Mg²⁺-Assisted Catalysis by B. stearothermophilus TrpRS is Promoted by Allosteric Effects

Abstract

Mn²⁺-assisted catalysis by B. stearothermophilus TrpRS parallels that in polymerases and reduces specificity in amino acid activation. As predicted by non-equilibrium molecular dynamics simulations, multi-variant thermodynamic cycles with [ATP]-dependent Michaelis-Menten kinetics and Mn²⁺ for Mg²⁺ substitution demonstrate energetic coupling of ATP affinities to the metal; to lysines K111 and K192, which interact via the PPi leaving group; and to K195, which couples differently to the metal via the α–phosphate. However, net coupling to the metal opposes catalysis in both ground (Km) and transition (k_cat) states. The 10⁵-fold rate acceleration by Mg²⁺-protein interactions therefore requires additional favorable protein-metal couplings. Examples include longer-range, i.e., allosteric, interactions previously illustrated by the remote F37I mutation, which both reduces k_cat and enhances catalytic assist by Mn²⁺, relative to that by Mg²⁺. These data support a model linking metal-assisted phosphoryl transfer catalysis to domain movement, and hence to free-energy transduction in a broad range of enzymes.

INTRODUCTION

Mg²⁺ ions assist nearly all enzymes that catalyze phosphoryl transfer from nucleoside triphosphates, yet they accelerate the uncatalyzed rate (Tetas and Lowenstein, 1963) by less than 10-fold in the absence of enzymes. Minimum energy configurations of Mg²⁺·ATP in water (Liao et al., 2004) involve coordination either to non-bridging oxygen atoms from all three phosphates, or to the terminal β- and γ-phosphates. Ground-state metal bridging of phosphates across the bond cleaved in the reaction, is problematic for phosphoryl transfer. The two bridging configurations are nevertheless quite generally observed in crystal structures of a broad range of transducing enzymes, including ATP synthase, myosin, T7 helicase, and GroEL (Liao et al., 2004), as well as kinesin (1IA0), signaling GTPases (1JAH, 1WQ1), DNA polymerases (1T3N, 1T7P, 2PFO, 1JX4), and aminoacyl-tRNA synthetases. Widespread use of bridged ground-state complexes in transducing enzymes suggests that catalysis must rearrange the metal, which could be useful in coupling phosphoryl transfer to conformation changes.

Tryptophanyl-tRNA synthetase (TrpRS) comprises an excellent system for study of long-range energetic coupling associated with Mg²⁺-assisted catalysis. Like other Class I aminoacyl-tRNA synthetases, it requires one Mg²⁺ ion for optimal catalysis of tryptophan activation. We recently quantified the contribution of Mg²⁺ to TrpRS-catalyzed ³²PPi exchange. It accelerates the rate by ~10⁵ fold, relative to a total rate enhancement of ~10¹⁴ fold over the uncatalyzed rate, and its affinity increases ~20-fold in the transition state (Weinreb and Carter, 2008). Considerable uncertainty remains about the mechanism of this rate enhancement, as the metal contribution arises almost entirely from energetic coupling between metal and protein.

Coupling must be indirect; no active-site residues bind to the metal. The crystallographic Mg²⁺·ATP configuration (Retailleau et al., 2003) involves Mg²⁺ ion-pair interactions with non-bridging oxygen atoms from each phosphate (Fig. 1). Three active-site lysine residues also bind to non-bridging oxygen atoms. Details of this coordination include: i) K192 and K195 derive from the KMSKS catalytic signature, while K111 derives from a mobile loop across the active site; ii) K111 and K192 interact with the eventual PPi leaving group, across the scissile anhydride bond from the adenosine α-phosphate also bound to K195; iii) K111 and K192 both compete with the Mg²⁺ for the same non-bridging oxygen atoms in the PPi moiety, while K195 does not. Leaving group interactions are thus more directly competitive with the metal; iv) all three Mg²⁺ oxygen distances are substantially longer than those in aqueous Mg²⁺·ATP complexes (Liao et al., 2004), suggesting that the lysine residues weaken metal interactions with the triphosphate prior to catalysis.

Fig. 1.

Mg²⁺ ion coordination in the PreTS complex with ATP involves only the ATP and two bound water molecules (blue spheres). Mg²⁺ interacts only indirectly with TrpRS, via the ε amino groups of K111, K192, and K195 (distances in Å). The five ligands to Mg²⁺ lie close to octahedral positions, leaving a sixth site vacant.

Catalytically relevant movement in TyrRS (Fersht et al., 1988) involves the KFGKT (consensus homolog of KMSKS) loop and K82 and R86 from a second loop across the active site cleft, positioned similarly to K109 and K111 in TrpRS. Further study (First and Fersht, 1993a; First and Fersht, 1993b; First and Fersht, 1993c; First and Fersht, 1995) revealed that energetic coupling between the two lysine residues affected ground-state and transition-state substrate binding differently. Interactions between these groups and the metal ion were not studied.

The unusual Mg²⁺ configuration in Fig. 1 is associated with the Pre-transition state (PreTS; (Retailleau et al., 2003)), a high-energy protein conformation in which the anticodon-binding domain containing the KMSKS loop is twisted by ~9°, relative to the Rossmann fold domain (Kapustina and Carter, 2006). Without Mg²⁺·ATP, this conformation is disfavored by 3.0 kcal/Mol relative to the open state (Retailleau et al., 2007). Circumstantial evidence suggests that it is also destabilized relative to the closed, Products conformation, which has a reduced twist angle of ~4.5°, and that the PreTS conformation passes through a conformational transition state as phosphoryl transfer occurs (Kapustina et al., 2007). ATP binding to the PreTS state therefore stores conformational free energy that is recovered in the product state.

An important clue to how Mg²⁺ contributes to conformational free energy changes arose from our observation that the CHARMM force field would not reproduce the crystallographic configuration (Fig. 1; (Kapustina and Carter, 2006)). Without restraining potentials, MD simulations drove the metal closer to the phosphate oxygen atoms, releasing the hydrogen bonds to lysine residues, K111 and K192, that form the PPi leaving group subsite. The crystallographic configuration could, however, be preserved by restraining potentials on either the relative domain orientation or the long Mg²⁺-oxygen distances. The potential of mean force required to restore the long crystallographic Mg²⁺-oxygen distances was 4–6 kcal/Mol (Kapustina et al., 2006). Reciprocally, any perturbation weakening the K111- and K192-phosphate interactions, including lack of restraint or virtual mutagenesis of K111 to glutamine, also reduced the high twist angle, supporting energetic coupling between the unfavorable twist angle and Mg²⁺·ATP via the lysine configurations that occur only in the proximity of the transition state, ie in PDB IDs 1MAU, 1M83, and 2OV4.

