J . Phys. Chem. 1990, 94, 959-961
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Brownian Dynamics Simulation of the Superoxide-Superoxide Dismutase Reaction: Iron and Manganese Enzymes J. Sines, S. Allison,* A. Wierzbicki, Department of Chemistry, Georgia State University, Atlanta, Georgia 30303
and J . A. McCammon Department of Chemistry, University of Houston at University Park, Houston, Texas 77204-5641 (Received: May 8 , 1989; In Final Form: July 21, 1989)
The technique of Brownian dynamics simulation is used to study the reaction of superoxide with Fe (from Pseudomonas ooalis) and Mn (from Thermus thermophilus) superoxide dismutases (SODs). Detailed models of the enzymes derived from crystal structures are employed. The active sites of both SODs are inaccessible to superoxide, but they are exposed upon displacement of a specific tyrosine residue. One possible explanation is that fluctuations in the structures of the enzymes are necessary to expose the active sites. Both Fe and Mn enzymes, like Cu/Zn SOD, carry charge distributions that serve to steer superoxide into the active site.
Introduction The superoxide dismutases (SODs) are a class of metalloto more benign proteins that convert toxic superoxide radicals (02-) species according to the overall reaction
Because of the important role they play in oxygen toxicity, interest in this class of enzymes has been considerable.1,2 To date, three distinct types (based on metallic cofactors) have been identified: Cu/Zn SOD, found in eukaryotes, with Cu as the reactive metal, and Mn and Fe SODs, which are found in prokaryotes, mitochondria, and plants. Although the Fe3 and Mn4 enzymes are structurally similar to each other, little similarity exists between them and the Cu/Zn enzyme. At present, it is unclear why totally different proteins catalyze the same reaction. These differences are kinetic in nature as well as structural. The Cu/Zn reaction is diffusion-controlled5 with little if any substrate saturation eff e c t ~ . ~Both ? ~ the Fe and Mn SODS exhibit saturation, and in the case of the Fe enzyme, a detailed mechanism has been proposed in which superoxide coordinates directly to iron, displacing a water molecule.6 The Mn enzyme displays more complex kinetic behavior, which has been interpreted in terms of slow and fast cycles.7 The diffusion-controlled kinetics of the bovine erythrocyte Cu/Zn reaction has been modeled by using Brownian dynamics simulation.*-lI These studies have helped confirm that electrostatic forces play an important role in steering superoxide into the active site. Despite the fact that both enzyme and substrate carry net negative charges, the rate constant decreases with in( I ) McCord, J . M.; Fridovich, I. Free Radical Biol. Med. 1988, 5, 363. (2) Bannister, J. V.; Bannister, W. H.; Rotilio, G. CRC Crir. Reo. Biochem. 1988, 22, 11 1. (3) Ringe, D.; Petsko, G. A.; Yamakura, F.; Suzuki, K.; Ohmori, D. Proc. Nail. Acad. Sci. USA 1983, 80, 3879. (4) Stallings, W. C.; Pattridge, K. A.; Strong, R. K.; Ludwig, M. L.J. Biol. Chem. 1985, 260, 16424. (5) Cudd, A.; Fridovich, I . J . Biol. Chem. 1982, 257, 11443. (6) Bull, C.; Fee, J . A. J . Am. Chem. SOC.1985, 107, 3295. (7) McAdam, M. E.; Fox, R. A.; Lavelle, F.; Fielden, E. M. Biochem. J . 1977, 165, 71. (8) Allison, S. A.; Ganti, G.; McCammon, J. A. Biopolymers 1985, 24, 1323. (9) Head-Gordon, T.; Brooks, C. L. J . Phys. Chem. 1987, 91, 3342. (IO) Sharp, K.;Fine, R.: Schulten. K.; Honig, B. H. J . Phys. Chem. 1987, 91, 3624. (1 I ) Allison, S. A.; Bacquet, R. J.; McCammon, J. A. Biopolymers 1988, 27, 25 1.
