Difference between revisions of "Team:RUM-UPRM/MathModels"
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Revision as of 01:30, 23 October 2020
Mathematical Modelling
Introduction
Mathematical Modelling was incorporated into Phase 1 of our project as a way to better describe our system. It is significantly important since it is an efficient way to optimize our system and devices for Phase 2 which will be focused on experimentally testing and characterizing our prototypes and parts, respectively. To build the mathematical models based on Ordinary Differential Equations (ODEs), SimBiology, a MATLAB feature, was used. This MATLAB feature provides tools to model, simulate and analyze biological systems and is highly beneficial for providing accurate quantitative results of our system. Mathematical models were built for both genetic circuits, Mercury and RDX, in order to simulate the expected behavior of each device.
Cell Signaling Kinetics
To model our system and the reactions that take place within our devices, we have used the Law of Mass Action kinetics to determine how the concentrations of the species change with respect to time. For the first part of our model in Phase 1, we have assumed that reactions are irreversible. For Phase 2, after sufficient experimental data is obtained, reactions will be assumed to be reversible due to the fact that most biological reactions are deemed reversible and enough data will be collected to be able to build these reversible models.
We consider a first order irreversible reaction as the following:
From the above reaction, we get the following differential equation which describes the change in concentration of the species B with respect to time.