These observations suggest how Mg²⁺·ATP binding invokes long-range conformational interactions that activate the Mg²⁺ ion for catalysis, storing some of the ATP binding free energy for subsequent catalytic use. Elements of this model, summarized schematically in Fig. 2, are: (i) weakening ground-state TrpRS ATP binding by coupling it to an unfavorable conformational change, (ii) activating the Mg²⁺ ion by weakening its interaction to the phosphates, (iii) breaking the rough equivalence between the three Mg²⁺-phosphate bonds that cross-link the leaving PPi group to the α-phosphate, and (iv) catalytic use of an effective restoring force stored in the unfavorable twist angle and weakened Mg²⁺-phosphate bonds, which allows the Mg²⁺-α-phosphate and ^αP-^βP bonds to weaken while progressively stabilizing emerging negative charge on the PPi moiety and displacing the K111 plus charge as domain untwisting pulls the leaving group away from the α-phosphate.

Fig. 2.

Effective forces in the PreTS configuration of Mg²⁺·ATP prior to tryptophan activation by B. stearothermophilus TrpRS (upper right) and their progressive resolution in the untwisted, post-transition state Products complex (bottom left). The dashed PreTS outline suggests conformational destabilization due to the high twist angle, which is exaggerated. (i) Twisting induces conformational forces (cyan) on the phosphate oxygen atoms via K111 and K192, opposing electrostatic forces (orange) from the Mg²⁺ ion. (ii) In the PreTS, the scissile bond (~) also opposes the effective force exerted by the unfavorable twist. Roughly comparable forces balance, activating the Mg²⁺. (iii) Conformational strain in the transition state breaks the equivalence of Mg²⁺-phosphate bonds and their tendency to “crosslink” the PPi and AMP, as metal-PPi interactions are maximal (intense red, green arrows). (iv) Breaking the scissile bond, left, allows the anticodon-binding domain to untwist, removing the PPi from K111 and Trp-5′ AMP. Tryptophan is included only in the final state.

This mechanism implements a strain model described as “the rack” (Lumry, 1959) and later elaborated in enzymological terms by Jencks (Jencks, 1975). It predicts that significant coupling free energies arise from the electrostatic interactions in the Mg²⁺-oxygen–lysine system, and that these change between the ground- and transition-state interactions with ATP. This paper derives experimental values for such coupling interactions from free energy changes associated with the Michaelis parameters, Km(ATP) and k_cat in thermodynamic cycles involving combinatorial mutagenesis of the three lysine residues to alanine or glutamine, together with substitution of Mn²⁺ for Mg²⁺. The data confirm aspects (i–iv) of the model in Fig. 2, validate subtle features of MD simulations (Kapustina and Carter, 2006), and implicate similar mechanisms in a broader class of transducing enzymes.

RESULTS

Fersht introduced combinatorial mutation and multi-mutant cycles to establish free-energy coupling between amino acids in proteins (First and Fersht, 1995; Horovitz and Fersht, 1990). We here establish a basis for combining such effects with those induced by metal substitution. Substituting Mg²⁺ by Mn²⁺ reduces native TrpRS pyrophosphate exchange activity by up to ~75-fold. This range of activities provided a way to use ATP-dependent Michaelis-Menten kinetics with mutation and metal substitution to measure experimentally the interactions that activate and utilize the metal. Exchange assays are carried out under equilibrium binding of both substrates, and fitted half-saturation values thus represent thermodynamic dissociation constants (Cleland, 1970), as has been verified by comparing experimental determinations of TyrRS ATP affinity measured by ³²PPi exchange and pre-steady state methods (Wells et al., 1991). We therefore interpret Km(ATP) as ground state and k_cat in terms of transition state ATP affinities.

Mn²⁺ ion concentration dependence of TrpRS ³²PPi-exchange activity resembles that of polymerases

We first examined whether or not metal substitution induces changes in the reaction mechanism that might qualify interpretations. Mn²⁺ ion is a functional substitute for Mg²⁺ in many nucleic acid polymerases, which are also synthetases. It has an unusual concentration dependence, in which activity increases to a sharp maximum at rather high concentration (~1 mM) and then falls (Frank and Woodgate, 2007). Mn²⁺ assisted activity also is frequently associated with decreased fidelity, relative to that observed with Mg²⁺ (Dominguez et al., 2000; El-Deiry et al., 1984; Goodman et al., 1983; Vartanian et al., 1999). The mutagenic activity of Mn²⁺ may be biologically relevant to the high somatic mutation rate associated with generating immunoglobulin sequence diversity (Dominguez et al., 2000). The role of Mn²⁺ in phosphoryl transfer and its mutagenic effects in polymerases, prompted us to investigate its role in TrpRS catalysis.

Fig. 3 summarizes relative metal dependences of TrpRS ³²PPi-exchange activities with Mg²⁺ and Mn²⁺. When plotted against [metal]_free, the two metals act similarly in all respects. Activities with both metals are maximal at ~8 μM [Metal]_free and fall less sharply, losing an order of magnitude by ~10 mM. We were unaware of this peak activity when we previously reported that TrpRS was unable to use Mn²⁺ to assist catalysis of ³²PPi exchange (Retailleau et al., 2003). Optimal Mn²⁺-assisted activity of the wild type enzyme at [Mn²⁺]_total = 0.9 mM is within ~6.3-fold of its activity with Mg²⁺. Although the molecularity of metal assist must be an integer and is likely 1.0, the slopes of log-log plots in Fig. 3a show that catalytic assist has an order of 0.51–0.65, while that of inhibition is smaller by nearly an order of magnitude, 0.11–0.14. The physico-chemical basis of this unusual behavior is unknown and we do not investigate it further here, except to note that it does not imply half-of-sites reactivity, which would change the intercepts but not the slopes. Similarities in Fig. 3a provide evidence that the two metals are mechanistically equivalent, and that Mn²⁺ substitution is a legitimate perturbation of catalyzed phosphoryl transfer.

Fig. 3.

Divalent metal-dependence of TrpRS activity. A. TrpRS ³²PPi exchange activities as a function of [Metal]_free. Mg²⁺ (squares; (Retailleau et al., 2003) and Mn²⁺ (circles; this work) both activate at low, and inhibit at higher concentration. Slopes indicate similar, complex reaction orders of each phase for both metals, and hence similar mechanisms. The general shape of activity curves and optimal [Mn²⁺] were determined for all mutant enzymes and were conserved (not shown). Arrows indicate metal concentrations used in this work. B. Relationship between free and total [Metal], diverging from unity in the inhibitory concentration range, and where the [Metal]_free increases more rapidly, owing to complete titration of competing ATP, and PPi.

Mn²⁺ relaxes amino acid specificity in TrpRS ³²PPi exchange

The mutagenic effect of Mn²⁺ in DNA polymerization suggests that it might also relax TrpRS amino acid specificity. We therefore compared tryptophan and tyrosine activation with both metals. Relative kcat/Km values favor specific recognition of tryptophan ~10⁴ fold with Mg²⁺, mediated to a significant extent by differences in Km (Praetorius-Ibba et al., 2000). Relative tyrosine activation increases ~3.5-fold with Mn²⁺, which increases Km for tryptophan five-fold while decreasing Km for tyrosine two-fold. Thus, although the metal has no direct linkage to the amino acid binding subsite, it does affect relative specificity, as observed for polymerases.

