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Team:UCL London/Modeling/Model1
From 2009.igem.org
Contents |
Oxygen and Cell concentration model
Description
On a larger scale, we will put cells at stress. With a selected number of stress we intend to determine how the cells react. Here we will focus on the Oxygen stress individually. At a later stage we will consider another stress independently, then build model onthis stress in order to determine characteristic parameters. Ultimately we will have a joint model for the two stresses and will come with r4ecommendation on such an environment.
Objectives
The objectives of this model is to determine Oxygen levels at which the cells are put at a stress they can not cope with so that the size of the colony is decreasing. Therefore the ultimate objective of the model is determining the minimum level of oxygen (kept constant) at which the size of the colony is stable.
From the lab we will verify the parameters taken are the right ones. We will also define the percentage error judged admissible.
Equations
We will assume the following equations:
- Equation of growth: x(t)=x0*exp(mu*t)
- x0 is the initial concentration of E Coli
- mu is the growth rate specific to the E Coli
- Growth and decline phases: rx=mu*x(t)
- rx is the volumetric rate of biomass production
- Number of cells at a time t: N=N0*Exp(-kd*t)
- kd is the specific death constant
- N0 is the initial number of cells
- Rate of cells death: rd=kd*N
- N is the number of viable cells
- kd is the specific death constant
- Oxydgen uptake rate: Q(t)=Q0*x(t)
- Q0 is the specific O2 uptake rate
- x is the cell concentration
- Rate of oxygen transfer per unit of volume of fluid: Na=kl*a*((Cal*)*Cal)
- kl is the liquid phase mass transfer coefficient
- a is the gas liquid interfacial area per unit of volume of liquid
- Cal* is the oxygen concentration in broth on equilibrium with gas phase
- Cal oxygen concentration in broth
