240 - Electrochemical studies of cytochromes c

Biodeclrochbzistry

and

Bioanarptics

240 - Electrochemical by

~fICHAEL

Studies

D. RYXKO

5,

478-

of

482(1g78)

Cytochromes

and BENJAXUN

c *

A_ FEINBERGOO

0 Marquette University. Todd \Vehr Chemistry Bldg. Milwaukee, \Vi. 53233 “0 University of \Visconsin, 3filwaukee. Dept. of Chemistry-. Milwaukee, Wi. 53201 (USA)

Manuscript

received

February

zSth 1975

. methods were developed and used to study with horse cytochrome c and Rhodos~iriUunr nrbrrsm cytochrome c2. These experiments served to demonstrate experimentally that for non-binding non-physiological redos agents. it is the overall protein charge that determines the kinetic-ionic strength relationships and not the localized charge of the presumed site of electron transfer. A theoretical discussion for earlier misconceptions of the simplified DEBYE-H~~CKEL theory is presented. This newchronoamperometric approach to kinetics affords a relatively simple methodology for doing otherwise difficult kinetic studies under anaerobic conditions with easily autooxidizable redox agents such as ferrous-EDTA’. the

Chronoamperometric reaction of iron-EDTA

Introduction The study of the redox kinetics of oxidation-reduction proteins small non-physiological redos agents has come to be a mechanistic tool of considerable importance during the last decade. Many of these studies are done with highly autooxidizable reductants such as ferrous EDTA and hesammine ruthenium with stopped flow kinetic methods which are difficult to do from a purely technical point of view. From these previous studies, the observed variation of the kinetic rate constants of proteins with ionic strength using small non-binding redox agents or proteins has been used to determine the charge on the presumed site of electron transfer. In the following work, which used chronoamperometry as the kinetic probe, the problems associated with earlier approaches to kinetic-ionic strength studies are discussed from a theoretical and experimental perspective to shed new light on their utility in the determination of the charge and location of .electron transfer sites. with

istry,

c Discussed at the 4th International Symposium Woods Hole (brass.). z-S October 1977.

on

Bioelectrochem-

Electrwhemical

Iollie

Studies

of Cytochromes

c

479

mlatloJuhips

strength-kinetic

The interaction of charged species in solution has been the object of considerable study since early this century. The most well known theory that has been used is based on the DEBYE-H~~CKEL theory of electrolytes. The form bmost commonly used in ehTerimental studies is called the simplified DEBYE-HUCKEL equationl. equation (I),

where z,4. 213are the charge on reactants A and B respectively, k is the observed rate constant at a given ionic strength, I, and k, isthe rate constant at zero ionic strength. By using this expression in the study of redox proteins, some workersf-4 have calculated values of protein charge which was significantly smaller than the probable protein charge. This charge has been attributed to the charge of the electron transfer site, even though there is no theoretical justification for this. The fallacy of this approach can be seen from examining the assumptions in the derivation of equation (I). The DEBYE-H%KEL espression was derived by assuming that the effect of the ionic atmosphere on the reaction rates can be accounted for in a single term, AG,+, AGr* = Gr* -

GI* -

GI*

(4

to the where GP, GP and GIB are the ionic atmosphere contributions It free energy of the transition state, reactant A and B, respectively. should be pointed out that there is a separate term for the. coulombic repulsion or attraction between the charged reactants and the transition By using the .D,EBYE-H~~CKEL model for ionic solutions, the acstate. tivity coefficient, f, can .he correlated to fhe ionic strength. l Since In f = GIRT, the change in free energy as a function of ionic strength can be Finally, using transition state theory, the rate constant, khcan derived. be correlated to AGr* and this leads to the complete form of the DEBYEH~CKEL equation,6 equation (3). In k = In k, +

(ZA

-t I+xR*

ZB)”

a

zA%

17 -

I+XRA

u

ZB% -

fl

I+%&

are the where a = 1.02,~x = 0.329 fl A-l, the R’s in the denominators radii of the transition state and of the reactants. respectively, and all other terms have been previously defined. If XR 4 I, then the. simplified form of the DEBYE-H~~CKEL equation, equation (I), is obtained. But for proteins, where R is about 15 A, the denominator differs significantly from unity at ionic strengths usually used in these kinds of studies. This can be seen in Table I. Thus, the denominators in equation (3) +re not only different from unity but are significantly different from each other even for the small redo-u molecules.

Ryan

480

Feinberg

and

In addition to equation (I), there are two other forms of the DEBYEequation that are often used. The first simplification involves assuming all the radii are equal. This leads to equation (4). HUCKEL

2 ZA ZB &-

In k = In k, +

(4)

I+&-

This equation is fairly accurate for ordimary chemical reactions but leads to considerable error for small molecule-protein reactions as can be seen in Table I. The other way of simplifying equation (3) is to assume that only XRB is much less than unity.6 This equation is shown below: In k = In k, +

(2

Hzg2) a r 1+X&,

zA ZB-

This equation is strictly true only at low ionic strengths (Table I). The analysis of these equations indicates that it is necessary to use the fuU form of the DEBYE-H&KEL equation if one is using transition state theory to analyze the data. In particular the deviations are considerable for equation (I). Equations (4) and (5) are much more accurate than equation (I), with equation (5) being the best of the simplified forms, especially at low values of ionic strength. Table

I. Effect of radii and ionic strength

R L-i)

T _-

on the denominators -

I

.-

0.01

1.20

0.X

1.67

0.01

I.49

0.1

2.36

j I

I-l-d2

-

of equation

(3)_

-.

