Non-adiabatic%20electron%20transfer%20in%20chemistry%20and%20biology

1
Non-adiabatic electron transfer in chemistry and
biology
Igor Kurnikov Dept. of Chemistry Carnegie Mellon
Univ.
2
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

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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

4
Marcus Theory 1992 Nobel
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Theory of unimolecular ET reactions.
Solvent
Donor
Acceptor
Bridge
Solvent
- electronic donor-acceptor coupling decays
rapidly with donor/acceptor distance
- free energy of the ET reaction
- ET reorganization energy - depends on changes
of solvation and redox-center geometries upon ET
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Marcus Theory
The reaction coordinate of ET reaction is a
nuclear coordinate with different equilibrium
values for the donor and acceptor states
e
Acceptor
Donor
ET reaction coordinate
XD reaction coordinate equilibrated with donor
charge distribution. XA reaction coordinate
equilibrated with acceptor charge distribution.
At the crossing point XC energies of the donor
and acceptor states are equal.
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Calculation of the crossing point.
Free energy of the donor state vs reaction
coordinate
Free energy of the acceptor state
The crossing point can be calculated using these
expressions
Activation energy can be expressed as
Where reorganization energy ? is
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Normal and Inverted Regimes of ET reactions
? G0
In reality other factors also play a role in the
electron transfer problem distance between
donor and acceptor, diffusion can be rate
limiting step. The inverted regime has only been
observed in rigid systems, such as proteins.
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Quantum expression for ET rate.
Slow(classical) coordinate y and Fast(quantum)
coordinate q
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Experimental Evidence for Inverted Region
1 eV 1.6 x 10-19 J
J. R. Miller et al. J. Am. Chem. Soc. 1984,
106,3047
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Finite-Difference Poisson-Boltzmann Equation
calculations of electrostatic energies.
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
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Calculations of outer sphere reorganization
energy for Electron Transfer reaction
Kurnikov, IV Zusman, LD Kurnikova, MG Farid,
RS Beratan, DN J. Am. Chem. Soc.(1997),v.119,p.
5690      
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Reaction rates and Marcus theory (16)
Duttons rule
In the photosynthetic reaction center (in this
case of bacteria) a number of electron transfer
reactions take place. By modifying amino acids in
the right places, ? G0 can be changed.
The distance dependence of the rate depends on
the environment. Proteins behave like other
solvents.
Dutton log10kET13-0.6(R-3.6)-3.1(? G0?)2/?
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Mcconnels Model for ET coupling.Superexchange
interactions.
VBB
VBB
VDB
EB
EB
VBA
ED
EA
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PATHWAYS calculations of ET electronic coupling.
prefactor 0.1 - 1.0 eV
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Adiabatic and non-adiabatic terms.
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Computation of HDA Minimization of energy
splitting of donor/acceptor localized electronic
states.
Energies of two lowest electronic states
2HDA
Electrical field in the direction from the donor
to the acceptor
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Using Koopmanns theorem to extract
donor/acceptor electronic coupling from the the
energy splitting of Hartree-Fock molecular
orbitals.
To compute ET coupling using Hartree-Fock method
consider a system with an extra electron and look
to the splitting of highest occuped orbitals or
the system with one electron removed and look to
the spliting of lowest unoccupied orbitals.
Connection between orbital energies and energies
of the lowest electronic states of the system is
given by Koopmanns theorem
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Electron transfer in Ru-modified azurins
Acceptor Ru(bpy)2(Im)(HisX)3
Azurins surface labeled with Ru (bpy)2
(im)(HisX)2 (bpy2,2 -bipyridine,imimidazole)
.(X83,107,109,122,124,126). ET from Cu to
Ru3 . ET monitored by laser transient
adsorption spectroscopy technique. Ru3 is
generates by exciting Ru2 and quenching by
Ru(NH3 )63 quencher (from the group of HB Gray
Caltech)
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ET rates computed for individual MD snapshots of
azurin derivatives
ET rate experiment (s-1)
ET rate theory for snapshots (s-1)
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Theory vs experiment for Electron Transfer in
ruthenated azurin derivatives.
(s-1)
102
104
106
108
(s-1)
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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 3ZnDMb with transient
  absorption spectroscopy.
• Zn-Myoglobin was modified by methylation(neutraliz
  ation) 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 didnt
  change substantially.

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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.

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Rate of bimolecular ET in rapid-equilibration
regime.
- unimolecular ET rate in the i-th configuration
strongly geometry dependent. The system
consist of two proteins in volume V
- Second-order bimolecular ET rate constant
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Effective energy approach to calculate relative
bimolecular ET rates.
Effective energy combines intermolecular energy
and ET rate for a configuration i
Ratio of bimolecular ET rates for different
experimental conditions (chemically modified
proteins, different pH etc.)
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).
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Computation of effective ET free energy
changes.
Effective free energy changes can be calculated
using free energy perturbation method and Monte
Carlo simulations with the effective energy
functional
Only a small number of configurations will be
sampled as donor-acceptor coupling rapidly
decays with distance and the effective energy
increases.
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Calculations of effective energies of protein
configurations (intermolecular interaction
energies and ET rates).
- Computed using PATHWAYS model
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.
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Electronic coupling of surface atoms of myoglobin
(left) and cytochrome- b5 (right) to their
hemes.
Red - strong electronic coupling to the heme Blue
- weak electronic coupling to the heme
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Mutation positions
S92D
V67R
Heme propionates
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MC trajectory of Zn-myoglobin and cytochrome b5
with effective ET energy.
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MC/effective energy calculations of changes of
bimolecular ET rate between ZnMb and cytb5 on
myoglobin surface modifications
CIF charges in the field electrostatic model CE
- 3 PB calculations in every MC point CE ?pKa
take into account pKa changes on protein
complex formations
Liang ZX, Kurnikov IV, Nocek JM, Mauk AG, Beratan
DN, Hoffman BM, JACS(2004)(accepted)
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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?

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Hydroxylamine oxidoreductase (HAO)
HAO, enzyme from autotrophic bacterium, Nitrosomon
as europaea, catalyzes the reaction (second step
in oxidation of ammonia to nitrite
(nitrification))
E1/2 -20 mV
Hydroxylamine oxidoreductase (HAO). Colors shows
three identical monomers of HAO and eight heme
cofactors of one of the monomer.
Nitrification is a part of geochemical nitrogen
cycle2. Important for environment control An
essential step of wastewater processing and in
agriculture - deactivation of fertilizers.
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Heme cofactors of HAO
Red Heme P460 active sites where
hydroxylamine is oxidized
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Electron Transfer in HAO during hydroxylamine
oxidation.Two paths for electron redistribution.
E0(mV)
-200
-100
?
0
100
?
200
?
- P260 heme active site
300

• E0 0 mV - electron acceptors

• E0 lt -40 mV oxidized

• E0 gt 100 mV reduced

• E0 lt -100 mV oxidized,
• exposed to solvent

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Electron Transfer in HAO during hydroxylamine
oxidation.Two paths for electron redistribution.
E0(mV)
-200
-100
?
?
0
100
200
- P460 heme active site
300

• E0 0 mV - electron acceptors

• E0 lt -50 mV unoccupied

• E0 gt 100 mV occupied

• E0 lt -100 mV unoccupied,
• exposed to solvent

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Electron Transfer from HAO to c554.A lock for
the electrons.
E0(mV)
no c554
-200
with c554
-100
3
0
c554 hemes
100
2
Reduced HAO
200
Oxidized HAO
8
300
1
E0 of the solvent-exposed heme 1 become more
positive by 100 mV upon specific complex
formation with c554 E0 of normally reduced heme 2
become more negative upon reduction of Hemes 3
and 8
to c554
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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.

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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).

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Nitrogenase complex.
Av1
FeMoco cofactor
P Cluster
Fe4S4S4Cys
Av2
20 Å
2 x MgATP
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Cofactors of the nitrogenase.
Fe protein (Av2)
MoFe protein (Av1)
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Cycle of delivery of an electron to the active
site of nitrogenase.
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Reduced
Oxidized
MgATP and MgADP
MoFe-cofactor
P-cluster
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Nitrogenase cofactors redox-potentials changes.
-1200
Experiment Theory Electron jump
eP4.0
-1100
-900
Av2-Av1 Complex
-800
-700
Em (mV)
-600
eP10.0
-500
eP4.0
Av2-MgATP Complex
-400
eP10.0
-300
P-cluster
FeMoco cofactor
-200
-100
Fe Protein (Av2)
MoFe Protein (Av1)
0
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Computation of ET rates in nitrogenase.
ET Step Don/Acc coupling HDA(eV) Reorg energy ?(eV) ET free energy ?G0(eV) ET rate kET(s-1)
Fe4S4S4 -gt P-cluster 3.10-6 0.3 - 0.5 -0.4- -0.2 4.104 - 2.105
P-cluster -gt FeMoco 1.10-5 0.2 - 0.4 0.1 - 0.2 5.0103 5.0104
Fe4S4S4 -gt P-cluster (concerted) 101 103
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Computing ET rates in nitrogenase.
Av2
101-103(s-1)
4.104-2.105(s-1)
4.104-2.105(s-1)
Av1
P-cluster
FeMoco-cofactor
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