Electron Transfer Reactions of Cytochrome c - Advances in Chemistry

9 Electron Transfer Reactions of Cytochrome c N. SUTIN

Downloaded by PURDUE UNIVERSITY on September 29, 2013 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0162.ch009

Brookhaven National Laboratory, Upton, NY 11973

Cristallographic studies have shown that the heme group of cytochrome c lies in a crevice of the protein with an edge of the porphyrin ring located at the molecule surface. The cytochrome c self-exchange rate, as well as the rates of cyto chrome c oxidation-reduction reactions with metal com plexes and metalloproteins, are reviewed and interpreted in terms of a model in which electron transfer occurs through the exposed edge of the heme group. Comparison of ΔΗ and ΔS for metal complex-metal complex, metal complex -metalloprotein,and metalloprotein-metalloprotein reactions indicates that the metalloprotein reactions feature signifi cantly different activation parameters. The use of the Marcus equations and corrections to these due to work terms and non-adiabaticity are discussed. / C y t o c h r o m e c, a s m a l l h e m e p r o t e i n ( m o l w t ^ 12,400) is a n i m p o r t a n t member

of t h e m i t o c h o n d r i a l r e s p i r a t o r y c h a i n .

I n this c h a i n i t

assists i n t h e t r a n s p o r t of electrons f r o m o r g a n i c substrates t o o x y g e n . I n t h e course of this e l e c t r o n t r a n s p o r t t h e i r o n a t o m o f t h e c y t o c h r o m e is a l t e r n a t e l y o x i d i z e d a n d r e d u c e d .

O x i d a t i o n - r e d u c t i o n reactions are

thus i n t i m a t e l y r e l a t e d t o t h e f u n c t i o n of c y t o c h r o m e c, a n d its e l e c t r o n transfer reactions h a v e therefore b e e n extensively s t u d i e d . T h e reagents u s e d to p r o b e its r e d o x a c t i v i t y r a n g e f r o m h y d r a t e d electrons ( J , 2, 3) a n d h y d r o g e n atoms (4) to t h e c o m p l i c a t e d oxidase

(5, 6, 7, 8) a n d

r e d u c t a s e (9, 10, 11) systems. T h i s c h a p t e r is c o n c e r n e d w i t h t h e r e a c tions of c y t o c h r o m e c w i t h t r a n s i t i o n m e t a l complexes a n d m e t a l l o p r o t e i n s a n d w i t h the e l e c t r o n transfer m e c h a n i s m s i m p l i c a t e d b y these studies. Electron

Exchange

Reactions

T h e s i m p l e s t e l e c t r o n transfer r e a c t i o n t h a t c y t o c h r o m e c c a n u n d e r go, a t least i n p r i n c i p l e , is t h e self-exchange r e a c t i o n . T h e rate o f this 156

In Bioinorganic Chemistry—II; Raymond, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1977.

9.

suTiN

Electron Transfer Reactions of Cytochrome c

157

r e a c t i o n is c o m p a r e d w i t h o t h e r e l e c t r o n e x c h a n g e reactions i n T a b l e I . T h e electron exchange between ferrocytochrome c a n d ferricytochrome c is n o t p a r t i c u l a r l y fast. F o r e x a m p l e , the c y t o c h r o m e c e l e c t r o n e x c h a n g e is m u c h less r a p i d t h a n e l e c t r o n e x c h a n g e of t h e b i p y r i d i n e or p h e n a n t h r o l i n e complexes of i r o n o r r u t h e n i u m . I n d e e d the e l e c t r o n e x c h a n g e rate of c y t o c h r o m e c is v e r y s i m i l a r to t h a t of t h e r u t h e n i u m h e x a a m m i n e couple.

T h e ΔΗ=¥ f o r the c y t o c h r o m e

c o u p l e at i o n i c s t r e n g t h 0 . 1 M

( t h e " p h y s i o l o g i c a l " i o n i c s t r e n g t h ) is s o m e w h a t m o r e p o s i t i v e a n d t h e AS=¥ less n e g a t i v e t h a n f o r t h e h e x a a m m i n e r u t h e n i u m e x c h a n g e

and


o t h e r c o m p a r a b l e systems. A q u e s t i o n arises as to w h y t h e c y t o c h r o m e c m o l e c u l e is so c o m p l i c a t e d w h e n one c a n o b t a i n r e l a t i v e l y r a p i d elec t r o n transfer w i t h v e r y s i m p l e m e t a l complexes. T h e s t r u c t u r e of c y t o c h r o m e c d e t e r m i n e d b y D i c k e r s o n a n d h i s colleagues

(23, 24, 25, 26)

is d e p i c t e d i n F i g u r e 1.

