Modeling in synthetic biology is a crucial tool that helps us to get a comprehensive vision of biological systems and the working principles while providing ways to improve the system. In our case, it significantly led to the design of our project while improving the part choices. Our project was based on the enhancement of fermentation by increasing the lifespan of an ethanologenic bacteria; E.coli strain KO11. Thus, we used simple models to simulate the kinetics of fermentation and enzymatic activities which provided insights on the formation of our experiments and the improvement of our project design.

What we have achieved

We constructed our gene circuit with the help of toxicity analysis and estimation of enzymatic reactions by Michaelis and Menten enzyme kinetics.
We used microbial growth and fermentation kinetics to simulate the expected behaviors of our system and the effects of our genes.
We used microbial growth and fermentation kinetics to simulate the expected behaviors of our system and the effects of our genes.
We improved the understanding of our project by demonstrating the pathways and effects of our genes.

Formation of Our Kinetic Models

Cell Growth Kinetic

The cell growth rate of bacteria depends on the number of cells and their specific growth rate. Thus, it can be expressed as:

dX/dt = µ * X

when we arranged the equation and integrated the both sides we get:

X = e ^ µ*t

We decided to use the Monod kinetics to make substrate and cell concentration-dependent equation. It is shown below:

dX/dt = (µmax * X * S) / Ks + S

“Ks” represents the saturation concentration where “µmax” represents the maximum specific growth rate. In the Monod equation, we can observe the lag, exponential and stationary phase. However, because our system also includes inhibitor by-products, the Monod equation turned into a new form where the cell growth also depends on the inhibitor concentration:

dX/dt = (1 - (C / Cm)) * [(µmax * X * S) / (Ks * ( 1 - (C / Cm))]

X = Number of Cell,

C = inhibitor concentration

Cm = Maximum inhibitor concentration cell can live

µmax = Maximum specific growth rate

Ks = Saturation concentration

S = Sugar concentration.

Enzymatic Reaction Kinetics:

Enzymatic reactions were one of the main components of our project where we aimed to catalyze the furfural reduction. The enzymatic reactions depend on the presence of the substrate and the enzyme which are multiplied by forward and reverse reaction rate constants. We can show the reaction by using mass kinetics.

E + S → ES → P + E
d[S]/ dt = -k1 * [E] * [S] + k-1* [ES]
d[E]/dt = -k1[E]*[S] + (k-1 + k2) * [ES] - (k-2 * [E]*[P])
d[P] /dt = k2 * [ES] - k-2 * [E] * [P]

However, like in the Monod model, the formula can be developed by adding different constants like “Km” and “Vmax” to form Michaelis and Menten equations which represent the enzyme reaction rate.

V = (Vmax * [S]) / Km + [S])