# Modeling

## What is the aim of our model?

The aim of our modeling project is to find the growth parameters from experimental data. Moreover, we hope to predict the reduction of the growth rate in the double knock-out *E. coli* strain *arcA-iclR-*. In order to do so, we use GroFit in R to find the parameters. GroFit is a package that allows us to fit many growth curves obtained under different conditions in order to derive a conclusive dose-response curve, such as for a compound that potentially affects growth. In addition, we had a collaboration with HKUST to predict the growth rate after the double KO.

## GroFit modeling

This is the overall flow of data analysis after getting experimental data from the lab.

Raw data is input into the GroFit package. GroFit outputs growth curves for each replicate and a table containing all parameters calculated by the program. Useful parameters are chosen and to produce boxplots. Statistical tests are carried out with the parameters.

### Raw data processing

The cell density was inserted and time data of the test samples in different excel files and were saved as .csv files.

### Input to GroFit

First, we installed packages for graphing and downloaded the GroFit via uri. Then, we transformed the y-axis in log scale. After that, we assigned the cell density and time data directories to the .csv files. Finally, GroFit compiled matrices to generate plots and parameters.

### GroFit output

For the output of GroFit, it showed growth curves for every replicate and a summary table is produced for the results.

### Choose the suitable fit for further steps

Growth curves and tangent lines, representing maximum growth rate is produced as one of the outputs of GroFit. For each replicate, there are two sets of lines, the black set represents model fit and the red set represents spline fit. From these two, the better fitting set is selected for further use. Here are two examples where we selected model fit (WT-Rep2) and spline fit (*iclR*_KO-Rep4) respectively.

Example comparison - model fit is chosen

Example comparison - spline fit is chosen

### Box plots of selected data

From the parameters chosen from GroFit output, box plots are created in R. The description and interpretation of experimental results can be found in [experiment] and [contribution]

### Statistical analysis

Analysis of variance is done, followed by a Tukey test, which is a post-hoc test.

#### ANOVA

Max. growth rate | Max. cell density | |
---|---|---|

Df | 3 | 3 |

F value | 3.396 | 2.245 |

P value | 0.0437 * | 0.122 |

#### Post-hoc Test - Tukey Test

When p value is lower than 0.05, the strains are said to be distinct.

Strain comparison | iclR- / arcA- |
iclR-rescue / arcA- |
Wild Type / arcA- |
iclR-rescue / iclR- |
Wild Type / iclR- |
Wild Type / iclR-rescue |
---|---|---|---|---|---|---|

P value | 0.0611592 | 0.8736779 | 0.1498436 | 0.2012448 | 0.9680145 | 0.4145053 |

## Simulating performance of double-knockout *E. coli*

We do this since the project depends on the double-knockout of *arcA* and *iclR* for the cell proliferation part. Unfortunately we cannot do the experiment due to the lack of resources and CRISPR technology. Therefore we hope to simulate the performance of double-knockout *E. coli* with a mathematical model using experimental data of single-knockout strains.

We have a collaborated with HKUST in which their team offered to help us with setting up the basics of our model. More details about the collaboration can be found in [collabration]. The pdf below describes the model HKUST team has developed with us.

[click for the clear version of pdf]

Unfortunately, the result in the experiment of single-knockout *E. coli* has a very large range and we thought the results were invalid. We plan to repeat the experiment before inputting the data into the model. The coming experiments will include more control and an increased number of replicates, in order to get valid results with a smaller data range within the group.

### Reference

G. T. Tsao and T. P. Hanson, “Extended monod equation for batch cultures with multiple exponential phases,” *Biotechnology and Bioengineering*, vol. 17, no. 11, pp. 1591–1598, 1975.

M. Kahm, G. Hasenbrink, H. Lichtenberg-Fraté, J. Ludwig, and M. Kschischo, “Grofit: Fitting biological growth curves with R,” *Journal of Statistical Software*, vol. 33, no. 7, Feb. 2010.

X. Dong, “Whisker of boxplot: R-bloggers,” *R-bloggers*, 26-Nov-2013. [Online]. Available: https://www.r-bloggers.com/2012/06/whisker-of-boxplot/. [Accessed: 13-Oct-2021].