Chapter 4: Biochemical redox reactions

Transcription

1 Chaptr 4: Biochmical ractions 4.1 Introduction 4.2 Biochmical half-ractions, th Faraday conststant and th uction potntial Dfining th uction potntial: Th standard uction potntial is also th midpoint potntial of a coupl 4.3 Dtrmining th valu of th midpoint potntial 4.4 Solution (ambint) potntials and lctrochmical clls 4.5 xampl: th potntiomtric titration of NAD 4.6 How midpoint potntials ar usd to dpict biochmical lctron transfr systms 4.7 Ambint potntial in a living cll and idativ strss Oxidativ strss. 4.8 Th ph-dpndnc of th midpoint potntial 4.9 xampl: Th ph-dpndnc of th midpoint potntial of th NAD /NAD coupl 4.10 Thrmodynamic rciprocity of intractions btwn proton binding and uction potntial 4.11 Application: Dtrmining th midpoint potntial of.coli thioin 4.12 Application: A mutation that raiss th midpoint potntial of th rgulatory disulfid th th γ-subunit of th chloroplast ATP synthas from Arabidopsis 4.13 Application: Impact of mutations on th midpoint potntial of an [4F-4S] clustr in th lctron transfr protin:ubiquinon idouctas 4.14 Application: Dtrmining th mitochondrial ambint potntial 4.15 Summary 1

2 Chaptr 4: Biochmical ractions 4.1 Introduction In Chaptr 3 w dvlopd th us of th chmical potntial in daling with biochmical ractions. This formalism applis to all ractions whthr or not thy involv hydrolysis of ATP, DNA clavag or idation/uction changs. Howvr, for th many ractions in chmistry which involv lctrons bing transfr from on spcis to anothr, i.., uction and idation (hnc, ), thr is a spcific languag and st of paramtrs that hav bn dvlopd, namly th concpts of th uction potntial and th halfraction or "half-cll raction". Chmical and biochmical ractions can all, in principl, b carrid out by transfrring th lctrons from th molcul bing idizd to an lctrod locatd in on solution, and thn dlivring lctrons to th molcul bing ucd via anothr lctrod locatd in a sparat solution. In many cass, chmical and biochmical ractions can in rality b prformd in this mannr. Th lctrical chargs nd to b abl to travl from on lctrod to anothr, and this can b don using a wir, in conjunction with a salt bridg in which ions (.g., K+ and Cl-) mov btwn th solutions in ordr to maintain charg nutrality in ach solution as lctrons ar addd to on sid and rmovd from th othr. A schmatic diagram is shown in Figur 4.1. Th thrmodynamics of such ractions ar, of cours, th sam as w discussd in th last chaptr. Th paramtr of intrst rmains th transformd raction Gibbs fr nrgy, Δ G ' r, but th trminology usd is oftn that of lctrochmistry whn daling with ractions. Th focus on lctron transfr, and th proton transfr ractions which ar frquntly linkd to lctron transfr, ar particularly hlpful in undrstanding many biochmical ractions. In addition to biochmical ractions, w will also discuss in this chaptr th charactrization of lctron carrirs in lctron transfr pathways or in othr procsss 2

3 and th charactrization of th prosthtic groups within -activ nzyms. Th first group includs c-typ cytochroms, quinols, NADH, tc., and th scond group includs protinbound hms, flavins, F/S clustrs, disulfids, and many mor. Figur 4.1: Schmatic of a raction bing carrid out in an lctrochmical dvic whr lctrons from th uctant ar dliv to th idant through a wir. Th maximal lctrical work that can b accomplishd is qual to th Gibbs raction fr nrgy of th raction. 4.2 Biochmical half-ractions, th Faraday conststant and th uction potntial Lt s tak a look at th idation of NADH by O, a raction catalyzd by th mitochondrial rspiratory chain. Th quation (4.1) indicats a raction with ygn, and it is indicatd that w will dtrmin th thrmodynamics with rspct to dissolvd ygn in th aquous phas (aq) NADH + 2 H + O (aq) 2 NAD + 2 H O 2 2 (4.1) Chmical raction vs biochmical raction notation: Th raction of NADH and O, as it appars in quation (4.1) is th way on typically would writ out a chmical raction. At constant ph, w nd to rcall that th proton concntration dos not chang, so formally in th biochmical raction, hydrogns and charg nd not b consrvd. Protons can appar 2 3

4 from or vanish into an infinit proton rsrvoir. Formally, th propr way to dscrib this biochmical raction at constant ph is 2 NAD + O (aq) 2 NAD + 2 H O 2 2 (4.2) This can b disorinting, spcially if on is not usd to it, so it can b xcusd to balanc th raction so as to kp track of what is going on. Howvr, in using th transformd Gibbs fr nrgy, th protons ar not includd in th quilibrium xprssion. In this raction, NADH (or NAD ) is th uctant. That is, lctrons ar takn from NAD and dliv to O, which is th idant. Th idant has th strongr tndncy than 2 th uctant to tak lctrons. W can sparat th biochmical raction in quation (4.2) into two half-ractions, half-raction 1: O (aq) H O half-raction 2: 2 NAD NAD (4.3) in which w hav, again, rmovd th protons sinc ph is hld constant. Th half ractions ar writtn following a convntion of placing th idant on th lft. Th nt raction in (4.2) is raction 1 minus raction 2 as thy ar writtn in (4.3). W can think of ths half-ractions as ractions that might tak plac at th surfacs of th two lctrods in Figur 4.1. In this lctrochmical st-up (Figur 4.1) lctrons ar donatd by th idation of NAD at on lctrod and dliv through a wir to th scond lctrod, whr O is ucd to watr. This is a currnt, and w could gt lctrical work from th systm if w had an lctrical dvic such as a motor insrtd into our circuit. Th maximal work w could obtain is givn by th transformd Gibbs fr nrgy of th raction, Δ G ' r. Rmmbr that this is th maximal work pr mol of raction progrss ( ξ, introducd in th prvious chaptr) at th particular concntrations prsnt. This is not th amount of work that w could gt if w lt th raction run down to quilibrium. Th ralization that th lctrical work is quivalnt to 2 4