T h e heme group,

w h i c h lies i n a c r e v i c e of the essentially g l o b u l a r p r o t e i n , is c o v a l e n t l y b o n d e d to t h e p r o t e i n b y t h i o e t h e r b r i d g e s b e t w e e n t h e p o r p h y r i n r i n g a n d t w o cysteine residues i n the p e p t i d e c h a i n . T h e i r o n a t o m is s i t u a t e d

Figure 1.

Skeleton of horse heart ferricytochrome c. Adapted from Ref. 26, Figure 8.


158

BIOINORGANIC C H E M I S T R Y

Table I .

Kinetic Parameters for

Reaction* 2

6

6

2

2 +

2 +

2 +

6

3

6

3

G

3

5

3


(M'

1

2

6

2

6

2

6

3

2 +

3 +

3

6

3

6

3 + 3 +

2 +

3

2 +

3

6

4

G

4

c

3

3

1

3

3

2 +

3

2 +

3

3

2 +

4

3 3

4

3 +

7

3 +

3

2 3

4

5

3 +

2

6

1

2

3 +

3 +

2 +

k sec' )

1 Χ 10" 3 Χ 10" 4.2 8.2 χ 1 0 3.6 Χ 1 0 5 Χ 10 4 Χ 10 3.0 Χ 1 0 25 9.6 Χ 10 1.2 Χ 10 1 X 10 ~ 10 3 Χ 10 ~ 10

V(H 0) + V(H 0) V(H 0) + V(H 0) Fe(H 0) + Fe(H 0) Ru(NH ) + Ru(NH ) Ru(NH ) + Ru(NH ) Ru(NH ) BzIm + R u ( N H ) B z I n r.3+ Co(phen) +Co(phen) Fe(EDTA) ' + Fe(CyDTA)" Fe(CN) - + Fe(CN) Fe(CN) - + Fe(CN) Hh(II) + H h ( I I I ) Hh(II) + H h ( I I I ) Fe(phen) + Fe(phen) Fe(phen) + Fe(phen) Ru(phen) + Ru(phen) 2

II

8

3 +

7

° H h , cytochrome c from horse-heart.

i n t h e p l a n e of the p o r p h y r i n r i n g w i t h the fifth a n d s i x t h c o o r d i n a t i o n sites o c c u p i e d b y a r i n g n i t r o g e n a t o m of h i s t i d i n e - 1 8 a n d the s u l f u r a t o m of m e t h i o n i n e - 8 0 . A n i m p o r t a n t feature of the s t r u c t u r e is that a n e d g e of t h e p o r p h y r i n r i n g is l o c a t e d at the surface of the m o l e c u l e .

This

f e a t u r e suggests a n e x p l a n a t i o n for the r e l a t i v e l y s l o w rate of the c y t o c h r o m e exchange r e a c t i o n . If i t is a s s u m e d that the e l e c t r o n occurs v i a the e x p o s e d e d g e of the h e m e g r o u p , t h e n the

exchange

cytochrome

reactions w i l l feature a steric or o r i e n t a t i o n f a c t o r w h i c h is not present to s u c h a degree i n the other reactions c o n s i d e r e d . I n terms of this i n t e r p r e t a t i o n the a c t u a l e l e c t r o n transfer occurs t h r o u g h t h e h e m e edge, a n d the s u r r o u n d i n g p r o t e i n acts as a n i n s u l a t o r . T h e steric f a c t o r f o r e l e c t r o n t r a n s p o r t is t h e n the area of the

exposed

h e m e e d g e d i v i d e d b y the surface a r e a of the c y t o c h r o m e c m o l e c u l e . T h e e x p o s e d h e m e area has b e e n e s t i m a t e d to b e a p p r o x i m a t e l y 3 %

of

the p r o t e i n surface. W e m i g h t expect a t o t a l l y e x p o s e d s y m m e t r i c a l h e m e g r o u p to t r a n s p o r t electrons a b o u t as w e l l as b i p y r i d i n e or p h e n a n t h r o l i n e , since b o t h

have

similar

structures a n d feature

n i t r o g e n a n d c o n j u g a t e d d o u b l e b o n d systems.

coordination

to

A c c o r d i n g l y , w e expect

t h e exchange reactions of horse-heart c y t o c h r o m e c to b e a p p r o x i m a t e l y (3 X

10' ) 2

2

o r 10" s l o w e r t h a n those of the i r o n b i p y r i d i n e or p h e n a n -

t h r o l i n e complexes.

3

T a b l e I shows t h a t this is a b o u t the rate r a t i o f o u n d .

