Theory and Practice of Electron Transfer within Protein−Protein Complexes: Application to the...

Theory and Practice of Electron Transfer within Protein −Protein Complexes:Application to the Multidomain Binding of Cytochrome c by Cytochrome c

Peroxidase

Judith M. Nocek,† Jian S. Zhou,† Sarah De Forest,‡ Satyam Priyadarshy,‡ David N. Beratan,‡Jose N. Onuchic,§ and Brian M. Hoffman*,†

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, Department of Chemistry, University of Pittsburgh,Pittsburgh, Pennsylvania 15260, and Department of Physics, University of California at San Diego, LaJolla, California 92093-0319

Received June 10, 1996 (Revised Manuscript Received August 28, 1996)

ContentsI. Introduction 2459II. Photoinitiated ETsExperimental Approaches 2460III. Multisite and Multidomain Binding: Microscopic

vs Thermodynamic Constants2462

A. 1:1 Stoichiometry 2462B. 2:1 Stoichiometry 2464

IV. Quenching as a “4-D” Experiment 2465A. Conventional Titrations (CN and CR) with 1:1

Stoichiometry2466

B. Conventional (C) Titrations with 2:1Stoichiometry

2467

C. Inverse Titrations (IN and IR) 2469V. Unimolecular and Bimolecular Electron Transfer

in Biomolecules2470

A. The Tunneling Pathway Model of ProteinMediated Electron Transfer

2470

B. Functional Docking 2472C. Classical Electrostatics and the Encounter

Surface2473

VI. ET between the Physiological Partners, Cc andCcP

2473

A. One Structure for the [CcP, Cc] Complex? 2474B. Dynamic ViewsExperimental Evidence for

Multiple Conformations2476

C. New Titration Strategies Show That CcP HasTwo Binding Domains

2476

D. Interactions between the Two CcP BindingDomains?

2479

E. Independent Confirmations of 2:1Stoichiometry

2481

F. Kinetic and Physical Characterization ofSite-Specific Mutants of CcP

2482

G. Surface Coupling Maps and ElectrostaticMaps of the [CcP, Cc] Complex

2484

VII. Discussion 2486

I. Introduction

Studies of long-range electron transfer (LRET) insystems where the redox partners are held at a fixedand rigid distance and orientation have achieved acentral role in modern chemistry.1-14 The paradig-matic system in nature is the photosynthetic reaction

center.2 Three levels of experimental design havebeen developed to study ET in an environmentamenable to synthetic and physical control: linkeddonor-acceptor model compounds,3,4 redox-modifiedproteins,5,11-13 and modified protein-protein com-plexes.6-8,14 In the first level, the ET process neces-sarily takes place through a covalent and/or H-bonded pathway amenable to changes in distance andcomposition. The second level, where a redox-activeinorganic complex is covalently attached to a surfaceamino acid residue of a redox protein, introduces thefull complexity of intraprotein ET between centerscovalently linked to well-defined sites within a pro-tein. This raises such issues as the relative impor-tance of “pathways” that involve through-space vsthrough-bond coupling, with the latter subdividinginto covalent bonds and hydrogen bonds.9 As avariant on this approach, mixed-metal hemoglobinhybrids exhibit intersubunit ET10 and thus neces-sarily introduce the issue of ET across a noncovalentprotein-protein interface, but do so in a contextwhere the intersubunit contacts and potential ETpathways are structurally well-defined.This review focuses on the study of ET between

proteins that form noncovalent complexes, a higherorder problem that introduces additional complexitiesnot seen in the other systems and not fully appreci-ated when the current interest in LRET began.15,16In the study of physiological protein-protein com-plexes such as that between yeast cytochrome cperoxidase (CcP) and cytochrome c (Cc),6,7,14,17 onebegins without certain knowledge of the stoichiom-etry of binding, much less the site or sites on theprotein surfaces where binding occurs, and withoutknowledge of the rules for protein-protein recogni-tion and conformational interconversion that mightcontrol the ET process! The ET event occurs withina protein-protein complex across a dynamic protein-protein interface, and as a consequence, the observedkinetics may depend not only on the ET process itselfbut also on the extent and stoichiometry of binding,as well as on the interfacial dynamics of docking. Inshort, as we18,19 and others20-22 have come to recog-nize, the first stage in the study of such interproteinET does not involve the study of ET, but rather theuse of ET measurements to study the stoichiometryand geometry of equilibrium binding as well as thedynamics of docking rearrangements. Only aftersuccesses in this stage of the enterprise does one

† Northwestern University.‡ University of Pittsburgh.§ University of California.

2459Chem. Rev. 1996, 96, 2459−2489

S0009-2665(95)00044-6 CCC: $25 00 © 1996 American Chemical Society

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achieve the ability to ask meaningful questions aboutthe ET event itself.The current era of studying electron transfer

between proteins originated with the recognition thatmixing experiments cannot achieve the time resolu-tion needed for in-depth analysis.23-26 Section IIbriefly discusses the strategies developed to general-ize the use of laser-flash techniques to initiateelectron-transfer processes. Section III recounts thefundamental concepts needed to use kinetic mea-surements to obtain stoichiometric information aboutprotein-protein binding and to obtain informationabout docking dynamics. Section IV begins the heartof the review. It presents a new “multidimensional”approach to performing measurements of excited-state quenching, one that has broadened and strength-ened the application of this venerable technique.Section V summarizes pathways models for thecalculation of ET rate constants and their applicationto bimolecular ET and discusses their combined usewith classical electrostatics calculations to under-stand “functional docking”. In section VI, thesevarious issues are illustrated by describing the

discovery of multidomain (2:1) binding of Cc by CcPand by a discussion of the ET reactivity within thecomplexes of Cc with CcP. Finally, a preliminaryintegration of these efforts is discussed in section VII.

II. Photoinitiated ET sExperimental Approaches

Laser-photolysis methods were introduced to thestudy of protein-protein binding and interproteinelectron transfer when it was recognized that re-placement of the heme (FeP) of one protein partnerby a closed-shell metalloporphyrin, MP (M ) Zn orMg; P ) protoporphyrin IX), introduces the possibil-ity of studying photoinitiated electron transfer be-tween the MP and the redox group in the part-

Judith M. Nocek graduated from Illinois Benedictine College, earning B.S.degrees in Chemistry and Mathematics. In 1986, she completed her Ph.D.studies at Iowa State University under the direction of Donald Kurtz. Afterperforming postdoctoral research at Northwestern University with BrianHoffman, she has continued at Northwestern University as a ResearchAssociate. Her current research interests include protein−protein interac-tions and electron transport.

Jian S. Zhou received his B.S. degree from Anhui Normal University (P.R.of China) and his Ph.D. degree from Universite Pierre et Marie Curie(Paris, France) in the field of surface and colloid science. Afterpostdoctoral studies at Bowling Green State University and then IowaState University, he joined Professor Brian M. Hoffman of NorthwesternUniversity in 1993 as a postdoctoral research fellow. His research interestsare in electron transfer and in the development and application ofbiomimetic materials.

Sarah de Forest began her undergraduate studies at the CommunityCollege of Philadelphia and she obtained her B.S. at the University ofPittsburgh in 1994. After graduating, she worked for a year with ProfessorDavid Beratan at Pitt, studying electron transfer and protein docking. Sheis currently pursuing a doctoral degree at the University of California,Berkeley, where she is working with Professor Martin Head-Gordon. Hercurrent studies focus on electronic excited states, with an eye towarddeveloping methods to treat large molecular systems.

Satyam Priyadarshy received his M.S. in 1984 from Agra University, Agra,India, and Ph.D. from the Indian Institute of Technology, Bombay (Mumbai)in 1990, working with Professor Sambhu N. Datta. After completing hisPh.D., he worked on rotational relaxation of molecular systems, with Dr.Petr Harrowell at the Physical and Theoretical Chemistry Department,University of Sydney, Sydney, Australia. His second postdoctoral positionwas with Professor David Beratan at the Department of Chemistry,University of Pittsburgh. There, the work was mostly on long-rangeelectron transfer in biomolecules and on nonlinear optics. Since January1996, he has been a Research Assistant Professor of Chemistry at theUniversity of Pittsburgh. His current research interests include theoreticalstudies of exciton dynamics in photosynthetic systems, applications ofquantum mechanical methods to advanced materials design, biomolecularprocesses, and nonlinear optics. Also of interest is the development ofefficient self-consistent Hartree−Fock codes for parallel and vectorcomputers.

2460 Chemical Reviews, 1996, Vol. 96, No. 7 Nocek et al.

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ner.7,27,28 A reversible electron transfer cycle withinsuch metal-substituted complexes can be initiated bya laser flash. Photoexcitation of the closed-shell MPsubstituted into a hemoprotein produces an excitedsinglet state that rapidly (and generally with highyield) crosses to a long-lived (typically milliseconds),triplet excited state (3MP). The 3MP is a strongreductant and in the presence of a redox-activepartner protein, commonly (but not necessarily) one

containing a ferriheme, the 3MP is quenched by long-range, intracomplex ET (eq 1).

Direct photoexcitation eliminates complicationsarising from the use of an external reductant, andthe MP-substituted metalloprotein can be mixed withits partner protein to preform the ET-competentcomplex. The resulting charge-separated intermedi-ate (I) returns to the ground state by thermallyactivated ET from Fe2+P to the porphyrin-centeredπ-cation radical (MP+) according to eq 2.

In studies of the photoprocess, both transientabsorption and emission techniques are used tomonitor the kinetic progress curves of 3MP, fromwhich the rate constant for reaction 1 is obtained.To study the thermal ET return (reaction 2) onlyabsorption techniques are applicable.Heme replacement is a valid method to the extent

that the modified protein is a structurally faithful,ET-active analogue of the native hemoprotein. Manystudies have addressed this issue and in doing sohave fully validated the replacement procedure.Thus, the structure of MgHb, in which all fourferroheme prosthetic groups of hemoglobin are re-placed by MgP has been determined crystallographi-cally at 2 Å, and its structure was found to be“indistinguishable” from the native protein at thisresolution (Figure II.1).29 Likewise, NMR studieswith ZnCc in aqueous solution30,31 have demonstratedthat the conformation (and ligation state) of Cc isunchanged by incorporation of Zn2+ in place of Fe2+.Similar findings have been reported for Cu32 and Co-substituted Cc.30 In all cases, these studies haveoverwhelmingly shown that closed-shell metallopro-teins are faithful structural analogues of their nativeproteins in the valence state corresponding to thatof the replacement metal ion.

David Beratan received a B.S. in chemistry from Duke University in 1980.After completing his Ph.D. in 1985 with J. J. Hopfield in the Departmentof Chemistry at Caltech, he moved to the Jet Propulsion Laboratory inPasadena, CA, as a National Research Council postdoctoral associate.He spent seven years at JPL, the later five as a Member of the TechnicalStaff. At JPL, he and Onuchic developed the Pathway model for analyzingprotein electron-transfer reactions. He also devised new strategies forimproving nonlinear optical materials and molecular-scale electronicdevices. Beratan was a Visiting Associate in Chemistry at Caltech’sBeckman Institute during his last few years in Pasadena. Since 1992,he has been an Associate Professor of Chemistry at the University ofPittsburgh. His current research interests include electron transfer inproteins and DNA, inverse design of materials, and the electronic structureof macromolecules. He currently holds a National Science FoundationNational Young Investigator Award.

Jose Nelson Onuchic received a B.S. in Electrical Engineering in 1980,a B.S. in Physics in 1981, and a M.S. in Applied Physics in 1982 fromthe University of Sao Paulo at Sao Carlos, Brazil. He received his Ph.D.from Caltech in 1987 under the supervision of John J. Hopfield. Histhesis work was on new aspects of the theory of electron-transfer reactionsin biology. He then spent six months at the Institute for Theoretical Physicsin Santa Barbara before returning to Brazil at the University of Sao Pauloas an Assistant Professor. During his two and one-half years there, hecontinued his work on electron-transfer theory, on the theory of chemicalreactions in the condensed phase, and on molecular electronics. Hejoined the faculty of the University of California at San Diego in 1990,where he has been working on electron transfer in proteins and otherbiological and chemical systems, and on the protein-folding problem. In1992 he received a Beckman Young Investigator Award and he waselected a Fellow of the American Physical Society in 1995.

Brian M. Hoffman earned a S.B. degree at the University of Chicago anda Ph.D. degree from Caltech (with Harden McConnell). After apostdoctoral year at MIT (with Alex Rich) he joined the faculty atNorthwestern University in 1967, where he holds a joint appointment inthe Department of Chemistry and in the BMBCB department. In additionto his interest in electron transfer, his group employs electron−nucleardouble resonance spectroscopy (ENDOR) to study metalloenzyme active-site structure and function and prepares new multimetallic porphyrazinemacrocycles. He and his wife Janet boast of four daughters, Tara, Abby,Alexandra, and Julia.

3MP + Fe3+P f MP+ + Fe2+P (1)

MP+ + Fe2+P f MP + Fe3+P (2)

Electron Transfer within Protein−Protein Complexes Chemical Reviews, 1996, Vol. 96, No. 7 2461

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The approach of covalently attaching a photoactiveinorganic redox complex to a specific surface aminoacid residue of a redox-active protein, which revolu-tionized the study of intraprotein ET,5,11-13 has beenextended recently to the study of interprotein ETbetween redox centers in noncovalent protein-protein complexes.33,34 In this procedure, a laserflash causes a metal complex (Ru2+) bound to theoutside of a redox protein (e.g., Cc) to exchange anelectron with the redox center located inside theprotein (eq 3a). Addition of a sacrificial donor (D )aniline or EDTA) reduces the surface-bound Ru3+

complex (eq 3b), so that the net effect of photoexci-tation is rapid generation of the reduced state of theredox protein. Photoexcitation in the presence of thepartner protein (M+) leads to interprotein ET (eq 3c).

This approach has the advantage, not yet realizedin experiment, that it can be used to study anyprotein pair, including those in which neither partnercontains a heme. However, the presence of the Rucomplex can strongly perturb the delicate balance ofinteractions that govern complex formation; therequired attachment of a large and often highlycharged group must have a profound effect on thestrength and even the mode of protein-proteinbinding. In short, the heme replacement and “redox-attachment” techniques are substantially comple-mentary to each other.

III. Multisite and Multidomain Binding:Microscopic vs Thermodynamic ConstantsWhen two proteins act as ET partners, the first

level of inquiry is to establish the stoichiometry ofthe reaction and to identify the domain or domains

where binding occurs. The second, experimentallycorrelated question is whether binding at a particulardomain involves multiple conformations and whetherinterconversion among domains and/or sites withinthem influences or even gates the ET process. Herewe define binding “domains” as nonoverlapping sur-face regions that can bind substrates simultaneously;a domain may exhibit one or more overlapping “sites”that cannot be occupied simultaneously. The kineticsof complex formation and dissociation, as well asthose of conformational interconversion, can controlthe experimental observations and are phenomenaof primary interest in their own right. However, theyalso must be understood before the ET event itselfcan be characterized. As we now discuss, in generalone does not measure the microscopic affinity orreactivity constants for an individual domain or site,but rather so-called thermodynamic or stoichiometricconstants that are fewer in number than the micro-scopic constants. Such distinctions and their conse-quences are well-known in studies of ligand bindingto proteins and receptors35-37 but have not beenappreciated in the study of protein-protein ETcomplexes.

A. 1:1 StoichiometryThe simplest case of 1:1 binding of one protein (the

“substrate”, S) by a second protein (“enzyme”, E) isdescribed by eq 4:

Taking the “enzyme” as the probe (denoted by a“dagger”), the fraction (f) of binding sites on E† thatare occupied with an S molecule is obtained bysolving the thermodynamic equation for binding (eq4). It is common practice to determine the bindingequilibrium constant (K1) and intraprotein ET rateconstant (k1) through kinetic measurements of the

Figure II.1. Superposition of the MgHb (thin lines) and deoxyHb (thick lines) structures in the regions of the R1 and â2heme pockets.

