widening (SI Appendix, Fig. S10B). Although the PCs explore a mains bound (Fig. 2A). This metastable state is separated from smaller range of values, the intersubunit angle variations in the the (essentially symmetric) global minimum by a free energy nucleotide-bound state clearly result in changes to the first two barrier that is less than 2 kcal/mol, indicating that interconver- PCs, which remain the most dominant modes. sion between the states is thermally accessible. To understand the significance of the large-angle asymmetric state, we pro- A-Loop Conformation Is Coupled to the Intersubunit Angle. We now jectedtheumbrellasamplingdataontoanewCVspacecon- use our simulation results to elucidate possible mechanisms of sisting of the subunit D–E angle and the electrostatic interaction KaiC regulation. As discussed in the Introduction, an outstanding energy of water with the active-site residues discussed above question is how KaiA promotes phosphorylation. Previous work (K294, T295, E319, and D378) (Fig. 2D). This free energy suggests that KaiA binding stabilizes structures known as the A- surface indicates that the subunits with a larger angle allow loops (residues 486–498, preceding the C-terminal tails of KaiC) stronger interactions between active-site residues and solvent, in an extended conformation (23, 62). Thus, we explored whether facilitating nucleotide release. The existence of asymmetric the umbrella sampling simulations resulted in structures with ex- quaternary states that are thermodynamically stable in CII is tended A-loops, with a view toward understanding the impact of consistent with the observation of a mixture of loose and tight KaiA binding on the KaiC structure. subunit interfaces in a high-resolution CI crystal structure We observed that the A-loop in subunit D sampled an ex- (PDB ID code 4TLA) (39), although the largest angle observed tended conformation during nucleotide release (Fig. 4A), albeit therein is only 61.7°. to a lesser extent than that in an NMR structure of a KaiA Given the existence of multiple metastable states distinguished fragment in complex with the KaiC C terminus (23). We only by the intersubunit angles, we sought to determine if there are observe this state in subunit D (Fig. 4A and SI Appendix, Fig. additional large-scale quaternary conformational changes that S11), which suggests that it is a specific response to Mg·ADP are associated with the release process but are not described by dissociation. To quantify this behavior, we calculated the angle the angles. To detect such motions, we applied principal com- formed by three atoms at the beginning, middle, and end of the

4of10 | www.pnas.org/cgi/doi/10.1073/pnas.1812555115 Hong et al. Downloaded by guest on September 26, 2021 Fig. 3. PCA reveals large-scale conformational changes during nucleotide release. (A) PC1 repre- sents the formation of a split washer structure in CII, and (B) PC2 represents a circular compression in both domains. In A and B, arrows show the Cα difference vectors between a pair of umbrella-sampling struc- tures representing the extremes of motion along each PC, aligned to minimize the difference in the CII domain of subunit D. Structures in A are chosen to have similar PC2 values, and structures in B are chosen to have similar PC1 values, such that the differences shown approximate motions in only the PC of interest. (C) Conformations of the CII domain in the low PC1 (Left) and high PC1 (Right) structure, respectively. The side-by-side comparison indicates BIOPHYSICS AND that the PC1 eigenvector points in the direction of increased helical pitch in the CII domain. COMPUTATIONAL BIOLOGY