5 Δ is hlpful bcaus is strsss th fact that th chmical driving forc for this G ' r raction is rlatd to th spontanous movmnt of lctrons from th uctant (lctron donor) to th idant (lctron accptor, which idizs th uctant). Th work capacity of this raction ( Δ G ' r ) is usually xprssd in trms of jouls, but can also b xprssd in trms of lctrical work, or volts. On joul is dfind as th amount of nrgy gaind whn 1 coulomb of charg is movd against a potntial of 1 volt, whr a coulomb is th amount of charg transportd by a currnt of 1 ampr in 1 scond. Rcall that th lctrical work rqui to mov an amount of charg (Q) from a position whr th potntial is ψ to a position whr th lctrical potntial is ψ is 2 w = ( Ψ Ψ )Q (4.4) l Th amount of absolut charg in 1 mol of lctrons is 96,485 coulombs, so th nrgy of moving 1 mol of lctrons, Q = -96,485 coulombs, to a mor ngativ potntial, ( Ψ Ψ ) = volt, is (-96,485)(-1) = 96,485 jouls. Doing work on th systm is positiv. This givs us a convrsion factor btwn jouls and volts, two diffrnt units of nrgy. 1 volt = 96,485 jouls (4.5) Th convrsion factor is calld th Faraday constant, F. F = 96,485 coulombs/mol (4.6) In th systm pictu in Figur 4.1, lctrical currnt will mov from lft (NAD right (O ), which mans that th lctric potntial of th lctrod on th lft is mor ngativ 2 than that on th right. Sinc lctrical work is nonpv work, this mans that it is quivalnt to rvrsibl work ( dw = dw = dg ). Th maximal lctrical work pr mol of raction l rv progrss (th xtnt of raction paramtr, ξ) must b qual to th transformd Gibbs fr nrgy of th raction undr th dfind conditions, as it would procd if both ractants wr ) to 5

6 prsnt in th sam solution. As th raction is writtn in quations (4.2) and (4.3), w can s that Q( Ψright Ψ lft ) = 4(96,485) ΔΨ =ΔrG ' (4.7) Th ngativ sign coms from th charg (Q) bing ngativ, and th 4 is th absolut valu of th stoichiomtry numbr of th lctrons as th raction has bn writtn in (4.2) and (4.3), four lctrons pr mol of O 2. W will us th notation ν to indicat th absolut valu of th stoichiomtry numbr, so in this cas, ν = 4. Th spontanous dirction of raction (4.2) is from lft to right, and th valu of Δ G ' r is ngativ. Th dirction of th currnt flow (NAD to O 2 ) is also from lft to right as w hav drawn our dvic in Figur 4.1, towards th mor positiv lctrod. Th potntial to do work is givn by th voltag diffrnc btwn th two lctrods and this work potntial must b quivalnt to Δ G ' r. ' From quation (4.7), sinc Δ G < 0 it follows that ( Ψ Ψ ) > 0. Clarly, if w know r right lft th valu of th transformd Gibbs fr nrgy of raction, w can radily calculat th potntial diffrnc btwn th two lctrods in th stup in Figur 4.1. Th rason for going through all of this is to mphasiz th rality that ractions can and oftn ar xamind using an lctrod as ithr an lctron sourc (uctant) or an lctron accptor (idant). Lt us now convrt th xprssion for th raction fr nrgy to units of volts. If w gnraliz quation (4.7) w s that ' ν FΔΨ =Δ G r or (4.8) ' ΔrG ΔΨ = ν F 6

7 Figur 4.2: Transformd Gibbs raction fr nrgy convrtd to an lctric potntial diffrnc for a raction for a 1-lctron and 2-lctron raction. This is a plot of quation (4.8). ach of th four lctrons drops down th potntial ΔΨ, so th total raction fr nrgy is qual to th votag drop, convrtd to units of jouls, multiplid by th numbr of mols of lctrons, 4 in this cas. Figur 4.2 shows a plot of th rlationship in (4.8). For a 1-lctron raction, th slop of th lin shows that 1 kj is quivalnt to about 10 mv. For a 2-lctron raction, th slop if half. By dividing th xprssion for Δ G ' r by ν F w gt th following. Δ =Δ ' rg rg RT [ NAD ] ln [ NAD ][ O ( aq )] 2 ' ΔrG ΔrG RT [ NAD ] = ln whr ν = 4 ν F ν F ν F [ NAD ][ O ( aq)] 2 (4.9) ' = RT [ NAD ] ln 4 F [ NAD ][ O ( aq)] 2 whr ' is th lctric potntial diffrnc btwn th two lctrods ' ( = ΔΨ ) and 'o is th lctric potntial diffrnc undr standard stat conditions (1 M of ach ractant, K, ph 7, spcifid ionic strngth). W can calculat th valu of 'o from th valus of th transformd Gibbs fr nrgis of formation for raction (4.2). 7

8 Δ G = 2Δ G + 2Δ G 2Δ G Δ G r f NAD f H O f NAD f 2 2 'o O Δ rg = + Δ = 2( ) 2( 155.6) 2( ) (16.4) rg kj / mol (4.10) ΔrG ( ) = = volts ν F 4(96485) If, for xampl, th concntrations of ucd and idizd NAD ar th sam and th concntration of O 2 (aq) is 250 μm (2.5 x 10 4 M), thn th potntial btwn th lctrods would b RT [ NAD ] (8.31)(298) 1 ln ln( ) 4 ν F [ NAD ][ O ( aq)] 4(96485) 2.5x10 ' = = 2 ' = (4.11) ' = volts Not that a ngativ valu of Δ ' ' convrts to a positiv valu of, and both indicat a r G spontanous raction dirction from lft to right as th raction is writtn (lctrons flowing towards th mor positiv sid). In this xampl, thr is a strong driving forc for th raction as writtn in (4.2) to procd from lft to right. Th numbrs confirm what is obvious, which is that NADH is a strong uctant for ygn Dfining th uction potntial: Th half-ractions dfind in (4.3) ach contain th idizd and ucd form of a ractant, such as NAD and NAD. Ths constitut a coupl. vry raction, such as (4.2), involvs two coupls. Dpnding on th conditions of th raction, th spontanous dirction of th raction will b from th ucd form of on of th coupls to th idizd form of th scond coupl. Th convntion is to 8

9 compar th thrmodynamics of " coupls" on th basis of thir uction potntials, which w will now dfin. Lt's gnraliz by splitting th following raction A + B A + B (4.12) into two half-ractions. 1 A + ν A B + ν 1 B (4.13) Th convntion in daling with biochmical half-ractions is to always writ thm with th lctrons on th lft, i.., th raction dirction from lft to right is a uction. Th transformd Gibbs fr nrgy of raction for (4.12) is givn by ' ' [ A ][ B Δ rg =ΔrG RTln [ A ][ B o ] ] (4.14) which w can also writ as ' RT [ A ][ B ] = ln (4.15) ν F [ A ][ B ] quation (4.15) is calld th Nrnst quaton. W will split quation (4.14) into two parts, corrsponding to th half-ractions in (4.13). ' ' ' [ ] o o A [ B ] Δ rg = ΔrGA RTln ΔrGB RTln [ A] [ B] (4.16) Th two xprssions on th right in (4.16) can b rlatd to th half-ractions in (4.13). W can now dfin a transformd raction Gibbs fr nrgy for ach half-raction. ' [ A ] Δ rga = ΔrGA RTln [ A ] ' [ B ] Δ rgb = ΔrGB RTln [ B ] (4.17) 9

10 Th xprssions in (4.17) can also b obtaind by starting with th half-ractions in (4.13) and using th procdurs dscribd in th Chaptr 3, considring th lctron to b formally on of th ractants, and assigning th lctron a chmical potntial of zro. Th standard stat transformd Gibbs raction fr nrgy of th half-ractions can b obtaind from th corrsponding Gibbs fr nrgis of formation. Δ G = μ μ = ( Δ G Δ G ) r A A A f A f A Δ G = μ μ = ( Δ G Δ G ) r B B B f B f B (4.18) For th full raction (4.12) th standard stat Gibbs fr nrgy of raction can b writtn as 'o rg rga rg B Δ =Δ Δ (4.19) Divid (4.17) through by ν F to convrt to units of volts to obtain th following. ' A ' B RT [ A ] = A ln ν F [ A ] RT [ B ] = B ln ν F [ Bo x ] (4.20) In (4.20), A and ar dfind as th standard uction potntials of th coupls 'o B A /A and B /B, rspctivly. Δ G r A A = ν F Δ G r B B = ν F (4.21) W also not that sinc Δ G =Δ G Δ 'o, (4.19), thn for th full raction (4.12) r r A rg B 'o A B = (4.22) 10

11 Th minus sign in front of 'o B in (4.22) rsults from th convntion of writing th half ractions with th idizd form on th lft, as in (4.13). Th full raction is qual to raction A minus raction B in(4.13). Th quantitativ rlationship btwn Δ G r 'o A and 'o A in (4.21)is xactly th sam as shown in Figur 4.2. To gt a bttr fling for quation (4.20), w will convrt to a log 10 instad of natural log, and assum T = K, to gt = 59 [ A ] log (mv units for and ) (4.23) ' ' A A A A ν [ A] Assuming a standard uction potntial of +100 mv, th data in Figur 4.3 for a 1-lctron and 2-lctron raction. For a 1-lctron raction th slop is -59mV pr log unit, or pr ordr of magnitud chang in th ratio of [ A ]. Th slop is half this valu for a 2-lctron [ A ] raction, about -30 mv/log unit. Figur 4.3: Plot of quation (4.23) assuming th tmpratur is 298K and A = 100mV. For a 1-lctron raction, th slop is 59 mv/log unit, and for a 2-lctron raction, th slop is about 30 mv/log unit. This is th chang in th uction potntial for vry 10- fold chang in th ratio [ A ]. Th largr this ratio, th bttr th ucing powr, or [ A] th mor ngativ th valu of th solution potntial. 11

12 4.2.2 Th standard uction potntial is also th midpoint potntial of a coupl In quation (4.20), whn 50% of A has bn ucd, thn [A ] = [A ] and th logarithmic trm is qual to zro. At this point, ' A = A whn 50% of A is ucd. (4.24) For this rason, th standard uction potntial is also rfr to as th midpoint potntial of th coupl, and is dsignatd as ' mph,, th potntial at which half of th coupl is ucd and half idizd. If w had an lctrod maintaind at a potntial of ' mph,, submrgd in a solution of A, at quilibrium half of A would b ucd. Oftn th ph is indicatd, and th suprscript prim indicats constant ph. If no ph is dsignatd, it should b assumd th ' m rfrs to ph 7. It is important to rcogniz that for biochmical ractions, it is convntional to dfin th standard stat as ph 7, whras for chmical ractions, th usual dfinition of th standard stat concntration (activity) of 1 M is usd. 4.3 Dtrmining th valu of th midpoint potntial Valus of many standard uction potntials (or midpoint potntials) ar tabulatd, and som ar shown in Tabl 4.1(1-3). Most of th coupls shown in Tabl 4.1 ar involvd in nzym catalyzd ractions in. coli (4)as wll as in many othr organisms. Not that ths all apply to standard conditions at ph 7 ([H + ] = 10-7 M). Rd coupl O 2 /H 2 O NO / NO NO / NH O 2 /H 2 O DMSO/DMS TMAO/TMA ubiquinon/dihydro-ubiquinol fumarat/succinat 2 30 mnaquinon/dihydro-mnaquinol 2-80 glucos/gluconat aloactat/malat pyruvat/l-lactat ν Standard uction 'o potntial( or ),mv m,7 12

13 dihydryacton phosphat/ glycrol-3-phosphat actaldhyd/thanol NAD /NAD H + /H CO 2 /format actat/actaldhyd actat/pyruvat dimthylsulfid (DMS) 2 trimthylamin N-id (TMAO); trimthylamin (TMA) If not, thy can b dtrmind ithr from xisting data or xprimntally. Thr approachs ar givn blow. Mthod 1: On way is to calculat 'o valus from th Gibbs fr nrgis of formation of th ucd and idizd forms of th coupl. Many of ths ar tabulatd. For xampl, NAD NAD NAD / NAD NAD / NAD Δ = = G f NAD f NAD ν F Δ G 3 3 ( ) ( ) x 2(96485) x (4.25) NAD / NAD = volts or -316 mv Not that w must convrt kilojouls to jouls by multiplying th transformd Gibbs fr nrgis of formation by Th sam xrcis can b don for th standard uction potntial of th O 2 /H 2 O coupl, yilding 13

14 O O / H O H O 2Δ G Δ G = ν F f H O f O 2 2 O / H O 2 2 = x 4(96485) 3 3 2( ) ( ) x (4.26) O / H O 2 2 = volts or 848 mv Mthod 2: Th quilibrium constants of many biochmical ractions ar also tablulatd, many dtrmind xprimntally. If on can dtrmin th quilibrium constant for a raction involving two coupls, and if on knows th midpoint potntial of on of th coupls, thn th scond is asily calculatd. For th gnralizd raction in (4.12), th quilibrium constant can b xprssd in trms of th standard uction potntials or midpoint potntials. ΔrG ν F ' RT RT K = = K ' = ν F( A / A B / B ) RT (4.27) Mthod 3: A third way is to xprimntally dtrmin th potntial dvlopd btwn th coupl of intrst and a rfrnc coupl. Th convntion is to rport standard uction potntials vrsus th standard hydrogn lctrod (SH). Th standard hydrogn lctrod is a platinum lctrod that is in contact with hydrogn gas at a prssur of 1 bar and an aquous solution of 1 M protons. ithr hydrogn gas can b idizd to yild protons or protons can b ucd to form hydrogn gas at this lctrod. Th convninc of this sotric choic of th standard hydrogn lctrod is that th uction potntial of th H + /H 2 coupl, o = 0. This is bcaus + H /H 2 o μ = 0 for hydrogn gas, th most stabl form of H 2 th lmnt undr standard conditions and, by dfinition, th standard stat chmical potntial 14

