THE JOURNAL OF BIOLOGICAL CHEMISTRY Q 1985 hy The American Society of Biological Chemists, Inc

Vol. 260, No. 9. Issue of May 10, pp. 5568-5573,1985 Printed in U. S. A .

Electrostatic Interactions during Electron Transfer Reactions between c-Type Cytochromes and Flavodoxin*

(Received for publication, July 30, 1984)

Patricia C. Weber and G . Tollin$ From the Protein Engineering Division, Gener Corporation, Gaithersburg, Maryland 20877

The interaction of three different C-type cytochromes with flavodoxin has been studied by computer graphics modelling and computational methods. Flavodoxin and each cytochrome can make similar hypothetical elec- tron transfer complexes that are characterized by nearly coplanar arrangement of the prosthetic groups, close intermolecular contacts at the protein-protein interface, and complementary intermolecular salt link- ages.

Computation of the electrostatic free energy of each complex showed that all were electrostatically stable. However, both the magnitude and behavior of the elec- trostatic stabilization as a function of solution ionic strength differed for the three cytochrome c-flavo- doxin complexes. Variation in the computed electro- static stabilization appears to reflect differences in the surface distribution of all charged groups in the com- plex, rather than differences localized at the site of intermolecular contact.

The computed electrostatic association constants for the complexes and the measured kinetic rates of elec- tron transfer in solution show a remarkable similarity in their ionic strength dependence. This correlation suggests electrostatic interactions influence electron transfer rates between protein molecules at the inter- molecular association step. Comparative calculations for the three cytochrome c-flavodoxin complexes show that these ionic strength effects also involve all charged groups in both redox partners.

Many recent studies have established that complementary electrostatic interactions play an important role in facilitating reactions between electron transfer proteins (1-5). A recently studied example is the nonphysiological reduction of horse heart ferricytochrome c by Clostridium pusteuriunum flavo- doxin semiquinone (5). At low ionic strengths and increasing cytochrome c concentration, the reaction shows saturation kinetics due to formation of a 1:l protein-protein complex. Under nonsaturating conditions, the rate constant for elec- tron transfer depends on solution ionic strength with larger values obtained at low ionic strengths.

A combination of computer graphics modelling (5) and computational studies (6) were carried out on the cytochrome c-flavodoxin system to both characterize the structural fea- tures of a putative reaction complex and quantitatively eval-

Institutes of Health Grants AM15057 to G. T. and GM33325 to F. R. *Work at the University of Arizona was supported by National

Salemme. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked ‘‘advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

$ Present address: Department of Biochemistry, University of Ar- izona, Tucson, AZ 85721.

uate the role of electrostatic interactions in its formation. These studies showed that flavodoxin and cytochrome c pos- sess complementary electrostatic fields localized about the partially exposed surfaces of their respective flavin and heme prosthetic groups. It was found that favorable electrostatic interactions between the positively charged region on cyto- chrome c and the complementary negatively charged region on flavodoxin could serve to orient the molecules along a productive reaction pathway and accelerate complex forma- tion. The magnitudes of the electrostatic component of the association constant for complex formation were computed as a function of ionic strength and shown to be in good agreement with experimental data.

Kinetic studies on the electron transfer rates between c- type cytochromes and flavodoxin have recently been extended to tuna cytochrome c, Rhodospirillum rubrum cytochrome CZ, and Pseudomonas aeruginosa cytochrome c551 (7). All cyto- chromes exhibit an ionic strength dependence on their elec- tron transfer rate constants with C. pusteuriunum flavodoxin semiquinone. As the ionic strength decreases, the rate con- stant is observed to increase for the reactions between flavo- doxin and either tuna cytochrome c or R. rubrum cytochrome cz. In contrast, the rate constant for the reaction between P. aeruginosa cytochrome c551 and flavodoxin decreases as the ionic strength is decreased.