A-loop (Fig. 4B) and projected the free energy onto this A-loop The simulation hints at two other potential mechanisms that angle and the subunit D–E angle. The resulting surface shows could couple the A-loop to the active site. First, the A-loop may that the A-loop is more likely to sample the extended state as the be both sterically and electrostatically coupled to the active site β – β subunit D–E angle widens (Fig. 4C). Because we expect allostery via a -hairpin (residues 436 459, which we denote AL)(SI β to be bidirectional (reflecting the fact that free energies are state Appendix, Fig. S12A). AL is located directly between the active site and the A-loop and harbors R451, which can interact elec- functions) (63), this finding is equivalent to A-loop extension trostatically with the ADP, as well as E444, which forms a salt favoring a larger intersubunit angle, or, taking this logic one step bridge with R496 in the A-loop. More specifically, βAL is in- further, KaiA binding favoring a larger intersubunit angle. Given volved in contraction of subunit D (SI Appendix, Fig. S12 B and the importance of the intersubunit angle for the energetics of C) as the ADP–subunit D distance reaches around 10–11 Å, a nucleotide release, detailed in previous sections, the coupling of point at which the free energy increases sharply (Fig. 2A). This KaiA binding to intersubunit angle opening may mechanistically contracted state is characterized by (i) a subtle movement of αlα, explain its ability to act as a nucleotide exchange factor. βAL, and the A-loop, (ii) a decrease in the distance between the

Fig. 4. The A-loop (residues 486–498) is coupled to nucleotide release. (A) The A-loop (blue) of subunit D (yellow) samples an extended conformation. (B) The structure of the subunit D A-loop in buried and extended states can be quantified using the angle formed by the Cα atoms at residues 486, 490, and 496, which are represented as gray spheres. The values of this A-loop angle are 33.6° and 75.8° in the buried and extended states shown in B. The subunit D–E angle values in the buried and extended structures are 62.9° and 65.7°, respectively. (C) Projection of the umbrella sampling data onto the CV space consisting of the A-loop angle and the subunit D–E angle shows that a more extended subunit D A-loop conformation is correlated with a larger subunit D–E angle.

Hong et al. PNAS Latest Articles | 5of10 Downloaded by guest on September 26, 2021 R451 side chain on βAL and the α-phosphate group on ADP from favored by reduced CI/CII contact. The simulations thus suggest ∼8.6 Å to 4.5 Å, and (iii) a remodeling of the release channel targets for further study of CI/CII interactions. due to the nucleotide movement. Among these conformational changes, the movement of ADP toward R451 has the most ob- Discussion vious consequences for the energetics of the release pathway. Our simulations can be synthesized into a model of the molec- βAL thus connects the binding affinity of ADP (through the ular events in the oscillator cycle. Near dawn, KaiC is largely R451–ADP interaction) with the A-loop conformation. unphosphorylated (9); while phosphorylation can occur, it is not Second, the simulation suggests that A-loop conformation is sustained because the ADP retained in the CII active site allows coupled to the active-site phosphorylation state through the 422- rapid dephosphorylation (18, 19). As KaiA is released from in- loop (64) (SI Appendix, Fig. S13), so called because the A422V hibitory complexes, it binds the A-loop and stabilizes an ex- mutation alters the amplitude and phase-resetting behavior of tended conformation (23), favoring the opening of subunit the oscillator in vivo (65). Our results suggest that the 422-loop interfaces and exchange of ADP for ATP in solution. This shifts couples to the active site via a water-mediated hydrogen-bond the equilibrium toward phosphorylation, which occurs first on network between pT432 and D417, a residue on the 422-loop. T432 and then on S431 (20). During this part of the cycle, CI This interaction, however, can be disrupted as the 422-loop slowly hydrolyzes ATP (39), but the product ADP molecules can moves away from the active site and forms hydrophobic con- be rapidly exchanged with ATP in solution (29), possibly because tacts with the A-loop. In the release simulation, these two states the CI/CII linker is in a favorable conformation similar to the appear to exist in a dynamic equilibrium, which presumably can extended A-loop (discussed below). Phosphorylation on T432 be shifted by the phosphorylation state of KaiC and the binding favors A-loop extension, encouraging further phosphorylation of KaiA, thus making the 422-loop a potential feedback mech- (67). However, subsequent phosphorylation of S431 presumably β anism that communicates the KaiC phosphorylation state back to results