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show for the first time a distinct N M R spectrum for the orthorhombic form of silicalite, they provide a means of examining which of the two space groups is most likely. Analysis of the NMR spectrum measured at 297 K (monoclinic material), gives the same result as observed previously;I0the lowest and highest field signals are relatively well resolved, and each has an intensity in the ratio 1:24 to that of the entire peak envelope. In the N M R spectrum measured at 353 K for the orthorhombic material, there are no such well-resolved peaks. The low-field peak at -1 13.9 ppm is the signal that is best separated from the main envelope, and the ratio of the integrated area of this peak to that of the whole peak multiplet is 1:6. If the assumption is made that the signal is composed of the sum of either 12 or 24 Gaussian-shaped peaks, each identical in intensity and half-width, then a simulation of the spectrum can be computed for each of these two cases. The results of a least-squares refinement with peak positions, intensity, and half-width3as independent variables are compared with the experimental trace in Figure 4. It is apparent that, for that part of the spectrum downfield of about -1 18 ppm, a 12-peak (and thus also a 24-peak) fit provides a reasonably accurate approximation. However, in the region between -1 18 and -120 ppm the agreement is better in the case of the 24-peak fit. In this case the region is reproduced by the sum of four Gaussian peaks, each of area 1/24 of the total intensity. Similarly the peak at -1 13.9 ppm also consists of four signals. With this approach, it seems likely that the orthorhombic space group for silicalite at this temperature is PnZ,a, with 24 unique tetrahedral Si atom sites in each unit cell. This result is in agreement with the previously suggested orthorhombic space group.lOJ’ -112
-114
-116
-118
-120
p.p.m. from TMS Figure 4. NMR spectrum (-) from orthorhombic (curve labeled 353 K, Figure 3) silicalite,simulated (...) by using 12 (bottom) and 24 (top)
identical Gaussian peaks. arising from one of the 24 nonequivalent Si atom sites in the monoclinic unit cell with the space group P 2 1 / n . 7 From XRD evidence it is not possible to decide which of two possible orthorhombic space groups is applicable, Pnma or PnZla with 12 or 24 unique Si atom sites, respectively.” Since the present results
Acknowledgment. We thank Dr. D. Seddon of The Broken Hill Proprietry Company Limited for providing the sample of silicalite which was prepared by Mr. K. Kinson and Mr. G. Marks. We thank also Dr. D. Muller who made the N M R measurements at the Bruker Analytische Messtechnik GMBH in Rheinstetten, West Germany. Registry No. SO2, 7631-86-9.
(11) E. M. Flanigen, J. M . Bennett, R. W. Grose, J. P. Cohen, R. L. Patton, R. M. Kirchner, and J. V. Smith, Narure (London),271,512 (1978).
Dynamics of Substrate Binding to Copper Zinc Superoxide Dlsmutase Stuart A. Allison*+ and J. Andrew McCammon* Department of Chemistry, University of Houston, Housron, Texas 77004 (Received: December 3, 1984)
The association dynamics of the substrate superoxide and the enzyme superoxide dismutase have been studied by computer simulation of the relative diffusion of these reaction partners. Electrostatic interactions are found to bias the substrate trajectories toward the active site of the enzyme, leading to a significant enhancement of the reaction rate.
Introduction Electrostatic interactions influence the rates of many biomolecular associations.’ Particularly interesting in this regard is the diffusion-controlled transformation of superoxide (02-) catalyzed by the enzyme copper zinc superoxide dismutase (SOD).233 Although the substrate and enzyme are both negatively charged a t physiologic pH, the reaction rate is high and increases with decreasing ionic strength at moderate salt concentration^.^^^ Chemical and structural studies of SOD suggest that these surPresent address: Department of Chemistry, Georgia State University, Atlanta, GA 30303.