E + S h ES (4)

K1 )[ES][E][S]

(*Ru2+-Fe3+) f (Ru3+-Fe2+) (3a)

(Ru3+-Fe2+) + D f (Ru2+-Fe2+) (3b)

(Ru2+-Fe2+) + M+ f (Ru2+-Fe3+) + M (3c)


+ +

intracomplex ET rate constant during the course ofa titration of one component by the other.38,39 In theclassical Stern-Volmer40 procedure this determina-tion would involve a quenching titration of a photo-active “probe” by its partner as the quencher. How-ever, to analyze the results it is necessary to considerthe dynamics for the equilibrium exchange betweenbound and free species. The decay traces in aquenching titration are determined by both theintracomplex quenching rate constant (k1) and therate constants for the formation and dissociation ofthe complex (kon and koff where K1 ) kon/koff). In therapid-exchange limit where koff . k1, the experimen-tal decay traces are exponential. The measuredquenching rate constant (∆k) at any point in atitration, given by eq 5, increases monotonically with

the weighted average population of the bound state(f ) [E†S]/[E†]0, where [E†]0 is the total concentrationof E). In the slow-exchange limit where koff , k1, thedecay traces are biexponential with rate constantsthat correspond to the lifetimes of the free and boundstates. In this case, the observed rate constants areinvariant with concentration, and instead, the frac-tional weight of the faster of the two kinetic phasesequals f. With intermediate exchange rate constants,detailed analysis of the process curves is required todetermine the affinity constant and the microscopicreactivity constant. Thus, a measurement of thebinding equilibrium necessarily yields informationabout the interconversion dynamics for binding.At the next level of complexity, one protein (E) may

bind another (S) with a 1:1 stoichiometry, but thebinding domain on the surface of E may havemultiple, overlapping (exclusive) binding sites. Analternate way to describe this is that there aremultiple binding conformations of ES. If there aren sites and thus n conformers of the 1:1 complex(1ES, 2ES, ..., nES), each configuration can be assignedits own binding constant (K10, K20,, ... Kn0) and its ownreactivity constant (1k1, 2k1, ... nk1). In such a case,the kinetics of the observed ET process can be alteredor even controlled (“gated”) by conformational inter-conversion, rather than by the ET event.15,41To explore the consequences of coupling ET to

conformational dynamics, we considered the simplestmodel for any gated reaction, a donor-acceptor pair,[E†,S], where E† is the photodonor and each of thethree system states involved in the photoinitiated ETcycle described in eqs 1 and 2 (ES, E†S, and I) exhibitstwo conformational substates (ES ) 1ES + 2ES, E†S) 1E†S + 2E† S, and I ) 1I + 2I).15 Within the presentcontext, such a reactive pair could also represent acomplex in the slow-exchange limit. The introductionof conformational interconversion expands the simplebound-state ET mechanism of eqs 1 and 2 to SchemeIII.1. This scheme includes ET rate constants onlyfor the E†S f I ET processes in which the systemconformation is conserved so that conformational andET steps only occur sequentially. Intuitively, itmight be expected that the kinetic scheme mustinclude ET that is synchronous with a conformationalchange in the medium coordinate. However, we

showed that, for all practical purposes, it is notnecessary to include the “diagonal” processes (e.g.,1E†S f 2I) when considering stable substates, onlythe “square scheme” shown.The complete solutions for the concentrations of

E†S(t) and I(t) for Scheme III.1 have been pre-sented,15,41 and in general one expects to observecomplex, multiexponential behavior. However, intwo limiting cases the functional forms for both E†S-(t) and I(t) will reduce to those predicted by thesimple cycle of eqs 1 and 2 for a complex with only asingle conformation. Thus, the direct kinetic obser-vations give no evidence of the existence of multipleconformations. However, the measured rate con-stants are not those for an ET event. In one extreme,the “gating” limit, the intrinsic ET rate constants aremuch faster than the conformational interconver-sions, which thus become rate limiting. Becausestandard detection methods monitor only the ETevent and do not reflect the identity of the conformerinvolved, in many, if not most, instances the mea-surements of the time course of an ET reaction arethemselves unlikely to distinguish whether or not thereaction is gated. Fortunately, the partial decouplingof the ET and conformational processes afforded bythe absence of synchronous events, in principle andin practice, allows for the identification of an observeddecay rate constant with a microscopic rate constant.Of critical importance to this discussion is a second

limiting case where the conformational substatesinterconvert rapidly compared with the ET rateconstants. Again, the kinetics are indistinguishablefrom those for a single conformation. In particular,when there are two rapidly interconverting confor-mations (two binding sites within a domain), themeasurements can be described with a single sto-ichiometric affinity constant (KA) which is related tothe microscopic site affinity constants through eq 6.

When exchange between the bound complexes andtheir free components is rapid, the observed quench-ing rate constant at any point in a titration (∆k) is aweighted average of the two site rate constants,where the weighting is given by the fractionalpopulations of photodonor incorporated in the indi-vidual conformers according to eq 7.

This can be rewritten in terms of a single stoichio-

Scheme III.1

KA ) K10 + K20 (6)

∆k ) 1k1[1E†S]

[E†]0+ 2k1

[2E†S]

[E†]0(7)

∆k ) k1[E†S]

[E†]0≡ k1f (5)


+ +

metric rate constant (kA) and the fractional popula-tion of E†S, f (defined in eq 5).

The stoichiometric rate constant (kA) is a weightedaverage of the individual site rate constants (1k1 and2k1), where the weighting factor, ig1, is the fractionof 1:1 complex where S is bound at site i. Extensionof this idea to the case where there are n exclusivebinding sites within a single domain shows that thestoichiometric binding constant is the sum of theindividual site binding constants and the stoichio-metric rate constant is a weighted sum of all theindividual site rate constants (eq 9).

Note that eq 8 is identical in form to eq 5 for simple1:1 binding. Thus, whereas 2nmicroscopic constantsare required to describe the n-site case (ik1, Ki0 foreach), measurements, such as quenching, that are notsite-specific give only the two stoichiometric param-eters (KA and kA), both of which represent configu-ration averages.

B. 2:1 StoichiometryTo illustrate the extension of these ideas to sto-

ichiometries greater than 1:1, consider an enzyme(E†) that simultaneously binds two molecules of asubstrate (S) at distinct and nonexclusive domains.When the two domains exhibit nonidentical affinities,there are two 1:1 complexes, one having the high-affinity domain occupied (1ES) and the other havingthe low-affinity domain occupied (2ES), giving fourpossible states for the ES2 system (Scheme III.2). Asillustrated, there are two alternative pathways forproceeding from free donor (E†) to the fully saturatedES2 complex, and these differ in the order in whichthe two independent domains become occupied. Ifthe affinity, but not the reactivity, of a given domainchanges when other domains are occupied, there aresix domain constants (1k, 2k, K10, K20, K12, and K21).In the most general case where the domain rate

constants depend on the occupancy of the otherdomains, there would be eight domain parameters.However, when binding studies do not probe the

properties of the individual domains, only the sto-ichiometric binding constants (K1 and K2) associatedwith eq 10 can be measured.

Moreover, under the common condition of rapidexchange only the stoichiometric rate constants (k1and k2) can be measured for the 1:1 and 2:1 species,respectively. We discuss binding constants first. Therelationships between the stoichiometric bindingconstants and the domain binding constants inScheme III.2 are given by eqs 11 and 12.

Here Ki0 (i ) 1,2) are the domain binding constantsfor binding S at domain i of E; K12 and K21 are thedomain binding constants for binding a second mol-ecule of S to the vacant domain of ES, where thesubscripts indicate the order in which the twodomains become occupied.Turning to rate constants, when the rapid-ex-

change limit holds for a system with 2:1 binding, theobserved quenching (∆k) depends on the fraction ofthe total concentration E†

0 that is incorporated intoE†S and E†S2 (f1 and f2) and the rate constantsassociated with the two stoichiometric binding stages(k1 and k2) (eq 13).

If one assumes that the reactivity of a given domainis independent of the occupancy of all other domains(thereby ignoring the possibility of “reactivity coop-erativity”), the stoichiometric rate constants (k1 andk2) of eq 13 are functions of the rate constants thatdescribe ET at an individual domain (1k and 2k; seeScheme III.2) as given by eqs 14 and 15

where the weighting factor ig1 is the fraction of E†

that is incorporated in a 1:1 complex in which S isbound to domain i, as in eq 8. Thus, binding at twodomains in the rapid-exchange limit is described byfour stoichiometric constants (K1, K2; k1, k2) but bysix domain constants (Scheme III.2). The thermo-dynamic relationships between domain binding con-stants expressed in eqs 11, 12, 14, and 15 supply an

Scheme III.2

∆k ) (1k1K10

KA+ 2k1

K20

KA)[E†S]

[E†]0(8)

≡ (1k11g1 + 2k1

2g1)f ≡ kAf

KA ) ∑i

Ki0 (9)

kA ) ∑iik1Ki0

KA

) ∑iik1

ig1

E + S {\}K1

E + S (10)

ES + S {\}K2

ES2

K1 ) K10 + K20 (11)

K1K2 ) K10K12 ) K20K21 (12)

∆k ) k1[E†S]

[E†]0+ k2

[E†S2]

[E†]0) k1f1 + k2f2 (13)

k1 ) 1kK10

K1+ 2k

K20

K1

) 1k1g1 + 2k2g1 (14)

k2 ) 1k + 2k (15)


+ +

additional constraint, so there are five independentdomain constants.A unique solution for all five independent domain

constants obviously cannot be obtained from the fourmeasured stoichiometric constants. If one treats onedomain constant as a parameter, then the combina-tions of domain constants that are compatible witha given set of stoichiometric constants can be calcu-lated using eqs 11, 12, 14, and 15. The upper panelof Figure III.1 illustrates the combinations of domainaffinity constants that are allowed for stoichiometricconstants of K1 ) 107 M-1 and K2 ) 104 M-1; theindependent parameter is chosen to be K21/K10, whichis a measure of the interactions between moleculesbound at the two domains. Thus, if K21/K10 > 1, it iseasier to bind a molecule of S at one domain whenthe other domain is already occupied (attractiveinteraction); if K21/K10 < 1, then molecules bound atthe two domains repel each other. For noninteract-ing molecules, K21/K10 ) 1.The middle panel of Figure III.1 presents the

derived distribution functions, 1g1 and 2g1, given byeq 14 as a function of K21/K10. When the domainsare noninteracting, binding at the high-affinity do-main dominates so that [1ES] > [2ES]. As K21/K10 isdecreased (which corresponds to increasing repulsionbetween molecules bound at the two domains), theweighting factor for 2ES increases while that for 1ESdecreases. Thus, for fixed domain constants, one seesthat repulsive interdomain interactions tend to equal-ize the populations of 1ES and 2ES. On the otherhand, attraction between molecules bound at the twodomains (K21 > K10 in Figure III.1) accentuates thedominance of the high-affinity domain, so that therelative populations of 1ES and 2ES approaches the

ratio of the stoichiometric affinity constants ([1ES]/[2ES] ) K1/K2).The lower panel of Figure III.1 presents the values

of the relative site reactivity constants (1k/k1 and 2k/k2) as a function of K21/K10, derived for severalassumed relative stoichiometric reactivities. For agiven set of stoichiometric parameters, 1k/k1 de-creases toward a lower bound of zero and 2k/k2increases, as repulsion between the two domainsbecomes more significant. As the difference betweenthe reactivity constants (k2/k1) becomes large, thevalue of K21/K10, for which 1k f 0, increases, indicat-ing that the degree to which repulsions can besignificant diminishes.The relationships between domain affinity con-

stants and stoichiometric affinity constants sum-marized in eqs 11, 12, 14, and 15 are useful wheninterpreting changes in the apparent stoichiometryand/or affinity that are induced either by a perturba-tion in the solution conditions or by an alteration ofthe complex itself through site-directed mutagenesisand/or chemical modification (see section VI). Whenbinding at one domain is weakened, eqs 11 and 12require that the change in one domain bindingconstant necessarily is accompanied by a change inthe other. For example, a mutation that weakensbinding at one domain will necessarily reduce bothK1 and K2. Because the formation of a ternarycomplex requires two consecutive stepssone withweakened binding followed by a second step involvingeven weaker bindingsthe amount of 2:1 complexcould become quite small.Likewise, such relationships between the stoichio-

metric constants and the domain constants providethe means for analyzing the dependence of ET rateconstants on state variables (temperature, pressure,ionic strength, etc.) in terms of changes in thedistribution among multiple forms of a complex. Ifthe domain binding constants change differentiallywith a state variable, the relative populations of themultiple conformers could shift, so that, according toeq 14, a measured stoichiometric rate constant couldchange even without changes in the domain rateconstants.

IV. Quenching as a “4-D” Experiment

In the “normal” (N) excited-state titration protocolthat originated with Stern and Volmer40 almostthree-quarters of a century ago, aliquots of thequencher molecule are added into a solution contain-ing a fixed concentration of the luminescent probemolecule, and the resulting plot of quenching (∆k)versus titrant is fit to a mechanism. (For conven-ience, we discuss rapid-exchange situations in thissection; slow exchange can be treated similarly.)Thinking of the quenching experiment in terms ofsuch curves hides the fact that the measured quench-ing rate constant is, in fact, a function of both theprobe and the quencher concentrations, and thevalues of this function can be represented by a two-dimensional surface. The goal of characterizing thebinding between E and S and the reactivity of thecomplex (or complexes) they form thus can be trans-lated into a goal of determining the shape of the 2-D∆k surface.

Figure III.1. Combinations of the domain affinity con-stants (upper), derived distribution functions (middle), anddomain rate constants (lower) that are compatible with thestoichiometric constants K1 ) 107 M-1 and K2 ) 104 M-1,as a function of the relative attractive (or repulsive)interaction between the two domains. Lower panel: De-rived site rate constants (1k and 2k) for k2/k1 ) 5 (-), 20(- -), and 200 (‚‚‚) with k1 ) 100 s-1.


+ +

This perspective opens avenues of approach thatgreatly enrich the productivity of quenching experi-ments. For example, the simplest case of 1:1 bindingis symmetric in that it makes no difference whichpartner contains the luminescent probe. (In thisreview E (or S) becomes the probe primarily throughheme replacement, although other types of experi-ments are possible.) However, if it is known orsuspected that higher stoichiometries may be in-volved, say if E binds two S molecules, then theresults are not symmetric. We denote as a conven-tional (C) experiment one in which E is the probemolecule; we denote the experiment where the probeis S as an inverse (I) experiment. In either case, aN titration, in which the quencher is the titrant,generates a slice through the ∆k surface that isparallel to the quencher axis (see Figures IV.2, IV.5,and IV.8). As we show below, and perhaps surpris-ingly, it is advantageous to use a new type ofexperiment, a “reverse” (R) titration, in which titrat-ing the probe into a solution containing a fixedconcentration of the quencher generates a slicethrough the ∆k surface that is parallel to the probeaxis. With each of the two options for metal substi-tution, C and I, titrations can be performed in thenormal way (N) or the reverse way (R). Thus, theresults of a traditional Stern-Volmer quenchingexperiment of the past are, in fact, best thought ofas one subset of a 4-D dataset generated from fourdistinct types of titrations: CN, CR, IN, and IR (TableIV.1).

A. Conventional Titrations (C N and CR) with 1:1StoichiometryConsider a representative ∆k surface for moder-

ately strong 1:1 binding of S to E (K1 ) 105 M-1), asindicated in Figure IV.1, where we have arbitrarilychosen S as the quencher and E† as the probe. TheN titration, in which quencher (S) is progressivelyadded to a solution containing the probe (E†) at fixed

concentration (Figure IV.2) corresponds to a slicethrough the ∆k surface that is parallel to the quench-er axis and has an intercept of ∆k0 ) 0 when [S]approaches zero. The binding and kinetic param-eters that describe quenching for 1:1 stoichiometry(K1 and k1) are derived from the hyperbolic shape ofthe ∆k titration curve. As binding gets weaker,however, it becomes increasingly more difficult toaccurately determine the curvature of the quenchingcurve, and finally one reaches a limit where only astraight line, the slope of which gives the productM) K1k1, is observable (Figure IV.3, upper).By representing ∆k as a surface, it is obvious that

there is an alternate “reverse” titration experiment(R) in which titration with the probe generates a slice

Table IV.1. Titration Protocols for ES2 Complexes

conventionalsubstitution

inversesubstitution

titration E† S E S†

CN titrantCR titrantIN titrantIR titrant

Figure IV.1. Surface plot describing quenching (∆k)within an E†S complex as a function of the concentrationsof substrate (S) and enzyme (E†). Simulation parameters:K ) 105 M-1 and k ) 100 s-1.