in conformational changes in the CI/CII linker and the I/II the A-loop to modulate KaiA binding. This idea is consistent hairpin, among others, that restrict the ability of CI to release with the observations that, even in the absence of KaiB, KaiC ADP. Inhibition of ADP release in CI when S431 is phosphory- phosphorylation is less sensitive to KaiA in the pS431 state (32) lated may explain why phosphomimetic mutants show decreased and the binding affinity of KaiA to KaiC is reduced in the ATP hydrolysis at steady state (68). As CI ATPase activity causes pS431 and doubly phosphorylated (pT432/pS431) states (66). ADP to accumulate, the B-loop adopts an extended conformation that allows KaiB to bind (28). KaiB cooperatively assembles in a CI/CII Interaction Is Mediated by a CI β-Hairpin. As discussed in the ring-like structure on the CI domain (31), which may further re- Introduction, KaiB binding to CI is an important feedback pro- strict nucleotide release from CI. KaiB bound to KaiC adopts an cess that allows oscillations to occur. The formation of the alternative fold which can then bind to and inhibit KaiA (27, 28, KaiB·KaiC complex appears to be determined by the retention 31). Sequestration of KaiA limits nucleotide exchange in CII, such of ADP in CI after hydrolysis (28, 31) and is critically dependent that CII tends to dephosphorylate (9), first T432 and then S431 on the S431 phosphorylation of the distal CII domain (20, 32, (20), returning KaiC to the beginning of the cycle. 33). How the phosphorylation state in CII is communicated to CI This model raises the question of how Kai systems that lack Prochlorococcus to allow KaiB binding is a major unresolved question. Based on KaiA, such as those from the marine cyano- bacterial species (69), are able to build up their KaiC phos- gel filtration experiments that monitor the binding of separated phorylation levels (70). A plausible answer comes from the fact CI and CII domains with phosphomimetic mutations, it has been that such KaiC sequences are truncated near the A-loop, com- suggested that, when CII is in the pS431 state, it “stacks” more pared with S. elongatus KaiC (70). Previous experiments on S. tightly with CI, even in the absence of the linker that tethers the elongatus KaiC demonstrated that truncating the A-loop can two domains together (67). Because ADP does not accumulate result in KaiA-independent, constitutive hyperphosphorylation in the isolated CI ring, but ATP hydrolysis still occurs (29), a (23), which suggests that an analogous mechanism may allow plausible hypothesis is that phosphorylation-dependent interac- Prochlorococcus KaiC to autophosphorylate without KaiA. Our tions between CII and CI inhibit nucleotide release from CI. We simulations thus make the prediction that Kai systems that lack thus examined the CI/CII interactions in our umbrella sampling KaiA should have KaiCs with active sites that are more acces- simulation data to determine if there were structures that could sible to molecules in solution, obviating the need for KaiA-like provide hints about how information is communicated between nucleotide exchange factors. Relative solvent accessibilities of CI and CII. different KaiCs should be measurable with hydrogen–deuterium We observed changes in linker-independent CI/CII contact, as exchange mass spectroscopy (71). measured by their van der Waals interaction energy (SI Appen- A striking feature of the simulation structures is their broken dix, Fig. S14A). We specifically did not include the linker in the C6 symmetry, especially the split washer and ring compression energy calculation to mimic the CI/CII domain stacking experi- motion observed in the PCA. This is consistent with a recent ment (67). Because the PCA results, detailed in a previous sec- crystal structure of the CI domain with a mixture of bound ATP tion, revealed motions between the two domains, especially and ADP, which resulted in heterogeneous subunit structures along PC1, we hypothesized that the CI/CII contact energy that correlate with the hydrolysis states of the active sites (39). should change with the values of the PCs. However, we found In addition to nucleotide binding, KaiA binding is another po- that its variance could not be explained by