Towards a computational design of an oxygen
tolerant H2 converting enzyme
Jochen Blumberger
University College London, UK
CCSWS4 workshop, IPAM
Los Angeles, 18 May 2011
Methods and properties
Electronic structure
theory (DFT)
Observables:
-ionic structure
-electronic structure
Ab-initio MD
Classical MD
QM/MM MD
-reaction free energies
-redox potentials
-pKa values
-reaction barriers
Statistical mechanics
-charge mobilities
H+
eeRedox and PT reactions in solution
Charge transfer in organic solar cell materials
e-
Electron flow in biological wires
Gas diffusion in proteins
Acknowledgment
Po-hung Wang (UCL): did all work
Robert Best (University of Cambridge, UK)
£££
• Taiwanese government: PhD scholarship
• UCL: PhD studentship
• Royal Society: University Research Fellowship
Outline
• Defining the optimization problem: hydrogenase & aerotolerance
• A microscopic model for gas diffusion in proteins (forward problem)
• Diffusion paths and rates of H2, O2 and CO in WT hydrogenase
• Optimization through amino acid mutations (reverse problem)
Hydrogenase: Nature’s solution to H2 production and
oxidation
FeS clusters
NiFe or FeFe
active site
cluster
• catalyses H2 production:
2H+ + 2e- + energy  H2
• catalyses H2 oxidation:
H2  2H+ + 2e- + energy
• highly efficient: turnover
rate ~ 1000 s-1
O2
Applications in Bio-energy
Catalyst in biofuel cells
H2 photo-biological production
(green algea, cyanobacteria)
• enzyme is renewable
• as active as Pt but less expensive
• selective for substrates
• simplified cell design as ion exchange membrane not needed
Problem: oxygen sensitivity of Hases
• Inhibited by O2 (atmosphere) and CO
• Inhibition is irreversible for FeFe-hases
(best H2 producers)
 O2 sensitivity hampers large
scale applications
• Intense research efforts world-wide
(Armstrong, Leger, Fontecilla-Camps,
Ghirardi,…)
Three strategies to make Hase oxygen-tolerant
3. Facilitating removal of oxidation
products
2. Restrict binding of O2
to active site
1. Restricting access of O2 molecules
Engineering a molecular filter into Hase
Can one modify hase by mutation so that
H2 can diffuse into/out of the active site,
but O2 and CO cannot ?
H
H
mass (g/mol)
van-der-Waals radius (A)
lowest nonv. multipole
moment
O
O
O
C
2
32
28
1.20
1.52
1.70
quadrup. quadrup.
dipole
Property to be optimized:
Diffusion rate of a gas molecule from the solvent to the enzyme active site
Outline
• Defining the optimization problem: hydrogenase & aerotolerance
• A microscopic model for gas diffusion in proteins (forward problem)
• Diffusion paths and rates of H2, O2 and CO in WT hydrogenase
• Optimization through amino acid mutations (reverse problem)
Previous work on gas diffusion in proteins
Elber and co-workers: locally enhanced sampling (LES)
Schulten and co-workers: LES, implicit ligand sampling
McCammon and co-workers: very long MD simulations
Ciccotti, Vanden-Eijnden and co-workers: temperature
accelerated MD
valuable but
no rates reported
MD simulation of gas diffusion in NiFe-hase
Trajectory of a single gas molecule
diffusive jumps
Gas transport by diffusive
`jumps’ between protein
cavities
From trajectories to probability density
average over many
trajectories
H2 gas probability density (brown contour)
From probability density to clusters
clustering
algorithm
clusters or cavities (red spheres)
A coarse master equation approach to gas transport
P. Wang, R. B. Best, JB, J. Am. Chem. Soc. 133, 3548 (2011).
P. Wang, R. B. Best, JB, Phys. Chem. Chem. Phys. 13, 7708 (2011).
Assuming detailed balance:
k56
k45
k24
k32
pi: population of cluster i
k23
k21
k12
kij: transition rate between
cluster i and j
Calculation of transition rates
• Transition rates between clusters from long equilibrium MD simulation
Nijsym: number of transitions from j to i
(symmetrised)
Tj: total time spent in j
N. V. Buchete, G. Hummer, J. Phys. Chem. B. 112,
6057 (2008).