Factorial analysis of lysine-metal free energy coupling via phosphate oxygen atoms

For lysines K111, K192, and K195, we constructed alanine mutants that cannot interact, and glutamine mutants that can form hydrogen bonds to oxygen, hence preserving limited interaction with phosphates. Mutants K111AK195A and K111AK192AK195A were constructed, but did not express into the soluble fraction. All other combinatorial mutations to alanine were expressed and purified. For these variants, we measured steady-state kinetic parameters for ³²PPi exchange with Mg²⁺ at our standard concentration (5 mM) and with Mn²⁺ at two concentrations, 0.9 mM and 10 mM (K111, K192 mutants), corresponding to its optimum and minimum values (Fig. 3a) or at the optimal 0.9 mM (K195 mutants). No glutamine mutants involving Q195 have thus far been stably expressed. We have not yet constructed mixed mutants involving both A and Q at different sites. These are thus absent from the dataset (Table 1).

Table 1. Experimental design matrix for K111, K192, K195, and metal substitution multi-mutant cycles.

Columns 2–8 encode the WT (=1) or mutant (=0) amino acid in positions 111, 192, and 195, the presence (=1) or absence (=0) of Mg⁺⁺, the number of glutamine (Q) and alanine (A) substitutions, and the Mn²⁺ concentrations (mM). Calculated values for ΔG_kcat and ΔG_Km were obtained from regression models for subsets of the data that provided ΔG values in Figs. 5 and 6. Typical regression statistics are given in Tables 2a,b.

Mutant	111	192	195	Mg	Q	A	[Mn]	kcat, s−1	ΔGkcat,obs	ΔGkcat,calc	Km	ΔGKm,obs	ΔGKm,calc
WT	1	1	1	1	0	0	0	1.76	−0.34	−0.30	0.00021	5.08	4.89
WT	1	1	1	1	0	0	0	1.62	−0.29	−0.30	0.00030	4.87	4.89
WT	1	1	1	1	0	0	0	1.44	−0.22	−0.30	0.00028	4.91	4.89
WT	1	1	1	1	0	0	0	1.76	−0.34	−0.30	0.00040	4.69	4.89
K111A	0	1	1	1	0	1	0	0.072	1.58	1.47	0.00021	5.08	4.98
K111A	0	1	1	1	0	1	0	0.076	1.55	1.47	0.00033	4.81	4.98
K111A	0	1	1	1	0	1	0	0.12	1.27	1.47	0.00022	5.05	4.98
K192A	1	0	1	1	0	1	0	0.045	1.86	1.85	0.00019	5.14	5.14
K192A	1	0	1	1	0	1	0	0.047	1.83	1.85	0.00019	5.14	5.14
K111AK192A	0	0	1	1	0	2	0	0.0043	3.27	3.17	0.00012	5.43	5.21
K111AK192A	0	0	1	1	0	2	0	0.0078	2.91	3.17	0.00026	4.96	5.21
K111AK192A	0	0	1	1	0	2	0	0.0040	3.32	3.17	0.00016	5.23	5.21
K111Q	0	1	1	1	1	0	0	0.24	0.86	0.81	0.00021	5.08	4.98
K111Q	0	1	1	1	1	0	0	0.24	0.86	0.81	0.00029	4.89	4.98
K111Q	0	1	1	1	1	0	0	0.24	0.86	0.81	0.00015	5.28	4.98
K111Q	0	1	1	1	1	0	0	0.33	0.67	0.81	0.00044	4.64	4.98
K192Q	1	0	1	1	1	0	0	0.27	0.79	0.79	0.00016	5.26	4.99
K192Q	1	0	1	1	1	0	0	0.26	0.81	0.79	0.00026	4.96	4.99
K192Q	1	0	1	1	1	0	0	0.28	0.76	0.79	0.00043	4.65	4.99
K111QK192Q	0	0	1	1	2	0	0	0.0033	3.43	3.13	0.00029	4.89	4.33
K111QK192Q	0	0	1	1	2	0	0	0.0033	3.49	3.13	0.00029	4.89	4.83
K111QK192Q	0	0	1	1	2	0	0	0.016	2.48	3.13	0.00036	4.76	4.83
WT	1	1	1	0	0	0	10	0.02200	2.29	2.10	0.00011	5.47	5.69
WT	1	1	1	0	0	0	10	0.036	2	2.10	0.00006	5.83	5.69
WT	1	1	1	0	0	0	10	0.035	2.01	2.10	0.00010	5.53	5.69
K111A	0	1	1	0	0	1	10	0.0015	3.92	4.05	0.00021	5.08	4.74
K111A	0	1	1	0	0	1	10	0.00093	4.19	4.05	0.00044	4.64	4.74
K192A	1	0	1	0	0	1	10	0.00023	5.03	5.03	0.00013	5.37	5.39
K192A	1	0	1	0	0	1	10	0.00023	5.03	5.03	0.00008	5.66	5.39
K111AK192A	0	0	1	0	0	2	10	0.00017	5.22	5.22	0.00091	4.20	4.45
K111AK192A	0	0	1	0	0	2	10	0.00017	5.22	5.22	0.00057	4.48	4.45
K111Q	0	1	1	0	1	0	10	0.00110	4.09	4.10	0.00010	5.53	5.23
K111Q	0	1	1	0	1	0	10	0.0016	3.86	4.10	0.00031	4.84	5.23
K111Q	0	1	1	0	1	0	10	0.00070	4.36	4.10	0.00015	5.28	5.23
K192Q	1	0	1	0	1	0	10	0.00043	4.65	4.46	0.00003	6.33	6.32
K192Q	1	0	1	0	1	0	10	0.00081	4.27	4.46	0.00003	6.31	6.32
K111QK192Q	0	0	1	0	2	0	10	0.000016	6.63	6.82	0.00024	5.00	5.04
K111QK192Q	0	0	1	0	2	0	10	0.00001	7.02	6.82	0.00021	5.08	5.04
WT	1	1	1	0	0	0	0.9	0.85	0.1	0.10	0.00044	4.64	4.64
K111A	0	1	1	0	0	1	0.9	0.0047	3.22	3.22	0.00040	4.69	4.69
K192A	1	0	1	0	0	1	0.9	0.00028	4.9	4.90	0.00005	5.90	5.90
K111AK192A	0	0	1	0	0	2	0.9	0.00004	5.08	5.08	0.0005	4.56	4.56
K111Q	0	1	1	0	1	0	0.9	0.023	2.26	2.40	0.00018	5.17	5.38
K111Q	0	1	1	0	1	0	0.9	0.015	2.54	2.40	0.00008	5.65	5.38
K192Q	1	0	1	0	1	0	0.9	0.0035	3.39	3.39	0.0006	4.45	4.39
K111QK192Q	0	0	1	0	2	0	0.9	0.003	3.49	3.49	0.00036	4.76	4.82
K195A	1	1	0	1	0	1	0	0.014	2.56	2.49	0.00012	5.42	5.75
K195A	1	1	0	1	0	1	0	0.018	2.42	2.49	0.00004	6.08	5.75
K195A	1	1	0	0	0	1	10	0.00030	4.86	4.84	0.00009	5.59	5.56
K195A	1	1	0	0	0	1	10	0.00033	4.81	4.84	0.00011	5.53	5.56
K192AK195A	1	0	0	1	0	2	0	0.0023	3.64	3.44	0.00018	5.17	5.35
K192AK195A	1	0	0	1	0	2	0	0.0043	3.24	3.44	0.0001	5.53	5.35
K192AK195A	1	0	0	0	0	2	10	0.000035	6.16	5.94	0.00013	5.37	5.20
K192AK195A	1	0	0	0	0	2	10	0.000072	5.72	5.94	0.00023	5.03	5.20
K195A	1	1	0	0	0	1	0.9	0.012	2.65	2.65	0.00006	5.83	5.83
K192AK195A	1	0	0	0	0	2	0.9	0.00020	5.11	5.11	0.0000026	7.72	7.72

