Team:British Columbia/modeling equ
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- | <div id="SubWrapper"> | + | <div id="SubWrapper"> <br/> |
+ | <center><h3>Summary of Equations</h3> | ||
<br></br> | <br></br> | ||
+ | <img src="https://static.igem.org/mediawiki/2010/4/41/UBC_model_equations.jpg"> | ||
+ | <br></br></center> | ||
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- | <div id="news" style="height: | + | <div id="news" style="height:1250px;"> <br/> |
- | <br></br> | + | <h3>Variables:</h3> |
- | < | + | <p><b> |
- | </ | + | z</b> = depth of the biofilm structure |
+ | <br></br><b> | ||
+ | x </b>= depth of the phage-infested layer | ||
+ | <br></br><b> | ||
+ | ε </b>= portion of the biofilm population susceptible to phage infection | ||
+ | <br></br><b> | ||
+ | B<sub>T</sub> </b>= total biofilm bacteria population | ||
+ | <br></br><b> | ||
+ | B<sub>u</sub></b> = uninfected biofilm bacteria subpopulation | ||
+ | <br></br><b> | ||
+ | B<sub>i</sub></b> = infected biofilm bacteria subpopulation | ||
+ | <br></br><b> | ||
+ | B<sub>L</sub></b> = bacteria subpopulation infected with phage in latent phase | ||
+ | <br></br><b> | ||
+ | B<sub>l</sub> </b>= bacteria subpopulation infected with phage in lytic cycle | ||
+ | <br></br><b> | ||
+ | P</b> = phage particle population | ||
+ | <br></br><b> | ||
+ | r<sub>in</sub> </b>= diffusion rate of phage particles into the biofilm structure | ||
+ | <br></br><b> | ||
+ | [DspB]</b> = extracellular DspB concentration (inside biofilm) | ||
+ | <br></br><b> | ||
+ | [AIP]</b> = extracellular AIP concentration (inside biofilm)</p> | ||
+ | |||
+ | <h3>Parameters:</h3><p><b> | ||
+ | A</b> = cross-sectional area of the biofilm container | ||
+ | <br></br><b> | ||
+ | D</b> = maximum biofilm thickness; related to K | ||
+ | <br></br><b> | ||
+ | d </b>= diameter of a biofilm bacterium | ||
+ | <br></br><b> | ||
+ | α</b> = EPS occupancy constant (corrects for the space EPS occupies around a bacterium) | ||
+ | <br></br><b> | ||
+ | K </b>= carrying capacity of the biofilm | ||
+ | <br></br><b> | ||
+ | p </b>= portion of the bacteria in the infected subpopulation that are infected by phage in latent phase | ||
+ | <br></br><b> | ||
+ | ρ </b>= bacterial growth rate of the total population (T), and the uninfected (u) and infected (i) subpopulations | ||
+ | <br></br><b> | ||
+ | λ </b>= host lysis rate | ||
+ | <br></br><b> | ||
+ | π</b> = rate at which phage switches from latent to lytic phase in its host cell after infection | ||
+ | <br></br><b> | ||
+ | κ</b>= portion of phage particles successfully infecting a host cell | ||
+ | <br></br><b> | ||
+ | η</b> = phage half-life | ||
+ | <br></br><b> | ||
+ | R</b> = number of phage particles released per lysis | ||
+ | <br></br><b> | ||
+ | δ</b> = percentage of phage and DspB diffusing out of the system (mechanical removal from biofilm) | ||
+ | <br></br><b> | ||
+ | Y</b> = diffusion linear proportionality constant | ||
+ | <br></br><b> | ||
+ | S </b>= amount of DspB enzyme released per lysis | ||
+ | <br></br><b> | ||
+ | σ </b>= rate of AIP production | ||
+ | <br></br><b> | ||
+ | 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> | ||
+ | [AIP]<sub>max</sub></b>= maximum level of AIP concentration inside the biofilm | ||
+ | <br></br><b> | ||
+ | r<sub>out</sub> </b>= diffusion rate of phage particles out of the biofilm and towards boundary layer | ||
+ | <br></br><b> | ||
+ | r<sub>max</sub></b> = max diffusion rate of phage particles into the biofilm | ||
+ | <br></br><b> | ||
+ | r<sub>min</sub></b> = min diffusion rate of phage particles into the biofilm, <i>i.e.</i> base rate | ||
+ | <br></br></p> | ||
+ | |||
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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