QM/MM Calculations

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2017

Electronic Supplementary Information for In silico analysis of interaction pattern switching in ligand···receptor binding in Golgi α- mannosidase II induced by inhibitors protonation state

V. Sladek,ab J. Kóňa a and H. Tokiwab

a) Institute of Chemistry – Centre for Glycomics, Slovak Academy of Sciences, Dubravska cesta 9, 845 38 Bratislava, Slovakia b) Dept. of Chemistry, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501 Japan E-mail: [email protected] ([email protected]); [email protected]

Starting geometry and protonation of AA Our models are based on geometries of the crystal structures (PDB ID: 3BLB 1,2 for swainsonine, PDB ID: 2F7O3 for Mannostatin A and PDB ID: 3DX34 for the ligand L5) and docked poses (ligand MAN, L2 and L6) calculated in our previous study.5 The GM enzyme model for docking calculations was based on the crystal structure of the complex swainsonine-GM (PDB ID: 3BLB 1,2) and structurally optimized (side chains of ionisable amino acids, positions and conformations of water molecules and positions of added hydrogen atoms) using Monte Carlo simulations as implemented in the Schrödinger package. -3 6 -3 6 -9 1 The Ki (or IC50) values of the individual inhibitors are: IC50(MAN) > 5 x 10 M , IC50(L2) = 2 x 10 M , Ki(SW) = 3 x 10 M , Ki(MSA) = 3.6 -8 3 -7 4 -5 7 5 x 10 M , Ki(L5) = 3 x 10 , Ki(L6) = 1.3 x 10 . They, along with many more, were comprehensively collected by Bobovska et al. The pKa values for the ligands bound in the receptor were estimated by the empirical calculations using the PROPKA 2.08,9 program considering

GM pH optimum of 6, and by DFT calculations (pKa values of ligands in water environment) including empirical corrections from the 10 Jaguar-pKa predictor module of the Schrödinger package.

pKa calculations The most potent inhibitors of GM are azasugars. They contain an amino functional group incorporated in a ring moiety of the inhibitor.

The pKa values of such ionisable group may range from 5 to 9 depending on the position of the nitrogen atom in the ring as well as on other structural factors (number and position of hydroxyl groups in the ring, the conformation of the ring, chemical external environment 11 of the amino group, etc.). For example, SW, MSA and L6 are of moderate basicity (pKa ≈ 7.5, Table S1) and in physiological pH of Golgi apparatus (pH ≈ 6) or lysosomes (pH ≈ 4.0) the most populated configuration should be expected with the protonated amino group (SW+, + + +2 MSA , L6 ). Yet, the pKa value of the inhibitors in the active site of GM may differ due to the proximity of the Zn ion and other ionisable

active-site amino acid residues. Thus, prior to interaction energy calculations of inhibitor···enzyme complexes, pKa calculations of the selected GM inhibitors in water and then in the GM enzyme were performed (Table S1). The main goal was to estimate the population of

neutral and protonated configuration in the bound inhibitor···enzyme complexes. According to experimental and the predicted pKa values

in water (pH=7), all ligands with the amino group (SW, MSA, L5 and L6) should prefer a protonated state (only for L6 calculated pKa=6.6

differs from experimental pKa=7.4, thus, a neutral form of L6 is incorrectly predicted as the most populated in water). The GM inhibitors 0 0 prefer the protonated form in water (~80-90%). On the other hand, most ligands prefer neutral form [pKa(SW )=5.0, pKa(L5 )=3.3, 0 + pKa(L6 )=4.7] after binding ligands to GM (pH=5.9). Only MSA has the pKa value higher than pH of GM (MSA pKa=6.8; MSA does not have

the amino group incorporated in the ring, thus, its pKa value may differ from the values for azasugars). Detailed analysis has shown that +2 +2 Zn , Arg228, His90, His471, Asp92, Asp204 and Asp472 had the most significant influence on the final pKa of the ligand. While Zn , Arg228, His90, and His471 tend to decrease its value, Asp92, Asp204 and Asp472 have the opposite effect. The Zn+2 ion had the major +2 suppressive impact on the pKa values. In conclusion: the shorter the distance of the amino group in the bound inhibitor to the Zn ion,

the lower pKa value may be expected. Thus, a position of amino group on the ring of the ligand dictates a preferred protonation state and influences interactions with the receptor. Therefore in general, both forms of the GM inhibitor (in the case of ligands with an ionisable functional group) have to be taken into account when their binding affinities are quantified.

Table S1. Calculated pKa values of ligands at the quantum mechanics level (in water) and at the empirical level (in the GM enzyme) as well as estimated ratios of neutral and protonated forms in water [LIG0/LIG+(aq)] and in GM 0 + [LIG /LIG (GM)] based on pKa calculations. pK pK a pK a a a LIG0/LIG+ LIG0/LIG+(GM) HN+-R (exp) (aq) (GM) 3 (aq)b (%) (%) pH=7 pH=5.9 + SW HN -R3 7.5 7.8 5.0 8/92 94/6 + MSA H3N -R 7.6 7.6 6.8 12/88 6/94 7.7 10/90 8.0 5/95 + L5 H3N -R 7.7 3.3 10/90 99.9/0.1 7.8 8/92 7.9 7/93 + L6 H2N - 7.4 6.6 4.7 80/20 97/3 R2 6.7 75/25 20/80c a pKa values for the secondary (in L6) and primary amino groups (in MSA and L5) for all two (or three) hydrogens were calculated. b a ratio calculated from predicted pKa(aq) in water c a ratio calculated from experimental pKa of 7.4 in water

