a r t i c l e s

The energy landscape of adenylate kinase during catalysis

S Jordan Kerns1,4,5, Roman V Agafonov1,5, Young-Jin Cho1,4,5, Francesco Pontiggia1,5, Renee Otten1, Dimitar V Pachov1, Steffen Kutter1, Lien A Phung1, Padraig N Murphy1, Vu Thai1,4, Tom Alber2, Michael F Hagan3 & Dorothee Kern1

Kinases perform phosphoryl-transfer reactions in milliseconds; without enzymes, these reactions would take about 8,000 years under physiological conditions. Despite extensive studies, a comprehensive understanding of kinase energy landscapes, including both chemical and conformational steps, is lacking. Here we scrutinize the microscopic steps in the catalytic cycle of adenylate kinase, through a combination of NMR measurements during catalysis, pre-steady-state kinetics, molecular-dynamics simulations and crystallography of active complexes. We find that the Mg2+ cofactor activates two distinct molecular events: phosphoryl transfer (>105-fold) and lid opening (103-fold). In contrast, mutation of an essential active site arginine decelerates phosphoryl transfer 103-fold without substantially affecting lid opening. Our results highlight the importance of the entire energy landscape in catalysis and suggest that adenylate kinases have evolved to activate key processes simultaneously by precise placement of a single, charged and very abundant cofactor in a preorganized active site.

Phosphate esters and anhydrides are high-energy linkages that are schemes to account for the role of Mg2+ in catalysis19. Other heated extremely resistant to nucleophilic attack and therefore are funda- debates have focused on the role of conformational changes in mental to genomic stability, long signaling-state lifetimes and stor- the enzymatic reaction20–25. Quantitative descriptions of the age of biochemical energy1–4. Although stability is critical, organisms entire energy landscape of catalysis are necessary to reconcile must respond rapidly and effectively to their environment and have these different mechanisms including the canonical role of Mg2+ in therefore evolved enzymes that catalyze transfer of phosphoryl groups kinase catalysis. with exquisite specificity and enormous rate accelerations relative To address this, here we have performed a comprehensive inves- to the uncatalyzed reactions in solution5–10. Impressive progress has tigation of the adenylate kinase (Adk) energy landscape and have been made in understanding protein phosphorylation in cellular quantified multiple kinetic states along the reaction pathway at atomic Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature processes11,12, and fundamental work on nonenzymatic phosphoryl resolution. Adk is a ubiquitous and essential P-transfer enzyme found transfer (P-transfer) has delivered a deep mechanistic understanding in all cells. Adks reversibly transfer a phosphoryl group from ATP of P-transfer in solution5–10; however, a comprehensive understand- to AMP, thereby maintaining the equilibrium between cytoplasmic npg ing of kinase-catalyzed phosphorylation is still lacking despite the nucleotides (Fig. 1a). During the enzymatic cycle, Adk undergoes wealth of literature on many different P-transfer enzymes5,13. This large conformational changes by opening and closing of the ATP lid includes crystal structures that reveal conservation in the active site and AMP lid, defined as the regions that close over the Mg-ATP– and accompanying domain architecture14; kinetic studies that estab- and AMP-binding sites, respectively (Fig. 1a). Unlike many protein lish the rate-limiting steps and the order of events13; and NMR that kinases that are activated by protein-protein interactions or covalent links local fluctuations to global protein dynamics15,16. modifications14, Adk is fully active in the presence of its nucleotide However, catalysis is typically composed of multiple microscopic substrates, and it catalyzes a reversible reaction. This provides a steps spanning a hierarchy of time and space, and this often obscures tractable framework for quantitative analysis of the reaction-energy the underlying molecular mechanisms. This has led to persistent landscape. Using complementary techniques to examine the enzyme controversies regarding, for example, the role of the Mg2+ cofac- during catalysis across many orders of temporal and spatial resolution, tor in kinase catalysis. Whereas some kinases are activated by a we separated the microscopic steps of P-transfer and conformational single Mg2+ ion, additional Mg2+ binding may be required for full motions with pre-steady-state kinetics and NMR dynamics experi- activation, may result in inhibition or may be involved in structural ments, investigated the mechanism of transition-state stabilization by stabilization13,17,18. The variety of different mechanisms attributed crystallography and explored the active site dynamics by molecular to the Mg2+ cofactor has resulted in arguments about the kinetic dynamics (MD) simulation. Combined, these results reveal the major

1Howard Hughes Medical Institute, Department of Biochemistry, Brandeis University, Waltham, Massachusetts, USA. 2Deceased. 3Department of Physics, Brandeis University, Waltham, Massachusetts, USA. 4Present addresses: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, USA (S.J.K.), New Drug Development Center, Daegu-Gyeongbuk Medical Innovation Foundation, Daegu, Korea (Y.-J.C.) and Department of Molecular, Cell, and Developmental Biology, University of California Santa Cruz, Santa Cruz, California, USA (V.T.). 5These authors contributed equally to this work. Correspondence should be addressed to D.K. ([email protected]). Received 20 October 2014; accepted 26 November 2014; published online 12 January 2015; doi:10.1038/nsmb.2941

124 VOLUME 22 NUMBER 2 FEBRUARY 2015 nature structural & molecular biology a r t i c l e s

players responsible for the overall rate acceleration and address the the active site, we soaked crystals in crystallization solution contain- key question of how the enzyme dramatically lowers the energy bar- ing 20 mM Mg2+ at an elevated pH of 9. A comparison between the rier of P-transfer and accelerates conformational changes essential for structures with and without Mg2+ bound showed that they are very both efficient catalysis and suppression of detrimental hydrolysis. similar (Fig. 1c) except for the extra electron density of the Mg2+ and its coordination to the six ligands. It is notoriously difficult to RESULTS distinguish Mg2+ from structural water by electron density alone, and Mg2+ as electrostatic ‘pivot’ for phosphoryl transfer therefore the position of the Mg2+ in the presence of natural substrates Expanding on previous structural studies and to set the stage for is ambiguous in many cases30. Consequently, in order to unequivo- experiments to characterize the free-energy landscape, we obtained cally determine the position of the metal cofactor in the active site of a number of Adk crystal structures in multiple biochemical states the enzyme–substrate complex, we also obtained a structure of the (for example, with substrates, with and without metals and with a ternary AAdk–ADP–ADP complex in the presence of Co2+ (AAdk7; ­transition-state mimic). Many available structures of Adks have Fig. 1d)31. The position of the Co2+ ion derived from anomalous revealed in atomistic detail the conformational cycle between ligand- signal collected with the X-ray source at the Co2+ edge, together with free and ligand-bound states26–29. However, few have been solved with the electron density, confirmed that the positions of the Co2+ and natural substrates in an active quaternary complex, thus making it dif- Mg2+ ions are identical (AAdk11; Fig. 1d). From these structures, ficult to dissect how the enzyme activates P-transfer16. Here we present we propose that the metal cofactor helps to anchor the flexible donor a number of Aquifex aeolicus Adk (AAdk) structures bound to natural phosphoryl group for a more favorable attack by the oxygen nucleo­ substrates that have provided mechanistic insight into the catalysis of phile of the acceptor nucleotide. P-transfer (Tables 1 and 2). An overlay of many high-resolution snap- What happens to the active site players in the transition state (TS) shots of the AAdk–ADP–ADP ternary complex (AAdks 1–4 and 6) of the P-transfer reaction? Using aluminum fluoride as a transition- 32–34 2+ − revealed that the transferable phosphoryl group of the donor ADP and state analog , a structure of the AAdk–Mg –ADP–AMP–AlF4 its active site partner R150 showed conformational heterogeneity while quaternary complex was solved, and it revealed first that a square − the acceptor ADP was held rigidly (Fig. 1b). This hinted at movement planar tetrafluoroaluminate (AlF4) and not a neutral AlF3 was in of only the phosphoryl group of the donor ADP and not the nucleotide the active site (AAdk8). This agrees with the fundamental work acceptor during P-transfer. We note that presenting multiple redun- by Baxter and colleagues on the importance of balancing charge dant structures of crystal isoforms is unusual; however, a single struc- in active sites, a general principle that has been demonstrated for ture even with partial occupancy refinement would not illustrate this many P-transfer enzymes, including β-phosphoglucomutase, phos- observed conformational sampling in the active site. phoglycerate kinase, protein kinase A and UMP–CMP kinase2,35–37. − One of the most important components of enzyme-catalyzed Second, the AlF4 was positioned equidistantly between the accep- P-transfer, the Mg2+ cofactor, was not detected in the X-ray structures tor and donor phosphates, owing to a 1-Å movement of the latter of the AAdk–ADP–ADP ternary complex ‡ despite being present in the mother liquor a Uncatalyzed (Fig. 1b). To obtain a high-resolution struc- Forward ture of AAdk–ADP–ADP with magnesium in Mg-ATP + AMP Mg-ADP + ADP Reverse

Figure 1 Adk free-energy landscape of ATP lid Conformational

Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature Conformational ‡ ‡ catalysis and exploration of the P-transfer AMP lid change change step by X-ray crystallography. (a) Overall Chemical ‡ Adk reaction, minimal reaction scheme and step

corresponding schematic of the catalytic energy Free energy npg landscape based on the measured enzyme kinetics (Table 3). E represents the Adk enzyme Mg-ATP Mg-ADP + AMP in the scheme. Rate-limiting lid opening + ADP k fwd k fwd fwd ( ) is shown in red and is visualized closing chem kopening kopening Mg-ATP Mg-ATP Mg-ADP Mg-ADP E EAMP EAMP EADP EADP E by the open and closed structures. Open krev Closed rev Closed rev Open opening kchem kclosing (b) Superposition of AAdk structures with ADPs Reaction coordinate bound. Conformational heterogeneity of the donor phosphate group and R150 is highlighted in color. (c) Superposition of AAdk structures b c d R150 with bound ADPs in the presence (PDB 4CF7, ATP site R161 R150 R124 blue) and absence (PDB 4JL5, red) of Mg2+. R36 (d) Superposition of AAdk complexed with AMP site Mg2+–ADP–ADP (blue) and Co2+–ADP–ADP (PDB 4JKY, orange). The anomalous Acceptor Donor K13 scattering of the electron density at the R85 Co edge (λ = 1.609 Å) is shown as anomalous difference map contoured at 5.5σ (orange). 2+ − (e) Superposition of Mg –ADP–AMP–AlF4 (PDB 3SR0, green) with Mg2+–ADP–ADP e (blue). Detailed structures of the active site of 1.61 Å both the substrate–enzyme complex (blue) and 3.14 Å 2.2 Å 1.98 Å transition-state analog (green) showing metal 2+ coordination and relevant O-P or O-Al distances Mg (dashed lines; values in black) and the covalent O-P bond length (value in blue).

