For the entirtiy of human history, information gathering and storing has been of huge interest to society. One of the most, important aspects about information is the capability of that information to be gathered, stored, read, and analysed.
The role of the mathematical model is explaining this and discovering particularities about the specifics of information, so that processes involving information are made better.
Specifically, answering questions as why, how, when, what, regarding our biological system is our objective.
The modeling of the system was approached through a progressive development of the model. The first model that was proposed consisted on a simple linear differential equation system based on mass-reaction laws of kinetics to describe the interaction of genetic material and the dependence of the productions of each genetic material with the concentrations of the other relevant genetic materials. That is, the various interactions that the compounds have are considered, and for each compound, these interactions define the shape of the differential equation that describes it. The most relevant information to model is the concentration of the CAS complex annexed to the to-be-inserted genetic information. The concentration of this compound is proportional to the probability that the genetic material is inserted into the bacterium, a binomial distribution was considered to describe the probability density function that portrays the behaviour of the insertion system.
A diagram encompassing the various biological interactions, as well as how and when they combine and transform, between all the interest compounds is as follows:
