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Latest revision as of 02:11, 18 June 2014
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Competitive Lotka–Volterra equations
Lotka–Volterra equations are a simple model for population dynamics.
dx/dt = rx (1 - x/K)
x refers to the population size, r refers to growth rate, and K is the carrying capacity
Competitive population model between AMP-producing bacteria (a) and the spoilage bacteria (b).
a = AMP-producing bacteria (Blue in graph)
b = the spoilage bacteria (Red in graph)
N = population
R = growth rate
K = carrying capacity
Equation:
Na+1 = Na*Ra (1 – (Na + Aab*Nb)/Ka)
Nb+1 = Nb*Rb (1 – (Nb + Aba*Na)/Kb)
Aab = the effect bacteria b has on the population of bacteria a
Aba = the effect bacteria a has on the population of bacteria b
bacteria a
bacteria b
At the 11th generation, the concentration of antimicrobial peptides (AMPs) produced by bacteria a reached the minimum inhibitory concentration (MIC) and are able to kill 95% of bacteria b. The population of bacteria a begins to out-compete and outgrow the population of bacteria b.
In our model, at the 11th generation, AMP-producing bacteria made enough antimicrobial materials against the spoilage bacteria. And at the 18th generation, AMP-producing bacteria reached a plateau and efficiently inhibited the growth of the spoilage bacteria.
The minimum inhibitory concentration of AMPs produced by our engineered bacteria has to be measured. Nevertheless, if the engineered bacteria can make effective concentration before the 11th generation, the spoilage bacteria will disappear at the 18th generation.
