Team:British Columbia/modeling equ

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<html><body id="modeling" onload="setPageSize()">
<html><body id="modeling" onload="setPageSize()">
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<div id="SubWrapper">  <br/>
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<h3>Summary of Equations</h3>
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<center><h3>Summary of Equations</h3>
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<i>Generalized biofilm population dynamics</i>
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<br></br>
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<img src="https://static.igem.org/mediawiki/2010/e/ec/UBC_eqnsum_set1.jpg" width=300px>
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<br></br>
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<i>AIP-regulated processes</i>
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<br></br>
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<img src="https://static.igem.org/mediawiki/2010/9/99/UBC_eqnsum_set2.jpg" width=200px>
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<br></br>
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<i>Diffusion rates</i>
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<br></br>
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<img src="https://static.igem.org/mediawiki/2010/c/c7/UBC_eqnsum_set3.jpg" width=300px>
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<br></br>
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<i>Biofilm structure dynamics</i>
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<br></br>
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<img src="https://static.igem.org/mediawiki/2010/a/af/UBC_eqnsum_set4.jpg" width=150px>
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<br></br>
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<i>General relations</i>
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<img src="https://static.igem.org/mediawiki/2010/d/d0/UBC_eqnsum_set5.jpg" width=200px>
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<br></br>
<br></br>
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<img src="https://static.igem.org/mediawiki/2010/4/41/UBC_model_equations.jpg">
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<br></br></center>
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</div> <!-- end SubWrapper -->
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<div id="news" style="height:700px;">  
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<div id="news" style="height:1250px;"> <br/>
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<b>Variables:</b>
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<h3>Variables:</h3>
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<br></br>
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<p><b>
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B<sub>T</sub> = total biofilm bacteria population
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z</b> = depth of the biofilm structure
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<br></br>
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<br></br><b>
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B<sub>u</sub> = uninfected biofilm bacteria subpopulation
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x </b>= depth of the phage-infested layer
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<br></br>
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<br></br><b>
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B<sub>i</sub> = infected biofilm bacteria subpopulation
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&epsilon; </b>= portion of the biofilm population susceptible to phage infection
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<br></br>
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<br></br><b>
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B<sub>L</sub> = biofilm bacteria population infected with phage in latent phase
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B<sub>T</sub> </b>= total biofilm bacteria population
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<br></br>
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<br></br><b>
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B<sub>l</sub> = biofilm bacteria population infected with phage in lytic cycle
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B<sub>u</sub></b> = uninfected biofilm bacteria subpopulation
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<br></br>
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<br></br><b>
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P = phage particle population
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B<sub>i</sub></b> = infected biofilm bacteria subpopulation
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<br></br>
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<br></br><b>
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z = depth of biofilm structure
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B<sub>L</sub></b> = bacteria subpopulation infected with phage in latent phase
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<br></br>
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<br></br><b>
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x = depth of phage-infested layer
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B<sub>l</sub> </b>= bacteria subpopulation infected with phage in lytic cycle
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<br></br>
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<br></br><b>
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r<sub>in</sub> = diffusion rate of phage particles into biofilm structure
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P</b> = phage particle population
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<br></br>
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<br></br><b>
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[DspB] = extracellular DspB concentration (inside biofilm)
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r<sub>in</sub> </b>= diffusion rate of phage particles into the biofilm structure
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<br></br>
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<br></br><b>
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[AIP] = extracellular AIP concentration (inside biofilm)
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[DspB]</b> = extracellular DspB concentration (inside biofilm)
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<b>Parameters:</b>
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<br></br><b>
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<br></br>
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[AIP]</b> = extracellular AIP concentration (inside biofilm)</p>
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ρ = bacterial growth rate for total population (T), and uninfected (u) and infected (i) subpopulations
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<br></br>
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<h3>Parameters:</h3><p><b>
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p = portion of latent bacteria in infected subpopulation
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A</b> = cross-sectional area of the biofilm container
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<br></br>
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<br></br><b>
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λ = lysis rate
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D</b> = maximum biofilm thickness; related to K
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<br></br>
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<br></br><b>
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κ = number of infections per phage particle per time unit
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d </b>= diameter of a biofilm bacterium
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<br></br>
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<br></br><b>
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κP = infection rate
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α</b> = EPS occupancy constant (corrects for the space EPS occupies around a bacterium)
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<br></br>
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<br></br><b>
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π = rate at which phage switches from latent to lytic mode
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K </b>= carrying capacity of the biofilm
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<br></br>
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<br></br><b>
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K = carrying capacity of biofilm
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p </b>= portion of the bacteria in the infected subpopulation that are infected by phage in latent phase
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<br></br>
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<br></br><b>
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δ = phage and DspB diffusion rate out of the system (mechanical removal from biofilm)
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ρ </b>= bacterial growth rate of the total population (T), and the uninfected (u) and infected (i) subpopulations
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<br></br>
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<br></br><b>
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η = phage half-life
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λ </b>= host lysis rate
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<br></br>
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<br></br><b>
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R = number of phage particles released per lysis
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π</b> = rate at which phage switches from latent to lytic phase in its host cell after infection
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<br></br>
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<br></br><b>
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S = amount of DspB enzymes released per lysis
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κ</b>= portion of phage particles successfully infecting a host cell
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<br></br>
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<br></br><b>
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σ = rate of AIP production
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η</b> = phage half-life
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<br></br>
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<br></br><b>
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γ = rate of AIP degradation and/or mechanical removal from system
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R</b> = number of phage particles released per lysis
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<br></br>
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<br></br><b>
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[AIP]<sub>thres</sub> = threshold level of AIP concentration above which phage and DspB production are activated
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δ</b> = percentage of phage and DspB diffusing out of the system (mechanical removal from biofilm)
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<br></br>
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<br></br><b>
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α = EPS occupancy constant
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Y</b> = diffusion linear proportionality constant
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<br></br>
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<br></br><b>
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d = diameter of a biofilm bacterium
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S </b>= amount of DspB enzyme released per lysis
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<br></br>
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<br></br><b>
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A = cross-sectional area of biofilm container
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σ </b>= rate of AIP production
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<br></br>
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<br></br><b>
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D = maximum biofilm thickness; related to K
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γ</b>= rate of AIP degradation and/or mechanical removal from the system
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<br></br>
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<br></br><b>
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r<sub>out</sub> = diffusion rate of phage particles out of biofilm, towards boundary layer
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[AIP]<sub>thres</sub></b>= threshold level of AIP concentration above which phage and DspB production are activated
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<br></br>
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<br></br><b>
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r<sub>max</sub> = max diffusion rate of phage particles into biofilm
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[AIP]<sub>max</sub></b>= maximum level of AIP concentration inside the biofilm
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<br></br>
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<br></br><b>
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r<sub>min</sub> = min diffusion rate of phage particles into biofilm (base rate)
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r<sub>out</sub> </b>= diffusion rate of phage particles out of the biofilm and towards boundary layer
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<br></br>
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<br></br><b>
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Y = phage diffusion proportionality constant
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r<sub>max</sub></b> = max diffusion rate of phage particles into the biofilm
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<br></br>
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<br></br><b>
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<ul>
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r<sub>min</sub></b> = min diffusion rate of phage particles into the biofilm, <i>i.e.</i> base rate
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</ul>
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<br></br></p>
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</div>  <!-- end news -->
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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

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