Mechanism of Rapid Electron Transfer Reactions Involving Cytochrome Bc1, Cytochrome C and Cytochrome Oxidase Jeremy Erik Durchman University of Arkansas, Fayetteville

University of Arkansas, Fayetteville ScholarWorks@UARK

Theses and Dissertations

8-2016 Mechanism of Rapid Electron Transfer Reactions involving Cytochrome bc1, Cytochrome c and Cytochrome Oxidase Jeremy Erik Durchman University of Arkansas, Fayetteville

Follow this and additional works at: http://scholarworks.uark.edu/etd Part of the Biochemistry Commons, and the Organic Chemistry Commons

Recommended Citation Durchman, Jeremy Erik, "Mechanism of Rapid Electron Transfer Reactions involving Cytochrome bc1, Cytochrome c and Cytochrome Oxidase" (2016). Theses and Dissertations. 1743. http://scholarworks.uark.edu/etd/1743

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! a! Though cytochrome c is not itself an enzyme of the electron transfer chain, its

significance is hardly overstated. The 12 kDa heme protein functions primarily as a

mobile electron shuttle between complexes III and IV, but is also the electronic recipient

in numerous other physiological redox pathways. Cytochrome c is discussed further in

chapters 2 and 3.

Complex IV (cytochrome c oxidase) is at the sequential end of the mitochondrial

electron transfer chain. The reducing equivalents passed from complexes I or II through

complex III are the terminal recipients of molecular oxygen, producing H2O. Complex

IV has a mass of over 160 kDa and consists of more than 10 subunits [2]. It contains two )D+8*,#!9*,!*!-)0#120*%!<#+&96!)3#%!GeZ;O*!*$8!1)$,+,6,!)(!-)%#!69*$!GZ!,2:2$+6,.!!C6!

different heme and copper cofactors (hemes a and a3, and CuA and CuB). Reducing 1)$6*+$,!6<)!7*+%,!)(!8+((#%#$6!9#-#!*$8!1)77#%!1)(*16)%,!>9#-#,!*!*$8!*N4!*$8!1)77#%!

equivalents are passed sequentially from CuA to heme a, then to the binuclear center of 1#$6#%,!U2?!*$8!U2fB.!_0#16%)$,!(%)-!1'6)19%)-#!1!*%#!7*,,#8!,#52#$6+*00'!(%)-!U2?!6)!

heme a3 and CuB. Stoichiometrically, complex IV pumps four protons across the 9#-#!*4!69#$!6%*$,(#%%#8!6)!69#!:+$210#*%!1#$6#%!)(!9#-#,!*NR!U2f.!!H%)-!*!,6)+19+)-#6%+1! membrane for every four electrons passed through the complex, additionally taking up ,6*$87)+$64!U)-70#D!Cc!72-7,!()2%!7%)6)$,!*1%),,!69#!-#-:%*$#!()%!#3#%'!()2%!#0#16%)$,! four protons from the matrix side to reduce one equivalent of molecular oxygen [2]. 7*,,#8!69%)2&9!69#!1)-70#D.!!@9#!)3#%*00!%#*16+)$!1*$!:#!<%+66#$!*,g!

L! TheI proton gradient establishedL! by the electron transfer chain yields an energetic YK >+$B!L![# !L!/"!IIP!"K"/!L![K >)26B!>"B.!!!

! potential@9#!7%)6)$!&%*8+#$6!#,6*:0+,9#8!:'!69#! consisting of both an electrical (!-+6)19)$8%+*0!) and concentration#0#16%)$!6%*$,(#%!19*+ difference across the$!'+#08,!

*$!#0#16%)19#-+1*0!7)6#$6+*04!<+69!:)69!#0#16%+1*0!*$8!1)$1#$6%*6+)$!+-7#62,#,!*16+$&!*,!*!inner membrane. As originally proposed by Peter Mitchell [3] (who later won the nobel

8%+3+$&!()%1#!()%!7%)6)$,!6)!(0)

T):#0!<+$$+$&!69#)%'4!6may be expressed as9#!(%##!#$#%&'!8+((#%#$1#!*1%),,!69#!+$$#%!-# a term accounting for both factors of the electrochemical-:%*$#!-*'!:#! potential

#D7%#,,#8!*,!*!6#%-!*11)2$6+$&!()%!:)69!(*16)%,!)(!69#!#0#16%)19#-+1*0!7)6#$6+*0!*,g!as: !

" [c2]% !G = RT ln$ ' + ZF!( # [c1]& !

<9#%#!1G!*$8!1"!*%#!69#!%#,7#16+3#!1)$1#$6%*6+)$!)(!69#!,7#1+#,!*1%),,!69#!-#-:%*$#\!i!+,!

69#!19*%&#!)$!69#!,7#where c1 and c2 are1+#,\!*$8!H!+,!H*%*8*'h,!1)$,6*$ the concentration of the species4 6!)(!Xe4[Ya across the! UR-)0#!#0#16%)$,membrane, Z is the!> NBcharge.!!