T h e m o d e l f o r the c y t o c h r o m e c exchange r e a c t i o n at this p o i n t has the e l e c t r o n transfer o c c u r i n g t h r o u g h the exposed h e m e edge. T h e f u n c t i o n of the p r o t e i n is to p r o v i d e the correct r e d u c t i o n p o t e n t i a l of t h e m e t a l center a n d also to p r o v i d e the necessary s p e c i f i c i t y i n terms of


9.


SUTIN

Electron Exchange Reactions

μ μ μ μ μ

(25°C)

ΔΗ+ (kcal mol' )

Medium

—


b

-25 -11

—

μ-*0 μΟΛΜΚ* μΟ.Ι,ρΉ.7 /χ1.0,ρΗ7 μ — 0.2 1.84MNa,S0 μ~0.2

12 12,13 Π 15 is; is

—

9.3 10.3

—

5.1 4.0 8.5

-34 -25 -24

12.4 6.4 ~2

- 3 -19 20

—

References

-25

12.6

/ i 0.1

6

AS+ (e.u.)

1

2.0 0.10 0.55 0.013 0.10

159

oo

16 17 18 18 19, 20 20 21 22 21

—

—

4

- 2

—

~

-20

C o r r e c t e d for ionic s t r e n g t h .

s t r u c t u r e a n d c h a r g e d i s t r i b u t i o n so that the c y t o c h r o m e c c a n r e c o g n i z e its n a t u r a l reductase a n d oxidase. T h e next q u e s t i o n is w h e t h e r the c h a r g e d i s t r i b u t i o n i n the v i c i n i t y of the exposed h e m e e d g e is consistent w i t h the p r o p o s e d e l e c t r o n t r a n s f e r m e c h a n i s m . W h i l e horse-heart c y t o c h r o m e c carries n o net c h a r g e at p H 10, i t carries a net p o s i t i v e c h a r g e at n e u t r a l p H ( 2 7 ) .

T h e x-ray

s t r u c t u r e of horse-heart c y t o c h r o m e c shows that most of the p o s i t i v e l y c h a r g e d residues are l o c a t e d o n the surface of the m o l e c u l e ( 2 6 ) .

In

p a r t i c u l a r , l y s i n e residues 13, 27, a n d 79 are p o s i t i o n e d so t h a t t h e y i m p a r t a net p o s i t i v e c h a r g e to t h e r e g i o n of the p r o t e i n i n the v i c i n i t y of t h e e x p o s e d h e m e edge. I n d e e d , as D i c k e r s o n a n d T i m k o v i c h p o i n t out

(26),

a l l the c y t o c h r o m e s c w h o s e t h r e e - d i m e n s i o n a l structures are k n o w n h a v e a r i n g of p o s i t i v e c h a r g e a r o u n d the h e m e c r e v i c e .

Studies of the effect

of i o n i c s t r e n g t h o n the e l e c t r o n transfer reactions of c y t o c h r o m e c are consistent w i t h this charge d i s t r i b u t i o n . T h e results of these studies are p l o t t e d i n F i g u r e 2. (phen)

3

3 +

(curve

A)

T h e rate of r e a c t i o n of c y t o c h r o m e a n d its self-exchange

increase w i t h i n c r e a s i n g i o n i c s t r e n g t h . of

cytochrome

(curve B )

c with

reaction (curve

D)

Coboth

B y contrast, the r e a c t i o n rates

c w i t h t h e n e g a t i v e l y c h a r g e d reactants F e ( E D T A ) " 2

and F e ( C N )

6

3

" (curve C )

decrease

w i t h increasing ionic

strength. I n t e r e s t i n g l y e n o u g h , i o n i c s t r e n g t h seems to h a v e o n l y a v e r y s m a l l effect o n t h e r e a c t i o n rate of horse-heart f e r r o c y t o c h r o m e

c with

f e r r i c y t o c h r o m e c 551, a b a c t e r i a l c y t o c h r o m e f r o m Pseudomonas aeriginosa ( c u r v e Ε ). T h e latter c y t o c h r o m e is b e l i e v e d to c a r r y a net n e g a t i v e c h a r g e at n e u t r a l p H

(34).