projection onto the tential source of KaiC asymmetry. Biochemical studies suggest 10 largest PCs. Instead, changes in CI/CII contact energy are that one dimer of KaiA is sufficient to stimulate the phosphor- largely mediated by interactions between the CII domain and six ylation of a KaiC hexamer (72). Even if this is the case, the β – β -hairpin structures (residues 203 226, which we denote I/II), structures that we observe in our simulations indicate that nu- β one in each KaiC subunit (SI Appendix, Fig. S14B). I/II is part of cleotide exchange is not likely to occur simultaneously at all sites. the β-sheet structure at the hydrophobic core of each CI globular This model is consistent with the asymmetric conformations domain, and its secondary structure can become frayed near the observed for other ring-shaped oligomeric ATPases, especially turn region. When the two domains separate, the turn region of those in the AAA+ and RecA/DnaB superfamilies (38, 73, 74). βI/II moves away from the CII domain while leaving the rest of The split washer structure of KaiC is also found in AAA+ the CI/CII interface largely unchanged (SI Appendix, Fig. S14 C ATPases such as the bacterial replicative helicase DnaB (75), the and D). Salt bridges connect neighboring βI/II hairpins: R216– simian virus 40 replicative helicase Ltag (76), as well as NSF, a E221 is stable throughout our simulations, and E214–R217 is eukaryotic protein involved in SNARE complex disassembly

6of10 | www.pnas.org/cgi/doi/10.1073/pnas.1812555115 Hong et al. Downloaded by guest on September 26, 2021 during membrane trafficking (35). In DnaB, NSF, and KaiC, the Conclusions split in the hexameric ring is located at an apo subunit interface, In this paper we implemented a pipeline of enhanced sampling suggesting that the split interface is implicated in nucleotide methods for MD to elucidate and quantitatively characterize the exchange. The parallel between KaiC and NSF is especially pathway for ADP release from KaiC, a homohexameric ATPase striking because, similar to KaiC, the D1 and D2 domains of NSF that serves as the central component of the cyanobacterial cir- also assemble into double-tiered ring structures with distinct cadian clock. Nucleotides bind at the interface of KaiC subunits, functions. These split washer structures are reminiscent of the and the energetics of its release are dominated by the interplay helical structures of the RecA filament, where the helical pitch is of active-site solvation with electrostatic interactions among + dependent on the states of the nucleotides bound to the subunits charged active-site residues, the Mg2 ion, and the ADP phosphate (49, 51). However, the helical pitches observed in the non- groups. The calculations suggest that the C6 symmetry of the filamentous proteins are much smaller. Taken together, it is hexamer is broken during operation, with the interface opening likely that the hexameric ATPases can access similar quaternary in a split washer fashion. We identify specific interactions that conformational spaces despite their significant sequence and couple this opening to extension of the A-loop, providing a functional divergences. This idea raises the possibility that KaiC molecular mechanism for the role of KaiA as a nucleotide ex- may be able to access other symmetry-broken states that are change factor for KaiC. Parallels between structural elements in notexploredinoursimulationsbutareobservedinother the two homologous domains of the protein suggest the intriguing hexameric ATPases, such as a conformation with C symmetry 2 possibility that CII may serve as a nucleotide exchange factor for (i.e., a dimer of trimers), observed in the unfoldase ClpX (34), CI. Overall, the information that the simulations provide about or a conformation with C3 symmetry (i.e., a trimer of dimers), observed in the replicative helicase DnaC of Geobacillus structures accessible to KaiC reveal fruitful connections to kaustophilus HTA426 (77). Analysis of cryo-EM data without other ATPases. symmetry averaging may reveal such states. Alternatively, a bis- Methods His motif (78) or disulfide bond can be engineered at the subunit System Setup. The initial coordinates of S. elongatus KaiC with bound ATP interface to limit the angle motion, which should lead to a de- + and Mg2 were obtained from the PDB (ID code 3DVL) (47). The structural crease in the nucleotide release rate. water was retained, and the C-terminal tail (residues 499–519) in each sub- An outstanding question for KaiC is whether its asymmetric unit was deleted to reduce the size of the system. In the 3DVL structure, + features propagate around the ring in an ordered fashion, as is which has a resolution of 2.8 Å, no Mg2 was present in the CI ATP binding

