Team:KAIST-Korea/Projects/report 1

Objective
Mathematical modeling is essential in qualitatively describing de novo genetic circuits that frequently arise in synthetic biology. We can use such models for two objectives: (1) predicting the behavior of combinations of BioBrick parts designed for the synthetic circuit that performs some task, and (2) choosing the appropriate promoter and RBS with suitable strengths for the circuit. Also, it will serve as a reference for others who use the BioBrick in the future. In summary, the model and the computer simulation are our beginning point for making testable predictions about the behavior of our system. We construct a computational model describing the genetic network encompassing relevant signal transduction pathways in order to help build E.coli that can draw pictures!
Modeling E. coli Type I. (Brush E. coli)
2.1 Modeling Approach There are several known Quorum sensing (QS) networks. All known QS networks operate as an “on-off” gene expression switch by controlling the level of a certain transcription factor whose expression is suppressed in the “off” state and is strongly induced in the “on” state.[2] Usually, the intracellular network that is controlled by the quorum sensing remains in the “off” state until the quorum reaches a certain concentration. After quorum reaches the threshold concentration, the genetic circuit changes its state into “on” state and activates the expression of the relevant genes.
In this model, we hypothesized that the typical E.coli cell volume is ~7.0×10-16L and cells are freely permeable to quorums. We used a standard chemical kinetic approach based on the mass-action rate law. The kinetic parameters used in our model are based on the published data. There were a lot of papers about the mathematical modeling of quorum sensing pathway, so we used the rate constants from these papers.
2.2 Model
Before moving on to how we model our system, it will be helpful to review how to model general protein production of a single gene here.
2.2.A. Protein Production of a Single Gene Model
An actual protein production from a single gene is composed of complex processes. However, in this model, protein production from a gene is simplified into two processes: Transcription and Translation.
The whole process can be represented by these chemical reactions (with ODE): [1]

mRNA □(→)∅ (Half time ≈5min)
Protein □(→)∅ (Half time ≈1hour)
The degradation rate of the mRNA and protein can be calculated from
k=ln2/t_(1/2)
Therefore, kmd(mRNA degradation rate), kpd(protein degradation rate) can be calculated. The values are in the constant table. [3. Constant Table of this page] Based on these facts and the law of mass action, we can write these equations:
d[mRNA]/dt=p_m [Gene]- k_md [mRNA]
d[mRNA]/dt=p_p [mRNA]- k_pd [Protein]