The present work examines the interactions of tuna cyto- chrome c (12), R. rubrum cytochrome c2 (8, 9), and P. aeru- ginosa cytochrome c551 (10) with flavodoxin by the computer graphics and computational methods previously used to study the interaction of horse heart cytochrome c and flavodoxin and compares these results with kinetic observations. Exten- sion of the approach to additional cytochrome c-flavodoxin systems provides a test of the model building and computa- tional approaches and additionally expands our understand- ing of the role of electrostatic interactions in facilitating electron transfer reactions.

MATERIALS AND METHODS’

RESULTS

Model Complexes-Fig. 1 shows hypothetical electron trans- fer complexes between flavodoxin and the three C-type cyto- chromes. The complexes share several structural features. These include 1) a nearly coplanar orientation of the flavin prosthetic group of flavodoxin and the heme group of the

The “Materials and Methods” are presented in miniprint a t the end of this paper. Miniprint is easily read with the aid of a standard magnifying glass. Full size photocopies are available from the Journal of Biological Chemistry, 9650 Rockville Pike, Bethesda, MD 20814. Request Document No. 84M-2340, cite the authors, and include a check or money order for $1.00 per set of photocopies. Full size photocopies are also included in the microfilm edition of the Journal that is available from Waverly Press.

5568

Electrostatic Interactions of Cytochrome c and Flavodoxin 5569

FIG. 1. Stereoscopic views of hypothetical electron transfer complexes between C. MP flavodoxin and C-type cytochromes. Molecules are represented by a-carbon backbone tracings. Solid circles indicate prosthetic group atoms. Ribityl side chain of the flavin is omitted for clarity. Atoms of residues involved in intermolecular salt linkages are shown by open circles and are listed in Table I. Flavodoxin is identically oriented in each complex and, in this orientation, acidic residues in the amino acid sequence from 55 to 65 are situated to the left of the flavin and residues 13 and 120 to the right. A , R. rubrum cytochrome cp and flavodoxin; B, P. aeruginosa cytochrome c551 and flavodoxin. C, tuna cytochrome c and flavodoxin, reproduced from Ref. 6.

cytochrome, 2) close packing between the molecules at the intermolecular interface, and 3) the formation of intermolec- ular salt linkages between lysine residues on the cytochrome and aspartate and glutamate side chains on flavodoxin (Table I). Despite these structural similarities, differences in amino acid composition and surface structural conformation in the region of intermolecular contact result in slightly different orientations for each cytochrome relative to flavodoxin. For example, glutamine residue 16 of tuna cytochrome c is closely packed against the flavodoxin surface in this complex and restricts closer intermolecular approach. Smaller residues at structurally homologous positions in cytochrome c2 and cy- tochrome c551 allow a closer approach to flavodoxin in this region of the intermolecular interface.

Differences in the location of lysine side chains involved in intermolecular salt linkages also influence the cytochrome position relative to flavodoxin. For example, lysine residues 12, 13, and 27 in cytochrome cz form salt linkages with glutamate residues on flavodoxin. Structurally homologous residues at sequence positions 8 and 21 in cytochrome cbS1 and

13,25, and 27 in tuna cytochrome c participate in salt linkages with flavodoxin. This positional variability in lysine side chains can be accommodated by correspondingly variable sets of negatively charged residues on the flavodoxin molecular surface. Painvise salt linkages and interprosthetic group geo- metrical features are summarized in Table I.

Electrostatic Potential Surfaces-Fig. 2 shows the computed electrostatic potential about the molecular surfaces of cyto- chrome cSs1, cytochrome c2, and tuna cytochrome c at pH 7.0 and a solution ionic strength of 0.01 M. Positive electrostatic potential is localized at the molecular surface near the exposed heme edge of all three cytochromes. The positive potential surface is largest for tuna cytochrome c. A smaller positive electrostatic potential surrounds the exposed heme edge on cytochrome cq. As shown in Fig. 2, cytochrome c551 has two small spheres of positive potential in this area of the molecule.