Figure IV.2. Slices through the 1:1 binding surface ofFigure IV.1 showing a normal (N) Stern-Volmer titration(upper panel) and a reverse (R) Stern-Volmer quenchingexperiment (lower panel).

Figure IV.3. Plot of ∆k/k1 for titrations simulated for arange of K1: Upper panel, N-titration, [E]0 ) 25 µM; Lowerpanel, R-titration, [S]0 ) 25 µM. Simulation parameters:(s) K ) 106 M-1, (- - -) K ) 105 M-1, (-‚-) K ) 104 M-1,(‚‚‚) K ) 103 M-1.


+ +

through the ∆k surface that is parallel to the probeaxis. At first thought this may appear useless,because there is nothing to measure in the earlyphases of such a titration! However, modern instru-mentation is so sensitive that it is trivial to performmeasurements with extremely low concentrations ofthe probe, and we find that the intercept as [E†] f 0(∆k0) can be measured quite reliably. Once this isrecognized, a look at the ∆k surface shows that thenormal and reverse experiments are not symmetry-equivalent, even for the assumed 1:1 stoichiometry.The reason for this lies in the recognition that reversetitrations necessarily give well-defined, nonzero val-ues for ∆k0, whereas the intercept in a normalquenching experiment is zero. For a 1:1 bindingmodel, ∆k0 for a reverse titration is given by eq 16:

A key advantage to a reverse titration is that thisexpression provides a further constraint on therelationship between the desired fitting parameters.The intercept can be used to eliminate either K1 ork1, thereby reducing the number of independentfitting parameters and greatly enhancing the reli-ability of an analysis of experimental data.Just as the characteristics of a traditional titration

change progressively from linear in the limit of weakbinding to hyperbolic in the limit of strong binding,the shape of a reverse titration varies characteristi-cally as K1 decreases. Figure IV.3 (lower) shows aset of simulated reverse titrations for 1:1 stoichiom-etry with 103 M-1 < K1 < 106 M-1. For strongbinding, ∆k remains roughly constant during areverse titration until a concentration ratio of ∼1:1,and then it decreases rapidly with subsequent addi-tions of the probe. If K1 has an intermediate value,then ∆k decreases smoothly and monotonically dur-ing a reverse titration. For the initial stages of thetitration, the decrease in ∆k is linear with increasingS, and by combining the measured values for theinitial slope and for ∆k0, one can obtain extremelywell-defined values for both K1 and k1. Finally forvery weak binding, ∆k is nearly invariant, even upto rather high concentrations of the probe, and theinitial slope can no longer be reliably measured. Inthis case, the product K1k1 can be determined fromthe intercept, but the individual parameters (K1 andk1) cannot be independently determined with eithera normal titration or a reverse titration. Thus, thesame limitations ultimately apply to both the tradi-tional CN titration experiment and the new CRtitration. However, in practice, it appears that onecan more often and more reliably determine theindividual parameters K1 and k1 with the R protocol.Even better than relying on but one type of experi-

ment is to combine them. The simultaneous analysisof data from a normal titration and a reverse titrationprovides an alternative method for independentlydetermining K1 and k1. The initial slope obtainedfrom a normal titration (M ) K1k1) and the interceptobtained from a reverse titration (∆k0), where theconcentration of S is fixed as [S]0 can be combined tocalculate K1

and this parameter then can be used with M tocalculate k1.

B. Conventional (C) Titrations with 2:1StoichiometryThe introduction of a broadened perspective is most

beneficial when stoichiometries other than 1:1 areknown or suspected to occur. In the present sectionwe focus on the case where E can bind up to twomolecules of S. Figure IV.4 shows the surfaces thatdescribe the fractions of probe E† that are incorpo-rated into the 1:1 and 2:1 complexes as a function ofthe two independent variables ([E†] and [S]) for aconventional titration where the stoichiometric bind-ing constants are K1 ) 107 M-1 and K2 ) 104 M-1.Clearly the shapes of the 1:1 and 2:1 surfaces differgreatly, and the proper choice of titration protocol cantake advantage of this.

CN TitrationWhen kinetic measurements are used to probe

binding affinity and stoichiometry, the observedquenching constant is a weighted average of thestoichiometric quenching constants for the 1:1 and

∆k0 )k1K1[S]01 + K1[S]0

(16)

K1 ) M∆k0

- 1[S]0

(17)

Figure IV.4. Surfaces for the conventional (C) substitu-tion mode describing the fractions of E† that are incorpo-rated into the E†S (1:1) and E†S2 (2:1) complexes as afunction of the concentrations of substrate (S) and enzyme(E†). Simulation parameters: K1 ) 107 M-1, K2 ) 104 M-1.


+ +

2:1 complexes, with the weighting corresponding tothe fractional populations of these species (eqs 14 and15). For the conventional (C) metal substitutionmode, titration curves generated by the CN protocol,where E† is the luminescent probe and the quencher(S) is the titrant, sequentially reflect the two stagesof binding; the 1:1 complex predominates in theinitial stage of the titration, and subsequent addi-tions of quencher ultimately convert the 1:1 complexto the 2:1 complex (Figure IV.5, left panel). Regard-less of the domain reactivities, the stoichiometric rateconstant for the second stage of binding (k2) isnecessarily larger than that for the first stage ofbinding (eqs 14 and 15). Thus, ∆k monotonicallyincreases with progressive addition of quencher (E†)regardless of the binding stoichiometry.Any attempt to differentiate between 1:1 binding

and 2:1 binding is only favorable when both thestoichiometric affinity constants and the stoichio-metric reactivities differ appreciably for the twobinding stages. If the two stages of binding are notwell-separated either because the affinities for thetwo stages are similar or because their reactivitiesare too similar, then the experiment is unreliable forestablishing the binding stoichiometry and certainlyprovides no reliable determination of the parametersfor the second binding step. If one domain is muchmore reactive and dominates the observed quenching,(i.e., if either 1k or 2k is much larger than the other),then the two binding steps can be clearly resolvedand the ∆k surface will track that of the dominantspecies.When binding is monitored by measuring proton

uptake (or release) or by binding-induced changes inchemical shift for an NMR experiment, the propertiesof the two domains may differ in both magnitude andsign (section VI.E). In such studies, there are

“reactivity” parameters analogous to k1 and k2 thatdescribe the properties of the individual bindingsteps, and when both the magnitudes and signs differfor the two stages of binding, the titration curves canhave unusual shapes that unambiguously signal thepresence of 2:1 binding (or higher). Figure IV.6shows a series of CN titration curves where thestoichiometric affinities are fixed (K1 ) 107 M-1 andK2 ) 104 M-1) but the relative stoichiometric reac-tivities are varied in both magnitude and sign. Inthe case where k2/k1 > 10, the titration curve showstwo phases and the observed reactivity increasesmonotonically. When the stoichiometric reactivitiesfor the two binding stages also differ in sign, themeasured reactivity (∆k) no longer increases mono-tonically but instead exhibits a maximum at R ≈[S]/[E] ) 1. Even though it is not possible todifferentiate two binding steps when the stoichio-metric reactivities have equal magnitude and sign,they can be resolved readily when the two stages ofbinding exhibit identical reactivities of opposite sign.

CR Titration

When E† is the probe, the two binding steps maywell be more readily resolved with a reverse titration(CR), in which E† is titrated into a solution containinga fixed concentration of S. The right panel of FigureIV.5 shows a slice through the 2-D surfaces for thefractional populations of the 1:1 and 2:1 complexesduring such a CR titration. As [E† ] increases, thepopulation of the 2:1 complex decreases monotoni-cally, while the population of the 1:1 complex in-creases slightly until R ) [E†]/[S] ) 1, then decreasessharply. In general, one can differentiate between1:1 binding and 2:1 binding by the shape of a CR

curve. Thus, for 2:1 binding when k2 is sufficientlymuch greater than k1 (recall from above that neces-sarily k2 > k1), ∆k exhibits a sharp decrease wellbefore [E†] ) [S], but as discussed above, for tight1:1 binding ∆k decreases gradually only after [E†] >[S]. Inspection of Figure IV.5 shows that the de-crease in ∆k beyond R ∼ 1/2 for the 2:1 case occursbecause further additions of E† convert the morereactive ternary complex to the less reactive binarycomplex.For 2:1 binding, as for 1:1 binding, the quenching

constant in a CR titration has a nonzero intercept as[E†] f 0, with ∆k0 for the 2:1 case given by eq 18

Figure IV.5. Slices through the two-dimensional surfacesof Figure IV.4 describing the fractions of E† that areincorporated into the 1:1 and 2:1 complexes for the con-ventional (C) substitution protocol: left panel, CN titration;right panel, CR titration.

Figure IV.6. Effect of the relative magnitude and sign ofthe reactivity parameters (k1, k2) on the CN titration curves(eq 13). Simulation parameters: [E†] ) 25 µM; K1 ) 107M-1, K2 ) 104 M-1, k1 ) 10 s-1; (s) k2 ) 100 s-1, (- - -)k2 ) 10 s-1, (-‚-) k2 ) -10 s-1, (‚‚‚) k2 ) -100 s-1.


+ +

where [S]0 again is the initial concentration of thequencher. The first term is the contribution to ∆k0arising from the 1:1 complex and the second termgives the contribution due to the ternary complex.Again, the extrapolated value for ∆k0 can be used toreplace one of the four stoichiometric fitting param-eters. When K1 is large, ∆k0 is least sensitive to thisparameter, so one would normally eliminate K1. Ifthe values of K1 and k1 can be obtained from a CNexperiment, then one could also fix these parametersand instead eliminate one of the two parameterscharacterizing the second binding step.

C. Inverse Titrations (I N and IR)When complex formation involves a ternary ES2

complex, the experiments are no longer symmetricwith respect to metal substitution; quenching mea-surements for C substitution, where the luminophoreis in E, and for I substitution, where the luminophoreis in S, yield complementary, not identical, results.The characteristics of the two types of titrations, Nand R, for the I substitution mode (S† as probe) areillustrated in 2-D surfaces plots describing the frac-tions of S† that are incorporated in the 1:1 and 2:1complexes (Figure IV.7) for a system that employsthe same stoichiometric binding constants used inFigure IV.4. These surfaces have complex shapes.

In particular, the surface for the 2:1 complex isstriking in that it shows local maxima in regionsaway from the axes. As a result, experiments with Isubstitution permit for a better determination ofbinding and kinetic parameters.

IN Titration

Consider first a slice parallel to the E-axis, gener-ated by an IN titration of S† by the quencher, E(Figure IV.8, left panel). During such an IN titration,the population of 1:1 complex increases monotoni-cally, while the population of ES2 increases from zeroat [E] ) 0 to a maximum at R ) [E]/[S†] ) 1/2, thendecreases toward zero as [E] increases. As discussedabove, if the stoichiometry of binding is 1:1, then ∆knecessarily increases monotonically with addition ofE. However, for 2:1 binding this need not be so. Ina system where quenching is dominated by thereactivity of the 2:1 complex, ∆k would be essentiallyproportional to f2 ) [ES†2]/[S†]0 and the IN quenchingcurve would show a maximum near R ) [S†]/[E] ) 2.The observation of such nonmonotonic changes in ∆kwould require a stoichiometry of 2:1 (or greater) (seesection VI).

IR Titration

Now consider a slice parallel to the S†-axis gener-ated by an IR titration (E titrated by S†); the fractionalpopulations of the 1:1 and 2:1 complexes are shownin Figure IV.8, right panel. Once again there willbe a nonzero intercept (∆k0), with the applicableexpression being that of eq 16, but with [S]0 replacedby [E]0. The concentration of the ternary complex islow in the limit where [S†] f 0, and consequently,the initial phase of the titration curve tracks thereactivity of the 1:1 complex; subsequent additionsof S convert the 1:1 complex to the 2:1 complex, but

∆k0 )k1K1[S]0 + k2K2[S]0

2

1 + K1[S]0 + K1K2[S]02

(18)

Figure IV.7. Surfaces for the inverse (I) substitution modedescribing the fractions of S† that are incorporated into theES (1:1) and ES2 (2:1) complexes as a function of theconcentrations of substrate (S†) and enzyme (E). Simulationparameters: Same as for Figure IV.4.

Figure IV.8. Slices through the two-dimensional surfacesof Figure IV.7 describing the fractions of S† that areincorporated into the 1:1 and 2:1 complexes for the inversesubstitution protocol: left panel, IN titration; right panel,IR titration.


+ +

the fractions of 1:1 and 2:1 complex are roughlyconstant as the concentration of S† increases toward[S†] ∼ [E]. Additions of S† beyond the R ) 1 pointwould necessarily cause ∆k to decrease if there istight 1:1 binding. However, when the stoichiometryis 2:1, ∆k can increase during the titration, if theternary complex exhibits appreciable quenching (k2is large), and the result would be a maximum in ∆kduring a titration. The observation of such behavioralso would require 2:1 stoichiometry (or greater).In summary, one can use either E (conventional

substitution) or S (inverse substitution) as the probe,and whenever possible one should use both. Eachexperiment is best understood in terms of its own 2-Dsurface plot, and each experiment can be performedin either the normal (N) way, where aliquots of thequencher are added into a solution containing a fixedconcentration of the probe, or the reverse (R) way,where aliquots of the probe are titrated into asolution in which the concentration of the quencheris fixed. Although we have emphasized how thesenew titration experiments can be applied to analyzethe kinetic data from a series of flash photolysisexperiments, these new titration experiments could,and indeed should, be used when designing andanalyzing titration experiments in which other prop-erties are monitored. As is shown in section VI forthe complex between CcP and Cc, the characteristicshapes of the inverse and reverse titration curvesprovide a far clearer distinction between 1:1 and 2:1stoichiometry than a traditional titration, but it isthrough combinations of these experiments that adefinitive determination of stoichiometry and reactiv-ity can best be achieved.

V. Unimolecular and Bimolecular ElectronTransfer in BiomoleculesIn a single fixed donor (D)-acceptor (A) geometry,

the ET reaction rate is well defined. In long rangeET systems, the donor and acceptor are weaklycoupled (electronically) by the intervening protein,and the rate is nonadiabatic and is proportional tothe square of the protein-mediated donor-acceptorcoupling multiplied by a nuclear Franck-Condonfactor (FC) (eq 19).9,42

FC reflects the thermal density of states for resonantdonor and acceptor levels. In the equilibrium mo-lecular geometry, these donor and acceptor electroniclevels are not necessarily of equal energy, so theprocess can be activated. By discussing the Franck-Condon factor in terms of density of states, the ratecan be thought of in the context of Fermi’s goldenrule with thermal averaging over the initial statedistribution.42 The tunneling matrix element, TDA,reflects the bridge-mediated coupling between donorand acceptor states at the resonant configuration(s).The tunneling matrix element is controlled not onlyby the chemistry and energetics of donor and acceptorbut also by the protein bridge that links them andcouples them electronically. The unimolecular rateis influenced by both the electronic and nuclearfactors, which are exponential in nature (in either

separation distance or energy). As such, a wide rangeof ET reaction rates can occur from the second topicosecond regime. The main goal of this section isto describe the strategy for computing the electronic(TDA) interaction between protein ET pairs that havedocked in a given geometry. We also describe somequalitative features of the intermolecular dockingenergetics.

