Team:British Columbia/modeling equ

Summary of Equations

Generalized biofilm population dynamics



AIP-regulated processes



Diffusion rates



Biofilm structure dynamics



General relations

Variables:

B_T = total biofilm bacteria population

B_u = uninfected biofilm bacteria subpopulation

B_i = infected biofilm bacteria subpopulation

B_L = biofilm bacteria population infected with phage in latent phase

B_l = biofilm bacteria population infected with phage in lytic cycle

P = phage particle population

z = depth of biofilm structure

x = depth of phage-infested layer

r_in = diffusion rate of phage particles into biofilm structure

[DspB] = extracellular DspB concentration (inside biofilm)

[AIP] = extracellular AIP concentration (inside biofilm) Parameters:

ρ = bacterial growth rate for total population (T), and uninfected (u) and infected (i) subpopulations

p = portion of latent bacteria in infected subpopulation

λ = lysis rate

κ = number of infections per phage particle per time unit

κP = infection rate

π = rate at which phage switches from latent to lytic mode

K = carrying capacity of biofilm

δ = phage and DspB diffusion rate out of the system (mechanical removal from biofilm)

η = phage half-life

R = number of phage particles released per lysis

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

α = EPS occupancy constant

d = diameter of a biofilm bacterium

A = cross-sectional area of biofilm container

D = maximum biofilm thickness; related to K

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

r_max = max diffusion rate of phage particles into biofilm

r_min = min diffusion rate of phage particles into biofilm (base rate)

Y = phage diffusion proportionality constant