F+$1#!69#!1)$1#$6%*6+)$!&%*8+#$6!+$!69+,!1*,#!+,!69*6!)(!JKon the species, and F is Faradays constant. Since the concentrationLM!*$8!+,!692,!,+$&0'! gradient 7),+6+3#4is that of!

#52*6+)$!G.G!1*$!:#!,+-70+(+#8!6)gsingle-positively charged protons,! equation 1.1 can be simplified as:

+ " [H out ]% !G = RT ln$ + ' + F!( # [H in ] & !

C$!69+,!-*$$#%4!69#!7%)6)$!&%*8+#$6!#,6*:0+,9#8!:'!69#!#0#16%)$!6%*$,(#%!19*+$!+,!%#*8+0'!In this manner, the proton gradient established by the electron transfer chain is readily

26+0+=#8utilized!:'!?@ byA!,'$69*,#!6)!7%)821#!?@A ATP synthase to produce ATP.!!f'!*00)<+$&!7%)6)$,!6)!69#$!6%*3#0!:*1;!*1%),,! [2].

69#!-#-:%*$#!6)!69#!+$$#%!-+6)19)$8%+*0!-*6%+D4!69#!#$#%+1*00'!(*3)%*:0#!8+%#16+)$!)(!

! e!

5 L L 7%)6)$!-):+0+=*6+)$4!+.#.!9+&9!JK M!6)!0)

,2:2$+6!:'!%)6*6+$&!*!7)%6+)$!)(!69#!HZ!,2:2$+64!6#%-#8!69#!1I%+$&.!!@9#!%)6*6+)$!)(!69#!1I%+$&!

1*2,#,!69#!$210#)6+8#!:+$8+$&!,+6#,!)(!69#!HG!,2:2$+6!6)!,'$69#,+=#!?@A!(%)-!?OA!*$8!A+.!!

@9+,!(+$*0!120-+$*6+$&!7%)1#,,!1)$1028#,!69#!7%)1#,,!)(!-#6*:)0+,-4!*,!?@A!+,!69#!#$#%+1!

12%%#$1'!69*6!+,!2,#8!:'!69#!1#004!*$8!692,!69#!)%&*$+,-4!6)!1*%%'!)26!69#!3*%+)2,!(2$16+)$,!

$#1#,,*%'!()%!,2%3+3*0!>"4[B.!!!

!!!!!!!!!!!!

!!!!!!!!!!!

! !!! !

! !!!!!!!!!!!!!

!!!!!!!!!

! j! "#$%&'!()(*(!!!!!O#7+16+)$!)(!69#!3*%+)2,!1)$,6+62#$6,!)(!69#!-+6)19)$8%+*0!#0#16%)$! 6%*$,7)%6!19*+$.!!@9#!#$='-*6+1!1)-7)$#$6,!(2$16+)$!+$!)%8#%!6)!7%)821#!*$! #0#16%)19#-+1*0!-#-:%*$#!7)6#$6+*0!<+69!KL!72-7#8!(%)-!69#!-*6%+D!6)!69#! +$6#%-#-:%*$#!,7*1#4!<+69!#0#16%)$,!,#%3+$&!*,!#0#16%)&#$+1!:*0*$1#! !

! Y! ()+!!!!!,-.&/0%1.#/-!./!'2'1.&/-!.&3-45'&!

! C$!69#!7%#3+)2,!,#16+)$4!69#!,+&$+(+1*$1#!)(!#0#16%)$!6%*$,(#%!#3#$6,!6)!0+3+$&! 1.2 Introduction to electron transfer )%&*$+,-,4!*,!)112%!:#6<##$!69#!7%)6#+$!1)-70#D#,!)(!69#!#0#16%)$!6%*$,(#%!19*+$!6)!

&#$#%*6#!*$!K In theL!&%*8+#$6 preceding4!+,!-*8#!*77*%#$6.!!/:6*+$+$&!*!2,*:0#!#$#%&'!1)2%,#!+$!69#!()%-!)(! section, the significance of electron transfer events within and

*!19#-+1*0!,7#1+#,!,219!*,!?@A!7%)3+8#,!69#!)%&*$+,-!<+69!*!-#*$,!:'!<9+19!6)!,6)%#!between the protein complexes of the electron transfer chain is made apparent. In

#$#%&'!*$8!1)$6%)0!#$#%&'!1)$,2-76+)$!#((+1+#$60'.!addition to these processes, electron transfer between_0#16%)$!6%*$,(#%!:#6<##$!7%)6#+$! protein cofactors is a salient feature

1)(*16)%,of several4!*$8!69#! other1)270+$&!)(! metabolic conversions69+,!#0#16%)$! [1].%#0)1*6+)$! Moreover,6)! sinceKL!(0)< catalysis4!+,!*!,*0+#$6!(#*62%#!)(! of any kind involves

,#3#%*0!)69#%!-#6*:)0+1!1)$3#%,+)$,!the making or breaking of chemical>GB. bonds,!!@9#!7)+&$*$1#!*$8!%#0*6+3#!2:+52+6'!)(!#0#16%)$! which fundamentally involves the movement

6%*$,(#%!%#*16+)$,!of electrons from9*3#!8%+3#$! one chemical1)00#16+3#!,1+#$6+(+1!#(()%6,!6)! species to another, electron*112%*6#0'!-)8#0! transfer is in a sense69#,#!6'7#,! a )(!