A. The Tunneling Pathway Model of ProteinMediated Electron TransferWe now consider how one might approximate the

ET rate constant for a given, fixed donor-acceptorgeometry. To begin with, we will focus on theelectronic contribution to the rate. The Franck-Condon analysis is discussed in detail elsewhere.42In many of the reactions considered here, the Franck-Condon factor is held nearly fixed, and differencesbetween ET rates are likely to arise from differencesin TDA.Assuming that a “tube” of orbitals between the

donor and acceptor sites dominates the electroniccoupling, the tunneling matrix element can be writ-ten in a pathway approach as43-49

More recently, new approaches by us50-55 and byothers56-59 have improved upon this simple strategy.These more advanced methods have validated thebasic assumptions of the pathway model, which arebased simply upon the qualitative difference betweenthrough-bond and through-space wave function propa-gation, represented in the parameters of eq 20.43-49

A description of this model and its extensive applica-tion in protein ET appear in refs 9, 43-49, and 61-65.Physically, the decay through a “single” pathway

should be understood to mean that coupling througha “tube” of bonds dominates the tunneling matrixelement.43-54 That is, many orbitals in the mediumintervening between donor and acceptor contribute(in a rather complex manner) to the D-A coupling,but the overall value can be approximated using eq20. Scattering of the propagating wave functionamplitude through orbitals in the core of this tube,as well as by orbitals appended to this core pathway,are all incorporated by the choice of the decayparameters. This kind of interference, however, iscalled trivial interference. For example, the couplingprovided by a protein backbone is a much strongerfunction of backbone length than it is of the types ofresidues encountered along the backbone. The amidehydrogens, lone-pairs, carbonyls, even the side-chainresidues themselves provide alternative pathwaysthat interfere in a way that can easily be included ina much simpler set of effective states with theconnectivity of a string of pearls.43-54 Even thoughrenormalized (effective) parameters are used, thefinal coupling still can be described by a decayingproduct through this core pathway. All of the scat-tering effects within the tube can be included througheffective parameters for the core orbitals; i.e., whenone gives a decay per bond value (and the relatedpicture), all of these effects are included. This

kET ) 2πpTDA

2FC (19)

TDA ) A∏iεibond∏

jεjH-bond∏

kεkspace (20)


+ +

renormalization procedure to obtain effective param-eters has been formally developed by us in severalrecent papers.50-54 A pathway tube is the set oforbitals defined by a single core physical pathway(the set of interacting covalent bonds between D andA that defines the single strongest coupling pathway),adding to this set all nearest neighbor interactingorbitals, and finally adding the neighbors of theseneighbors. This procedure captures all relevantorbitals that are off the core physical pathway, andthis subset of the bridge is called a pathway tube.The single pathway description will break down if

multiple tubes are important in the mediation of theelectronic coupling. In such a case, interferencebetween tubes is a concern when predicting thedonor-acceptor coupling. It is important, however,to distinguish interferences between tubes from trivialinterferences or scattering within a single tube(described above). While the latter is important forthe determination of the effective decay parameters,it does not modify the qualitative pathway concept.Another possible limit is that coupling is dominatedby so many tubes that their interferences are impor-tant. In this regime, the independent tube descrip-tion would break down and the protein could bethought of as an average medium in which details ofthe protein structure need not be important. Previ-ous studies on chemically modified proteins have notyet shown such “average” behavior. New methodsfor predicting when a specific folded configurationwill cause a protein to fall into one of these limitingregimes or another are under current investigation.Recent progress has been made to analyze theimportance of specific contacts for the final couplingmatrix element and to construct improved effectivehamiltonians for electron transfer.60,61 Qualitatively,it is easy to understand that when the coupling isdominated by a single tube, a few individual contactscan be of major importance. The importance of suchspecific contacts will decrease as more and morepathway tubes contribute to the coupling. Thenumerous protein and pathway analysis tools nowavailable5,50-54,56-59,62-66 provide a means of determin-ing the pathway regime at play and the key contactsthat mediate a specific protein ET reaction.The single pathway picture has been remarkably

successful in explaining electron transfer in numer-ous unimolecular and bimolecular protein ET experi-ments.5,62-70 One of the most important examples isthe family of chemically modified proteins studied byGray and co-workers.5,11,12,71 Rates of ET were mea-sured between the native redox center inside theprotein to a surface-histidine-bound ruthenium spe-cies. Time-resolved studies (luminescence quenchingand flash-quench techniques) were used to measurethe ET rates. In specific families of experiments, thedonor and acceptor species were nearly the same, sothe relative rates reflect TDA rather directly. In aseries of free-energy studies, Gray and Winkler5,11,12further modified the Ru site to estimate the activa-tionless rates. Ratios of these activationless ratesprovide even better estimates of the relative tunnel-ing matrix element values.Experimental rates in the Ru-protein systems

show that the simple model with an exponentialdecay with donor-acceptor separation is inadequate.

In one case, where a long through space jump existsin the main pathway, the tunneling matrix elementis much smaller than one would otherwise expect forthat donor-acceptor separation. This single path-way “tube” description fully explains the collectionof rates in these modified cytochromes. More recentexperiments and calculations in modified azurinprovide examples where multiple tube effectsappear.5,62-66 Even though the tunneling matrixelement is not a simple product of decay factors here,the pathway description for individual tubes still isthe appropriate way to describe the protein media-tion. Figure V.1 presents the strongest couplingpaths from the Fe of Cc to the five surface sitesexamined by Gray and co-workers.72 In this figure,the experimental rates were measured as a functionof two distances, the conventional physical separationbetween the donor and acceptor sites and the equiva-lent covalent distance. For a given coupling betweenD and A, the equivalent covalent distance providesthe length of the chain if D an A were fully covalentlycoupled. If through space occurs in the dominantpathway, because the decay through space is muchstronger, this jump will provide a much largercontribution to the covalent distance than its ownlength. This is exactly what happens to the Ru(His72) Cc case.

Figure V.1. Strongest coupling paths between the Fe andfive different surface histidines examined in ruthenatedCc experiments of Gray and co-workers.5,11,12 Solid linesindicate covalent bonds, dashed lines show hydrogen bonds,and dotted lines show through-space contacts. The activa-tionless electron transfer rates are plotted vs distance andlength of the tunneling pathways. The tunneling pathlength, σL, is defined as the through-bond distance alongan extended covalent chain that would produce a couplingdecay equal to that arising from the specific strongesttunneling pathway in the system of interest. Note theimproved fit when the activationless rates are plotted vstunneling pathway length and the fact that the contactdistance rate is ∼1012-1013 s-1 in the pathway lengthcorrelation.


+ +

The utility of the the pathway approach, as a guideto interpretation, is not lost even when it breaksdown, and the quantitative coupling estimates of eq20 are poor approximations in the multitube regime.Figure V.2 shows pathway tubes for ET between theCu- and Ru-sites in Ru-modified azurin. Five differ-ent Ru-sites are shown in this figure. Because theelectronic coupling between the Cu and the proteinis dominated by Cys 112, ET rates to residues 107and 109 are dominated by the single tube shown inFigure V.2. The pathway model predicts the ratioof the rates between them very effectively. Thesituation changes when residues 122, 124, and 126are considered. Since the coupling pathways ofimportance go through residue 112, one can now seea collection of equivalent pathways for each of themby choosing different hydrogen bonds. Since thepathways are equivalent, tube interference is con-

structive, and the pathway approach underestimatesthe coupling. Residues further down the strand willhave more equivalent pathways and, therefore, largerconstructive interference effects. Using our Green-path approach,50-54 we have quantified these effects,but just using the pathway description we have beenable to understand the mechanism involved andpredict the results qualitatively.Using pathway calculations to determine the domi-

nant core paths, the following strategy is used todetermine the tubes. The pathway “tube” is the setof bonds one finds by first identifying a core pathway(between some D and A) which never visits the samebond twice, then one adds to this set all nearestneighbors of the core bonds and then again adds theneighbors of these extra bonds. This captures allhanging orbitals off of the core pathway, and thissubset of the bridge is called the pathway “tube”.Green’s function calculations are then performedusing the “tube” orbitals and the full protein. In allcalculations performed for Cc and azurin, this re-duced “tube” representation captures all the essentialparts of the protein that contribute to the coupling.

B. Functional DockingDetermining the equilibrium distribution of docked

protein geometries is a central challenge both in theexperimental measurements of binding and in mod-ern computational biophysical chemistry. We havedefined a complementary view for thinking about thecombined role of coupling pathways and binding inET complexes. Instead of beginning with a fixedcomplex geometry, we analyze the two proteinsindividually and estimate the electronic couplingbetween the two redox centers and the proteinsurfaces in each reaction partner. By analyzing thesurface coupling maps for each partner, we can learnhow sensitive the electronic coupling is to the dockinggeometry. If the protein surface has extensive areaswith similar coupling magnitudes, this provides anindication of weak specificity for docking. In thiscase, there is no need to compute, precisely, thedocking geometry if the goal is to compute theinterprotein electronic coupling. Alternatively, if thesurface maps present specific areas of strong cou-pling, the question arises of whether or not thesespecific sites are physiologically responsible for ETcontrol in the complex. Comparison of the bindingsites obtained from docking simulations or fromexperiments with those obtained from this approachshould lead to a mechanistic understanding of thesereactions. Phrased differently, two factors will con-trol ET in these systems. One is the probability ofbinding in a given geometry and the other is the ratein this geometry. Since the final rate depends onboth of these terms, it is not guaranteed that themost stable conformation is the one that controls theET rate. Therefore, the comparison proposed abovewill allow us to estimate the contribution of each ofthese terms.It is important to observe that the electronic

coupling for a given geometry, if dominated by asingle pathway tube, can be written as a product

Figure V.2. Pathway tubes between the blue-Cu centerand numerous ruthenation sites in modified azurin.52,65Rates to residues 107 and 109 are dominated by a singletube, while coupling between Cu and residues 122, 124,and 126 involve multiple tubes, leading to importantinterference effects not incorporated in a single pathcalculation.

TDA(biomolecular) ) A[∏

iεiprotein-I ∏

jεjprotein-II]εinter (21)


+ +

Functional docking analysis uses information aboutthe surface coupling in both proteins, but it saysnothing about the coupling between the proteins. Forany tight contact between proteins, the interproteincoupling is likely to be about the same. However,there is no guarantee that the tube through thethermodynamically most-favored binding contact willinclude the dominant tube. The most favorableconformation for ET need not be the most stable.Thus, calculations for the full complex are neededprior to reaching final conclusions; the strategydescribed above provides the basis for attaining abroad understanding of the interprotein interactionsbecause it provides the theoretical tools for analyzingdata in such systems and for guiding future experi-ments. It is important to understand that all of thecomputational tools developed to analyze electronicinteractions in single proteins can be used in thebimolecular problem, even though additional com-plications, described above, arise as well.We have studied ET between the proteins cyto-

chrome c2 (Cc2) and the photosynthetic reactioncenter (RC) using this strategy.73 The electroniccoupling decay between electron donor and acceptorcan be separated into three parts: (i) the couplingfrom the cytochrome heme to the surface of thecytochrome, (ii) the coupling from the RC surface tothe bacteriochlorophyll dimer, and (iii) the couplingfrom the surface of the cytochrome to the surface ofthe reaction center. As discussed above, calculatingthe coupling between the surface amino acids and theredox center allows the simple estimate of interpro-tein electronic coupling and, for a given dockedstructure, provides a functional criterion for evaluat-ing that structure. Central to this strategy is thedefinition of protein surface. The main assumptionis that an electron must tunnel through a surfaceresidue to leave the protein. To generate a smoothersurface that prevents atoms in border invaginationsof the protein from being considered surface residues,this surface may be defined by rolling a sphericalprobe of radius 3 Å (instead of the standard 1.4 Å)along the protein surface. To examine the effect ofdocking on electron transfer in the RC, we generatedsurface coupling maps of the electronic couplingbetween the redox sites and solvent exposed atomsin each protein before docking occurred. When weanalyzed the strongest path between the special pairand the surface residues on the RC, we found a largeregion with similar coupling to the special pair(Figure V.3).The reactive surface of the RC is large, whereas

Cc2 has a small region with much stronger couplingthan the rest of the surface. Thus, electron transferout of the Cc2 is likely to be highly specific, whereaselectron transfer into the RC is probably less specific.From this analysis of the coupling surfaces, we canlearn quite a bit about protein surface patches thatcould play important roles in interprotein ET, but onestill has to deal with the problem of the couplingbetween the two protein surfaces. The functionaldocking strategy suggests which surface regions ofthe proteins one should dock in order to optimize theET rate without addressing the question of dockingcomplex stability.

C. Classical Electrostatics and the EncounterSurfaceIn this section we describe the analysis of the

surface electrostatics of Cc and CcP. In sections VI.Gand VII this analysis is combined with the Pathwaycalculations to develop a unified theoretical view ofthis bimolecular ET reaction. In order to discoverthe most significant docking site(s) using theoreticalmethods, it is necessary to consider both locationsthat optimize the electrostatic interactions betweenthe enzyme and the substrate and associations thatlead to efficient ET pathways. We present an analy-sis of the docking sites and their relation to ET usingboth the ET Pathways approach43-49 and the encoun-ter surface approach74 for docking based upon theclassical electrostatic calculations obtained from thePoisson-Boltzmann equation.75-78

Electrostatic potentials were computed by iteratingthe finite difference solution of the linearized Pois-son-Boltzmann (PB) equation

where ε(rb) is the position dependent dielectric con-stant, æ(rb) is the electrostatic potential, κ is theDebye-Huckel screening constant, and F is theinterior charge density. The numerical methods forcomputing the potential are described by Honig andco-workers75-78 and are implemented in the programDelPhi.79,80 The PB equation enables one to accountfor the discontinuity in the dielectric constant acrossthe protein surface, the roughness of this surface, andscreening arising from ions in the medium. In thepresent calculations, a dielectric constant (ε) of 80was assigned to the water-accessible regions. Theinterior of the protein was assigned ε ) 2. Thecalculations were performed using a 20 mM concen-tration of a 1:1 electrolyte and an electrolyte exclu-sion zone of 2 Å around the protein. Amino acidatomic charge assignments are based upon theAmber force field, which accounts for the charges ofionizable amino acids.The electrostatic potential map generated using

DelPhi was then used to generate the encountersurface following the procedure given by Tiede andco-workers.74 This encounter surface was computedwith a 5 Å Connolly surface. Connolly surfacesgenerated in this manner have been of use to predictinterprotein docking sites when limited rearrange-ment of protein side chains occur upon interaction.The Connolly surface can also be used to search forregions of complementary electrostatic potentials inthe bimolecular complexes that do not depend uponspecific charge pairing or mutual rearrangement ofside chains. Such surface regions are relativelyinsensitive to the precise positions of amino acids.

VI. ET between the Physiological Partners, C cand CcPAs an illustration of the ideas presented above, we

consider ET between the physiological partners CcPand Cc. CcP is found in the periplasmic space ofyeast mitochondria and catalyzes the two-electronreduction of H2O2 by two molecules of Fe2+Cc as thespecific electron source.17,81-83

∇B‚(ε(rb) ∇B æ(rb)) - ε(rb) κ2(rb) æ(rb) + 4πF(rb) ) 0(22)


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In the first step of the CcP catalytic cycle, theferriheme resting state of CcP undergoes a two-electron oxidation by H2O2 (eq 24). The first stable

species produced in this reaction, historically denotedcompound ES, is oxidized by 2 equiv above the restingstate. In this high-valence intermediate, one oxidiz-ing equivalent is stored as a ferryl iron-oxo [FeIVdO]2+

species and the other as a radical on Trp 191.84-86

To complete the catalytic cycle, one molecule ofFe2+Cc reduces ES by 1 equiv to form CcP-II (eq 25)which, is then reduced by a second molecule of Fe2+Ccto the resting state (eq 26).The first reduction step can occur either at the

heme or the Trp radical, and thus CcP-II exists intwo electronic configurations that are 1-equiv oxi-

dized relative to the ferriheme resting state, one withan oxidized heme (CcP-IIh) and one with an oxidizedTrp (CcP-IIr).87-90 These two forms exhibit a pH-dependent equilibrium89,91 and the oxidizing equiva-lent can transfer between the two redox sites throughan intramolecular ET process that is not fully un-derstood and can be surprisingly slow.87,88,92 Becausethis catalytic cycle involves two Ccmolecules and twospatially and electronically distinct redox centers ofCcP, the key question is whether the reductions occurby sequential reactions at a single binding domainon the CcP surface or whether there might be twoET-active domains, opening the possibility that thereare even different “pathways” for heme and Trpreduction.

A. One Structure for the [C cP, Cc] Complex?CcP is an acidic protein having a net negative

charge at pH 7.0. In 198093 the crystal structure ofCcP revealed that the surface of CcP surrounding theedge of the heme that bears the heme propionatescontains a large number of negatively charged aminoacids. Cytochromes c generally are basic proteinswith net positive charges at pH 7, and it was shown

Figure V.3. Electronic coupling surfaces, computed from the pathway model, from the chlorophyll special pair to thesurface of the RC and and from the heme of cytochrome c2 to the protein surface. Electrons transferred from cytochromec2 to the special pair of RC fill the hole left following photoinduced charge separation in the RC. Note the broad strongcoupling surface on the RC and the narrower strong coupling surface on cytochrome c2. (Scale is logarithmic.)

H2O2 + 2Fe2+Cc + 2H+ f 2Fe3+Cc + 2H2O (23)

Fe3+CcP + H2O2 f ES (24)

ES + Fe2+Cc f CcP-II + Fe3+Cc (25)

CcP-II + Fe2+Cc f Fe3+CcP + Fe3+Cc (26)


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in 1971 that these two proteins can form a complexthrough forces that are predominantly electrostatic.94Margoliash and co-workers showed that modificationof specific Lys residues on the surface of Cc inhibitedits reaction with CcP, which led to the hypothesisthat docking to CcP involves the ring of positivelycharged Lys residues surrounding the exposed edgeof the heme crevice on the “front” surface of Cc.95,96To locate the binding site for Cc on the surface of CcP,Bechtold and Bosshard97 compared the reactivity ofsurface carboxyl groups in free peroxidase to theirreactivity in the presence of Cc.The possible significance of the high degree of

complementarity between the region of positivelycharged Lys of Cc and the negatively charged resi-dues of CcP led to attempts to use computer studiesto visualize the [CcP, Cc] complex. The first computer-generated structure of the 1:1 complex98 was obtainedby manipulating the X-ray structures of the twocomponent proteins to achieve optimal hydrogen-bonding distances and geometries between pairs ofnegatively charged Asp residues of CcP and thepositively charged Lys residues of Cc. The interven-ing medium is comprised of portions of the twoprotein polypeptides and includes Phe 82 of Cc andHis 181 of CcP. On the basis of this structure it wasproposed that the pathway for heme-heme ETinvolved π-π superexchange interaction between His181 of CcP and Phe 82 of Cc.The structure of a 1:1 complex studied crystallo-

graphically by Pelletier and Kraut99 shows a Ccbound at roughly the same region as proposed bymodeling, but with rather different contacts andrelative orientations of the hemes. According to thehigh-salt crystal structure of the [Fe3+CcP, Fe3+Cc-(yeast iso-1)] complex, pyrrole ring C of Cc is in closecontact with residues Ala 193 and Ala 194 of CcP.The shortest ET pathway connecting this corner ofthe heme to the heme of CcP travels along thebackbone of CcP and passes through residues Ala194, Ala 193, Gly 192, and Trp 191.72 The latter, ofcourse, is the radical site and is in van der Waalscontact with the peroxidase heme. According to thePelletier-Kraut structure, the dominant interactionsbetween Fe3+CcP(MI) and Fe3+Cc(yeast iso-1) includevan der Waals forces and hydrogen bonds, ratherthan predominantly electrostatic interactions, asproposed earlier by Poulos and Kraut98 and asinferred from solution studies. Given that the crys-tals were partially dried prior to diffraction measure-ments, the precise relationship between the diffrac-tion results and protein-protein interactions that aresignificant in solution is uncertain. Nonetheless,publication of the hypothetical structure of the[Fe3+CcP, Fe3+Cc(tuna)] complex by Poulos and Krautin 1980 and the subsequent solution of the X-raycrystal structure of [Fe3+CcP(MI), Fe3+Cc] complexesby Pelletier and Kraut in 1992 provided a ground-breaking glimpse of the static structure of suchcomplexes.Results from H/D exchange experiments have been

used to compare the crystallographic structure withthe structure of the complex in solution.100,101 Hy-drogen-deuterium exchange labeling of the backboneamide protons of Fe3+Cc in both the CcP-bound state

and the free state has been used to map the bindingsite of CcP on Cc. The interface region identified bycomparing the H/D exchange rate constants of thefree and bound states is similar to the bindinginterface obtained from the solid-state crystal struc-ture. However, a second protected region locatedaway from the crystallographically derived interfaceand encompassing the “back” side of Cc(yeast) alsowas detected, evidence for the existence of a secondbinding domain. The protection factors for H/Dexchange are significantly smaller for the [CcP,Cc(horse)] complex than for [CcP, Cc(yeast)], evidencethat the details of complex formation are differentfor the two cytochromes.Chemical cross-linking reagents have been used to

covalently link CcP and Cc.102-105 Cross-linkingreactions are generally nonspecific and generatemultiple products. Separation and characterizationof these products are tedious and time-consuming.Studies with these covalent complexes show that ifthe spacer is too long, the complex can be quiteflexible so that the distance between the redoxcenters can be difficult to determine and may, in fact,exceed the separation that is achieved by the non-covalent, electrostatic complexes. For these reasons,a focal point of this research has involved the designof new cross-linking reagents with the intent ofminimizing the length of the linker molecule so asto obtain maximum rigidity within the covalentcomplex.Today the conventional chemical modification strat-

egy is being applied in more elegant ways usingmolecular biology to genetically modify surface resi-dues that are not easily modified using conventionalchemical modification reagents. Aided by the elec-trostatic model and the crystallographic structure,new molecules are being designed to probe thespecific interactions that define the protein-proteininterface. Preparation of 1:1 complexes that havebeen covalently coupled at specific sites created bysite-directed mutagenesis provides a new strategy formapping the structure of the interface and studyingthe dynamics of the protein-protein complex as theypertain to ET. With advances in molecular engineer-ing, one can manipulate the attachment site withrelative ease by introducing a specific target site forthe cross-linking reagent. Wang and Margoliash106have prepared mutants of Cc that will bind cross-linking reagent at a specific site on Cc, while notrestricting the cross-link to a specific site on CcP.Poulos and co-workers107,108 have taken this strategyone step further and prepared covalent complexes inwhich there is a unique site on both Cc and CcP forcross-linking. In this approach, the “zero-length”cross-link is an intermolecular disulfide bond formedby mixing mutants of CcP having a single Cys residuewith a mutant of Cc that also has a single Cysresidue. Such restricted mobility may, however,mask the conformational dynamics that are signifi-cant for optimal ET. Thus, the ultimate test of thesignificance of any chemical or biochemical modifica-tion requires kinetic measurements, and the inter-pretation of such measurements must necessarilyinclude a study of binding and dynamic processes.


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B. Dynamic View sExperimental Evidence forMultiple ConformationsCrystallographic studies provide a static snapshot

of a single form of the complex. However, theBrownian dynamics simulations of Northrup and co-workers109-112 graphically suggested that more thanone conformation of the [CcP, Cc] complex may beaccessible. As seen in Figure VI.1, several discreteand energetically accessible energy minima are sug-gested for the binding of Cc on the surface of CcP.The most stable minimum is that found by Poulosand Kraut and overlaps with the structure found byPelletier and Kraut. However, it appears not to bethe one with the smallest metal-metal separation,consistent with the possibility that conformationalprocesses influence and/or control ET.In fact, considerable experimental evidence sug-

gested that the thermodynamically most stable elec-trostatic complex is not optimally configured for ETand that rearrangement of the proteins within thecomplex is necessary for efficient ET. For example,at an equimolar Cc/CcP ratio, where is it universallyagreed that only 1:1 binding is significant, ET isinhibited at low ionic strength102,113 but becomes moreefficient when the ionic interactions are maskedeither by increasing the ionic strength or throughinterface mutations on the Cc. Furthermore, the rateconstant for ET in a 1:1 cross-linked complex is lessthan the maximum rate constant for the noncovalentcomplex.102 Both results can be explained by confor-mational gating15,41 of ET through movement of Ccamong several sites on the surface of CcP.Low-temperature measurements of triplet-state

quenching rate constants114,115 have directly revealedthe importance of conformational interconversion forreactions within the complex between CcP and Cc.As shown in Figure VI.2, the triplet decay traces forthe quenching of 3ZnP within ZnCcP by Fe3+Cc arerigorously exponential down to ∼250 K, but uponfurther lowering of the temperature, the triplet decaytraces become nonexponential and the quenchingabruptly vanishes. This phenomenon was inter-

preted as the manifestation of a novel intracomplexconformational transition. It has been modeled as a“phase transition” between a thermodynamicallystable, but inactive, low-temperature conformationand a high-temperature, active form. This processmay well prove to be a paradigm for interfacialregulation of interprotein interactions. A reinvesti-gation of this process using a combination of metalsubstitution and site-directed mutagenesis shouldunravel the structural features involved in thistransition. It has also been found that the kineticprogress curves describing the thermal back ET fromFe2+Cc to the π-cation radical of ZnCcP behaves in amanner consistent with gated ET.116

C. New Titration Strategies Show That C cP HasTwo Binding DomainsThe most direct demonstration that ET between

Cc and CcP could occur at distinct domains on theCcP surface would be to show that CcP could actuallybind two Cc to form a ternary complex. During themore than 2 decades since it was first shown thatCcP and Cc form a complex at low ionic strength,94the stoichiometry of binding was a matter of somedispute. The formation of a 2:1 complex at low ionicstrength was first indicated by size-exclusion chro-matography,117 the first molecule binding with a highaffinity and the second with a much lower affinity.Furthermore, the steady state kinetics with eukary-otic Cc are biphasic at low ionic strength, leading toa model of CcP with two catalytically active sites.117Nonetheless, it was the general consensus that onlya 1:1 complex was formed.118-124

This consensus held until 1993, when studies of thephotoinduced ET between ZnCcP and Fe3+Cc revital-ized the idea that a 2:1 complex, and thus twobinding domains, is biologically significant.18 For thestudies with ZnCcP (C-type heme substitution), thethermal back reaction (eq 2) is a structurally andfunctionally faithful model for heme reduction of bothcompound ES and CcP-IIh in that it involves ETbetween the ferroheme of Fe2+Cc and the oxidizedZnP heme of ZnCcP. Such studies, using cyto-chromes from a variety of species as well as cyto-chrome surface mutants, helped to initiate the mod-ern wave of studies of long-range ET.27,28,116,125 Inexperiments with ZnCc (I-type heme substitution),which is a structural and electrostatic analog ofFe2+Cc, photoinitiated ET from ZnCc to the ferri-heme of resting state CcP is a comparably excellentmodel for the reduction of the heme site in ES andCcP-IIh.19,126 A key virtue of using Zn-substituted

Figure VI.1. Electrostatic potential energy contour plotfor the interaction of Fe3+CcP and Fe2+Cc(tuna) as afunction of the center of mass position of the cytochrome.The cross section is through the heme plane of CcP. Theprimary binding domain centered near Asp 34 on the“right” includes three overlapping sites. A second domain,located to the “left” of the heme, that has not been observedcrystallographically is centered near Asp 148. The figurehas been adapted from refs 109 and 110.

Figure VI.2. Temperature dependence of the tripletquenching rate constant for complexes of ZnCcP with Ccfrom several species.


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proteins to study the reactions of CcP is that theysimplify the complicated problem presented by thepresence of the two redox-active centers in CcP andof the two interconverting forms of CcP-II. Byeliminating the oxidized Trp as a possible participantin most or even all of the reactions, one isolates andcan cleanly address questions of binding and inter-facial dynamics. Once these are understood, one canbegin to characterize the heme-heme ET event itself,without complication from the involvement of the Trpradical and interconversion between the two formsof CcP-II. The processes that involve the Trp thencan be addressed by the complementary techniqueof surface-bound metal complex,33,34 and the resultsembedded in the overall picture of binding, docking,and heme-heme reactivity can be obtained from theheme substitution experiments. However, as we nowdiscuss, progress in obtaining this picture requiredthe use of the new experimental strategies explainedin section IV above.

Combining Quenching and ET-Product DetectionThe first heme substitution experiments to study

the complex between CcP and Cc employed the CNtitration protocol in which Fe3+Cc as quencher (S)was titrated into a solution containing a fixed con-centration of ZnCcP as the ET photodonor (E†).18 Theearly studies27,28 in which quencher was only addedto a moderate excess disclosed (Figure VI.3) a breakin the curves at R ) [Fe3+Cc]/[ZnCcP] ∼ 1. Whenhigher values of R were used, it was found that thisbreak is followed by a further gradual increase in ∆kfor R > 1.18 The break in behavior at R ∼ 1 clearlyshows that CcP tightly binds one molecule of Cc. Thesubsequent gradual increase could represent bindingof a second Cc with a low affinity. However it couldequally well reflect nonspecific, collisional Stern-Volmer quenching of the excited state 1:1 complexby a second molecule of Cc without formation of a2:1 complex. It is not possible to distinguish betweenthese two alternatives through use of the CN quench-ing protocol alone. However, this was achieved bycorrelating measurements of ET quenching withdirect observation of the [ZnP+CcP, Fe2+Cc] charge-

transfer intermediate (I) produced by the quenching(eq 1).18 The observation that the appearance of theET intermediate lags behind the triplet quenching,with appreciable formation occurring only for [Cc]/[CcP] > 1 (Figure VI.3), was interpreted to resultfrom the formation of a 2:1 complex, where oneFe3+Cc binds to a high-affinity domain that is ET-inactive (but exhibits strong energy-transfer quench-ing), while the second cytochrome binds to a low-affinity domain that allows efficient ET quenching.The observation that raising the ionic strength18eliminates most of the ET quenching but not thatfrom energy transfer confirmed that ET occurs pref-erentially at the low-affinity domain, which is lesssensitive to ionic strength.Experiments of this type were used to compare the

binding affinities of fungal Cc and mammalian Ccfor ZnCcP.18 The fungal Cc show higher quenchingat the strong binding domain than the nonfungalCc.18,115 This dependence of the reactivity and affin-ity on the identity of the Cc likely reflects subtledifferences in the structures of the two classes ofcomplexes, and indeed, slight differences were de-tected in the X-ray crystal structures of the 1:1complexes of Fe3+Cc(yeast iso-1) and Fe3+Cc(horse)with Fe3+CcP.99The time-resolved kinetic profiles obtained during

such CN titration experiments with MgCcP have beenused to study the dynamics of complex formation atthe strong binding domain.127 The rate constant fordissociation of Fe3+Cc(yeast iso-1) from the strongbinding is much less than the rate constant fordissociation from the weak binding domain. Similarexperiments with Fe3+Cc(horse) showed that dis-sociation from both the weak and the strong bindingdomains is fast compared to the rate of intracomplexET.

New Titration Protocols at Low Ionic StrengthThe inverse heme substitution strategy19 and re-

verse-titration protocol126 were developed as part ofan effort to test the conclusion that CcP binds Cc attwo nonexclusive domains. Figure VI.4 presents an

Figure VI.3. Triplet quenching (O) and yield of the ETintermediate (4) for a CN titration in which Fe3+Cc(Candidakruseii) is added into a solution of ZnCcP. The dotted lineis a simulated 1:1 binding isotherm (K ) 0.001 µM, k )159 s-1). The dashed line is a fit of the quenching profileat R g 1 to a 2:1 binding isotherm assuming K1 ) 0.001µM and k1 ) 159 s-1 (K2 ) 10 µM and k2 ) 60 s-1). Thesolid line through the [I] data is a fit to a 2:1 bindingisotherm assuming the quenching for the first binding steparises from 3ZnP f Fe3+P Forster energy transfer so thatthe high-affinity step is ET-inactive. K1 ) 0.001 µM, k1 )0, K2 ) 10 µM. Conditions: 5 µMZnCcP, 1.0 mMKPi buffer(pH 7.0), 20 °C.

Figure VI.4. IN titration of ZnCc(horse) by Fe3+CcP. Thesolid line is the fit to the 2:1 binding isotherm. Stoichio-metric binding parameters are given in Table VI.1. Thedotted line shows the contribution to the quenching from1:1 complexes and the dashed line is the contribution fromthe 2:1 complex. Conditions: [ZnCc] ) 8.5 µM, 2.5 mM KPibuffer (pH 7.0); 20 °C.


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IN titration in which a fixed amount of ZnCc(horse)as photoprobe (S†) is titrated with increasing aliquotsof the quencher, Fe3+CcP (E), at low ionic strength(µ ) 4.5 mM). In this titration, the quenching rateconstant increases with addition of quencher, reachesa maximum value near [ZnCc]/[Fe3+CcP] ) 1/2, andthen decreases with subsequent additions of Fe3+CcP.This shape could not arise with a simple 1:1 stoichi-ometry. Rather, it reflects quenching in which the2:1 ternary complex (ES2†) dominates (k2 . k1) andthus quenching follows the f2 surface as plotted inFigure IV.8. Such a result demonstrates unambigu-ously that at low ionic strengths CcP can simulta-neously bind Cc at two distinct domains with highlydifferent affinities and reactivities. Analysis of thecharacteristic shape of this titration curve accordingto eq 13 yielded precise values of the stoichiometricrate constants and the stoichiometric affinity con-stants. Estimates of the domain parameters that arecompatible with the stoichiometric parameters aregiven in Table VI.1.These measurements are complemented by a CR

titration in which the probe (ZnCcP, E†) is added toa solution of Fe3+Cc(horse) (S) in 5 mM KPi buffer(pH 7) (Figure VI.5).128 In this experiment, theobserved quenching rate constant decreases uponaddition of ZnCcP, regardless of stoichiometry. How-ever, as discussed above, the sharp drop in ∆k thatoccurs as R ) [E†]/[S] approaches 1:1 indicates that

two molecules of Cc can simultaneously bind to CcP.The 2:1 complex contributes to ∆k for R < 1, and thenonzero value of ∆k0 allows a more precise estimateof the stoichiometric constants describing the secondbinding step.

High Ionic Strength

With 2:1 stoichiometry having been established forlow ionic strengths, the next question is whetherreactions at two domains occur at higher, physiologi-cally relevant ionic strengths, µ g 100 mM. Whenthe IN titration is done at slightly higher ionicstrength (18 mM) (Figure VI.6), the titration curveagain departs from the hyperbola expected for a 1:1binding stoichiometry, but the difference between thetitration curves for the 1:1 and 2:1 binding models issharply reduced. At 118 mM ionic strength, however,the IN titration gives no evidence for a 2:1 complex(Figure VI.6). Instead, the dependence of ∆k onFe3+CcP quencher concentration can be describedextremely well by a 1:1 binding equation.126

Establishing the binding stoichiometry and influ-ence of the second domain at higher ionic strengthrequired IR titrations, where ZnCc (S†) as the titrantis added to Fe3+CcP (E) as quencher.126 Figure VI.7shows IR titrations at three ionic strengths. In theexperiment at µ ) 4.5 mM, there is a low value forthe intercept, ∆k0. As shown in the lower panel ofFigure IV.3, for 1:1 binding the quenching wouldnecessarily decrease further during this reverse ti-tration. Instead, there is a lag in ∆k for R ) [ZnCc]/[FeCcP] < 1, and then ∆k increases with increasingadditions of ZnCc. This lag occurs because whenFe3+CcP is in excess (R < 1), essentially all the ZnCcmolecules form a 1:1 complex which has low reactiv-ity. Quenching increases upon further additions ofZnCc (R > 1) because the additional ZnCc binds to

Table VI.1. Domain Constants for 2:1 Binding ofZnCc by Fe3+CcP Estimated from the StoichiometricConstants Obtained from an IN Titration at 4.5 mMIonic Strength, pH 7.0, and 20 °C

K10 (M-1) K20 (M-1)a K12 (M-1) K21 (M-1) 1k (s-1) 2k (s-1)

7.7 × 106 <1.9 × 104 7.5 × 103 3.0 × 106 <2.4 1620a K20 > K12.

Figure VI.5. CR titration of Fe3+Cc(horse) by ZnCcP. Thesolid line is a three-parameter fit to the 2:1 bindingisotherm. Stoichiometric parameters: k1 ) 16 s-1, K1 ) 1.6× 106 M-1 (Calculated from the measured value of ∆k0 )43 s-1 and the three fitting parameters, k2, K2, and k1), k2) 408 s-1, K2 ) 5.4 × 103 M-1. The dashed line is asimulation for 1:1 binding using the parameters obtainedby fitting a CN titration with a 1:1 binding isotherm (K )7.4 × 104 M-1 and k ) 67 s-1). Conditions: [Fe3+Cc(horse)]) 25 µM, 5.0 mM KPi buffer (pH 7.0), 20 °C.

Figure VI.6. IN titrations of ZnCc by Fe3+CcP as afunction of ionic strength. Conditions: [ZnCc]0 ) 10 µM,KPi buffer (pH 7.0), 20 °C. (A) µ ) 18 mM. The solid line isthe best fit to the 2:1 binding equation. Stoichiometricbinding parameters are given in Table VI.1. The dashedline is a simulated curve for 1:1 binding: K ) 5 × 107 M-1,k ) 43 s-1. (B) µ ) 118 mM. The dashed line is the best fitto the 1:1 binding equation: K ) 1 × 104 M-1, k ) 170 s-1.


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Fe3+CcP to form a highly reactive 2:1 complex. Thequenching eventually falls because the fraction of thetotal ZnCc that is bound in the 2:1 complex decreasesas the titration proceeds. Thus, the data confirmsthe presence of two binding domains and the func-tional importance of the ternary (2:1) complex at thislow ionic strength. Figure VI.7 also presents IRtitrations at 18 and 118 mM ionic strengths. In bothcases, parameters that best describe the IR titrationsat the corresponding ionic strengths require that ∆kdecrease over the course of the reverse titrations.Instead, ∆k increases during the initial phases of bothtitrations and actually shows a maximum during thetitration at 18 mM ionic strength. The explanationfor these results is the same as for the titration at4.5 mM ionic strength; again, the experimental datacannot be described by 1:1 binding but can be wellfit with a 2:1 model. Thus, the IR experimentsconfirm the functional importance of two bindingdomains and the presence of the ternary (2:1) com-plex at physiological ionic strength.

Analysis of the IN and IR curves shows that the twostoichiometric binding constants change differentiallywith ionic strength (Table VI.2). This requires anaccompanying change in the distribution of the singlybound Cc between the two binding domains on CcP,namely a change in the relative amounts of the[1ES] and [2ES] forms of the 1:1 complex (SchemeIII.2). The stoichiometric ET rate constant of the 1:1complex (k1) increases with increasing ionic strength,whereas the stoichiometric ET rate constant of the2:1 complex (k2) is almost insensitive to changes inionic strength. The changes in k1 are best interpretedas reflecting changes in the ig1 weighting factors thatresult from changes in the binding constants (eq 14);the constancy of k2 suggests that the domain rateconstants are insensitive to ionic strength (eq 15).As a result of the changes in the Ki, the 1:1 complex

contributes increasingly more to the overall reactivityas the ionic strength approaches physiological values.Because the differences in affinity and reactivitydiminish with increasing ionic strength, it becomesmore difficult to discriminate between a 1:1 bindingmodel and a 2:1 binding model. Only with thereverse titration, where ZnCc is the titrant, was itpossible to clearly demonstrate the presence of the2:1 complex at physiological ionic strengths and toextract reliable stoichiometric parameters.Variations in the binding of Cc to CcP as a function

of ionic strength indicate that there are strongelectrostatic interactions within the binding interface.Table VI.2 shows that electrostatic interactions aremore significant for the first binding step than forthe second binding step. This difference in theelectrostatic properties of the two binding steps likelyarises because binding of the first Cc involves inter-action of two highly charged proteins having oppositepolarity, whereas binding of the second Cc to the 1:1complex involves interaction between the positivelycharged Cc and a weakly charged complex.

D. Interactions between the Two C cP BindingDomains?The conclusion that CcP binds Cc at two distinct

domains, with greater reactivity for the 2:1 complexthan for the 1:1, could mean that the high-affinitydomain itself has intrinsically low reactivity forheme-heme ET, while the weakly binding domainhas high reactivity, but it also is possible that thedomain reactivities themselves are altered when thesecond Cc binds. The simplest, limiting 2:1 kineticmodel would involve binding and reaction at twoindependent domains (each possibly with multipleoverlapping sites) (Scheme VI.1). However, CcP istoo small to bind two Cc without some interactionbetween them, and one must therefore consider“cooperativity” between the two bound Cc. As wediscussed in section III.B, one consequence of inter-

Figure VI.7. IR titrations of Fe3+CcP by ZnCc(horse) as afunction of ionic strength. The solid lines represent the bestfit to the 2:1 binding isotherm. The stoichiometric constantsare summarized in Table VI.2. The dashed lines aretheoretical curves generated for 1:1 binding. Conditions:(A) µ ) 4.5 mM, [Fe3+CcP]0 ) 10 µM. Kinetic constants forthe 1:1 simulation: K ) 5 × 107 M-1, k ) 4 s-1. (B) µ ) 18mM, [Fe3+CcP]0 ) 10.4 µM. Kinetic constants for the 1:1simulation: K ) 5 × 106 M-1, k ) 38 s-1. (C) µ ) 118 mM,[Fe3+CcP] 0 ) 10 µM. Kinetic constants for the 1:1 simula-tion: K ) 1 × 104 M-1, k ) 170 s-1.

Table VI.2. Stoichiometric Constantsa for 2:1 Bindingof ZnCc(horse) by Fe3+CcP as a Function of IonicStrengthb

µ (mM) K1 (M-1) K2 (M-1) k1 (s-1) k2 (s-1)

4.5 8.8 × 106 7.6 × 103 4.2 156018 8.5 × 105 4.3 × 103 38 1540118 6.6 × 103 1.4 × 103 200 2000a The average of IN and IR values. b pH 7.0, 20 °C.


+ +

actions between domains is that the affinity of onedomain changes when other domains are occupied.Measured stoichiometric constants provide no clueas to the extent of interdomain interactions. Wangand Margoliash106 addressed this problem by prepar-ing covalently linked, 1:1 complexes of Cc and CcP.By studying the binding of a second Cc to such acomplex they could probe the interaction between thelow- and high-affinity domains.There are, in addition, other possible consequences

of interactions. The first Cc might bind tightly atone domain, but in a nonreactive conformation. This“tight” site could then become reactive upon bindinga second Cc at a nonreactive, “remote” site, in a modelthat recalls the proposal of substrate-assisted productdissociation14 discussed in section VI.E. Such issuesof binding specificity and of reactivity in protein-protein reactions are analogous to those in enzyme-substrate reactions, but studies of ET complexes havelacked parallels to the imaginative uses of substrateanalogues and inhibitors in enzymology. We recentlydemonstrated129 that this kind of fundamental mecha-nistic question about the reaction between proteinET partners can be resolved by the use of a metal-loprotein that has been converted into a redox-inert,mechanism-based inhibitor through appropriate metalsubstitution. This strategy was illustrated by usingCu2+-substituted Cc32 as a structurally faithful butredox-inert analog of Fe2+Cc to probe ET within theternary complex. The utility of this probe is en-hanced by using Cc from multiple sources. FungalCc, such as that from Pichia membranefaciens (Pm),have a greater affinity for CcP than those fromvertebrates, and either type can be prepared with aselected metal ion: Fe, Zn, or Cu. Thus, it is possibleto perform an experiment in which CcP preferentiallybinds a fungal metallo-Cc having a selected metaland reactivity (Fe3+Cc, ET quencher; ZnCc, ET photo-donor; and CuCc, inhibitor) in the presence of avertebral Cc with a different metal and a differentreactivity.Two types of titration experiments were performed

where redox-inert CuCc(Pm) blocks the tight-bindingdomain on CcP from access by a redox-active Cc-(horse); in one case the redox-active species was

ZnCc(horse) (I protocol), in the other it wasFe3+Cc(horse) (C protocol). Figure VI.8 shows thetitration of an equimolar solution of ZnCcP andhorse-heart Fe3+Cc(horse) (pH 7.0, µ ) 4.5 mM; 20°C) by a solution of the CuCc(Pm) inhibitor. Priorto addition of inhibitor, photoinduced ET from3ZnCcP to Fe3+Cc(horse) is manifested in quenchingwith a rate constant of ∆k ) 26 s-1. If this ETquenching were associated with a 1:1 complex, thequenching would be described by eq 5. Within thismodel, the quenching of 3ZnCcP by Fe3+Cc(horse)must decrease monotonically with increasing con-centration of the competitive inhibitor, CuCc(Pm),because Cc(Pm) binds more tightly to CcP than doesCc(horse); thus, ∆k would decrease by more than afactor of 2 over the course of the titration withCuCc(Pm). Instead, the quenching is slightly en-hanced with increasing concentration of the inhibitorCuCc(Pm). This result transparently shows that thestoichiometry of the [Cc, CcP] complex is not 1:1 but2:1 or higher. This measurement was complementedwith one using CuCc in an IN type of experimentwhere the ZnCc(horse) is titrated by an equimolarmixture of Fe3+CcP and the strongly binding inhibitorCuCc(Pm).The two titration experiments with the inhibitor

CuCc(Pm) actually were designed to test for “coop-erative” ET at the strongly binding domain in the 2:1Cc-CcP complex (Scheme VI.1). In both experi-ments, the tight-binding domain on CcP is occupiedby a redox-inert CuCc(Pm), which blocks access tothis domain by a redox-active Cc, either ZnCc(horse)or Fe3+Cc(horse). Thus, the enhanced ET quenchingin the presence of inhibitor is inconsistent with thecooperative model of Scheme VI.1 in which ETbetween CcP and a Cc bound at its strongly bindingdomain is enhanced when a second Cc binds at thenonreactive second domain. The experiments insteadindicate that the strongly binding domain of CcP haslow heme-heme ET reactivity. The ET rate constantobtained by fitting the data from the IN titration (2k∼ 1530 s-1) is associated with the low-affinity domainwithin the 2:1 Cc-CcP complex.The CuCc inhibitor also has been used to probe the

mechanism of the Fe2+Cc f ZnCcP+ thermal ETwithin the [ZnCcP+, Fe2+Cc] ET intermediate. We

Scheme IV.1

Figure VI.8. Titration of a 1:1 mixture of ZnCcP andFe3+Cc(horse) by the inhibitor Cu2+Cc(Pm). The straightsolid line is included to guide the eye. The shaded arearepresents the range of results that could be observed for1:1 binding, with the upper boundary arising with equalaffinities for Fe3+Cc(horse) and Cu2+Cc(Pm) and the lowerboundary arising when Cu2+Cc(Pm) has a far higheraffinity. Conditions: [ZnCcP] ) [Fe3+Cc(horse)] ) 40 µM,µ ) 4.5 mM, pH 7.0, 20 °C.


+ +

reported previously116,125 that this reaction displaysmultiphasic, intracomplex kinetics and provisionallyinterpreted this in terms of gating by conformationalinterconversion. The discovery that photoinitiatedET primarily occurs within a 2:1 complex means thatthe ET intermediate actually has the 2:1 stoichiom-etry of [ZnCcP+, Fe2+Cc, Fe3+Cc]. This, in turn,raises the possibility that multiphasic kinetics dis-played by this intermediate reflects enhanced elec-tron self-exchange between Fe2+Cc and Fe3+Cc on thesurface of ZnCcP, prior to the reduction of ZnCcP+.However, the kinetics of this intermediate is notperturbed significantly when the strong-binding do-main is occupied by the CuCc(Pm) inhibitor, a situ-ation that would eliminate self-exchange ET withinthe ET intermediate.The use of CuCc as an ET inhibitor thus provides

evidence against both the hypothesis of cooperativephotoinitiated ET within the 2:1 complex and thatof intracomplex self-exchange within the ET inter-mediate. The simplest kinetic scheme that is con-sistent with current data involves sequential binding,where the first Cc binds strongly at a nonreactivedomain and the second binds weakly at a reactiveone, with the observed ET largely occurring in the2:1 species.

E. Independent Confirmations of 2:1StoichiometryAlthough the stoichiometry of binding is still

sometimes disputed, the majority of the recent in-vestigations have confirmed and/or extended theoccurrence of 2:1 binding as demonstrated by thekinetic measurements just described.