2+ BIOPHYSICS AND believed for F1-ATPase, or in a stochastic fashion, as is believed sites. We introduced Mg into all six CI nucleotide-binding sites using the 2+ for ClpX (79). An indirect way of distinguishing these possibili- Mg coordinates from a 1.94 Å resolution KaiC CI structure (PDB ID code COMPUTATIONAL BIOLOGY ties would be a mutant doping (80) or covalent linking (79) ex- 4TL7) (39) after aligning the ATP molecules modeled in each chain in the two + periment where WT and CII-catalytically dead subunits are structures. In 4TL7, the CI Mg2 is coordinated by T53Oγ1, Oγ3, and Oβ2of mixed in a single KaiC hexamer. Because a stochastic mechanism ATP and three water molecules, which are absent in 3DVL. To complete the 2+ implies independent catalytic cycles at individual active sites, the octahedral Mg coordination geometry, we added three water molecules hybrid protein should still be able to function in the full oscil- to each CI active site based on the 4TL7 crystal water positions and changed lator. However, a sequential/rotary mechanism would predict the coordinates of the three phosphate groups in ATP to those in 4TL7. We used a similar procedure to model Mg·ADP in the CII nucleotide-binding abolition of oscillation, because the dead subunits would prevent sites, using the Mg·ADP coordinates in a 1.8-Å resolution, ADP-containing propagation of activity around the ring. Indeed, it is already CI structure as a reference (PDB ID code 4TLA) (39). known that catalytically dead CII subunits can be efficiently The subunits in the 3DVL crystal structure are in either the pT432 or pT432/ phosphorylated when mixed with WT CII (81). pS431 states. In the doubly phosphorylated subunits, we deleted the phos- We also speculate here on how our analysis of the nucleotide phate group on S431 and retained the phosphate group on T432 to mimic the release pathway in CII may shed light on the regulation of nu- pT432 phosphorylation state. Together, the nucleotides and phosphorylation cleotide release in CI. Given that the CI/CII double-ring struc- states mimic a KaiC with CI in the prehydrolysis state and CII in a kinase ture likely arose as a result of gene duplication (16), it is product state during the initial phosphorylation phase of the oscillator. unsurprising that the CI and CII structures share many similar- The model system was solvated in a cubic box of TIP3P water molecules, ities (Fig. 5). In particular, the CI structural element homologous and the final dimensions of the box were 132 × 132 × 132 Å. The system was neutralized and then brought to a final concentration of 150 mM KCl, which to the A-loop is the linker between the CI and CII domains, + − which adopts a conformation in the crystal structure that is represents 194 K ions and 122 Cl ions. The total number of atoms in the – reminiscent of an NMR A-loop structure in complex with KaiA system was 216,892. The system was setup using CHARMM-GUI (82 84). All (23, 24). Given the importance of the A-loop in regulating nu- molecular visualizations were made in VMD 1.9.2 (85). Further details on the system setup are provided in SI Appendix, Supplementary Methods. cleotide release in CII, this apparent analogy raises the possi- bility that CII may act on CI through the linker in a way that is Minimization and Equilibration. Unless otherwise specified, all MD simulations similar to how KaiA acts on CII through the A-loop. If KaiA is were performed using GROMACS 5.1.4 (86), with the CHARMM36 force-field a nucleotide exchange factor for CII, then it follows that CII parameters for the protein (with CMAP correction) (87–89), TIP3P water (90), may act as a nucleotide exchange factor for CI and regulate its ions (91), and the nucleotides (92). The energy of the system