Team:British Columbia/modeling equ

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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_u = uninfected biofilm bacteria subpopulation

B_i = infected biofilm bacteria subpopulation

B_L = bacteria subpopulation infected with phage in latent phase

B_l = bacteria subpopulation infected with phage in lytic cycle

P = phage particle population

r_in = diffusion rate of phage particles into the biofilm structure

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

r_out = diffusion rate of phage particles out of the biofilm and towards boundary layer

r_max = max diffusion rate of phage particles into the biofilm

r_min = min diffusion rate of phage particles into the biofilm, i.e. base rate