nature structural & molecular biology VOLUME 22 NUMBER 2 FEBRUARY 2015 125 a r t i c l e s

Table 1 Data collection and refinement statistics AAdk1 AAdk2 AAdk3 AAdk4 AAdk5 AAdk6 ADP–ADP ADP–ADP ADP–ADP ADP–ADP AMPPN–AMPPN ADP–ADP

Data collection

Space group P 212121 P 212121 P 212121 P 212121 P 212121 P 212121 Cell dimensions a, b, c (Å) 66.17, 69.56, 85.39 66.64, 70.54, 85.88 67.00, 73.73, 87.52 67.00, 74.72, 88.15 66.47, 71.56, 86.30 66.94, 73.89, 87.80 Resolution (Å) 29.0–1.24 (1.31–1.24) 42.9–1.55 (1.64–1.55) 37.6–1.53 (1.61–1.53) 38.0–1.79 (1.88–1.79) 43.2–1.65 (1.74–1.65) 43.9–2.12 (2.23–2.12)

Rmerge 0.062 (0.427) 0.139 (1.287) 0.072 (1.342) 0.105 (0.566) 0.065 (0.653) 0.174 (1.698) I / σI 22.1 (5.7) 8.1 (1.4) 18.8 (1.9) 14.5 (3.2) 11.9 (2.0) 7.8 (1.8) Completeness (%) 99.4 (96.2) 97.6 (93.5) 100.0 (99.8) 100.0 (100.0) 99.1 (98.0) 91.1 (99.9) Redundancy 14.0 (12.1) 11.5 (9.4) 14.0 (13.3) 12.0 (9.3) 6.8 (6.2) 6.5 (6.8)

Refinement Resolution (Å) 29.0–1.24 36.1–1.55 36.6–1.53 38.0–1.79 42.4–1.65 43.9–2.12 No. reflections 111,278 57,161 62,870 42,421 49,227 22,909

Rwork / Rfree 0.130 / 0.159 0.185 / 0.229 0.173 / 0.232 0.180 / 0.232 0.208 / 0.241 0.186 / 0.256 No. atoms Protein 7,181 3,360 3,306 3,386 3,365 3,256 Ligand/ion 195 108 108 108 108 108 Water 797 471 510 644 361 227 B factors Protein 16.1 24.6 28.1 21.5 33.5 39.2 Ligand/ion 9.7 18.7 21.2 16.7 26.0 31.4 Water 26.7 37.6 38.2 31.8 40.6 37.8 r.m.s. deviations Bond lengths (Å) 1.501 1.215 1.204 1.234 1.237 1.234 Bond angles (°) 0.010 0.006 0.005 0.007 0.007 0.008 The number of crystals for each structure is one.

(Fig. 1e and Supplementary Fig. 1a,b). Third, the Mg2+ cofactor was to execute P-transfer efficiently and avoid unproductive hydrolysis is clearly present and maintained its position and coordination partners impressive. From an evolutionary perspective, this striking difference ­relative to the AAdk–Mg2+–ADP–ADP quaternary complex (Fig. 1e in hydrolysis rates can be rationalized because Adks are abundant and Supplementary Fig. 1a,b). The position of the divalent ion proteins that are always active to maintain nucleotide homeostasis, (Fig. 1d,e and Supplementary Fig. 1a–c) was identical while the whereas many protein kinases are activated only transiently while phosphoryl group was transferred between the donor and acceptor participating in signaling cascades11,12. Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature sites, thus suggesting that the Mg2+ cofactor acted as an electrostatic What possible mechanisms does Adk use for such efficient suppres- pivot during P-transfer. In contrast, the active site R150 shifted in sion of destructive hydrolysis? An obvious way to prevent hydrolysis concert with the movement of the phosphoryl group. would be to exclude water from the active site; however, X-ray struc- npg tures showed that about 20 water molecules were trapped in the AAdk Active site dynamics probed by molecular-dynamics simulation active site cavity (Fig. 2d). It is likely that these waters helped reduce To test our hypothesis that Mg2+ helps organize the Adk active site the energetic penalty associated with desolvating the highly charged architecture by positioning the donor and acceptor phosphates in nucleotide substrates when binding to the active site. Rather than proximity, we performed 200-ns MD simulations on the closed excluding water from the active site to minimize hydrolysis, Adk AAdk–ADP–ADP ternary complex with and without Mg2+. tightly coordinates these water molecules, thereby sequestering them Simulations with Mg2+ showed a stable active site configuration from the phosphoryl groups. We investigated the stability of water in which both nucleotides experience limited fluctuations (Fig. 2a). molecules, present at the same positions in the active site of all crystal Water-molecule ligands to the metal ion were also stable and remained structures (AAdks 1–11), in long MD simulations (Supplementary coordinated during the simulation (Supplementary Fig. 1c,d). Figs. 1d and 2 and Supplementary Movie 1). Although the aver- In contrast, simulations in the absence of Mg2+ revealed that the active age positions occupied by these water molecules inside the pocket site, and in particular the donor phosphoryl group, samples a much agreed well with those identified in the crystal structures (Fig. 2d), larger distribution of states (Fig. 2b). These simulations indicate a the dynamic behavior of these waters was very different in the pres- substantially reduced probability of sampling productive conforma- ence and absence of Mg2+. Without Mg2+, the waters initially present tions without Mg2+, suggesting an appreciable stabilization of pre- inside the active site exchange with bulk solvent on a timescale of catalytic states by the cofactor38. 100 ns. However, in the presence of the metal cofactor the water mol- A major challenge for kinases is catalyzing P-transfer efficiently ecules inside the active site pocket are prevented from exchanging while suppressing the more favorable hydrolysis side reaction. For Adk with bulk solvent throughout the simulations (Supplementary Fig. 2 we measured an extremely slow hydrolysis rate of about 2 × 10−6 s−1 and Supplementary Movie 1). The terminal phosphates of the sub- (Fig. 2c) relative to the productive rate of P-transfer of about strates, Mg2+, and the four water molecules coordinating the metal 2 × 102 s−1. In comparison to other members of the kinase family with ion form a very stable complex (Supplementary Fig. 1d), serving hydrolysis rates in the range of 10−2 to 10 s−1 (refs. 39,40), Adk’s ability as a cap to block water exchange. In all simulations we performed

126 VOLUME 22 NUMBER 2 FEBRUARY 2015 nature structural & molecular biology a r t i c l e s

Table 2 Data collection and refinement statistics AAdk7 AAdk8 AAdk9 AAdk10 AAdk11 2+ 2+ − 2+ Co –ADP–ADP Mg –ADP– AMP–AlF4 R150K R150K Mg –ADP–ADP

Data collection

Space group P 212121 P 212121 P 212121 P 212121 P 212121 Cell dimensions a, b, c (Å) 67.55, 73.53, 87.47 65.95, 69.58, 85.67 67.17, 71.01, 85.83 67.01, 70.46, 85.58 64.09, 64.70, 86.26 Resolution (Å) 56.3–2.37 (2.50–2.37) 41.8–1.57 (1.65–1.57) 48.8–1.73 (1.82–1.73) 36.6–1.43 (1.51–1.43) 64.7–1.59 (1.64–1.59)

Rmerge 0.062 (0.198) 0.085 (0.310) 0.054 (0.123) 0.053 (0.268) 0.088 (0.622) I / σI 25.6 (9.8) 11.9 (3.7) 18.1 (6.5) 17.5 (4.3) 12.2 (3.1) Completeness (%) 99.7 (97.9) 99.7 (98.3) 99.9 (100.0) 99.9 (99.8) 100.0 (100.0) Redundancy 13.5 (12.7) 6.4 (4.8) 6.4 (5.0) 6.7 (5.1) 6.5 (6.7)

Refinement Resolution (Å) 53.5–2.37 41.8–1.57 42.4–1.73 36.1–1.43 40.3–1.59 No. reflections 17,150 56,016 43,855 74,937 48,566

Rwork / Rfree 0.199 / 0.267 0.148 / 0.189 0.161 / 0.210 0.153 / 0.195 0.182 / 0.216 No. atoms Protein 3,245 6,995 3,367 3,365 3,300 Ligand/ion 110 160 108 108 159 Water 144 759 518 703 335 B factors Protein 42.0 16.0 21.1 20.0 20.5 Ligand/ion 34.0 10.6 15.6 14.8 14.0 Water 37.4 28.1 32.7 33.6 28.0 r.m.s. deviations Bond lengths (Å) 1.276 1.515 1.222 1.253 1.328 Bond angles (°) 0.008 0.014 0.006 0.005 0.007 The number of crystals for each structure is one.

