Team:H14Z1 Hangzhou/Model

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Model

GSH and SAM are becoming more and more popular health care product, and our project focus on producing and accumulating GSH and SAM in L. lactis and improving its adhesivity, and, finally, getting “Smart yoghourt” by using the engineered strain. During our experiments, we have collected some data about cell growth and GSH and SAM production, and then modelled according to the theory kinetics equations. Through these analyses, we wonder a better optimizing strategy to increase both of the production of GSH and SAM in fermentation.

Genes and GSH and SAM production

We have transferred plasmid pNZ-GMcA to L. lactis, containing gene gshF, metK and cwaA, resulting in improvement of producing GSH and SAM and adhesivity of the strain while using for producing “Smart yoghourt”. As GSH and SAM were the main characteristic of this strain, to get more production of GSH and SAM was important in Smart yoghourt fermentation (Figure 1). Thus, we collected experimental data about cell growth and GSH and SAM production and constructed models to guide fermentation process in producing “Smart yoghourt”.

Figure. 1 The schematic diagram of biosynthesis synthesis of GSH and SAM in L. lactis/pNZ-GMcA.

Experimental data collection

The experimental data were collected as followed:

4ml L. lactis glycerol stock from -80oC were inoculated to 50 ml GM17 medium and grown overnight at 30oC without aeration. Then, the pre-culture were inoculated to 50 ml of GM17 medium with a dilution of 1:100 and grown at 30oC without aeration. OD600 was measured every 2 hours. While OD600 reached 0.4, 50ng/ml nisin were added to the culture to induce the expression of proteins in the plasmid. OD600, GSH and SAM titer were measured every 2 hours.

Theory

Kinetics of Cell Growth

Growth kinetic can be described by a modified logistic model[1-3,5]:

where X is biomass concentration, t time, K empirical equation constant depending on maximum specific growth rate, Xm maximum biomass concentration achievable under the specified conditions, and n inhibition exponent. Xm in Eq. 1 represents the maximum carrying capacity of the system (medium and conditions) for a particular strain and (1-X/Xm) represents the fraction of remaining carrying capacity. The empirical inhibition exponent n is a lumped indicator corresponding to the inhibitive effects of biomass and product accumulation to cell growth. The larger the n value, the more significant the inhibition effects.

Kinetics of Cell Growth

In fermentation processes, product formation associates either with cell growth or with cell maintenance. Formation of products can thus be portrayed by the classic Luedeking–Piret Equation [4,5]:

where X is biomass concentration, t time, α and β are equation coefficients that correspond to growth-associated and non-growth-associated product formation, respectively. Growth-associated product, as indicated by its name, is synthesized in association with cell growth. On the other hand, non-growth-associated product is formed in association with cell maintenance. Accordingly, products accumulated in a fermentation process can be classified into three categories according to the values of α and β as follows:

α > 0 and β = 0, growth-associated product, accumulated as a result of cell growth only;

α = 0 and β > 0, non-growth-associated product, accumulated as a result of cell maintenance only; and

α > 0 and β > 0, mixed-growth-associated product, accumulated as results of both cell growth and cell maintenance.

Modeling

The cell growth (X) model, GSH Formation (P1) model and SAM Formation (P2) model should be integrated into a complete mathematical model:

The Levenberg-Marquardt nonlinear regression algorithm was used to seek the best values of the equation parameters in Eq. 3 that minimize the sum of the squared deviations between the calculated values and the experimental data. The values of those parameters is listed in Table 1. Then the time courses of cell growth (X), GSH Formation (P1) and SAM Formation (P2) were obtained by integration of Eq. 3 using the ode45 solver in MATLAB 2016 as illustrated in Figure 2, and the results were shown in Figures 3, 4 and 5.

Figure. 2 The source program of MATLAB for fitting Eqs. 1 and 2.

Results and discussion

Kinetics of growth of L.lactis/pNZ-GMcA

Figure 3 shows the time courses of cell growth of L. lactis. The experiment was conducted at 30oC. The initial glucose concentration was 10 g/L. As shown in Figure 2, cell growth under those conditions is described using the modified logistic cell growth model with a K value of 0.605/h, maximum biomass concentration of 0.511 g/L, and a power index (n) of 1.29. The exponential phase started after inoculation with about 5 hour’ lag phase and lasted for about 6 h, followed by the deceleration phase. The end of exponential phase might be caused by the inhibition of metabolites such as lactate or low concentration of nutriment.

Figure. 3 Cell growth of L. lactis. Solid lines are best-fit curves of experimental data using corresponding models using Eq. 1. The scatters were samples at different time.

Kinetics of GSH Formation

As shown in Table 1 and Figure 4, GSH formation shows different with all the three categories with a α value of -6.97 and β value of 2.64 GSH per DCW per time (g/g/h). This observation may be attributed to the fact that gene gshF for GSH production was induced by nisin at 7 h, while wild-type L. lactis cannot synthesize GSH. Thus, we supposed GSH formation in L. lactis shows a mixed with induction associated and non-growth–associated product.

Figure. 4 GSH production of L. lactis/pNZ-GMcA. Solid lines are best-fit curves of experimental data using corresponding models using Eq. 2. The scatters were samples at different time.

Kinetics of SAM Formation

As shown in Table 1 and Figure 5, SAM formation shows mixed-growth-associated kinetics with a α value of 1.07 and β value of 0.493 SAM per DCW per time (g/g/h). It is worth noting that the Eq. 2 is good for fitting the SAM production data from 0 to 7 h. While after 7 h, the experimental data were slightly deflected from the fitted curve. We supposed that L. lactis can synthesize little SAM by itself and this might be typical mixed-growth-associated kinetics. Expression of gene metK was induced by nisin at 7 h, and then more SAM were formed, resulting in deflected from the fitted curve.

Figure. 5 SAM production of L. lactis/pNZ-GMcA. Solid lines are best-fit curves of experimental data using corresponding models using Eq. 2. The scatters were samples at different time.

Reference

  1. Messens W, Verluyten J, Leroy F, et al. 2003. Modelling growth and bacteriocin production by Lactobacillus curvatus LTH 1174 in response to temperature and pH values used for European sausage fermentation processes. Int J Food Microbiol. 81(1):41-52.
  2. Pirt SJ. 1965. The maintenance energy of bacteria in growing cultures. Proc R Soc Lond B 163:224–231.
  3. Shuler ML, Kargi F. 2001. Bioprocess engineering: basic concepts, 2nd edn. Manufactured: Prentice Hall.
  4. Luedeking R, Piret EL. 1959. A kinetic study of the lactic acid fermentation. Batch process at controlled pH. J Biochem Microbiol Technol Eng. 1:393–421.
  5. Lan C Q, Oddone G, Mills D A, et al. 2010. Kinetics of Lactococcus lactis growth and metabolite formation under aerobic and anaerobic conditions in the presence or absence of hemin. Biotechnol Bioeng. 95(6):1070-1080.