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creasing salt, which is opposite the behavior expected for simple (repulsive) point charges. Simulations have been successful in reproducing the unusual salt dependence of the rates observed experimentally. In the most realistic simulation detailed account is taken of protein shape and charge distribution, the protein interior's impermeability to mobile ions, and its lower dielectric constant relative to the surrounding solvent. The electrostatic force on superoxide is derived from a finite-difference solution of the Poisson-Boltzmann equation. These forces are needed to simulate the motion of superoxide in the vicinity of SOD. From these studies, diffusion-controlled rates within a factor of about 2 of experimental values have been obtained. The purpose of the present work is to apply the Brownian dynamics technique to the Fe and Mn enzymes in a preliminary study. Because the mechanisms are undoubtedly more complex in these c a s e ~ , 6 * we ~ 3 ~shall ~ focus our attention on the initial association of enzyme and substrate rather than on overall reaction rates. A number of issues shall be addressed. By varying the geometric criteria for a "reaction", one can determine the accessibility of the Fe and Mn active sites to superoxide. This will provide insights into the detailed mechanisms of the reactions. If, for example, the active sites are readily accessible, then an activation barrier of some kind must be overcome in order to account for the differences between the observed rates and those predicted on the basis of simple diffusional encounter (see below). This barrier could, for example, reflect desolvation of the metal and the substrate, or inner-sphere rearrangements of the kind seen in many electron-transfer proce~ses.'~If, on the other hand, the active sites are inaccessible, a possible mechanism would require fluctuation in the protein structure in the active site region in order to allow the substrate to reach the active site. Such "gate opening" motions have been observed in and other ~r0teins.l~ Although the gated mechanism seems particularly likely in view of the high mobility of surface residues in proteins,I7 electron transfer to an inaccessible metal could also occur through intervening amine acid residues.I3 In addition, the association rate as a function of salt is studied in order to understand the role the enzyme charge distributions play in guiding superoxide to the active site. (12) Fee, J . A,; McClune, G. J.; O'Neill, P.; Fielden, E. M. Biochem. Biophys. Res. Commun. 1981, 100, 377. (13) Newton, F. D.; Sutin, N. Annu. Reo. Phys. Chem. 1984, 35, 437. (14) Perutz, M. F.; Mathews, F. S . J . Mol. Biol. 1966, 21, 199. (15) Case, D. A,; Karplus, M. J . Mol. Biol. 1979, 132, 343. (16) Case, D. A,; McCammon, J. A. Ann. N.Y. Acad. Sci. 1986,482, 222. (17) McCammon, J. A,; Harvey, S . C. In Dynamics of Proteins and Nucleic Acids; Cambridge University Press: Cambridge, 1987.
0 1990 American Chemical Society
960 The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
Methods The Brownian dynamics method employed here has been described in detail elsewhere.]’ Briefly, the crystal structures of the Fe SOD dimer (from Pseudomonas oualis3) and Mn SOD tetramer (from Thermus thermophilus4) are overlaid onto loo3 or 1 I O 3 Cartesian lattices with I-A resolution. The dimeric and tetrameric forms of the enzymes are chosen in this way since they correspond to the known quaternary structure of these enzymes in s ~ l u t i o n . ~The , ~ Fe and Mn SOD coordinates were generously provided by the D. Ringe and G. Petsko labs (Fe) and the M. Ludwig lab (Mn). To each lattice site are assigned fixed charges (from charged enzyme residues), dielectric constants ( 2 / 7 8 inside/outside the protein), exclusion criteria for superoxide and mobile salt penetration, and reactivity criteria. A finite-difference method is then used to solve the linearized Poisson-Boltzmann equation at each lattice point. The electrostatic potentials at the lattice boundary and beyond are approximated by using DebyeHuckel potentials for a finite ion (radius = 30 8,)and a charge corresponding to the net enzyme charge. The net charges, based on standard charge assignments for amino acid residues at neutral pH, are -I 2 and 0 for Fe and Mn SODS, respectively, in protonic units. (At the grid boundary and beyond, the electrostatic potential of the Mn enzyme is set to 0). Diffusional trajectories of superoxide relative to SOD are carried out by Brownian dynamics. With hydrodynamic interaction ignored, the trajectory propagation formula is r(t
+ At) = r(t) + ( k B T ) - ] D , A t f ( t +) s
(2)
where r ( t ) is the position of superoxide relative to the center of SOD, Ar is the time step, k B T is the Boltzmann constant times absolute temperature ( T = 298 K), D, is the mutual diffusion constant of superoxide relative to SOD, f is the electrostatic force on superoxide, and s is a vector of independent Gaussian random numbers of zero mean with variance (s:) = 2D,At ( i denotes x , y , or I component). D, is the sum of the diffusion constants of superoxide and SOD. Hydrodynamically, substrate and enzyme are treated as spheres of radius 2.05 (02-), 28.5 (Fe SOD), and 35.9 8, (Mn SOD) with stick boundary conditions. A particular trajectory is initiated at Irl = b (typically, b = 50 A) and continues until superoxide either “reacts” by diffusing to within 4.5 A of an active site metal or “escapes” by reaching Irl = q = 500 A. To calculate a bimolecular rate constant, we have carried out 12 000 independent trajectories per simulation. Each simulation is broken down into 24 independent subsimulations, and from the variation in the subsimulation rate constants, standard deviations are determined.* From a simulation or subsimulation, one calculates p, the probability that a trajectory ”reacts” rather than “escapes”. From this recombination probability, the bimolecular rate constant k can be calculated from the equations18
k = k ~ ( b ) P / (-l ( 1 - P ) k D ( b ) / k D ( q ) )
(3)
kD(b) = 4 ~ D , / x - r -exp(U(r)/kBT) ~ dr
(4)
where U ( r ) is the electrostatic potential energy of superoxide at r.