(with a combined run time of several microseconds), the water the inability to measure conformational dynamics for AAdk by NMR, molecules remained tightly coordinated at positions incapable of as explained in the next paragraph. To eliminate traces of divalent nucleophilic attack. We note that the discussed points are merely a metals from solution, we included EDTA in excess in all metal-free hypothesis, because hydrolysis happens on the timescale of hours, reactions performed (Supplementary Fig. 3d). For EAdk, Mg2+ accel- well beyond the timescales of lid opening and closing and the erated overall turnover by about five orders of magnitude, a result in MD regime41,42. agreement with the general notion that Mg2+ is essential for enzyme- Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature catalyzed P-transfer reactions. However, because lid opening and not Dissecting microscopic steps by rapid kinetics experiments P-transfer is rate limiting in the presence of Mg2+ (ref. 44), the actual Although Mg2+ has minimal impact on the Adk structure (Fig. 1c), it rate acceleration of the chemical step by Mg2+ must be even greater. npg is generally known that Mg2+ has an enormous effect on the turnover To catch the chemical step directly, we measured the pre-steady-state rate of P-transfer enzymes5,6,8,13. To determine the energetic contribu- rate of product formation by quench flow13 (Fig. 3 and Supplementary tion of Mg2+ to the overall rate acceleration of P-transfer, we measured Fig. 3e). With Mg2+, P-transfer on the enzyme was faster than lid turnover rates in the absence of Mg2+. a b For all kinetic and NMR experiments described below, we used R124 R150 Escherichia coli Adk (EAdk), which has identical active site architec- R150 R124 ture, catalytic mechanism and rate-limiting steps as AAdk (comparison AMP site of Fig. 3, Supplementary Fig. 3a–c and refs. 43 and 44), and higher AMP site catalytic efficiency at room temperature. This choice was rooted in

ATP site ATP site Figure 2 Role of active site dynamics in efficient P-transfer versus Mg2+ unproductive hydrolysis. (a,b) Superposition of representative snapshots of 200-ns MD simulations (n = 4) of the ADP–ADP ternary complex of AAdk 2+ 2+ c 2.0 d with Mg (yellow; a) and without Mg (b). (c) Unproductive ATP hydrolysis ADP by 100 µM of EAdk. Fit of the time dependence of nucleotide concentrations 1.9 −6 −1 yields a hydrolysis rate of ~2 × 10 s . (d) Overlay of the active site of 1.8 the crystal structure of AAdk bound to Mg2+–ADP–AMP–AlF − (green) 4 1.7 including bound water molecules (green spheres) and a typical snapshot AMP from a 200-ns MD simulation of the AAdk–Mg2+–ADP–ADP complex 1.6

(yellow). The transparent yellow spheres represent the isosurface of Concentration (mM) 1.5 ATP value 0.75 for the fractional occupancy of the water oxygen atoms 1.4 during the MD simulation. A cavity excluded from access to bulk solvent 0 50 100 150 200 250 (transparent green) is solvated by a number of water molecules. Time (h)

nature structural & molecular biology VOLUME 22 NUMBER 2 FEBRUARY 2015 127 a r t i c l e s

Figure 3 Catalytic effect of the Mg2+ a b c cofactor. (a–c) Pre-steady-state kinetics 2+ M) 60 2+ 2+ M) 500 500 120 µ

+Mg –Mg M) –Mg of EAdk at 25 °C measured by quench µ µ flow with Mg2+ in the forward (green) and 400 400 100 40 2+ 80 reverse (blue) direction (a) or without Mg in 300 300 200 60 150 M) either the forward direction (b) or reverse (c) 200 200 µ 20 40 100 direction (mean ± s.e.m.; n = 3 experiments). 100 100 ATP ( 50 20 0 0 20 40 60 80 100

In a, conditions are 113 µM EAdk, 4 mM ATP, ATP concentration ( 0 0 Time (s) ATP concentration ( ADP concentration/2 ( 0 0 4 mM AMP and 8 mM MgCl2 in the 0 0.005 0.010 0.015 0 10 20 30 40 50 0 1,000 2,000 3,000 4,000 forward direction (green) and 4 mM ADP Time (s) Time (s) Time (s) and MgCl2 in the reverse direction (blue). In the forward direction (b), a resolved burst phase with 20 µM EAdk and 4 mM ATP and AMP provides the rates of both the P-transfer and lid opening. In the reverse reaction (c), no burst phase is visible with 20 µM or 500 µM EAdk (inset) and 4 mM ADP.

opening, which resulted in an initial burst of product formation as ­previously been used to quantify the millisecond lid-opening rates the enzyme completed its first turnover followed by a linear prod- during catalysis in the presence of Mg2+ (ref. 44). Strikingly, when we uct increase that was identical to the rate of lid opening (Fig. 3a). measured EAdk during catalysis without Mg2+, the dispersion profiles Remarkably, P-transfer was faster than ~500 s−1 because the burst phase were flat (Fig. 4a and Supplementary Note 1), thus indicating that the was completed within the dead time of the instrument (~5 ms). The rate of lid opening could be shifted into the slow-exchange regime and ratio of the pre-steady-state burst amplitudes reports directly on the therefore was too slow to be detected. Such NMR relaxation behav- on-enzyme equilibrium of EAdk–Mg2+–ADP–ADP to EAdk–Mg2+– ior of the enzyme agrees with the rate of lid opening of 0.05 s−1 as ATP–AMP concentration of about ten, with the sum of the two burst determined by pre-steady-state kinetics (Table 3). We note that in the amplitudes equal to the total enzyme concentration (Fig. 3a). This is in slow-exchange regime, one would expect to see signals for both states contrast to the free-nucleotide equilibrium of about one. We confirmed in the HSQC spectrum, which we did not observe here for EAdk the values for the on-enzyme nucleotide equilibrium by nucleotide (Fig. 4b). A plausible explanation for this phenomenon is a small pop- saturation experiments (Supplementary Fig. 3f,g). We note that an ulation of the minor, open state that would give rise to weak signals. on-enzyme equilibrium of 10:1 is equivalent to a small difference in In addition, the line broadening of signals corresponding to the open free energy (~1.3 kcal/mol) between the states; this is fully consistent state is proportional to the closing rate, which is considerably faster with the idea that optimal enzyme catalytic efficiency is achieved when than the opening rate and could broaden the already weak signals the free energies of reaction intermediates are balanced8. beyond detection. However, the absence of NMR dispersion could In the absence of Mg2+, P-transfer is severely impaired. In the also be caused by a lack of motions. To differentiate between these reverse reaction, we observed no burst phase, and the turnover scenarios, we measured the temperature dependence of the NMR rates were identical between the pre-steady-state and steady-state relaxation dispersion profiles45. For an exchange process that is slow regimes, thus indicating that P-transfer was rate limiting (Fig. 3c). on the NMR timescale, the exchange contribution (Rex) is equal to Unexpectedly, in the forward direction a resolved burst followed by the lid-opening rate, whereas for a fast exchange process it is inversely a second phase seemed to imply that a step following P-transfer was proportional to the sum of the lid-opening and lid-closing rates. −1 2+ also drastically slowed down to about 0.05 s without Mg (Fig. 3b We observed an increase in Rex by raising the temperature from Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature and Supplementary Fig. 3e). 20 to 40 °C, with a uniform amplitude of ~1 s−1 for all residues that experience the exchange process (Fig. 4c). When plotted on the struc- Mg2+ greatly accelerates lid opening tures (Fig. 4d), these residues are very similar to the ones that report npg Could this other slow step in the absence of Mg2+ be the lid open- on the lid opening and closing in the presence of magnesium44. These ing? 15N-CPMG NMR relaxation dispersion experiments have results confirm that the lid opening in the absence of magnesium is indeed slow on the NMR timescale. Consequently, Rex reflects the rate of lid opening; however, the dispersion data provide neither 122 105.0 56 its accurate value nor information about the closing rate and the a b 12 46 89 30 7 ­relative population of the states. Therefore, we conclude that a second, 110.0 198 72 130 2+ 18 ­unexpected role for the Mg cofactor is to dramatically accelerate lid 114 24 105 ) 25 115.0 51 Rex 121 175 163 –1 19 opening by about three orders of magnitude (Table 3). 14 137 120.0 136 135 N (p.p.m.) eff (s 123

2 58

20 15 17 3 R 2 126 125.0 6 110 5 156 83 196 8 176 Figure 4 EAdk structure and dynamics during catalysis with and without 124 15 130.0 109 2+ 15 29 Mg , studied by NMR. (a) N-TROSY CPMG relaxation dispersion NMR 0 200 400 600 800 1,000 10.0 9.0 8.0 7.0 experiments at 25 °C on WT EAdk saturated with 20 mM nucleotides. 1 �CPMG (Hz) H (p.p.m.) Representative dispersion profile from a group of 30, showing that residues c d sensitive to lid opening and closing in the presence of Mg2+ (blue) are fully 1.5 20 °C suppressed in the absence of Mg2+ (red). (b) Overlay of 1H-15N-TROSY-HSQC 30 °C k close spectra of WT EAdk during turnover with Mg2+ (blue) and without Mg2+ (red).

) 1.0 40 °C

–1 15 kopen (c) Temperature dependence of normalized N-TROSY CPMG relaxation Rex 0.5

eff (s dispersion profiles of WT EAdk. (d) Residues with dispersion curves at 40 °C 2

R 2+

∆ without Mg , plotted on the EAdk–ADP–ADP open and closed structures 0 (red); residues with no data, owing to overlap or missing signals, are shown in –0.5 gray; nucleotides are shown in stick representation. Uncertainties (s.d.) in the 0 200 400 600 800 1,000 effective transverse relaxation rate (R2eff) in a and c are estimated from the (Hz) �CPMG variance for a number of nonexchanging peaks (n = 7).

