Team:XHD-Wuhan-China/Model

Model

Glucose dehydrogenation and hydrogen ion production

In order to dissolve the insoluble phosphate in the soil, we plan to decrease the pH of the soil, promote the dissolution of phosphate, and release the metal ions in the phosphate to meet the needs of normal plant growth. The purpose of this modeling is to screen out a suitable glucose dehydrogenase (GDH) for experiment which can efficiently complete the conversion of glucose to gluconic acid in low pH environment. It is expected that under the conditions of low pH and substrate concentration, the reaction rate catalyzed by GDH remains high. GDH enzyme with optimal kinetic characteristics is selected from E. coli,Sulfolobus solfataricus,Bacillus megaterium,Lysinibacillus sphaericus,Bacillus amyloliquefaciens.

Figure 1. Reaction of glucose to gluconic acid.

Glucose dehydrogenation reaction is shown in Figure 1, to search the optimal concentration of substrate, the Michaelis-Menten equation was used:

V is the rate of reaction, V_max 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.

As for GDH, proteins were used from E. coli,Sulfolobus solfataricus,Bacillus megaterium,Lysinibacillus sphaericus G10,Bacillusamyloliquefaciens SB5,and kinetic parameters could be found in public.

Table 1. Literature kinetic parameters (Basner & Antranikian, 2014; Pongtharangkul et al., 2015)

Organism	Abbreviations	Km[mM]	Kcat[1/s]	pH
E. coli	E. coli	1.7	160.7	6.0
Sulfolobus solfataricus	S. s	0.44	48	8.0
Bacillus megaterium	B. m	11	260	6.5
Lysinibacillus sphaericus G10	L. s	5.1	93	9.5
Bacillus amyloliquefaciens SB5	B. a	5.5	70	10

Figure 2. Assumes enzyme(Et) concentration of 0.05 Mm, comparing rate of reaction of glucose dehydrogenation from 5 different species.

GDH from E. coli has the highest reaction rate when the substrate concentration is low. At the same time, the overall reaction rate is high, and its optimal pH is low, so it can have high enzyme activity when hydrogen ion is released in the reaction.

Glucose is undergoing a process of continuous consumption, and under actual Martian culture conditions, excessive glucose will not be used for culture, so the glucose concentration in the culture environment will be maintained at relatively low level. In general, it is more appropriate to choose GDH enzyme from E. coli.

Later, in order to understand the change of hydrogen ion concentration over time, a time course kinetic analysis was calculated using the Schnell-Mendoza equation:

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(Omega function), which satisfies the following equation: W ( x ) e x p ( W ( x ) ) = x (Schnell & Mendoza, 1997).so this model the asymptotic approximation W ( x ) ~ l n ( x ) − l n ( l n ( x ) ).

Figure 3. Time course kinetic analysis of Glucose dehydrogenation.

Assuming that the initial concentration of hydrogen ion is 0, the comparison results show that the GDH enzyme from E. coli can release hydrogen ion in a short period of time and has strong activity in a low pH environment. The modeling results show that considering the comprehensive reaction rate and the optimal pH of the enzyme, the GDH enzyme from E. coli should be selected to complete the catalysis of glucose to gluconic acid, which can quickly and effectively decrease the pH and promote phosphate to dissolve.

In addition, we constructed the Phosphate dissolving system (PGroES-gcd) during the experiment, and measured the pH change of the solution in the TGY liquid medium, as shown in the Figure 4. The experimental results show that the pH value decreased from 7.0 to 4.8 within 12 hours, which is not consistent with the theoretical modeling result. The reason may be that the effective concentration of GDH holoenzyme in the experiment is low, the consumption of glucose is insufficient. We fit the experimental result data with the theoretical model, and get the theoretical prediction result as shown in the Figure 5. The result show that after 12 hours, the amount of hydrogen ions generated is relatively stable, which is the same as the experimental result, except that the final content of hydrogen ions is higher than the experimental result. This may be due to the total consumption of glucose that we considered in the modeling process. In the actual process, glucose also participates in other metabolic processes and will not all be converted into gluconic acid. The experimental results have a guiding role in the revision of the modeling and can improve the theoretical model.

Figure 4. Changes in pH value of TGY liquid medium culturing DR R1 and DR containing gcd-pRADK respectively from experiment.

Figure 5. Time course kinetic analysis of Glucose dehydrogenation according to experiment result by modeling.

Then, in order to have a deeper understanding of the effect of enzyme activity on the reaction rate, we use Python to develop a software that can visually display the influence of each parameter in the Michaelis-Menten equation on the reaction rate and substrate concentration.

Figure 6. Dynamic display of reaction rate and substrate concentration.

Discussion

In this model, the GDH enzyme concentration is regarded as a constant amount. However, in practice, GDH can only function with the participation of the pyrroloquinoline quinone (PQQ) Coenzyme, so the level of binding between GDH and PQQ will also affect the reaction rate. The combination of GDH and PQQ may be regulated by gabY, which affects the effective concentration of the enzyme, thereby changing the reaction rate. Moreover, after introducing the above genes into Deinococcus radiodurans, it is not certain that the catalytic effect and reaction rate will be the same as in E. coli.

References

Basner, A., & Antranikian, G. (2014). Isolation and Biochemical Characterization of a Glucose Dehydrogenase from a Hay Infusion Metagenome. PloS one, 9(1).

Pongtharangkul, T., Chuekitkumchorn, P., Suwanampa, N., Payongsri, P., Honda, K., & Panbangred, W. (2015). Kinetic properties and stability of glucose dehydrogenase from Bacillus amyloliquefaciens SB5 and its potential for cofactor regeneration. AMB Express, 5(1), 68-68.

Schnell, S., & Mendoza, C. (1997). CLOSED FORM SOLUTION FOR TIME-DEPENDENT ENZYME KINETICS. Journal of Theoretical Biology, 187(2), 207-212.