rates&of&electron&transfer:&...
TRANSCRIPT
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Rates of Electron Transfer: Marcus Theory
Chem 204 March 31, 2014
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Scheduling Note:
• Wednesday: We will cover baEeries, fuel cells, some Big Picture Energy
• Friday: no lecture! Email homework to TA! • Monday: Solar Energy Conversion (not on Exam III)
• Next Wednesday, April 9: Review for Exam III; Exam III in evening (!), usual places, conflict exam sign-‐up
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How does an electron get from one atom to another?
• Through orbitals that overlap from one atom to another?
• Through space?
• In one concerted step from electron donor to acceptor (“superexchange”)?
• In mulYple steps from electron donor to acceptor (“hopping”)?
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How fast can an electron go from one atom to another?
• Faster than the speed of light? (hint: no)
• Within a femtosecond (10-‐15 s)?
• Within a nanosecond (10-‐9 s)?
• Within a millisecond (10-‐3 s)?
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How fast can an electron go from one atom to another?
• Faster than the speed of light? (hint: no)
• Within a femtosecond (10-‐15 s)?
• TheoreYcal max: rate constant ~1013 s-‐1
• Within a nanosecond (10-‐9 s)?
• Within a millisecond (10-‐3 s)?
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How fast can an electron go from one atom to another?
• Faster than the speed of light? (hint: no)
• Within a femtosecond (10-‐15 s)?
• TheoreYcal max: rate constant ~1013 s-‐1
• Within a nanosecond (10-‐9 s)?
• Within a millisecond (10-‐3 s)?
Range: down to 1 per sec or less!
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Redox potenYals and band edges
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Redox in nature: Overview of the metabolism of S. aciditrophicus.
McInerney M J et al. PNAS 2007;104:7600-7605
©2007 by National Academy of Sciences
Before we think about rates of electron transfer, let’s think about energy, reactants, and products
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• What is K?
• What is ∆G?
• What is k (rate constant)?
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
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• What is K? K = 1
• What is ∆G?
• What is k (rate constant)?
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
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• What is K? K = 1 (by inspecYon)
• What is ∆G? ∆G = 0 (by inspecYon)
• What is k (rate constant)?
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
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• What is K? K = 1 (by inspecYon)
• What is ∆G? ∆G = 0 (by inspecYon)
• What is k (rate constant)? “slow” (by measurement using isotope labels)
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
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Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
Draw reacYon coordinate diagram: energy vs. reacYon coordinate; If k is small, what does imply about the acYvaYon energy?
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Many proteins have metal ions that undergo electron transfer
Native Cyt c: E° = 262 mV Met80His: E° = 41 mV
These cytochrome proteins have iron ions bound in “heme” groups; Iron is redox acYve and its redox potenYal is tuned with metal ion environment (an inducYve effect)
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Different types of hemes
NN
NN
CH3
CH3
CH3 CH3
CH3
S
C47
OOH
C53 O
OH
S
CH3Cys
Cys
Fe
NN
NN
CH3
CH3
CH3
CH2
C47
OOH
C53 O
OH
O
H
OH
Fe
NN
NN
CH3
CH3
CH3 CH3
CH2
CH2
CO
OHC O
OH
Fe
heme b heme a heme c
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Nitrogen Fixation
N2 + 8 H+ + 8 e− + 16 ATP → 2 NH3 + H2 + 16 ADP + 16 Pi
nitrogenase, from Protein Data Bank; FeMo cluster has 7-8 Fe’s and one Mo
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Other redox mediators in biology NAD+/NADH
E for reduction = 0.32 V NAD+ structure nicotinamide adenine dinucleotide
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Other redox mediators in biology
Coenzyme Q (ubiquinone)
O
O
CH3
O
O
CH3
CH3CH2 CH C
CH3
CH2 Hn
O
OH
CH3
OH
O
CH3
CH3CH2 CH C
CH3
CH2 Hn
2e-, 2H+
n = 6-10
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Flavin mononucleotide
(FMN): colors change with redox
form NH
N
N
NCH3
CH3
CH2(CHOH)3CH2OPO3
O
O
2-
NH
N
NH
NCH3
CH3
CH2(CHOH)3CH2OPO3
O
O
2-
.
NH
NH
NH
NCH3
CH3
CH2(CHOH)3CH2OPO3
O
O
2-
e-, H+
e-, H+
lmax = 337, 445 nm
lmax = 565 nm
colorless
Q
SQ
HQ
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Flavodoxins: FMN in a protein
J Mol Biol 1999 Dec 3;294(3):725-43
Reduction potentials of FMN couplesEo’Q/SQ Eo’SQ/HQ
Free FMN -238 mV -172 mV
FMN in Flavodoxins -50 to -260 mV -400 mV
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How can you tell if an organic molecule is oxidized or reduced?