128 VOLUME 22 NUMBER 2 FEBRUARY 2015 nature structural & molecular biology a r t i c l e s

Table 3 Microscopic rate constants for EAdk catalysis that the active site chemistry is optimized for Rate constant (s−1) Mg2+ (Fig. 5a, Supplementary Fig. 4, Table 3 P-transfer Lid opening and Supplementary Table 1). In contrast, Forward Reverse Forward Reverse the rates of lid opening and closing meas- 2+ 2+ ATP ADP ADPATP ADP ATP ured in the presence of Mg and Ca were EE→ EE→ E E Metal AMP ADP ADP AMP ADP AMP similar (Fig. 5b, Table 3, Supplementary WT None 0.14 ± 0.1a 0.005 ± 0.003a 0.05 ± 0.01a,h 0.09 ± 0.05a Table 2, and Supplementary Note 2), thus Mg2+ >5,000c >500b 190 ± 30d,i 2,800 ± 200d implying that electrostatics is the predomi- Ca2+ >500b 24 ± 4e 260 ± 30d,j >2,600f nant cause for this strong acceleration of lid Co2+ >500b 150 ± 15e 190 ± 20d >1,900f opening. Simple electrostatic-potential and R150K None (4.6 ± 0.2) × 10−5 e (6.5 ± 1.2) ×10−6 e <1g <1g interaction-energy calculations reveal that Mg2+ 0.7 ± 0.2e 0.5 ± 0.1e 300 ± 75g the coordination of a divalent cation to the aFrom the observed forward and reverse rates from quench-flow data and on-enzyme equilibrium.b Lower limit determined from nucleotides opposite to the coordinating the burst within the dead time of the quench-flow instrument (~5 ms). cLower limit from the quench-flow dead time and on-enzyme equilibrium. dFrom the steady-state (linear) phase of the quench-flow experiment and on-enzyme equilibrium.e From arginine side chains weakens the strong elec- f the linear phase of the quench-flow experiment. Calculated from kcat,obs and probability of being in the corresponding states. trostatic interactions between the phosphates gFrom NMR relaxation dispersion data. hIn good agreement with the upper limit established by NMR (<1 s−1). iIn good agreement with the NMR value of 210 ± 80 s−1. jIn good agreement with the NMR value of 370 ± 140 s−1. of the nucleotides and the arginine residues from the lids (Fig. 5c,d). Because these inter- How can Mg2+ lower the activation barriers of the two major steps actions need to be broken for the lids to open, the placement of Mg2+ in the catalytic cycle? Mg2+ may simultaneously help shield the strong in Adk indeed accelerates lid opening via electrostatics. electrostatic interactions between active site arginines and substrates We note that the lid-opening rates of AAdk without Mg2+ were too to facilitate lid opening and may correctly orient the active site players slow to be measured by 15N-CPMG relaxation dispersion experiments45; for efficient P-transfer. This suggests that substituting other diva- therefore, we used EAdk for all kinetic and NMR experiments. lent metals for Mg2+ should activate lid opening similarly, whereas P-transfer might be more specifically tuned to the charge density of A conserved arginine accelerates P-transfer 103-fold Mg2+. Indeed, we found that P-transfer for all divalent cations other than In an effort to inventory the contribution of other players in lower- Mg2+ was much slower and, in fact, was rate limiting, thus indicating ing the energy barrier of catalysis, we focused our attention on the

a 750 c d R124 600 2+ –600 –500 –400 –300 –200 –100

Mg Simulations with Mg )

–1 450 R150 (s –600 –500 –400 –300 –200 –100 rev rev chem 300 k Co2+ ATP site AMP site 2+ 150 Mn2+ Ni 2+ –600 –500 –400 –300 –200 –100 Ca Mg2+ 2+ 0 3.30 3.75 4.20 4.65 5.10

Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature –600 –500 –400 –300 –200 –100 Charge density (e 2/Å) R124 c R150

b 30 –600 –500 –400 –300 –200 –100 Simulations without Mg Normalized distribution npg ) AMP site –1 25 –600 –500 –400 –300 –200 –100 ATP site eff (s 2

R 20 –600 –500 –400 –300 –200 –100

–2 0 +2 2+ 15 Electrostatic potential (k T/e ) 0 200 400 600 800 1,000 B c –600 –500 –400 –300 –200 –100

�CPMG (Hz) Electrostatic interaction energy (kJ/mol)

e R124 f g Figure 5 The nature of the divalent cation R150K 30 ATP site

drastically affects P-transfer but not Adk ) R36 25 conformational dynamics. (a) The P-transfer step of –1

EAdk in the reverse reaction measured as a function R161 eff (s

2 20 of different divalent metals. The unit refers to the R ec AMP site K13 elementary charge constant. The rate constant shown 15 2+ 15 R85 for Mg is a lower limit. (b) N-TROSY CPMG 0 200 400 600 800 1,000 relaxation dispersion profiles of EAdk with Mg2+ (blue) �CPMG (Hz) or Ca2+ (purple). (c) Active site electrostatic potential computed from representative structures extracted from the MD simulations with (top) or without (bottom) Mg2+, plotted on a plane cutting through the active site. (d) Distribution of the electrostatic interaction energy between the ADP molecules and R124 and R150, plotted for four MD simulations with and without Mg2+. The histograms show the electrostatic interaction energies computed for configurations evenly distributed in time along the trajectories. (e,f) The two molecules in the asymmetric unit of AAdk R150K with ADP bound (blue and green), superimposed with WT AAdk (gray). (g) 15N-TROSY CPMG relaxation dispersion at 25 °C on the EAdk R150K mutant saturated with 20 mM nucleotides. Dispersion curves for residues 2+ 2+ sensitive to lid opening and closing in the presence of Mg (red) are fully suppressed in the absence of Mg (orange). Uncertainties (s.d.) in R2eff in b and g are estimated from the variance for a number of nonexchanging peaks (n = 7).

nature structural & molecular biology VOLUME 22 NUMBER 2 FEBRUARY 2015 129 a r t i c l e s

conserved active site R150. We have already seen that this residue is each microscopic step. Our experiments reveal the catalytic strategies flexible and mirrors the donor phosphoryl group position (Fig. 1b). that Adks use to both preorganize the active site for P-transfer and Mutation of R150 has previously been shown to drastically inhibit the destabilize the quaternary complex for efficient product release. As rate of enzyme turnover46. A comparison between the X-ray crystal was elegantly demonstrated by Mayo and collaborators, the princi- structures of wild-type (WT) AAdk (AAdk1) and the R150K mutant ples of reducing unproductive active site fluctuations and minimizing (AAdks 9 and 10) showed that this mutation disrupts the hydrogen- solvent accessibility is essential to improve the design of enzymes48. bonding between R150 and the donor β-phosphate. This implies However, despite remarkable progress48–51, nature’s enzymes remain that a specific coordination of the bidentate guanidinium group of far superior, thus highlighting the urgent need to understand the the arginine side chain to the transferring phosphoryl group, rather entire energy landscape of enzymatic catalysis. than a positive charge, is needed to position the reactants for catalysis A complete description of the tremendous rate acceleration (Fig. 5e,f). By quantifying the change in the P-transfer and lid-opening achieved by biological catalysts continues to be a captivating topic rates for the EAdk R150K mutant (AAdk numbering; Supplementary in biology38,52–55. A large number of X-ray structures of active com- Fig. 3a) we found that this arginine residue has a 103-fold effect on plexes, detailed kinetic characterizations and computational studies P-transfer but a negligible effect on lid opening (Fig. 5g, Supplementary on kinases have been reported, and these may lead to the assumption Fig. 5, Table 3, Supplementary Table 2 and Supplementary Notes 3 that little is left to be discovered about kinase function. However, the and 4). The total acceleration from Mg2+ and R150 together was there- understanding of free-energy landscapes underlying the impressive fore larger than 108-fold on the rate of P-transfer (Table 3). acceleration of P-transfer by kinases has been limited. For hydrogen- transfer enzymes, the role of active site preorganization and DISCUSSION conformational sampling in catalysis has been extensively investi- 38,53–56 Our results reveal how Adks accelerate the rate of P-transfer (kchem gated . It has been 27 years since Fierke and co-workers quan- >500 s−1) by more than 14 orders of magnitude relative to the uncata- tified the microscopic steps of the dihydrofolate reductase energy lyzed reaction (3.9 × 10−12 s−1; ref. 6) while minimizing the hydrolysis landscape57, and the exquisite distance sensitivity of hydride transfer side reaction. We find that Mg2+ specifically accelerates P-transfer continues to make this and similar systems attractive for studies of (>105-fold) by reducing nonproductive active site fluctuations enzyme catalysis54. We hope that the comprehensive catalytic frame- (Fig. 2a,b), stabilizing an architecture resembling the TS and serv- work described here for Adk will provide a similar foundation for ing as an anchor to the phosphoryl group pivoting between donor and understanding the catalytic power of one of the most important class acceptor nucleotides (Fig. 1e). In addition, the Mg2+ cofactor accel- of enzymes, kinases. erated lid opening (103-fold) by weakening the strong electrostatic interactions of the closed quaternary complex (Fig. 5c,d). The multi- Methods ple catalytic roles for Mg2+ are remarkable considering that P-transfer Methods and any associated references are available in the online and lid opening are very different molecular events: one involves a version of the paper. subtle 2-Å transfer of a phosphoryl group and the other a large-scale coordinated motion of domains. In contrast, nonenzymatic P-transfer Accession codes. Coordinates and structure factors have been depos- was accelerated only ten-fold by Mg2+ (ref. 6), thus highlighting ited in the Protein Data Bank under accession codes 4JL5 (AAdk1), the evolutionary impact of this highly charged and abundant cation 4JLD (AAdk2), 4JLB (AAdk3), 4JL8 (AAdk4), 4JL6 (AAdk5), 4JLA on the enzyme’s energy landscape. R150 contributed an additional (AAdk6), 4JKY (AAdk7), 3SR0 (AAdk8), 4JLO (AAdk9), 4JLP Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature 103-fold acceleration to the P-transfer step (Table 3) on top of the (AAdk10) and 4CF7 (AAdk11). 1H and 15N chemical-shift assign- large acceleration provided by converting a bimolecular reaction in ments have been deposited in the Biological Magnetic Resonance Data solution to a unimolecular one with a preferred active site geometry47. Bank under accession codes 19089, 19090, 19091, 19092 and 19093. npg Our results rule out a previously proposed mechanism of activation of Adk by direct binding of a second Mg2+ (ref. 19); the data from Note: Any Supplementary Information and Source Data files are available in the online version of the paper. the previous study can be fully explained by our model and the well- 2+ known Kd of Mg to nucleotides. Acknowledgments We note that there is extensive literature on Adks, and on kinases We dedicate this manuscript to Tom Alber, a truly amazing and inspiring scientist, in general, that can be confusing and contradictory because enzyme and a close friend who will live in our hearts forever; his creativity, joy and generosity have deeply influenced several generations of scientists. We are grateful catalysis is often reduced to an observed rate constant (kcat/Km) that to the staff at the Advanced Light Source–Berkeley Center for Structural Biology is a convolution of multiple reaction steps. This has contributed and the Advanced Photon Source (APS) for support, Y. Xiong, T. Lang, P. Afonine, to mechanistic misinterpretations because critical conformational R. Read and mentors from the Collaborative Computational Project No. 4 School motions are often hidden and therefore are ignored. The impor- at APS (2011) for advice in the refinement of X-ray data, members of the C. Miller laboratory for handling crystals, the staff at the National Energy Research Scientific tance of characterizing kinase catalysis in molecular detail has Computing Center, and K.A. Johnson for assistance with the KinTek Explorer 5,16,46 been emphasized many times but has unfortunately lagged software and fitting kinetic data. We thank P. Varilly (University of Cambridge) for far behind the understanding of nonenzymatic P-transfer5. Here kindly providing scripts. This work was supported by the Howard Hughes Medical we have quantified the microscopic states along the Adk energy Institute (HHMI), the Office of Basic Energy Sciences, Catalysis Science Program, landscape (Fig. 1a and Table 3) by analyzing the enzyme during US Department of Energy (award DE-FG02-05ER15699), the US National 13 Institutes of Health (RO1-GM100966) and the Teragrid (XSEDE) allocation catalysis, shedding light on long-standing controversies and pro- TG-MCB090166 (D.K.). R.O. is supported as an HHMI Fellow of the Damon viding a general framework for understanding the role of divalent Runyon Cancer Research Foundation (DRG-2114-12). metals and conformational changes in kinase function. However, we prefer to avoid speculation about associative versus dissociative AUTHOR CONTRIBUTIONS S.J.K., R.V.A., Y.-J.C., D.V.P., F.P., M.F.H. and D.K. designed experiments; S.J.K., transition states in enzymatic P-transfer. R.V.A., Y.-J.C., F.P., R.O., D.V.P., L.A.P. and P.N.M. performed experiments; S.J.K., We have characterized the free-energy landscape of catalysis and R.V.A., Y.-J.C., F.P., R.O., D.V.P., S.K., L.A.P., P.N.M., V.T., T.A. and D.K. analyzed have quantified the energetic contributions of individual players to data; S.J.K., R.V.A., F.P., R.O. and D.K. wrote the manuscript.