,',6#-,.fundamental!!H2$8*-#$6*00'4! feature of69#!%*6#!)(!*!19#-+1*0!%#*16+)$! all biochemical processes. Typically,+,!%#0*6#8!6)!69#!?%%9#$+2,! the rate of a chemical

#52*6+)$4!<9+19!+$1)%7)%*6#,!69#!reaction may be related to the Arrhenius1)$1#76!69*6! equation,)-#!+$+6+*0!69#%-)8'$*-+1!92%80#! through the idea of overcoming some-2,6!:#!

)3#%1)-#!initial 6)!*19+#3#!*$!*16+3*6#8!,6*6#thermodynamic hurdle towards!6)!*19+#3#!69#! an activated transition1%#*6+)$ !state.)%!:%#*; This+$& may!)(! be*!19#-+1*0!

:)$8represented4!%#7%#,#$6#8!:'!69#!()00)<+$&!#52*6+)$g as: !

" !E $ k = Aexp A # RT % !

where EA is the activation energy, and A is a proportionality constant called the pre- <9#%#!_?!+,!69#!*16+3*6+)$!#$#%&'4!k!+,!69#!1)$,6*$6!Y.NG[a!lR>-)0R`B4!@!+,!6#-7#%*62%#!+$!`4!

*$8!?!+,!69#!7%#exponentialI term.#D7)$#$6+*0!7%)7)%6+)$*0+6'!6#%-.!!K)<#3#%4!()%!%#*16+)$,!0+-+6#8!6)!6%2#! However, for reactions limited to true electron transfer between two

6%*$,(#%!)(!species,#0#16%)$,!:#6<##$!6<)!,7#1+#, the making and breaking of chemical!,219!*,!69),#!()2$8!+$ bonds is not a factor!69#!-+6)19)$8%+* (i.e., the reaction4!69#! is

-*;+$&!*$8!:%#*;+$&!)(non-adiabatic) [4]. In!19#-+1*0!:)$8,!+,!$)6!*!(*16)% other words, for electron transfer.!!?,!69# between!6%*$,(#%!)(!69#!#0#16%)$! two species in solution,+,! it

+6,#0(!is$)6! assumed*!%*6# Ithat0+-+6+$&! the actual%#*16+)$!1))%8+$*6# charge transfer !is+$!69#,#!6'7#,!)(!,',6#-, rapid compared to any nuclear4!?%%9#$+2,!69#)%' !

8)#,!$)6rearrangements!*8#52*6#0'!-)8#0!#D7#%+-#$6*00'!8#6#%-+$#8!8*6* which follow [1, 5], and a theoretical description!>aB.!!k*69#%4!* of a true! 69#)%#6+1*0!electron

8#,1%+76+)$!)(!*transfer event$!#0#16%)$!6%*$,(#%!#3#$6! must take into account the-2,6! energetics+$1)%7)%*6#! of this69#!H%*$1; type of reactionIU)%8)$!7 [5-7].%+$1+70#4! Almost

<9+19!*,,#%6,!69*64!+$!)%8#%!()%!#0#16%)$!6%*$,(#%!6)!)112%!:#6<##$!6<)!,7#1+#,!+$!,)026+)$4!fifty years ago, Rudolph Marcus realized that for an electron transfer event, application of

the typical Arrhenius theory was incompatible with energy conservation [7, 8]. For ! X! instance, for an electron transfer reaction proceeding in the dark, and following charge

8 +6!-2,6!:#!*,,2-#8!69*6!69#!*162*0!19*%&#!6%*$,(#%!+,!-219!-)%#!%*7+8!69*$!*$'!%#52+,+6#!

$210#*%!%#*%%*$&#-#$6,.!!@9#,#!$210#*%!%#*%%*$&#-#$6,!*%#!+$!(*16!2$8#%,6))8!6)!:#!69#!

%*6#I0+-+6+$&!%#*16+)$!1))%8+$*6#,!<9#$!$)!19#-+1*0!:)$8!+,!:#+$&!-*8#!)%!:%);#$4!*$8!

<9#$!$)!,0)<#%!1)$()%-*6+)$*0!&*6+$&!+,!%#52+%#8.!!]9+0#!69+,!(*1#6!)(!69#!7%+$1+70#!

7%#,#$6,!*!%#0#3*$6!8+,6+$16+)$!6)!?%%9#$+2,4!H%*$1;IU)%8)$!+$!+6,!72%#,6!()%-!*0,)!(*00,!

,9)%6!+$!*112%*6#0'!,2--*%+=+$&!:+)0)&+1*0!#0#16%)$!6%*$,(#%.!!F7#1+(+1*00'4!)$#!7%):0#-!

<+69!69#!H%*$1;IU)$8)$!7%+$1+70#!+,!69*6!+6!*,,#%6,!69*6!3#%6+1*0!#D1+6*6+)$!(%)-!*!&%)2$8!6)!

