# Team:NCTU Formosa/Model-PC

### From 2010.igem.org

# Modeling >Population Control Modeling

**The dynamics model constructed for 'Population Control System**'

# Motivation

Our team constructed a genetic circuit with population control functions (Fig. 1). When these Mosquito Intelligent Terminator (MIT or Terminator) are released into the environment, the Terminator population is self-maintained, thus a surplus will never exist. To quantify the population control system, a dynamic model was used to simulate the bacterial population and the protein concentration changes that would occur once these Terminators are released into the environment. This simulation enables us to analyze system behavior and ultimately determine which experimental parameters should be adjusted to optimize system performance.

# Modeling and simulations

Population control system consists of three genes: LacI, LuxR, and ccdB. The initial population size of Terminator is the input to the system. The concentrations of LacI, LuxR, and ccdB proteins and bacterial population are the outputs.

This system can be modeled by differential equations as follows.

Alpha-C, D and bac are production rates of the corresponding targets, which are assumed to be given constants. Gamma-LuxR, gamma-ccdB, gamma-AHL and gamma-bac are decay rates of the corresponding targets. For an activator AHL/LuxR complex, Hill function is an S-shaped curve which can be described in the form x^n / (K +x^n). K is the activation coefficient and n determines the steepness of the input function (Alon, 2007). The k2 is the production rate of AHL that synthesized by the LuxI protein. For an inhibition of bacterial population, Hill function can be described in the form 1 / (1 +x^n). Because many of the in vivo rates of the biochemical reactions we simulated are unknown, the values of the kinetic parameters used in the simulation were initially obtained from the literature and educated guesses. From the gene network design procedure, initial values and numerical configurations were given, which lead to several rounds of simulation and results. (Fig.2).

Fig.4: The simulation result of the population control system. When the population size of* E. coli *rises to the threshold level, ccdB proteins are induced by AHL to restrict the population size.

At present, we have satisfactory *in-silico* results. The next step is to implement the “population control system” into the genetic circuit and ultimately the host bacteria for experimental data.

# References

Alon, U. (2007) An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman & Hall/CRC.