QM/MM calculations Complexes (enzyme-inhibitor) were optimized at the hybrid QM/MM level using the QSite12 program which couples the Jaguar13 and Impact14 programs of the Schrödinger package10. The QM/MM methodology (an additive scheme) with hydrogen caps on boundary QM atoms and electrostatic treatment at the interface between the QM and MM regions using Gaussian charge distributions represented on a grid (keyword HCAPESCHG=3) was employed. The QM part of the model consisted of 156 atoms from enzyme: side chains of Trp95, His90, Asp92, Asp204, Phe206, Arg228, Asp341, Trp415, His471, Asp472, Tyr727, Arg876 and Zn+2 ion, and of atoms of the bound inhibitor. For the QM part, the DFT methodology was used, applying the meta hybrid Minnesota functional with double the amount of nonlocal exchange (M06-2X) with the Los Alamos national laboratory effective core potential (LACVP**) basis set.15–17 In the LACVP** basis set the valence electrons are described by the Pople’s split valence double-ξ basis set [6-31G(d,p)]18 augmented by polarization on all atoms. The M06-2X functional was chosen based on previous benchmark studies on sugars19,20 and sugar phosphates21 in which Minnesota functionals with double the amount of nonlocal exchange together with functionals parametrized for kinetics gave the best prediction for reactivity of the O-glycosidic bond. The MM part of the system was treated with the OPLS2005 force fields with no cut-offs introduced for nonbonding interactions.22 All stationary points were characterized as minima or transition states by vibrational frequency calculations calculated from Hessian from the end of the optimization (keyword IFREQ= −1). Convergence thresholds for the energy and gradient change were set to be 5×10−5Hartree and 4.5×10−4Hartree Bohr−1, respectively. The ultrafine integration grid (the Mura-Knowles radial shell distribution scheme),23 which has 125 radial shells and uses an angular offset of 30 (434 angular points per shell) with no pruning as defined in the Qsite program (keywords GDFTFINE= −14, GDFTGRAD= −14, GDFTMED= −14), was set for all calculations because of the systematic grid errors found for the Minnesota functional family with a standard integration grid.17,24 In mapping the potential energy surface (PES) of the catalytic reaction, one-dimensional scan procedures were performed along the

O1–C1 and C1–OAsp204 reaction coordinates stepped by 0.1 Å with remaining coordinates optimized. A transition state was refined from the maxima found on the scanned PES and optimized without any geometry constraints. Transition state searches (keywords IQST = 0, IGEOPT = 2) were performed by using a quasi-Newton method.25–27 The transition state was verified as having one large imaginary frequency by a vibrational frequency calculation. In addition, intrinsic reaction coordinate (IRC) calculations were performed to prove that TS connects the right reactant and product minima. The IRC calculations allowed sliding downhill from the TS along the TS eigenvector, calculating the gradient and taking a small step in the negative gradient direction to reach energy minima corresponding to the TS.

Fragment definition and geometries After the QM/MM optimization the whole receptor site was formally separated into four domains; D1, D2, D3 and D4. This separation was necessary in order to reduce the calculation requirements in the SAPT analysis. However, this separation enables one to analyse the contributions to the total binding mode in a more detailed and localized manner. The fragment composition is the following: D1: His90, Asp92-1, Asp204-1, Asp3410, His471, Asp472-1, Zn+2 D2: Phe206, Trp415, Tyr727 D3: Trp95, Arg876+1, Gly877 D4: Arg228+1, Tyr269 The fragments were not re-optimized after separation. This allows us to study the interactions for geometries representing realistic positions of the ligand and amino acids in the ligand-receptor complexes.

Asp472−

− Asp92 Tyr727 Trp415 Asp341

Asp204−

His471

His90 Phe206

+2 a) D1 (The sphere in magenta represents the Zn ion). b) D2

Gly877 Trp95 + Arg876 + Arg228 Tyr269

c) D3 d) D4 Figure S1. The four domains constituting the catalytic receptor pocket in GM as used for the interaction analysis. Examples of clusters with the ligand mannose (with green carbons, grey carbons are used for the amino acids.) The boundary atoms were capped by hydrogens. In D1 only side chains of the Asp and His residues were included in order to reduce the size of the cluster and make the SAPT calculations feasible.

