Team:St Andrews/project/modelling/model 3/spatial

Spatialality

Previous models contained no element of spatiality whatsoever, so in order to improve on this we decided on a fixed volume in which our simulations would take place.

Implementation

A new constant was created called 'Volume' which was given a value of 10¹² ml³ which was chosen as it is the typical volume of a standard laboratory petri dish. Furthermore, any additional HSL which is produced by cells spreads immediately through the entire volume, such that it is diluted to fill the volume. There is no distinction between the internal and external volume however, so it is as if the cells do not posses cells membranes, but are more like areas of the total volume in which certain chemicals are found.

An example of where the volume constant is used is in the differential equation for HSL:

dy[1] = ( (y[9] * kConvHSL * y[6])  / Volume ) - ( 2 * kAssHSLLuxR * y[1] * y[7] ) + ( ( y[9] * 2 * kDissHSLLuxR * y[2] ) / Volume ) 
        - (kDegHSL * y[1] ) + ( (y[9] * kDegHSL * y[2]) /  Volume ) + ( (2 * kDegLuxR  * y[2]) / Volume ) ;

Number of cells

A further addition to this model is a new variable labelled "No. of cells/ml". This variable was introduced in tandem with the concept of cell growth and cell death, the reasoning being that if an increase in HSL is due to an increase in cell density then we want a tangible measurement of this in our model. Initially the value is set to 10⁶. When used in conjunction with the cell growth and cell death functions, the value decreases according to which phase we are in. The other effect is that every time a new cell is added, (or taken away), the HSL concentration already present in the volume is multiplied by the new number of cells. In this fashion, each additional cell adds the same amount of HSL as the existing cells currently produce, such that the cells are in a sense identical.