Results and Discussion One of the approximations made in this study as in previous “detailed” studies of Cu/Zn SOD is the treatment of the enzyme as a rigid structure. In ref 11, reaction rates for Cu/Zn SOD were found to be negligible if the “exclusion radius”, u, was set to the sum of the van der Waals radius of superoxide (2.05 A) and the nearest non-hydrogen atom of SOD (1.5-1.7 8, for C, N , or 0). Significant rates were obtained when u was lowered to 2.75 8, in the channel regions (within 9 8, of Cu atoms). This approach accounts in a simple way for the fact that actual enzymes in solution exhibit some flexibility. Recent molecular dynamics simulations of Cu/Zn SOD confirm that the active site region (18) Northrup, S. H.; Allison, S . A,; McCammon, J. A. J . Chem. Phys. 1984, 80,1517.
Sines et ai.
A
Figure 1. Active site region of a monomer unit of Mn SOD. The dotted spheres denote van der Waals radii of non-hydrogen atoms for active site residues. Mn is denoted by the cross (to the right and slightly below tyrosine 36).
r! r?
Figure 2. Active site region of Mn SOD with tyrosine 36 removed. Otherwise identical with Figure 1.
fluctuates, making the channel down which superoxide must diffuse alternately constrict and widen with time.I9 When this approach is applied to the Fe and Mn SOD enzymes, the reaction rate is zero, even with u = 2.75 8, within 9 8,of the metal ion active sites. The criteria for reaction are that superoxide must diffuse to within 4.5 8, of Fe or Mn. Shown in Figure 1 is one active site region of Mn SOD from the crystal s t r ~ c t u r e . ~ The solid line represents the backbone of a single chain. Residues near the active site are labeled and their van der Waals radii indicated by the dotted spheres. The small cross to the right and slightly below tyrosine 36 indicates active site Mn. All residues except for phenylalanine 128 come from the same chain. It is evident from this figure that the active site is inaccessible to superoxide in the crystal structure. In solution, the active site region undoubtedly fluctuates, and in the process, protein con(19) Shen, J.; Subramanian, polymers, in press.
s.;Wong, C. F.; McCammon, J. A. Bio-
10.0
-
J. Phys. Chem. 1990,94, 961-968
-..._ .....
9.5
-
Y
-
0
-
-
9.0
-..... -.. ...-.. ....
0.5
0
0:2
0:4
0:6
J T Figure 3. Ionic strength dependence of association rate (k)for the three varieties of SOD. The ordinate is in log base 10. The squares correspond to Mn and the diamonds to Fe SOD. The vertical bars represent standard deviations in the simulated rates. The dashed line represents simulated rates for Cu/Zn SOD.
