Team:Sweden/Mathematical Modelling

Design obstacles and Solutions

Several problems needed to be taken care of when implementing a biological model.

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

The theory

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

• I1 is always active at t=0, meaning that every sentence begins with and intermediate input to activated I1.
• The strength of every inhibition is the same
• 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>

For activation and repression we used a hill function:

          act = ((conc*k)^m)/(1+(conc*k)^m),

where k is the responsible for when the activation occurs and m for how fast it is. The repression is simply

             rep = 1 – act

This way we set up a model as in the figure. This model does not represent the full automaton, but only the first four states.

The full model

here are links to the ODE model in Matlab.

act.m

This is the activation function.

    link to act.m

rep.m

This is the repression function.

    link to rep.m

FSA_ODE_full.m

This is the ODE function.

    link to FSA_ODE_full.m

main.m

This is the main program. If run, you can choose which PoS to input. The program aborts immediately if you have a wrong input otherwise it will only stop with a stop-input. Correct sentences are according to the following rules.

• S --> NP VP
• NP --> (det)(adj) N
• VP --> V (NP)

     link to main.m