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prising results are due to the noncentrosymmetric electric field of SOD, which may act to steer 02-into the active site of the e n ~ y m e . ~Dynamical .~ trajectories of interacting SOD and 02molecules have now been computed and anayzled by a new simulation method that can provide rates of diffusion-controlled (1) E. Neumann in “Structural and Functional Aspects of Enzyme Catalysis”,H. Eggerer and R. Huber, Ed., Springer, Berlin, 1981, pp 45-58. (2) A. Cudd and I. Fridovich, J . Eiol. Chem., 257, 11443-1 1447 (1982). (3) E. D. Getzoff, J. A. Tainer, P. K. Weiner, P. A. Kollman, J. S. Richardson, and D. C. Richardson, Nature (London),306,287-290 (1983). (4) D. Klug, J. Rabani, and I. Fridovich, J. Eiol. Chem., 247,4839-4842 ( 1972).
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985
Letters
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TABLE I: Relative Rate Constants for Various Models
SOD charge 44-
0 0 4+ 4+
model monopole monopole plus quadrupole monopole monopole plus quadrupole monopole monopole plus quadrupole
klko” 0.056 0.079 0.12 0.19
0.26 0.41
“The rate constant k is normalized by that, ko, expected for an SOD model with no embedded charges and a uniformly reactive surface. 25 000 trajectories were computed for each model, which yields standard deviations in the range of 3-8% for each result. The same quadrupole was used in the three “monopole plus quadrupole” calculations; Le., only the central one of the five charges was changed.
I Figure 1. Schematic illustration of the SODOF reaction model. Crosses indicate positions of charges. Active sites are indicated by the dark caps on the SOD sphere; Bo = loo.
reactions between molecules with complicated structures and interaction^.^*^ The results support the reactant steering mechanism and show how the reaction rate is influenced by such factors as the charge distribution on the enzyme and the ionic strength of the solution.
Methods For the initial studies described here, the SOD dimer was modeled as a sphere of 30-A radius. Two reactive patches corresponding to the active site regions of the dimer were defined by surface points within loo of an axis running through the center of the sphere (Figure 1). Five charges were embedded within the sphere to reproduce the monopole, dipole, and quadrupole terms associated with the charged groups in the 2-A resolution X-ray structure of bovine erythrocyte SOD.’,* The net charge is 4- (in units of the protonic charge), and the dipole moment approximately vanishes due to the symmetry of the dimer. Examination of contour maps of the electrostatic potential outside of the sphere shows that the field produced by the five-charge model is a good approximation to that produced by all the charges in the X-ray structure. The 02-molecule was represented by a sphere of radius 1.5 A with a central charge of 1-. A dielectric constant of 78 was assumed throughout the system in this initial work. Representative diffusional trajectories of 02-relative to SOD were generated by a Brownian dynamics simulation p r o c e d ~ r e . ~ Hydrodynamic interactions were neglected in this initial work. The trajectory propagation formula is R(t At) = R(t) (kBT)-lD,lAt F(t) S (1)
+
+
+
where R(t) is the vector from the center of SOD to the center of 0,at time t, kBTis the Boltzmann constant multiplied by absolute temperature ( T = 298 K), DreIis the relative diffusion constant for 02-and SOD in water based on the Stokes law with slip boundary conditions, At is the time step for trajectory propagation, F(t) is the electrostatic force on 02-at time t , and S is a vector of Gaussian random numbers that represents the nonsystematic displacement due to collisions with solvent molecules. To calculate the rate constant for bimolecular reaction of 02and SOD, a new trajectory analysis method was sed.^,^ In this method, it is necessary to consider trajectories only in the small R region where the interactions and/or the diffusional flux density (5) S. H. Northrup, S. A. Allison, and J. A. McCammon, J. Chem. Phys., 80, 1517-1524 (1984). (6) S. A. Allison, N. Srinivasan, J. A. McCammon, and S. H. Northrup, J . Phys. Chem., 88, 6152-6157 (1984). (7) J. A. Tainer, E. D. Getzoff, K.M.Beem, J. S. Richardson, and D. C. Richardson, J . Mol. Biol., 160, 181-217 (1982). (8) F. C. Bernstein, T. F. Koetzle, G. J. B. Williams, E. F. Meyer, M. D.
Brice, J. R. Rodgers, 0. Kennard, T. Shimanouchi, and M. Tasumi, J . Mol. Biol. 112, 535-542 (1977). (9) D. L. Ermak and J. A. McCammon, J . Chem. Phys., 69, 1352-1360 (1978).
are noncentrosymmetric. Contributions to the rate due to effects in more distant regions (e.g., where the long-range, centrosymmetric monopole term dominates the electrostatic interaction) are incorporated analytically. In the present study, trajectories were initiated at points on a surface of radius b (typically 300 A) from the center of SOD. At this distance, the quadrupole field is negligible so that the quantity kD(b)given below can be calculated easily. Computing efficiency can be improved by using a smaller b and a modified trajectory method (Allison et al., to be submitted). Trajectories that intersected either active site region on SOD were terminated and counted as successful reaction attempts. Trajectories that intersected other parts of the SOD surface were reflected back into the solvent and continued. Trajectories that intersected a surface of radius q > b (typically 500 A) from the center of SOD were terminated. The fraction 0 of trajectories that react successfully yields the bimolecular rate constant k through the equationsS k=
kD(bM 1 - (1 - p)n (3)
Here, kD(b)is the Debye rate for 02-molecules that occupy the region where the electrostatic potential energy U ( R ) is approximately centrosymmetric to diffuse toward SOD and be absorbed a t radius b, and n corrects for those trajectories that were terminated at R = q but which might ultimately have been reactive if continued.
Results and Discussion Several calculations have been carried out to explore effects that have been suggested to contribute to the high reactivity of SOD. Table I displays the changes in rate constant that occur when the noncentrosymmetric charge distribution in SOD (monopole plus quadrupole) is replaced by a centrosymmetric distribution (monopole). For the native-like model with monopole charge of 4-, inclusion of the quadrupole increases the reaction rate by 40%; the quadrupole field increases the rate by steering 0,into the active sites. Comparison of the results for the other models in Table I with those for the native-like model yields two other interesting conclusions. First, the rates for the native-like models are smaller than those for the corresponding neutral and positively charged models by factors of only about 2.5 and 5, respectively. The net charge of 4- on native SOD does not result in a very dramatic reduction of reaction rate with 02-because the R 1repulsive potential associated with the monopole is not large outside of the SOD molecule ( R > 30 A). Second, the steering effect of the quadrupole field is present even in the neutral and positive SOD models. This suggests that the steering effect will persist in the presence of added salt, which will suppress the effects of the monopole field more strongly than those of the shorter-ranged quadrupole field.
J. Phys. Chem. 1985, 89, 1074-1077
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.05
I
T
-
i' 1o - ~
I
I
I
16'
16'
1
SALT (M)
FFgure 2. Dependence of rate on ionic strength ("salt"). Solid and dotted lines connect monopole + quadrupole and monopole rates, respectively. The electrostatic potential energy between the charge on OF ( q l )and a particular SOD charge (q2) separated by r was taken to be qlq2e-"'/er where e is the dielectricconstant and K is the Debye-Hockel parameter. The error bars indicate plus and minus one standard deviation.
