Non-adiabatic electron transfer in chemistry and biology

Igor KurnikovDept. of ChemistryCarnegie Mellon Univ.

Electron Transfer reactions in biology.

• Part of enzymatic oxidation-reduction reactions

• Photosynthesis• Energy storage and

transfer• Synthesis and chemical

degradation• Protein folding control (S-S

bridge formation)• DNA repair• Enzyme activation

Unimolecular vs bimolecular ET reactions

• Unimolecular ET reactions - same molecule or intermolecular complex.

• Only “one” conformation although fluctuations of the structures can be important.

• Bimolecular reactions - diffusion of reagents, many orientations and conformations.

• A small fraction of configurations contributes to ET.

• Bimolecular ET = Unimolecular ET + Docking

Marcus Theory: 1992 Nobel

Theory of unimolecular ET reactions.

Tk

G

TkHk

BB

DAnaET

4

exp4

1220

2

DAH - electronic donor-acceptor coupling decays rapidly with donor/acceptor distance

0G - free energy of the ET reaction

- ET reorganization energy - depends on changes of solvation and redox-center geometries upon ET

Donor AcceptorBridgeSolvent Solvent

Donor Acceptor

e

Donor

Acceptor

Fre

e en

ergy

Nuclear coordinateXD XAXC

XD: reaction coordinate equilibrated withdonor charge distribution.XA: reaction coordinate equilibrated withacceptor charge distribution.

At the crossing point XC energies of the donor and acceptor statesare equal.

Marcus TheoryThe reaction coordinate of ET reactionis a nuclear coordinate with different equilibrium values for the donor and acceptor states

ET reaction coordinate

Calculation of the crossing point.

22

1D

eqDD XXKGG

Free energy of the donor state vs reaction coordinate:

Free energy of the acceptor state:

22

1A

eqAA XXKGG

The crossing point can be calculated using these expressions:

DAADC XXK

GXXX

0

2

1

Activation energy can be expressed as:

4

20GGa

Where reorganization energy λ is:

22

1AD XXK

Normal and Inverted Regimes of ET reactions

G0

Normal: increase of G0

decreases the rateNo activation barriermaximum kET

Inverted: decrease of G0 decreases the rate

G0

invertednormal

In reality other factors also play a role inthe electron transfer problem: distance between donor and acceptor, diffusion can be rate limiting step. The invertedregime has only been observed in rigidsystems, such as proteins.

Tk

G

TkHk

BB

DAnaET

4

exp4

1220

2

Quantum expression for ET rate.

.).(2 2 CFHk DAET

Slow(classical) coordinate y and Fast(quantum) coordinate q:

Tk

mG

mTk

Hk

By

y

m

mqq

yB

DAET

4exp

!

/exp

4

2202

Experimental Evidence for Inverted Region

J. R. Miller et al. J. Am. Chem. Soc. 1984, 106,3047

4/)(lnln

/lnln2

/

oET

aET

RTEET

EAk

RTEAk

Aek a

1 eV = 1.6 x 10-19 J

Finite-Difference Poisson-Boltzmann Equation calculations of electrostatic

energies.

TkB/)(sinh)(4)]()([ 2 rrrr

Poisson-Bolzmann equation is solved on a rectangular grid by finite-difference method. Atomic charges are from AMBER force-field. PARSE atomic radii parameter set.

Electrostatic energy calculated with: i

iieltot qE

2

1

Calculations of outer sphere reorganization energy for Electron Transfer reaction

E2 - E1

+1e -1e

Prot

solv

E2

+1e -1e el

E1

Kurnikov, IV; Zusman, LD; Kurnikova, MG; Farid, RS; Beratan, DN;

J. Am. Chem. Soc.(1997),v.119,p.5690      

Reaction rates and Marcus theory (16)

Dutton’s rule

In the photosynthetic reaction center(in this case of bacteria) a number ofelectron transfer reactions take place.By modifying amino acids in the rightplaces, G0 can be changed.

The distance dependence of the rate depends on the environment.Proteins behave like other solvents.

Dutton: log10kET=13-0.6(R-3.6)-3.1( G0+)2/

Mcconnel’s Model for ET coupling.Superexchange interactions.

ED EA

EB

VBB VBB

VDB

VBAEB

1

n

DB

BBDADBDA EE

VVVH

PATHWAYS calculations of ET electronic coupling.

))8.2(7.1exp(36.0

))4.1(7.1exp(3.0

6.0

R

R

prefactorH

HBondi

TSi

Bondi

HBondi

TSi

Bondi

iDA

prefactor = 0.1 - 1.0 eV

Adiabatic and non-adiabatic terms.

Computation of HDA: Minimization of energy splitting of donor/acceptor

localized electronic states.

2HDA

Energies of two lowest electronic

states

Electrical field in the direction from the donor to the acceptor

Electron transfer in Ru-modified azurins

Acceptor Ru(bpy)2(Im)(HisX)3+

Azurins surface labeled with Ru (bpy)2 (im)(HisX)2+ (bpy=2,2~ -bipyridine,im=imidazole) .(X=83,107,109,122,124,126). ET from Cu+ to Ru3+ .

ET monitored by laser transient adsorption spectroscopy technique. Ru3+ is generates by exciting Ru2+ and quenching by Ru(NH3 )6

3+ quencher

(from the group of HB Gray – Caltech)

ET rate theory for snapshots (s-1)

ET

rat

e ex

peri

men

t (s-1

)

104 108102 106

108

106

104

102

1

1

His122

His126His124

His83

His107

His109

ET rates computed for individual MD snapshots of azurin derivatives

102 104 106 108

(s-1)

(s-1

)

Average ET rate theory

ET

ra

te e

xp

eri

me

nt

11

102

104

106

108 His122

His83His109

His124

His126

His107

Theory vs experiment for Electron Transfer in ruthenated azurin derivatives.

ET between Zn-myoglobin and cytochrome b5

• Photoinduced ET from Zn-substituted Mb to (Fe3+)cyt b5 was studied by monitoring quenching by cyt b5 of photoexcited 3*ZnDMb with transient absorption spectroscopy.

• Zn-Myoglobin was modified by methylation(neutralization) of heme propionates and mutations to introduce positive (V67R mutation) or negative (S92R) aminoacids near heme.

• Large variations of ( range of ~1000) bimolecular rate constant has been observed while binding constant measured by NMR and calorimetry didn’t change substantially.

Diffusion and rapid-equilibration limits of bimolecular ET reactions

• Diffusion limit: ET in “active” configuration reactions are faster than equilibration.

• One needs to consider explicitly diffusion from initially prepared configurations to the “active” configurations. ET rates in “active” configurations are not important as long as they are large enough.

• Rapid-equilibration limit: the system is equilibrated over configurations. Only free energies of different configurations and unimolecular rates in these configurations are important. Diffusive dynamics is not important. This regime is realized for weakly bound protein-protein complexes and slow ET rates in the complex.

Rate of bimolecular ET in rapid-equilibration regime.

iET

i

i B

i

B

i

iET

ii

BMET

ET k

TkE

TkE

kpkV

k

exp

exp)2(

iETk - unimolecular ET rate in the i-th configuration

strongly geometry dependent.

The system consist of two proteins in volume V

)2(ETk - Second-order bimolecular ET rate constant

Effective energy approach to calculate relative bimolecular ET rates.

Tk

G

Tk

Tk

TkE

TkE

Tk

Tk

k

k

B

eff

i B

effi

i B

effi

i B

i

i B

i

i B

effi

i B

effi

ET

ET exp

exp

exp

exp

exp

exp

exp

)2(

)1()2(

)1(

)1(

)2(

)2(

)1(

)2(

)2(

E

E

E

E

0/ln kkTkE iETBi

effi E

Ratio of bimolecular ET rates for different experimental conditions(chemically modified proteins, different pH etc.):

Effective energy combines intermolecular energy and ET rate for a configuration i:

Second bracket is close to 1 if zero energy correspond to isolated proteins and bimolecular ET is described by second order rate constant k(2).

Computation of effective “ET free energy” changes.

Tk

G

Tk

Tk

B

eff

i B

effi

i B

effi

exp

exp

exp

)2(

)1(

E

E

Effective free energy changes can be calculated using free energy perturbation method and Monte Carlo simulations

with the effective energy functional:

effeffeffii H

effeff

H

effeff

iH

effeffeff HHHHHHG21

1 12122

1

Only a small number of configurations will be sampled as donor-acceptor coupling rapidly decays with distance and

the effective energy increases.

Calculations of effective energies of protein configurations (intermolecular interaction

energies and ET rates).

0/ln kkTkE iETBi

effi E

2DA

iET Hk - Computed using PATHWAYS model:

HBondk

TSj

Bondi

ijkDA prefactorH

Ei – interaction energies computed using continuum electrostatics FDPB approach ( charges in the field model – one protein in the field of another or more expensive – 3 FDPB calculations in each point of MC trajectory – take care of desolvation). VdW contribution computed with excluded volume approach (fast) or with Lennard-Jones atom-atom interaction potentials.

Electronic coupling of surface atoms of myoglobin

(left) and cytochrome- b5 (right) to their hemes.

Red - strong electronic coupling to the hemeBlue - weak electronic coupling to the heme

Mutation positions:

S92D

V67R

Heme propionates

MC trajectory of Zn-myoglobin and cytochrome b5 with effective “ET”

energy.

MC/effective energy calculations of changes of bimolecular ET rate between ZnMb and cytb5 on

myoglobin surface modifications

k2/(k2)WT [Experiment]

10-1 100 101 102 103 104

k 2/(k

2)W

T [

Cal

cula

ted]

10-1

100

101

102

103

104

CIFCE

CE + pKa

CIF – charges in the fieldelectrostatic modelCE - 3 PB calculations in every MC pointCE + ΔpKa – take into accountpKa changes on protein complexformations

Liang ZX, Kurnikov IV, Nocek JM, Mauk AG, Beratan DN, Hoffman BM, JACS(2004)(accepted)

Bimolecular ET. Conclusions.• New Monte-Carlo/effective energy approach for quantitative

studies of bimolecular ET reactions in fast-equilibration regime has been introduced and applied to study ET reaction between Zn-myoglobin and cytochrome b5

• ET rate between Zn-Mb and cyt b5 is controlled by the stability of the interprotein configurations with strong donor/acceptor coupling. Configurations with strongest binding energy do not contribute to ET.

• Protonation pKa changes upon Zn-myoglobin modifications and on protein binding are important.

• Torsional flexibility is needed? Fast-equilibration limit is not valid for most positively charged derivative? Are pKs needed to be recomputed dynamically?

Hydroxylamine oxidoreductase (HAO)

HeNOOHOHNH 54222

Hydroxylamine oxidoreductase (HAO). Colors shows three identical monomers of HAO and eight heme cofactors of one of the monomer.

HAO, enzyme from autotrophic bacterium,Nitrosomonas europaea, catalyzes the reaction(second step in oxidation of ammonia to nitrite (nitrification)):

Nitrification is a part of geochemical nitrogen cycle[2].Important for environment control – An essential step of wastewater processing

and in agriculture - “deactivation” of fertilizers.

E1/2 ≈ -20 mV

Heme cofactors of HAO

Red – Heme P460 – active sites where hydroxylamine isoxidized

Electron Transfer in HAO during hydroxylamine oxidation.

Two paths for electron redistribution.

0

-100

-200

+100

+200

+300

E0(mV)

?

?

