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1 Mechanical Control of ATP Synthase Function: Activation Energy Difference between Tight and Loose Binding Sites Supporting Information Tamás Beke-Somfai* 1,2, Per Lincoln 1, Bengt Nordén* 1 1 Department of Chemical and Biological Engineering, Physical Chemistry, Chalmers University of Technology, SE Göteborg, Sweden, 2 Protein Modelling Group MTA-ELTE, Institute of Chemistry, Eötvös Loránd University, P.. Box 32, H-1538 Budapest, Hungary Considerations on the Model To investigate the difference in the reaction mechanism between the loose and tight binding sites, the coordinates of the two sites were obtained from the recent X-ray structure of F 1 ATPase with 1.9 resolution. 1 Since there are only small structural differences between the two sites, the constitution of them were chosen with emphasis placed on obtaining similar optimized structures for both the β TP and β DP sites as found in the X-ray structure. After several trial runs the model contained fragments from residues in the P-loop region of the β- subunit: 158A, 159G, 160V, 161G, 162K, 163T, 164V and also 188E, 189R, 192E, 260R (SFigure 1). Note that the active sites also contain residues from the neighboring α-subunit, thus fragments from 373R, and 344S, 345I were also included. To reduce the model into a computationally feasible size the residues of the P-loop region were transformed into glycines, with exception to 162 Lys, where the end of the side chain was kept in a separate CH 3 -NH 3 form. Further on 163T was mutated to Ser, fragments from 158A, 164V and 345I were only used to end the cut peptide chains, e.g. only their terminal C= or N-H groups were included and transformed into -C(H)= or -N(H)-H, respectively, mimicking formyl and NH terminal protecting groups. For the arginine residues only the guanidino side chains were kept and the neighboring CH 2 groups were converted into CH 3. Similarly, for the two glutamic acids, the CH 2 C fragments were kept and transformed into CH 3 C. ut of the 344S residue the N-terminal was not included, it was substituted by a hydrogen on the Cα. Five water molecules were found in the active site, out of which three was coordinated on the magnesium ion. In the AMP-PNP, which was used as an ATP analog during crystallization 1, the triphosphate part was kept until the 5' carbon which was turned into methyl group. The NH group was substituted to in order to model the triphosphate part of ATP. To keep the characteristic geometry of both β TP and β DP sites several atoms were fixed to their initial X- ray coordinates marked by an asterisk in SFigure 1. The distance of the nucleophilic water ( wat ) from the γ-phosphate (γp) was 3.87 (X-ray: ~3.8) and 3.40 (X-ray: ~3.1) for the β TP and β DP site in the optimized structures, respectively. The selection of fixed atoms was based on the extent of stabilizing interactions (H-bonds, etc.) acting on the chosen atom or its direct environment. Accordingly, most of the fixed atoms are either part of a relatively rigid secondary structural motif, i. e. a helix, or have multiple H-bonds towards the rest of the protein. However, although one should be aware of the possibility of a certain bias arising from the constraints on atoms around the active site, results using a QM/MM approach S1
2 indicate that relaxing them does not introduce any significant changes in the relative differences between the two active sites, and between reactant and transition state geometries (data not shown). A detailed comparison of the various theoretical approaches will be published elsewhere. Nature of the Transition States To characterize the nature of the transition states, natural bond orbital analysis was performed on the obtained structures. The bond orders for the β DP site: wat -P P3 =0.24, P P3 - ADP =0.17; and for the β TP site: wat -P P3 =0.21, P P3 - ADP =0.11. These low bond order values suggest that this concerted reaction has a dissociative character for both sites, with higher, but still relatively low associativity, in the β DP site. Note, that bond orders alone obtained for the transition state do not always predict the nature of the reactions adequately, however, further investigations are beyond the scope of this study. Upon request, cartesian coordinates of the obtained structures are available from the authors. S2
3 SFigure 1. The geometry optimized (B3LYP/6-31G(d) ) model of the β DP and β TP sites with ATP bound from side (A) and top (B) view. For details on the modifications see the Considerations on the Model section in this Supporting Information. The atoms which were fixed during optimizations are labeled with an asterisk. S3
4 Computational Details The structures containing an overall of 152 atoms were submitted to geometry optimization at the B3LYP/6-31G(d) level of theory, using 1308 basis functions. In the ATP-bound ground state the optimized distances of the nucleophilic water from the γ-phosphate were 3.87 (X-ray: ~3.8) and 3.40 (X-ray: ~3.1) for the β TP and β DP sites, respectively. To obtain a more accurate energetic distribution, the optimized structures were submitted to single point energy calculations at the B3LYP/ G(d,p) level of theory. At the same level of theory, polarization effects of the protein environment were considered using the integral-equation-formalism polarizable continuum model (IEFPCM), with a dielectric constant of 4, solvent radius: 2.5Å. Zero point energy (ZPE) correction and thermal corrections to energy were acquired from frequency calculations, which were also used to confirm the nature of the obtained critical points, with no negative eigenvalues for minima and one negative eigenvalue for TSs. Note that due to constrained cartesian coordinates in the model some additional imaginary frequencies occured which were tipically low, on the order of 40-50i cm -1, thus not contributing significantly to the obtained zero point energies. However, they render harmonic entropy