Overview

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Since the bacteria growth model is a kind of logistic function variation with numerous parameters. We've used three parameters in this function, L for the maximum value of bacteria, k for the growth rate of log phase and t_i for the end of the lag phase. We are trying to find the relation between those parameters in some specific situations.

Variables:

Variable	Description
tre	OD600 value for re-growth time from different phases
qi	OD600 value for different initial quantity
L	Maximum growth of bacteria
k	Maximum growth rate
ti	Duration of the lag phase

Environmental Parameters:

Parameter	Value
Culture Temperature	37°C
Medium	50ml LB+CM
Bacteria Strain	E. coli DH5α
Shaker Speed	200rpm

Model

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First, we take the re-growth time from different phases as a variable to examine the influence for each parameter. By using GRG nonlinear regression in Excel to find the best solution for parameter fitting, we can conclude that L first rises up then goes down and rises up in the end, k goes up then remains in constant, t_i goes down with the trend then rises up in the end.After calculating the function by the fitting for each parameter, we can theoretically take the function generated by the calculating engine for each parameter because the total errors for each parameter are 0.06%, 0.14%, and 3.64% respectively.

Second, we take the initial quantity of the bacteria as another variable by doing the same examination to the first condition. We can conclude that the more initial value the parameters go down with the trend. After calculating the function by the fitting for each parameter, we can theoretically take the function generated by the calculation engine for each parameter, since the total error for each function is 0.03%, 0.003%, and 2.0%, respectively.

Re-Growth Time from Different Phases

First, we choose to take out the colonies at different phases then re-grow, and observe its effect on the growth curve. The following figure is the growth curve drawn from the experimental data, and the OD value is already subtracted from the blank value.

The following figure shows the results of the fitting of the data for each of the five cases according to the logistic function.

Next, there are five sets of three parameters, and the three parameters are fitted according to the current OD value of the bacterium selected. Since these variables have not been studied for growth curves, we used a polynomial to do the fitting. Since the error of the summation result is a bit large from the square fitting, and more than the 4th power of the polynomial is too much under-fitting, we use the third power of the polynomial after many times of validation.

Initial Quantity

Secondly, we choose to observe the effect on the growth curve according to the different initial quantities. The following figure is the growth curve drawn by the experimental data, and the OD value of which is also the value that has subtracted the blank.

The following figure shows the results of fitting the data of each of the four cases according to the logistic function.

Then, there are four sets of three parameters, and the initial OD value is used to fit the three parameters respectively. The initial OD value may be less than 0 due to instrument or personal error. For the same reason, the final fitting result is done by using the third power of the polynomial.

 

Conclusions

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By simulating the predicted curve, we can know the growth status of the bacteria under different conditions and the correlation between various environmental parameters and growth.

It also allows more people to obtain the predicted growth curve before the experiment, using two known parameters including re-growth time from different phases and initial quantity, then adjust the experiment according to their needs.