Team:British Columbia/Modeling

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(Difference between revisions)
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We've decided to use Monod substrate limited growth kinetics for to model population dynamics.
We've decided to use Monod substrate limited growth kinetics for to model population dynamics.
-
 
\begin{align}
\begin{align}
\mu = \mu_{max} \frac{S(t)}{K_s + S(t)}
\mu = \mu_{max} \frac{S(t)}{K_s + S(t)}
\end{align}
\end{align}
 +
Since growth rate is defined as:
 +
\begin{align}
 +
\mu = \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:
 +
 +
Combined Reaction Kinetics/Population Dynamics:
Combined Reaction Kinetics/Population Dynamics:
- Creating a function for product produced as a function of phage added.
- Creating a function for product produced as a function of phage added.

Revision as of 00:46, 9 August 2013

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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} Since growth rate is defined as: \begin{align} \mu = \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:



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