was minimized intersubunit angle opening. This proposal makes the prediction with the steepest descent method, until the largest force in the system was that when CII is in a pS431 state that favors KaiB binding, the smaller than 1,000.0 kJ/mol·nm. The system was equilibrated in the NVT en- CI/CII linker may adopt an alternative conformation that is more semble for 25 ps with a 1-fs integration time step, followed by the NPT en- similar to the buried A-loop in CII. Furthermore, the βAL and βI/II semble for 10 ns with a 2-fs integration time step. The positions of all hairpins, two structural features that our simulations suggested nonhydrogen atoms in the protein and its ligands were constrained during energy minimization and the NVT equilibration runs to stabilize the protein deserve further study, are also homologous in the two domains 2+ (Fig. 5). It would be interesting to disrupt contacts at the CI/CII structure and enforce the octahedral Mg coordination geometry. The interface by mutating residues in the R216–E221 and E214– temperature of the simulations was set at 303.15 K using the modified Berendsen thermostat with a time constant of 1.0 ps. For the NPT simulations, R217 salt bridges, in the hope of decoupling the two rings from the pressure was set at 1 bar using Parrinello–Rahman coupling with a time each other, which should result in dysregulation of KaiB binding β constant of 5.0 ps. Periodic boundary conditions were employed, and the and/or KaiA sequestration. Because AL likely couples the A-loop particle-mesh Ewald method (93) was used to calculate electrostatic forces to the active site, this parallel suggests that there may be un- with a real space cutoff distance of 1.2 nm. The Lennard-Jones forces were explored similarities between the mechanism of CI/CII interaction smoothly switched off from 0 to 1.2 nm. All bonds to hydrogen atoms were and KaiA∙KaiC interaction. constrained using the LINCS algorithm (94) in the NVT and NPT simulations.

Hong et al. PNAS Latest Articles | 7of10 Downloaded by guest on September 26, 2021 Fig. 5. CI and CII share similar conformations. In A and B, Secondary structural elements identified by the simulations as important for nucleotide release from CII (A) and their homologs in CI (B) are colored in blue. In each case, the structure shown is the domain from the D subunit of the crystal structure (PDB ID code 3DVL).

Locally Enhanced Sampling. Locally enhanced sampling (40–42) was used the residues in the two subunits separately largely decouples the inter- initially to explore the structural changes at the active sites during nucleo- subunit angle from the progress of the Mg·ADP out of the protein. tide release (Fig. 1B and SI Appendix, Fig. S1). All locally enhanced sampling simulations were performed using the implementation available in NAMD String Method. To initialize the images of the string, we selected 24 structures 2.9 (95) with CHARMM36 force-field parameters. The structure and topology that are roughly equally spaced along the SMD pathway in the CV space of files required for the simulations were generated using the psfgen plugin subunit D–E angle and ADP–subunit D distance and then equilibrated them for VMD 1.9.2 (85). Specifically, each of the six Mg·ADP bound to CII active for 5 ns with restraints in the same CV space. The pathway was then refined sites was duplicated 200 times. The Mg·ADP copies at each active site do not by the string method with fixed end points, as described in ref. 44, imple- interact with each other, while their intra- and intermolecular interactions mented as an in-house Python wrapper for GROMACS and PLUMED. Briefly, were scaled down by a factor of 200. To preserve the structural integrity of at each iteration of the calculation, each structure was equilibrated with a the ADP molecules, the force constants for all bond, angle, dihedral angle, harmonic restraint centered on the images for 20 ps. The string path was and improper dihedral angle terms for ADP were manually multiplied by then updated via 200; in addition, an artificial bond with a force constant of 60,000.0 kcal/mol·Å2 and equilibrium bond length of 2.91 Å was added between the P and X8 ∂FðxnðτÞÞ xnðτ + ΔτÞ = xnðτÞ − Δτ P ðxnðτÞÞ α β i i ij ∂ n . P3 atoms