• Solvent-to-protein cluster transitions depend on gas concentration and are
pseudo-unimolecular at constant gas pressure:
 they must be multiplied by Vsim (H2O)/V0(H2O).
• Enhanced sampling methods for transitions that are poorly sampled in
equilibrium MD.
Constant force pulling
• Pulling of gas molecule from cluster n to m.
• Average over initial conditions gives mean first passage time τmn
• Obtain MFPT for different pulling forces, τmn (F) = 1/kmn(F)
• Extrapolation to zero force using the Dudko-Hummer-Szabo model (Kramers theory)
O. Dudko, G. Hummer, A. Szabo, Phys. Rev. Lett. 96, 108101 (2006)
• Insert k0mn= kmn (0) into the rate matrix
Solution of master equation
G
Initial conditions (t = 0):
pSOLVENT = 1, all other pi = 0
Destination cluster:
G (geminate)
k56
k45
k24
Then solve
k32
k23
k21
k12
to obtain pG (t).
Link to phenomenological rate constants
P. Wang, R. B. Best, JB, J. Am. Chem. Soc. 133, 3548 (2011).
P. Wang, R. B. Best, JB, Phys. Chem. Chem. Phys. 13, 7708 (2011).
diffusion only
Fit gives phenomenological
diffusion rates k+1 and k-1 that
can be compared to experiment.
Summary of computational steps
Long equilibrium MD simulation of protein + gas
Clustering of gas probability density
Transition rates between clusters
Solve master equation for given initial conditions
Fit time-dependent population of destination cluster
to phenomenological rate equation
k1, k-1
Simulation details
Molecular models
Protein: Gromos96 43a1 (united atom)
Water: SPC/E
H2, O2 and CO:
• 3 interaction sites
• charges to reproduce experimental
quadrupole moment (H2, O2) and
dipole moment (CO)
• Lennard-Jones parameter to fit
experimental solvation structure
Experimental diffusion constant in water
reproduced to within 7% and in n-hexane
to within 43 %.
Simulation details (contd)
Equilibrium simulation of hase:
Constant force pulling:
• 100 gas molecules initially placed
outside protein (225 mM)
• 50-100 trajectories per force
• 50 ns NVT, 300 K
• mean first passage times fit well
to DHS model
• Gromos clustering algorithm of
probability density
• relative stat. error in diffusion rates
(from block averaging): 30 %.
 protein RMSD ca. 2 A with and
without gas
 most transitions between clusters
well sampled
 Transitions into G not well sampled
Outline
• Defining the optimization problem: hydrogenase & aerotolerance
• A microscopic model for gas diffusion in proteins (forward problem)
• Diffusion paths and rates of H2, O2 and CO in WT hydrogenase
• Optimization through amino acid mutations (reverse problem)
Probability density maps of gas molecules for Hase
P. Wang, R. B. Best, JB, J. Am. Chem. Soc. 133, 3548 (2011).
P. Wang, R. B. Best, JB, Phys. Chem. Chem. Phys. 13, 7708 (2011).
Clusters and diffusion pathways
H 2, O2
CO
Constant force pulling 68G
CO
Diffusion kinetics
H2, O2
k+1(104 s-1 dm3 mol-1)
CO
H2
O2
CO
exp CO
99
17
11
10-20
Committors and reactive flux
H2
O2
CO
CO
spheres = committor ΦG
blue: ΦG = 0, red: ΦG = 1
tube diameter prop to flux J
Conclusions
• We have developed a
general microscopic model for gas diffusion in
proteins (forward problem)
• Computed diffusion rate agrees well with experimental rates
(same order of magnitude)
• Simulations can suggest possible mutation sites to block access of
inhibitor molecules (inverse problem)