160


0.3

0.4

0.6

0.5

II

0.7

Figure 2. Ionic strength dependence of the electron transfer rate constants. (A) Co(phen) + Hh(II) (28); (B) Fe(EDTA) ' + Hh(III) (29); (C) Fe(CN) *' + Hh(II) (31) (see also (32)); (D) Hh(II) + Hh(III) (19); (E) Hh(U) + Ps(III) (31). 3+

3

2

e

I f i t is a s s u m e d that t h e B r 0 n s t e d - B j e r r u m e q u a t i o n ( E q u a t i o n 1) logiofc =

logiofco +

ZAZBV^

(1)

o b t a i n s i n these systems ( a n d i t v e r y p r o b a b l y does n o t ) t h e n f o r m a l charges of a p p r o x i m a t e l y 1 + a n d 2 + of r e d u c e d a n d o x i d i z e d c y t o c h r o m e

c a n b e a s s i g n e d to the a c t i v e sites c, r e s p e c t i v e l y

(Table II).

The

m a g n i t u d e s of these charges are n o t u n r e a s o n a b l e a n d a p p e a r consistent w i t h the structural data. Table II. Slope of Br0nsted—Bjerrum Plot for Some Horse-Heart Cytochrome c Reactions (25 ° C ) Charge Reaction

0

Hh(II) +Co(phen) F e ( E D T A ) ' + Hh(III) Hh(II) +Hh(III) Hh(II) + P s ( I I I ) 3

2

1

3 +

Slope

Hh(II)

+1.2 -3.4 +2.2 -0

+0.4 +1.0

Hh, horse-heart cytochrome c; Ps, Pseudomonas

Hh(III)

Reference 28 29 19 31

+1.7 +2.2

cytochrome

c

551.


9.

suTiN


161

Cross-reactions N e x t w e t u r n to the i n t e r p r e t a t i o n of t h e rate constants f o r e l e c t r o n transfer reactions of c y t o c h r o m e c t h a t are a c c o m p a n i e d b y a net c h e m i cal change of

(Tables III and I V ) .

cytochrome

c

with

both

*Ru[-(OSO 0) phen] -) 3

*Ru(bipy)

3

2 +

2

3

T h e rate constants f o r t h e r e a c t i o n

negatively

charged

(Fe(CN) L ~ 5

and positively charged ( F e ( b i p y ) ( C N )

4

2

and

3

2

+

and

) complexes c a n b e v e r y great.

M a r c u s has s h o w n (44, 45)

t h a t a r e l a t i v e l y s i m p l e r e l a t i o n exists


b e t w e e n the rate constants for reactions a c c o m p a n i e d b y a net c h e m i c a l change ( A G ° ^

0 ) a n d those for the c o m p o n e n t self-exchange reactions.

P r o v i d e d A G ° is not too n e g a t i v e , this r e l a t i o n i s : fc

12

where k

12

and K

12

=

(fciifc 2#l ) 2

2

(2)

%

are t h e rate a n d e q u i l i b r i u m constants, r e s p e c t i v e l y ,

for a n e l e c t r o n transfer r e a c t i o n a c c o m p a n i e d b y a n e t c h e m i c a l c h a n g e , a n d ku a n d k

22

are the c o r r e s p o n d i n g exchange rate constants. A n a n a l o

gous r e l a t i o n is e x p e c t e d entropies

to h o l d for the

activation enthalpies

and

(46). Aff

1 2

t =

ASiaf =

0.5 ( Δ ^ π ^ + Δ # * = + Δ # 22

0.5(AS += + n

Δθ

2 2

1 2

°)

(3)

* + AS °)

(4)

12

I n d e r i v i n g E q u a t i o n 2 i t is a s s u m e d that the w o r k terms r e q u i r e d to b r i n g together t h e v a r i o u s p a i r s of reactants are c a n c e l l e d . T h i s m a y b e a r e a s o n a b l e a s s u m p t i o n w h e n the cross-reaction i n v o l v e s s i m i l a r l y c h a r g e d reactants b u t c a n result i n a serious u n d e r e s t i m a t e of the crossr e a c t i o n rate w h e n o p p o s i t e l y c h a r g e d reactants are i n v o l v e d .

T h i s is

b e c a u s e the electrostatic i n t e r a c t i o n b e t w e e n the reactants i n t h e crossr e a c t i o n is a t t r a c t i v e w h e r e a s the i n t e r a c t i o n b e t w e e n the reactants is r e p u l s i v e i n t h e self-exchange reactions.

T h e cross-reaction w i l l , as a

c o n s e q u e n c e , p r o c e e d faster t h a n p r e d i c t e d b y the s i m p l e s q u a r e - r o o t r e l a t i o n i n w h i c h differences b e t w e e n the w o r k terms are n e g l e c t e d . I t is n o t a l w a y s easy to correct f o r t h e differences i n t h e electrostatic c o n t r i b u tions to t h e w o r k t e r m s , a l t h o u g h some progress is b e i n g m a d e i n this r e g a r d (47, 48).