*$!#D1+6#8!,6*6#!27)$!9*%-)$+1R3+:%*6+)$*0!)3#%0*7!+,!*!$#1#,,+6'4!<9+19!-*$8*6#,!*$!

#$#%&'!+$726.!!K)<#3#%4!,+$1#!:+)0)&+1*0!#0#16%)$!6%*$,(#%!,6+00!)112%,!#3#$!+$!69#!8*%;4!69#!

H%*$1;IU)$8)$!7%+$1+70#!*0)$#!0#*3#,!*$!+-7)%6*$6!52#,6+)$!2$*$,<#%#8!II!+$!69#!*:,#$1#!

)(!0+&964!(%)-!<9#%#!-+&96!69+,!#D1+6*6+)$!#$#%&'!)%+&+$*6#m!^7)$!69#!*0+&$-#$6!)(!69#!

&%)2$8!*$8!#D1+6#8!,6*6#,4!69+,!#$#%&'!-2,6!1)-#!(%)-!,)-#<9#%#!>G4!eIYB.!!

! k28)079!W*%12,4!6)!<9)-!1%#8+6!()%!%#3)026+)$+=+$&!69#!6)7+1!)(!#0#16%)$!6%*$,(#%!

%#*16+)$,!-2,6!:#!&+3#$4!%#1)$1+0#8!69#!+$1)$&%2#$1+#,!7%#,#$6#8!:'!:)69!69#!?%%9#$+2,!

*$8!H%*$1;IU)$8)$!69#)%+#,.!!W*%12,!#,,#$6+*00'!1)-:+$#8!69#!?%%9#$+2,!*$8!H%*$1;I

U)$8)$!*77%)*19#,4!*,!()00)<,g!!n+3#$!*$!#0#16%)$!6%*$,(#%!%#*16+)$!:26!7%+)%!6)!69#!19*%&#!

6%*$,(#%4!69#!$210#+!)(!*6)-,!+--#8+*6#0'!,2%%)2$8+$&!#*19!%#8)D!1#$6#%!>6#%-#8!+$$#%!

,79#%#4!)%!!+$B!*$8!69#!0)$&!%*$&#!$210#*%!)%+#$6*6+)$,!+$(02#$1#8!:'!69#!19*%&#!*6!#*19!

%#8)D!1#$6#%!>6#%-#8!)26#%!,79#%#4!)%!!)26B!-2,6!:#!+$!1)$(+&2%*6+)$,!$#1#,,*%'!6)!

*11)--)8*6#!69#!19*%&#!6%*$,(#%.!!@9#!,2-!)(!!!)26!*$8!!+$!+,!:%)*80'!8#,1%+:#8!,+-70'!*,!

!, *$8!+,!6#%-#8!69#!%#)%&*$+=*6+)$!#$#%&'.!!@9#!*770+#8!%*6+)$*0#!)(!%#)%&*$+=*6+)$!#$#%&'!

+$!69#!1)-70#D!*%#$*!)(!:+)0)&+1*0!#0#16%)$!6%*$,7)%6!-*$8*6#,!*!1#%6*+$!&#)-#6%+1!*$8!

9*%-)$+1!,'--#6%'!69*6!-2,6!:#!+$!70*1#!:)69!:#()%#!*$8!+--#8+*6#0'!*(6#%!69#!*162*04!

! GZ! transfer,transfer, thethe atomicatomic nucleinuclei immediatelyimmediately surroundingsurrounding each each redox redox center center ( !(!inin)) as as well well as as the the

longlong rangerange nuclearnuclear configurationsconfigurations influencedinfluenced by by the the charge charge at at the the redox redox center center ( !(!outout) )were were

+$,6*$6*inin$#)2,!#0#16%)$!6%*$,(#%!)112%,. configurationsconfigurations necessarynecessary toto accommodateaccommodate!!!C$!)%8#%!6)!(2,# the the charge charge!69#,#!+$8#7#$8#$6! at at the the redox redox center center69#)%+#,!+$6)! prior prior to to

-*69#-*6+1*0!electronelectron*770+1*6+)$4! transfertransfer (since(sinceW*%12,! thethe electronicelectronic-)820*6 #8 eventevent!?%%9#$+2,h!#52*6+)$ isis assumed assumed to to be be rapid rapid.!!K#! relative *11)-70+,9#8!relative to to subsequent subsequent69+,!:'!

o %#8#(+$+$&!69#!nuclearnuclear ?%%9#$+2,! reconfigurations)reconfigurations)*16+3*6+)$!#$#%&'! [8,[8, 9].9]. InIn thisthis> " manner,manner,n !)%!_ ?energy energyB!*,!69#!1)-7),+6#!)(!6<)! would would have have to to be be further further supplied supplied

+$8#7#$8#$6toto thethe! '#6!0+$;#8systemsystem inin order4!order*$8! to7),,+:0'!to allowallow thethe#3#$! necessarynecessary1)2$6#%*16+$& nuclear nuclear! 3*%+*:0#,rearrangements, rearrangements,!>8#7#$8+$&!)$!,7#1+(+1! and and for for such such

1+%12-,6*$1#Breactionsreactions.!k proceeding#(#%%#8!6)!*,!69#!%#8)D!7)6#$6+*0!proceeding thethe inin thethe dark,dark, thethe typicaltypical8%+3+$&!()%1#!> description description was "wasnB!*$8!%#)%&*$+=*6+)$! incomplete incomplete [8, [8, 9]. 9].