The assays comprise full factorial designs of the K111-K192-metal (3 factors, each at three levels, 3³ = 27 conditions) and K192-K195-metal (3 factors at two levels (Alanine mutation, Mg²⁺ vs Mn²⁺ 0.9 mM; 3² = 9 conditions) systems. Using 96-well format, we examined all 36 conditions using four-fold replicates of [ATP]-dependent ³²PPi exchange kinetics to determine both steady-state parameters. These measurements repeated individual assays previously done for most conditions, giving a total of 56 values for Michaelis-Menten parameters Km and k_cat for the 36 different conditions (Table 1).

Multiple independent assays (as opposed to internal four-fold replicates) document experimental reliability. Dimensionless coefficients of variation, c_v = σ/μ, the ratio of the standard deviation to the mean value of repeated determinations were 0.069 ± 0.08 (0<c_vk_cat<0.18) and 0.043 ± 0.027 (0>c_vKm>0.096). These are acceptable error estimates to support our interpretations of Δ(ΔG) values in Table 2 and Figs. 5 and 6.

Table 2. Regression Parameter Estimates.

(α) Δ(ΔGKm) N=22 experiments, R2 = 0.95
Term	Estimate	Std Error	t Ratio	Prob>|t|
111	0.10	0.118	0.83	0.4277
192	−0.22	0.101	−2.19	0.0534
195	−0.68	0.128	−5.33	0.0003
Mg	−0.27	0.113	−2.35	0.0406
(111)*(192)	−0.40	0.239	−1.67	0.1251
(192)*(195)	−0.59	0.258	−2.28	0.0460
(111)*(Mg)	−0.66	0.271	−2.42	0.0360
(192)*(Mg)	0.96	0.226	4.26	0.0017
(195)*(Mg)	1.10	0.280	3.91	0.0029
(111)*(192)*(Mg)	1.37	0.543	2.51	0.0307
(192)*(195)*(Mg)	−1.67	0.559	−2.98	0.0138

(β) Δ(ΔGkcat), N=22 experiments, R2 = 0.996
Term	Estimate	Std Error	t Ratio	Prob>|t|
111	−1.62	0.0816	−19.88	<.0001
192	−2.05	0.0699	−29.31	<.0001
195	−2.04	0.0884	−23.07	<.0001
Mg	−1.48	0.0780	−18.97	<.0001
(111)*(192)	−1.12	0.164	−6.83	<.0001
(192)*(195)	−1.51	0.178	−8.47	<.0001
(111)*(Mg)	0.22	0.187	1.18	0.2656
(192)*(Mg)	1.44	0.156	9.21	<.0001
(195)*(Mg)	−0.76	0.193	−3.93	0.0028
(111)*(192)*(Mg)	2.50	0.374	6.67	<.0001
(192)*(195)*(Mg)	1.15	0.386	2.99	0.0136

Fig. 5.

Catalytic effects of K111, K92, K195, and Mg²⁺ estimated from multiple alanine mutations at 0.9 mM. Main effects are on light grey, two-way coupling-energies on clear, and three-way coupling energies on darker grey backgrounds. Ground-state interactions (ΔG_Km; open bars) differ significantly from those in the transition state (ΔG_Km; shaded bars), especially the 192-195-Mg²⁺ interaction involving the KMSKS loop (far right), which stabilizes the ground state complex but destabilizes the transition state complex. Inset: net impacts of the four, coupled charges.

Fig. 6.

Energetic coupling in the PPi leaving group subsite. K111 and K192 were mutated to both A and Q and assayed at optimal (0.9 mM) and inhibitory (10 mM) [Mn²⁺], and with Mg²⁺. Inhibitory [Mn²⁺] significantly reduces coupling, strengthening main effects, especially of Mg²⁺. Hydrogen bonding by Q, relative to A in the transition state (shaded histograms) enhances the ternary coupling of 111 and 192 to the metal and reverses the sign of the 111-192 interaction.

As described with an example in Methods, we encoded independent variables in Table 1 with binary (0 or 1) values according to the presence of K111, K192, K195, Mg²⁺, and either alanine or glutamine. We converted dependent variables Km and k_cat into free energy changes and built linear models for ΔG_calc(k_cat,Km) as functions of predictors derived from column entries 2–5 or 6–8 in Table 1, representing main effects, and their 2, 3, and 4-way products, representing interactions. Regression model coefficients, β_ij, for interaction terms, factor_i*factor_j, are equivalent to the non-additivity of thermodynamic cycles and estimate the energetic coupling between factors i and j. We follow First’s convention for interactions within the KFGKT loop of TyrRS (First and Fersht, 1995; Horovitz and Fersht, 1990) in which free energy changes are evaluated as ΔΔG) = Δ G(WT) − ΔG(mut) to represent ground- and transition-state ATP affinities.

A response surface model for ΔGk_cat evaluated as a quadratic polynomial function of the numbers of A and Q mutants, and the [Mn²⁺] from columns 6–8 of Table 1 (ie for the extensive independent variables; Fig. 4) accounts for 0.88 of the total variation in ΔGk_cat and its coefficients estimate the contributions of each type of substitution. Other things being equal, K->A mutations increase <ΔGk_cat> by ~+2.9 kcal/Mol, K->Q mutations by ~+1.9 kcal/Mol, and substituting Mg²⁺ with Mn²⁺ costs ~+2.1 kcal/Mol. Significant, nonzero β(#Ala)² and β[Mn²⁺]² terms in the response surface model imply that Δ(ΔGk_cat) values depend non-linearly on both variables. The nonlinearities complicated joint analysis of the full range of the factorial design. Analyses involving only a single amino acid type and a single [Mn²⁺] all gave similar statistics to those in Table 2. Thus, results are presented in that framework.

Fig. 4.

Quadratic response surface models for Δ(ΔGk_cat) fitted to all data in Table 1 as a function of the three types of substitution used in this study as independent variables. The abscissas for the three graphs are derived from columns 6–8 in Table 1. Parallel dashed lines represent 95% confidence levels output by JMP. Profile curvatures indicate that Alanine and Mn²⁺ substitution act non-linearly.

