Team:Exeter/Model

Perchlorate Reductase and Chlorite Dismutase Discussion and Conclusion

Perchlorate Reductase and Chlorite Dismutase

The purpose of this model is to investigate the feasability of producing oxygen from perchlorate, using perchlorate reductase from Azospira oryzae and chlorite dismutase from Azospira oryzae, Azospira suillum, Dechloromonas aromatica and Nitrospira defluvii. This model will also give us information on what concentrations of substrate to use.
It is expected that the rate of reaction for perchlorate reductase is slower than for chlorite dismutase. Otherwise the chlorite concentration would become too high and the bacteria would die. This is not necessarily true for chlorite dismutase from A. oryzae, A. suillum, and D. aromatica which is also a reason why they need to be modelled.

Figure 1: Reaction of perchlorate to chlorite.

Figure 2: Reaction of chlorite to oxygen.

Perchlorate reductase facilitates the reaction in Figure 1. While chlorite dismutase facilitates the reaction in Figure 2.
To find the optimal concentration of substrate the Michaelis-Menten equation was used:

$$v= {V_{max} \times [S] \over K_M+[S]}$$

$$V_{max}≡k_{cat} \times [E]$$

where $v$ is the rate of reaction, $V_{max}$ is the maximum rate of reaction, $[E]$ is the enzyme concentration, $[S]$ is the substrate concentration, $k_{cat}$ is the turnover number and $K_M$ is the Michaelis constant.

*Table 1: Literature kinetic parameters (Hofbauer *et. al.,*, 2014)*
Enzyme	Abbreviations	$V_{max}$μM/s	$K_{M}$μM	[E]μM	$k_{cat}s^{-1}$
A. oryzae-Pcr	Pcr	98.7	96	357	N/A
A. oryzae-Cld	AoCld	N/A	170	1	1200
A. suillum-Cld	AsCld	N/A	N/A	N/A	N/A
D. aromatica-Cld,pH 7.6	DaCld,pH7.6	N/A	430	1	3000
D. aromatica-Cld,pH 6.8	DaCld,pH6.8	N/A	212	1	7500
D. aromatica-Cld,pH 5.2	DaCld,pH5.2	N/A	620	1	20000
N. defluvii-Cld	NdCld	N/A	69	1	43

For the chlorite dismutase, DNA sequences were used from A. oryzae, A. suillum, D. aromatica, and N. defluvii, while kinetic parameters could only be found for A. oryzae, D. aromatica, and N. defluvii (Hofbauer et.al.,, 2014). For perchlorate reductase, only the kinetic parameters for A. oryzae were available (Hutchinson & Zilles, 2015).

Figure 3: The perchlorate reduction rate of Azospira oryzae assuming enzyme concentration of 1μM.

Figure 4: Assumes enzyme concentration of $1\times10^{-3}$ μM. Comparing rate of reaction of Chlorite dismutase from 3 different species (Ao-Azospira oryzae, Da-Dechloromonas aromatica, Nd-Nitrospira defluvii), with D. aromatica at 3 different pH values.

D. aromatica at pH of 5.2 has the highest activity at a factor of 2.6 times higher than D. aromatica at pH of 6.8, while N. defluvii had the lowest.
The concentration of chlorite dismutase for the transformed E. coli was found by measuring the amount of oxygen produced(see experiment here), comparing this to the rearranged Michealis-Menten equation $$E=V \times {K_{M}+[S] \over k_{cat}} \times [S]$$ where $v$ is the rate of oxygen measured with the Clark electrode, $[E]$ is the clorite dismutase concentration, $[S]$ is the chlorite concentration, $k_{cat}$ is the turnover number and $K_M$ is the Michaelis constant. Thus finding the effective enzyme concentration. The results for the relevant genes can be found in Table 2. Prior to the effective enzyme concentration of chlorite dismutase being calculated a placeholder value of 1μM was used, but it was replaced with 0.001μM.

*Table 2: Enzyme concentration*
cld genes source	O2 production [μM $s^{-1}$]	Effect. enzyme conc. [μM]
D. aromatica	3.015	0.0027
A. oryzae	1.412222	0.002