#$#%&'!> !B4!69 Marcus’s Marcus’s+,!%#7%#,#$6,! reconcilingreconcilingW*%12,h,!,#-+$*0!*19+#3#-#$6 theoremtheorem involvedinvolved viewing viewing! >both bothX4GZ the B.the!!C$!)%8#%!6)!,+-70+('!69#! product product and and reactant reactant

69)2&96!7%)1#,,!<+69!%#,7#16!6)!69#,#!1)-70states,states, andand allall thethe nuclearnuclear configurationsconfigurations#D!,',6#-,4! contributingcontributingW*%12,! to to both, both,3+#<#8 as as an an energetic !energetic:)69!69#!7%)8216! parabola parabola as as

*$8!%#*16*$6!,6*6#,aa functionfunction ofof4!*$8!*00!69#!$210#*%!%#1)$(+&2%*6+)$,!7#%6*+$+$&!6)!:)694! nuclearnuclear configurations,configurations, andand inin accordance accordance with with Hooke’s Hooke’s law law*,!#$#%+1! [9] [9] (as (as 7*%*:)0*.!!@9+,!&%#*60'!,+-70+(+#,!92$8%#8,!)(!7),,+:0#!%#*16+)$!1))%8+$*6#,!8#(+$+$&!69#! discusseddiscussed byby Marcus,Marcus, thisthis isis aa muchmuch simplifiedsimplified view view of of the the many many hundreds hundreds of of coordinates coordinates ,',6#-!+$6)!6<)!,+-70#!7*%*:)0+1!(2$16+)$,!8#,1%+:#8!:'!69#!,*-#!:*,+1!1)$,6%*+$6,4!'#6! ofof thethe systemsystem [7,[7, 9]).9]). Thus,Thus, bothboth statesstates ofof thethe system system are are described described by by the the same same basic basic 8+,70*1#8!*0)$&!:)69!*D#,!*,!,9)<$!+$!H+&2%#!G."IG.!!C$!*11)%8*$1#!<+69!K));#h,!d*<4!*$8! function,function, onlyonly displaceddisplaced alongalong bothboth axes.axes. PartPart of of the the beauty beauty of of Marcus’s Marcus’s theorem theorem is is it’s it’s *,!,##$!+$!simplicity,69#!(+&2%#4!69#!*16+3*6+)$!#$#%&'!-*'!:#! as shown and derived in figure 1.2-1.#D7%#,,#8!+$! From the figure,69+,!-)8+(+#8!3#%,+)$!)(!69#! it is easily seen that the simplicity, as shown and derived in figure 1.2-1. From the figure, it is easily seen that the ?%%9#$+2,!#52*6+)$!activation energy*,g! described by the Arrhenius equation may be quantified as: activation energy described by the Arrhenius equation may be quantified as:

2 $ "(!G + #) 2' !E A = &$ "(!G + #) )' !E A =%& 4#RT () % 4#RT ( ! and thus the rate of electron transfer may be related as: @92,4!69#!%*6#!)(!#0#16%)$!6%*$,(#%!-*'!:and thus the rate of electron transfer#!8#,1%+ may be:#8!*,g related! as:

2 $ !("G + #) 2' k = Aexp&$ !("G + #) )' k = Aexp%& 4#RT () % 4#RT ( !! In a simplified sense, the pre-exponential term may also be expressed as the rate of @9#!7%#IIn#D7)$#$6+*0!6#%-4!?4!-*'!*0,)!:#! a simplified sense, the pre-exponential8#,1%+:#8! term *,!69#!%*6#!)(!#0#16%)$!6%*$,(#%!may also be expressed as the rate69*6! of

activation-less electron transfer, k0, as follows: <)208!7%)1##8!+$!69#!*:,#$1#!)(!*activation-less electron transfer,!%#52+%#8 k0, as! *16+3*6+follows:)$!#$#%&'4!*,!,219g!

$ !("G + #)2 ' k k exp = 0 & 9 ) % 4#RT ( 9 !

where k0 is that rate of electron transfer when -!G = ! [4, 10]. Given this description, it

is easy to see that Marcus’s theorem makes an unusual prediction for increasing values of ! GG! -!G [10]. Namely, when -!G is greater than !, Marcus theory predicts the rate of electron

transfer will actually decrease, and such a case is denoted as the Marcus inverted region

[5, 10]. The qualitative significance of this finding is that biological redox proteins must

tune and balance both the free energy of the redox reaction as well as the reorganizational

energy in order for efficient electron transfer to occur [1, 5, 11].