?- P260 heme – active site- E0 ~ 0 mV - electron acceptors- E0 < -40 mV – oxidized- E0 > +100 mV – reduced- E0 < -100 mV – oxidized, exposed to solvent

Electron Transfer in HAO during hydroxylamine oxidation.

Two paths for electron redistribution.

0

-100

-200

+100

+200

+300

E0(mV)

??

- P460 heme – active site- E0 ~ 0 mV - electron acceptors- E0 < -50 mV – unoccupied- E0 > +100 mV – occupied- E0 < -100 mV – unoccupied, exposed to solvent

Electron Transfer from HAO to c554.A lock for the electrons.

to c554

0

-100

-200

+100

+200

+300

no c554

with c554

c554 hemes

E0(mV)

Reduced HAO

Oxidized HAO

E0 of the solvent-exposed heme 1become more positive by ~100 mV uponspecific complex formation with c554E0 of normally reduced heme 2 become more negative upon reduction ofHemes 3 and 8

1

2

3

8

Biological nitrogen fixation reaction.

Even without MgATP ammonia synthesis is favored at 298 K and pH 7, with an estimated G0=-15.2 kcal/mol.

Substrate reduction by nitrogenase involves three basic types of electron-transfer reactions:• the reduction of Fe protein by electron carriers such as ferredoxin and flavodoxin in vivo or dithionite in vitro • transfer of single electrons from Fe protein to MoFe protein in a MgATP-dependent process with a minimal stoichiometry of two MgATP hydrolyzed per electron transfered•electron transfer to the substrate at the active site within the MoFe protein.

Motivation.

• In the nitrogenase cycle the role for ATP hydrolysis is to control the electron-transfer “gate” between protein components. How this is accomplished is the one of the two main unanswered questions about the nitrogenase mechanism (the other being how substrates are reduced at the cofactor).

2 x MgATP

[Fe4S4]S4Cy

s

P Cluster

FeMoco cofactor

Av1

Av2

20 Å

Nitrogenase complex.

Cofactors of the nitrogenase.

S Fe S

S Fe

Fe S

Fe

Fe

Fe S

S

Fe

Fe

S

S

Cys

Cys

Cys

Cys

Cys PN Cluster

Cys Ser

Fe

Fe

Fe

SS Mo

Fe

Fe

S

S

S

SCys

O

O

O

OO

O

OS

S

Fe

S

S

Fe

-

-

FeMoco cofactor

S

Fe S

Fe

Fe

S Fe

S

S

SCys

SCys Cys

S Cys

[Fe4S4]S4Cys Cluster(3-/2-)

Fe protein (Av2): MoFe protein (Av1):

P-cluster

MoFe-cofactor

Reduced

Oxidized

MgATPandMgADP

Nitrogenase cofactors redox-potentials changes.

-100

Em

(mV

)

-200

-300

-400

-500

-600

-700

-800

-900

-1100

-1200

0

Fe Protein (Av2) MoFe Protein (Av1)

P-cluster FeMoco cofactor

εP=4.0

εP=10.0

Experiment

Theory

Electron jump

εP=4.0εP=10.0

Av2-Av1Complex

Av2-MgATPComplex

Computation of ET rates in nitrogenase.

ET StepDon/Acc coupling HDA(eV)

Reorg energy λ(eV)

ET free energy ΔG0(eV)

ET rate kET(s-1)

[Fe4S4]S4 -> P-cluster

3.*10-6 0.3 - 0.5 -0.4- -0.2 4.*104 - 2.*105

P-cluster ->

FeMoco

1.*10-5 0.2 - 0.4 +0.1 - +0.2

5.0*103 –

5.0*104

[Fe4S4]S4 -> P-cluster

(concerted)

101 – 103

Computing ET rates in nitrogenase.

P-cluster FeMoco-cofactor

Av2

Av1

4.*104-2.*105(s-1)

4.*104-2.*105(s-1)

101-103(s-1)