While these cytochromes share common features of positive electrostatic potential near their exposed heme edges, their surfaces differ in the distribution of negative potential. Under the conditions simulated in these calculations, very little

5570 Electrostatic Interactions of Cytochrome c and Flavodoxin

TABLE I of the computations suggest substantial differences in both Structural parameters for flauodoxin-cytochrome c complexes the magnitude of electrostatic stabilization and its depend-

Intermolecular salt-linkaees ~~

Flavodoxin Cytochrome cssl Cytochrome c2 Cytochrome

Glu 13 Lys 12 Asp 58 Lys 90 Lys 79 Glu 62 Lys 27 Glu 63 Lys 27 Glu 65 Lys 21 Lys 25 Glu 120 Lvs 8 Lvs 13 Lvs 13

C -

Interprosthetic group dihedral angle, degrees

Cytochrome cssl Cytochrome c2 Cytochrome c

Heme to flavin 32.1 45.8 31.2 ~~

Interprosthetic group distances A Flavin atoms to ~~~~ Cytochrome cMl Cytochrome cp Cytochrome c

C7M C8M N5 N10 C7M C8M N5 N10

c 3 c 5.1 c 3 c 5.8 c 3 c 9.4 c 3 c 9.9 c 2 c 5.8 c 2 c 5.9 c 2 c 9.8 c 2 c 9.9

5.2 4.8 8.8 8.6 6.0 4.8 9.3 8.7

4.7 4.7 8.6 8.7 5.5 4.7 9.1 8.8

negative potential occurs near the molecular surface of tuna cytochrome c. In contrast, both cytochromes c551 and cp possess sizable regions of negative electrostatic potential. These re- gions are localized at the rear of each molecule distant from the exposed heme edge (Fig. 2).

Fig. 3 shows the electrostatic potential of flavodoxin com- puted for pH 7.0 and a solution ionic strength of 0.10 M. The electrostatic potential on this molecule is almost wholly neg- ative and extends over a large portion of the flavodoxin surface. The negative field distribution is roughly centered near the exposed portion of the flavin prosthetic group.

Electrostatic Stabilization of Flauodoxin-Cytochrome c Com- plexes-Estimates of the electrostatic stabilization as a func- tion of ionic strength were computed for flavodoxin-cyto- chrome c complexes with either oxidized or reduced cyto- chrome c , corresponding to complexes before and after the electron transfer event. As shown in Fig. 4, the ferri- and ferrocomplexes between flavodoxin and both cytochrome cp and tuna cytochrome c are electrostatically favorable in so- lutions of 0.01-0.50 M ionic strength. Electrostatic stabiliza- tions for these complexes increase with lowered ionic strength and for the ferricomplexes relative to the ferrocomplexes. The tuna cytochrome c-flavodoxin complex shows a greater elec- trostatic stabilization a t all ionic strengths than does the cytochrome cp-flavodoxin complex.

Results of the computation suggest that solution ionic strength exerts less influence on the electrostatic free energy of stabilization for the cytochrome ~ ~ ~ ~ - f l a v o d o x i n complexes. Unlike the cytochrome c2 and tuna cytochrome complexes, the cytochrome ~ ~ ~ ~ - f l a v o d o x i n complexes are electrostatically less stable a t low ionic strengths. As discussed below, these differences in computed electrostatic stabilization correlate directly with the observed reactivities of these cytochromes as a function of ionic strength.

DISCUSSION

The computer modelling studies show that three different C-type cytochromes, tuna cytochrome c , R. rubrum cyto- chrome cp, and P. aeruginosa cytochrome c551, can form similar electron transfer complexes with Clostridium MP flavodoxin. Despite the structural similarities of these complexes, results

ence on solution ionic strength. An experimental approach to estimating the magnitude of

the electrostatic component of molecular association involves measuring the electron transfer rate constant as a function of solution ionic strength (1). For charged macromolecules, low ionic strength conditions favor association of oppositely charged species and disfavor the association of like-charged molecules. Dashed lines in Fig. 5 show the observed kinetic rate constants as a function of ionic strength for the electron transfer reaction between flavodoxin semiquinone and the three oxidized C-type cytochromes (7).

