# Team:Valencia UPV/Modeling/DetModel

## What is our circuit supposed to do?

The idea of our circuit can be simply represented by this picture:

**Figure 1. Light sequences that control paths of production.**

Basically, our aim is the biological design of a decoder that only expresses the codified genetic information **when, where** and **which** is desired by the user. The election of the output to decode, is achieved by the combination of two kinds of light: red and blue. Two inputs are given at times t_{1} and t_{2} with the possibility of election between red or blue light. This, this would be the truth table of our circuit:

**Figure 2. Truth table of our circuit.**

The biological components that allow us this implementation in living organisms are two switches, two recombinases and a library of different binding domains. All those elements have been coordinated in this cascade of three different levels:

**Figure 3. Our biological circuit separated in its three levels.**

**Figure 4. Elements of our circuit. Real name (Model name) | Graphic representations.**

In order to predict the results of our biological circuit, we must be able to express its performance in numerical terms. Using Mass Action Kinetics we got our deterministic model with all its equations describing interactions between all elements of the circuit.

## From biochemistry to mathematics

## Parameters

All parameters involved in our mathematical model, must take some values in order to be simulated. The table below contains all these parameters with its values.

*, **

Paramerers M and N as seen in the Pdf explanation are agrupations of different values:

We can also asume that the k’s that represent the inverse process are much smaller than the principal one.So k_x/k_(-x) is usually between 10-150. Choosing 75 as an intermediate ratio and taking into account that the value in brackets always amplifies the result 1+n>0 for every n>0, we estimated N and M as 100.