Then, to see how the production of O2 evolves over time, a time course kinetic analysis was calculated using the Schnell-Mendoza equation: $$[S]=K_M \times W\Biggl[{[S]_0 \over K_M} \times exp\Biggl({[S]_0 \over K_M}-{V_{max} \times t \over K_M}\Biggr)\Biggr]$$ where $[S]$ is the substrate concentration, $K_M$ is the Michaelis constant, $[S]_0$ is the initial substrate concentration, $V_{max}$ is the maximum rate of reaction, $t$ is time, and $W[]$ is the Lambert-W function, which satisfies the following equation: $W(x)exp(W(x))=x$ (Schnell & Mendoza, 1997).
From the previous work on activity varying with substrate concentration it is known that maximum activity occurs at a perchlorate concentration of ~1000μM. However, this high concentration is not feasible using just the Lambert-W function as the numbers are too high for the program used, causing the substrate concentration to go to infinity. The model used the asymptotic approximation $W(x)$ ~ $ln(x) - ln(ln(x))$ to avoid the computations which otherwise exceeded the maximum storable value in MATLAB. This approximation results in a relative error of less than 0.004% ($2.75\times10^{-6}$ absolute) for all inputs. The error was found by taking the difference between Lambert-W function and $ln(x) - ln(ln(x))$ at the transition point between them.

Figure 5: Decrease of perchlorate and subsequent increase of chlorite with only perchlorate reductase present.

Figure 6: Time course kinetic analysis of chlorite dismutase using the output of perchlorate reduction as the initial substrate concentration for the chlorite dismutase reaction. Blue line represents chlorite concentration with no cld present.

Discussion and Conclusion

While it is evident that D. aromatica with pH 5.2 had the highest activity, using these conditions would most likely not be feasible due to the low pH, which would recquire buffered growth media, leading to more components to bring to Mars. A pH of 6.8 is close to the neutral pH of water. The perchlorate reductase can maximally reduce 98.7 μM per second (this occurs at substrate concentrations of >1000 μM with enzyme concentrations of 1μM), which means that the maximum substrate concentration of chlorite is also 98.7 μM. The enzyme concentration of the chlorite dismutase was found to be maximum 0.0027 μM (see experiment) and thus the maximum rate of production of oxygen was 6.43μM/s. Given that the average human at rest requires 310 μmol/s (Wang & Coates, 2017) a bioreactor volume of 48 litre of perchlorate and bacteria mixture per person should be sufficient for a person at rest. We have a 1:10 scale bioreactor of volume 4.8 litres. These activity levels assume that the substrate concentration is constant.
This information was used to test our genetically modified bacteria at perchlorate concentrations of 1000 μM and chlorite concentrations of 100 μM.
If a bacterium had the pcr operon from A. oryzae with the cld genes from D. aromatica the bacterium should survive, because the concentration of chlorite will not be high enough to kill the bacteria. This is also true if using the cld genes from A. oryzae. This is not true if the cld genes from N. defluvii are used.

The concentration of chlorite when using chlorite dismutase from D. aromatica and A. oryzae never reaches a significant level, because the reaction rates of chlorite dismutase is faster than the production of chlorite from perchlorate reductase. It is also evident that the reaction rate of the Cld from N. defluvii is too slow and cannot prevent the high concentrations of chlorite caused by perchlorate reductase from A. oryzae. This means N. defluvii Cld is not a candidate for this project.

Considerations: To make these predictions, both reactions were considered as single substrate reactions, which is not true. Perchlorate reductase reduces both perchlorate and chlorate, but the single substrate Michaelis-Menten equation fit the data well (Hutchinson & Zilles, 2015). Additionally, when these genes are put into E. coli we cannot be certain that the reaction rates will be the same.

Acknowledgements:
Leigh Murphy (BSc Maths and Physics at University of Exeter) has been invaluable in troubleshooting and assisting with this model, especially with the asymptotic approximation of the Lambert-W function.
Bibliography:

S. Hofbauer, I. Schaffner, P. G. Furtmüller, C Obinger (2014) Chlorite dismutases - a heme enzyme family for use in bioremediation and generation of molecular oxygen (https://onlinelibrary.wiley.com/doi/epdf/10.1002/biot.201300210)
J. Kostana, B. Sjöbloma, F. Maixnerb, G. Mlyneka, P. G. Furtmüllerc, C. Obingerc, M. Wagnerb, H. Daimsb, K. Djinović-Carugo (2010) Structural and functional characterisation of the chlorite dismutase from the nitrite-oxidizing bacterium "Candidatus Nitrospira defluvii": Identification of a catalytically important amino acid residue (https://kundoc.com/pdf-structural-and-functional-characterisation-of-the-chlorite-dismutase-from-the-ni.html)
J. M. Hutchinson, J. L. Zilles, (2015) Biocatalytic perchlorate reduction: kinetics and effects of groundwater characteristics, Environmental Science: Water Research and Technology, 1,913.
S. Schnell, C. Mendoza,(1997) Closed Form Solution for Time-dependent Enzyme Kinetics, Journal of Theoretical Biology , 187,207-212. (https://doi.org/10.1006/jtbi.1997.0425)
Ouwei Wang and John D. Coates (2017) Biotechnological Applications of Microbial (Per)chlorate Reduction, Microorganisms (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5748585/)

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