Team:British Columbia/modeling equ
From 2010.igem.org
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<h3>Summary of Equations</h3> | <h3>Summary of Equations</h3> | ||
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z = depth of biofilm structure | z = depth of biofilm structure | ||
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A = cross-sectional area of biofilm container | A = cross-sectional area of biofilm container | ||
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Revision as of 20:28, 23 October 2010
Summary of Equations
Variables:
z = depth of biofilm structure
x = depth of phage-infested layer
BT = total biofilm bacteria population
Bu = uninfected biofilm bacteria subpopulation
Bi = infected biofilm bacteria subpopulation
BL = bacteria population infected with phage in latent phase
Bl = bacteria population infected with phage in lytic cycle
P = phage particle population
rin = diffusion rate of phage particles into biofilm structure
[DspB] = extracellular DspB concentration (inside biofilm)
[AIP] = extracellular AIP concentration (inside biofilm)
Parameters:
A = cross-sectional area of biofilm container
D = maximum biofilm thickness; related to K
d = diameter of a biofilm bacterium
α = EPS occupancy constant
K = carrying capacity of biofilm
p = portion of latent bacteria in infected subpopulation
ρ = bacterial growth rate for total population (T), and uninfected (u) and infected (i) subpopulations
λ = lysis rate
π = rate at which phage switches from latent to lytic phase post-infection
κ = portion of phage particles causing infection
η = phage half-life
R = number of phage particles released per lysis
δ = phage and DspB diffusion rate out of the system (mechanical removal from biofilm)
Y = phage diffusion proportionality constant
S = amount of DspB enzymes released per lysis
σ = rate of AIP production
γ = rate of AIP degradation and/or mechanical removal from system
[AIP]thres = threshold level of AIP concentration above which phage and DspB production are activated
rout = diffusion rate of phage particles out of biofilm, towards boundary layer
rmax = max diffusion rate of phage particles into biofilm
rmin = min diffusion rate of phage particles into biofilm (base rate)