Investigation of the chemical step of phosphoryl transfer by QM/MM calculations in the enzymatic reaction of Adk.

a) Complete reaction scheme with corresponding illustrative free-energy landscape highlighting the chemical phosphoryl-transfer step (modified from ref. (Kerns et al., 2015)). Protein structures shown are apo Adk in the open conformation and Adk in the closed conformation with two bound ADP molecules and one Mg2+ atom (active-site arginine side chains are shown in stick representation). b) Phos-phoryl-transfer step is drawn with corresponding distances used to define the reaction co-ordinate as used in panels d,e. c) Free-energy profiles for the Adk catalyzed interconversion of ADP-ADP into ATP-AMP in the absence (blue) and presence of Mg2+ (orange) from QM/MM calculations. AD(T)P is fully charged for the reaction with Mg2+, and singly protonated on one ADP β-oxygen for reaction without Mg2+. The reaction coordinate is defined as the difference between the distance of the leaving oxygen to the transferring phosphorus d(Oleaving-P) and the distance of the attacking oxygen to the transferring phosphorus d(Oattacking-P). d,e) Distance between acceptor and leaving oxygens along the reaction co-ordinate in the presence (e) and in the absence (d) of Mg2+. The transition state regions in c-e are highlighted in orange and grey, respectively.

Free-energy profile estimates of the free-energy parameters of the reaction, using SCC-DFTB (all values in kcal/mol).

ΔG°: Overall reaction free-energy; ΔfG‡: Activation free-energy of the forward reaction. ΔbG‡: Activation free-energy of the backward reaction. ξ(TS) is the range of the reaction coordinate in the TSE (in Å); ζ(TS) is the improper dihedral angle of the transferring phosphate in the TS. The estimated errors of the free energies are in parenthesis and are computed as described in materials and methods.

Mechanism of phosphoryl transfer.

Diagram of Moore-O’Ferrall-Jencks (Jencks, 2002; O’Ferrall, 1970) from the QM/MM simulations, plotting the two P-O distances involved in the P-transfer for the reaction a,c) with Mg2+ and b,d) without Mg2+ (PT for transferring phosphate). The theoretical transition pathways for a tight, synchronous, and loose transition state are shown in c,d (as defined in ref. Roston et al. (Roston & Cui, 2016)).

Broad transition-state ensemble (TSE) in fully active enzyme.

a) Repre-sentative snapshots for structure of reactants, transition states, and products in the Adk active site in the presence and absence of magnesium. d(Oattacking-P) and d(Oleaving-P) are shown. Labels in black indicate the length of the bonds involved in the phosphate transfer and in green, the dihedral angle of the phosphoryl group. b,c) Superposition of the transition-state ensembles reveals a wider TSE with Mg2+ (b) relative to the one without the cation (c) with mean rmsd (± s.d.) of distances of the central P atom from its “average” position of 0.30 ± 0.11 Å (b) and 0.13 ± 0.06 Å (c). The TSE’s are superimposed with the X-ray structure solved with a transition-state analogue in green (AMP, AlF4- and ADP) reported in ref. (Kerns et al., 2015) (PDBID: 3SR0). d) Superposition of two extreme structures out of the large TSE for the enzyme with Mg2+, one where the phosphoryl group is closest to the donor oxygen (blue) and the other closest to the acceptor oxygen (red) high-lighting the asymmetric character of TSE members. e, f) superposition of most symmetric snapshot from TSE of QM/MM calculations (ball and stick representation in cyan) with the X-ray structure of transition-state analogue (green, PDBID: 3SR0 (Kerns et al., 2015)) including coordinating water molecules in f). g) zoom into the active site to display the broad TSE in the presence of Mg2+ aided by flexible Arg and Lys side chains in the active site.

Experimental testing of the computational findings.

a,b) Turnover rate constants that represent the chemical step (kchem) under these conditions were measured with 8 mM ADP/Mg2+ by HPLC detection of build-up of ATP and AMP. a) Temperature dependence of the phosphoryl transfer step measured in presence of calcium and in absence of divalent any cations, plotted as Eyring plots. Fits to the Eyring equation (dashed lines) result in ΔH‡ = 70.0 ± 4.1 kJ mol-1 and ΔS‡ = -80.0 ± 12.8 J mol-1 K-1 without metal, and ΔH‡ = 64.1 ± 2.2 kJ mol-1 and ΔS‡ = -23.8 ± 6.8 J mol-1 K-1 with Ca2+. b) pH dependence of kchem measured in the presence of calcium and in absence of any divalent cation.

Experimentally determined observed rate constants of the forward and backward chemical reactions for mutant forms of Adk in the presence of Mg2+.

Note that the corresponding rate constants for the phosphoryl transfer in the wild-type protein are too fast to be directly measured and have been estimated to be more than three orders of magnitude faster than in the mutants (Kerns et al., 2015).

QM/MM system.

The QM subsystem is shown in CPK representation and the MM subsystem is in lines representation.

Superposition of the starting model structure for QM/MM and the crystallographic structure (PDB ID: 4CF7 (Kerns et al., 2015)) of Adk with 2 ADP/Mg bound.

a) Comparison of ADPs, main amino acids and Mg2+ ion in the active site against the crystallographic model in green (starting structure for QM/MM as ball and stick), b) zoom-in showing Mg2+ ion coordinated by water molecules and the phosphates, and c) the Adk backbone of the starting model (cyan) and the crystallographic structure (green) with a backbone RMSD of 0.98 Å.

Forward and backward QM/MM reactions for Adk with two ADP and Mg2+ bound

a) Free energy profile (FEP) for the forward (solid grey line) and backward (solid blue line) reactions for the nonprotonated system in the presence of Mg2+. The dashed lines are the standard deviation for the forward and backward reactions in grey and blue, respectively. b,c) Works profiles obtained for the forward (b) and backward (c) reaction.

