Team:Sweden/Mathematical Modelling

     i.   Repeated input (e.g. det det adj)

    ii.   Wrong input (e.g. det adj det)

For the repeatedly inputting the same PoS we used a counter (with courtesy of ETH iGEM 2005) which counts how many times an input occurs in a row. It uses an interval state and an intermediate input to move the automaton from one state to the other. For the wrong input we set inhibitions in the model in a specific way.

2 The theory Several assumptions have been made to make the model work the way we want it to.

     i.   I1 is always active at t=0, 
          meaning that every sentence begins with and intermediate input to activated I1.

    ii.   The strength of every inhibition is the same

   iii.   We introduce a stop signal, so we know when a sentence is finished

We used ODEs to model the system. In general, it the ODEs look like this:

      State i = synthesis * (every incoming activation and repression) – degradation of i

<math>\text{dydt}_i = syn_i \prod \limits_{j\in i} \begin{cases} act_j, & \text{if } j \text{ activates } i \\ rep_j, & \text{if } j \text{ inhibits } i \end{cases} - \text{deg}_i</math>