Multi-lysine-metal thermodynamic cycles

We could not determine the 111-195-metal ternary or the quadruple interaction between all three lysines and the metal without the K111-K195 multiple mutants. Regression models for the triple lysine cycles using data for all mutants with 0.9 mM Mn²⁺ nevertheless provided unbiased estimates of ground- and transition-state Δ(ΔG) values for the remaining interactions. These are shown as histograms in Fig. 5 with statistics summarized in Table 2. Fits are excellent for Δ(ΔG^‡_kcat), R² = 0.996 and for Δ(ΔG_Km) (R² = 0.95) and most Student t-test probabilities are <0.001 except for factors contributing marginally to Δ(ΔG_Km).

Main effects – Δ(ΔG) values due individually to K111A, K192A, K195A and Mg²⁺ – are comparable to values measured for the homologous K82A, K230A, and K233A residues in TyrRS (Fersht et al., 1988). As for TyrRS, main effects, including that of Mg²⁺, have little effect on the TrpRS ground-state complex with ATP (<Δ(ΔG_Km)> = −0.27 ± 0.32 kcal/Mol) while substantially and uniformly stabilizing the transition state (<Δ(ΔG^‡_kcat)> = −1.79 ± 0.29 kcal/Mol). Together with the K111*K192 and K192*K195 pairwise interactions, these contributions could accelerate catalysis by a factor of ~1.4 × 10⁷, providing roughly half of overall transition-state stabilization.

However, significant energetic couplings between the metal and all three lysine residues offset the net catalytic effect of Mg²⁺ (Fig. 2, inset). In the WT enzyme, metal-lysine interactions with the leaving group (K111, K192) increase ΔG_Km by 1.67 kcal/Mol, weakening the ground-state complex, while those involving K195 strengthen it by −0.57 kcal/Mol. Their combined effect is destabilizing (+1.1 kcal/Mol). In the transition state, multiple metal-lysine interactions increase ΔG^‡_kcat by a net of +4.55 kcal/Mol, slowing catalysis more than 10³-fold. Most of this transition-state destabilization, +4.16 kcal/Mol, arises from interactions between the metal, K111, K192 and the PPi leaving group. Transition-state K195*metal interactions balance one another and contribute only +0.39 kcal/Mol to ΔG^‡_kcat.

Interactions in the PPi leaving group subsite

We characterized metal interactions involved in binding PPi further by examining how they changed with K->Q mutations and with inhibitory [Mn²⁺] (Fig. 6). Although ground-state interactions and lysine main effects are almost unaffected by these perturbations, two effects are notable in the transition state. The higher [Mn²⁺] reduces interactions to the metal, strengthening the main effect of [Mg²⁺] (lower two panels), whereas glutamine significantly enhances coupling to the metal and reverses the sign of the K111-K192 interaction (right-hand panels).

Loss of both lysine residues in the double alanine mutant induces substantial loss of activity, Δ(ΔG^‡_kcat) = +5.2 kcal/Mol with 10 mM Mn²⁺ and +5.1 kcal/Mol with 0.9 mM (Table 1). Curiously, the least active variant is the double glutamine mutant assayed with 10mM Mn²⁺ (Δ(ΔG^‡_kcat) = +6.8 kcal/Mol)). That mutant is considerably more active with 0.9 mM Mn²⁺ (Δ(ΔG^‡_kcat) = +3.5 kcal/Mol)). Thus, optimal [Mn²⁺] restores more than an order of magnitude in rate to the K111QK192Q mutant but has no effect on the K111AK192A mutant. This ternary coupling, (+3.4 kcal/Mol; P(t) <0.0001) is substantially larger than that for the other three quadrants in Fig. 6. It arises because the double glutamine mutant retains the ability to form an electrostatic interaction and hence to interact with the metal via the common non-bridging oxygen atoms.

Ternary coupling on ΔG_Km is expressed differently. The K192Q/A mutants, which have nearly tenfold higher apparent affinity for ATP than wild-type enzyme at either Mn²⁺ concentration, show approximately wild-type affinity when accompanied by the K111Q/A mutations (Table 1). Thus, the strongest ground-state association with ATP occurs with the configuration K111, Q192, 10 mM Mn²⁺ while the weakest occurs with A111, A192, 0.9 mM Mn²⁺.

Catalytic interactions with outer-sphere metal ligands

Fig. 7A suggests the possible transition-state involvement of residues Q9 and/or D146 with the metal ion. Functional groups of both residues are ~3.5 Å from the metal ion, and the D146 carboxylate not only bears a complementary negative charge, but also could fulfill the vacant sixth coordination position in the octahedral coordination of the Mg²⁺. Fersht (Fersht, 1987) identified the homologous D194 in TyrRS as a possible transient Mg²⁺ ligand. Neither structural nor multi-mutant thermodynamic data implicated this participation experimentally.

Fig. 7.

A. Catalytically important outer-sphere metal interactions with Q9 and D146, may modulate in the transition state, as the metal moves to accommodate the separation of PPi from AMP. Residues Q9 (B) and D146 (C) both show significant coupling to the metal ion. Δ(ΔG^‡k_cat) values (Student t-test probabilities) were obtained as in Figs. 5, 6. Interactions with the metal are of opposite sign and effectively cancel.

We therefore investigated coupling of the metal to both D146 and Q9 as shown in Fig. 7b,c. Both side chains couple to the metal ion in the transition state. Coupling to D146 is synergistic (−0.8 kcal/Mol), that to Q9 is antisynergistic (+1.1 kcal/Mol). The net impact of coupling to the two side chains is minimal.

DISCUSSION

Transducing NTPases couple catalysis of phosphoryl-transfer to conformational changes that drive formation and dissociation of other useful intermolecular complexes. Experimental (Admiraal and Herschlag, 1995) and computational (e.g. (Fothergill et al., 1995)) studies provide considerable evidence that the divalent metal ion(s) associated with phosphoryl-transfer reactions lower transition-state free energies by stabilizing changes in the electrostatic charges on the reacting nucleophile and phosphate groups. Such studies do not address the essentially total, experimentally observed non-additivity of the metal’s catalytic contribution of ~−6.5 kcal/Mol to the TrpRS-catalyzed synthetase reaction (Weinreb and Carter, 2008). This non-additivity results from the minimal catalytic assist of Mg²⁺ in aqueous solution (Tetas and Lowenstein, 1963), which has been attributed to differences in the dielectric constant of water and enzyme active sites (Fothergill et al., 1995). However, dielectric is a macroscopic property. When applied to a subtle molecular machine, “dielectric” conceals mechanistic details that couple the metal to the enzyme, allowing the coupled metal to accelerate the enzymatic reaction by overcoming barriers that preclude stabilizing transition-state configurations in aqueous solution. We have begun here to experimentally measure the coupling constants responsible for the non-additivity of thermodynamic cycles involving the metal. Key to such coupling (see Fig. 1 of (Fothergill et al., 1995)) is the ability of the metal ion to rearrange as the system passes through the transition state. Data presented here complement other mechanistic descriptions (Warshel et al., 2006) by providing new, quantitative molecular details for how coupling effects analogous metal rearrangement, Fig. 2, linking catalysis to domain movement in TrpRS.