Proton Uptake/Release upon Complex Formation

The existence of two binding domains on CcP andthe formation of a 2:1 complex was confirmed at µ )50 mM for an extended range of pH values, 5.5 <pH < 7.75, by potentiometric titration experimentsthat monitor the uptake and/or release of protonsaccompanying binding of Fe3+Cc(yeast iso-1) toFe3+CcP130 (Figure VI.9). The titration curves ob-tained by adding the cytochrome to the peroxidase(N titration protocol) show a maximum near R ) 1.These curves require 2:1 binding and, as the simula-

tions in Figure IV.6 predict, a maximum is observedbecause the “reactivity parameters”, in this case thenumber of protons taken up during the two stagesof binding (q1 and q2), have opposite signs. For pH<7, the first stage of binding results in proton release(q1 < 0) and the second binding step results in protonuptake (q2 > 0). The magnitude of the proton uptakefor the first binding step (q1) decreases with increas-ing pH while that for the second step (q2) increases(Figure VI.9) until, for pH >7, protons are consumedin the first binding step (q1 > 0) and released in thesecond step (q2 < 0). The opposing reactivities forthe two binding steps at both low and high pH valuesmake the proton uptake experiment exquisitelysensitive in these ranges, while the signals obtainedat pH 7 are small and difficult to analyze. Since mostkinetic experiments so far have been performed atpH 7, the results from the proton uptake titrationsbeautifully complement those obtained in kineticexperiments. Together they demonstrate that the 2:1complex forms over a wide pH range.Measurements of proton uptake also disclosed that

the oxidation state of Cc influences its interactionwith CcP,130 indicating a thermodynamic linkagebetween ET and binding. At pH 6 and µ ) 100 mM,the titration of Fe3+CcP with Fe2+Cc shows thecharacteristic maximum indicating the presence ofa 2:1 complex, whereas results with Fe3+Cc do notgive clear evidence for the existence of a 2:1 complex.The difference arises under these conditions be-cause: (i) proton uptake during the second bindingstep is greater for Fe2+Cc than for Fe3+Cc and (ii) thestoichiometric affinity constant for the first step ofbinding (K1) is less for Fe2+Cc than for Fe3+Cc.Comparison of the kinetic and proton-uptake mea-surements over a wider range of pH values will be ofkeen interest.

Steady-State KineticsA reanalysis of the steady-state kinetics131,132 also

shows that two domains and a 2:1 stoichiometry arenecessary to interpret the data with Cc(yeast iso-1)for a broad range of ionic strengths (10-200 mM).With Cc(horse) a 1:1 stoichiometry seems sufficient,but given that there are two binding domains on CcP,even if the ternary complex does not form to asignificant extent, the measured stoichiometric rateconstant for 1:1 binding must be a weighted averageof the parameters for the two domains (eq 14).Consistent with this interpretation, the binding af-finities reported in this study are quite comparableto those obtained by heme substitution flash pho-tolysis and by proton-uptake titrations.Recently Miller et al.133 studied the stoichiometry

of binding through use of a surface-modified CcPdouble mutant in a variety of kinetic experiments,including steady-state measurements, stopped-flowmeasurements, and photooxidation experiments uti-lizing Ru-labeled Ccs. The steady-state measure-ments support the conclusion that at least two sites(H-mode and Y-mode) exist within the high-affinitydomain, and as expected, covalent attachment of thebulky 3-(N-maleimidylproprionyl)biocytin (MPB) re-agent to the genetically engineered Cys at position193 (which lies within the interface for the high-affinity domain) lowers the observed reactivity (kcat)and decreases the measured affinity constant (Km)

Figure VI.9. Effect of pH on proton release during thetitration of CcP with Fe3+Cc (µ) 50 mM, 25 °C, KNO3):(∆) pH ) 5.51, Pinitial ) 33.9 µM; (O) pH ) 5.99, Pinitial )34.3 µM; (0) pH ) 6.50, Pinitial ) 36.9 µM; (]) pH ) 7.00,Pinitial ) 37.0 µM; and (O, dashed line) pH ) 7.75, Pinitial )37.2 µM. The lines are unweighted least-squares fits for amodel with two binding domains for Cc per molecule of CcP.


+ +

to a value that is comparable to that of the low-affinity domain of CcP(MI). In contrast to thecomplex with CcP(MI), both Km and kcat are insensi-tive to ionic strength, so two stoichiometric bindingsteps were not discerned even at low ionic strengths.These steady-state measurements with the MPB-modified double mutant were interpreted as rulingout the importance of a second domain. However thisis not correct. The observed ionic strength depen-dence also is consistent with a two-domain modelwhere the measurement has yielded a stoichiometricrate constant that reflects the weighted sum of thecontributions from both the low-affinity and high-affinity domains. (See section VI.F for further dis-cussion of such a situation.) Alternatively, it maybe that binding at the high-affinity domain is com-pletely blocked by MPB, so the steady-state measure-ments actually monitor a reaction that occurs exclu-sively at the low-affinity domain.A key problem with a simple one-domain mecha-

nism for the kinetics of the reaction of CcP and Cc isthat the rate of ET from Fe2+Cc to oxidized states ofCcP can exceed the rate of release of the productFe3+Cc, an impossibility if a second reactant moleculecannot bind until the product molecule dissociates.The contradiction obviously is resolved if reaction canoccur at two separate domains. An alternate resolu-tion to the problem, “substrate-assisted product dis-sociation” was proposed by McLendon.14 The idea isthat a second molecule binds and interacts with thefirst so as to enhance the rate of dissociation of thefirst molecule from the principal, tight-binding do-main. This is described by eq 27, which requires thatboth domains be in fast exchange.

In the present context, the requirement of weakbinding by a second Cc implies the existence of asecond interaction domain, and thus the proposal canbe viewed as a variant of the two-domain model inwhich all reaction occurs at the high-affinity domain.

NMR TitrationsThe chemical shifts for most of the proton NMR

signals detected in a one-dimensional NMR spectrumfrom equimolar amounts of Fe3+CcP(CN-)134,135 (orFe3+CcP)119,136 and Fe3+Cc are not significantly dif-ferent from those in the isolated proteins. However,a small subset of the observed signals are perturbedupon binding, and these perturbations have beenused to quantitatively describe the binding of CcPand Cc. Because the observed binding-induced shiftsare small, efforts to unambiguously detect the 2:1complex by this technique have been unsuccessful.However, Yi, Erman, and Satterlee137 found that thedissociation rate constant of 180 s-1 obtained frominversion transfer and saturation transfer experi-ments with either the [Fe3+CcP, Fe3+Cc(yeast iso-1)]complex or the [Fe3+CcP(CN-), Fe3+Cc(yeast iso-1)]complex is inconsistent with a mechanism for cata-lytic turnover involving sequential oxidation of twomolecules of Fe2+Cc at a single Cc binding domain.Rather, these NMR experiments support either atwo-domain binding mechanism or the substrate-assisted-dissociation variant of the two-domain model.In either case, the concentrations of CcP and Cc

employed for NMR experiments should produce ap-preciable levels of 2:1 complex, so the measureddissociation rate constant is likely a composite of thedissociation rate constants for the individual do-mains.

Fluorescence Line-Narrowing Spectroscopy

Because ET reactions in the [CcP, Cc] complexinvolve long-range processes, spectroscopic tech-niques that predominantly monitor the redox-activechromophores often are unperturbed by complex-ation. For example, resonance Raman measure-ments showed no evidence of changes in Cc uponcomplexation with CcP.138,139 Fluorescence line-nar-rowing (FLN) studies140 at 4 K showed that bindingof Cc to meso-porphyrin-substituted CcP induceschanges in the relative distribution of luminescentcomponents. Furthermore, the distribution of thecomponents for a sample containing equimolaramounts of CcP and Cc and for a second samplecontaining excess Cc are different. Such results isconsistent with formation of a 2:1 complex.

F. Kinetic and Physical Characterization ofSite-Specific Mutants of C cP

Site-directed mutagenesis is being used to identifythe structural elements that are responsible for thestability of the higher oxidation states of CcP141-146

and for promoting heterolytic fission of the peroxideO-O bond,147 to probe the details of the mechanismin which the two distinct redox centers of ES arereduced by Fe2+Cc to the resting state,91,148-153 andto identify the amino acid residues that comprise thetwo surface binding domains.107,108,154-156 We discussonly those mutations that address issues of bindingand reactivity. Studies with mutants of Cc that affectits interaction with CcP have been reviewed thor-oughly by Mauk,157 so we focus here on mutants ofCcP.

Trp 191

This residue is the radical site in H2O2-oxidizedintermediate, compound ES, and in CcP-IIr. Thus,substitution of Trp 191 is an obvious strategy foraddressing the mechanism of heme reduction in CcP.The indole ring of Trp 191 lies parallel to and in vander Waals contact with the proximal ligand His 175.Extensive kinetic and physical characterization stud-ies have been reported for the Phe 191 mutant, andto a lesser extent for the Gly 191 and Gln 191mutants. Replacement of Trp 191 with Gly enablesexogenous cations, such as imidazolium, to bind inthe space vacated by Trp 191.158 Resonance Ramanstudies141 with the resting state of the Phe 191mutant indicate that the heme is predominantlypentacoordinate and high-spin, like the native pro-tein. Optical studies indicate that reaction of thismutant with H2O2 leads to oxidation of the heme tothe ferryl state but that the oxidized product has beensignificantly destabilized relative to CcP-I(MI). Astable radical not associated with Phe 191 wasobserved by EPR,159,160 suggesting that there is analternative amino acid site capable of storing oxidiz-ing equivalents. Significant changes in the kinet-ics161 for the initial formation of the oxidized inter-

D+A- + A h D+A + A- (27)


+ +

mediate and its subsequent reduction by ET fromFe2+Cc were observed for the Trp 191 f Phe mutant.The absence of heme-heme ET when Trp 191 ismutated is fully consistent with a picture whereheme-heme ET is dominated by reactions at the low-affinity domain and thus fully consistent with theheme substitution measurements described above.

Proximal Side Mutation Sites

Examination of the X-ray structure of CcP93 showsthat Trp 191 is connected to the heme site by ahydrogen-bond network that includes Asp 235 andthe proximal ligand (His 175), with Asp 235 forminghydrogen-bonds to both Trp 191 and His 175. Thisnetwork is expected to modulate the electronic prop-erties of the heme, to stabilize the indole group ofTrp 191, and to modify the redox potentials of theheme and the Trp radical. The Asp-His interactionis believed to deprotonate the His to form an imida-zolate ligand, which leads to an increase in themetal-ligand bond strength. In addition, Asp 235provides a conduit for mediating coupling betweenthe Trp 191 radical and the heme.Goodin and McRae162 have shown that the CcP-

(D235E) mutant retains many of the coordination andfunctional properties of wild-type CcP, despite sig-nificant structural changes. The H-helix (residues233-242) is sufficiently flexible and reorients slightlyto accommodate the additional CH2 group of Glu 235,without disrupting the hydrogen-bonding network.Although there is a small rotation of His 175, theoverall position of the carboxylate group is nearlyunchanged. In contrast, ET reactivity is greatlychanged in the CcP(D235N)163 and CcP(D235A)153mutants. X-ray analysis162 shows that replacementof Asp by either Asn or Ala disrupts both of thesehydrogen bonds and that the indole side chain of Trp191 has flipped over to form a new hydrogen bondbetween the indole NH and the backbone carbonylof Leu 177.164 Although the heme can be oxidized tothe ferryl state, both of these mutants show negligibleenzymatic activity, and no photoinitiated ET reactionwas observed with Ru27-Cc(horse).163

By comparing the X-ray structure of CcP to thoseof other peroxidases, in particular that of ascorbateperoxidase (APX),165 Bonagura et al.166 found acation-binding site located 8 Å from the proximal Trpin APX that is absent in CcP. The absence of thiscation-binding site is believed to be one reason whya stable Trp radical is formed in CcP but is absentin APX. To test the importance of this cation-domainin controlling whether oxidizing equivalents can bestored on the proximal Trp, site-directed mutagenesiswas used to create a cation-binding site in CcP.166Spectroscopic characterization of this mutant showedthat a stable Trp radical does not form but that theoxidizing equivalent resides instead on the porphryinring. The steady-state activity for the oxidation ofFe2+Cc is significantly decreased for this mutant,confirming the hypothesis that long-range electro-static effects destabilize the Trp radical and lowerthe redox activity of CcP.

Surface Mutation Sites on CcP

Kinetic studies with the wild-type yeast CcP con-firm the occurrence of 2:1 stoichiometry for [Cc, CcP]

complexes and therefore the existence of two distinctbinding domains with different reactivities, but thephysiological significance of the domain identified bycrystallography and the location of the well-estab-lished “second” domain on CcP remain fundamentalunanswered questions. The most promising methodfor experimentally locating these recognition domainscouples kinetic studies with site-directed mutagen-esis. The initial set of target surface sites wasinspired by the Poulos-Kraut electrostatic model98and subsequently by the crystal structure,99 both ofwhich focus on the high-affinity domain. The resi-dues suggested by the Poulos-Kraut model includeAsp 34, Asp 37, Asp 79, Gln 86, Asn 87, and Asp 216,whereas the set of CcP surface residues specifiedfrom the [CcP, Cc(horse)] crystal structure include(i) Ala 193 and Ala 194, which predominantly interactwith the heme of Cc; (ii) Glu 35, Asn 38, and Glu 290,which form H-bonds with surface Lys of Cc; and (iii)Tyr 39 and Asp 34, which are involved in van derWaals interactions with the Cc surface. Additionalresidues that are potentially important in stabilizingthe [CcP, Cc(yeast iso-1)] complex include Arg 31, Gln120, and Val 197, which are in van der Waals contactwith the surface of Cc. Although the Browniandynamics calculations of Northrup109-112 suggest thatthe second domain lies in the vicinity of Asp 148, thelocation of the well-established “second” domainremains a challenge for future studies.Miller et al.155 have used stopped-flow experiments

and flash photolysis to study a set of mutants whereindividual carboxylate side chains have been con-verted to amides; these include CcP(E32Q), CcP-(D34N), CcP(E35Q), CcP(E290N), and CcP(E291Q).Residues 32 and 291 are remote from the high-affinity domain, and consequently, the kinetics forthe CcP(E32Q) and CcP(E291Q) mutants is similarto that of the native protein. On the other hand,when mutations were made at positions that liewithin the interface identified by X-ray diffraction(34, 35, and 290), the reactivity is decreased relativeto that of the native protein. Although the decreasedreactivity could represent either a perturbation inbinding affinity and/or ET reactivity, the perturba-tion in the kinetics indicates that these residues maybe functionally important.Corin et al.123,156 have prepared a set of charge-

reversal mutants where one surface Asp has beenconverted to Lys at positions 37, 79, or 217. Thekinetic behavior of the CcP(D217K) mutant wassimilar to that of the native protein, whereas theinstability of the ES state of the CcP(D79K) mutantprevented a complete kinetic characterization of thismutant. The CcP(D37K) mutant showed remarkablydifferent kinetics from the native CcP. This is notunexpected, since the Poulos-Kraut model recog-nized Asp 37 as one of the interface residues involvedin charge-pair interactions with surface Lys on Cc,and in the crystal structure Asp 37 lies proximal tothe recognition site for Fe3+Cc(horse).As an illustration of how kinetic studies with point-

mutations can be used to begin to locate the strong-binding domain, we now discuss photoinduced ETbetween ZnCc and the charge-reversal CcP mutantin which the negatively charged Asp 37 residue is


+ +

replaced by a positively charged lysine residue. TheCcP(D37K) mutant behaves very differently fromCcP(WT) in binding and heme-heme ET.167 In theIR titration of Fe3+CcP(D37K) by ZnCc, ∆k decreasesmonotonically as ZnCc(horse) increases, in contrastto the IR titration of wild-type CcP by ZnCc (FigureVI.7). The behavior of the mutant is perfectlydescribed by a 1:1 binding isotherm with an inter-mediate value for the stoichiometric binding constant(K1 ∼ 104 M-1), indicating that the amount of 2:1[Cc,CcP] complex in solution is negligible. Thesignificant decrease in K1 from 8.5× 105 M-1 for CcP-(WT) to 104 M-1 for CcP(D37K) clearly indicates thatthe surface area identified by Pelletier and Kraut isthe strong binding domain or at least part of it.Although the stoichiometric constant for binding ofCc is greatly decreased by the mutation of Asp 37 toLys in CcP, the stoichiometric intracomplex ET rateconstant (k1) is greatly increased: k1(WT) ) 40 s-1;k1(D37K) ) 3900 s-1. Furthermore, the ionic strengthdependence of the intracomplex ET rate constant (k1)within the 1:1 complex differs sharply for CcP(WT)and CcP(D37K): k1 decreases for CcP(D37K) as theionic strength increases, whereas it increases for CcP-(WT).This kinetic behavior can be understood easily by

recognizing that Cc binds with widely differentreactivities at two different domains on CcP and thatthe mutation of Asp 37 to Lys differentially affectsthe Cc-binding affinities at these two binding do-mains. Since residue 37 is proximal to the high-affinity domain, substitution of the negatively chargedAsp 37 residue with a positively charged Lys greatlyweakens the Cc-binding affinity at the high-affinitydomain (reduces K10) because of the net loss of twonegative charges on CcP along with the introductionof a repulsive interaction between the now positivelycharged Lys 37 of CcP(D37K) and the positivelycharged lysine residues of Cc located at the exposededge of its heme. According to eqs 11 and 12, amutation that lowers the stoichiometric bindingconstant K1 also lowers the stoichiometric bindingconstant K2, so that only the complexes with 1:1stoichiometries contribute to the quenching of 3ZnCcby Fe3+CcP(D37K) under our experimental condition.However, this does not mean that only one domainis involved! The increase in k1 from 40 s-1 for CcP-(WT) to 3900 s-1 for CcP(D37K) can be understoodin terms of eq 8, which shows that even for a 1:1binding stoichiometry, the stoichiometric rate con-stant k1 is a weighted average of the two domain rateconstants, weighted according to the relative popula-tions of the two conformers of the 1:1 complex. Themutational weakening of the binding at the high-affinity domain effectively acts to increase 1:1 bindingat the highly reactive second domain by ca. 2 ordersof magnitude. The result, described by eq 8, is thatthe stoichiometric rate constant (k1) is increasedsignificantly, even though the domain rate constantsare not affected by the mutation.The ionic strength dependence of k1 for the [ZnCc,

Fe3+CcP(D37K)] complex likewise can be explainedby considering the relationships between the mea-sured stoichiometric parameters and the deriveddomain constants (eqs 5 and 8). Because of adifference in the ionic strength dependence of the

binding affinities, K10 and K20, the fraction of theheme-et-inactive 1:1 complex (1ES) increases as theionic strength increases, resulting in the decrease ink1 from 3900 to 1000 s-1.