T h e r e are also n o n e l e c t r o s t a t i c c o n t r i b u t i o n s to the w o r k

terms, a n d n e g l e c t of these m a y r e s u l t i n a n overestimate of t h e crossr e a c t i o n rate i n c e r t a i n systems (46).

T h e l a t t e r s i t u a t i o n arises w h e n one

exchange i n v o l v e s a h y d r o p h i l i c p a i r of reactants a n d the other e x c h a n g e r e a c t i o n a h y d r o p h o b i c p a i r of reactants.

U n d e r these c o n d i t i o n s

the

cross-reaction features a n u n f a v o r a b l e h y d r o p h i l i c - h y d r o p h o b i c i n t e r a c t i o n a n d w i l l p r o c e e d m o r e s l o w l y t h a n p r e d i c t e d b y E q u a t i o n 2.


162

BIOINORGANIC

Table III.

E° -

3

6

II

Observed and Calculated Rate Involving Cytochrome c and

Reaction Hh(II) + F e ( C N )

CHEMISTRY

(mv)

b

260,° 4 2 0

d

Hh(II) + F e ( C N ) C N S 3


5

Hh(II) + F e ( C N ) N 5

3

-

3

Hh(II) + F e ( C N ) P 0

3

Hh(II) + F e ( C N ) N H

3

5

5

260/240

e

2

'

260/ 540

2

'

260/330

e

e

Hh(II) + Fe(bipy) ( C N ) "

2 6 0 / 550

F e ( E D T A ) - + Hh(III)

120/260°

4

2

*Ru[ (OS0 ^) phen] - + Hh(III) 3

2

3

-

4

e

- 9 0 0 / 260°

° A t 0 . 1 M i o n i c strength, p H 6.8-7.2, a n d 2 5 ° C . b

0

d

T h e E° v a l u e s are the r e d u c t i o n p o t e n t i a l s for t h e t w o r e a c t a n t R e f . 37. C a l c u l a t e d f r o m Κ = 450, R e f . 35.

Table I V .

Observed and Calculated Rate Involving Cytochrome c and

Reaction *Ru(bipy) Hh(II) + Ru(NH ) 3

3

6

2 +

5

0

+ Hh(III) Fe(bipy) (CN)

-830/260° 2

+

+ Hh(III)

Ru(NH ) BzIm 3

E (mv)

2

2 +

2 +

51/260°

+ Hh(III)

Hh(II) + Co(phen)

couples.

3

1 5 0 / 260° 260/370°

3 +

° A t 0.1M i o n i c s t r e n g t h , p H 6.8-7.2, a n d 2 5 ° C . * R e f . 40. R e f . 37. ΔΗ° a n d Δ £ ° f o r H h ( I I I ) + X H ^ H h ( I I ) + H are - 1 4 . 4 k c a l m o l " a n d —28 e.u., r e s p e c t i v e l y , at 0.1M i o n i c strength, p H 7.0, 2 5 ° C . R e f . 42. R e f . 41. T h e r e d u c t a n t is t h e charge-transfer excited state of t h e R u ( I I ) c o m p l e x . 0

2

+

d

e

1


1

9.

163


suTiN

Constants for Electron Transfer Reactions Negatively Charged Reactants a

k(25°) (M' sec )


1

obsd. obsd. calcd. obsd. obsd. calcd. obsd. calcd. obsd. calcd. obsd. calcd. obsd. calcd. obsd. €

f

0

h

1.2 8.0 8 1.0 9.0 2 3.0 2 2.5 4 1.6 3 2.6 7 1.2

ΔΗ+ (kcal mol' )

1

Χ Χ Χ χ Χ Χ Χ X Χ Χ Χ Χ Χ Χ Χ

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

1

6

References

1.1

-26 -24

31 32

1.2 2.9

-23 -22

32 32

1.2

-21

32

2.4

-22

32

- 0

7

ASf (e.u.)

4 7 5

r

3 7

t

6 6

t

4

32

8

r

7 4

6.0

-18

29

4.4

+2

33

4 9

h

R e f . 86. E x c h a n g e rate d a t a f r o m R e f . 36. R e f . 38. T h e r e d u c t a n t is t h e charge-transfer e x c i t e d state of the R u ( I I ) c o m p l e x .

Constants for Electron Transfer Reactions Positively Charged Reactants a

k(25°) (M sec ) 1

obsd. obsd. obsd. calcd. obsd. calcd. obsd. calcd.

< 2 1.9 3.8 1.2 5.8 6.3 1.5 2.0

1

χ Χ Χ χ Χ Χ Χ Χ

10 10 10 10 10 10 10 10

AHt (kcal mol' ) 1

ASf (e.u.)

