Team:Tartu TUIT/Model

Biological systems modeling, among other things, can help to put together data from different sources to predict the system’s behavior in conditions of interest. The main goal of our project is to create a strain that could be used by researchers and industry to produce and subsequently extract various compounds. In our project, the model aims to calculate the best time point for induction of yeast cell autolysis.

We started from the determination of the time point, at which we would like to have the majority of cells lysed (further referred to as t_L). We decided to demonstrate induction time point determination using the example of β-carotene production in a batch fermentation culture. We chose β-carotene as it is well-studied, and although it is not native to Saccharomyces cerevisiae, its production in this species was previously successfully performed and modeled [1] [2] [3]. Batch type of fermentation allows a defined growth period and is cheaper. Also, for research purposes, S. cerevisiae cultures are usually grown using this method.

Products of biosynthetic pathways can be divided into growth-associated, non-growth-associated and mixed. Depending on the type, product formation takes place in exponential growth or stationary phase, or both.



Figure 1. Types of product formation. X is biomass concentration, P is product concentration.

Further growth after the production rate starts to decrease is inefficient in the case of batch fermentation, as lysing cells and collecting the product and starting the new batch enables to gain of the same yield faster. Moreover, in the case of our strain cultivation, lysis should be induced while the majority of cells are alive and can produce glucanases.

The first step to model compound production is to model biomass growth. The rate of biomass growth depends on the carbon source. During glucose abundance, S. cerevisiae uses it for fermentation, producing ethanol, which is used as a carbon source after glucose is consumed. Basic biomass growth models use specific growth rates on these substrates to calculate the total biomass growth.


Figure 2. A general example of biomass growth dependence on glucose and ethanol concentrations.

To do so, we adapted the batch cultivation model from Ordoñez et al., 2016 [3] to the strain we modified during our project. The model connects β-carotene production to biomass growth on glucose, ethanol and acetic acid. We neglected acetic acid-related growth, as it is insignificant in comparison to the other two.

The model consists of four differential equations:

1.
biomass growth rate equation, where X is biomass and μ_g and μ_e are specific growth rates on glucose and ethanol, respectively.

2. Specific growth rates were calculated using the following equations:

where G is glucose concentration, E is ethanol concentration, μ_max is maximal possible specific growth rate on glucose (G) or ethanol (E) under given conditions, K_s is the concentration of substrate (G or E) at which half the value of μ_max was observed, and a_ij represents the inhibition effect of the jth substrate on the utilization of the ith substrate by the organism.

3.
glucose consumption equation, where Y_X/G is the biomass yield coefficient on glucose.

4.
ethanol consentration change equation, where k₁ is a parameter representing the ethanol formation during glucose consumption and Y_X/E is the biomass yield coefficient on ethanol.

5.
product formation equation, where α₁ and α₂ are coefficients for growth-associated product formation rates related to the yeast growth on glucose and ethanol respectively, and β is the coefficient for non-growth-associated carotenoid production.

To approximate constants for the specific growth rate equations (2) and to calculate maximum specific growth rates and yield coefficients (2, 3, 4) specifically for the modified strain, we performed OD measurements and HPLC experiment on a growing W303 (MATa {leu2-3,112 trp1-1 can1-100 ura3-1 ade2-1 his3-11,15 bar1::hisG} [phi+]) culture. OD₆₀₀ and glucose and ethanol concentrations (g/L) were measured at time points of 0, 4, 6, 8, 10, 12 and 24 hours (Fig. 3). To derive dry cell weight from the OD₆₀₀, we used the coefficient 0.33 g/L*OD. More information about the experiment can be found in HPLC section of our Experiments page.


Figure 3. Time course of biomass growth, glucose consumption and ethanol concentration in batch cultures of S. cerevisiae with initial glucose concentration 10 g/L.


Figure 4. Simulation of cell growth, glucose consumption, ethanol concentration and β-carotene production in batch cultures of S. cerevisiae with initial glucose concentration 10 g/L. The black dashed vertical line represents the t_L.

We decided to find the time point with maximal product concentration-to-time ratio and use it as t_L (Fig. 5). In this case, lysis is induced before the production rate starts to decrease.


Figure 5. β-carotene concentration to time ratio dynamics through the simulation. The peak of the graph marked with the red dot is the t_L, which is equal to 35.4 hours.

After t_L is found, the next step is to calculate the time point at which the LexA-ER-B112 target promoter has to be induced in order to get the majority of cells lysed at t_L (further referred to as t_I).

Shortly after induction the glucanase concentration starts to increase. In order to significantly damage the cell wall, glucanase should accumulate at the cell wall. Expression, transportation and hydrolysis itself take a considerable amount of time. We estimated it using the experimental data (see Results). We made an assumption that the period of time from the induction to the actual t_L is 370 minutes for a strain with Ost1-BBa_K2711000 construct integrated and 420 minutes for a strain with Ost1-GLC1 construct integrated.


Figure 6. t_I for two different strains: Ost1-BBa_K2711000 and Ost1-GLC1. t_I Ost1-GLC1 is equal to 28.4 hours and t_I Ost1-BBa_K2711000 is equal to 29.2 hours.

There are several details which require further development in the model. First, growth conditions for the cultivation should be selected accordingly to the product formation type. Second, the expression of glucanases will require resources from the cell and therefore might affect product formation. Third, we hope to get better estimation of the t_L-t_I, as the estimation from microscopy pictures is not very precise.

To conclude, our model will allow potential autolytic strain users to calculate t_L and t_I specifically for the product of their choice, as production rate equation can be substituted with the analogous one, linking production to biomass growth on glucose and ethanol.

Supplementary part

Table 1. Optimal parameter estimates for the batch kinetic models.

Parameter	Value	Units
YXG	0.1669	g(Cells)/g(Glucose)
YXE	0.680952381	g(Cells)/g(Ethanol)
KSG	0.4137	g(Glucose)/L
KSE	0.5618	g(Ethanol)/L
k1	2.8	g(Ethanol)/g(Cells)
α1	0.7545	mg(Product)/g(Glucose)
α2	13.9280	mg(Product)/g(Ethanol)
β	0.2804	mg(Product)/g(Cellc*h)
μmax, G	0.4048	1/h
μmax, E	0.0595	1/h
aeg	1.2964
age	1.0636

Table 2. Initial conditions for the system.

Variable	Description	Value	Units
X	Biomass concentration	0.03938	g/L
E	Ethanol concentration	0.095	g/L
G	Glucose concentration	10	g/L
P	Product (β-carotene) concentration	0	mg/L

References: