Kinetic model

In our project different transistor elements are putted together in order to create logic gates and the idea is to chain these gates in order to create complex logic circuits within cells. Because of this chainability of different elements, we have a cascade of reactions which will eventually reach a stationary state. In order to study in depth the behavior of our system we decided to use a kinetic model, where time dependency of the concentration of different species is taken into account explicitly.

Assumptions

A model which is too complex and too detailed can surely describe experimental results with precision, but it is often difficult to interpret and to understand in details. It is therefore useful to come out with the simplest model that can reproduce the system behavior, which can then be understood in details and used to predict new results.

In order to find a simple model which can reproduce experimental results we have to do many simplifications and assumptions over reality. In this section we will try to keep track of the assumptions we made in order to clarify our model. Every assumption is analyzed details: assumptions are generally not uniques, but we will try to justify our choices.

The most important assumption underlying the kinetic model is the fact that the concentration of a given specie does not depends on spatial coordinates, i.e. it is the same in every region of the cell. This assumption is quite strong but it's a common approach in the literature and usually gives good results. Note however that within a cell the validity of concentration idea itself can be doubtful, since the number of molecules can be small and since these molecules can be localized to membranes or particular organels; in these cases it is necessary to consider the stochastic behavior of individual trajectories rather than global averages [1].

Constants

Equations

Simplation

Bibliography

[1] R. Phillips et al., Physical Biology of the Cell, Second Edition, Garland Science, 2013.