Mg²⁺ ion accelerates TrpRS-catalyzed tryptophan activation ~10⁵ fold, providing 35% of the catalytic reduction in ΔG^‡_kcat by an almost entirely indirect process (Weinreb and Carter, 2008). Lysine-Mg²⁺ coupling actually reduces the overall rate enhancement. Favorable longer-range interactions from outside the active site are therefore required to explain the overall catalytic effect of the metal. Further, as the energetic coupling affects ground- and transition-state ATP affinities differently, our results support all four elements of the model for how long-range and lysine-Mg²⁺ couplings combine to produce the overall rate acceleration contributed by the metal (Fig. 2). The data illustrate the advantages of multiple regression methods in the analysis of increasingly complex coupled systems, and validate conclusions drawn initially from non-equilibrium MD simulations. We conclude by considering parallels to DNA polymerases and broader implications of the model in Fig. 2 to transducing enzymes that share aspects of TrpRS metal coordination.

Regression methods are beneficial in the analysis of increasingly complex energetic coupling

Multiple regression allows simultaneous estimation and statistical assessment of Δ(ΔG_calc) values previously calculated separately (Horovitz and Fersht, 1990). The R.M.S.D. between regression coefficients and values calculated directly from averaged experimental observations is ~0.015 kcal/Mol. Four advantages of regression methods become increasingly important for more ambitious investigations of higher-order energetic coupling in macromolecules. i) Significant effects are identified and assessed jointly and hence more efficiently. ii) The impact of experimental errors is distributed statistically, rather than associated with individual observations. iii) Student t-tests assess the relative significance of different predictors (Table 2). iv) Comparison of coupling energies with those derived using the methods of Horovitz and Fersht is a supplemental check on the quality of both data and models.

Metal substitution reveals novel electronic coupling

The multi-lysine-metal system represents energetic coupling that has not previously been studied, because it is mediated by the phosphate oxygen atoms. By using both Mn²⁺ and K->Q substitutions, in addition to alanine mutagenesis, we found evidence for unexpectedly subtle electronic effects. The 111A192A and 111Q192Q double mutants provide the clearest evidence. With Mg²⁺, there is essentially no difference between double A and Q mutants (Table 1). With 0.9 mM Mn²⁺, the double Q mutant is more active than the double A mutant by ~0.7 kcal/Mol. With 10 mM Mn²⁺, however, the situation is reversed, and the double Q mutant is less active by ~0.9 kcal/Mol, and is indeed, the least active combination. Optimal [Mn²⁺] is a surprisingly good catalytic match for glutamine. Moreover, the high coupling energies suggest that simultaneous and less drastic perturbations (glutamine mutations to residues 111 and 192 and 0.9 mM Mn²⁺) preserve a functional electronic balance.

As the effective radii of the hexacoordinated metals are almost the same, 0.86 Å for Mg²⁺ and 0.81 Å for Mn²⁺ (http://www.webelements.com), both should “fit” equally well into the coordination field provided by the TrpRS-bound ATP. However, Mg²⁺ is an alkaline earth metal, while Mn²⁺ is a transition metal. They differ in electronegativity and hence in the degree of ionic character in metal-oxygen bonds (Pauling, 1970). These differences may help explain their behavior. The Mn²⁺-oxygen bond is ~14% more covalent than the Mg²⁺-oxygen bond, which may allow it to interact better with the glutamine amide nitrogen hydrogen bond, whereas optimal coupling to the more ionic Mg²⁺-oxygen bond requires a stronger electrostatic field provided by the positively charged lysine εNH₂ group.

A mechanism for metal activation and its catalytic function

Our data document the dynamic behavior of the Mg²⁺ coordination during catalysis. Energetic coupling evolves dramatically from ground state to transition state (Figs. 5,6). As with similar multi-mutant cycle analysis of the KFGKT (consensus KMSKS) loop in TyrRS (First and Fersht, 1993a; First and Fersht, 1993b; First and Fersht, 1993c; First and Fersht, 1995), ternary coupling is relatively more significant for Δ(ΔG_Km) than for Δ(ΔG_kcat). Because we did not examine coupling to the tryptophan subsite, and the previous studies did not examine coupling to the catalytic metal, detailed comparison is not appropriate. Our data complement the structural data on the catalytic mechanism (Fig. 8) by providing significant key supporting evidence for items (i–iv) of the model in Fig. 2:

Fig. 8.

Crystal structures show the structural evolution of the PPi binding subsite during catalysis, from of the PreTS (1MAU, A), PostTS (2OV4, AQP; B) and Products (C). Of special relevance are changes in interatomic distances for hydrogen bonding by K111 and K195. The presence of PPi in the Products complex structure with tryptophan-5′ sulfoamyl adenylate (unpublished) documents the relocated PPi binding site due to untwisting the two domains.

1. Ground-state coupling weakens ATP affinity. Metal effects on ground-state ATP affinity are dominated by higher-order interactions that sharply divide between destabilizing K192-Mg²⁺ and K111-K192-Mg²⁺ and stabilizing, K192-K195-Mg²⁺, effects (Fig. 5). We showed elsewhere that Mg²⁺ weakens ATP binding (Kapustina et al., 2007).

2. Coupling weakens metal affinity. The antisynergistic net ground state coupling of Mg²⁺ to the three lysine residues (+1.1 kcal/Mol) reciprocally weakens metal affinity.

3. Equivalence of the three phosphate-Mg²⁺ bonds breaks in the transition state. Ground state interactions between the metal and oxygen atoms from all three phosphates oppose phosphoryl transfer because they “cross-link” moieties on either side of the scissile bond. The large contributions of ternary (111*192*Mg²⁺) coupling to the two Michaelis-Menten parameters have the same sign and hence opposite effects on the enzymatic second-order rate constant, k_cat/Km. The coupled system, K111-K192-Mg²⁺, is effectively independent and acting exclusively on the leaving group. In contrast, ground and transition state coupling effects involving K195 are stabilizing, providing persuasive evidence that the three interactions seen as roughly equivalent in the PreTS crystal structure evolve differently in the transition state. We previously determined that Mg²⁺ affinity increases ~20-fold in the transition state (Weinreb and Carter, 2008), consistent with an electrostatic basis for its catalytic effect (Warshel et al., 2006). Of particular relevance, the evolution of the bifurcated hydrogen bond distances between K195 and the α-phosphate suggest that K195 serves a transitional role of charge stabilization on both _αP and PPi (Fig. 8).

4. Restoring force in the unfavorable twist angle favors bond cleavage and replacement of K111 by K195. It is perhaps surprising that the localized coupling to Mg²⁺ is almost entirely antisynergistic (Δ(ΔGk_cat)≫0). However, this result is consistent with the conclusion that significant sources of transition-state stabilization are extrinsic to the coupled metal-lysine system. We return to this point below. Fig. 8C documents the evolution of hydrogen bonding by the three lysine residues in the product complex with tryptophan-5′ sulfoamyl-adenosine (Huang, unpublished) in which the PPi leaving group is evident.

