Molecular Dynamics at Constant pH and Reduction Potential: Application to Cytochrome c 3 Miguel Machuqueiro † and Anto ´ nio M. Baptista* Instituto de Tecnologia Química e Biológica, UniVersidade NoVa de Lisboa, AV. da República, EAN, 2780-157 Oeiras, Portugal Received October 28, 2008; E-mail: baptista@itqb.unl.pl Abstract: Here we present a new implementation and extension of the stochastic titration method which makes it possible to perform MD simulations at constant pH and reduction potential. The method was applied to the redox titration of cytochrome c 3 from Desulfovibrio vulgaris Hildenborough, and a major finding of this study was that the method showed a better performance when the protein region is assigned a high dielectric constant. This dependence on the value of the protein dielectric constant was not found in previous constant-pH MD simulations and is attributed to excessively high heme-heme interactions at low dielectric constants. The simulations revealed strong coupling between hemes in close proximity, and we also showed how these couplings can be used to estimate the sensibility of the heme reductions to small pH changes. Introduction It is well-known that redox processes, often coupled with protonation events, are essential for living organisms, being particularly important in respiration, photosynthesis, and other energy transduction systems. In terms of computational studies, two different and largely complementary approaches can be used to study reduction and protonation processes in proteins: molecular mechanics/dynamics (MM/MD), 1-16 where protein conformation changes are explicitly treated for a fixed ionization (protonation or reduction) state, and more simplified electrostat- ics-oriented methods (Poisson-Boltzmann (PB), generalized Born (GB), protein dipoles Langevin dipoles (PDLD), etc.), 17-30 where ionization changes are explicitly treated for a fixed protein conformation. The inherent complementarity of these two classes of methods, and their consequent incompleteness when taken individually, prompted several attempts to devise methods explicitly treating both conformation and ionization changes (e.g., see ref 31 for a succinct overview), eventually leading to the development of constant-pH MD methods. 31- > 48 The theoretical aspects behind most constant-pH MD methods can in principle be extended to address also redox processes, so † Current address: Department of Chemistry and Biochemistry, Faculty of Sciences, University of Lisbon, Campo Grande, Building C8, 1149-016 Lisbon, Portugal. (1) Soares, C. M.; Martel, P. J.; Mendes, J.; Carrondo, M. A. Biophys. J. 1998, 74, 1708. (2) Karplus, M.; Petsko, G. A. Nature 1990, 347, 631. (3) van Gunsteren, W. F.; Berendsen, H. J. C. Angew. Chem., Int. Ed. Engl. 1990, 29, 992. (4) Churg, A. K.; Warshel, A. Biochemistry 1986, 25, 1675. (5) Cutler, R. L.; Davies, A. M.; Creighton, S.; Warshel, A.; Moore, G. R.; Smith, M.; Mauk, A. G. Biochemistry 1989, 28, 3188. (6) Langen, R.; Jensen, G. M.; Jacob, U.; Stephens, P. J.; Warshel, A. J. Biol. Chem. 1992, 267, 25625. (7) Langen, R.; Brayer, G. D.; Berghuis, A. M.; Mclendon, G.; Sherman, F.; Warshel, A. J. Mol. Biol. 1992, 224, 589. (8) Mark, A. E.; van Gunsteren, W. F. J. Mol. Biol. 1994, 240, 167. (9) Alden, R. G.; Parson, W. W.; Chu, Z. T.; Warshel, A. J. Am. Chem. Soc. 1995, 117, 12284. (10) Apostolakis, J.; Muegge, I.; Ermler, U.; Fritzsch, G.; Knapp, E. W. J. Am. Chem. Soc. 1996, 118, 3743. (11) Muegge, I.; Qi, P. X.; Wand, A. J.; Chu, Z. T.; Warshel, A. J. Phys. Chem. B 1997, 101, 825. (12) Warshel, A. Biochemistry 1981, 20, 3167. (13) Russell, S. T.; Warshel, A. J. Mol. Biol. 1985, 185, 389. (14) Warshel, A.; Sussman, F.; King, G. Biochemistry 1986, 25, 8368. (15) Lee, F. S.; Chu, Z. T.; Warshel, A. J. Comput. Chem. 1993, 14, 161. (16) Del Buono, G. S.; Figueirido, F. E.; Levy, R. M. Proteins Struct. Funct. Genet. 1994, 20, 85. (17) Sharp, K. A.; Honig, B. Annu. ReV. Biophys. Biophys. Chem. 1990, 19, 301. (18) Honig, B.; Nicholls, A. Science 1995, 268, 1144. (19) Martel, P. J.; Baptista, A. M.; Petersen, S. B. Biotechnol. Annu. ReV. 1996, 2, 315. (20) Soares, C. M.; Martel, P. J.; Carrondo, M. A. J. Biol. Inorg. Chem. 1997, 2, 714. (21) Baptista, A. M.; Martel, P. J.; Soares, C. M. Biophys. J. 1999, 76, 2978. (22) Bashford, D.; Karplus, M.; Canters, G. W. J. Mol. Biol. 1988, 203, 507. (23) Gunner, M. R.; Honig, B. Proc. Natl. Acad. Sci. U.S.A. 1991, 88, 9151. (24) Bashford, D.; Karplus, M. Biochemistry 1990, 29, 10219. (25) Bashford, D.; Gerwert, K. J. Mol. Biol. 1992, 224, 473. (26) Bashford, D.; Case, D. A.; Dalvit, C.; Tennant, L.; Wright, P. E. Biochemistry 1993, 32, 8045. (27) Yang, A. S.; Gunner, M. R.; Sampogna, R.; Sharp, K.; Honig, B. Proteins Struct. Funct. Genet. 1993, 15, 252. (28) Demchuk, E.; Wade, R. C. J. Phys. Chem. 1996, 100, 17373. (29) Warshel, A. Biochemistry 1981, 20, 3167. (30) Lee, F. S.; Chu, Z. T.; Warshel, A. J. Comput. Chem. 1993, 14, 161. (31) Baptista, A. M.; Teixeira, V. H.; Soares, C. M. J. Chem. Phys. 2002, 117, 4184. (32) Mertz, J. E.; Pettitt, B. M. Int. J. Supercomp. Ap 1994, 8, 47. (33) Baptista, A. M.; Martel, P. J.; Petersen, S. B. Proteins Struct. Funct. Genet. 1997, 27, 523. (34) Machuqueiro, M.; Baptista, A. M. J. Phys. Chem. B 2006, 110, 2927. (35) Machuqueiro, M.; Baptista, A. M. Biophys. J. 2007, 92, 1836. (36) Machuqueiro, M.; Baptista, A. M. Proteins Struct. Funct. Bioinf. 2008, 72, 289. (37) Borjesson, U.; Hunenberger, P. H. J. Chem. Phys. 2001, 114, 9706. (38) Baptista, A. M. J. Chem. Phys. 2002, 116, 7766. (39) Borjesson, U.; Hunenberger, P. H. J. Phys. Chem. B 2004, 108, 13551. (48) Stern, H. A. J. Chem. Phys. 2007, 126, 164112. Published on Web 08/17/2009 10.1021/ja808463e CCC: $40.75  2009 American Chemical Society 12586 9 J. AM. CHEM. SOC. 2009, 131, 12586–12594 Downloaded by UNIV NOVA DE LISBOA on September 2, 2009 | http://pubs.acs.org Publication Date (Web): August 17, 2009 | doi: 10.1021/ja808463e