Calculation of gas diffusion rates in the
[NiFe]-hydrogenases
Po-hung Wang*, Robert B. Best, and Jochen Blumberger
Department of Physics and Astronomy, University College London
Introduction
Objectives: Calculation of diffusion rates of H2 , O2 , and CO molecules inside hydrogenases using a novel multiscale approach provides insights into gas diffusion in proteins.
Background:
Hydrogenases (Hases) might be used as potential substitutes for expensive metals (ex:Pt), in the next-generation fuel cell.
H2 H+ + H− 2H+ + 2e−
Experiments have shown that H2 and CO could easily penetrate the tunnel in the wild-type Hase. A series of single- and double- mutations on V74 and L122 could lower the diffusion rate
constants by up to three orders of magnitude. Among them, the V74M mutant exhibited the best aero-tolerance in air-equilibrated solutions.
Method
1. Molecular dynamics simulations for the wildtype hydrogenase with gases and construction of a rate matrix using a coarse master equations approach.
ṗi (t) =
P
j
Rij pj (t);
pi (t) =
P
j (e
tR
)ij pj (0).
2. Pulling simulations at specific microscopic transitions for the wildtype and the V74M mutant and then extrapolation to obtain the transition rates at zero force using a model for
force-dependent kinetics.
νF x‡ 1 −1 ∆G‡ [1−(1−( νF x‡‡ ))1/ν ]
ν
∆G
e
k1D (F ) = k0 (1 −
)
∆G‡
3. Insertion of the microscopic rates obtained from pulling simulations into the rate matrix and then fitting to a phenomenlogical model.
k+1 [Gas]
pG (t) =
[1 − exp(−(k+1 [Gas] + k−1 )t)]
k+1 [Gas] + k−1
k1
k2
GGGGGGB
GGGGGGGGB
E + Gas F
GG G F
GG F
k−1
k−2
Results
O2 (E←X)
H2
O2 (G←E)
H2
CO(E←68)
O2
CO(E←G)
CO
Computed (comp) rates for diffusion of H2 , O2 , and CO from the solvent to the wildtype and a In units 104 s−1 mM−1 . b In units 108 s−1 . c Pathway 1 blocked. d In units s−1 mM−1 .
the V74M [NiFe]-hydrogenase active site, k+1 , for diffusion out of the active site, k−1 , and units s−1 .
the experimentally (exp) determined on-rate for CO, kin .
H2 (Comp)
H2 (Exp)
O2 (Comp)
O2 (Exp)
CO(Comp)
CO(Exp)
A
0.48
2.31
2.02
2.02
2.25
2.24
H2 (comp)
O2 (comp)
CO (comp) CO (exp)
a
b
a
b
Dw
4.75
5.11
2.58
2.42
2.57
2.43
k+1
k−1
k+1
k−1
k+1 k−1
kin
Dh
20.5
16.36
14.2
9.9
9.38
8.12
total
9.9
1.9
1.7
0.11 1.1a 0.09b
1-2a
Solvation free energy (A) unit in kcal/mol;
blockedc 7.7
1.2
0.5
0.09
−5 cm2 /s.
d
e
d
Diffusion
constants
in
water
(D
)
and
in
hexane
(D
)
unit
in
10
w
h
V74M
9.7
1.5
2.3
0.12 3.6
2823
19
Conclusion
1. A novel approach was developed to calculate gas diffusion rates in proteins, and the results
were consistent with the experiments.
2. Contributions from two specific microscopic transitions (G←E and E←68) were identified,
and we found the rate-limiting step induced by the mutation could be the final transition to
cluster E (E←68).
References:
1. Wang, P.; Best, R. B.; Blumberger, J. J. Am. Chem. Soc. 2011, 133, 3548-3556.
2. Wang, P.; Best, R. B.; Blumberger, J. Phys. Chem. Chem. Phys. 2011, 13, 7708-7719.
*Corresponding email: po-hung.wang.09@ucl.ac.uk
e
In