An alternate approach has been derived by GRAY and WHERLXSD,~ which is based on &IARCUS theory kinetics rather than transition state kinetics. Using this approach, the following In k-ionic strength expression was obtained: In k = ln k, -

3-576

exp (--&A) I+dB

+

exp_(--fiB) -It'dA

Ii

ZA

ZB (6)

RA+RB

I

where k, is the rate constant at infinite ionic strength. In this case, the free energy has been partitioned between eIectrostatic and non-electrostatic terms and this expression incorporates all the electrostatic effects

Electrochemical

Studies

of Cytochromes

t

481

:

on the rate constant, including the coulombic interactions-of the react&ts. Five equations have been shown here which canzbe ‘used to correlate the variation of the rate constant with ionic strength_ The first fqur.are derived from transition state theory and involve different dkgrees’-6f simplification of the DEBYE-H~CKEL theory; while. the last equation (6). involves a different approach to r-action kinetics. These equations will be used in this work to analyze the kinetic-ionic strength data from two proteins that have identical charges around the presumed site of, electron transfer. ExpMmental Both horse cytochrome c and Rhodospi&%m% rub~utzr cytochrome. cp The chronoamp-erowere prepared by methods previously described.’ metric methodology including a discussion of the catalflic case and the preparation of the EDTA complex is, described in detail by RYAN ef aL8 The ionic strength-rate constant data for cytochromes i: and c2 and its interpretation can be found in FEINBERG et uL7 Ffepnltsand dIscussion

:

Horse cytochrome c has a calculated overall charge. of +-g, ,when the unit charges of acidic and basic residues of the primary sequence are. summed at pH 7; likewise; the calculated overall charge, zpn, for. cytoThese overall charges can be compared to the char@ chrome c, is +3. calculated on the basis of equations (I) and (3)-(6) in Table z... If the full DEB--H~~CKEL equation (3), is simplified such that both radii a¬ considered [equation (I)], very low values of the calculated overall ‘charge .ex@ssion~ and were obtained. However, when the full DEBYE-_H~CJCEL any of the other simplified forms were used, then higher. values of 2; which were reasonably close -c&‘z,; were obtained. Excellent agreement waS also obtained for the GR_~Y-WHERLKND equqtion [e’quation (6)]. I. It is known that the heme edge region of. both cytochrome c :&nd. cytochrome cg are nearly identical, s but the overall ~calculated~charges ‘L: are quite diflerent. The remarkable agreement between the calculated charge; z,, and the charges calculated from the -GRAY-WHERLACD equation and the DEBYE-H~~CKEL equations that- take’ into’- account. or= or both of the radii indicate clearly that it is the-‘oveiall charge of the reactants, and more critically the overall charge of the protein,, that controls the observed kinetic-ionic strength effects. It is further concluded that in the case of non-binding small molecule redox dgents, the kineticionic strength effects do not reflect the influence of 1ocalized”‘charge and thus cannot be used to probe the charge of the region ‘of elt5ctron transfer_ An additional consideration which make%’ the. local&d -charge effect less plausible is that the charges on the otherside of the- protein are not well shielded by the protein because of the. very low-dielectric of the interior of the protein. Thus, the smaller charges calculated by the simplified DEBYE-H~~CKEL equation are due to the.- appro,xima-

Ryan

482

Table H~~CKEL

z_

and Feinherg

Calculation of the protein charge from various equation and the GRAY ~IHERLAKD equation. ._

cytochrome

t

cytochrome

9 1

2.2

I

0.6

"cq.3

IO-7

I

I.0

zcq.4

12.9

zcq.1

rather

than

any

cz

2 .i I 2.3

10.0

zcq.6

of the DEBYE-

3

8.1

tions involved chemistry.

forms

fundamental

of their

interactions

redos

Acknowledgements Both B.A.F. and M.D.R. acknowledge the Donors of the Petroleum Research Fund, administered by the American Chemical Society. for B.A.F. also gratefully acknowledges partial support of this research. the Research Corp. and t\vo awards from the University of WisconsinMilwaukee Graduate School Research Committee in support of this research_ References C.H. I.D. CLARK and R.P. \VAYNE, in Compralransizra Clrar~ricnl Kitadics, B_IMFORD and C.F.H. TIPPER (Editors), Xew York (1969) vol. 2, p. 315-328 1V.G. MILLER and KA. CUSASOVICH, Biophys. Strztcl. M~cJranism 1, 97 (1975) I._\. MIZRAHI. F.E. \VOOD and b1.A. CUSANOVICH, Biochsmistry 15, 343 (1976) L. HODGES, R-A. HOLWERDA and H.B. GRAY, J_ Anr. Chsnr. Sot. 96, 3132

(I974 S. \VHERLAND and H.B. GRAM, Proc. Natl. Acad. Sci. USA 73, 2950 (1976) 1V.H. KOPPEXOL, Ph. D. Thesis, University of Utrecht, 1978 B.A. FEISBERG, M.D. RYAN and J.-F. \%'EI,Biochnt. Bio$?zys. Rss. Co~~~trru~~. 79, 769 (1977) ALD. RYXS, J--F.

lication F.R SXLEWIE,

\VEI, B.A. FEINBE~G

J. KRAUT

and MD.

and Y.-K.

KAJIEX,

J. Biol.

LAU,

submitted

Chsm.

for pub-

248, 7701 (1973)