Team:NFLS/Model
Abstract
An ordinary differential equation model was established to describe the process of cellulose decomposition and glucose production. Using this model, we can infer the consumption of cellulose by engineered bacteria by detecting the amount of glucose.
Background
Engineered bacteria can secrete endoglucanase and exoglucanase to break cellulose outside the cell into cellobiose, which is later transported into the bacteria through transporter and is hydrolyzed into glucose by β-glucosidase. Once we have glucose, we have the energy source for bacteria to generate electricity inside the microbial fuel cell.
Aim
When expressing three kinds of enzymes for dissolving cellulose, bacteria can break down cellulose into glucose. Since quantifying cellulose is complex and dangerous reagents like concentrated sulfuric acid are needed, while it is easy quantify glucose directly with ferin reagent, so this model calculates the consumption of cellulose of bacteria by ordinary differential equation and the amount of glucose.
Assumption
It is assumed that the rate of cellulose decomposition into glucose is linear with the concentration of cellulose.
It is assumed that there is a linear relationship between the rate of glucose consumed by growing bacterial and the concentration of glucose.
Notation
Cc：concentration of cellulose
Cs：concentration of glucose
Kc：the velocity of degrading cellulose by three kinds of enzymes
Ks：speed of glucose consumption by growing bacteria
Model establishment and solving
We build ordinary differential equation model to describe the changing in concentration of cellulose and glucose. The diagram of the model is shown in the following figure:
In the culture solution of engineered bacteria, cellulose is mainly decomposed into glucose by three kinds of enzymes expressed in the engineered bacteria, and its equation about concentration change is as follows:
Glucose is mainly produced by cellulose decomposition by three kinds of enzymes in engineered bacteria and consumed in the process of bacterial growth. Equation about its concentration change is as follows:
We use the data in reference (1) and use Berkeley Madonna software to fit the differential equations. The results are shown in the figure below.
The model parameters obtained by fitting are shown in the table below:
| parameter | value |
|---|---|
| Kc | 0.01435 |
| Ks | 0.00809 |
Prediction
According to the model, we can predict the process of cellulose being decomposed by three enzymes in engineered bacteria. The prediction of cellulose decomposition’s time versus concentration curve is shown in the figure below:
Summary
We established an ordinary differential equation model to describe the process of cellulose decomposition and glucose production. With this model, we can detect the amount of glucose and deduce the consumption of cellulose by bacteria. The establishment of this model can avoid the tedious and dangerous process of measuring the concentration of cellulose, and can indirectly calculate the concentration of cellulose by measuring the amount of glucose.
Source Code:
References
Engineering Pichia pastoris with surface-display minicellulosomes for carboxymethyl cellulose hydrolysis and ethanol production