G. Surface Coupling Maps and ElectrostaticMaps of the [C cP,Cc] ComplexWe now compare the pathway surface coupling

maps and the surface electrostatics maps of the [Cc,CcP] reaction pair. Our goal is to use theoreticalmethods to propose logical choices for the experimen-tally determined weak-binding/fast heme-heme ETand tight-binding/slow heme-heme ET domains onCcP. Our method of reconciling the informationabout docking geometry and electronic coupling is toseek correspondence between the surface couplingmaps and the electrostatic maps. In order to identifythe loci on the Cc and CcP surfaces that are stronglycoupled to the hemes, a pathway global couplingcalculation was performed (section V.B). FigureVI.10a-d shows the surface coupling maps forFe3+CcP and Fe3+Cc(horse). The Trp 191 indole ringis delocalized when treated as the ET-active site inthe pathway coupling calculation of CcP. Asymmetryof the Trp wave function on the indole ring andcomplications arising from coupled deprotonationdynamics are beyond the scope of this simple analy-sis. We analyzed the protein electrostatics using theDelPhi program (section V.C). Figure VI.10e,f showsthe electrostatic maps for both proteins. Both theelectrostatic studies and the surface coupling studieswere performed on the isolated proteins (investiga-tions on docked structures are in progress).We have identified a crescent-shaped region on the

surface of CcP that exhibits relatively strong elec-tronic coupling to the heme (Figure VI.10c,d). Withinthis region are areas that are electrostatically comple-mentary to the Cc surface (Figure VI.10e,f). Onecomplementary area on the CcP surface falls betweenTyr 39 and Asp 217. This area comprises a singlebinding domain with two overlapping binding sites(sites 1and 2) or a continuum of binding sites. Asecond distinct complementary area lies near Asp148. This area comprises a second binding domainwith a single site (site 3). Pathway couplings to Trp191 are strongest for site 1, intermediate for site 2,and weakest for site 3. In the region surroundingsites 2 and 3 on the CcP surface, strong coupling andstrong negative potentials coincide. Because ourinitial studies have focused on the individual process,it is difficult to quantitatively differentiate the elec-tronic coupling strengths and electrostatic contribu-tions across the three interaction surfaces.Figure VI.11 shows a schematic view of the pro-

posed docking regions on the CcP surface. Site 1(labeled as Tyr 39) has the strongest concentrationof surface charges and is the only site that wasdetected in the 1:1 [CcP, Cc] crystalline complex.99Other amino acid residues in this region are Asn 38and Glu 290. Site 2 is in the region of the Poulosand Kraut hypothetical complex obtained by optimiz-ing the intracomplex hydrogen bonding interac-tions.93 Other nearby amino acids are Asp 37, Asp34, and Asp 79. Site 1 and site 2 clearly overlap andthus comprise a single domain with two overlappingsites (or a continuum of binding sites). Site 3, which


+ +

meets the docking criteria for ET, based on Browniandynamics simulation, was described by Northrup andco-workers109,110 and is centered near Asp 148. Otherparticipating residues include Gln 152, Phe 140, andLeu 221. The residue located between these twodomains is Asp 217. The surface coupling maps forCcP are qualitatively similar for the analysis ofpathways into both the heme and Trp 191.

The encounter surface for Fe3+Cc(horse) (generatedby tracing with a 5 Å radius probe) is shown in FigureVI.10e,f. Here the front view of the encounter surfaceis shown along the Fe to heme C4C direction. Thecolor of the encounter surface ranges from blue to redfor electrostatic potential values of -5kBT to 5kBT,respectively. The amino acid region of strongestpositive potential includes Lys 4, 5, 11, 13, 72, 73,

Figure VI.10. Pathway couplings (eq 20) from the heme to the surface atoms in (a, upper left) Fe3+Cc(horse) and (b,upper right) Fe3+Cc(yeast iso-1). The coupling scale shows the logarithm of the pathway coupling value ∏iεi. Note thestrong coupling surface associated with the heme crevice. Pathway couplings are shown from (c, middle left) the hemep-electron ring and (d, middle right) the Trp 191 side chain of CcP to the protein surface. Note the crescent-shaped strongcoupling surface. Electrostatic potential surfaces computed with the program Del Phi79 for (e, lower left) the Fe3+Cc(horse)encounter surface and (f, lower right) the Fe3+CcP encounter surface. The scale shows electrostatic potential in units ofkBT/e, with T ) 25 °C. There is complementarity between the potentials, strong coupling pathways, and encounter surfaceshapes between CcP residues Thr 39 and Asp 217. A third complementary site on the CcP surface lies near Asp 148.These potential docking and ET regions are in the same regions as those proposed by Northrup and co-workers.109,110


+ +

86, and 89. Regions on the Cc surface (FigureVI.10a,b) that are most strongly coupled to the hemelie around the heme crevice and coincide with regionson the electrostatic maps where the electrostaticpotential is largely positive (Figure VI.10e,f). Tiede74computed electrostatic maps for a number of cyto-chromes c with the program DelPhi.79 Our calcula-tions are consistent with those, and with the Brown-ian dynamics calculations of Northrup and co-workers.109

We have mentioned the challenge of understandingsingle pathway vs pathway “tube” coupling mecha-nisms. The propensity toward one mechanism oranother in unimolecular reactions need not be thesame as in bimolecular reactions. That is, interpro-tein coupling interactions at the protein-proteininterface are somewhat different in magnitude andnumber from the kinds of electronic interactionswithin each protein. As such, it remains to be seenwhether the protein-protein interface presents singlepathway, pathway “tube”, or average medium effectsand how substantially they perturb the nature ofpathways within the individual reaction partners. Aparticularly important application of multipathwayGreen function techniques will be to probe the natureof multipathway interferences at protein-proteininterfaces.

VII. Discussion

This review has had several central purposes.Section III discusses the critical connection betweenthe binding and kinetic parameters that are obtainedfrom experimental measurements and the micro-scopic constants that are the ultimate goal of thosemeasurements. In part, this represents the rebot-tling of old wine in new bottles, as these consider-ations have been thoroughly explored in the contextof ligand binding,35-37 but their extension to thedefinition of stoichiometric rate constants is new. Thewhole issue is not well-embedded into the literature

of interprotein electron transfer. In section IV wepresent an expanded view of titration experimentsas generating four-dimensional data sets, with quench-ing measurements yielding not curves but 2-D sur-faces. This in turn naturally leads to the expansionof quenching protocols to include the four types oftitration listed in Table IV.1. As reviewed in sectionVI, the four types of titration experiments (TableIV.1) together demonstrate that (i) Cc reacts at twodistinct and nonexclusive surface domains of CcP; (ii)two molecules of Cc can bind simultaneously to CcP;(iii) the ternary complex is more reactive than thebinary complex for the heme-heme ET reaction; and(iv) the use of CuCc as inhibitor suggests that theseresults are to be interpreted as meaning that onedomain has a high affinity for Cc but a low reactivityfor the heme-heme ET reaction, while the low-affinity domain is highly reactive in heme-heme ET.Taken together, these results suggest a mechanismwhere ET at the strongly binding domain leads toreduction of the Trp radical and ET at the weakbinding domain is optimized for reduction of theferryl-heme.It has been generally accepted that the high-

affinity domain on the surface of CcP is in the generalvicinity of the binding domain first identified byPoulos and Kraut98 or perhaps at the different butoverlapping site detected in the cocrystal,99 but withthe proviso that multiple binding orientations mustexist, as evidenced by instances of gated electrontransfer. Section V extends the “pathways” model forcalculating ET rate factors to protein-protein ET viathe concept of functional docking and discusses theuse of classical electrostatics calculations to charac-terize the encounter surface. As to the location ofthe second domain, the Brownian dynamics calcula-tion of Northrup and Thomasson suggests that thelow-affinity domain may be found in the vicinity ofAsp 217 (Figure VI.1).We performed three kinds of theoretical analyses

on the Cc/CcP system. The first is a surface couplingtunneling pathway analysis. This calculation ap-proximates the coupling between the protein redoxcenters and the protein surface. Strongly coupledregions of Cc appear near the heme crevice, whilestrongly coupled regions around the CcP appear in abroader, crescent-shaped region. Strongly coupledsurface amino acids in this crescent couple to theheme edge. A second strategy of analysis, functionaldocking, suggests that the interactions betweensurface amino acids of the two proteins in these twostrong pathway patches, taken together with thepathway couplings to each redox center from itscorresponding surface patch, set an upper bound onthe ET rate. A third calculation was performed inorder to further refine this analysis. Electrostaticencounter surface potentials were computed for twoproteins to examine electrostatic complementaritythat might exist in the region of relevance suggestedin the functional docking analysis. Two domainswere found with similar pathway couplings to theheme and with complementary electrostatics. Thedomains differ somewhat in their radii of curvature.Also, the first domain is more strongly coupled to theTrp 191 than is the second domain. This analysis

Figure VI.11. Schematic representation of the low-energybinding sites associated with [Cc, CcP] functional docking.The regions were determined on the basis of (1) strongcoupling pathways to the redox centers in the individualproteins, (2) electrostatic complementarity, and (3) roughencounter surface shape complementarity.


+ +

has not sought out alternative domains with consid-erably weaker electronic interactions between the tworedox centers, although many such docking geom-etries surely exist.Support for the definitive finding that heme-heme

ET is more efficient in the 2:1 complex than in the1:1 complex and the resulting suggestion that thebinding domain identified by the X-ray structure maybe optimized for reactions with the Trp+ radical site,but may not be the physiologically active site forheme-centered reactions, in fact is given by flashphotolysis studies of ET between ruthenium-labeledCcs and compound ES.33,34 These studies indicatethat Cc bound at the high-affinity domain reducesthe Trp radical, not the heme site, so that the productof the first reduction step of ES is CcP-IIh, in whichthe one oxidizing equivalent is on the heme. It wasfurther suggested that this is followed by rapidintramolecular ET between the oxidized heme andthe Trp to generate CcP-IIr (eq 24).

Return to the resting state then involves reductionof the Trp radical in CcP-IIr. In this mechanism,ferryl-heme reduction is not the result of directtransfer to the heme but of a two-step process thatinvolves the Trp. From this the authors of this studyconcluded that the heme-centered reduction and theTrp-centered reduction proceed along a common“pathway” and that both oxidizing equivalents neces-sarily are transferred to the Cc through a commonbinding domain. However, a number of consider-ations show this conclusion to be invalid. Firstly, thestopped-flow studies and photoinitiated ET studieswith Ru-labeled Ccs are carried out under highlynonphysiological conditions in which the concentra-tion of Fe2+Cc is comparable to or less than that ofcompound ES. But, this assures that binding occurspredominantly at the high-affinity domain and pre-cludes examination of the weakly binding one! Inother words, while the experiments elegantly dem-onstrate that heme reduction at the high-affinitydomain can regenerate the resting state in a two-stage process, from Cc to Trp to ferryl-heme, theexperimental conditions in fact eliminate the pos-sibility of detecting direct heme-heme ET from acytochrome that binds and reacts at the low-affinitydomain. Thus, the “conclusion” that heme reductionoccurs only by reaction at a single domain is invalidand rather is a consequence of the measurementtechnique. One should also recall that, as notedabove, intraprotein ET between the ferryl-heme andthe Trp of CcP is a poorly understood process thatunder some circumstances can be far slower thanthe measured rate constant for reduction byFe2+Cc.87,88,92,148,168,169The heme substitution titration procedures, in

contrast, are successful in characterizing the two-domain binding and in demonstrating direct heme-heme reactivity at the more weakly binding domain.This is true in part because metal substitutionsimplifies the reaction mechanism, looking only atthe heme-heme process, but also because the quench-ing measurements more accurately mimic the physi-ological situation in which Cc is in abundance, whichfacilitates the operation of parallel reaction processes

(and pathways), one in which the CcP ferryl-heme isdirectly reduced by Fe2+Cc bound at the low-affinitydomain. In fact, the heme substitution measure-ments described above show that Fe2+Cc bound atthe high-affinity domain does not undergo heme-heme ET when the Trp radical is not oxidized andthat this does not eliminate heme-centered ET toFe2+Cc, thereby disproving the notion that there isbut one “portal” for the entry of reducing equivalentsinto CcP-I. Indeed, the rate constant for the reduc-tion of ZnCcP+ by Fe2+Cc is quite similar to the rateconstant reported for the heme-centered reduction ofCcP-II,133 and thus, metal substitution demonstratesthe presence of an ET pathway to the CcP heme thatdoes not involve transient oxidation of Trp 191.The conclusions from the work described are (i)

reduction of the Trp radical occurs preferentially atthe high-affinity domain; (ii) under conditions whereequilibration of CcP-IIh and CcP-IIr is slow comparedto the direct heme-heme reduction at the low-affinitydomain, heme reduction also occurs preferentially atthe high-affinity domain; (iii) under conditions whereequilibration is rapid, heme reduction by Fe2+Ccoccurs independently at both domains, through a two-step process at the high-affinity domain but directlyat the low-affinity domain; (iv) functional dockingcalculations suggest a possible (and testable) identityfor the low-affinity domain. It also seems probablethat under conditions where CcP-IIh and CcP-IIrequilibriate that the Trp radical is reduced througha two-step process at the low-affinity domain. Onemight surmise that misplaced emphasis on reactivityat a single domain in part may be inspired byinappropriate use of the X-ray structure of the 1:1complex. Whereas, crystallization selects the leastsoluble species from a solution, this need not cor-respond to the most active species and certainly neednot be the only reactive one. The reasonable conclu-sion from this review itself is that new methods ofapproaching ET in protein-protein complexes haveopened a new era in this enterprise.

AcknowledgmentsThis work has been supported by the NIH through

Grants HL13531 (B.M.H.) and GM48043 (D.N.B.,J.N.O.). We thank Jeff Regan and Paul Beroza fortheir assistance in the preparation of Figures V.2 andV.3, respectively.

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