3 SAPT The DF-SAPT(DFT) calculations were carried out in the SAPT2012 package.28–30 The DFT treatment of monomers was implemented by Zuchowski et al.31,32 The rank reduction of the evaluated molecular integrals was done via density fitting (DF).30,31,33–36 In order to reduce the extreme computational requirements we opted for the reduced Dimer Centred Basis Set (rDCBS) approach. The Monomer Centred BS (MCBS) approach does not guarantee satisfactory convergence of induction and dispersion contributions.37 The validity of rDCBS has been checked on the several systems against a full DCBS calculation with a difference of 1% in the total SAPT energy. Our reduction scheme included only the isotropic functions on the ghost monomer (i.e. only orbitals which are occupied in the atoms ground state).37 It was argued that in some cases double ζ basis sets may perform better than triple ζ in SAPT0 due to error cancelation.38 Even though we do not employ SAPT0 formalism as Lao et al.38, our own tests on ion containing systems with multiple molecules in one monomer showed no significant differences in double and triple ζ results (unpublished data). In the case of interactions of ionic systems the lucky 39 δ HF coincidence of error cancelation in Def2-SVP basis sets was reported by Matczak. He also recommends the use of Eint, resp to reproduce experimental data. However, since we do not strive to calculate super-accurate reference values rather than good qualitative data with reasonable quantitative value, we allowed ourselves to omit this term. The total SAPT (also SAPT(DFT)) interaction energy consists of physically interpretable terms:

(10) (10) ( 20) ( 20) ( 20) ( 20) ESAPT=+++ EEEE els exch ind ex-ind ++ EE disp ex-disp (1) The first two terms arise from first order corrections (perturbations) of the interaction potential and the remaining ones come from second-order perturbations. The dispersion and exchange dispersion terms are so called “correlation” terms. The second index in the superscript loses sense in SAPT(DFT) as monomers are not treated with a perturbation approach.29–31 All SAPT calculations were linked to the ORCA package in which the monomer wave functions and molecular integrals were calculated.40 The orientation of the ligands and fragments was kept almost identical (obviously, minor shifts were caused by the optimization for each ligand) in all calculations.40 This should eliminate the non-physical rotational invariance of DFT calculations on the numerical grid which can have some effect on long range properties.41,42 The PBE0(AC) functional was used in all calculations.43,44 Asymptotic correction (AC) to the exchange correlation was used, which is necessary for correct SAPT(DFT) results, even though the values of the ionization potentials (IP) do not need to be extremely precise.29– 31,45,46 In general, monomer specific IP are recommended as opposed to the lowest IP of one of the monomers in fragment based SAPT approaches such as XSAPT (XPol+SAPT(KS)+D2).38 However, in our case, the fragment approach is not applied and the IP is characteristic for the whole monomer/fragment D1(2,3,4) and not identical to the IP of one separated amino acid due to accounting to the effects of the close surroundings. The IP values calculated at PBE0/Def2-TZVP level of theory and used in our work are compiled in Table S2.

Table S2. Ionization potentials of the ligands and receptor domains calculated at PBE0/Def2-TZVP level of theory. Ligand MAN / TSMAN L2 SW+ / SW0 MSA+ / MSA0 L5+ / L50 L6+ / L60 IP / eV 9.01 / 13.09 8.28 13.25 / 7.98 11.87 / 7.92 13.41 / 8.55 13.34 / 8.39 Domain D1 D2 D3 D4 Zn+2 IP / eV 3.71 7.17 8.51 10.23 39.72

4 FMO – PIEDA The FMO – PIEDA/RI-MP2/cc-pVDZ calculations were carried out in the GAMESS package.36,47–52 All fragments were in the same layer, so this method was applied to all of them. The calculation was carried out in one single point with the ligand and all amino acids from D1, D2, D3 and D4 present. The HOP – Hybrid Operator Projection technique was adopter in the generation of fragments for the covalently 53–58 bounded amino acids. The separate amino acids as well as the bond behind Cα were capped by hydrogen atoms. The vdW radius of zinc, which in GAMES is not defined by default, was set to 1.9 Å. This relatively small number had to be adopted due to an internal restriction which stops the FMO calculation if the relative distance of two fragments is below 0.6 (the relative distance is evaluated for the closest atoms as rrelat = rreal / (Ra + Rb), where Ra,b are the vdW radii of atoms a and b, respectively). Nevertheless, the vdW parameters should have no impact on the actual FMO or PIEDA results according to the manual.52 The fragment assignment and GAMESS input generation was achieved by means of the free utility Facio.59 Output was analysed by our in-house script. In order to elucidate the many-body effects which are in FMO included via the electrostatic mean field we calculated also individual pair-wise interactions energies for two selected systems – SW0 and SW+. RI-MP2/cc-pVDZ single point calculations were chosen analogously to the FMO – PIEDA calculations. Both Counter Poise (CP) corrected and uncorrected values are presented in the extended Tables S17 and S18. We opted for both CP corrected and uncorrected versions as some authors do not recommend correction for Basis Set Superposition Error (BSSE) for close range vdW interactions.60 The presented data do not suggest any systematic behaviour. The CP corrected individual pair-wise interaction energies in the SW+ cluster vary in the range of ~2% to ~730% with respect to the FMO – PIEDA interaction energies. The extreme case is Phe206. The CP uncorrected energies fall into the range of ~5% to 430% deviation with respect to the FMO – PIEDA values. The deviations spectrum in the SW0 cluster is somewhat narrower with ~4% to 120% and ~13% to 210% for the CP corrected and uncorrected values, respectively. Two test cases, one negatively charged and one positively charged, Asp92− and Arg228+ were recalculated in RI-MP2/cc-pVTZ for the SW+ cluster to assess the error introduced by the relatively small basis set. The values were −89.3 kcal mol−1 and 51.9 kcal mol−1 for Asp92−···SW+ and Arg228+···SW+, respectively. Therefore the RI-MP2/cc-pVDZ interaction energies may be considered relatively reliable in terms of the basis set incompleteness error. Finally, we bring a short note on the computational efficiency of the three respective methods used in this work. Even though the calculations were not carried out with a thorough analysis of this matter in mind a rough estimate can be established. All calculations were performed on SMP machines (Single Machine Parallelism), so network communication between nodes was excluded. The RI- MP2/cc-pVDZ calculation is very cheap with respect to computational resources. One single point for a ligand···amino acid dimer takes only a few minutes so the whole supermolecular interaction energy is evaluated very quickly (both CP corrected or uncorrected). In this case all calculations were done on 12 CPUs (even though we did not seek to optimize the number of CPUs to achieve fastest performance). The FMO – PIEDA calculations were performed in SMP setup on four CPUs, however on CPUs with different (higher) frequency. Here only one single point is needed to obtain the interaction energies and the PIEDA decomposition analysis. One job took roughly ten hours. In general, FMO – PIEDA calculations can make use of parallelization very well. The DF-SAPT(DFT) calculations were the most time consuming. Unfortunately, SAPT is not well parallelized (in any of the software packages known to us, except partially in SAPT2012, but not all SAPT versions). Therefore the advantage of parallel calculations was restricted mainly to the construction of monomer wave functions in the ORCA package and subsequently only parts of SAPT routines. The SCF calculation in ORCA was run on 12 CPUs but this took only a fraction of the total time for one DF-SAPT(DFT) job (roughly 10 to 20%). One DF-SAPT(DFT) calculation took roughly from 10 hours for the D4 complexes up to 2 to 4 days for the D1 complexes. The concluding remark is that many-body effects seem to alter the fragment interaction energies, however, a consistent/systematic shift cannot be observed. Pair-wise analysis of the ligand···amino acid interactions may be used for fast screening perhaps of a large set of ligands albeit for interpretations of interactions, methods including many-body effects may be advantageous.