The computed electrostatic free energies of association can be used to calculate apparent association constants for the flavodoxin-cytochrome c complexes. These are shown by solid lines in Fig. 5 . Inspection of the data in Fig. 5 indicates a strong correlation between the measured kinetic rate con- stants and computed association constants. The overall be- havior of the kinetic constants as a function of solution ionic strength is quite similar to that of the calculated association constants. Greater association constants at low ionic strength are computed for the flavodoxin complexes with cytochromes c and c2 and at higher ionic strengths for the flavodoxin- cytochrome c551 complex. The computational results also re- flect the relative magnitudes of the ionic strength dependence of the rate constants for the three different cytochrome c- flavodoxin reactions. For example, the reaction of flavodoxin with tuna cytochrome c shows the greatest dependence on solution ionic strength. In this case, the measured rate con- stants vary by a factor of 143 over the range of solution ionic strengths from 0.05 to 0.50 M. Over this same ionic strength range, the rate constants vary by a factor of 64 for cytochrome cp and by a factor of 3 for cytochrome c551. The calculated association constants with flavodoxin differ by a factor of 210 for tuna cytochrome c , 61 for cytochrome c2, and 1.2 for cytochrome c551 over the corresponding range of ionic strengths.

The structural basis for the observed ionic strength effects can be understood by comparing the electrostatic potential surfaces of the isolated molecules (Figs. 2 and 3). The electro- static potential surface for tuna cytochrome c is primarily positive. Association of this molecule with flavodoxin, whose electrostatic potential is primarily negative, is electrostati- cally favorable. In the cases of R. rubrum cytochrome cp and P. aeruginosa cytochrome c55], association of the positive electrostatic potential about the exposed heme edge with the negative potential surface of flavodoxin similarily contributes to complex stabilization. However, complex formation brings negatively charged regions of flavodoxin and the cytochromes cp and c551 into close proximity. This contributes to electro- static destabilization of the complex. The computed electro- static free energy of the protein-protein complexes then rep- resents a balance between short range stabilization due to interaction of oppositely charged regions and longer range destabilization due to the close proximity of like-charged regions.

The balance between the opposing electrostatic forces is mediated by solution ionic strength. At higher ionic strength, longer range electrostatic effects are masked by solution coun- terions. This effect can be seen in the ionic strength depend- ence of the computed free energies of complex stabilization between flavodoxin and the three cytochromes c. For example, at low ionic strength the flavodoxin-cytochrome c p complex is destabilized relative to the cytochrome c complex, owing to unfavorable interactions occurring between flavodoxin and

Electrostatic Interactions of Cytochrome c and Fluvodoxin 5571

FIG. 2. Calculated electrostatic potential surfaces for three C-type cytochromes at pH 7.0 and a solution ionic strength of 0.01 M. Two orthogonal views are shown for each cytochrome. In the top row, the molecule is viewed parallel to the heme plane with the solvent-exposed atoms of the prosthetic group toward the viewer. The molecules are rotated 90” in the bottom row, so that the solvent-exposed heme atoms are situated in the upper left quadrant of the molecule. All pictures are on the same scale. Molecules from left to right are P. aeruginosa cytochrome cml, R. rubrum cytochrome c2, and tuna cytochrome c. The calculated net protein charge is -2.0 for cytochrome cG1, +1.3 for cytochrome cz, and +8.1 for tuna cytochrome c. Blue dots define the +2kT potential surfaces and red dots outline the corresponding -2kT levels. Backbone atoms, C, N, and Ca, define the polypeptide fold and are colored white. Heme atoms are colored dark red.

the rear surface of cytochrome q (Fig. 2). However, this longer range destabilization is progressively masked with increasing ionic strength so that both complexes have similar stabilities at higher (0.50 M) ionic strength.