Our data validate predictions based on non-equilibrium MD trajectories

Active-site lysine residues weaken ground-state metal-triphosphate interactions by hydrogen bonding to non-bridging phosphate oxygen atoms that coordinate the Mg²⁺. MD simulations showed that these interactions could be manipulated by restraining the Mg²⁺ ion positions, the lysine ligand positions, or the high inter-domain twist angle (Kapustina and Carter, 2006), suggesting that the crystallographic configuration (Retailleau et al., 2003) arises from coupled equilibria between them. We confirmed these virtual experiments experimentally here, by measuring coupling free energies with mutagenesis and thermodynamic cycles. The ground-state antisynergy involving K111 and K192 confirms the conclusion from virtual MD experiments (Kapustina and Carter, 2006) that their hydrogen bonds to phosphate oxygen atoms compete with bonds to Mg²⁺. The synergy of K195-metal coupling is also consistent with the observation that the K195-oxygen hydrogen bond with the α-phosphate is retained when the unrestrained Mg²⁺ ion moves closer to the oxygen atoms.

Longer-range interactions are necessary to account for the catalytic contribution of Mg²⁺

Whereas the main effects and the synergistic interaction within the three lysine side chains themselves favor catalysis in both the ground and transition states (Fig. 5), metal interactions have, in general, the opposite effects, significantly reducing its catalytic effect. This predominant antisynergy of local interactions with the metal cannot explain its catalytic contribution. The net catalytic effect of all influences arising from the local K111-K192-195-Mg²⁺ system (taken from Fig. 5) actually increases the activation energy for kcat/Km by +1.87 kcal/Mol. The overall impact of the metal, on the other hand, is to favor catalysis by ~ −6.5 kcal/Mol (Weinreb and Carter, 2008).

It follows from this conundrum that catalytically productive interactions between TrpRS and the Mg²⁺ ion must arise from longer-range, allosteric effects. Some of these could arise from outer coordination shell interactions with Q9 and D146 (Fig. 7). Thermodynamic cycles for these residues, Fig. 7B,C, suggest that transition-state interactions with D146 and Q9 are of opposite sign, however, and favorable coupling of D146 cannot compensate for the deficit created by the unfavorable impact of the local interactions.

Computational experiments show that the PreTS configuration is also coupled to the high twist angle between the Rossmann fold and anticodon-binding domain, which is energetically unfavorable (Kapustina, 2007) and untwists if lysine–phosphate-Mg²⁺ interactions are disrupted. Elsewhere, we have identified interactions from quite distant residues in the TrpRS monomer. One mutant, F37I (Kapustina et al., 2007), behaves analogously to D146A, increasing ΔG^‡_kcat both by its main effect and by its coupling to the metal. This example establishes that long-range interactions can act synergistically with the metal. Comparative behavior of the mutants examined here in the minimal catalytic domain (Pham et al., 2007); would provide further insight concerning the impact of the full native TrpRS dimer.

The TrpRS [Mn²⁺]-dependence reinforces mechanistic parallels to polymerases

The “B-site” metal of the incoming NTP in most or all DNA polymerase families is coordinated to non-bridging oxygen atoms of all three phosphates (Yang et al., 2006), as is the Mg²⁺ in the TrpRS PreTS complex. That Mn²⁺ assists TrpRS catalysis efficiently only within a very narrow concentration range (0.05–1.5 mM) as observed for polymerases reinforces the suggestion that the two enzyme families share mechanistic similarities. Increasing metal concentration leads to inhibition of both classes of enzymes. It is unlikely that the inhibition by high [Mn²⁺] can be explained without invoking binding of additional metal atom(s) and a consequent change in mechanism, as implied by the much reduced metal-lysine coupling in TrpRS at 10 mM Mn²⁺. Possibly, binding of Mn²⁺ at site B in polymerases may activate, while binding in site A may inhibit. In that case, the inhibitory phase of the Mn²⁺ effect in TrpRS may result from binding of a second metal to a site similar to the polymerase A site, which would imply even deeper homology between the class I aaRS and polymerase families.

Relaxation of amino acid specificity by Mn²⁺ implies additional coupling to the amino acid site

The [Mn²⁺]-dependence of TrpRS activity is especially reminiscent of that for the mutagenic Y-family DNA polymerases, Polι̇ and Polη (Frank and Woodgate, 2007). The mutagenic effects of Mn²⁺ in polymerases are generally attributed to relaxed stereochemical constraints in metal coordination (Yang et al., 2006). While this argument may explain why incorrect (d)NTPs are incorporated in the elongation cycles of polymerases, it is somewhat surprising that this effect extends to the TrpRS amino-acid binding site, especially as the effect arises from opposite effects on Km. Loss of amino acid specificity is especially remarkable in light of the robust resilience of the tryptophan binding site to mutations designed to favor the activation of tyrosine (Praetorius-Ibba et al., 2000). We offer no explanation, except to observe that the relaxed specificity induced by Mn²⁺ is prima facie evidence for coupling between the ATP and amino acid-binding subsites, as also observed for TyrRS (First and Fersht, 1993b; First and Fersht, 1995), and hence to other, as yet unexamined allosteric effects.

Allosteric metal ion activation for catalysis has general implications

The need to invoke long-range energetic coupling to explain the 10⁵-fold catalytic assist by Mg²⁺ and the evident communication between the ATP and amino acid-binding subsites are two aspects of the complexity of the TrpRS catalytic utilization of ATP. Do our observations apply more broadly? As described by Jencks (Jencks, 1987) divalent metal coordination by the triphosphate moiety of NTPs affords a variety of potential catalytic effects. Unlike class II aaRS, CTP-, and UTP-dependent biosynthetic enzymes, transducing NTPases all use bridging metal configurations to convert purine NTP hydrolysis into biologically useful work or information, by making catalysis contingent on domain rearrangement. The bridging metal appears to enforce that contingency by stabilizing the transition state, if and only if domain motion occurs.

Metal rearrangement has long been implicated in the conformational changes of Switch regions 1 and 2 upon GTP hydrolysis and which are responsible for signaling functions (Schlichting, 1990). The correlation between the bridging metal configuration and the transduction of NTP hydrolysis into biological functions implies a link between catalysis and long-range energetic coupling to the metal, and suggests a new interpretation for this configuration in which domain movement provides mechanisms both to rearrange the metal coordination and to regulate its catalytic functions. A much broader class of transducing phosphoryl-transfer enzymes with similar metal coordination would seem to require similar coupling mechanisms.

EXPERIMENTAL PROCEDURES

Mutagenesis and Protein Purification

Mutations were constructed using the GeneTailor kit (Invitrogen). The expression plasmid pET11a containing wild type TrpRS was methylated by DNA methylase and used as template for mutagenic PCR. Primers were designed to prime in opposite directions, with a 15–20 nucleotide overlap for efficient circularization. The PCR product was used to transform DH5α E. coli cells, and plated on LB plates with ampicillin. The resulting plasmids were sequenced to confirm the successful introduction of the mutations.