References 33' 32 39

8 8 4 5

2.9 7

-28 -14

11.3 11.1

- 6 - 6

58 58 28 h

4 4

3 3

' U s i n g AH° a n d Δ £ ° f r o m R e f s . 37 a n d Jfl. AH° a n d AS° f o r R u ( N H ) + &H τ± R u ( N H ) e + H are —5.8 k c a l m o l a n d - 1 4 . 2 e.u., r e s p e c t i v e l y , a t 0 . 5 - 1 . 0 M ionic strength, 2 5 ° C . U s i n g Δ # ° a n d Δ £ ° of 4.66 k c a l m o l " a n d + 2 4 . 4 e.u., r e s p e c t i v e l y , f o r t h e Hh(II) + Co(phen) ^± H h ( I I I ) + C o ( p h e n ) reaction i n 0.05M phosphate, p H 6.8, 2 5 ° C , R e f . 41. R e f . 58. 3

3

2 +

+

- 1

Λ

1

3

3 +

3

2 +

1


6

3 +

2

164

BIOINORGANIC

CHEMISTRY

II

A s e c o n d a s s u m p t i o n m a d e i n the d e r i v a t i o n of E q u a t i o n 2 is that a l l of the reactions i n v o l v e d i n the rate comparisons

are a d i a b a t i c , that is,

t h a t the e l e c t r o n transfer occurs w i t h u n i t p r o b a b i l i t y o n c e t h e reactants h a v e a t t a i n e d the a p p r o p r i a t e n u c l e a r configurations. cussed p r e v i o u s l y (44, 45, 46, 49),

A s has b e e n d i s

the a c t u a l e l e c t r o n transfer occurs i n

t h e i n t e r s e c t i o n r e g i o n of the reactants' p o t e n t i a l e n e r g y c u r v e w i t h t h e p r o d u c t s ' p o t e n t i a l e n e r g y c u r v e . E s s e n t i a l l y w h a t is a s s u m e d is that the s p l i t t i n g i n the i n t e r s e c t i o n r e g i o n is large e n o u g h so that t h e

system


r e m a i n s o n the l o w e r p o t e n t i a l e n e r g y surface o n p a s s i n g t h r o u g h t h e intersection region. T h e p r o b a b i l i t y that the system w i l l r e m a i n o n this l o w e r p o t e n t i a l e n e r g y surface c a n b e c a l c u l a t e d f r o m the L a n d a u - Z e n e r f o r m u l a ( E q u a tion 5).

I n this expression,

2E

is t h e s p l i t t i n g at the

I f I I

, p

Sj a n d s

u

=

Γ -4τγ Ε 2

-

1

e

x

p

(si

=

2

Ί

L^^Wj

are the slopes of t h e z e r o - o r d e r

the intersection

ϊ λ ι

(5)

p o t e n t i a l e n e r g y surfaces

for a n e x c h a n g e r e a c t i o n ) ,

—s

u

intersection,

at

a n d ν is t h e

v e l o c i t y w i t h w h i c h the p o i n t r e p r e s e n t i n g t h e system m o v e s t h r o u g h t h e intersection region. interactions Ei

tU

F o r t y p i c a l c o n d i t i o n s i t is f o u n d that ρ ^

of m o r e t h a n 0.5 k c a l m o l "

1

(50).

1 for

U n d e r these c o n d i t i o n s

the reactions w i l l b e a d i a b a t i c , a n d the square root r e l a t i o n is e x p e c t e d to h o l d p r o v i d e d E

I > n

is n o t too large. H o w e v e r , for s m a l l E i , n :

nv\Si —

s\ u

a n d E q u a t i o n 2 w i l l as a c o n s e q u e n c e also b e satisfied b y those n o n a d i a b a t i c reactions

(small Ει,π)

for w h i c h the i n t e r a c t i o n e n e r g y i n t h e

cross-reaction is a p p r o x i m a t e l y e q u a l to the g e o m e t r i c m e a n of the i n t e r a c t i o n energies i n the c o r r e s p o n d i n g e x c h a n g e reactions ( E q u a t i o n s 7, 8 ). , I l ) l 2 = [ (El,ll) 11 ( E i n ) 2 2 ] i

(PllP22)

Pl2 —

(7)

1/2

(8)

1/2

I n other w o r d s , the square-root r e l a t i o n m a y also h o l d for c e r t a i n classes of n o n d i a b a t i c reactions

reactions

(51).

obeys the square-root

Conversely,

the fact

that a series

of

r e l a t i o n does not r e q u i r e that a l l of

t h e reactions i n v o l v e d be a d i a b a t i c . C o n f o r m i t y w i t h E q u a t i o n 2 also does not r u l e out m o r e c o m p l e x mechanisms

(28).

