Team:British Columbia/modeling equ

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<h3>Variables:</h3>
<h3>Variables:</h3>
<p><b>
<p><b>
-
z</b> = depth of biofilm structure
+
z</b> = depth of the biofilm structure
<br></br><b>
<br></br><b>
-
x </b>= depth of phage-infested layer
+
x </b>= depth of the phage-infested layer
 +
<br></br><b>
 +
&epsilon; </b>= portion of the biofilm population susceptible to phage infection
<br></br><b>
<br></br><b>
B<sub>T</sub> </b>= total biofilm bacteria population
B<sub>T</sub> </b>= total biofilm bacteria population
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B<sub>i</sub></b> = infected biofilm bacteria subpopulation
B<sub>i</sub></b> = infected biofilm bacteria subpopulation
<br></br><b>
<br></br><b>
-
B<sub>L</sub></b> = bacteria population infected with phage in latent phase
+
B<sub>L</sub></b> = bacteria subpopulation infected with phage in latent phase
<br></br><b>
<br></br><b>
-
B<sub>l</sub> </b>= bacteria population infected with phage in lytic cycle
+
B<sub>l</sub> </b>= bacteria subpopulation infected with phage in lytic cycle
<br></br><b>
<br></br><b>
P</b> = phage particle population
P</b> = phage particle population
<br></br><b>
<br></br><b>
-
r<sub>in</sub> </b>= diffusion rate of phage particles into biofilm structure
+
r<sub>in</sub> </b>= diffusion rate of phage particles into the biofilm structure
<br></br><b>
<br></br><b>
[DspB]</b> = extracellular DspB concentration (inside biofilm)
[DspB]</b> = extracellular DspB concentration (inside biofilm)
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<h3>Parameters:</h3><p><b>
<h3>Parameters:</h3><p><b>
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A</b> = cross-sectional area of biofilm container
+
A</b> = cross-sectional area of the biofilm container
<br></br><b>
<br></br><b>
D</b> = maximum biofilm thickness; related to K
D</b> = maximum biofilm thickness; related to K
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d </b>= diameter of a biofilm bacterium
d </b>= diameter of a biofilm bacterium
<br></br><b>
<br></br><b>
-
α</b> = EPS occupancy constant
+
α</b> = EPS occupancy constant (corrects for the space EPS occupies around a bacterium)
<br></br><b>
<br></br><b>
-
K </b>= carrying capacity of biofilm
+
K </b>= carrying capacity of the biofilm
<br></br><b>
<br></br><b>
-
p </b>= portion of latent bacteria in infected subpopulation
+
p </b>= portion of the bacteria in the infected subpopulation that are infected by phage in latent phase
<br></br><b>
<br></br><b>
-
ρ </b>= bacterial growth rate for total population (T), and uninfected (u) and infected (i) subpopulations
+
ρ </b>= bacterial growth rate of the total population (T), and the uninfected (u) and infected (i) subpopulations
<br></br><b>
<br></br><b>
-
λ </b>= lysis rate
+
λ </b>= host lysis rate
<br></br><b>
<br></br><b>
-
π</b> = rate at which phage switches from latent to lytic phase post-infection
+
π</b> = rate at which phage switches from latent to lytic phase in its host cell after infection
<br></br><b>
<br></br><b>
-
κ </b>= portion of phage particles causing infection
+
κ</b>= portion of phage particles successfully infecting a host cell
<br></br><b>
<br></br><b>
η</b> = phage half-life
η</b> = phage half-life
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R</b> = number of phage particles released per lysis
R</b> = number of phage particles released per lysis
<br></br><b>
<br></br><b>
-
δ</b> = phage and DspB diffusion rate out of the system (mechanical removal from biofilm)
+
δ</b> = percentage of phage and DspB diffusing out of the system (mechanical removal from biofilm)
<br></br><b>
<br></br><b>
-
Y</b> = phage diffusion proportionality constant
+
Y</b> = diffusion linear proportionality constant
<br></br><b>
<br></br><b>
-
S </b>= amount of DspB enzymes released per lysis
+
S </b>= amount of DspB enzyme released per lysis
<br></br><b>
<br></br><b>
σ </b>= rate of AIP production
σ </b>= rate of AIP production
<br></br><b>
<br></br><b>
-
γ </b>= rate of AIP degradation and/or mechanical removal from system
+
γ</b>= rate of AIP degradation and/or mechanical removal from the system
 +
<br></br><b>
 +
[AIP]<sub>thres</sub></b>= threshold level of AIP concentration above which phage and DspB production are activated
<br></br><b>
<br></br><b>
-
[AIP]<sub>thres</sub> </b>= threshold level of AIP concentration above which phage and DspB production are activated
+
[AIP]<sub>max</sub></b>= maximum level of AIP concentration inside the biofilm
<br></br><b>
<br></br><b>
-
r<sub>out</sub> </b>= diffusion rate of phage particles out of biofilm, towards boundary layer
+
r<sub>out</sub> </b>= diffusion rate of phage particles out of the biofilm and towards boundary layer
<br></br><b>
<br></br><b>
-
r<sub>max</sub></b> = max diffusion rate of phage particles into biofilm
+
r<sub>max</sub></b> = max diffusion rate of phage particles into the biofilm
<br></br><b>
<br></br><b>
-
r<sub>min</sub></b> = min diffusion rate of phage particles into biofilm (base rate)
+
r<sub>min</sub></b> = min diffusion rate of phage particles into the biofilm, <i>i.e.</i> base rate
<br></br></p>
<br></br></p>

Latest revision as of 00:33, 26 October 2010



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

BT = total biofilm bacteria population

Bu = uninfected biofilm bacteria subpopulation

Bi = infected biofilm bacteria subpopulation

BL = bacteria subpopulation infected with phage in latent phase

Bl = bacteria subpopulation infected with phage in lytic cycle

P = phage particle population

rin = 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

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

rmax = max diffusion rate of phage particles into the biofilm

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