The computed ionic strength dependence for formation of the cytochrome ~~~~-f lavodoxin complex reflects a similar bal- ance between short-range stabilization from interaction be- tween oppositely charged regions and destabilization due to the close proximity of like-charged regions. However, in this case, the long-range destabilizing interactions make the greater contribution to the electrostatic free energy of asso- ciation. The complex is most stable at higher ionic strength

FIG. 3. Electrostatic potential surface for Clostridium MP flavodoxin. Contour levels are at + and -2kT for a solution at pH 7.0 with ionic strength 0.10 M. Flavin prosthetic group is colored yellow. Other colors are the same as for cytochromes in Fig. 2.

5572 Electrostatic Interactions of Cytochrome c and Flavodoxin

1.0 F

-3.0 -2'ol -6.0 1 _""

"" I

-10.0 -1 I I 1 & I

O.! 0.05 0.10 0.15 I

FIG. 4. The computed electrostatic free energy of associa- tion (AG,) is plotted as a function of solution ionic strength for the electron transfer complexes between Clostridium MP flavodoxin and P. aeruginosa cytochrome c661(0), R. rubrum cytochrome cz (O), and tuna cytochrome c (A). Solid lines inter- connect values for the ferricytochrome c-flavodoxin complexes; dashed lines for the ferrocytochrome c-flavodoxin complexes.

FIG. 5. Comparison of measured kinetic rates of electron transfer (M-' s-') and computed electrostatic association con- stants ("') as a function of solution ionic strength. Kinetic data, shown by dashed lines, is reproduced from Ref. 7. Solid lines indicate the computed association constants derived from the electro- static free energies of stabilization (Fig. 4) for three cytochrome c- flavodoxin complexes (log K = AGel/2. 3 RT). Panels from left to right show data for flavodoxin complexes with P. aeruginosa cytochrome cSSl, R. rubrum cytochrome c2, and tuna cytochrome c. I, ionic strength.

where the unfavorable interaction between like-charged re- gions is partially masked. As the ionic strength decreases, longer range destabilizing effects progressively dominate, and the complex consequently becomes less stable.

To summarize, the present work has shown that structur- ally similar complexes can be formed between flavodoxin and three different C-type cytochromes. Both the model building and computational results suggest that lysine residues near the exposed heme edge are conserved functional features of the cytochromes c that are important in conferring reaction specificity with other electron transfer proteins. However, the interactions among all charged groups in both protein mole- cules play a role in determining the electrostatic stability of the protein-protein complex. Computational studies on the cytochrome-flavodoxin complexes show a correlation between the measured kinetic rate constant for the electron transfer reaction and the association constant derived from the cal- culated electrostatic stabilization of the protein-protein com- plex. The correlation holds for both the rate constant behavior as a function of ionic strength and for the relative magnitude of ionic strength effects on the rate constants for the various cytochromes c with flavodoxin. This correlation supports the previous suggestion that electrostatic interactions affect elec- tron transfer rates between cytochrome c and flavodoxin by influencing the rate of intermolecular association (6). The comparative results on three different cytochrome c-flavo- doxin complexes are also consistent with previous proposals suggesting that electrostatic interactions can assist in preo- rienting molecules along a productive reaction trajectory. In this context, the reaction of flavodoxin with cytochromes c2 and cSs1 apparently involves both attractive and repulsive electrostatic forces that serve to orient the molecules during formation of productive electron transfer complexes.

Acknowledgments-We thank J. B. Matthew and F. R. Salemme for valuable discussions and J. B. Matthew for use of his computer programs to calculate the electrostatic potential surfaces and free energies. Graphic representations of electrostatic potential surfaces were computed using software developed by D. H. Ohlendorf. We also thank S. Sheriff for help with the stereo plots.

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Electrostatic Interactions of Cytochrome c and Flavodoxin 5573

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Supplwlental M t e r i a l TO

Electrostat ic lnteract ions Dur ing Electron Transfer React ions Between C-type Cytochromes and Flavodoxin

P a t r t i c i a C. Weber and 6. T o l l i n

METHWS

Atomic coordinates for the crys!.allographicallY re f ined s t ru tu res o f C los t r id ium I P flavodox.in.l~O tuna cytochrome c " R - r u b r m -cytochrome c ' and aeru nosa cytochrom c 5 were obtained fra'th;' B-ven Protein Da$a Bank& dkii'i o r i g i n a l -or; i e s c r i b i n t h e complex f o m t i o n b e t m n horse heart cytochrome c and C. Dasteurianum flavodoxin8. of the s t ruc tu re C. UP flavodoxin. a molecule harina cloze amino a c i d sequence h m l o w w i t h 4. E e u T e f lavodor in. has been used ii these studies.

c i n an e lec t ron t rans fer cmplex inc lude an i n te rp ros the t i c group distance and geometry Structural considerat ions i n model l ing the Interact ion of f lavodoxin and c y t o c h r m

favorab le fo r e lec t ron t rans fer , op t ima l in te rac t ion gemet ry fo r res idues invo lved in intermolecular sal t - l inkages and prevention of van der ma16 over lap at the contact interface. The proposed e lect ron t ransfer cowlexes represent the best so lu t ion to the s iu l taneovs op t im iza t ion o f these model bu i l d ing parameters.

cente::TcT. Therefore. flavodoxin and Cytochrome c were or iented to min imize lecu la r e lec t ron t rans fer ra tes depend on the separation between r e d a x

the d is tance between solvcnt-exposed atoms o f t he p ros the t i c groups. I n addit ion.

a s i t u a t i o n t h a t would favor o rb i ta l over lap o f the i r ex tended p i -o rb i ta l systems.lb a t t e w t s were made t o achieve coplanarity between the heme and f l a v i n p r o s t h e t i c groups

Another c r i t e r i o n i n f i t t i n g these molecules involved maximizing the nu-r of

whi le a l l have lysine residues near t he exposed h a edge. the spa t ia l and sequential in te rmluu la r sa l t - l inkages . S t ruc tura l cmpar isons o f these cytochromes shod t h a t

d i s t r i b u t i o n s o f t h e s e r e s i h e s d i f f e r l 7 . B o t h t u n a cytochrome c and R. rubrum cyto- ch rme cz have a number of surface lysine residues that are potential candidates fo r

exposed a t m of the f lavodoxin prosthet ic group. In contrast. only two Iysiy,fesidues intermolecular sal t - l inkages wi th negat ively charged s ide chains Clustered about the

are local ized near the exposed hae edge o f PI. aery inosa cytochrme c551 . Sap r e o r i e n t a t i o n o f s i d e c h a i n s i n v o l v e d i n i n t & l & t - l i n k a ~ s was a l l a r e d i n o r d e r t o w t i m i z e t h e i r i n t e r a c t i o n geometry.

20. Matthew, J . B., and Richards, F. M. (1982) Biochemistry 21,

21. Lee, B. K., and Richards, F. M. (1971) J . Mol. Biol. 55,379-400 22. Matthew, J. B., Friend, S. H., and Gurd, F. R. N. (1981) Biochem-

