Characterizing Active Site Conformational Heterogeneity along the Trajectory of an Enzymatic Phosphoryl Transfer Reaction

Abstract States along the phosphoryl transfer reaction catalyzed by the nucleoside monophosphate kinase UmpK were captured and changes in the conformational heterogeneity of conserved active site arginine side‐chains were quantified by NMR spin‐relaxation methods. In addition to apo and ligand‐bound UmpK, a transition state analog (TSA) complex was utilized to evaluate the extent to which active site conformational entropy contributes to the transition state free energy. The catalytically essential arginine side‐chain guanidino groups were found to be remarkably rigid in the TSA complex, indicating that the enzyme has evolved to restrict the conformational freedom along its reaction path over the energy landscape, which in turn allows the phosphoryl transfer to occur selectively by avoiding side reactions.


Table of Contents
. Cooperative nucleotide binding Table S2. 15 N ε relaxation data of UmpK Table S3. Order parameters S 2 , local correlation times τ e and exchange contributions R ex

UmpK:
We sought to define three representative states along the phosphoryl transfer reaction of UmpK, that is, (1) a nucleotide-free state, (2) a substrate/product-bound state and (3)  We also tested the possibility of creating a representation of a substrate-bound state by a UmpK † :UMP:ATP and/or UmpK † :UDP:ADP complex, where UmpK † symbolizes an inactive form of UmpK. We considered such a strategy by removing the catalytically important Mg 2+ ion with EDTA, which renders UmpK (nearly) inactive. However, slow but significant turnover was observed, which would interfere with our NMR experiments.
Furthermore, the loss of cooperativity in nucleotide binding in the absence of Mg 2+ indicates that the functional conformation of the active site is at least partially impaired (Table S1).
We therefore arrived at the conclusion that the best reference for a substrate/product-bound state is provided by a complex between UmpK and the bi-substrate inhibitor AP 5 U, in which a phosphate links ATP and UMP (or ADP and UDP) covalently, such that nucleotide-like binding occurs but without turnover.

Transition state:
There is an on-going debate in the literature on whether the molecule that mimics the transferring phosphoryl group in various kinase:TSA complexes is an aluminium or a magnesium fluoride species. The planar tetragonal or trigonal molecules observed in TSA crystal structures at different pH were initially interpreted as AlF 4 − or AlF 3 species [4] , respectively, but there is evidence that at neutral and high pH, trigonal MgF 3 − may be the dominant species, as it provides a favorable negative charge [5] . We addressed this matter by Based on the similarity of 1 H ε -15 N ε correlation maps available for different states, these experiments indicated that nucleotides are bound but no transition state analog is formed under these conditions. However, in the presence of significantly less aluminium fluoride, the TSA complex was fully formed and it is characterized exclusively by slow nucleotide exchange kinetics and a long lifetime. Although the ADP:AlF x :UMP (TSA) complex decays at a rate that is substantially lower than dissociation of individual nucleotides or even bisubstrate inhibitor, it only displays moderate affinity for AlF x (K D ≈ 30 µM; Figure S2).
Initially this may seem surprising given it is considered to be a bona fide TSA, but one shall not forget that this TSA "construct" consists of 3 individual molecules, which are not linked covalently, and that a substantial entropic penalty for assembly of the components has to be contoured by binding energy [6] .

Sample preparation for NMR experiments
All NMR experiments were performed in buffer containing 50 mM Tris/HCl pH 7.5, 20 mM KCl, 2 mM DTE, 1 mM sodium azide. The D 2 O required for locking the NMR spectrometer was inserted into the NMR tube using an inset. This strategy has the advantage that splitting of peaks due to deuterium isotope shifts is avoided, thereby leading to higher quality NMR spectra. The AlF x stock solution was prepared from AlCl 3 and NaF in 1:5 molar ratio at pH 6.

