Team:British Columbia/Modeling

From 2013.igem.org

(Difference between revisions)

Revision as of 00:46, 9 August 2013

Reaction Kinetics: - Modelling the production of cinnamaldehyde, vanillin and caffeine production

Population dynamics: - Modelling the population of a bacteria in a batch reactor with phage dependency

We've decided to use Monod substrate limited growth kinetics for to model population dynamics. \begin{align} \mu = \mu_{max} \frac{S(t)}{K_s + S(t)} \end{align}

Where $\mu$ growth rate in units hr$^{-1}$, $\mu_{max}$ is the maximum growth rate, $K_s$ is the amount of substrate remaining when $\frac{\mu}{\mu_{max}} = \frac{1}{2}$, and $S(t)$ is the substrate remaining at a given time.

Since growth rate is defined as: \begin{align} \mu \equiv \frac{1}{X(t)} \frac{dX}{dt} + k_d \end{align}

Substituting (1) into (2) and rearranging we arrive at a description of rate of population change:

Combined Reaction Kinetics/Population Dynamics: - Creating a function for product produced as a function of phage added.

@@ Line 13: / Line 13: @@
 \mu = \mu_{max} \frac{S(t)}{K_s + S(t)}
 \end{align}
+Where $\mu$ growth rate in units hr$^{-1}$, $\mu_{max}$ is the maximum growth rate, $K_s$ is the amount of substrate remaining when $\frac{\mu}{\mu_{max}} = \frac{1}{2}$, and $S(t)$ is the substrate remaining at a given time.
 Since growth rate is defined as:
 \begin{align}
-\mu = \frac{1}{X(t)} \frac{dX}{dt} + k_d
+\mu \equiv \frac{1}{X(t)} \frac{dX}{dt} + k_d
 \end{align}
-Where $\mu$ growth rate in units hr$^{-1}$, $\mu_{max}$ is the maximum growth rate, $K_s$ is the amount of substrate remaining when $\frac{\mu}{\mu_{max}} = \frac{1}{2}$, and $S(t)$ is the substrate remaining at a given time.
 Substituting (1) into (2) and rearranging we arrive at a description of rate of population change: