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From 2011.igem.org

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At the completion of the experimental work, we should expect a working clock BioBrick, which should exhibit oscillatory behaviour. We wish to characterise how our clock BioBrick oscillates. Of interest is the frequency and regularity at which it oscillates and whether multiple cells containing our BioBrick oscillate in time with each other.

The modelling will involve the mathematical characterisation of the kinetics and synchronisation of the oscillation of our bacteria. The kinetics involve modelling how fast our bacteria cells will oscillate and the shape of their oscillation pattern. The synchronisation is to characterise how quickly nearby cells would couple any synchronise their oscillation.

To give a rough idea of how our cells should be oscillating, mathematical models were described from literature. These would ideally be compared with experimental characterisation of the oscillation.

Kinetics

The BioBrick circuit has been represented as a network in a figure yet to be uploaded. For every reaction indicated in imaginary figure, we have assumed a first order reaction rate. The reaction constants have been taken from literature. From this, we would then have a system of first order linear ordinary differential equations. This should be solvable and thus give us a prediction as to the nature of the oscillatory behaviour of a cell. To test the appropriateness of this model, we would then experimentally measure the expression of arbitrary protein and see how close it fits.

Synchronisation

We have our cells, which are oscillating. Experimentally, we would have a dish of many cells, most of which will be oscillating, but not necessarily oscillation in time with each other. Realistically, for most practical purposes, we would require that the cells are oscillating in a manner such that they are synchronised. Of interest to us would be how each cell synchronises itself with its neighbour. We could mathematically characterise this synchronisation. To generalise this, we could model this as the behaviour of many oscillators.

So, of particular interest to us would be the behaviour of, at the very simplest step, two oscillators coupling with each other. Thus we intend to investigate the coupling of two oscillators in a biological context.