In addition, since biological redox reactions often occur between redox centers

separated by some distance, the pre-exponential term may be expressed as:

1 3 2 # 4! & 2 A = H AD % 2 k T( $ ! " B '

where HAD is an electronic coupling term which represents the probability of an electron

tunneling between the redox donor, D, and acceptor, A [1]. Thus the full expression of the

semiclassical Marcus theorem is as follows:

1 2 3 2 # ° & # 4! & 2 )(*G + ") ket = % 2 ( H AD exp% ( $ ! "k T' 4"RT B $ '

Furthermore, since the electronic coupling term is itself a function of the distance

between the two redox centers, the HAD term may be represented, as originally proposed

by Hopfield [12]:

0 HAD = H AD exp(!"(rDA ! r0 ))

10 <9#%#!;Z!+,!69#!%*6#!)(!#0#16%)$!6%*$,(#%!<9#$!"n!p!I! (5,10,11).!!!

! H%)-!*!-*69#-*6+1*0!7#%,7#16+3#4!W*%12,h!69#)%#-!-*;#,!*$!2$2,2*0!7%#8+16+)$!()%!

%*6#,!*,!*!(2$16+)$!)(!3*%'+$&!3*02#,!)(!I"n.!!^,+$&!H+&2%#!G."I"!*,!*!%#(#%#$1#4!)$#!-+&96!

0)&+1*00'!1)$1028#!(%)-!69#!)26,#6!69*6!*!&%#*6#%!8%+3+$&!()%1#4!*,!-*%;#8!:'!+$1%#*,+$&!

3*02#,!)(!I"n4!<)208!)$0'!,7##8!27!*$!#0#16%)$!6%*$,(#%.!!@9+,!+,!1)$,+,6#$6!<+69!69#!

79',+1*0!1)$1#76!)(!()%1#!*$8!+6,!+$(02#$1#!)$!%*6#,!II!()%!#D*-70#4!*!-)3+$&!):q#164!0+;#!*!

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69#!#3)026+)$*%'!,#52#$1#.!!F7#1+(+1*00'4!:+)0)&+1*0!%#8)D!7%)6#+$,!9*3#!0+;#0'!2$8#%&)$#!*!

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6)!-*D+-+=#!69#!#((+1+#$1'!*$8!%*6#!)(!#0#16%)$!6%*$,(#%.!!@9+,!79#$)-#$)$!7*%6+*00'!

#D70*+$,!<9'!#D6%#-#0'!0*%&#!>P!.YaI.XZcB!7)6#$6+*0!8+((#%#$1#,!*%#!$)6!):,#%3#8!:#6<##$!

:+)0)&+1*0!%#8)D!1)270#,4!*,!69#!+-70+1+60'!9+&9!"no 206+-*6#0'!-*;#,!69#!#0#16%)$!6%*$,(#%!

#3#$6!,0)<#%!*$8!0#,,!#((+1+#$6.!@9+,!-+&96!*0,)!:#!2,#8!6)!%*6+)$*0+=#!9)

1)-70#D+6'4!+$3)03+$&!,',6#-,!<+69!-)%#!,6#7,!$ !("G*$8R)%!+ #)2 ' %#8)D!1#$6#%,4!-+&96!9*3#!#3)03#8! k = k0 exp& ) % 4#RT ( (%)-!7%+-)%8+*0!,+-70+1+6'!6)!*19+#3#!7%#,#$6!8*'!0#3#0,!)(!#0#&*$1#!*$8!+$6%+1*1'.!!@9#!

where k0 is that rate of electron transfer when -!G = ! [4, 10]. Given this description, it ,#0#16+3#!()%1#,!)(!#3)026+)$!*16+$&!)$!,219!*!-206+I1)-7)$#$6!,',6#-!6)!*19+#3#!-*D+-*0!

is easy to see that Marcus’s theorem makes an unusual prediction for increasing values of #((+1+#$1'!-2,6!*6!*!-+$+-2-!+$1028#!I"n!*$8!!, *,!69#'!7#%6*+$!6) I"no!()%!*$'!&+3#$!,6#7.!! -!G [10]. Namely, when -!G is greater than !, Marcus theory predicts the rate of electron A%)3+8#8!69*6!1)$()%-*6+)$*0!&*6+$&!+,!$)6!69#!%*6#I0+-+6+$&!,6#7!+$!*$!#0#16%)$!6%*$,(#%4!"n! transfer will actually decrease, and such a case is denoted as the Marcus inverted region *$8!! <+00!8+16*6#!69#!6%2#!%*6#!)(!#0#16%)$!6%*$,(#%!>;#6B!()%!*!,6#7!>G4e4G"4GNB.!!!!

! [5,@9#!+$1)%7)%*6+)$!)(!W*%12,h!7#%,7#16+3#,!+$6)!69#!:+)0)&+1*0!*%#$*!%#52+%#8!,)-#! 10]. The qualitative significance of this finding is that biological redox proteins must

-)8+(tune+1*6+)$ and4 !balance<9+19!+,!8+,12,,#8!+$!69+,!,#16+)$.!!H)%!#D*-70#4!, both the free energy of the redox reaction as +$1#!:+)0)&+1*0!%#8)D!well as the reorganizational

%#*16+)$,!()%!69#!-),6!7*%6!)112%!:energy in order for efficient electron#6<##$! transfer%#8)D!1#$6#%,!,#7*%*6#8!:'!,)-#! to occur [1, 5, 11]. 8+,6*$1#4!69#!