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istry 20,571-580

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417

occurred bet& atoms a t the i n t e r m l e c u l a r i n t c r f r c e . m ease o f r a t i n g t h i s c r i t e r i o n F ina l l y in te ra tomic distances were checked t o insure mar no van der Waals overlap

dspmded on the surface t o p o l w of f lavodoxin and cytochrmc c i n t h e reqions about the exposed atolls of t h e i r p r o s t h e t i c groups. S i m i l a r t o t h e s i t u a t i o n f o r t h e c m p l e x b e t m n horse heart cytochrome c and flavodoxin. a close correspondence i n molecular surface loops fomed by residues 7-10 i n f lavodoxin and residues 14-17 i n tuna cytochrome c res t r i c t mo lecu la r ro ta t tons a t t he i n te ra lecu la r i n te r face and thereby g rea t ly con t r i - bute t o t h e uniqueness of the proposed complexes. There e x t e r i o r n i n o a c i d s are Ala 15 a n d i l l n 16 i n tuna cytochrome c and Leu 15 and Ala 16 i n R. rubrum cytochrome c2. The presence of v a l l e r u i n o a c i d s i d e chains. Ala 14 a n d % m i n the s t ruc tu ra l l y h m l o g w s r e g i o n o f Cytochrome c551 resul ts i n less correspondence i n surface topolopy f o r t h i s molecule with f lavodorin. The cmbination of poorer surface correspondence and locat ion o f f n r lysine residues near the exposed heme edge makes s a t i s f a c t i m o f i n t e r - p ros the t i c group distance and a n g l e t h e p r i u r y c o n s t r a i n t s i n f i t t i n g f l a r o d o x i n and cytochrome ~551 .

E lect rostat ic potent ia l sur faces and f ree energies were computed using the solvent access ib i l i t y d isc re te charge model developed by Matthew and co-workcrs.18-20 This ndel takes in to account a l l p a i r w i s e i n t e r a c t i o n s b e t m n t i t r a t a b l e amino acids. ana we igh ts the con t r ibu t ion o f each charged group by i t s a c c e s s i b i l i t y i n t h e p r o t e i n r e l a - t i v e t o a c c e s s i b i l i t y i n t h e f r e e amino acid. For amino acids containing two possible charge centers, e.g. aspartate. the a t n i n v o l v e d i n an i n t e r - o r i n t r a m l e c u l a r s a l t - l inkage or, for unpaired residues. the atom having the greatest solvent accessibi l i ty was used t o define the charge pos i t i on i n t he ca l cu la t i on . Charged atol ls of the prosthe- t i c groups were also included. The heme i r o n was assigned a charge o f +1 i n t h e f e r r i - cytochrome and the heme propionates. were assigned i n t r i n s i c pK values of 4.0. Thc terminal phosphate of the f lavin mononucleotide was also taken in to account and assigned an i n t r i n s i c pk of 4.5 and a charge of '2.

Solvent a c c e s s i b i l i t i e s were Calculated by the a l g o r i t h o f Lee and Richards21 using a 1.4A rad ius fo r the probe sphere o f water. The in te rna l p ro te in and external bu lk so lvent d ie lec t r i cs were assumed t o be 4.0 and 78.5. respect ively. The external d i e l e c t r i c i s also affected by the so l ven t access ib i l i t y o f t he charged s i t e s and the

plexes was obtained by subtract ing the S tab i l i za t ion o f the i so la ted mlecv les from solut ion ionic strength.20 The free e n e r w o f e l e c t r o s t a t i c s t a b i l i z a t i o n o f t h e c m -

tha t ca lcu la ted fo r the complex. Regions o f h i g h e l e c t r o s t a t i c p o t e n t i a l were located by c q u t i n g t h e e l e c t r o s t a t i c p o t e n t i a l about the prote in . and contouring it a t l e v e l s o f kTle.

ParamterS have been r e ~ o r t e d . ~ ~ . ~ 0 . ~ ~ Addi t ional aspects o f the caqutat ional approach. Detai ls of the theory and s e n s i t i v i t y o f t h e COnputations t o v a r i a t i o n s i n model

i t s a p p l i c a t i o n s t o b i o l o g i c a l systems and i t s r e l a t i o n s h i p t o o t h e r e l e c t r o s t a t i c mdels have recent ly been reviewed by Matthew.23.24