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Team:British Columbia/Modeling
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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.
