"
Team:HZAU-China/Modeling/Gray logistic
From 2013.igem.org
Aim:
To know the growth curve in the dog’s blood
Steps:
1.Do experiment to measure the number of bacteria;
2.Establish the gray logistic model to simulate the growth of bacteria;
3.Determine the parameter through the experiment;
4.Test the predicted results.
Results:
The gray logistic model gets the good forecasting result.And the model precision is excellent.
Background:
The color of blood is so deep that it is not fit to measure the OD value to determine the growth of bacteria in the blood.Then we choose dilution-plate method to detect the number of total bacteria. So we coated a large number of plates.The logistic model of population can well predict the increase of population.
Establish the logistic model:
In the environment of the blood,the number of bacteria have a maximum value K.And when the number of bacteria approach K,the growth rate is next to nil.Then the population growth equation is as follows:
The solution of the equation is :
N0 is the number of bacterial population.r is population growth rate.To make it convenient to calculate,we simplify the equation
;A,B and r are unknown parameters. is the logarithm of the CFU of Bacillus subtilis.
Using the gray system theory to determine the parameters:
To determine the parameters of the equation,we use the gray system theory.The equation can be rewritten:
;
;
;
Using the matrix equation in linear algebra we could determine the parameters α and β .
,
,
From the result ,we know the value of posterior-variance is 0.1931.The posterior-variance is lower than 0.35 so that the model precision is excellent.
In a conclution,Our engineering bacterium growth curve is in the dog's blood is
;is the logarithm of the CFU of Bacillus subtilis.
