Kinetic modelling of compartmentalised reaction networks

This paper presents a comprehensive treatment of kinetic modelling of compartmentalised reaction networks in the context of systems biology. There is still a lot of confusion about how to go about constructing compartment models, and many published models are flawed with respect to how they handle compartmentation. The modelling framework described here answers two key questions: Which rate laws should be used to describe the rates of reactions in compartmentalised systems? How should these rate laws be incorporated in the ordinary differential equations (ODEs) that describe the dynamics of the compartmentalised system? The framework rests on the fundamental definition of reaction rate as the number of reaction events per time, which is related to the time derivative of mole amount of reactant or product, an extensive property that is directly proportional to the size of the compartment in which the reaction events occur. This means that the rates of reactions that occur in a 3-dimensional compartment are proportional to the volume of the compartment, while the rates of transfers over a 2-dimensional compartment boundary or interface between compartments are proportional to the area of the boundary. Transfer rates are often incorrectly scaled with a volume instead of an area, and the reasons why this is wrong are extensively discussed. I also show how 'textbook' rate equations, which I term canonical rate equations, should be modified for compartmental modelling and how they should be incorporated into either amount-change or concentration-change ODEs.