Chemical shift assignment of the arginine side-chains of UmpK:
The general strategy was to make use of arginine-to-lysine mutations as suggested previously [7] , in order to identify the eight arginine side-chains of UmpK one by one, simply by observing peaks disappearing in the NMR correlation spectra ( Figure S3). Due to the nanomolar affinity of AP 5 U, the "substrate-bound" AP 5 U state is resilient to arginine-tolysine mutations and we successfully used the strategy of arginine-to-lysine mutation for the chemical shift assignment of both the AP 5 U-bound state and the nucleotide-free state of UmpK. However, this approach fell short for the TSA state as most mutations impaired the formation of this sophisticated transition state complex. The arginine side-chain chemical shifts were therefore assigned via backbone resonances of the TSA state, which in turn were obtained using standard triple-resonance NMR experiments (HNCA [8] , HN(CO)CA [8a, 8b] , 9] , HNCACB [10] ). To aid the assignment procedure we also utilized specifically labelled samples [ 13 C, 15 N-Arg; U-12 C, 14 N]-UmpK and [ 13 C, 15 N-Arg,Lys; U-12 C, 14 N]-UmpK, in which only the arginine (and/or lysine) residues were labelled with 15 N and 13 C. The arginine side-chain carbon chemical shifts were subsequently obtained by an HCCH-TOCSY [11] experiment and the link between backbone and side-chain assignment was obtained by comparing the 13 C δ chemical shifts that are available from HNCA-type experiment via the magnetization transfers 1 Of note is that the side-chain of R127 forms a π-stacking interaction with the adenine moiety of the bound ligands, which may be the cause of the particularly low 13 C ζ chemical shift of this residue. In the nucleotide-free state, only R28 and R176, which are both integrated in hydrogen bonding networks, are visible in the proton-detected spectrum.

Nuclear spin-relaxation measurements:
Overall correlation time τ m : For model-free analysis [12] , the overall correlation time τ m of the protein is required as an input, which we determined from 15 N backbone relaxation rates in the AP 5 U state. The obtained value of τ m = (11.2 ± 0.1) ns is in agreement with previous measurements of the highly homologous adenylate kinase in complex with AP 5 A [13] and can also be assumed for the TSA complex since their overall structures are identical.

