# Model Overview

## Why did we model? What did we want to achieve?

The goals for modeling are firstly to design and optimize the project (how to produce the results), and secondly to simulate and analyze (what the results are and how they are) the expected behaviors in conjunction with experiments in the wetlab. So we calculate the response of lysis protein production in front of Ara per os oral administration of arabinose , and modify the gene circuit by introducing attenuator based on calculation. For simulating the locomotion of bacteria in human colorectum, we introduce Young's modulus https://en.wikipedia.org/wiki/Young%27s_modulus of bacteria, and simulate its fluid mechanic behavior. We analyse the ultrasonic response of gas vesicles in our device, by firstly building the rigid ball model, develop it to covered elastic ball model, and modify the key parameters by experimental results.

## Method description

Tools: COMSOL Multiphysics

We perform three simulations in Comsol.

1. Using a single-phase flow Laminar (SPF) model, the steady state parameters are added, the particle tracking model (based on particle size, viscous force, charge number, etc.) is applied to analyze the velocity and probability distribution of particles in laminar flow (PDF).

2. Using the laminar flow model of Multiphase stream (solid-liquid solid), the velocity of particle motion is simulated.

3. Using convection wave equation, time domain explicit (CWE), for different characters and sizes of the bubble protein, as well as different ultrasonic emission power and collapse power, the ultrasonic signal simulation.

### Ultrasonography

In this part, we simplify the realistic situation to model the gas-vesicle's response in the ultrasonic field using two methods.

We suppose the incident wave is plane wave and the gas-vesicles in bacteria is spheres. In model 1, the scattering of rigid sphere in ultrasonic field is analyzed based on Rayleigh scattering theory. In model 2, we take the acoustic properties of bubbles and the surrounding environment into consideration, analyzing resonance conditions of gas-bubbles and scattering intensity at different frequency. At the same time, we also provide some technical support for the ultrasound experiment.

### Gene Circuit

Tools: SimBiology Toolbox in MATLAB

1.The regulation of expression of acoustic reporter genes—ARG1 and combined fluorescent signal reporter gene amiGFP is closely related to NO-sensitive promoter. And the density and distribution of NO in gastroenterological microenvironment is crucial to the switch-on/off state of the promoter. We will build a synthetic gene circuit in MATLAB in SimBiology Toolbox , to determine the cut-off value of this switch, for downstream gene expression in a time-dependent manner.

2.In the context of cell lysis gene X174E expression and anti-tumor drug release, we will assist to choose the proper promoter based on their startup parameters, and create negative-feedback control loop for persistent drug production.

## Content outline

Adhesion: We simulated the locomotion and attachment behavior of E.coli in colon.

Ultrasonography: We built the ultrasonic imaging model to figure out the mechanism of signal transmission from gas vesicles to imaging.

Gene Circuit: We simulate the output respond of gene circuit and analyze the parameter's influence on the gene product.