# Team:British Columbia/modeling equ

### From 2010.igem.org

### Summary of Equations

### Variables:

**
z** = depth of the biofilm structure
**
x **= depth of the phage-infested layer
**
ε **= portion of the biofilm population susceptible to phage infection
**
B _{T} **= total biofilm bacteria population

**B**= uninfected biofilm bacteria subpopulation

_{u}**B**= infected biofilm bacteria subpopulation

_{i}**B**= bacteria subpopulation infected with phage in latent phase

_{L}**B**= bacteria subpopulation infected with phage in lytic cycle

_{l}**P**= phage particle population

**r**= diffusion rate of phage particles into the biofilm structure

_{in}**[DspB]**= extracellular DspB concentration (inside biofilm)

**[AIP]**= extracellular AIP concentration (inside biofilm)

### Parameters:

**
A** = cross-sectional area of the biofilm container
**
D** = maximum biofilm thickness; related to K
**
d **= diameter of a biofilm bacterium
**
α** = EPS occupancy constant (corrects for the space EPS occupies around a bacterium)
**
K **= carrying capacity of the biofilm
**
p **= portion of the bacteria in the infected subpopulation that are infected by phage in latent phase
**
ρ **= bacterial growth rate of the total population (T), and the uninfected (u) and infected (i) subpopulations
**
λ **= host lysis rate
**
π** = rate at which phage switches from latent to lytic phase in its host cell after infection
**
κ**= portion of phage particles successfully infecting a host cell
**
η** = phage half-life
**
R** = number of phage particles released per lysis
**
δ** = percentage of phage and DspB diffusing out of the system (mechanical removal from biofilm)
**
Y** = diffusion linear proportionality constant
**
S **= amount of DspB enzyme released per lysis
**
σ **= rate of AIP production
**
γ**= rate of AIP degradation and/or mechanical removal from the system
**
[AIP] _{thres}**= threshold level of AIP concentration above which phage and DspB production are activated

**[AIP]**= maximum level of AIP concentration inside the biofilm

_{max}**r**= diffusion rate of phage particles out of the biofilm and towards boundary layer

_{out}**r**= max diffusion rate of phage particles into the biofilm

_{max}**r**= min diffusion rate of phage particles into the biofilm,

_{min}*i.e.*base rate