to prevent the - and -phosphate groups from collapsing onto = x + j 0 j each other. To preserve the interaction between each Mg2 and its associ- ated ADP, another artificial bond with a force constant of 40,000.0 kcal/mol·Å2 nðτÞ τ Here, the ith CV evaluated at the nth image is denoted as xi , and tracks and equilibrium bond length of 2.50 Å was added between the P3 and MG the progress of the gradient descent in the CV space. The local gradient ∇F atoms. Further details on the simulation setup are provided in SI Appendix, was computed as the average displacement from each image during a 50-ps Supplementary Methods. production run, scaled by the force constants. The matrix P removes the component of ∇F parallel to the string at each image. The string was SMD. Constant-velocity SMD simulations (43) were done using the moving propagated with a constant multiplier Δτ = 0.0001. The updated string is restraint functionality in PLUMED 2.3 (96), which applies a time-dependent linearly interpolated and smoothed before the next iteration. We did not 2 bias of the form UðxÞ = ð1=2Þκðx − x0ðtÞÞ to a given CV x; here, κ is the force apply any correction for nonlinear dependences between the CVs. constant and x0ðtÞ is the center of the biasing potential. The CVs used in the The string calculation employed nine CVs, described in SI Appendix, Table SMD and subsequent string and umbrella sampling calculations are defined S1. The force constants used in the production runs were 10,000 kJ/mol·rad2 in SI Appendix, Table S1. for the angle variables and 2,000 kJ/mol∙nm2 for the distance variables. The As described in Results, we used SMD to construct an initial pathway for force constants used in equilibration were twice as large. We found that the string calculations; this pathway was generated in three steps. First, to 30 iterations of the string simulations were sufficient for generating a open the intersubunit angle, a harmonic bias with a force constant of qualitatively reasonable pathway, which we used to initialize the umbrella 100,000 kJ/mol·rad2 was applied to the subunit D–E angle, and the center of sampling (SI Appendix, Supplementary Methods and Figs. S15 and S16). the potential was moved linearly, over the course of 1 ns, from 1.04 rad to 1.23 rad. Second, to pull out the ADP, a harmonic bias with a force constant Umbrella Sampling and Analysis. We performed umbrella sampling calcula- of 1,000 kJ/mol·nm2 was applied to the ADP–subunit D distance, and the tions (46) using the harmonic restraint functionality in PLUMED 2.3. Images center of the potential was moved linearly from 0.8 nm to 3.0 nm over the from the string simulations were used as starting structures, and additional course of 1 ns. During the ADP pulling simulation, the subunit D–E angle was windows were added iteratively using structures generated from existing restrained at 1.23 rad. Finally, the subunit D–E angle was closed from windows until overlapping coverage was achieved for the free energy basin 1.23 rad to 1.13 rad using the same protocol as that in the first step, while surrounding the minimum free energy pathway in the 2D subspace of the the ADP–subunit D distance was restrained at 3.0 nm. ADP–subunit D distance and subunit D–E angle. The force constant on the We note that splitting the active-site residues by their subunit membership ADP–subunit D distance ranged from 2,000 to 60,000 kJ/mol·nm2,and and steering on ADP–subunit D distance and/or ADP–subunit E distance in- the force constant on the subunit D–E angle ranged from 10,000 to dependently provided better control of nucleotide position in SMD simula- 600,000 kJ/mol·rad2, depending on the local free energy gradient. Each tions (and subsequent string and umbrella sampling simulations) than a window was simulated for either 5 ns or 3 ns, depending on the area of the single CV measuring distance to the center of mass of all active-site residues. CV space covered, and the first 1 ns was discarded for subsequent analysis. This is because the value of the intersubunit angle variable affects the Overall, a total of 3.18 μs of simulation time distributed over 849 windows overall center of mass of the active-site residues; tracking the distances to was used to construct the free energy surface.

8of10 | www.pnas.org/cgi/doi/10.1073/pnas.1812555115 Hong et al. Downloaded by guest on September 26, 2021 EMUS (97) was used to construct the free energy surface (SI Appendix, Fig. Interaction Energy Calculations. Energy calculations for the analyses in Fig. 2D S17A) and estimate the error associated with the free energy (SI Appendix, and SI Appendix, Figs. S7 and S14 A and B were done with the NAMDEnergy Fig. S17C). WHAM (98, 99) yielded comparable results (SI Appendix, Fig. 1.4 plugin for VMD using the same force field as that in the simulation. The S17B). The method for calculating averages conditioned on the CV coordi- energy calculation used a switch function with a distance of 10 Å and a nates (SI Appendix, Figs. S7, S14A, and S16) is detailed in SI Appendix, cutoff distance of 12 Å for nonbonded interactions and did not employ Supplementary Methods. To find the free energy projection onto additional periodic boundary conditions. CVs not used in the umbrella sampling (Figs. 2D and 4C), we reran the EMUS calculation with a fictitious restraint on the additional CVs with zero force constant and then averaged over the original CVs that were not of interest. PCA. The PCA of KaiC structures (Fig. 3 and SI Appendix, Figs. S10 and S16) was done using the NMWiz 1.0 plugin for VMD (102). KaiC structures + Mg2 Standard Binding Free Energy Calculation. The standard binding free obtained from umbrella sampling were down-sampled to every 1 ns and energy of Mg2+ to a CII active site populated with ADP is estimated indirectly aligned by their CII subunit D structures. Only the Cα positions for residues via a thermodynamic cycle using the double annihilation method; the 20–497 in all six subunits were used for the analysis. No reweighting was method is outlined in ref. 59, and the discussion below uses the notation performed for the PCA. The projection of each structure onto a PC was therein. The starting structure was obtained from an equilibrated system calculated by finding the dot product of the normalized PC eigenvector with · 2+ with CII-bound Mg ADP. The Mg to be removed is restrained at its equi- the displacement vector of each structure from the average umbrella sam- Δ site librium position using a set of harmonic biasing potentials ( Gt ) to elimi- pling structure (without reweighting). nate the wandering ligand problem (100) before decoupling from the −Δ site ligand-binding pocket ( Gint ) using alchemical free energy perturba- Structural and Sequence Alignment. All structural alignment (Fig. 5) was done tion (AFEP) (101). The harmonic positional restraints are then removed ∘ using STAMP (85, 103, 104), and all sequence alignment (SI Appendix, Table (−RT ln Ft C ; discussed further in SI Appendix, Supplementary Methods). A + S2) was done using CLUSTAL Omega (105, 106). The sequences used in the separate cubic TIP3P water box (60 Å each side) with one Mg2 and 150 mM analysis in SI Appendix, Table S2 and their annotation were directly obtained KCl was used to calculate the coupling free energy in water (ΔGbulk). Taken int from datasets published with (60), which are available at https://figshare. together, the standard binding free energy is com/articles/Processed_Data/3823899/3. Δ ∘ = −Δ site + Δ site + ∘ − Δ bulk Gbind Gt Gint RT ln Ft C Gint . ACKNOWLEDGMENTS. We thank Andy LiWang and Glen Hocky for critical The values for each individual term contributing to the standard binding free readings of the manuscript. This work was supported by NIH Grants energy are listed in SI Appendix, Fig. S8, along with a thermodynamic cycle GM109455-02, GM107369, and EY025957 and by a MolSSI Fellowship Δ site (to E.H.T.). Computations were performed on resources provided by the Univer- illustrating their relations. With the exception of Gint , the free energy calculations appeared well-converged (SI Appendix, Fig. S9). The value of sity of Chicago Research Computing Center, the Beagle computer at the BIOPHYSICS AND

Δ ∘ Δ site University of Chicago and Argonne National Laboratory (NIH Award COMPUTATIONAL BIOLOGY Gbind reported in Results is based on the value of Gint in the forward AFEP transformation, which most favors the alternative mechanism. Further de- 1S10OD018495-01), and the Extreme Science and Engineering Discovery tails of the simulation protocol are provided in SI Appendix, Supplementary Environment (107) (NSF Grant ACI-1548562) Comet (SDSC) and Bridges (PSC) Methods. computing nodes through allocation TG-MCB180007.

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