T h i s m a y b e i l l u s t r a t e d b y c o n s i d e r i n g the o x i d a t i o n

of f e r r o c y t o c h r o m e c b y C o ( p h e n )

3

3 +

. L e t us assume that the


reactive

9.

165


suTiN

f o r m of f e r r o c y t o c h r o m e c is not the n a t i v e p r o t e i n b u t is i n s t e a d a c o n f o r m e r t h a t exists i n r a p i d e q u i l i b r i u m w i t h the n a t i v e f o r m . H h ( I I ) ^± H h ( I I ) *

K

u

H h ( I I I ) + H h (II) * — H h (II) * + H h ( I I I ) Co(phen)

3

3 +

+ H h ( I I ) * ^± C o ( p h e n )

n

+ Hh(III)

2 +

3

/c * k *,K * 12

12

I n terms of the a b o v e scheme, the o b s e r v e d rate constant f o r the o x i d a t i o n


of f e r r o c y t o c h r o m e b y C o ( p h e n )

/ci2 =

fc

n

and K

12

is g i v e n b y :

3 +

K ki * u

-

where

3

2

Xii(fcil*fc22#12*)

=

K

^ -

=

(fciifc ifl2)

U

%

k ^-J 22

22

%

are t h e o b s e r v e d exchange rate constant a n d e q u i

l i b r i u m constant, r e s p e c t i v e l y .

E v i d e n t l y the p r e - e q u i l i b r i u m constant

cancels, a n d the n o r m a l square-root r e l a t i o n obtains.

Agreement

with

E q u a t i o n 2 thus does n o t p r e c l u d e a r a p i d c o n f o r m a t i o n a l c h a n g e ferrocytochrome

c

(and/or

ferricytochrome

c)

p r i o r to t h e

on

electron

transfer step. W i t h these reservations i n m i n d , w e c a n c o m p a r e

observed

and

c a l c u l a t e d rate constants. W h e r e a p p r o p r i a t e , the f u l l M a r c u s expression, w h i c h i n c l u d e s the l o g / t e r m ( E q u a t i o n 9 ) , has b e e n u s e d i n t h e c a l c u l a t i o n of the e l e c t r o n transfer rates. .

(logi£i ) 2

l o g /

"-41o (fe 8

1 1

2

( Γ ί λ

( 9 )

Wg')

T a b l e I I I shows that the c a l c u l a t e d rates are 1 0 - 1 0 2

3

times faster

t h a n t h e o b s e r v e d rates for t h e complexes w h i c h c a r r y a r e l a t i v e l y h i g h n e g a t i v e charge ( F e ( C N )

6

3

~ and F e ( C N ) N 5

3

3

~ ) a n d that the agreement

b e t w e e n the o b s e r v e d a n d c a l c u l a t e d rates i m p r o v e s as the c h a r g e o n the c y a n o i r o n ( I I I )

complex

decreases.

T h i s t r e n d suggests

that the

e n h a n c e d rates for these complexes are c a u s e d b y electrostatic effects, a n d i n d e e d there is g o o d e v i d e n c e c y t o c h r o m e c (52, 53, 54, 55),

that f e r r i c y a n i d e is s t r o n g l y b o u n d

to

p r e s u m a b l y i n the v i c i n i t y of t h e h e m e

g r o u p (53, 54, 55). A l s o , the c a l c u l a t e d rate constant for the F e ( E D T A ) 2

Hh(III)

r e a c t i o n is l a r g e r t h a n the

observed

value.

This may

be

e x p l a i n e d b y p o s t u l a t i n g that, f o r this r e a c t i o n , t h e n o n e l e c t r o s t a t i c c o n t r i b u t i o n s o u t w e i g h the electrostatic c o n t r i b u t i o n s to t h e w o r k t e r m s . T h e effect is, h o w e v e r , s m a l l .


166


II

N o n c a n c e l l a t i o n o f t h e electrostatic w o r k terms is p r e s u m a b l y less i m p o r t a n t f o r t h e reactions o f c y t o c h r o m e c w i t h t h e p o s i t i v e l y c h a r g e d c o m p l e x e s s h o w n i n T a b l e I V . I n d e e d i t is a p p a r e n t f r o m T a b l e I V t h a t t h e r e is excellent a g r e e m e n t b e t w e e n t h e o b s e r v e d a n d c a l c u l a t e d rate constants a n d a c t i v a t i o n p a r a m e t e r s f o r t h e R u ( N H ) B z I m 3

a n d f o r the H h ( I I ) - C o ( p h e n )

3

3 +

5

and C o ( p h e n )


hydrophobic.