15 of a solution of 1 M protons th standard stat (ph 7, 1 M concntrations) in rlation to th standard hydrogn lctrod is simply its standard uction potntial. o μ 0. Hnc, th masu potntial for any coupl in H + = = o masu vssh A / A + H / H2 = masu vssh A / A (4.28) It is usful to kp in mind that th sign of th standard uction potntial rfrs to whthr th coupl will b mor ucing (ngativ valu of A / A ) or mor idizing (positiv valu of A / A ) than th proton/hydrogn coupl in th standard hydrogn lctrod. Also, a ngativ A / A mans that currnt will flow from th lctrod masuring th coupl of intrst to th standard hydrogn lctrod, and a positiv A / A mans currnt will flow from th standard hydrogn lctrod to th ractants in th stup in Figur 4.1. Not that in Tabl 4.1, th biochmical dfinition of th standard potntial for th H coupl is -420 mv vs SH. This is bcaus th biochmical dfinition of th standard stat is at ph 7, or [H + ] = 10-7 M. At 298K, going from 1 M to 10-7 M is a chang of 7 log units, or - 7( 60 mv/log unit) = -420 mv (s Figur 4.3). Th standard hydrogn lctrod is convnint from a computational viwpoint sinc th midpoint potntial of th H + /H 2 coupl is zro. Howvr, from a practical viwpoint, th standard hydrogn lctrod is not convnint at all. Instad, it is common to us ithr a saturatd caloml rfrnc lctrod or a silvr chlorid rfrnc lctrod. Ths ar radily purchasd and ar packagd with a salt bridg and porous glass frit, rady to b insrtd into th lctrochmical solution. + /H 2 Th caloml lctrod uss th coupl of mrcury mtal (liquid) and Hg 2 Cl 2. 1 Hg2Cl Hg(l) + 2 Cl 15

16 Th nam drivs from th fact th Hg 2 Cl 2 is also calld caloml. Th uction potntial dpnds on th concntration of chlorid, and ths rfrnc lctrods ar most oftn usd with a saturating solution of KCl. At room tmpratur, =+ 241 mv vrsus SH. Hnc, if a caloml rfrnc lctrod is usd, on can simply add +241 mv to th potntial obtaind to th valu vrsus th standard hydrogn lctrod. Anothr choic as rfrnc lctrod is th silvr chlorid lctod. This uss th coupl of silvr mtal and silvr chlorid. caloml AgCl Ag (s) + Cl As with th caloml lctrod, th silvr chlorid lctrod uction potntial dpnds on th concntration (activity) of chlorid, and is routinly usd with saturatd KCl solution. Th solution potntial of th silvr chlorid lctrod at room tmpratur is +205 mv vs SH. For any biochmical raction, th data obtaind ar always convrtd to valus vrsus th standard hydrogn lctrod by adding 205 mv to th valu obtaind with th Ag/AgCl rfrnc lctrod. To xprimntally dtrmin th midpoint potntial of a -activ biochmical substanc, it is ncssary to us an lctrochmical cll and to manipulat th solution potntial, as dscribd in th following sction. 4.4 Solution (ambint) potntials and lctrochmical clls Lt s considr a simpl lctrochmical cll containing a biochmical coupl of intrst. In this xampl w hav two lctrods and th dvic is concptually idntical to that shown in Figur 4.1. On lctrod is in dirct contact with th solution containing th matrial bing studid. Th scond lctrod is th rfrnc lctrod which is in contact with th lctrochmical solution through a salt bridg. Th most commonly usd rfrnc lctrods ar th saturatd caloml lctrod and th silvr chlorid lctod, discussd in th prvious sction. Th voltag masu btwn th two lctrods (Figur 4.4) will b 16

17 dpndnt on th uction potntial of th coupl in solution and th uction potntial of th rfrnc lctrod. Figur 4.4: Schmatic of a simpl lctrochmical cll. This vrsion has two lctrods. Th solution must b mad anarobic bcaus O 2, bing a strong idant, will intrfr with th systm. Argon gas is frquntly usd to flush th systm. Th working lctod is oftn platinum gauz, incrasing th surfac ara that can ract with -activ solution componnts. Th rfrnc lctrod is usually a saturatd caloml lctrod or a silvr chlorid lctrod. Mdiators ar rqui to convy lctrons btwn most biochmical ragnts and th working lctrod. What happns if w hav mor than on coupl prsnt in th sam solution at quilibrium? At quilibrium, th uction potntials of all th coupls must b th sam, and this uction potntial will b monito by th lctrod that is in lctrochmical contact with th solution. This is calld th solution potntial or ambint potntial and is dsignatd as h. If th solution potntials ar not th sam for th coupls, this indicats that th solution is not in quilibrium. Mdiators hlp attain quilibrium: It is almost aways ncssary to includ mdiators in th lctrochmical solution sinc most biochmical compounds will not radily ract at th surfac of th lctrod. Th mdiators ar slctd basd on thir ability to undrgo chmistry at th lctrod surfac and also by thir ability to quilibrat with th biochmical coupls in solution. Th mdiators ar thmslvs coupls, xisting in ucd and idizd forms, and thy ar ach charactrizd by a midpoint potntial, 'o m. If th 17

18 solution potntial is far from th 'o m valu of a particular mdiator, th concntration of ithr th valu of [ A ] for th mdiator will b ithr vry small ( [ A ] h >> ) or vry larg 'o m ( h << ). In th first instanc, this mans th [A ] is vry small and in th scond cas, 'o m [A ] is vry small. Undr ths conditions, th rat by which th mdiators can transfr lctrons and hlp rach quilibrium will b vry slow. For this rason, a numbr of mdiators with a rang of 'o m valus is oftn prsnt in th lctrochmical solution in addition to th biochmical coupl(s) bing studid. A list of svral mdiators is shown in Tabl 4.2. Mdiator/Rductant/Oxidant 'o m potassium frricyanid +430 p-bnzoquinon ,6-dichlorophnol indophnol +217 mv 2,5-dimthyl bnzoquinon +180 phnozin mthosulfat +80 mv ascorbat +30 duroquinon +5 mthyln blu +11 mv mnadion 0 pyocyanin 34 mv 2,5-dihydry-p-bnzoquinon -60 anthroquinon -100 indigo carmin -125 mv anthroquinon 1,5-disulfonat ,10-anthraquinon 2,6-disufonic acid -185 mv anthroquinon 2-sulfonat -225 bnzyl viologn -350 dithionit Th midpoint valu of dithionit is vry dpndnt on ph and also concntration. S (5) Potntiomtric titrations: On can prform a potntiomtric titration by changing th solution potntial whil, simultanously, monitoring th A A ratio of th coupl of intrst using som chmical or spctroscopic mthods. Th lctrochmical clls ar constructd to facilitat rmoving sampls at diffrnt h valus or to dtrmin th absorbanc spctrum, for xampl, as a function of th solution potntial. Obviously, on 18

19 must b abl to chang th solution potntial systmatically to do this. Most commonly, an lctrochmical cll such as that schmatically shown in Figur 4.4 is usd, along with a caloml or silvr chlorid rfrnc lctrod. Thr ar svral ways to manipulat th solution potntial. Rgardlss of which mthod is usd, on is changing th ratio A A for all of th coupls in solution and, thus, changing th solution potntial. 1. On can add uctant (.g., a buff solution of dithionit) or idant (.g., a buff solution of frricyanid) to chang th solution potntial. 2. On can us a potntiostat, which is a dvic that uss a third lctrod to add or rmov lctrons from solution using an xtrnal sourc of lctrons, and in this way altr th solution potntial. 3. On can us a dominant coupl which will quilibrat with th systm to b studid, and whos total concntration is substantially gratr than that of othr -activ componnts in th solution. On adds a known amount of [A ] and a known amount of [A ]. In this way, during th quilibration, th [ A ] ratio for th dominant coupl [ A ] rmains ssntially fixd (sinc it is prsnt at much highr concntration than any othr coupl), and dtrmins th solution potntial. Th solution potntial can b radily calculatd by using quation (4.20) if th valus of A and ν ar known for th dominant coupl. Th concntrations of all th othr coupls will quilibrat to b consistnt with th solution potntial. potntial, If on has, for xampl, two coupls prsnt at quilibrium, th solution h, must b th sam as th uction potntials of ach coupl. 19

20 = = ' ' h A B or ' ' [ ] o o RT A RT [ B ] h = A ln = B ln ν F [ A] ν F [ B] (4.29) Not that in quation (4.29) th lctron stoichiomtry numbrs ν ar thos that apply for ach coupl sparatly. From quation (4.23) w can s that for a 1-lctron raction, a chang of th solution potntial by about 60 mv will chang th ratio of [ A ] by 10-fold, [ A ] incrasing th ratio for -60 mv, and dcrasing it for a chang of +60 mv. 4.5 xampl: th potntiomtric titration of NAD Now lt s look at an xampl of how th quations w hav drivd can b usd to dtrmin th valu of a midpoint potntial as wll as th numbr of lctrons transfr in a half-raction. Figur 4.5 illustrats simulatd data of a potntiomtric titration of NAD, which shows th fraction of NAD that is ucd as a function of th solution potntial, h. W xpct th data to fit to th following quation. ' RT [ h = NAD = m ν F NAD ] ln [ NAD ] (4.30) In practic it is common to switch to from th natural logarithm to log 10. h 2.303RT [ m ν F = NAD ] log [ NAD ] (4.31) At 298K, RT (2.303)(8.31)(298) = = volts or 59 mv (4.32) F Thrfor, with this valu insrtd, assuming 298K w gt (using mv units) 59 [ NAD log ] h = m ν [ NAD ] (4.33) 20

21 By dtrmining th fraction of NAD that is ucd as a function of h, w can dtrmin th valus of both ν and xprimntally. NAD Th data ar plottd in two ways in Figurs 4.5 and 4.6. In Figur 4.5, th prcntag of th total NAD that is ucd is plottd as a function of h. Th uction of NAD can b dtrmind by monitoring its optical absorbanc, making this a spctro-lctrochmical titration. Th valu of prsnting data in this way is that on can radily s that th ovr th rang of h valus th NAD has gon from fully idizd to fully ucd. Figur 4.5: Potntiomtric titration of NAD showing th fraction of NAD that is ucd (NAD /NAD total ) as a function of th solution potntial ( h ). Th midpoint is about -320 mv (vs SH). Sinc this is an quilibrium masurmnt, it should mak no diffrnc in which dirction on dos th titration, ucing or idizing. In practic, it is important to dmonstrat rvrsibility to b sur that quilibrium has bn attaind at ach point. Th potntial at which 50% of th NAD has bn ucd, radily sn by inspcting th plot in panl A, is qual to th midpoint potntial of NAD undr th conditions bing xamind. At ph 7, this is about 320 mv. 21

22 [ NAD ] In Figur 4.6, log is plottd vrsus th solution potntial, h. W xpct from [ NAD ] quation (4.33) to gt a straight lin whr th intrcpt will b 'o m and th slop will b 59. Th data do fit a straight lin with a slop of 30 mv, indicating, as w xpct, th ν ν = 2 and this is a 2-lctron raction. Th solution potntial whr [ NAD ] log = 0 is th midpoint potntial [ NAD ] Figur 4.6: Th sam data as in Figur 4.5 plottd as th logarithm of th ratio NAD. Th data fit a straight lin with a slop of -30 mv/log unit, consistnt with NAD ν = How midpoint potntials ar usd to dpict biochmical lctron transfr systms Any coupl that has a mor ngativ standard uction potntial will b a strongr uctant than any coupl whos standard uction potntial is mor positiv (s Tabl 4.1). This applis, of cours, to standard stat conditions (ph 7, 1 M concntrations). So, for xampl, NAD is th uctant for O 2. Th standard potntial for th raction btwn NAD and O 2, as writtn in (4.2) is 22

23 = O 2/ H2O NAD / NAD = 848 ( 316) (4.34) = 1164 mv Notic that w do not multiply NAD / NAD in (4.34) by a factor of two bcaus of th diffrnc in th stoichiomty numbrs for th lctrons ( ν = 2 for th NAD coupl and 4 for th O 2 half-raction. This is bcaus th uction potntials ssntially ar alrady normalizd pr lctron. Figur 4.7 is an xampl of th us of uction potntials in th biochmical litratur. This shows th "Z schm" dscribing th nrgtics of th light-drivn ractions in plant photosynthsis. Th various componnts that mak up th photosynthtic lctron transfr chain ar all locatd according to thir standard uction potntials. Mor ngativ valus ar intrprtd as "highr nrgy", maning that thy ar bttr uctants. Th Z schm shows th rol of th two photosynthtic raction cntrs, photosystm I (PSI and photosystm II (PSII). Th absoption of a photon of light rsults in crating an xcitd stat of chlorophyll P680, which bcoms a vry strong uctant. Th uction potntial is dcrasd about 1.5 volts, and th lctron is transfr through a chain of activ groups whos uction potntials gt progrssivly mor positiv. Th ChlP680 + /ChlP680 coupl has a mor positiv uction potntial than O 2 /H 2 O, and idizs watr to O 2, with intrmdiats bing a Mn clustr and a tyrosin. Aftr a scond light raction in in photosystm I, followd by anothr linar chain of ractions, th nd product is NADP. W will not go into any furthr dtails, but just point out that this kind or scal is frquntly usd to rprsnt lctron transport chains in biochmistry. Th tndncy is that lctrons ar transfr from coupls with mor ngativ uction potntials to thos with mor positiv potntials. Sinc ths ar standard stat potntials, on must bwar that 23

24 th tru uction potntials will b alt by concntrations of th ucd and idizd forms. Howvr, in many instancs, th cntrs ar fixd within protins or protin complxs, so thr is no chang in concntration possibl as lctrons ar transfr within a complx with fixd gomtry. Howvr, in th functioning lctron transport chain, th ratios of ach componnt, A A, will b dtrmind by th stady stat concntrations. If A is idizd vry rapidly by th nxt componnt along th chain thn A << A and th uction potntial will b considrably mor positiv (i.., bttr idant) than indicatd by th midpoint potntial. Although thr ar a numbr of xcptions (6), gnrally, lctron transfr is in th dirction towards componnts with th mor positiv midpoint potntial. Th thrmodynamics of lctron transfr ractions ar no diffrnt than othr biochmical ractions and must always progrss towards th minimum Gibbs fr nrgy. W will considr th kintics of lctron transfr ractions in a sparat chaptr. Figur 4.7: Th Z schm diagram, illustrating th us of uction potntials of a sris of coupls involvd in lctron transfr chains. ach activ participant is placd at a hight in th diagram corrsponding to its uction potntial with H 2 O/O 2 at about +0.8 volts. Light gnrats strong uctants and th lctron nds up ucing NADP to NADP. Th lctron- 24

25 dficint P680 Chlorophyll is a strongr idant than O 2, and watr is idizd to form O 2 as th lctrons from watr r-uc chlorophyll P680. Govindj wbsit Figur 4.8 shows anothr xampl, illustrating th photosynthtic schm for grn sulfur bactria (Chlorobiaca). In this cas, light activats a bactriochlorophyll (P 840 ) which bcoms a strong uctant, ucing th primary accptor (A 0 ), which is a modifid bactriochlorophyll. lctrons thn flow to a quinin-lik molcul, A 1, and thn, via svral F/S cntrs to a frin. Thr ar two options at this point. Thr is a cyclic lctron transfr pathway in which th lctrons ar passd to a mnaquinon within th mmbran and, vntually, ucs th idizd P 840. This pathway includs th bc 1 complx which coupls th lctron transfr raction to th gnration of a transmmbran proton lctrochmical gradint, Δp in this diagram. This will b discussd in th nxt chaptr. Altrnativly, th frin can uc NADP to NADP. In this non-cyclic pathway, lctrons from th idation of H 2 S ar usd to uc P 840, yilding lmntal sulfur, which can b furthr idizd by ths organisms to sulfat. Figur 4.8: Schmatic of th photosynthtic lctron transfr pathways of th grn sulphur bactria. Th componnts ar placd according to thir midpoint potntials. Light (hν) xcits th P 840 activ-sit chlorophyll, which bcoms a strong uctant, initiating lctron transfr which can b ithr cyclic or non-cyclic. (Figur is Fig. 5.5 in (7)) 25

26 4.7 Ambint potntial in a living cll and idativ strss In addition to th many mtabolic ractions, thr ar many othr dpndnt procsss in both ukaryotic and prokaryotic clls, including protin folding, transcriptional rgulation, nzym rgulation and signal transduction. Whras in th laboratory on is usually striving to rach quilibrium to mak a masurmnt, in living clls, as w hav alrady discussd th ractant concntrations ar maintaind in a stady stat that is distinctly not at quilibrium. Th concntrations of th ucd and idizd forms of coupls within clls is dtrmind by th rats by which thy ar producd and utilizd in a myriad of biochmical ractions. W saw, for xampl, in Sction 3.13, th rsults of on mathmatical modl of glycolysis showing that many, but not all of th ractions wr clos to quilibrium conditions. In gnral, in som sts of biochmical ractions will b nar quilibrium bcaus th rats of th ractions ar fast compa to th ractions coupling th ractions to othrs taking plac within th cll. On natural st of barrirs to rapid quilibration within clls ar th boundaris btwn intracllular compartmnts and organlls(8, 9). Hnc, th ambint potntial of th cytoplasm of a mammalian cll is distinct from that of th nuclus or that of th ndoplasmic rticulum or th mitochondrion. Howvr, vn within ths organlls, not all th ractions ar ncssarily maintaind at or vn nar a singl solution potntial. In th cytoplasm, for xampl, thr ar sts of ractions that ar quilibratd with th NAD /NAD coupl, and anothr st of ractions quilibratd with th NADP /NADP coupl. Ths ar not ncssarily in quilibrium with ach othr bcaus of th kintics of th ractions linking ths raction ntworks(9). Many cllular procsss that ar -rgulatd dpnd on th status of disulfid bonds btwn cystins is ky nzyms or transcription factors, for xampl. Th formation of disulfid bonds may also b simply part of th protin folding procss rqui for forming 26

27 a stabl, nativ protin. On has an quilibrium btwn th ucd and idizd cystin pair within a protin 1 protin(cysscy) + 2 protin(cysh) 2 (4.35) W can also rfr to this as th cystin/cystin or sulfhydryl/disulfid coupl. As this raction has bn writtn, th ucd cytins ar assumd to b protonatd, but this dpnds ntirly on th ph. Protons hav not bn includd to balanc th raction to mphasiz that this raction occurs at constant ph. Figur 4.9: Th structur of glutathion. Oxidation forms a disulfid-linkd dimmr. In ukaryotic clls, thr ar two major systms which dtrmin th status of Prot(CySH) 2 /ProtCySSCy in protins: 1) glutathion, a tripptid with on cystin (Figur 4.9), which can xist in ithr a ucd (GSH) or idizd form (GSSG); and 2) thioins (Trx) or protins within th thioin family(10). Thioins ar small protins which contain a pair of cystins in an xposd loop (s Figur 4.10) which can also b ithr ucd or idizd, Trx(SH) 2 /TrxSS. Thr ar a numbr of diffrnt thioins with spcific rols, as wll as protins with thioin folds or domains that ar -activ. In mammalian systms, fr cystin circulats in th plasma and th status of this cytin pool is th major dtrminant of th quilibratd coupls that ar xtracllular. 27

28 Figur 4.10: Structur of th ucd form of yast thioin 1 from yast (Saccharomycs crvisia). (Figur is from (11). ) Th rportd status of a cll or cllular compartmnt is usually dtrmind xprimntally by th status of on of th ky coupls listd abov(9, 10). Of cours, th ffctiv solution potntial will b diffrnt for various compartmnts within a ukaryotic cll, such as th cytoplasm, mitochondrion, ndoplasmic rticulum, tc. Dpnding on th procss, th ambint potntial of intrst may b on rportd by glutathion, but on of th othr ky dominant coupls (such as thioin or NAD) may b mor significant. Figur 4.11 shows som rprsntativ ambint potntials for diffrnt ukaryotic cllular compartmnts. Gnrally, th mitochondrion and cll cytoplasm ar consid to b ucing nvironmnts, and this is supportd by th quantitativ masurmnt of th stady stat potntials indicatd in Figur

29 Figur 4.11: stimats of th ambint potntials of cllular compartmnts in a ukaryotic cll, including th circulating blood plasma. Diffrnt dominant coupls ar indicatd. Ths valus will b dpndnt on th physiological stat of th cll (Figur is from (9)). Th glutathion-linkd solution potntial within th mitochondrion is about -300 mv, which is significantly mor ucing than th GSH/GSSG potntial in th cytoplasm (-260 mv for prolifrating clls). Ths valus will dpnd on th physiological stat. Th ndoplasmic rticulum, which is whr protin disulfids ar mad, is much mor idizing, with a GSH/GSSG potntial of about -150 mv. In gnral, protin disulfids ar rarly found within th cytoplasm but ar much mor common in scrtd protins. Howvr, th formation of disulfids as part of protin folding, is not a spontanous raction with O 2 in most cass, but is catalyzd by spcific nzyms(10, 12, 13), both in ukaryotic clls (in th ndoplasmic rticulum) and in prokaryots (in th priplasm of Gram ngativ bactria) Oxidativ strss. Oxidativ strss (14)dscribs pathological situations usually rsulting from th production of ractiv ygn spcis (ROS), which includs hydrogn prid (H 2 O 2 ), suprid (O 2 - ), prynitrits (OONO - ), organic hydroprids (ROOH) and hydryl radicals (HO ). Ths ar pro-idants and can promot th idation of cllular componnts, rsulting in disas stats. Ractiv ygn spcis can b gnratd by lmnts of th rspiratory chain in mitochondria. Raction of ractiv ygn spcis with th glutathion pool will rsult in ucing th concntration of ucd glutathion and may 29