Forward and backward QM/MM reactions for Adk with ADP, ADP and Mg2+ bound

a) Free energy profile for the forward (solid grey line) and backward (solid blue line) reactions for the monoprotonated system with Mg2+. The dashed lines are the standard deviation for the forward and backward reactions in grey and blue, respectively. b,c) Works profiles obtained for the forward (b) and backward (c) reaction.

Forward and backward QM/MM reactions for Adk with two ADP and without Mg2+ bound

a) Free energy profile for the forward (solid grey line) and backward (solid blue line) reactions for the monoprotonated system without Mg2+. The dashed lines are the standard deviation for the forward and backward reactions in grey and blue, respectively. b,c) Works profiles obtained for the forward (b) and backward (c) reaction.

Representative snapshots for the reactant, TS and product states in the monoprotonated system with Mg2+. The labels in black describe the distances that are part of the phosphate transfer and the label in green show the dihedral angle. Label of the phosphates in orange.

A representative transition state structure is compared against the x-ray structure PDB ID: 3SR0 (Kerns et al., 2015).

The superposition is showed for: the main active site’s residues the atoms taking part of the reaction and backbone of the Adk.

Reaction with Mg2+ and fully charged nucleotides.

a-b) The change in geometrical parameters along the reaction coordinate are shown for (a) forward and (b) backward reaction. Parameters: distance Oleaving – Ptransferring (red), distance Oattack- ing – Ptransferring (black), transferring phosphate dihedral angle (light blue), distance Mg2+ – O from transferring phosphate (blue), and distance Mg2+ – O from beta-phosphate of ADPATP- lid (orange). c, d) The charge (mulliken charge) variation of different moieties involved in the reaction are shown for (c) forward and (d) backward reaction: Mg2+ (green), alpha-phosphate of ADPATP-lid (red), alpha-phosphate of ADPAMP-lid (orange), beta phosphate of ADPATP-lid (black), transferring phosphate (blue). Note that a proton is transiently transferred from one water molecule coordinating the Mg2+ to an oxygen of Pα in ADPAMP lid (leaving group). In all plots, the FEP is shown in the background as light grey dashed line.

Reaction without Mg2+.

a,b) The change in different geometrical parameters along the reaction coordinate are shown for (a) forward and (b) backward reaction. Parameters shown: distance Oleaving – Ptransferring (red), distance Oattacking – Ptransferring (black), transferring phosphate dihedral angle (light blue). c,d) The charge (mulliken charge) variation of different moieties involved in the reaction are shown for (c) forward and (d) backward reaction: alpha phosphate of ADPATP-lid (red), alpha phosphate of ADPAMP-lid (orange), beta phosphate of ADPATP-lid (black), transferring phosphate (blue). e,f) The distances involving the proton transfer are shown for (e) forward and (f) backward reaction: H – Oattacking (black), H – O of transferring phosphate (red) and H – O of alpha phosphate of ADPAMP-lid (green). In all plots, the FEP is shown in the background as light grey dashed line.

Reaction with Mg2+ and protonated in an oxygen of the beta phosphate of ADPATP-lid.

a,b) The change in different geometrical parameters along the reaction coordinate are shown for (a) forward and (b) backward reaction. Parameters shown: distance Oleaving – Ptransferring (red), distance Oattacking – Ptransferring (black), transferring phosphate dihedral angle (light blue), distance Mg2+ – O from transferring phosphate (blue), and distance Mg – O from beta phosphate of ADPATP-lid (orange). c,d) The charge (mulliken charge) variation of different moieties involved in the reaction with Mg2+are shown for (c) forward and (d) backward reaction: Mg2+ (green), alpha phosphate of AD-PATP-lid (red), alpha phosphate of ADPAMP-lid (orange), beta phosphate of ADPATP-lid (black), transferring phosphate (blue). e,f) The distances involving the proton transfer are shown for (e) forward and (f) backward reaction: H – Oattacking (black), H – O of transferring phosphate (red) and H – O of alpha phosphate of ADPAMP-lid (green). In all plots, the FEP is shown in the background as light grey dashed line.

Representative snapshots for the reactant, TS and product states in the system with Mg2+.

The main interactions between the phosphate moieties of the nucleotides and the amino acid side-chains in the active site are shown (in gray dashed lines).

Representation of the interactions between the nucleotides with the active-site amino acids and Mg2+ in the active site of Adk for a representative snapshot from the TSE.

Superposition of reactant (blue), TS (red), and product (green) states focusing on the transferring phosphate and the main amino acids assisting phosphoryl transfer, for the system with Mg 2+.

Free-energy profiles for the Adk catalyzed interconversion of ADP-ADP into ATP-AMP and presence of Mg2+ employing higher level DFT(PBE) free energy calculations (see methods for details). Reaction coordinate is the same as in Fig. 1. a) Superposition of the forward and backward free-energy profiles. b) The free-energy profile as result of the combination of the forward and backward free-energy profiles. The transparent pink region shows the transition state region. c) Distance between acceptor and leaving oxygens along the reaction coordinate in the presence of Mg2+. The transition state region is highlighted in pink. d,e) Diagram of Moore-O’Ferrall-Jencks (Jencks, 2002; O’Ferrall, 1970) from the simulations, plotting the two P-O distances involved in the P-transfer for the reaction with Mg2+, using DFT level at the QM region (PT for transferring phosphate). The theoretical transition pathways for a tight, synchronous, and loose transition state are shown in e (as defined in ref. Roston et al.(Roston & Cui, 2016)).