# Modeling Overview

Since our system is designed to work in the human intestine, it depends heavily on the physiological condition in human body. There’s usually a gap between the reality and the models, especially for those regarding true physiological conditions. To solve this, we take the real conditions into consideration as much as possible, either incorporates them into the model design or adjust our model parameters to fit to the conditions, and again, evaluate if our results are compatible to reality. Our ultimate goal is to bring our simulation closer and closer to the real conditions.

The intimate interaction between our system and the physiological environment can be seen from the very beginning in our circuit design. There is in fact a baseline level of fatty acid in the gut even during the time without food intake. However, we don’t want our E.coli cells to respond to this noise. Therefore, we designed a filter in our circuit to filter out the baseline noise. After a fatty meal, the concentration of fatty acid around the cells gradually increases. When fatty acid level rises above the threshold, the circuits in the cells are turned on and express GLP-1 in response. In this way, we aim to make our cells to respond sensitively to fat intake, but remain silent to the baseline noise.

To achieve this, we have to first ensure that the filter will work. Therefore, we start our modeling effort with the single cell model to verify the filter function of our circuit.

## Single Cell Model

The single cell model is the basis of our modeling. It described each species involved in our circuit by a set of ordinary differential equations and shows the function of our modules. With the single cell computational model, we verified the filter function of our circuit, and found the initial threshold of our circuit as 100 uM.

 $$X_{FadR}=FadR\times (\frac{\beta^{n2}_{FadR}}{FA^{n2}+\beta^{n2}_{FA}})$$ $$\frac{\text{d}TetR_{1}}{\text{d}t}=\alpha_{TetR_{1}}\times (\frac{\beta^{n1}_{FadR}}{\beta^{n1}_{FadR}+X^{n1}_{FadR}})-\gamma_{TetR_{1}}\times TetR_{1}$$ $$\frac{\text{d}LuxI}{\text{d}t}=\alpha_{LuxI}\times (\frac{\beta^{n1}_{FadR}}{\beta^{n1}_{FadR}+X^{n1}_{FadR}})-\gamma_{LuxI}\times LuxI$$ $$\frac{\text{d}FadR}{\text{d}t}=\alpha_{FadR}-\gamma_{FadR}\times FadR$$

In addition, the single cell model helps us to have a complete view of how modules act together as a system in a single E.coli cell and provides a quantitative visualization of the dynamical behavior of our sensor, high pass filter and quorum sensing module.

In order to have a better experimental (wet) characterization of each module, we performed functional tests for each module individually – i.e. PfadBA-RBS-mRFP (BBa_K817033) to characterize sensor, J23119 (constitutive promoter)-RBS-SP1-GLP1-xx (BBa_K817008) to characterize the effector, etc.

So far, we have verified the filter function of our circuit. However, we didn’t know if the current threshold, which is about 100 uM, would be appropriate for the real physiological condition. Therefore, we have to investigate the true condition of the environment in human gut. After a series of literature review, we decided to fix the filter threshold at 800 uM. Furthermore, we seek to construct a model to simulate the concentration of fatty acid after a meal.

## System Analysis

To have better understanding of the roles each parameter plays in our single cell model, we performed system analysis, which explores extensively into the parameter space. With the help from system analysis, we are able to determine which parameters should be adjusted in order to achieve our desired circuit response. This quantitative information will in the future feed into the design and actual construction of our system - for instance, the strength of promoter, copy number of an operator site, degradation rate of a repressor protein, etc.

## Cell Population Response Model

To move further from single cell response to the response of a cell population, we conducted another two dimensional spatial-temporal model in COMSOL, which simulate the communication of cells through quorum sensing in our synthetic system.

## Fatty Acid Reaction Absorption Model

We also created a two dimensional dynamic reaction- absorption model, using the mechanical engineering software platform COMSOL, to describe the spatial-temporal change of fatty acid level in the extracellular environment after a meal.

## Partition System Model

Last but not least, we performed a simulation of the partition system. As our PepdEx system consists of several plasmids and will function outside of the laboratory (human gut) which lacks of antibiotic selection pressure, plasmid segregation stability is critical that determines whether every single E. Coli cell contains the original system with the designated function. Inspired by natural plasmid & mobile gene element, we cope with segregation instability by incorporating three modules, i.e. partition system, Multimer resolution system and toxin antitoxin system, on top of our system. Choosing which module to stabilize the system needs modeling and stability assay, at this section, we will use cooper’s model as an example.

Overall, we think that modeling was valuable to the decision process in constructing our synthetic network. With the communication between the biologists and modelers, we will be able to, from a simulation result, guide experimentalists in choosing a ‘part’ with appropriate parameter sets (e.g. promoter strength, protein degradation rates) from the sea of iGEM registry, and provide quantitative insights to our flexible and expandable PepdEx system.