Mutant proteins were expressed in E. coli BL21(DE3)pLysS, with both ampicillin and chloramphenicol, Simultaneous 2L cultures of three mutants at a time were harvested and resuspended in 50 mM Tris, 10% Sucrose, pH 7.5 and rapidly frozen. The cell paste was homogenized with an EmulsiFlex C-5 homogenizer and cleared by centrifugation at 4°C. The resulting supernatant, the K111A, K192A, and K195A mutants were first chromatographed on DEAE cellulose. These and the remaining mutants were then dialyzed against 20 mM HEPES, 0.1 mM PMSF, 50 mM KCL, 10 mM 2-mercaptoethanol, pH 7.0, loaded onto a HiTrap Blue HP Column (Amersham Biosciences) using a BioCAD Sprint chromatography workstation (GMI, Inc., Ramsey, MN), and then eluted using a 0–1.0 M KCl₂ gradient. Peak fractions then were dialyzed against 20mM HEPES, with the same additions, and loaded onto a Poros HS column (Perceptive Biosystems) and eluted with a 0.1–1.0 M KCl gradient. Purified mutant proteins were concentrated using an Amicon PM10 Ultra membrane and stored at −20°C in 50% Glycerol.

Assays and Michaelis-Menten kinetics

PPi-exchange assays were done at 37°C and initiated with 10 μl of enzyme to 190 μl of assay mix: 0.1 M Tris-Cl, 0.01 M KF, 5 mM MgCl₂, 2 mM ATP, 50 mM Tryptophan, 70 mM 2-mercaptoethanol pH 8.0 plus 2mM ³²PPi at a specific radioactivity between 1×10⁵ and 2×10⁵ CPM/μM. Varying enzyme concentrations (4–400 μM) and incubation times (15–90 minutes) were used, depending on the activity level. Michaelis-Menten kinetics were examined by varying the [ATP] (0.01, 0.1, 0.3, 0.5, 1.0, 1.5, 2.0 mM). For metal substitution assays the mix was made without Mg²⁺ and treated with Chelex 100 for 30 min at 4°C to remove the trace metals and supplemented with either 0.9 mM or 10 mM MnCl₂. Assays were initially performed with three replicates in individual vials. As the need for higher throughput became apparent, however, we transitioned to the use of 96-well plates with four replicates, using Varian Captiva filter plates and a Promega Corportion Vacman vacuum manifold for filtrations. As indicated in Table 1, several mutant proteins were analyzed using both formats, and some were assayed multiple times, until there was satisfactory reproducibility of their kinetic parameters. All assays were processed by eluting ³²P-ATP from charcoal with pyridine as described (Pham et al., 2006). This procedure is ~ 4 times more sensitive than counting the charcoal directly. Steady-state k_cat values for all variants, including native TrpRS, are reported per mole of monomer.

Estimation of free [metal]

Free metal ion concentrations were estimated from total metal concentrations using the MAXCHELATOR web server, http://www.stanford.edu/~cpatton/downloads.htm under the assumptions that the pH = 8.0, [ATP] = 2 mM, I = 0.114 M, and the dissociation of ADP was used to represent the PPi (2 mM).

Regression analysis

Michaelis-Menten parameters obtained by non-linear least squares from [ATP]-dependent Michaelis-Menten experiments were converted to free energies, ΔG^‡ = −RT ln(k_cat) and ΔG_(Km) =−RT ln(K_m), where RT = 0.6 kcal/Mol; assembled in matrix form (eg., Table 1), and input to JMP (SAS, 2004), a stand-alone statistics program devised by SAS with an intuitive interface for scientific data analysis and experimental design. Regression models take the form of the factorial design for a given thermodynamic cycle: ΔG_calc = β₀ + Σ_i(β_i*(X_i)) + Σ_iΣ_j(β_ij*(X_i)*(X_j) + ε, where β_i and β_ij are coefficients in kcal/Mol (e.g., Table 2) and X_i (1 or 0, according to whether the observation was made with WT and Mg²⁺ or mutant residue(s) and/or Mn²⁺) are predictors from columns 2–8 of Table 1. Full factorial regressions test all columns (2–5 for Table 2 and Figs. 5,6; 6–8 for Fig. 4), and products of all pairs of columns, all triples, all quadruples, and so on, as predictors. Relatively few of the potential predictors have coefficients with significant Student t-tests. Alternative models were thus evaluated using stepwise regression to eliminate insignificant effects (with P > 0.15) and then re-evaluated by standard least squares to minimize the mean squared prediction error, ε = ΔG_calc − ΔG_obs (Cols 9,12). The resulting coefficients {β_i,_,β_ij,…} represent the energies of the important main effects and interactions.

We illustrate the robustness of multiple regression by comparing models fitted to two different subsets from Table 1 for the thermodynamic cycle formed by the K192A mutation with 0.9 mM Mn²⁺. The regression models in this case are: ΔG^‡_calc = β₀ + β₁₉₂*K192[Col3] + β_Mg*Mg²⁺[Col5] + β_192·Mg*K192[Col3]*Mg²⁺ [Col5] + ε. and ΔG^Km_calc = β′₀ + β′₁₉₂*K192[Col3] + β′_Mg*Mg²⁺ +β′_192·Mg*K192[Col3] *Mg²⁺[Col5] + ε. Nine experiments in Table 1 are directly related to this system (5 WT with Mg²⁺, 2 K192A mutants with Mg²⁺, 1 each with WT and K192A using 0.9 mM Mn²⁺), and 24 experiments were done with alanine mutants in the presence of either Mg²⁺ or 0.9 mM Mn²⁺. Fitting both models to the sets of 9 and 24 experiments yields two slightly different sets of estimates for the six unknown parameters, {β₁₉₂, β_Mg, β_192·Mg; and β′_192, β′_Mg, β′_192·Mg}, {−2.75, −1.3, 2.63; −0.47, −0.08, 1.01} for 9 experiments and {−2.45, −1.79, 1.25; −0.4, −0.1, 1.3} for 24 experiments. Correlation between these two vectors, is 0.95, and all values are quite similar to those represented in Fig. 5. The squared correlation coefficients for ΔGk_cat and ΔGKm are 0.99 and 0.93 for regression against the limited data set and 0.70 and 0.28 for regression against the larger data set, which includes additional variation arising from other factors, K111 and K195. Moreover, Student t-test probabilities indicate statistical significance, even in the presence of variation induced by the “missing” factors. The advantages of regression methods – joint estimation of all relevant effects and interactions, robustness of estimates to the presence of “hidden” sources of variation, and natural estimation of statistical significance, increase with a system’s complexity.

Δ(ΔG) values were derived from ΔG_calc values from regression models, rather than from averages of replicate ΔG_obs measurements. As the regression models reproduced the latter average values extremely well, R² = 0.99, they are not significantly different from those derived in the traditional way (Horovitz and Fersht, 1990).