30 rsult in lowring th total concntration of glutathion. A cascad of consquncs rsults, lading to various pathological conditions, dpnding on th contxt. 4.8 Th ph-dpndnc of th midpoint potntial Th majority of or lctron transfr ractions in biochmistry ar accompanid by proton transfr ractions, such as th uction of a disulfids in (4.35). For xampl, if thr is a proton binding sit on ractant A, th uction of A to A will incras th ngativ charg on th molcul and, if thr is a proton binding sit availabl, th positivly chargd proton might bind. In principl, ach ractant in (4.12) could b comprisd of multipl protonatd spcis, as discussd in th prvious chaptr. Hnc, ractant A will consist of a mixtur of A, A (H + ) 1, A (H + ) 2, A (H + ) 3 tc. up to som maximum numbr of bound protons, dpnding on th numbr of availabl sits. Upon uction, A will, similarly, b comprisd of a distribution of protonatd spcis. This is important bcaus th uction potntial of ach diffrnt protonatd spcis may b uniqu. It is likly to b asir to uc a mor protonatd spcis sinc it carris mor postiv charg, i.., th protonatd spcis will hav a mor positiv uction potntial. Howvr, by using th transformd thrmodynamic functions, assuming a constant ph, w nd not b concrnd about th spcifics of th distributions of th protonatd spcis in ordr to dfin th basic thrmodynamics. This assums, as w did in dfining th transformd Gibbs fr nrgy function, that th protonation ractions ar rapid and th protonatd spcis ar always quilibratd. Howvr, it is clar that upon uction, th distribution of th protonatd spcis may chang and, mor important for us at this tim, th avrag numbr of bound protons may also chang. In Chaptr 3 w drivd th xprssion in quation (3.47) dscribing th phdpndnc of th transformd Gibbs raction fr nrgy, Δ G ' r, and th sam rlationship is 30

31 also valid for th ph-dpndnc of th standard stat transformd Gibbs raction fr nrgy, Δ G 'o r. Δ ( rg ) ( ph ) ' TP,, ξ = 2.303RTΔ N r H (4.36) In this xprssion, rcall that Δ r N H is th chang in th numbr of bound protons (pr mol of raction progrss) for th raction undr th spcifid conditions. Lt s go back to raction (4.12), but assum that thr ar coupld protonation ractions. Substituting from quation (4.22), w gt Δ ( rga) Δ ( rgb ) = 2.303RTΔ rnh (4.37) ( ph ) ( ph ) ' ' TP,, ξ TP,, ξ or for ach half raction ( m ( A)) 2.303RT = ΔrN ( ph ) ν F ' TP,, ξ ( m ( B)) 2.303RT = ΔrN ( ph ) ν F ' TP,, ξ H H ( A) ( B) (4.38) whr Δ rn ( H A ) and ΔrNH( B) ar th changs in numbr of bound protons (pr mol) for ach half raction, and Δ N =Δ N ( A) Δ N ( B) r H r H r H (4.39) For ach half-raction, w can substitut numrical valus at 298K in quation (4.38) to gt th following. ( m ( A)) ΔrNH chang in protons bound = 59 = 59 ( ph ) ν numbr of lctrons transfr ' T, P, ξ (4.40) If Δ r N H is constant ovr th ph rang of intrst, this is simply intgratd to yild 31

32 Δ N = 59 ( ph ph ) (4.41) r H mph, 2 mph, 1 2 ν 1 This says that th ph-dpndnc of th midpoint potntial can b usd to dtrmin th chang in th numbr of bound protons for a half-raction, providd that w know th numbr of lctrons ( ν ) involvd in th raction. 4.9 xampl: Th ph-dpndnc of th midpoint potntials of th NAD /NAD and aloactat/malat coupls. W will considr as an xampl th quation L-malat + NAD aloactat + NAD half-raction 1: NAD + 2 NAD (4.42) half-raction 2: aloactat + 2 malat This raction is catalyzd by malat dhydrognas and is part of th TCA cycl. W saw in Sction 4.5 that both th ν and valus for a NAD half-raction could b xprimntally m dtrmind by potntiomtric titration, as in Figur 4.5. W can now dtrmin th valu of Δ r N H for th uction of NAD by plotting th valu of th midpoint potntial m ( NAD) as a function of ph by using quation (4.40). Th rsult is a straight lin, shown in Figur 4.12, with a slop of -30 mv pr ph unit. Th fact that this is a straight lin mans that Δ r N H is not changing ovr th ph rang bing xamind (ph 5 to 9). Th fact that th slop of th lin in Figur 4.12 is not zro mans that thr is a chang of protonation of NAD upon uction, as w alrady know. Th slop of 30 mm/ph unit tlls us that ΔrN ν H is 1/2, so Δ N = 1 r H ovr th full rang of ph (sinc ν = 2 ). Th midpoint potntial of NAD gts mor ngativ as th ph is incrasd. NAD is a bttr uctant at highr ph. 32

33 NAD +2 +H NAD or NAD +2 +H NADH (4.43) Also shown in Figur 4.12 is th ph-dpndnc of th midpoint potntial of th aloactat (OAA)/malat coupl. From Tabl 4.1, w s that m,7 = 165mV for this coupl, which is also indicatd in Figur Th ph-dpndnc of th midpoint potntial is a straight lin with a slop of -59 mv/log unit. Sinc this is a 2-lctron raction ( ν = 2 ), w conclud from quation (4.40) that Δ rnh = 2 throughout th ph rang. At any ph, th diffrnc btwn th two lins is Δ = ( NAD / NAD ) ( OAA / malat) ' ' ' m, ph m, ph m, ph ΔrG Δ mph, = ν F (4.44) Undr standard stat conditions (1 M concntrations) th raction would go in th opposit dirction than indicatd in (4.42). Undr mtabolic stady stat conditions, howvr, th dirction of th raction is as writtn, as rqui by th TCA cycl to produc NAD. Figur 4.12: Th ph-dpndnc of th NAD /NAD and th OAA/L-malat coupls. 33