The qualitative effect of added salt has been examined directly by computing trajectories with a screened potential of the Debye-Hiickel type (Figure 2).5 The expected persistence of the steering effect is observed through the physiologic range of salt concentration. For the native-like monopole plus quadrupole model, the rate initially increases with added salt as the monopole repulsion is screened. Above an ionic strength of about 3 X M, the rate decreases with added salt as the steering field due to the quadrupole is screened; a similar trend is observed experimentally.2 Concluding Remarks
This work represents the first attempt to study the diffusioncontrolled reaction of biological molecules by explicit calculation
and analysis of molecular trajectories. The model used for the SOD-02- system is certainly far from exact. The charge distribution on SOD would be better represented by the partial charges of all 2196 atoms observed in the X-ray structure plus their attached hydrogens.' Although the uniform dielectric model is a standard one in small ion electrolyte theory1° and may even be qualitatively reasonable for proteins,lI it would be desirable to replace this with an inhomogeneous model that distinguishes the protein interior from the solvent.'2 A proper description of salt effects would exclude ions from the protein interior and go beyond the Debye-Huckel approximations.I0 The irregular topography of the enzyme surface, including an accurate model of the active sites, should be incorporated.' The above complications should not obscure the two major conclusions of this work. First, the new trajectory analysis method of Northrup et aL5 can be applied to study the diffusional encounter of biological molecules. Refinements such as those outlined above can be incorporated in straightforward fashion. Second, the rate constant of the SOD-0,- system is enhanced by substrate steering. The simple model used in this initial work is qualitatively reasonable. The refinements outlined above are being incorporated in continuing work. A fully detailed analysis will not be available for some time, but the results obtained to date (e.g., incorporating the full complement of SOD charges) are fully consistent with the steering picture presented here. Acknowledgment. We thank Prof. Jane Richardson for a helpful discussion on the structure of SOD. This work has been supported in part by grants from the Robert A. Welch Foundation and from NIH. J.A.M. is an Alfred P. Sloan Fellow and the recipient of N I H Research Career Development and Camille and Henry Dreyfus Teacher-Scholar Awards. S.A.A. is the recipient of a Camille and Henry Dreyfus Grant for Newly Appointed Faculty in Chemistry. (10) H. L. Friedman, Annu. Rev.Phys. Chem., 32, 179-204 (1981). (11) D. C. Rees,J. Mol. Biol., 141, 323-326 (1980). (12) J. Warwicker and H. C. Watson, J. Mol. Biol., 157,671-679 (1982).
Colloidal Catalysis: The Effect of Sol Size and Concentration Paul L. Freund* Departamento de Quimica, Universidad SimBn Bolhar, Apartado 80659, Caracas, Venezuela
and Michael Spiro Department of Chemistry, Imperial College of Science and Technology, London SW7 2AX United Kingdom (Received: November 17, 1984; In Final Form: January 16, 1985) The reaction between ferricyanide and thiosulfate ions was found to be strongly catalyzed by citrate-stabilized gold sols. Use of lower citrate concentrations made it possible to prepare larger gold particles with greater geometric eccentricities. For every preparation, the catalytic rates increased linearly with the concentration of catalyst, in contrast to the more complicated behavior reported for the colloidal catalysis of reactions producing hydrogen gas. The magnitude of the catalytic rate constant and its dependence on the particle dimensions of the various sols showed that the reaction was surface and not diffusion controlled. Introduction The current interest in noble metal and semiconductor colloidal suspensions stems from their potential use as catalysts in schemes for the photodecomposition of water. The main reaction investigated has beenl-10 MV+ H+ MV2+ 1/2H2 (1)
+
-
+
(1) Kiwi, J.; GrBtzel, M. J . Am. Chem. SOC.1979, 101, 7214. In Figure
3 the rate rises less than proportionately to the platinum concentration while the opposite behavior is shown in Figure 4d.
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(MV = methyl viologen). It is a curious feature of these studies that the rate (Vat)of hydrogen evolution has not been proportional (2) Griitzel, M. Faraday Discuss. Chem. SOC.1980, 70, 359. (3) Keller, P.; Moradpour, A. J. Am. Chem. SOC.1980, 102, 7193. (4) Meisel, D.; Mulac, W. A.; Matheson, M. S. J . Phys. Chem. 1981.85,
179.
( 5 ) Johansen, 0.;Launikonis, A.; M e r , J. W.; Mau, A. W.-H.; Sasse, W. H. F.; Swift, J. D.; Wells, D. Ausr. J . Chem. 1981, 34, 981. (6) Miller, D. S.; Bard, A. J.; McLendon, G.; Ferguson, J. J . Am. Chem. SOC.1981, 103,
5336.
0 1985 American Chemical Society
