Team:Sweden/Mathematical Modelling

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Contents

The Linguistic Cell


Model Structure.

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 an intermediate input to activate 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. ODEs are used for describing how a system changes over time. In general, our ODEs look like this:

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

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. so the hill function tells you how long it takes for a protein to be synthesized and if it is synthesized how fast it is done. 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.

Dydt-1.gif

The full model

here are links to the ODE model in Matlab.

act.m

This is the activation function.

<a href="https://static.igem.org/mediawiki/2009/8/8d/Act.m">Activation File</a>

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