## Overview

Function switching of engineering bacteria

Lactose is decomposed by other bacteria in a short time, at this time lactose signal can be equivalent to a pulse signal. Then our pathway can filter this signal and begin to switch smoothly. As pH decline due to lactic acid, our bacteria can feel this signal and begin to express iLDH which can decompose lactic acid.

We designed our protocol for lactose intolerance based on prokaryotic pathways, which continue to secrete β-galactosidase at high pH, and lactate dehydrogenase when pH decreases due to elevated lactate concentrations.

Gastrointestinal diffusion model

- For the treatment of lactose intolerance

Through previous modeling and modeling of our prokaryotic pathways, we learned some of the necessary data to aid our application. The pathways we use to treat lactose intolerance are the same as our prokaryotic pathways.

To further model our application we created a model based on the diffusion equation. We modeled a portion of the intestinal tract with a 20 x 20 x 20 three-dimensional matrix and used it to model the state of our engineered bacteria in the stomach.

We hope that this part of the simulation model to test our loop in the treatment of lactose intolerance of the feasibility and make more improvements.

Since our loop has a filtering effect, for the sake of convenience we will set the rate for most of the following models to constant.

Hypothesis

In order to make the model rigorous, we hypothesized the following prerequisites:

- The total number of our Engineered bacteria and other bacteria is constant. No bacteria will be born or dead during the process.

- The other substances in the intestinal tract have no effect on our engineered bacteria or it could be ignored.

- The effect of gravity in the free diffusion process is negligible.

- The squares that produce matter only spread outward.

Formulary

The PDEs (Partial Differential Equations) of this model are listed below.

We use the difference method to find the approximate solution of this PDEs, and get the solution of the change of matrix concentration with time. Next we will analyze our results.

## Lactose absorption

Assuming that there is one engineered bacteria in each matrix, lactose flows through the matrix. We want to see the change in lactose concentration over time in the matrix to see if our engineering bacteria can consume a significant amount of lactose and reduce lactose absorption by other flora.

(To simulate the flow of lactose in the intestine)

It is a pity that we have found that even if we adjust the lactose absorption rate of our engineered bacteria to a considerable value, we cannot prevent the spread of lactose, even the impact of the surrounding lactose concentration is not as large as we thought, which means that Our ability to compete for lactose is not strong, but if we increase the number of flora, it may cause other problems of the human body. This means that in our next step we will use secretory enzymes to help break down the lactose.

## Decomposition of lactic acid

We assume that there is one engineering bacterium (center) in each matrix and four other bacteria (random positions). Assuming that the other bacteria consistently produce lactic acid after absorbing lactose, our engineered bacteria are experiencing a pH transition due to lactic acid buildup (pH<7) and then began to secrete lactate dehydrogenase. Secretory lactate dehydrogenase can break down lactic acid and reduce gastrointestinal irritation.

We need to confirm the change in lactic acid concentration by diffusion model to determine whether our engineered bacteria play a corresponding role.

(Lactic acid diffusion [without engineered bacteria])

(Lactic acid diffusion [with engineered bacteria])

(Lactic acid final time concentration [with engineered bacteria])

(Lactic acid final time concentration [without engineered bacteria])

We can clearly see that lactate dehydrogenase produced by our engineering bacteria can effectively reduce the lactate concentration in the whole matrix through the comparison of the dynamic state and the final state. According to our summation of lactic acid concentration in the matrix, the engineered bacteria reduce the overall lactic acid concentration by 20% and could reduce irritation to the gastrointestinal tract. However, in practice, we estimate the number of engineering bacteria can reach 16 per matrix, which means the effect could be higher.

## Summary

We have obtained some useful results by simulating the intestinal tract. It is concluded that our engineered bacteria can sense the lactose signals, it has great effect on inhibiting the increase of lactic acid concentration with secreted enzymes, which can relieve lactose intolerance to a certain extent.