Thermodynamics of electron flow in the bacterial decaheme cytochrome MtrF
Breuer M.(1), Zarzycki P. P.(2), Rosso K. M.(2), Blumberger J.(1)*
(1) University College London, Gower Street, London WC1E 6BT, UK
(2) Pacific Northwestern National Laboratory, 902 Battelle Boulevard, Richland, WA 99352, USA
* Email: j.blumberger@ucl.ac.uk
Abstract
Very recently the first crystal structure of a bacterial decaheme ctype cytochrome has been resolved1. Shewanella oneidensis and
other metal-respiring bacteria use such biological `wire’ proteins to
shuttle electrons across the outer membrane on to extracellular
solid metal oxides, e.g. Fe2O3, which serve as terminal electron
acceptors. Investigation of the electron transport properties of
these multi-heme proteins not only serves to promote
understanding of biological charge transfer and transport
processes but also holds out the prospect of promising bionanotechnological applications. The heme cofactors in the
particular protein under investigation, MtrF, are arranged as a
chain of four approximately coplanar heme groups separating two
triple-stacks of approximately parallel heme cofactors, altogether
constituting a ‘molecular wire’. In order to investigate the electron
transport properties of MtrF, reduction potentials of individual
heme cofactors have been calculated using classical molecular
dynamic simulation combined with thermodynamic integration
along two different paths. Results from these calculations are
discussed and compared with each other as well as with
experimental reduction potentials obtained from protein film
voltammetry measurements. Finally, electronic coupling matrix
element values for adjacent hemes as obtained using the
fragment-orbital DFT method are presented.
Background
• Shewanella oneidensis strain MR-1: a dissimilatory
metal-reducing bacterium
• Capable of using extracellular solid metal oxides as
terminal electron sinks
• A complex system of many multiheme proteins transfers
electrons to the cell exterior
Electron transfer model
• Marcus theory is used to model electron transfer from
heme to heme4:
• Rate constant of electron transfer kET depends on
electronic coupling matrix element H12, reorganization
energy λ and free energy of electron transfer ∆ A for a
given temperature T
• These quantities can be calculated using computational
methods
Reduction potentials
• Free energy difference between two states can be
computed via thermodynamic integration:
where the potential energy U is a function of λ and the
canonical average is taken over the corresponding
potential energy surface
• Classical molecular dynamics simulations were used to
obtain reduction potentials via thermodynamic integration,
scaling atomic charges linearly with λ:
• MtrF: the first outer membrane decaheme c-type
cytochrome whose crystal structure was determined
• This yields:
• Crystal structure enables new insights into biological
charge transport processes
• Two different pathways were used:
Fig. 7: Free energy landscapes based on the reduction potentials
obtained via the two thermodynamic integration pathways.
Negative values from fig. 5 are used and shifted to 0.0 eV for
heme 6; free energy barriers are approximated by assuming λ =
0.7 eV.
Electronic couplings
• Electronic coupling matrix element is defined as:
between two diabatic states a and b
• Fragment-orbital DFT (FO-DFT): Approximate H12 by
i.e. as Kohn-Sham Hamiltonian matrix elements between
HOMOs of donor and reduced acceptor; both are treated
as isolated
– Oxidation of a reduced heme to directly yield its
reduction potential
– Electron transfer between a reduced and an oxidized
heme to yield electron transfer free energies (which
in turn provide relative reduction potentials)
• Assumption: Electron supply to protein is a limiting factor
Fig. 2: Proposed electron transfer
Fig. 1: Shewanella
oneidensis strain MR-1.2 pathways in S. oneidensis from
cytoplasmic membrane (CM) to outer
membrane (OM) involving different
cytochromes.3
--> Electron transport, not hole transport
--> Treat all hemes but one as oxidized
5
MtrF: Structure
Fig. 8: Electronic coupling matrix elements (absolute values)
between adjacent hemes in units of mHa as calculated using FODFT. Each coupling was calculated on a structure minimized with
both respective hemes half-reduced (and all others oxidized).
4
3
Conclusions
2
1
7
6
8
• Thermodynamic integrations along two different
pathways have been carried out in order to calculate
reduction potentials of individual hemes
9
10
Fig. 3: Crystal structure of MtrF. Heme groups are highlighted in
colour.1
Fig. 5: Reduction potentials for individual hemes in eV as
obtained via the two thermodynamic integration pathways. Blue:
values from oxidation, green: from electron transfer. (The latter
obtained from the transfer free energies using an arbitrary offset
and shifting to best match values from oxidation pathway.) Red:
differences.
• MtrF: a c-type cytochrome containing ten heme
cofactors
• Both data sets show correlation with experimental data
to some degree but disagree with each other
• No conclusions yet regarding possible thermodynamic
preferences regarding direction of electron flow
• Electronic coupling matrix elements between hemes
have been calculated using FO-DFT, showing variations
over two orders of magnitude
References
• Two of four domains contain α -helices, the other
containβ -sheets; many random coils present
[1] Clarke T.A. et al. PNAS 2011, published ahead of print May 23,
2011, doi:10.1073/pnas.1017200108.
[2] Image source: http://idw-online.de/pages/de/news370736
(16/05/2011).
[3] Coursolle D. and Grainick J. A. Mol. Microbiol., 2010, 77, 995.
[4] Marcus R. A. J. Chem. Phys., 1965, 43, 679.
• Each heme is covalently bound by two cysteines
(CXXCH binding motif) and coordinated by two histidines
Fig. 3: Individual heme cofactor
including covalently bound
cysteine
and
coordinated
histidine
(both
truncated).
Green: iron; blue: nitrogen;
light blue: carbon; red: oxygen;
yellow:
sulphur;
white:
hydrogen.
• The first crystal structure of a bacterial decaheme c-type
cytochrome enables new insights into biological charge
transfer processes
Acknowledgements
Fig. 6: Comparison of individual heme reduction potentials and
experimental values (protein film voltammetry, PFV). PFV values
are relative to the standard hydrogen electrode; values from
thermodynamic integration are shifted (values from each method
individually) to the best possible match to PFV values.
M. Breuer gratefully acknowledges a joint studentship sponsored
by University College London and the Pacific Northwestern
National Laboratory.
The work in this study has been carried
supercomputers Hector, Chinook and Legion.
out
on
the