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Towards a computational design of an oxygen tolerant H 2 converting enzyme

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Jochen Blumberger

University College London, UK

CCSWS4 workshop, IPAM

Los Angeles, 18 May 2011

Electronic structure

theory (DFT)

Observables:

-ionic structure

-electronic structure

-reaction free energies

-redox potentials

-pKa values

-reaction barriers

-charge mobilities

Ab-initio MD

Classical MD

QM/MM MD

Statistical mechanics

e-

Charge transfer in organic solar cell materials

e-

H+

e-

Electron flow in biological wires

Redox and PT reactions in solution

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

- catalyses H2 production:
- 2H+ + 2e- + energy H2
- catalyses H2 oxidation:
- H2 2H+ + 2e- + energy
- highly efficient: turnover
- rate ~ 1000 s-1

NiFe or FeFe

active site

cluster

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 ofHases

- Inhibited by O2 (atmosphere) and CO
- Inhibition is irreversible for FeFe-hases
- (best H2 producers)
- Intense research efforts world-wide
- (Armstrong, Leger,Fontecilla-Camps,
- Ghirardi,…)

- O2 sensitivity hampers large
- scale applications

Three strategies to makeHaseoxygen-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

O

O

H

O

C

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

Elberand 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

k32

k24

pi: population of cluster i

kij: transition rate between

cluster iand j

k23

k21

k12

Calculation of transition rates

- Transition rates between clusters from long equilibrium MD simulation
- 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.

- 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).

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)
- Insert k0mn= kmn(0) into the rate matrix

O. Dudko, G. Hummer, A. Szabo, Phys. Rev. Lett.96, 108101 (2006)

Solution of master equation

G

Initial conditions (t = 0):

pSOLVENT = 1, all other pi = 0

Destination cluster:

G (geminate)

Then solve

to obtain pG (t).

k56

k45

k32

k24

k23

k21

k12

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:
- 100 gas molecules initially placed
- outside protein (225 mM)
- 50 ns NVT, 300 K
- Gromos clustering algorithm of
- probability density

- Constant force pulling:
- 50-100 trajectories per force
- mean first passage times fit well
- to DHS model
- 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

H2, O2

CO

Constant force pulling 68G

CO

Diffusion kinetics

H2, O2

CO

Committors and reactive flux

H2

O2

CO

CO

spheres = committorΦG

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)