7%#I#D7)$#$6+*0!6#%- In addition, !since>?B!1*$!:# biological!(2%69#%! redox10*%+(+#8!*, reactions! *!(2$16+)$!)(!often occur betweenf)06=-*$$h,!1)$,6*$6!*$8! redox centers

6#-7#%*62%#4!separated*,!,219 by someg! distance, the pre-exponential term may be expressed as:

1 3 2 # 4! & 2 A = % 2 ( H AD $ ! "kBT' !

<9#%#!Kwhere?O! +H,!*$AD is!#0#16%)$+1!1)270+$&!6#%-!69*6!%#7%#,#$6,!69#!7%):*:+0+6'!)(!*$!#0#16%)$! an electronic coupling term which represents the probability of an electron

:#+$&!6%*$,(#%%#8!:#6<##$!69#!%#8)D!8)$)%!*$8!tunneling between the redox donor, D, and acceptor,69#!*11#76)%! A [1]. Thus>GB.!! the@92,4!69#!(200!#D full expression7%#,,+)$! of the

)(!69#!10*,,+1*0!W*%12,!69#)%#-!:#1)-#,semiclassical Marcus theorem is as follows:g!!

1 2 3 2 # ° & # 4! & 2 )(*G + ") ket = % 2 ( H AD exp% ( $ ! "k T' 4"RT B $ ' ! GN! Furthermore, since the electronic coupling term is itself a function of the distance

between the two redox centers, the HAD term may be represented, as originally proposed

by Hopfield [12]:

0 HAD = H AD exp(!"(rDA ! r0 ))

10 $ !("G + #)2 ' k = k0 exp& ) % 4#RT ( $ !("G + #)2 ' k = k0 exp& ) 4#RT where k0 is that rate of electron transfer when% -!G = !( [4, 10]. Given this description, it

iswhere easy kto0 seeis that that rate Marcus’s of electron theorem transfer makes when an unusual-!G = ! prediction [4, 10]. Given for increasing this description, values ofit

-is! Geasy [10]. to Namely,see that Marcus’swhen -!G theorem is greater makes than an!, Marcusunusual theory prediction predicts for increasingthe rate of valueselectron of

transfer-!G [10]. will Namely, actually when decrease, -!G isand greater such athan case ! ,is Marcus denoted theory as the predicts Marcus theinverted rate of region electron

[5,transfer 10]. The will qualitative actually decrease, significance and suchof this a findingcase is denotedis that biological as the Marcus redox inverted proteins region must

tune[5, 10]. and The balance qualitative both the significance free energy of of this the findingredox reaction is that biological as well as redoxthe reorganizational proteins must

energytune and in balanceorder for both efficient the free electron energy transfer of the toredox occur reaction [1, 5, 11]. as well as the reorganizational

energy In inaddition, order for since efficient biological electron redox transfer reactions to occur often [1, occur 5, 11]. between redox centers

separated In addition, by some sincedistance, biological the pre-exponential redox reactions term often may occur be expressed between redoxas: centers

separated by some distance, the pre-exponential1 term may be expressed as: 3 2 # 4! & 2 A = 2 H AD % ( 1 $ ! "kBT' 3 2 # 4! & 2 A = % 2 ( H AD $ ! "k T' where HAD is an electronic coupling term whichB represents the probability of an electron

tunnelingwhere HAD between is an electronic the redox coupling donor, D, term and which acceptor, represents A [1]. Thus the probability the full expression of an electron of the

semiclassicaltunneling between Marcus the theorem redox donor, is as follows: D, and acceptor, A [1]. Thus the full expression of the

1 semiclassical Marcus theorem is as follows: 2 3 2 # ° & # 4! & 2 )(*G + ") ket = % 2 ( H AD exp% ( $ ! "k T' 1 4"RT B $ ° '2 3 2 # & # 4! & 2 )(*G + ") ket = % 2 ( H AD exp% ( $ ! "k T' 4"RT Furthermore, since the electronic couplingB term is $itself a function' ! of the distance

H2%69#%-)%#4!betweenFurthermore, the:#1*2,#! two since redox #0#16%)$+1!1)270+$&!6#%-!+,the centers,electronic the coupling HAD term term may! +6,#0(!*!(2$16+)$!)(!69#!8+,6*$1#!:#6<##$!is be itself represented, a function as of originally the distance proposed

69#!%#8)D!1#$6#%,4!K)7(+#08!7%)7),#8!69*6!69#!Kbybetween Hopfield the [12]: two redox centers, the HAD term may?O!6#%-!-*'!:#!%#7%#,#$6#8!*, be represented, as originallyg !proposed

0 by Hopfield [12]: HAD = H AD exp(!"(rDA ! r0 )) ! 0 H = H AD exp !"(rDA ! r ) <9#%#! # +,!*!-#*,2%#!)(!69#!1*7*1+6'!)(!69#!,#7*%*6+$&!-#8+2-!6)!*00)G[B.!!! 10 ! !F#3#%*0!8+((#%#$6!*77%)*19#,!9*3#!:##$!2,#8!6)!8#6#%-+$#!69#!3*02#!)(!