130 VOLUME 22 NUMBER 2 FEBRUARY 2015 nature structural & molecular biology a r t i c l e s

COMPETING FINANCIAL INTERESTS 28. Berry, M.B., Bae, E.Y., Bilderback, T.R., Glaser, M. & Phillips, G.N. The authors declare no competing financial interests. Crystal structure of ADP/AMP complex of Escherichia coli adenylate kinase. Proteins 62, 555–556 (2006). 29. Berry, M.B. et al. The closed conformation of a highly flexible protein: the structure Reprints and permissions information is available online at http://www.nature.com/ of Escherichia coli adenylate kinase with bound AMP and AMPPNP. Proteins 19, reprints/index.html. 183–198 (1994). 30. Cowan, J.A. Metal activation of enzymes in nucleic acid biochemistry. Chem. Rev. 98, 1067–1088 (1998). 1. Westheimer, F.H. Why nature chose phosphates. Science 235, 1173–1178 31. Kladova, A.V. et al. Cobalt-, zinc- and iron-bound forms of adenylate kinase (AK) (1987). from the sulfate-reducing bacterium Desulfovibrio gigas: purification, crystallization 2. Bowler, M.W., Cliff, M.J., Waltho, J.P. & Blackburn, G.M. Why did nature select and preliminary X-ray diffraction analysis. Acta Crystallogr. Sect. F Struct. Biol. phosphate for its dominant roles in biology? New J. Chem. 34, 784–794 Cryst. Commun. 65, 926–929 (2009). (2010). 32. Wittinghofer, A. Signaling mechanistics: aluminum fluoride for molecule of the 3. Schroeder, G.K., Lad, C., Wyman, P., Williams, N.H. & Wolfenden, R. The time year. Curr. Biol. 7, R682–R685 (1997). required for water attack at the phosphorus atom of simple phosphodiesters and 33. Coleman, D.E. et al. Structures of active conformations of Gi alpha 1 and the of DNA. Proc. Natl. Acad. Sci. USA 103, 4052–4055 (2006). mechanism of GTP hydrolysis. Science 265, 1405–1412 (1994). 4. Kamerlin, S.C., Sharma, P.K., Prasad, R.B. & Warshel, A. Why nature really chose 34. Sondek, J., Lambright, D.G., Noel, J.P., Hamm, H.E. & Sigler, P.B. GTPase phosphate. Q. Rev. Biophys. 46, 1–132 (2013). mechanism of Gproteins from the 1.7-Å crystal structure of transducin α-GDP − 5. Lassila, J.K., Zalatan, J.G. & Herschlag, D. Biological phosphoryl-transfer AIF 4. Nature 372, 276–279 (1994). reactions: understanding mechanism and catalysis. Annu. Rev. Biochem. 80, 35. Cliff, M.J. et al. Transition state analogue structures of human phosphoglycerate 669–702 (2011). kinase establish the importance of charge balance in catalysis. J. Am. Chem. 6. Stockbridge, R.B. & Wolfenden, R. The intrinsic reactivity of ATP and the catalytic Soc. 132, 6507–6516 (2010). proficiencies of kinases acting on glucose,N -acetylgalactosamine, and homoserine: 36. Baxter, N.J. et al. Atomic details of near-transition state conformers for enzyme a thermodynamic analysis. J. Biol. Chem. 284, 22747–22757 (2009). phosphoryl transfer revealed by rather than by phosphoranes. Proc. Natl. Acad. 7. Jencks, W.P. Catalysis in chemistry and enzymology (Dover, New York, 1987). Sci. USA 107, 4555 (2010). 8. Knowles, J.R. Enzyme-catalyzed phosphoryl transfer reactions. Annu. Rev. 37. Baxter, N.J. et al. Anionic charge is prioritized over geometry in aluminum and Biochem. 49, 877–919 (1980). magnesium fluoride transition state analogs of phosphoryl transfer enzymes. 9. Cleland, W.W. & Hengge, A.C. Enzymatic mechanisms of phosphate and sulfate J. Am. Chem. Soc. 130, 3952–3958 (2008). transfer. Chem. Rev. 106, 3252–3278 (2006). 38. Warshel, A. et al. Electrostatic basis for enzyme catalysis. Chem. Rev. 106, 10. Thatcher, G.R.J. & Kluger, R. Mechanism and catalysis of nucleophilic-substitution 3210–3235 (2006). in phosphate-esters. Adv. Phys. Org. Chem. 25, 99–265 (1989). 39. Armstrong, R.N., Kondo, H. & Kaiser, E.T. Cyclic AMP-dependent ATPase activity 11. Hunter, T. Tyrosine phosphorylation: thirty years and counting. Curr. Opin. Cell of bovine heart protein kinase. Proc. Natl. Acad. Sci. USA 76, 722–725 Biol. 21, 140–146 (2009). (1979). 12. Jura, N. et al. Catalytic control in the EGF receptor and its connection to general 40. Prowse, C.N. & Lew, J. Mechanism of activation of ERK2 by dual phosphorylation. kinase regulatory mechanisms. Mol. Cell 42, 9–22 (2011). J. Biol. Chem. 276, 99–103 (2001). 13. Adams, J.A. Kinetic and catalytic mechanisms of protein kinases. Chem. Rev. 41. Wang, Y., Gan, L., Wang, E. & Wang, J. Exploring the dynamic functional landscape 101, 2271–2290 (2001). of adenylate kinase modulated by substrates. J. Chem. Theory Comput. 9, 84–95 14. Endicott, J.A., Noble, M.E. & Johnson, L.N. The structural basis for (2013). control of eukaryotic protein kinases. Annu. Rev. Biochem. 81, 587–613 42. Gur, M., Madura, J.D. & Bahar, I. Global transitions of proteins explored by a (2012). multiscale hybrid methodology: application to adenylate kinase. Biophys. J. 105, 15. Henzler-Wildman, K., Lei, M., Thai, V., Karplus, M. & Kern, D. A hierarchy of 1643–1652 (2013). timescales in protein dynamics linked to enzyme catalysis. Nature 450, 913–916 43. Henzler-Wildman, K.A. et al. Intrinsic motions along an enzymatic reaction (2007). trajectory. Nature 450, 838–844 (2007). 16. Masterson, L.R. et al. Dynamics connect substrate recognition to catalysis in 44. Wolf-Watz, M. et al. Linkage between dynamics and catalysis in a thermophilic- protein kinase A. Nat. Chem. Biol. 6, 821–828 (2010). mesophilic enzyme pair. Nat. Struct. Mol. Biol. 11, 945–949 (2004). 17. Mukherjee, K., Sharma, M., Jahn, R., Wahl, M.C. & Sudhof, T.C. Evolution of 45. Palmer, A.G. NMR characterization of the dynamics of biomacromolecules. Chem. CASK into a Mg2+-sensitive kinase. Sci. Signal. 3, ra33 (2010). Rev. 104, 3623–3640 (2004). 18. Bao, Z.Q., Jacobsen, D.M. & Young, M.A. Briefly bound to activate: transient 46. Yan, H.G. & Tsai, M.D. Nucleoside monophosphate kinases: structure, mechanism, binding of a second catalytic magnesium activates the structure and dynamics and substrate specificity. Adv. Enzymol. Relat. Areas Mol. Biol. 73, 103–134

Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature of CDK2 kinase for catalysis. Structure 19, 675–690 (2011). (1999). 19. Tan, Y.W., Hanson, J.A. & Yang, H. Direct Mg2+ binding activates adenylate kinase 47. Page, M.I. & Jencks, W.P. Entropic contributions to rate accelerations in enzymic from Escherichia coli. J. Biol. Chem. 284, 3306–3313 (2009). and intramolecular reactions and the chelate effect. Proc. Natl. Acad. Sci. USA 20. Bhabha, G. et al. Divergent evolution of protein conformational dynamics in 68, 1678–1683 (1971). dihydrofolate reductase. Nat. Struct. Mol. Biol. 20, 1243–1249 (2013). 48. Privett, H.K. et al. Iterative approach to computational enzyme design. Proc. Natl. npg 21. Bhabha, G. et al. A dynamic knockout reveals that conformational fluctuations Acad. Sci. USA 109, 3790–3795 (2012). influence the chemical step of enzyme catalysis. Science 332, 234–238 49. Röthlisberger, D. et al. Kemp elimination catalysts by computational enzyme (2011). design. Nature 453, 190–195 (2008). 22. Kamerlin, S.C.L. & Warshel, A. At the dawn of the 21st century: is dynamics the 50. Kiss, G., Celebi-Olcum, N., Moretti, R., Baker, D. & Houk, K.N. Computational missing link for understanding enzyme catalysis? Proteins 78, 1339–1375 enzyme design. Angew. Chem. Int. Edn Engl. 52, 5700–5725 (2013). (2010). 51. Blomberg, R. et al. Precision is essential for efficient catalysis in an evolved 23. Adamczyk, A.J., Cao, J., Kamerlin, S.C. & Warshel, A. Catalysis by dihydrofolate Kemp eliminase. Nature 503, 418–421 (2013). reductase and other enzymes arises from electrostatic preorganization, not 52. Schwartz, S.D. & Schramm, V.L. Enzymatic transition states and dynamic motion conformational motions. Proc. Natl. Acad. Sci. USA 108, 14115–14120 in barrier crossing. Nat. Chem. Biol. 5, 551–558 (2009). (2011). 53. Benkovic, S.J. & Hammes-Schiffer, S. A perspective on enzyme catalysis. Science 24. Nagel, Z.D. & Klinman, J.P. A 21st century revisionist’s view at a turning point 301, 1196–1202 (2003). in enzymology. Nat. Chem. Biol. 5, 543–550 (2009). 54. Klinman, J.P. An integrated model for enzyme catalysis emerges from studies of 25. Klinman, J.P. & Kohen, A. Hydrogen tunneling links protein dynamics to enzyme hydrogen tunneling. Chem. Phys. Lett. 471, 179–193 (2009). catalysis. Annu. Rev. Biochem. 82, 471–496 (2013). 55. Boehr, D.D., Dyson, H.J. & Wright, P.E. An NMR perspective on enzyme dynamics. 26. Müller, C.W., Schlauderer, G.J., Reinstein, J. & Schulz, G.E. Adenylate kinase Chem. Rev. 106, 3055–3079 (2006). motions during catalysis: an energetic counterweight balancing substrate binding. 56. Rozovsky, S. & McDermott, A.E. The time scale of the catalytic loop motion in Structure 4, 147–156 (1996). triosephosphate isomerase. J. Mol. Biol. 310, 259–270 (2001). 27. Müller, C.W. & Schulz, G.E. Structure of the complex between adenylate kinase 57. Fierke, C.A., Johnson, K.A. & Benkovic, S.J. Construction and evaluation of the from Escherichia coli and the inhibitor Ap5a refined at 1.9 Å resolution: a model kinetic scheme associated with dihydrofolate reductase from Escherichia coli. for a catalytic transition-state. J. Mol. Biol. 224, 159–177 (1992). Biochemistry 26, 4085–4092 (1987).

nature structural & molecular biology VOLUME 22 NUMBER 2 FEBRUARY 2015 131 ONLINE METHODS of nearby water molecules and the nucleotides. Moreover, the Mg2+ position is in X-ray crystallography structure determination. For crystallization, Aquifex agreement with the position in the AAdk8 structure and the anomalous density aeolicus adenylate kinase (AAdks 1–8 and 11) and its R150K mutant (AAdks in the Aadk7 Co2+-structure. We note that there is partial occupancy of ~25% 9 and 10) were expressed and purified as described before44. AMP in the donor site in chain B. In chain A, we did not model a Mg2+ because AAdk crystals were grown at 18 or 22 °C with 20–50 mg/mL protein in the little electron density is seen in this site, and the coordination to the nearby water following conditions: 20 mM MgCl2, 20 mM ADP, and 25 mM in citric acid, molecules is not perfect, similarly to what is observed in the crystal structures 2+ pH 4.6 (AAdk1); 25 mM MgCl2, 25 mM ATP, 25 mM AMP, and 20 mM Tris-HCl, AAdk1–8 in which no Mg is present. pH 7.4 (AAdk2); 35 mM ADP and 20 mM citric acid, pH 4.6 (AAdk3); 38 mM Structural alignments were done with maximum-likelihood algorithms imple- MgCl2, 38 mM ADP, and 20 mM MES, pH 5.0 (AAdk4); 22 mM AMPPNP and mented in the program Theseus, which produces more accurate results compared 67 20 mM MES, pH 5.0 (AAdk5); 15 mM MgCl2, 15 mM ADP, and 20 mM Tris- to conventional least-square criteria . HCl, pH 7.0 (AAdk6); 17.3 mM ADP, 41.2 mM CoCl2, and 20 mM Tris-HCl, pH 7.4 (AAdk7); 25 mM ADP, 20 mM MgSO4, and 20 mM AlFx (AAdk8); 20 mM Molecular dynamics simulations. The A molecule of the AAdk1 crystal structure ADP, 20 mM MgCl2, and 20 mM Tris-HCl, pH 7.0 (AAdks 9–11). All complexes (Table 1) in complex with two ADP molecules was used as an initial model for were mixed with the crystallization solution containing 0.1 M sodium acetate all-atom classical molecular dynamics (MD) simulations. Parameterization was trihydrate, pH 4.6, 0.2 M ammonium acetate, and 30% (w/v) polyethylene glycol performed with the CHARMM 22-protein all-atom force field with the CMAP 4000 in a 1:1 (v/v) ratio. backbone energy correction included68,69 with CHARMM70. The parameters for During the growth of AAdk5 crystals with AMPPNP, the AMPPNP analog the bound ADP molecules, singly protonated on the terminal phosphates, were hydrolyzed to AMPPN. Because the electron density of AMPPN’s nitrogen is derived by combining parameters for a fully charged ADP and for inorganic − 71 indistinguishable from the density of ADP’s oxygen, we used ADP for modeling. phosphate PO4H2 included in the standard force field . The system was solvated For AAdk8 crystals, AAdk was premixed with ADP and incubated for 1 week in a truncated octahedral TIP3P72 water box with Solvate (http://www.mpibpc. 70 before addition of 20 mM MgSO4 and AlFx (from the mixture of Al(NO3)3 • 9 H2O mpg.de/home/grubmueller/downloads/solvate/index.html/) and CHARMM . and NaF). After another day of incubation, crystal trays were set up with the Regarding the choice of a classical treatment for the active site, a complete aforementioned conditions, and crystals were grown for another week. We quantitative understanding of the impact of the magnesium ion on the catalyzed note that this structure has a minor occupancy of ADP–ADP in the active reaction may require an accurate quantum-mechanical description of the active site, but owing to low occupancy we did not refine it further and used only site region73–76. However, the size of the system, the timescale of the dynamical 2+ − Mg –ADP–AMP–AlF4 for modeling. For AAdk11, crystals were soaked in crys- properties under study and the difficulties in the characterization of precise struc- tallization solution in which the pH had been raised to 9 after the addition of 20 mM tural and geometrical properties of the active site in terms of the magnesium-ion Mg2+. We note that for AAdk11 there is ~25% AMP occupancy in the AMP lid. positioning and protonation states of the ADP nucleotides make a direct quan- Diffraction data were collected at 100 K at the Advanced Light Source tum-mechanical approach infeasible without a previous mechanistic exploration (Lawrence Berkeley National Laboratory) beamline 8.2.1 for AAdks 2–3, 5 and at classical level77,78. Furthermore, even though the classical nonpolarizable force 8–11 and beamline 8.2.2 for AAdks 4,6 and 7. Diffraction data for AAdk1 were fields with fixed atom charges have limited accuracy, they have been success- collected at 100 K at the Advanced Photon Source beamline 23ID-B. The details fully applied to similar metal-ion– and/or nucleotide-dependent problems79–81. of the data collection are listed in Tables 1 and 2. A quantitative QM investigation of the catalyzed chemical step of the P-transfer Data were processed, scaled, phased, and refined with iMOSFLM58, Scala59, reaction is currently underway, but it is beyond the scope of the present study. Phaser60, and REFMAC5 (ref. 61) in CCP4 (ref. 62). The space groups were deter- The simulation boxes for both systems, with and without the Mg2+ ion in the 59 70 mined by Pointless and are identical for all data sets: P212121. The AAdk struc- active site, were neutralized, and then 50 mM NaCl was added with CHARMM . ture (PDB 2RGX43) without ligand was used as the search model for molecular The solvated structures were minimized with the conjugate gradient method replacement. Initial refinement was carried out, and this was followed by manual as implemented in NAMD 2.7b2 (ref. 82) and then were gradually heated to rebuilding in Coot63,64 and further iterative refinements in PHENIX65 (except 300 K with a time step of 1 fs while gradually releasing positional restraints in a

Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature for AAdk11, for which REFMAC5 was used). Hydrogen atoms were added and MD simulation of 2 ns. Periodic boundary conditions were applied to the simu- refined as isotropic for the AAdk1 and AAdk8 models, whereas other models lation cell. Electrostatics were treated with the particle mesh Ewald scheme83. did not include protons. For data sets with an atomic resolution better than The bonds of all hydrogens were constrained with the SHAKE algorithm84. 1.7 Å (except for AAdk11), the individual anisotropic ADP-refinement method was The structures were equilibrated for an additional 20 ns in the NPT ensemble npg applied. The final structural models of each data set were validated with the tools (T = 300 K, P = 1.01325 bar) with NAMD 2.7b2. The temperature was control- available in PHENIX (phenix.model_vs_data)66 or CCP4. The collection wave- led with the Langevin dynamics method85 while keeping the pressure constant lengths for AAdk1–6 and AAdk8–11 were between 0.973900 and 1.00001 Å. with the combined Langevin piston Nose-Hoover method86,87 as implemented For AAdk1–6 and AAdk8–11, there were no residues in the disallowed regions in NAMD 2.7b2. of the Ramachandran plot, and the lowest percentage of favorable Ramachandran Equilibrated structures were then converted to GROMACS 4.5.3 (ref. 88) with angles was 98.76% for AAdk6. The highest percentage of rotamer outlier for these a set of in-house scripts. For each of the two setups, with and without the Mg2+ ion data sets was also for AAdk6, with 2.26% of residues. bound to the active site, four independent replicas of 100 ns each were simulated For AAdk7 crystals, the diffraction data were collected at the Cobalt absorp- in the NPT ensemble (T = 300 K, P = 1.01325 bar), constraining the hydrogen tion edge (λ = 1.608600 Å). The anomalous scattering was identified by running bond lengths with LINCS89 and constraining the TIP3P waters with SETTLE90. Phaser-EP in PHENIX. In MR-SAD phasing mode, a refined protein model from The temperature was controlled with the Nose-Hoover thermostat91,92, and Phaser and REFMAC5 was used as a partial model for detecting the anomalous pressure was controlled with the Parrinello-Rahman pressure coupling93,94, as peak positions. The anomalous difference map confirms the location of cobalt implemented in GROMACS 4.5.3. Four of the trajectories were further extended in the active site. The locations of not only Co2+ atoms but also the P and S to 200 ns. atoms could be confirmed and are consistent with anomalous scattering at this To define the protein cavities during the analysis of the water dynamics (Fig. 2d wavelength. While fixing the Co2+ atom on the basis of the anomalous peak and Supplementary Fig. 2), we used an algorithm based on the clustering of the position, further refinements were carried out. The occupancy of cobalt was not alpha spheres95 implemented in Fpocket96. Fpocket relies on the Voronoi tessel- full, although cobalt in the active site of chain A displayed anomalous scattering lation of space implemented in Qvoronoi (http://www.qhull.org/). The volume of up to 17 sigma level. The anomalous multiplicity for the AAdk7 refinement was the cavity and the water molecules present inside those cavities were determined 7.2 (6.7), and the anomalous completeness was 99.4% (96.4%). For this data set, with a set of scripts that can partition a complex geometry by defining a convex 0.74% and 96.03% of residues were in the disallowed and favorable regions of the hull on the basis of atomic positions (kindly provided by P. Varilly97). Ramachandran plot, respectively. In addition, 4.53% of AAdk7 residues were in The calculations of the electrostatic potential (Fig. 5c) have been performed rotamer outlier configurations. with APBS98 with the interface built into VMD 1.9 (ref. 99). The linearized form For AAdk11 crystals, the presence of Mg2+ in the active site of chain B was of the Poisson-Boltzmann equation (LPBE) at 298.15 K was solved, thus placing established from the electron density and from the perfect six-fold coordination the protein in a cubic box of size 80 Å and 129 grid points in each dimension.

nature structural & molecular biology doi:10.1038/nsmb.2941 The solvent dielectric constant was set to 78.54. To account for the solution the real quench delay and the delay value specified in the instrument. To take buffer, 50 mM monovalent positive and negative mobile ions were included in into account this apparent dead time of the instrument, data were corrected, the calculation. with quenched-flow experiments performed in the forward and reverse direc- All trajectories were analyzed with VMD 1.9 (ref. 99). Grace (http://plasma- tions. Instrumental delay calculations were based on the fact that the sum of the gate.weizmann.ac.il/Grace/) was used for the plots, and Tachyon ray tracer pre-steady-state bursts for forward and reverse reactions must be equal to the (built into VMD 1.9, http://jedi.ks.uiuc.edu/~johns/raytracer/) was used for the total enzyme concentration. molecular renderings. Experimental bursts can be found as: A′+= A + + k + × td Pre-steady-state kinetics measurements. Pre-steady-state kinetics was measured A′ = A + k × t with a three-syringe rapid quench-flow apparatus RQF-3 (KinTek Corp). Protein − − − d solution was loaded into one of the syringes, nucleotides (ADP or AMP + ATP where A′± are experimentally measured bursts in the forward and reverse direc- mixture with or without divalent ions) into the second syringe and quench solu- tion, k± are kinetic rates in the forward and reverse direction, and A± are true tion (30% TCA + 6 M HCl mixture) into the third syringe. The reaction was initi- bursts in the forward and reverse direction. ated by a simultaneous push of all three syringes by a high-precision servo-motor. Thus the delay time td is The required delay between the initial mixing of the reagent and the following = ′ + ′ − + + = ′ + ′ − + quench with acid was achieved by selecting aging loops of different length (which tAAAAkkAAd [(+ − ) ( + − )]/[ + − ] [( + − )1 ]/[ kk + − ] increases the path length for the acid component, thus delaying the quench). The forward and reverse reactions were initiated by mixture of ADK with AMP Finally, the true experimental delay in the experimental data can be calculated as and ATP or ADP, respectively. The protein concentration in the syringe (before t= t′ + t mixing) was varied between 40 and 1,000 µM while the nucleotide concentration d (in the syringe) was 8–32 mM, depending on the experiment. The buffer con- where t′ is a delay without the dead-time correction. tained 100 mM Tris, pH 7.0, 80 mM KCl, and equimolar (with total concentration All values reported in Table 3 were obtained from individual fits. Consistent of nucleotides) concentrations of Mg2+ or 50 mM EDTA. The temperature was results were also obtained through global fitting with KinTek Explorer, linking controlled with a circulating water bath Isotemp 2150 Nano (Fisher Scientific) the values of all rate constants among the data sets including the values from set to 25 °C unless specified otherwise. in-solution and on-enzyme nucleotide equilibrium. The amount of product was quantified with high-pressure liquid chroma- tography (HPLC). Protein precipitated by quench was separated with Spin-X NMR dynamics. 15N-TROSY CPMG relaxation dispersion experiments100 were centrifugal tube filters (Costar), filtered supernatant was diluted to avoid HPLC collected on either Varian Inova 500 or 600 MHz or Bruker Avance 800 MHz detector saturation, and the pH was brought to 6.0 to achieve optimal separation. (cryoprobe) spectrometers. Adk concentrations were usually 2 mM. Substrate The samples were analyzed on an HPLC system (Agilent Infinity 1260) with a saturation of Adk was achieved with 20 mM ADP in 100 mM HEPES, 50 mM high-precision autosampler (injection error <0.1 µL) and analytical HPLC col- NaCl, pH 7.0, and 5 mM TCEP. The concentration of divalent metal used in umn ACE (i.d. 2.4 mm, length 250 mm, C18-AR, 5-Å pore size) and separated CPMG dispersion experiments was kept equimolar with the concentration of with isocratic elution with potassium phosphate mobile phase (100 µM, pH 6.0). ADP. Samples measured in the absence of divalent metals were conducted in the Control experiments were performed to determine residual contamination in the presence of 5 mM EDTA. commercially purchased ADP, ATP, and AMP stocks. Typical parameters for 15N-TROSY CPMG relaxation dispersion experiments The rate constants of the P-transfer in the forward and reverse direction were a 40-ms constant time period; 2-s delay between transients; 12 different (kT.M.→D.D. and kD.D→T.M., respectively) reported in Table 3 were calculated con- refocusing field strengths from 50–1,000 Hz collected interleaved, with 1,024 sidering (i) the exponential phase of the forward reaction EATP.AMP → EADP.ADP, and 128 direct and indirect points, respectively, and 25 °C. For experiments which is determined by the sum of the constants kT.M.→D.D.+ kD.D.→T.M. and conducted at 30 °C and 40 °C, the constant time period was increased to 60 and

Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature (ii) the on-enzyme equilibrium, which gives the ratio between the two constants 72 ms, respectively. 1 15 (kT.M.→D.D.)/(kD.D.→T.M.). Standard H- N-TROSY-HSQCs were always collected before and after the CPMG experiment to check sample stability. CPMG experiments usually took 2.5 d to complete. 15N-CPMG dispersions collected on the Avance 800 MHz were kDDTM....→ kTM. npg  → ADP. ADP → ATP. AMP  → Eopen + ADP + ADP←  Eclosed ← Eclosed ←collected  Eopen as downfield+ ATP + and AMMP upfield pairs to minimize off-resonance effects for the kDD.. kTM..→DDD.. 15 k k larger sweep width and for lower N pulse powers required on cryoprobes.  → ADP. ADP DDTM....→ → ATP. AMP TM. → E+ ADP + ADP←  E ← E ←  Eopen + ATPData + A MMPwere processed with the NMRPipe suite101 and visualized by either CCPN k closed k closed DD.. TM..→DDD.. or NMRViewJ102,103. Relaxation dispersion profiles were calculated from peak TM. intensities and analyzed with the general Carver-Richards equation for two-site Eopen + ATP + AMMP exchange with in-house scripts104–107. Uncertainties were estimated from the average variation in dispersion for residues not experiencing exchange together Lid opening in the forward direction (opening out of the EADP.ADP state) can be with the signal-to-noise ratio of each resonance to be analyzed. Global fit uncer- determined directly from the slope of the linear phase in Figure 3b, because the tainties were estimated by a jackknife method. equilibrium is highly skewed toward the EADP.ADP state. Lid opening in the reverse direction (opening out of the EATP.AMP state) cannot Steady-state kinetics measurements. Steady-state kinetics measurements were be directly read from the slope in Figure 3c, because in this direction P-transfer collected with 4 mM ADP and equimolar (with nucleotide) concentrations of is rate limiting. Instead, one can calculate the lid-opening rate constant from the divalent metal. The enzyme concentration was varied between 0.5 nM and 25 nM; observed rate of P-transfer after accounting for the probabilities of opening and buffer was 100 mM HEPES, pH 7.0, and 80 mM KCl; measurements were col- going back into the EADP.ADP state. The rate constant can be calculated from the lected at room temperature. The amount of product produced over 16 min was observed rate constant according to the following equation: quantified with HPLC as described above for pre-steady-state kinetics. open obs kATP. AMP kADP.. ADP→ ATP AMP = kADP.. ADP→ ATP AMP ⋅ oppen kATP. AMP + kATP. AMP→ ADP. ADP 58. Battye, T.G., Kontogiannis, L., Johnson, O., Powell, H.R. & Leslie, A.G. iMOSFLM: a new graphical interface for diffraction-image processing with MOSFLM. Time-correction procedure for very fast kinetics in the quench-flow experi- Acta Crystallogr. D Biol. Crystallogr. 67, 271–281 (2011). 59. Evans, P. Scaling and assessment of data quality. ments. Data obtained in the presence of Mg2+, Ca2+, or Co2+ (very fast kinetics) Acta Crystallogr. D Biol. Crystallogr. 62, 72–82 (2006). displayed unphysical amplitudes of the burst phase. The apparent amplitude was 60. McCoy, A.J. et al. Phaser crystallographic software. J. Appl. Crystallogr. 40, greater than the enzyme concentration; this indicated a discrepancy between 658–674 (2007).

