"

From 2014.igem.org

Chemical Dynamics Model

Introduction

According to the design of experiment, how the system works from the chemical dynamics respective can be described using ordinary differential equations (ODEs) and statistics mechanics.

By solving the differential equations numerically, the replication of M13 phages can be simulated quantitatively. Moreover, how the interaction between antibody-antigen influence the number of progeny, which is a very important in evolution system, can be investigated quantitatively. Surprisingly, by introducing the selectable binding energy interval of two-hybrid system, such investigations not only unravel an unexpected limitation of two-hybrid, but also provide some practical suggestions for improving the function of our system.

Symbols and Definitions

[Table]

Model Analysis

To simulate the process of M13 replication and budding, many data about M13 is required. Limited by time and capacity, it’s impossible for us to investigate all the data needed in our experiment. As a result, data used in this model partly comes from our experiment, partly comes from related materials, and partly comes from crudely estimation.

Assumptions

To modeling with the help of chemical dynamics and statistics mechanics, several assumptions are required.
1）Since it takes some time for the synthesis of molecule, many process in biological system are time-discrete, such as the number of DNA replicated, the number of protein synthesized. In order to apply the ordinary equations, the effect of time-discrete is neglected.
2）Different biochemical process may happens at different part of the bacteria and the distribution of molecular in the bacteria is probably uneven. Also, it takes some time for a chemical reaction to reach the equilibrium state. For simplification, all of these are neglected in this model.