34 4.10 Thrmodynamic rciprocity of intractions btwn proton binding and uction potntial In th xampl of NAD, dscribd abov, th idizd form rmaind dprotonatd and th ucd form rmaind fully protonatd throughout th ph rang. Now lt s look at a situation whr w hav a coupl, A /A, in which both th idizd and th ucd forms can bind 1 proton, but that th proton affinity, or pk, is shiftd upon uction. W will assign th pk of th idizd form, pk a valu of ph 6. Upon uction from A to A, th proton affinity is gratr so it will bcom protonatd at a highr ph valu (lowr [H + ]). Furthrmor, w will spcify that w ar abl to masur th xtnt to which A is ucd, but cannot distinguish whthr it is protonatd or unprotonatd. Th xprimnt will b to chang th solution potntial, and masur th apparnt midpoint potntial, mph,, at a sris of diffrnt ph valus, as in Figur Th qustion is how dos th apparnt midpoint potntial vary with ph from ph 4 to 10, a span that ncompasss both th pk of th ucd and idizd forms of th coupl. This is a usful problm to xamin bcaus w will introduc som of th procdurs that will b usd throughout th txt whn approaching problms daling with thrmodynamics in a numbr of diffrnt contxts. To bgin, lt's idntify th numbr of diffrnt molcular spcis w hav in our solution. Ths ar A : idizd, not protonatd A H + : idizd, protonatd A : ucd, not protonatd A H + : ucd, protonatd Ths four spcis ar rlatd by svral quations. Th protonation ractions ar writtn in th dirction of dprotonation, and th quilibrium constant is a proton dissociation 34

35 quilibrium constant, usd to dfin th pk. Not that th ph at which half of th spcis (.g., A ) is protonatd, (.g., [A ] = [ AH + ]), thn [H + ] = K, or ph = pk. Also, sinc w ar daling with chmical spcis and not biochmical componnts, w hav droppd th prims ovr th thrmodynamic paramtrs. 1) A = A + A H + A + A H total + + 2) protonation of th idizd spcis: A H A + H [A ][ H ] ; ( + = Δ r ) = + log [ AH ] K G H pk K + 3) protonation of th ucd spcis: A H A + H + H K G H pk K + [A ][ ] ; ( + = Δ r ) = + log [ A H ] 4) uction of th idizd spcis: A + A [ A ] [ A ] = 59log ; Δ G ( ) = 2.303RT log = F o o o h m1 r 1 m1 [ A ] [ A ] 5) uction of th protonatd idizd spcis: A H + A H + + (4.45) [ A H ] [ A H ] G RT F + + o o o h = m2 59log ; Δ r 2( ) = log = + + m2 [ AH ] [ AH ] In quations 4 and 5, abov, it is assumd that th tmpratur is 298K, in ordr to gt th valu of 59 mv. In ths quations, h is th solultion potntial, xprimntally dtrmind. It is usual to us units of mv in plac of volts, but rmmbr to us volts whn changing units to jouls. Th protonation and ractions abov can b put into a simpl thrmodynamic cycl, shown in Figur W can s from Figur 4.10 that thr ar two diffrnt pathways to go from th idizd spcis A to th protonatd, ucd spcis, A H +. 35

36 Sinc, th transformd Gibbs raction fr nrgy is a stat function, th fr nrgy chang must b idntical no mattr which way w go. A can b ithr protonatd first and thn ucd, or ucd first and thn protonatd. Th th fr nrgy chang will b th sam. Hnc, w can conclud that + Δ G ( H ) +Δ G ( ) = - Δ G ( ) +Δ G ( H ) + r r 2 r 1 r (4.46) Th ngativ sign in front of th raction fr nrgy trms for th protonation ractions com from th fact that w dfind ths in th dirction of dprotonation in (4.45). From (4.46) it follows that RT K RT K ln = log F K F K 59( pk pk ) = ( ) o o m2 m1 (4.47) Figur 4.13: Thrmodynamic cycl showing two quivalnt pathways of going from A to A H + (indicatd by th arrows). quation (4.47) tlls us that if th diffrnc in th midpoint potntials btwn th protonatd and dprotonatd forms is spcifid, this also dfins th diffrnc btwn th pk valus of th ucd and idizd forms. This is mor radily sn in a fr nrgy diagram, Figur 4.14, which shows th drop in th standard stat molar fr nrgy as 36

37 ractants ar convrtd to products. W will ncountr ths diagrams at many points in th txt, particularly whn w discuss th thrmodynamics of ligand binding. Figur 4.14: Fr nrgy diagram showing th rlativ valus of th standard stat molar Gibbs fr nrgy valus of th systm in diffrnt chmical stats. ach lvl is lablld by th spcis prsnt. For xampl, th top lin (A + H ) stands for th o o o sum of th standard stat chmical potntials for ach of th spcis, ( μ + μ + μ ), A + H tc. Th bottom lin is th lvl of th standard stat chmical potntial of A H +. Th two sts of vrtical lins on th lft show th situation in which uction incrass th proton affinity of molcul A. By ncssity, protonation of molcul A must also incras th affinity for th lctron, indicatd by th largr magnitud of th drop in fr nrgy associatd with uction of A H + compa to A. Th two sts of vrtical lins on th right dpict th situation whr uction of molcul A has no ffct on th proton affinity, and vic vrsa. Th coupling fr nrgy quantifis th mutual influnc btwn th protonation and lctron transfr ractions. On important concpt that is asily undrstood in trms of a fr nrgy diagram is th ida of thrmodynamic coupling or cooprativity. In th currnt problm, w hav stipulatd that uction of th molcul A rsults in incrasing th affinity for proton binding. Lt s rarrang quation (4.46) + Δ G ( ) Δ G ( ) = Δ G ( H ) Δ G ( H ) o o o + o r 2 r 1 r r (4.48) Th diffrnc in th raction fr nrgy of ucing th protonatd and dprotonatd forms is xactly matchd by th diffrnc of th raction fr nrgy of protonating th 37

38 ucd and idizd forms. Ths diffrncs ar calld th coupling fr nrgy, Δ G r o coupling. Δ G =Δ G ( ) Δ G ( ) = Δ G ( H ) Δ G ( H + ) o o o o + o r coupling r 2 r 1 r r (4.49) If th raction fr nrgy of binding a proton is favo by, say -20 kj/mol by uction, thn th binding of a proton will, by ncssity, mak th uction mor favorabl by th sam -20kJ/mol. If uction has no influnc on th protonation, thn protonation will o hav no influnc on th uction potntial, i.., Δ G = 0 and thr is no r coupling cooprativity. This is calld rciprocity, and is a form of cooprativity. This concpt is ncount vry frquntly in biochmical ractions and in ligand binding. Th coupling fr nrgy is shown on th fr nrgy diagram in Figur 4.14 by showing th cas whr o it is assumd that thr is no coupling ( Δ G = 0 ) on th right sid. Th standard stat r coupling fr nrgy of th systm is lowr du to th addition of th favorabl (ngativ) coupling fr nrgy, which stabilizs nrgy in th diagram. A H + rlativ to A, shown by th lowr standard stat fr Th quations in (4.45) rprsnt a spcific modl that w can us to simulat data or, if w wr rally doing an xprimnt, to fit to data. Although w hav quations dfining o o m 1and m2, ths cannot b dirctly masu. Instad, w masur th "apparnt" or transformd midpoint potntial,. W ar now back to th prim in bcaus m, app m, app w ar kping th ph constant during th raction and grouping spcis in psudo-isomr groups that diffr only by th stat of protonation. This is simply th transformd thrmodynamic paramtr, as w discussd in th prvious chaptr. Th valu of is mapp, what w can actually masur by a potntiomtric titration sinc w hav no way to know whthr th molcul is protonatd or not. It is usful to s how mapp, is rlatd to th non- 38