5 Results

The DF-SAPT(DFT) interaction energies and the relevant energy terms for the ligand···D1(2,3,4) are presented in Tables S3 to S12.

Table S3. DF-SAPT(DFT) interaction energies between ligands and D1 in kcal mol-1. MAN L2 SW+ MSA+ L5+ L6+

Eels -190.8 -190.0 -293.7 -309.7 -294.2 -292.4 Eind 224.4 219.1 259.8 292.1 249.2 253.4 Eexch -245.3 -228.5 -259.4 -300.5 -252.0 -253.8 Eex-ind 187.3 170.7 184.9 216.2 181.4 180.7 Edisp -43.3 -43.6 -49.3 -52.7 -44.4 -47.1 Eex-disp 6.8 8.6 7.7 7.9 5.3 6.9 SAPT -60.9 -63.7 -149.9 -146.5 -154.7 -152.3

Table S4. DF-SAPT(DFT) interaction energies between ligands and D2 in kcal mol-1. MAN L2 SW+ MSA+ L5+ L6+

Eels -22.1 -29.9 -18.9 -15.2 -15.5 -21.3 Eind 36.8 57.2 48.5 37.9 32.1 51.1 Eexch -15.6 -23.2 -22.8 -16.1 -16.1 -25.3 Eex-ind 11.9 18.1 16.3 11.9 11.5 17.8 Edisp -13.4 -21.8 -16.7 -14.4 -9.2 -16.2 Eex-disp 1.3 2.3 1.2 1.0 0.6 1.1 SAPT -1.1 2.8 7.5 5.0 3.4 7.4

Table S5. DF-SAPT(DFT) interaction energies between ligands and D3 in kcal mol-1. MAN L2 SW+ MSA+ L5+ L6+

Eels -23.1 -26.2 15.1 16.8 11.0 9.6 Eind 31.9 40.4 22.5 20.3 23.1 26.4 Eexch -14.6 -19.6 -12.9 -11.0 -12.5 -14.8 Eex-ind 11.4 13.9 8.0 6.9 7.9 9.1 Edisp -16.1 -22.7 -13.6 -13.0 -13.1 -14.2 Eex-disp 1.8 2.6 1.1 1.0 2.0 1.1 SAPT -8.6 -11.5 20.2 21.1 18.4 17.1

Table S6. DF-SAPT(DFT) interaction energies between ligands and D4 in kcal mol-1. MAN L2 SW+ MSA+ L5+ L6+

Eels -8.2 -15.0 49.9 47.4 45.0 49.3 Eind 3.6 12.5 5.4 2.8 7.5 2.1 Eexch -2.5 -8.6 -5.6 -5.7 -8.9 -3.7 Eex-ind 1.0 4.7 1.6 1.1 2.9 0.6 Edisp -2.6 -7.3 -3.8 -2.1 -2.9 -1.9 Eex-disp 0.2 0.7 0.3 0.1 0.3 0.1 SAPT -8.3 -13.1 47.9 43.6 44.0 46.6

6 Table S7. DF-SAPT(DFT) interaction energies between neutral ligands and D1 in kcal mol-1. (MAN and L2 data are repeated from Table S2) MAN L2 SW0 MSA0 L50 L60 L6u0

Eels -190.8 -190.0 –192.5 -230.8 -166.2 -198.2 * Eind 224.4 219.1 258.9 284.4 194.8 236.5 Eexch -245.3 -228.5 –256.8 -302.0 -221.2 -249.6 Eex-ind 187.3 170.7 190.3 227.3 172.3 188.6 Edisp -43.3 -43.6 –49.6 -52.9 -38.6 -45.8 Eex-disp 6.8 8.6 8.8 8.3 5.2 7.2 SAPT -60.9 -63.7 –40.9 -65.8 -53.7 -61.3 * Eind and Eex-ind did not converge

Table S8. DF-SAPT(DFT) interaction energies between neutral ligands and D2 in kcal mol-1. (MAN and L2 data are repeated from Table S3) MAN L2 SW0 MSA0 L50 L60 L6u0

Eels -22.1 -29.9 -16.8 -24.9 -26.4 -32.7 -33.5 Eind 36.8 57.2 59.3 45.0 40.6 59.4 59.9 Eexch -15.6 -23.2 -38.3 -18.2 -19.8 -26.3 -27.4 Eex-ind 11.9 18.1 22.8 14.2 14.3 19.9 20.2 Edisp -13.4 -21.8 -17.6 -16.0 -11.0 -18.3 -19.3 Eex-disp 1.3 2.3 1.4 1.4 0.8 1.7 4.1 SAPT -1.1 2.8 10.9 1.5 -1.6 3.8 4.0

Table S9. DF-SAPT(DFT) interaction energies between neutral ligands and D3 in kcal mol-1. (MAN and L2 data are repeated from Table S4) MAN L2 SW0 MSA0 L50 L60 L6u0

Eels -23.1 -26.2 35.6 -8.6 -14.2 -15.2 -15.4 Eind 31.9 40.4 26.2 20.2 20.6 26.4 27.4 Eexch -14.6 -19.6 -31.9 -8.4 -8.2 -10.6 -11.2 Eex-ind 11.4 13.9 12.4 6.8 7.1 9.2 9.7 Edisp -16.1 -22.7 -13.9 -13.3 -12.8 -14.6 -15.4 Eex-disp 1.8 2.6 1.1 1.3 2.2 1.6 2.8 SAPT -8.6 -11.5 29.4 -2.0 -5.4 -3.2 -2.1

Table S10. DF-SAPT(DFT) interaction energies between neutral ligands and D4 in kcal mol-1. (MAN and L2 data are repeated from Table S5) MAN L2 SW0 MSA0 L50 L60 L6u0

Eels -8.2 -15.0 107.9 -4.3 -16.9 -5.5 -6.0 Eind 3.6 12.5 6.8 0.4 9.0 3.2 2.6 Eexch -2.5 -8.6 -16.7 -1.7 -5.9 -2.5 -2.2 Eex-ind 1.0 4.7 2.9 0.2 3.5 1.0 0.8 Edisp -2.6 -7.3 -3.7 -1.3 -3.8 -2.4 -2.2 Eex-disp 0.2 0.7 0.3 0.0 0.6 0.2 0.2 SAPT -8.3 -13.1 97.4 -6.6 -13.4 -6.0 -6.8

Table S11. DF-SAPT(DFT) interaction energies between ligands and Zn+2 from D1 in kcal mol-1. MAN L2 SW+ MSA+ L5+ L6+

Eels -83.8 -69.0 74.2 80.5 87.3 76.3 Eind 33.3 29.7 27.7 34.8 28.2 27.1 Eexch -191.0 -178.0 -164.1 -198.1 -167.4 -159.5 Eex-ind 112.8 97.7 90.6 116.8 94.6 88.5 Edisp -1.6 -1.4 -1.4 -1.6 -1.4 -1.3 Eex-disp 0.2 0.1 0.1 0.2 0.1 0.1 SAPT -130.0 -120.9 27.2 32.6 41.5 31.1

Table S12. DF-SAPT(DFT) interaction energies between neutral ligands and Zn+2 from D1 in kcal mol-1. (MAN and L2 data are repeated form Table S10) MAN L2 SW0 MSA0 L50 L60

Eels -83.8 -69.0 -93.2 -88.2 -80.6 -80.6 Eind 33.3 29.7 31.3 38.7 32.0 30.8 Eexch -191.0 -178.0 -186.1 -219.3 -188.9 -183.8 Eex-ind 112.8 97.7 108.1 133.7 112.0 107.8 Edisp -1.6 -1.4 -1.5 -1.7 -1.5 -1.4 Eex-disp 0.2 0.1 0.2 0.3 0.2 0.2 SAPT -130.0 -120.9 -141.2 -136.5 -126.9 -127.0

Polarizabilities given in the paper were obtained from relaxed MP2 densities in the Sadlej pVTZ basis sets and for the geometries from the QM/MM optimization.61

Table S13. MP2(relaxed)/Sadlej-pVTZ polarizabilities in Å3 for the QM/MM geometries of the ligands bound in the receptor. MAN L2 SW+ MSA+ L5+ L6+ SW0 MSA0 L50 L60 L6u0 α 14.71 27.92 15.76 16.40 12.05 12.93 17.25 17.28 12.97 14.66 14.70

8 FMO – PIEDA/RIMP2/cc-pVDZ interaction energies in Tables S14 to S25.

Table S14.FMO – PIEDA interaction energies between MAN and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 1.3 5.0 0.4 -2.2 -1.9 Asp92 -26.0 -35.6 35.8 -18.1 -8.1 Asp204 16.2 20.1 6.8 -4.2 -6.5 Asp341 -14.8 -20.3 18.5 -7.9 -5.1 His471 5.2 9.1 3.4 -3.2 -4.0 Asp472 -80.3 -95.0 54.6 -27.0 -12.8 Zn+2 -142.7 -125.8 27.5 -21.7 -22.7 Phe206 -2.3 -1.5 7.1 -2.5 -5.4 Trp415 -3.1 -1.0 0.9 -1.1 -1.8 Tyr727 -21.5 -22.5 18.0 -7.9 -9.1 Trp95 -16.8 -11.5 15.1 -5.8 -14.6 Arg876 -4.5 -2.1 2.4 -2.4 -2.4 Gly877 -13.4 -13.5 6.6 -3.3 -3.2 Arg228 -12.3 -10.0 0.3 -1.0 -1.6 Tyr269 -3.4 -1.5 1.5 -1.3 -2.1

Table S15.FMO – PIEDA interaction energies between TSMAN and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 -4.4 -0.4 1.0 -2.6 -2.4 Asp92 -92 -97.2 29.5 -15.9 -8.4 Asp204 -82.8 -83.4 16.6 -6.6 -9.3 Asp341 -114.1 -115.8 22.9 -13.4 -7.8 His471 -1.3 3.5 2.5 -3.5 -3.7 Asp472 -145.8 -160.4 55.3 -27.8 -12.9 Zn+2 13.1 29.9 27.3 -21.3 -22.8 Phe206 0.3 2.8 1.8 -1.2 -3.1 Trp415 -3.3 -0.8 0.6 -1.3 -1.8 Tyr727 -7 -4.4 6.7 -4.1 -5.2 Trp95 -18 -12.5 15.1 -5.8 -14.7 Arg876 27.6 29.9 0.4 -1.2 -1.4 Gly877 -20.2 -18.8 4.1 -2.7 -2.7 Arg228 45.1 47.5 0.6 -1.1 -1.9 Tyr269 -8.7 -7.3 6.7 -3.6 -4.3

9 Table S16. FMO – PIEDA interaction energies between L2 and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 -0.9 3.2 0.7 -2.5 -2.3 Asp92 -23.2 -18.5 11.5 -9.5 -6.7 Asp204 2.1 7.1 9.6 -5.7 -9.0 Asp341 -16.4 -23.9 21.0 -8.7 -4.8 His471 3.7 8.2 2.3 -3.2 -3.7 Asp472 -101.2 -128.6 77.2 -36.1 -13.7 Zn+2 -116.9 -100.8 25.3 -19.9 -21.6 Phe206 -2.3 -3.1 11.7 -3.1 -7.8 Trp415 -5.7 -2.3 5.4 -2.6 -6.2 Tyr727 -18.0 -24.9 30.7 -12.0 -11.7 Trp95 -17.9 -10.9 15.7 -6.1 -16.6 Arg876 -10.8 -7.7 8.4 -4.0 -7.6 Gly877 -16.7 -15.6 7.0 -3.1 -5.0 Arg228 -21.0 -18.5 6.8 -2.8 -6.4 Tyr269 -5.4 -2.2 2.3 -2.3 -3.2

Table S17. FMO – PIEDA interaction energies between SW+ and all amino acids from D1, D2, D3 and D4 in kcal mol-1. The last two columns list the total interaction energies from supermolecular pair-wise RI-MP2/cc- pvdz calculations with Counter Poise (CP) correction and without.

Etot Ees Eex Ect Edisp Etot (RI-MP2/CP) Etot (RI-MP2/no CP) His90 -6.8 -2.7 0.8 -2.5 -2.5 -3.6 -5.1 Asp92 -105.1 -125.0 66.8 -37.2 -9.7 -87.8 -100.4 Asp204 -101.4 -97.7 16.0 -9.3 -10.4 -103.3 -115.8 Asp341 -7.3 -6.9 14.6 -8.9 -6.0 -0.3 -5.8 His471 -2.3 3.0 1.5 -3.5 -3.4 -5.2 -7.2 Asp472 -160.5 -177.7 65.3 -33.6 -14.6 -112.5 -126.9 Zn+2 21.7 37.3 22.9 -18.3 -20.3 6.6 -6.7 Phe206 0.3 -1.9 12.6 -2.8 -7.6 2.5 -1.0 Trp415 -2.1 -1.5 2.4 -0.5 -2.4 -1.8 -2.6 Tyr727 -11.9 -19.6 26.5 -10.1 -8.7 1.4 -5.1 Trp95 -22.4 -19.0 19.3 -6.0 -16.6 -8.8 -14.8 Arg876 33.4 34.1 0.1 -0.1 -0.6 27.2 26.2 Gly877 -12.0 -10.0 0.1 -1.0 -1.2 -0.4 -0.4 Arg228 53.1 54.7 2.3 -1.1 -2.9 52.2 50.6 Tyr269 -6.5 -4.2 1.2 -1.2 -2.2 -4.1 -10.6

10 Table S18. FMO – PIEDA interaction energies between SW0 and all amino acids from D1, D2, D3 and D4 in kcal mol-1. The last two columns list the total interaction energies from supermolecular pair-wise RI-MP2/cc- pvdz calculations with Counter Poise (CP) correction and without.

Etot Ees Eex Ect Edisp Etot (RI-MP2/CP) Etot (RI-MP2/no CP) His90 1.8 5.5 0.6 -2.1 -2.2 -0.4 -2.1 Asp92 -32.4 -51.7 61.4 -33.2 -8.9 -15.0 -27.6 Asp204 23.0 30.5 3.6 -5.1 -6.1 11.5 1.7 Asp341 -15.8 -23.3 28.2 -14.1 -6.6 -2.8 -9.4 His471 5.8 10.8 1.3 -3.2 -3.2 2.2 0.0 Asp472 -73.9 -85.1 47.3 -23.4 -12.7 -35.2 -48.9 Zn+2 -157.4 -136.8 26.0 -20.9 -25.7 -163.8 -178.6 Phe206 -1.9 -2.9 10.6 -2.6 -7.0 1.1 -2.8 Trp415 -1.3 -0.8 2.4 -0.5 -2.4 -0.4 -2.1 Tyr727 -22.0 -31.7 31.8 -12.5 -9.5 -4.6 -12.3 Trp95 -13.6 -12.1 19.8 -5.7 -15.6 -2.5 -8.7 Arg876 -2.2 -1.4 0.1 -0.2 -0.8 -1.8 -3.0 Gly877 -3.3 -1.2 0.3 -1.0 -1.4 -0.5 -0.5 Arg228 -9.1 -7.7 2.7 -1.1 -2.9 -4.7 -6.4 Tyr269 -1.8 -0.1 1.2 -0.9 -1.9 -0.4 -2.1

Table S19. FMO – PIEDA interaction energies between MSA+ and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 -6.1 -1.9 1.0 -2.6 -2.7 Asp92 -107.6 -119.1 47.8 -25.5 -10.8 Asp204 -114.8 -132.6 51.0 -22.3 -10.8 Asp341 -7.0 -3.8 7.5 -4.8 -6.0 His471 -4.0 1.5 2.5 -4.0 -4.0 Asp472 -158.1 -180.9 78.4 -40.6 -15.0 Zn+2 29.3 42.9 29.5 -20.7 -22.4 Phe206 -1.8 -0.4 7.9 -2.6 -6.6 Trp415 -1.1 -2.1 5.0 -0.8 -3.1 Tyr727 -10.8 -13.3 18.6 -7.7 -8.3 Trp95 -20.2 -15.9 16.0 -5.2 -15.1 Arg876 27.3 27.9 2.1 -1.0 -1.8 Gly877 -6.7 -4.0 0.4 -1.6 -1.5 Arg228 50.7 52.3 0.4 -0.6 -1.3 Tyr269 -9.7 -7.5 1.1 -1.2 -2.0

11 Table S20. FMO – PIEDA interaction energies between MSA0 and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 0.8 4.8 0.8 -2.4 -2.4 Asp92 -26.8 -36.8 38.5 -18.9 -9.6 Asp204 11.7 15.0 9.6 -5.9 -7.0 Asp341 -31.8 -55.5 56.0 -25.0 -7.3 His471 4.7 9.5 2.4 -3.5 -3.8 Asp472 -84.5 -104.6 66.3 -32.2 -14.0 Zn+2 -146.2 -132.3 32.4 -22.6 -23.6 Phe206 -3.8 -3.0 8.9 -2.7 -6.9 Trp415 -0.5 -1.9 5.6 -0.9 -3.3 Tyr727 -17.7 -21.9 22.6 -9.5 -8.9 Trp95 -14.3 -10.4 15.0 -4.7 -14.3 Arg876 -4.6 -3.9 2.3 -1.1 -1.9 Gly877 -0.8 1.7 0.5 -1.5 -1.4 Arg228 -9.2 -7.7 0.3 -0.6 -1.2 Tyr269 -3.7 -2.5 0.1 -0.4 -0.8

Table S21. FMO – PIEDA interaction energies between L5+ and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 -6.4 -3.0 0.3 -2.0 -1.8 Asp92 -98.2 -100.3 28.1 -17.0 -9.1 Asp204 -111.2 -129.5 48.0 -19.6 -10.1 Asp341 -9.2 -6.1 0.1 -1.6 -1.6 His471 -4.2 0.6 3.1 -3.8 -4.1 Asp472 -150.3 -177.2 78.4 -36.7 -14.8 Zn+2 29.1 46.6 22.8 -19.1 -21.2 Phe206 -1.6 -0.1 5.5 -2.9 -4.1 Trp415 -1.9 -0.9 0.0 -0.4 -0.5 Tyr727 -13.7 -17.4 19.7 -9.3 -6.7 Trp95 -18.2 -17.3 21.3 -6.4 -15.9 Arg876 30.5 30.8 0.0 -0.1 -0.2 Gly877 -12.4 -10.7 0.1 -0.8 -1.0 Arg228 53.3 54.6 0.3 -0.6 -1.0 Tyr269 -12.2 -11.5 4.4 -2.1 -2.9

