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From 2010.igem.org

Mathematical models are very important in the design of an iGEM project. The Michigan modeling team is composed of Josh, Kevin, Candy and Jennifer. We are currently researching different models that have been previously done that can help us in our own modeling endeavors. To construct our models, we have taken advantage of MATLAB's Simbiology toolset.

There are several components to a good mathematical model. These include assumptions, parameters, and equations.

Pili

We have decided to model the growth of a biofilm using pili. By modeling the flocculation of the algae, we hope to be able to predict how our reactions will proceed and determine quantities such as the optimal initial concentration of E. coli.

Assumptions
There is no growth or degradation of cells and algae.

• I made this assumption to simplify the model.

Floc formation only involves two particles. Collision efficiency is perfect.

• This assumption greatly simplifies the model.

Parameters
All rate constants set to 0.1.

• This is obviously unrealistic, but with experimental data, we can refine the numbers.

Initial quantities of E. coli and algae are 1 mol.

• We can perform assays to determine the ideal starting conditions.

The pili neural network has been characterized in several papers [1][2]. Essentially, the two recombinases FimB and FimE control an invertible DNA element that acts as a switch, known as FimS. When FimS is in the "on" position, the cell becomes fimbriated. It has been previously determined that the level of piliation depends on the ratio [FimE]/[FimB]. The goal of the modeling team is to determine the optimal ratio to promote flocculation.

Quorum Sensing

Quorum sensing has been modeled by other iGEM teams for previous competitions, including: Bangalore and Singapore

This model is based on the paper WILLFINDEVENTUALLYI'MSORRY and was created with the help of Alex who is also on the quorum sensing team. More information about quorum sensing can be found here: Team:Michigan/Project and their notebook can be found here: Team:Michigan/Quorum_Sensing.

This model shows the movement of AI2 (Autoinducer-2) from outside the cell (AI2_o) to inside the cell (AI2_i). The final output after transcription and translation is GFP in the case of the Lux- mutants recieved; however, at the end of the project, this will hopefully cause flocculation of the microalgae.

This model is also specific to the Lux- mutants as it is not understood how LuxS works or is produced. (need to cite)

Assumptions

• Assume all massaction
  • This greatly simplifies the model and gives a good estimate; however, it is unrealistic.
• Initially, all LsrR bound to all operators to inhibit.
  • This also simplifies the model and allows us to assume that basal expression is 0.
• Creation of LsrS is unknown so simply exists in the cell at a fixed concentration. Any output that occurs is due to the addition of AI2 from the person performing the experiment.
• Assume that the proteins that bring in AI2 (Lsr A, B, C, and D) exist in a protein complex and can be called one "species" in Matlab. Also assume that the protein complex is created and formed at the same time.
  • This simplifies the number of species in Matlab and also simplifies the model.
• Assuming no degradation for now... Molecule is "used" up in reaction.
  • This simplifies the model by removing degradation from the equations.

Parameters

• For now, all rate constants are 1.
  • This simplifies the model; however, it is not realistic.
• Assumptions with quantities
  • A lot of AI2_o in comparison with all other molecules.
    • This is saying that the experimenter will add a higher concentration of AI2 than the concentrations of various molecules that exist in the cell.
  • Initially low concentration of Lsr A,B,C,D transport proteins
    • Low basal expression of the transport proteins.
  • Low concentration of LsrK
    • Low basal expression of LsrK.
  • Low concentration of LsrR + Operator
    • In comparison with the protein concentration, the number of plasmids containing the Operator is low.

Surface Display

Oil Sands

We are developing a mathematical model which describes the degradation of naphthenic acids by Pseudomonas putida and Pseudomonas fluorescens in a biofilm.

References

1. Kuwahara, H., Myers, C., Samoilov, M., Abstracted Stochastic Analysis of Type 1 Pili Expression in E. Coli.

2. Wolf, D., and Arkin, A., Fifteen Minutes of fim: Control of Type 1 Pili Expression in E. Coli. OMICS 6 2002