# ()%!:+)0)&+1*0!%#8)D!%#*16+)$,4!*,!+6!+,!)(!7*%6+120*%!-*69#-*6+1*0!+-7)%6*$1#!6)!K)7(+#08h,!

#D7*$,+)$!)(!W*%12,h!7%#I#D7)$#$6+*0!6#%-.!!H)%!#D*-70#4!n%*'!!"#$%&#-#*,2%#8!

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Figure 1.3-1 ! (see caption on preceding page) !

! Tungsten lamp Laser ! Lens !

! Filter

! sample holder ! Prism

! monochromator !

! Photomultiplier Tube Detector !

! Oscilloscope 1.0 -3 x10 ! 0.0

-1.0

5.39

a b s o ! 5.35 r -1 b x10 a n c e 5.31 ! SI Fittings software 5.27

5.22 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

-3 ! Seconds x10

File: 2009-9-01-002.KFT Comment: 20mMTRISpH8/5mMCo/3.9uMWTRsphbc1/100uMdUBQ/2.5mMsucc/2uLscr/N2/T=19degC/552nm12/26/02 1 2-KE31---LC7200 Date printed: 09/02/2009 Program Version: SI Fitting 5.4

18 Model: Y = A1*exp(-X*k1) + A2*exp(-X*A2) + B Baseline: None Chi squared: 3.197E-05 LM Iterations: 5

Rate (k1): (4.92178±0.23124)*E04 Start pt: 222 Amp1: (-3.83651±0.09781)*E-03 End pt: 1996 Rate (k2): (2.78171±0.07075)*E03 Amp2: (-2.64706±0.03851)*E-03 ! "G! Background (B): 5.2880E-01 <83;.'&!+=!>#-'.#1!?.%0#'4!/5!.8'!1:./18&/9'!@1(!'-A:9'!/5!!"#$#%&'()*+'&,-./&(.-!

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Fig. 1. Cytochrome c oxidase. (A) Conventional catalytic cycle. The squares show different states of the binuclear heme a3–CuB site and how electrons and substrate protons are taken up during activity. Proton translocation is not shown. (B) Overall reaction scheme and location of redox centers. Blue arrows show the redox reaction and its orientation with respect to the membrane. Red arrows depict proton translocation coupled to the redox reaction. The heme groups and CuB lie within the membrane at a relative dielectric depth d from the positively charged P surface. Electron transfer across d, proton consumption across 1-d, and proton pumping across the entire membrane contribute to generation of electric membrane potential (adapted from ref. 9). (C) Modiﬁed catalytic cycle. Yellow squares depict the main cycle. White squares show a side path initiated by decay of the metastable OH intermediate to O. Red arrows indicate proton translocation, and blue arrows show uptake of substrate protons. For details, see text. initially fully reduced in the presence of carbon monoxide to the mutant enzyme is indeed not affected during the oxidative form the CO complex of heme a3.RuBiPywasalsopresentto phase (Fig. 3B,blue)butisstronglyinhibitedduringreduction allow light flash-induced electron injection into the enzyme (11, (Fig. 3B,red),whichconfirmsthatthewild-typeenzymeindeed 12, 14). The novel rationale here is first to induce the oxidative enters the reductive phase during the electron photoinjections. phase by CO photolysis in the presence of O2 (flash no. 1; Fig. Fig. 3C shows membrane potential formation on electron 3A)andthentoinducethereductivephasebyphotoinjectionof injection in more detail. In wild-type enzyme that has previously electrons soon after (flashes 2–16). As shown in Fig. 3A (blue), undergone the oxidative phase, membrane potential is generated the oxidative phase is accompanied by fast generation of mem- (second flash in Fig. 3A)inthreekineticallydistinguishable brane potential (see ref. 13). A subsequent train of flashes injects phases (Fig. 3C,red):anϷ17-␮sevent(seeFig.3CInset)is electrons into the recently oxidized enzyme with a yield of Ϸ20% followed by two slower phases with characteristic time constants per flash (see Materials and Methods). The enzyme enters the of 0.2 and 1.4 ms (see ref. 20) and roughly equal amplitudes. In reductive phase, which is also associated with formation of contrast, when the first electron is injected into oxidized wild- membrane potential (Fig. 3A,red;seebelow).Mutationofthe type enzyme that has not recently undergone oxidation by O2, conserved lysine-354 in subunit I to methionine (K354M mu- only the fast phase is observed (Fig. 3C,green;seeref.11). tant) or its equivalent is known to have little effect on the Similarly, in the K354M mutant enzyme (Fig. 3C,blue),thereis oxidative phase of the catalytic cycle but to dramatically inhibit only very little formation of membrane potential beyond the fast the reductive phase (17–19). Membrane potential generation in phase. Clearly, formation of membrane potential during the

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