Compound is reduced if: number of C-H bonds increases; or if number of C-O, C-N, or C-X bonds decreases
Compound is oxidized if: number of C-H bonds decreases; or if number of C-O, C-N, C-X bonds increases
X = halide
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Photosynthesis
6 CO2 (g) + 6 H2O (l) à C6H12O6 (aq) + 6 O2 (g)
thermodynamically uphill; requires photons
What is being oxidized and what is being reduced?
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Photosynthesis
6 CO2 (g) + 6 H2O (l) à C6H12O6 (aq) + 6 O2 (g)
thermodynamically uphill; requires photons
What is being oxidized and what is being reduced? Carbon dioxide is reduced, and water is oxidized to oxygen gas
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Electron Transfer in Aerobic Respiration and Photosynthesis
CO2
anabolic cycles
organic compounds
catabolic cycles
aerobic respiration photosynthesis
O2
2H2O ATP ADP + Pi ATP ADP + Pi
2H2O
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http://people.ok.ubc.ca/wsmcneil/bio/electronchain.htm
NADH → Complex I → Q → Complex III → cytochrome c → Complex IV → O2 ↑ Complex II
Mitochondrial Electron Transport Chain
O2 acts as a terminal electron acceptor in cellular respiration
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ET in Aerobic Respiration
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• NoYce that Nature does things in liEle reversible steps to maximize the useful work!
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OK, now let’s think about mechanism
A. Is a version of the Fe(II)/Fe(III) reacYon we saw earlier.
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Rudolph A Marcus: “Marcus Theory”
Professor, Department of Chemistry, Caltech (1978-present) B.Sc. (1943) & Ph.D. (1946), McGill University Polytechnic Institute of Brooklyn (1951-64) University of Illinois (1964-78) Nobel Prize in Chemistry, 1992
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Rudolph A Marcus: “Marcus Theory”
Consider a system where you have an electron donor linked to an electron acceptor: “D-‐-‐-‐L-‐-‐-‐A” which will become D+ -‐-‐-‐L -‐-‐-‐A-‐ once electron is transferred
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orbital overlap integral = HAB
Lambda is “reorganizaYon energy”: Atoms in environment have to move around to accommodate changes in charge; Lambda is energy that product system has at its lowest energy nuclear configuraYon compared to the energy it would have at reactant’s lowest energy nuclear configuraYon.
Energy vs. nuclear coordinate
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Marcus treats reorganizaYon energy as a classical Hooke’s Law (spring)
system….eventually…
⎭⎬⎫
⎩⎨⎧
⋅⋅⋅+°Δ−⋅
⋅⋅⋅⋅
TRGH
TRh = k ABET
λλ
λπ
4)(exp4 2
22
3
So the rate constant for electron transfer depends on reorganizaYon energy in a complex way; free energy change for the reacYon; temperature; and the degree of orbital overlap of the iniYal and final states.
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Acc. Chem. Res., 1996, 29, 522
-DG
Log
k -DG = l
Marcus Theory’s Really Weird Prediction: The Inverted Region
⎭⎬⎫
⎩⎨⎧
⋅⋅⋅+°Δ−⋅
⋅⋅⋅⋅
TRGH
TRh = k ABET
λλ
λπ
4)(exp4 2
22
3
-∆G = lambda at max. So rate of ET should slow down as ∆G gets more negative
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Theory: late 1950’s; Experiment: 1988
G. L. Gloss & J. R. Miller Science,240, 440 (1988)
kET vs ∆G for different donor acceptor pairs across the same bridge
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Two proteins with irons that undergo ET
Cyt c/CcP complex: 26.5 Å is Fe-Fe distance
FeIII(H2O)6 ------ FeII(H2O)6
Vacuum: 1017 years H2O: 5 x 104 years Polypeptide: ms - micros
20 Å
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Clearly, the bridge is important!
Experiment: Modify the hisYdines of a redox-‐acYve protein with a metal complex that can do ET and measure rates by monitoring spectroscopy
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Harry Gray’s lab, Caltech
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Protein Bridges Rate of ET in proteins as a funcYon of distance
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Heme iron proteins ET rate influence by local amino acids
Cyt c Mb/Hb Catalase HRP/CcP Cyt P450
N
N
Fe
NNH
OO Fe
O
Coord. Sat. Min.
H-bond Tyr push Asp-His H-bond push Arg pull
Cys push H-bond pull
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Homework! Due Wed.! 5 points!
• 1. Why do we draw potenYal energy curves as parabolas?
• 2. People think that electrons would move through delocalized orbitals like pi orbitals faster than in localized orbitals like s orbitals. Suggest an experiment to test this hypothesis.