formations could develop which allow penetration by superoxide. This would occur, for example, if tyrosine 36 were to flip out of the active site cleft. Figure 2 is identical with the previous figure except that tyrosine 36 has been removed, thereby exposing Mn. A completely analogous situation exists for the crystal structure of the Fe enzyme, although the blocking residue is tyrosine 34. To determine, in an approximate way, the effect of tyrosine 36 (or 34) placement in the active site region on the ability of superoxide to reach Mn (or Fe), simulations have been carried out with this residue simply removed. In these cases, electrostatic potentials are recomputed since the low dielectric region occupied by tyrosine is replaced with high-dielectic water. As expected, a substantial association rate results. Shown in Figure 3 are rate constants for Mn SOD (squares) and Fe SOD (diamonds) as a function of ionic strength. The dashed line denotes the corresponding rates for Cu/Zn SOD obtained previous1y.lI Experimental turnover rates for Fe12 and Mn SOD' are 3 X lo8 (M s)-I at I = 0.1 M and 5.5 X IO8 (M s)-I at I = 0.002 M, respectively. Although the actual rates are smaller than the simulated rates by factors of 5.3 (Fe SOD) and 14 (Mn SOD), the fact that they agree as well as they do indicates a low activation barrier. A simple mechanism whereby the active site is blocked by the tyrosine most but not all of the time would, by itself, largely reconcile simulated and experimental rates.20 The simulations, of course, do not prove that this simple mechanism is necessarily (20) McCammon, J. A.; Northrup, S.H.Nature 1981, 293, 316.
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the actual mechanism. Electron transfer through the tyrosine side chain is among other possible mechanisms that could account for the observed kinetics. The salt dependence of the simulated rates merits some discussion. For Mn SOD, where the net charge on the enzyme is 0, the decrease in rate with increasing salt indicates that there is a net electrostatic attraction of the superoxide toward the active site. If the net electrostatic interaction were repulsive, the opposite salt dependence would be observed. Similar behavior has been previously reported for Cu/Zn SOD where the net protein charge is -4. Except at the lowest salt, there also appears to be a net electrostatic attraction for Fe SOD as well, despite the fact the net enzyme charge is -12. The rate at the lowest salt ( I = 0.005 M) for Fe SOD may be somewhat unreliable since the final potentials and consequently the rate constants depend on the relaxation parameter'' used in the finite-difference method. However, this uncertainty is small (about 10% in k ) and limited to this one particular case. In conclusion, all three SODSexhibit electrostatic attraction of superoxide toward the active site despite significant differences in net enzyme charge. Summary
On the basis of the crystal structures, the active sites of both the Fe and Mn SOD enzymes appear to be inaccessible to superoxide. Fluctuations in the solution structure, such as the movement of a specific tyrosine residue, may be required to expose the active site metal centers prior to reaction with superoxide. An alternative mechanism might involve direct electron transfer through amino acid residues. Simple removal of active site tyrosines results in predicted diffusion-controlled rate constants that are 5-15 times larger than experimental rates. Like the Cu/Zn enzyme, Fe and Mn SODS appear to carry charge distributions that attract superoxide toward the active sites. This result is somewhat surprising considering the significant differences in net charge of the three enzyme varieties. Since protein fluctuations appear to play a significant role in these reactions, we plan to use molecular dynamics to study atomic motions of the active site regions of Fe and Mn SOD in the near future. Acknowledgment. We thank Dagmar Ringe and Gregory Petsko at MIT for providing us with the Fe SOD coordinate and Martha Ludwig's lab at the University of Michigan for providing the Mn SOD coordinates. S.A.A. acknowledges an N S F Presidential Young Investigator Award. J.A.M. is the recipient of the 1987 George H. Hitchings Award from the Burroughs Wellcome Fund. His research is supported in part by grants from NIH, the Robert A. Welch Foundation, and the Texas Advanced Research Program. Registry No. SOD,9054-89-1; 02-,11062-77-4.
A Continuum Diffuslon Model for Viscoelastic Materials Y.Weitsman? Mechanics and Materials Center, Civil Engineering Department, Texas A & M University, College Station, Texas 77843-3136 (Received: November 14, 1988; In Final Form: June 6. 1989)
A model for diffusion in polymers is established from basic principles of irreversible thermodynamics,employing the methodology of continuum mechanics. The polymeric materials are considered to respond viscoelastically,with ageing. It is shown that effects of stress on diffusion and certain anomalies in the moisture sorption process can be explained by the present model.
l. Introduction The processes of moisture transport and sorption in polymers have been studied by numerous investigators for more than 50 Present address: Department of Engineering Science and Mechanics, The University of Tennessee, Knoxville, TN 37996-2030. 0022-3654/90/2094-0961$02.50/0
years. Most of these studies, which involved experimental, analytical, and materials science aspects, were conducted by researchers in the fields of Physical and polymer chemistry. These investigations were mostly focused toward applications in membrane twhnologY and therefore c ~ ~ c e r n aspects ed of permeability and seepage. It is far beyong the scope of the present article to 0 1990 American Chemical Society
