Our modeling team consisted of Leon Lin and Mary Yang.

Goal

• To model and optimize the kinetics of these devices.
• Population dynamics: analyze the conditions to switch between Th17 and Tregs.
• To predict the results of experiments which we could not perform in the lab
• Below is a chart of all the individual processes in our respective devices. This page contains mathematical models many of those processes and provides a quantitative description for how our devices work.

Anti-Inflammatory Device

The IPP-->B-carotene-->RA Model

Fig 2.1 A quick sketch of the IPP-->RA process

Fig 2.2 The B-carotene production pathway [1]

The process above can be devided into two procedures:

• IPP*8-->B-carotene
• B-carotene(+Blh)-->Retinal(+RalDH)-->Retinoic Acid

Modeling on the production of B-carotene

The process of IPP producing B-carotene is quite complex, as shown in the Fig 2.2.
In this process, we basically care about two main issues:

1. Yield output of B-carotene ([B-carotene]/[All Caronoids]).
2. Velocity of the whole process

Yield output of B-carotene

We found the B-carotene distribution in yeast in [1]. Below is an important form as to the issue.

<center>Form 2.1 B-carotene distribution [1]</center>
Basically, using the cluster of "YB/I/E I", in the final product of caronoids, we get 68% of B-carotene, highest percentage in the paper. (Also 29% Phytoene, and 3% Neurosporene.) "YB/I/E tHMG1 I", producing 52% of B-carotene, might be another choice.

Production rate of B-carotene

As this is a really long process....Basically, the velocity is mainly dependent on the most time-consuming reaction in the whole chain. Thus, Leon and I looked for the kcat values of different enzymes in the procedure, as shown in the cart below:

Apparently, cyclization of Lycopene is the slowest reaction, as the concentration of enzymes are approximately in the same level.

Modeling on the B-carotene-->RA process

The production of RA is mainly based on a chain of two catalyzed reactions, as shown in the graph below:

<center>Fig 2.3 The production of RA</center> Neither Retinal nor RA has any other degrading process in E.coli. Degrading rate of B-carotene is 9.769e-9 s^-1. Other paremeters we use in this model are shown in the form below:

<center>Form 2.3 Parameters used in the B-carotene-->RA model</center>

Simulation and Analysis

• Equations for the IPP-->RA process:

References

[1] High-Level Production of Beta-Carotene in Saccharomyces cerevisiae by Successive Transformation with Carotenogenic Genes from Xanthophyllomyces dendrorhous. APPLIED AND ENVIRONMENTAL MICROBIOLOGY, July 2007, p. 4342–4350

The NO->SoxS-SoxR Model

This model illustrates the level of SoxS-SoxR binding over time

Anti-Immunosuppresion Device

Models of the Tryptophan System

Wild Type Model Ignoring Cooperativity

Base on the fitting to Fig 1 from Reference [2], we came to the result kT=1.62e4 molecules/cell. While the kT measured by Schmitt et al. (1995) is 1.97e4 molecules/cell. The figure below shows the result of our fitting, and the comparison to standard kT value.

Thus, it is reasonable to calculate k_T values for trp with mutant repressor, 5MT with wildtype repressor, and MT with mutant repressor.

Wild Type Model Including Cooperativity