3

-Hh(III)

reactions. T h i s r e s u l t is n o t u n e x p e c t e d

i n v i e w of t h e fact that, of t h e reactants c o n s i d e r e d , 3 +

2 +

Ru(NH ) BzIm 3

5

2 +

are b o t h p o s i t i v e l y c h a r g e d a n d , at least t o s o m e extent,

These properties should favor cancellation of the electro

static as w e l l as of the n o n e l e c t r o s t a t i c c o n t r i b u t i o n s to t h e w o r k terms f o r t h e cross-reaction since t h e h e m e g r o u p of c y t o c h r o m e c is h y d r o p h o b i c , a n d t h e v i c i n i t y o f its e x p o s e d e d g e is p o s i t i v e l y c h a r g e d .

Conversely,

t h e excellent a g r e e m e n t of t h e o b s e r v e d a n d c a l c u l a t e d rates is s t r o n g evidence

that t h e H h ( I I ) - H h ( I I I )

exchange,

like

these

reactions, features e l e c t r o n transfer t h r o u g h t h e e x p o s e d

t w o crossheme

edge.

M o r e o v e r , g o o d o v e r l a p of t h e p o r p h y r i n w i t h t h e b e n z i m i d a z o l e a n d p h e n a n t h r o l i n e π-systems is l i k e l y , a n d this s h o u l d ensure that t h e crossreactions w i l l b e a d i a b a t i c ( o r at least t h a t p

12

=

(ρηΡ22) )· 1/2

K i n e t i c d a t a f o r e l e c t r o n transfer b e t w e e n t w o m e t a l l o p r o t e i n s a r e p r e s e n t e d i n T a b l e V . T h e rate constants a n d a c t i v a t i o n parameters f o r the P s ( I I ) - P s ( I I I )

and Az(I)-Az(II)

exchange reactions w e r e c a l c u

l a t e d f r o m t h e k i n e t i c d a t a f o r t h e first three reactions Κ ~

1, Δ Η ° ~

Hh(II)-Ps(III)

0, AS° ~

(for which

0; i n a d d i t i o n , t h e rate constant f o r t h e

r e a c t i o n is i n d e p e n d e n t of i o n i c s t r e n g t h ( 3 1 ) ) . T h e

c a l c u l a t e d exchange d a t a w e r e t h e n u s e d to p r e d i c t the k i n e t i c p a r a m e t e r s for the P s ( I I ) - A z ( I I )

r e a c t i o n . A s is e v i d e n t f r o m T a b l e V , t h e agree

m e n t of t h e o b s e r v e d a n d p r e d i c t e d p a r a m e t e r s is satisfactory, p a r t i c u l a r l y since the P s ( I I ) - A z ( I I ) r e a c t i o n has a r e l a t i v e l y c o m p l e x m e c h a n i s m ( 57 ) i n v o l v i n g c o n f o r m a t i o n a l changes o n b o t h Ps ( I I I ) a n d A z ( I ) .

Table V . Observed and Calculated Rate Constants for Electron Transfer Reactions betwen T w o Metalloproteins" k(25°) (Mr sec' )

Reaction Hh(II) + Hh(III) Hh(II) +Ps(III) Az(I) + H h ( I I I ) Ps(II) + P s ( I I I ) Az(I) + Az(II) Ps(II) + Az(II) Ps(II) + Az(II)

1

obsd. obsd. obsd. calcd. calcd. calcd. obsd.

1.2 7.9 1.7 5.2 2.4 1.1 6.1

1

χ Χ Χ Χ Χ X Χ

10 10 10 10 10 10 10

3

4 3 6 3 5 6

ΔΗ4= (kcal mol' ) 1

12.4 12 13.4 11.6 14.4 13.0 7.8

(e.u.) - 3 0 1 3 5 4 -1

Refer ences 19, 20 31 56

57

" A t p H 6.8-7.2 a n d 2 5 ° C . T h e s y m b o l s H h , A z , a n d P s d e n o t e h o r s e - h e a r t c h r o m e c, a z u r i n , a n d Pseudomonas c y t o c h r o m e c 551, r e s p e c t i v e l y .


cyto

9.

20

Ί—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—Γ

ο

I0

ο ο

9

0

©3

.8

•2 • 13

°5

J4

Η 15

ο o7

χ


167


suTiN

oil

Electron Transfer Reactions of Cytochrome c - Advances in Chemistry

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