Arginine side-chain spin-relaxation:
Arginine side-chain R 1 (N z ) and R 2 (N x ) relaxation rates were obtained to gain access to the level of conformational heterogeneity of the catalytically essential arginine side-chains. Such measurements are possible from proton-detected spectra following standard procedures and also from the carbon-detected spectra employing techniques that were recently developed [7] . Specifically, the transverse relaxation rate R 2 (N x ) is obtained via the corresponding relaxation rate in the rotating frame. The direction of the effective field for the 15 N nucleus during the application of a spin-lock field, ω SL , along x is ẑ ' = sin(θ)x + cos(θ)ẑ , where x and ẑ are direction vectors in the rotating frame, tan(θ)=ω SL /Ω N , and Ω N is the offset of the 15 N nucleus from the RF carrier, respectively.
Here ω SL ≈ 2π×1500 Hz to minimize the contributions from micro-millisecond exchange dynamics. The relaxation rate of the in-phase and anti-phase coherences in the rotating frame, which are used as input for the model-free analysis, are then given by [14] , The transverse relaxation rates, which form the basis for obtaining S 2 order parameters, can in some instances have small contributions from slower micro-millisecond exchange dynamics, even when obtained via relaxation rate in the rotating frame. We therefore also employed a set of exchange-free relaxation rates, R dd , that yield the "uncontaminated" dipole-dipole 15 N transverse relaxation rate [15] . Because of the nature of carbon-detected experiments, the anti-phase rates, R 2 (2C z N x ) and R 1 (2C z N x ) are obtained, however, as detailed previously the inphase rates can easily be obtained by, which leads to systematic errors less than 4.5% of the obtained rate. We assumed a uniform R 1 (C z ) of 0.5 s -1 throughout the analysis based on data from AP 5 U-bound UmpK.
For the nucleotide-free form of UmpK all active-site arginines give rise to strong peaks in the carbon-detected experiment, but are invisible in the proton-detected correlation maps. We therefore obtained the transverse relaxation rate of the arginine side-chains of nucleotide-free UmpK at a static magnetic field of 16.4 T using the newly developed carbon-detected experiments [7] . In contrast, in the TSA bound state most arginine peaks could be identified in the proton-detected spectra (with the exception of R148), while the carbon-detected spectra yielded no extra information. We therefore employed proton-detected relaxation experiments of R 1 , R 1ρ and R dd at 11.7 T for this state. In the AP 5 U-bound state many arginine side-chains were visible in both, the proton-and carbon-detected spectra, but the two types of spectra  Table S2.
Extracting motional parameters: As described previously [7, 12b, 15-16] , for an 1 H ε -15 N ε spinpair, the longitudinal relaxation rate, R 1 (N z ), the transverse relaxation rate, R 2 (N x ), and the dipole-dipole exchange-free transverse relaxation rate R dd can be expressed in terms of the spectral density function, J(ω): and J(0), J(ω N ) and J(ω H ) are the values of the spectral density function evaluated at frequencies of 0 rad s -1 , ω N , and ω H , respectively, where ω N is the 15 N Larmor frequency and ω H is the proton Larmor frequency. The contribution to the transverse relaxation that originates from fluctuations of the Zeeman Hamiltonian due to chemical exchange processes is R ex . Δσ is the chemical shift anisotropy (in ppm), assuming axial symmetry for the 15 N chemical shift tensor (Δσ Ν = −114 ppm for 15 N ε of the arginine side-chain [17] ), µ 0 is the permeability of free space, h is Planck's constant, γ H and γ N are the magnetogyric ratios of 1 H and 15 N, respectively, and r NH = 1.03 Å is the N-H bond length [16][17] .
The spectral density function, J(ω), can be expressed in the model-free formalism [12a, 18] as a function of the generalized order parameter, S 2 , the overall rotational correlation time of the protein, τ m , and a time-constant for the local motion, τ e .
The exchange-free experiment which provides the R dd rate is feasible only in a protondetected fashion, which excludes the nucleotide-free state from the more sophisticated analysis described in the following. In contrast, in the AP 5 U-bound state many arginine sidechains are visible in both the proton-detected ( 15 N-1 H) and carbon-detected ( 15 N-13 C) spectra.
Thus, we used this large dataset to check the robustness of the fitting procedure by including exclusively the proton-or carbon-detected data or forcing the exchange contribution R ex to be zero. We obtained consistent results in all cases. Furthermore, all local correlation times τ e were below 1 ns, thus at least one order of magnitude faster than the overall tumbling described by τ m , which is a prerequisite for the applied model. It should also be mentioned that the contribution from chemical exchange (R ex ) is at most 20% of the respective R 2 value even at the highest magnetic field strength (Table S3).
Overall, proton-and carbon-detected relaxation experiments performed at the different magnetic field strengths for AP 5 U-bound and TSA state were analyzed in a global fitting routine applying the model-free approach [12a, 18] to extract order parameter S 2 , local correlation time τ e and the exchange contribution R ex for each arginine side-chain.

