Team:Edinburgh UG/Modelling Collaboration
Modelling Collaboration
Introduction
Team Vilnius-Lithuania aims to use the PURE cell free system [1] in order to integrate proteins into the membrane of the liposome from the inside. The BamA complex is responsible for integrating these proteins; OmpA and lgA hence in order to ensure quick integration BamA needs to be consistently present at high levels throughout the expression of OmpA and lgA. This mechanistic model aims to examine the simultaneous expression of these proteins and compare results primarily across different starting volumes of BamA RNA in order to quantify the effectiveness of an initial addition of RNA in ensuring fast expression of BamA.
Mass Action Equations
Mass Action Equations are commonly used to represent chemical reactions and provide a starting point for mechanistic modelling of a variety of phenomena. The laws of mass action state that the rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation [2]. The mass action equations in Figure 1 can be used to represent protein expression:
Each of these equations is used in triplicate to represent expression of BamA, OmpA and lgA respectively and from these mass action equations a system of ordinary differential equations can be derived.
Ordinary Differential Equations
The model uses a simple set of ordinary differential equations (ODEs):
In order to solve this system it is first necessary to derive values for all the parameters used:
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