doi:10.1038/nsmb.2941 nature structural & molecular biology 61. Murshudov, G.N. et al. REFMAC5 for the refinement of macromolecular crystal 84. Ryckaert, J.P., Ciccotti, G. & Berendsen, H.J.C. Numerical-integration of Cartesian structures. Acta Crystallogr. D Biol. Crystallogr. 67, 355–367 (2011). equations of motion of a system with constraints: molecular-dynamics of 62. Winn, M.D. et al. Overview of the CCP4 suite and current developments. N-alkanes. J. Comput. Phys. 23, 327–341 (1977). Acta Crystallogr. D Biol. Crystallogr. 67, 235–242 (2011). 85. Brünger, A.T. X-PLOR, Version 3.1: a system for X-ray crystallography and NMR 63. Emsley, P. & Cowtan, K. Coot: model-building tools for molecular graphics. (Yale University Press, New Haven, 1992). Acta Crystallogr. D Biol. Crystallogr. 60, 2126–2132 (2004). 86. Feller, S.E., Zhang, Y.H., Pastor, R.W. & Brooks, B.R. Constant-pressure molecular- 64. Emsley, P., Lohkamp, B., Scott, W.G. & Cowtan, K. Features and development dynamics simulation: the Langevin piston method. J. Chem. Phys. 103, of Coot. Acta Crystallogr. D Biol. Crystallogr. 66, 486–501 (2010). 4613–4621 (1995). 65. Adams, P.D. et al. PHENIX: a comprehensive Python-based system for 87. Martyna, G.J., Tobias, D.J. & Klein, M.L. Constant-pressure molecular-dynamics macromolecular structure solution. Acta Crystallogr. D Biol. Crystallogr. 66, algorithms. J. Chem. Phys. 101, 4177–4189 (1994). 213–221 (2010). 88. Hess, B., Kutzner, C., van der Spoel, D. & Lindahl, E. GROMACS 4: algorithms 66. Afonine, P.V. et al. phenix.model_vs_data: a high-level tool for the calculation of for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. crystallographic model and data statistics. J. Appl. Crystallogr. 43, 669–676 Theory Comput. 4, 435–447 (2008). (2010). 89. Hess, B., Bekker, H., Berendsen, H.J.C. & Fraaije, J.G.E.M. LINCS: a linear 67. Theobald, D.L. & Steindel, P.A. Optimal simultaneous superpositioning of multiple constraint solver for molecular simulations. J. Comput. Chem. 18, 1463–1472 structures with missing data. Bioinformatics 28, 1972–1979 (2012). (1997). 68. MacKerell, A.D. et al. All-atom empirical potential for molecular modeling and 90. Miyamoto, S. & Kollman, P.A. Settle: an analytical version of the shake and dynamics studies of proteins. J. Phys. Chem. B 102, 3586–3616 (1998). rattle algorithm for rigid water models. J. Comput. Chem. 13, 952–962 69. MacKerell, A.D., Banavali, N. & Foloppe, N. Development and current status of (1992). the CHARMM force field for nucleic acids. Biopolymers 56, 257–265 (2000). 91. Nose, S. A molecular-dynamics method for simulations in the canonical ensemble. 70. Brooks, B.R. et al. Charmm: a program for macromolecular energy, minimization, Mol. Phys. 52, 255–268 (1984). and dynamics calculations. J. Comput. Chem. 4, 187–217 (1983). 92. Hoover, W.G. Canonical dynamics: equilibrium phase-space distributions. 71. Pavelites, J.J., Gao, J.L., Bash, P.A. & Mackerell, A.D. A molecular mechanics Phys. Rev. A 31, 1695–1697 (1985). force field for NAD+, NADH, and the pyrophosphate groups of nucleotides. 93. Parrinello, M. & Rahman, A. Polymorphic transitions in single-crystals: a new J. Comput. Chem. 18, 221–239 (1997). molecular-dynamics method. J. Appl. Phys. 52, 7182–7190 (1981). 72. Price, D.J. & Brooks, C.L. A modified TIP3P water potential for simulation with 94. Nose, S. & Klein, M.L. Constant pressure molecular-dynamics for molecular- Ewald summation. J. Chem. Phys. 121, 10096–10103 (2004). systems. Mol. Phys. 50, 1055–1076 (1983). 73. Gresh, N. et al. Analysis of the interactions taking place in the recognition site 95. Liang, J., Edelsbrunner, H. & Woodward, C. Anatomy of protein pockets and of a bimetallic Mg(II)-Zn(II) enzyme, isopentenyl diphosphate isomerase. a parallel cavities: measurement of binding site geometry and implications for ligand design. quantum-chemical and polarizable molecular mechanics study. J. Phys. Chem. Protein Sci. 7, 1884–1897 (1998). B 114, 4884–4895 (2010). 96. Le Guilloux, V., Schmidtke, P. & Tuffery, P. Fpocket: an open source platform for 74. Pontikis, G., Borden, J., Martinek, V. & Florian, J. Linear energy relationships for ligand pocket detection. BMC Bioinformatics 10, 138 (2009). the octahedral preference of Mg, Ca and transition metal ions. J. Phys. Chem. 97. Patel, A.J., Varilly, P., Chandler, D. & Garde, S. Quantifying density fluctuations A 113, 3588–3593 (2009). in volumes of all shapes and sizes using indirect umbrella sampling. 75. Yang, S.Y. et al. Whether proton transition to the triphosphate tail of ATP occurs J. Stat. Phys. 145, 265–275 (2011). at protein kinase environment: a Car-Parrinello ab initio molecular dynamics study. 98. Baker, N.A., Sept, D., Joseph, S., Holst, M.J. & McCammon, J.A. Electrostatics Int. J. Quantum Chem. 108, 1239–1245 (2008). of nanosystems: application to microtubules and the ribosome. Proc. Natl. Acad. 76. Peters, M.B. et al. Structural survey of zinc containing proteins and the Sci. USA 98, 10037–10041 (2001). development of the zinc amber force field (ZAFF). J. Chem. Theory Comput. 6, 99. Humphrey, W., Dalke, A. & Schulten, K. VMD: visual molecular dynamics. 2935–2947 (2010). J. Mol. Graph. 14, 33–38 (1996). 77. Ditzler, M.A., Otyepka, M., Sponer, J. & Walter, N.G. Molecular dynamics and 100. Loria, J.P., Rance, M. & Palmer, A.G.A. TROSY CPMG sequence for characterizing quantum mechanics of RNA: conformational and chemical change we can believe chemical exchange in large proteins. J. Biomol. NMR 15, 151–155 (1999). in. Acc. Chem. Res. 43, 40–47 (2010). 101. Delaglio, F. et al. NMRPipe: a multidimensional spectral processing system based 78. Banás, P., Jurecka, P., Walter, N.G., Sponer, J. & Otyepka, M. Theoretical studies on UNIX pipes. J. Biomol. NMR 6, 277–293 (1995). of RNA catalysis: hybrid QM/MM methods and their comparison with MD and 102. Johnson, B.A. & Blevins, R.A. NMR View: a computer program for the visualization QM. Methods 49, 202–216 (2009). and analysis of NMR data. J. Biomol. NMR 4, 603–614 (1994). 79. Venkatramani, R. & Radhakrishnan, R. Computational study of the force 103. Vranken, W.F. et al. The CCPN data model for NMR spectroscopy: development dependence of phosphoryl transfer during DNA synthesis by a high fidelity of a software pipeline. Proteinss 59, 687–696 (2005). polymerase. Phys. Rev. Lett. 100, 088102 (2008). 104. Davis, D.G., Perlman, M.E. & London, R.E. Direct measurements of the

Nature America, Inc. All rights reserved. America, Inc. © 201 5 Nature 80. Banás, P., Walter, N.G., Sponer, J. & Otyepka, M. Protonation states of the key dissociation-rate constant for inhibitor-enzyme complexes via the T1 rho and T2 active site residues and structural dynamics of the glmS Riboswitch as revealed (CPMG) methods. J. Magn. Reson. B. 104, 266–275 (1994). by molecular dynamics. J. Phys. Chem. B 114, 8701–8712 (2010). 105. Carver, J. & Richards, R. A general two-site solution for the chemical exchange 81. Khavrutskii, I.V., Grant, B., Taylor, S.S. & McCammon, J.A. A transition path produced dependence of T2 upon the Carr-Purcell pulse separation. ensemble study reveals a linchpin role for Mg2+ during rate-limiting ADP release J. Magn. Res. 6, 89–105 (1972). npg from protein kinase A. Biochemistry 48, 11532–11545 (2009). 106. Jen, J. Chemical exchange and NMR T2 relaxation: the multisite case. 82. Phillips, J.C. et al. Scalable molecular dynamics with NAMD. J. Comput. Chem. J. Magn. Res. 30, 111–128 (1978). 26, 1781–1802 (2005). 107. Millet, O., Loria, J.P., Kroenke, C.D., Pons, M. & Palmer, A.G. III. The static 83. Darden, T., York, D. & Pedersen, L. Particle mesh Ewald: an N•log(N) method magnetic field dependence of chemical exchange linebroadening defines the NMR for Ewald sums in large systems. J. Chem. Phys. 98, 10089–10092 (1993). chemical shift time scale. J. Am. Chem. Soc. 122, 2867–2877 (2000).

nature structural & molecular biology doi:10.1038/nsmb.2941