12 Table S22. FMO – PIEDA interaction energies between L50 and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Table S23. FMO – PIEDA interaction energies between L6+ and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 -6.4 -2.4 0.7 -2.4 -2.3 Asp92 -105.4 -124.1 65.0 -36.7 -9.7 Asp204 -98.5 -94.8 13.0 -8.2 -8.5 Asp341 -7.4 -8.2 15.5 -9.0 -5.7 His471 -1.6 3.9 1.7 -3.4 -3.7 Asp472 -163.3 -180.0 64.6 -33.4 -14.5 Zn+2 22.1 37.8 22.4 -18.1 -20.1 Phe206 0.7 -2.1 12.3 -2.7 -6.8 Trp415 -2.9 -1.2 1.5 -1.1 -2.1 Tyr727 -12.7 -22.1 30.5 -11.7 -9.3 Trp95 -21.0 -17.3 18.4 -6.0 -16.1 Arg876 32.7 34.4 0.3 -0.9 -1.1 Gly877 -17.8 -16.6 2.9 -1.9 -2.3 Arg228 52.8 54.0 0.1 -0.4 -0.9 Tyr269 -5.9 -4.1 1.1 -1.1 -1.9

13 Table S24. FMO – PIEDA interaction energies between L60 and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 1.1 4.7 0.5 -2.1 -2.1 Asp92 -31.3 -49.2 57.8 -31.2 -8.6 Asp204 8.4 12.5 8.4 -5.9 -6.5 Asp341 -16.6 -24.3 28.1 -14.0 -6.4 His471 6.5 12.0 1.4 -3.4 -3.5 Asp472 -76.6 -86.3 45.1 -22.7 -12.6 Zn+2 -143.8 -121.5 25.1 -21.3 -26.1 Phe206 0.0 -2.9 12.3 -2.5 -6.9 Trp415 -2.7 -1.1 2.2 -1.4 -2.4 Tyr727 -22.6 -33.0 35.6 -14.7 -10.5 Trp95 -12.9 -10.1 17.5 -5.5 -14.8 Arg876 -6.7 -4.0 0.6 -1.7 -1.7 Gly877 -3.3 -2.5 2.6 -1.4 -2.1 Arg228 -9.5 -7.2 0.3 -1.0 -1.6 Tyr269 -1.9 -0.6 1.5 -0.9 -1.9

Table S25. FMO – PIEDA interaction energies between L6u0 and all amino acids from D1, D2, D3 and D4 in kcal mol-1.

Etot Ees Eex Ect Edisp His90 1.9 5.4 0.5 -2.0 -2.0 Asp92 -30.8 -48.8 58.1 -31.4 -8.7 Asp204 26.5 33.4 2.4 -4.4 -4.9 Asp341 -15.9 -23.6 27.9 -13.9 -6.3 His471 8.1 13.3 1.4 -3.2 -3.4 Asp472 -75.3 -85.6 45.7 -22.8 -12.6 Zn+2 -153.9 -135.6 24.8 -20.1 -23.0 Phe206 -0.9 -3.1 11.5 -2.5 -6.7 Trp415 -2.8 -0.9 2.0 -1.5 -2.4 Tyr727 -23.6 -34.7 36.7 -15.1 -10.4 Trp95 -12.4 -10.3 18.6 -5.7 -15.0 Arg876 -4.5 -2.0 0.5 -1.5 -1.5 Gly877 -5.5 -4.6 2.7 -1.5 -2.1 Arg228 -12.1 -9.7 0.2 -1.0 -1.6 Tyr269 -1.3 0.0 1.2 -0.9 -1.7

Figure S2. FMO – PIEDA total interaction energies of MAN (left) and TSMAN (right) and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated (Asp341 became negatively charged after its proton transferred to MAN during the formation of the positively charged transition state TSMAN).

Figure S3. FMO – PIEDA total interaction energies of L2 and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated.

Figure S4. FMO – PIEDA total interaction energies of SW+ (left) and SW0 (right) and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated.

Figure S5. FMO – PIEDA total interaction energies of MSA+ (left) and MSA0 (right) and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated.

Figure S6. FMO – PIEDA total interaction energies of L5+ (left) and L50 (right) and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated.

Figure S7. FMO – PIEDA total interaction energies of L6+and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated.

Figure S8. FMO – PIEDA total interaction energies of L60 (left) and L6u0 (right) and all amino acids from the receptor cavity decomposed into electrostatic, exchange, charge-transfer and dispersion terms. The formal charge of each amino acid is indicated.

Table S26. Partial ESP CHELP/M06-2X/LACVP** charges on atoms O2, O3, O4 on MAN (TSMAN) and their analogues in SW and MSA. Charges were calculated in the QM/MM setup. Atoms O2, O3 are coordinating the zinc atoms. MAN / TSMAN SW0 / SW+ MSA0 / MSA+ O2 −0.72 / −0.64 −0.49 / −0.65 −0.50 / −0.69 O3 −0.73 / −0.61 −0.42 / −0.48 −0.64 / −0.61 O4 −0.58 / −0.78 −0.59 / −0.57 0.01 / 0.09 Zn 1.30 / 1.20 0.97 / 1.09 1.11 / 1.06 Asp204(Zn) −0.72 / −0.74 −0.69 / −0.72 −0.65 / −0.67 Asp204 −0.78 / −0.79 −0.83 / −0.75 −0.68 / −0.73 Asp92(Zn) −0.83 / −0.82 −0.76 / −0.78 −0.79 / −0.76 Asp92 −0.72 / −0.71 −0.70 / −0.71 −0.76 / −0.75 His90(Zn) −0.27 / −0.23 −0.23 / −0.28 −0.23 / −0.20 His471(Zn) −0.37 / −0.34 −0.21 / −0.28 −0.28 / −0.25

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