contributions unreliable, thus energies presented in the paper correspond to enthalpies only. Note that the obtained relative Gibbs free energy values for barrier heights are 65.3 kj/mol and 99.1 kj/mol for the β DP and β TP sites, respectively, which, due to cancellation of errors in the entropy term, are mentioned here to give a qualitative comparison. Structural properties of the transition states are depicted in SFigure 2 while the shifting of the β TP residue along the reaction coordinate is shown in SFigure 3. As outlined in the paper, αarg-373 was gradually shifted from its position in β DP towards its position in β TP. This way, several TSs were optimized for the β DP site with αarg-373 moving towards its β TP position, as well as for the β TP site with αarg-373 moving towards its β DP position. In practice, these scans were performed by a simple procedure, increasing/decreasing the distance between the methyl group of βarg-260 and the methyl group of αarg-373 by 0.285Å per step. The four steps mentioned above resulted an overall of 1.14Å, which is the exact relative difference between the distances of the two methyl groups in 152 QM models of β DP and β TP sites. When superimposed, the shifted β DP and β TP αarg- 373 residues arrived within 0.2Å range of the original αarg-373 positions in β TP and β DP, respectively. The energies of the TSs along the scans were obtained at the B3LYP/ G(d,p)/B3LYP/6-31G(d) level of theory and were corrected with polarization effects using the IEFPCM method. As these TSs are very similar in character to the original TSs obtained in the β DP and β TP sites, ZPE corrections and thermal corrections were added from frequency calculations of the original β DP and β TP TSs. For both scans a monotonic increasing/decreasing barrier height was observed for the β DP and β TP, respectively with final changes in the order of kj/mol. Precision and Accuracy: The applied basis set was confirmed for optimizations by further calculations made on the ATP and ADP+P i states of the β DP site at the B3LYP/6-31G(d,p) level of theory. The distance of the nucleophilic water from the γ-phosphate obtained at this level was 3.48Å, which is 0.08Å shift compared to the geometry obtained at the B3LYP/6-31G(d,p). S4
5 Verification of the obtained activation energy barrier values was also done using the M05-2X functional 2 at the same level of theory with the same IEFPCM model and parameters. This functional was described to perform better than B3LYP in estimating barrier heights for bond dissociation. 2 The obtained relative energies for the β DP and β TP TSs (lacking ZPE correction) were 51.1 kj/mol and kj/mol, respectively. The same values of B3LYP without ZPE correction were 55.9 kj/mol and kj/mol. Further on, to see the accuracy of hybrid density functional B3LYP on the magnesiumcoordinated phosphate ester hydrolysis, we built a smaller neutral model, {Mg 2+ [H 2 ] 4 [H 2 P ]} + H 2 and obtained the critical points along the reaction coordinate using both B3LYP/6-31+G(d,p) level of theory as well as second order Møller-Plesset (MP2) calculations at the MP2/6-31+G(d,p) level of theory. Nature of the critical points were confirmed by frequency calculations, having zero negative eigenvalues for minima and one negative eigenvalue for transition states. The obtained critical points and their energies relative to the initial geometry are shown on SFigure 4. The average difference and its standard deviation for three TSs is 4.8 and 4.3 kj/mol between the two methods. The same values for the four minima are 5.7 and 4.0 kj/mol, thus, the obtained B3LYP values show an excellent correlation with MP2 energies. REFERENCES (1) Bowler, M. W.; Montgomery, M. G; Leslie, A. G.; Walker, J. E. J. Biol. Chem., 2007, 282, (2) Zhao, Y.; Schultz, N. E.; Truhlar, D.G. J. Chem. Theory Comput. 2006, 2, (3) Adachi, K.; iwa, K.; Nishizaka, T.; Furuike, S.; Noji, H.; Itoh, H. Yoshida, M. Kinosita, K. Jr Cell, 2007, 130, Complete Reference of Gaussian 03 Gaussian 03, Revision D.01: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao,.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev,.; Austin, A. J.; Cammi, R.; Pomelli, C.; chterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas,.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; rtiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al- Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A., Gaussian, Inc., Wallingford CT, S5
6 βarg189 αarg373 HN HN 2.88 (2.87) H 2 N + NH (2.72) αser344 H (2.62) 2.13 (2.17) NH 2.71 βarg260 (2.75) βglu188 H 2 N 2.78 (2.73) 2.71 (2.68) P 2.80 (2.83) + NH 3 βlys162 NH (2.50) 3.90 (2.77) H 2 N (2.06) (2.01) Mg P 2.63 (2.60) NH (4.02) AMP SFigure 2. Schematic diagram describing the transition structures in β DP and β TP catalytic sites as obtained at the B3LYP/6-31G(d) level of theory. Besides the ---γp----adp distance, hydrogen bond interactions are also shown as dashed lines. Bridge atom distances (in Ångströms) are given for β DP and in parenthesis for β TP. S6
7 SFigure 3. Positions of the αarg-373 side chain in β TP site from top (left column) and side (right column) view as obtained at the B3LYP/6-31G(d) level of theory. It can be seen that in the reactant (ATP + H 2 ) as well as in the intermediate product (ADP + P i Int.) states two hydrogen bonds are present with the corresponding oxygens of the γ- and β-phosphates, respectively. In contrast, the same side chain in the transition structure forms only one H-bond with the nucleophilic oxygen of β-phosphate. See the text in the paper for further details. The corresponding ---H distances are in Ångströms and labeled with green dashed lines. S7
8 SFigure 4. The reaction coordinate in the selected reference model investigated at the B3LYP/6-31+G(d,p) and at the MP2/6-31+G(d,p) levels of theory. The different critical points are illustrated in the same order as their obtained energies along the reaction coordinate. S8
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