Estimation of conformational entropy from arginine side-chain order parameters:
Side-chain order parameters have been shown to generally fall within bands [19] indicating the nature of motion that give raise to the order parameter, and side-chain order parameters between 0.3 and 0.7 indicate that one side-chain dihedral angle is involved in jumps between rotameric states [17, 19b, 19d] , while order parameters above 0.7 indicate that there is no dihedral disorder. The order parameters obtained from 15 N ε relaxation data of the active-site arginine residues are therefore directly related to the conformational heterogeneity of the catalytically essential chemical groups and therefore directly related to the conformational entropy of the active site.
We here base our estimations of conformational entropy from side-chain order parameters on the work by Wand and co-workers [19a, 19c] , which was guided by work by Karplus [20] , Akke et al. [21] and Yang & Kay [22] . In their models, the internal protein dynamics between disjoint states forms the basis for calculating the conformational entropy as: where S i is the intrinsic entropy in the ith state due to fast intra-well motions, k B is Boltzmann's constant, and p i is the population of the ith side-chain dihedral rotameric state. It was shown previously that the conformational entropy varies primarily through changes in the populations of rotameric states and that changes in the first term of Eq (S9) are small.
This means, in turn, that the change in conformational entropy can be predicted from the change in population of distinct rotameric states, or to a good approximation from the number of side-chain dihedral angles significantly engaged in rotameric jumps.
To support the above approach is that it has been shown previously that the conformational entropy associated with the general restriction of one rotor (dihedral angle) is 2−5 kJ/mol [23] .
In the limit, where one rotameric state is populated to 90% and one other state populated 10% gives a conformational entropy change of 0.8 kJ/mol relative to a rigid conformation [19d] .
With focus on the arginine side-chain, the χ 3 angle populates in the random coil gauche+ with 22%, trans with 50%, and gauche− with 28% [24] , which leads to a change of conformational entropy of −TΔS = −2.6 kJ/mol compared to a rigid χ 3 angle. Moreover, for an arginine side-chain with random coil populations [24] one can calculate according to the second term of Eq (S9) that −TΔS = −8.1 kJ/mol.
The basis for our simulation is the 34 states of the arginine side-chain that have been assigned previously [24] ; {s i } i≤34 . In a Monte Carlo approach we first assigned the number of states, n s , being sampled and subsequently assigned, randomly, the populations of the n s sampled states. In order to calculate the 1 H ε -15 N ε order parameters for different dynamic distributions, the 34 arginine side-chain structures were constructed and the angles between the 1 H ε -15 N ε bond vectors in the structures were calculated. The order parameter can subsequently be calculated from the equilibrium populations [18] according to where P 2 (z) is the second Legendre polynomial, Ω i describes the orientation of the internuclear N-H vector v i , and θ 12 is the angle between the vectors v 1 and v 2 , that is, v 1 •v 2 = cos(θ 12 ). For the discrete scenario considered here, where n s of the 34 discrete states are sampled, the order parameter is calculated as For each combination of the populations, the conformational entropy was calculated according to Term 2 of Eq S9 and the order parameter calculated according to Eq S11. The result of a Monte Carlo simulation involving 8×10 6 randomly selected n s and populations is shown in Figure 4. Also shown is the correlation between conformational entropy and 1 H ε -15 N ε order parameters obtained previously for RNaseH using molecular dynamics [17] . Since   [3] . All binding parameters obtained from these experiments are listed in Table S1. R42 and R137 in the AP 5 U state, a slight ambiguity remained due to both, the close spatial proximity of these arginine side chains in the structure as well as the proximity of these peaks in the spectra.
Mutation of one residue (e.g. R42K) led to substantial peak movement of the neighboring side chain (e.g. R137). In this case, we chose to assign the respective residue based on the shortest distance of the cross-peak in question to the respective cross-peak in the carbon-detected spectrum of wild-type UmpK in the AP 5 U state. In (c) the spectra of the arginine-to-lysine mutant were widely different from UmpK wild-type, thereby indicating that the TSA complex is not formed in the presence of the mutation. Here, the assignment was obtained via the backbone resonances as described in the Online For both S 2 CN and S 2 HN the parameters were determined using all available rates within each type of experiment and it was for this comparison assumed that the contribution from chemical exchange processes is negligible. RMSD = root-mean-square-deviation, and R 2 is the Pearson coefficient of linear correlation. The correlation obtained here for the UmpK:AP 5 U is very similar to that obtained previously. [7]