Team:Exeter/Modelling

Modelling the e-candi System - Andrew J. Corbett

This section of the project is focused on describing the skeleton of our system in the language of Mathematics; the language underpinning any physical system. By making somebasic, but reasonable, assumptions on how the system works, one can make future predictions on the functionality of the system. This is done by making a mathematical construct that simulates events occurring at a given time, this is what we call our 'model'.

The assumptions are crucial to the success of the model's prediction. To ensure accurate assumptions, real data is taken in conjunction with modelled data being simulated. Using statistical methods, it is possible for the parameters in the model to be adjusted until the modelled data fits the graph generated by the real data. It is by this technique that one can derive the parameters needed for the model. If the parameters remain robust in a number of situations, one can then be sure that the assumptions were accurate to the real system. If not, a rethink is in order!

In our case, we have a system for the production of a chosen polysaccharide. The polysaccharide selection shall be the variable of the system. The output is a graphical (& numerical) representation of the concentration of the production of this polysaccharide as a function of time. The input is some chosen polysaccharide. The particular is for the production of a Disaccharide system. It would be a simple task to extend the algorithm to the production of any sugar with a finite repeat unit (see 'assumptions of the model').

How it works is to take the joining of two general sugars A&B and consider every possible enzymatic reaction involved in producing the combined disaccharide AB. By considering the rate at which each reaction occurs allows one to write a set of ordinary differential equations (ODEs) which give the rate of change of concentration of each compound/enzyme at any point in time. By solving this system of ODEs using a numerical 'time-stepping' method (Runge-Kutta IV) gives the concentration of each compound/enzyme as a function of time. Plotting this allows the user to see and compare rates of production (efficiency) & amounts of production (yield). Comparing these factors may provide a ranking system for the enzymes combinations issued to the user by glycobase.

Specifically, entering a polysaccharide (AB) in our case would, in the future involve recalling the parameters specific to that polysaccharide and entering these as the true input to the model. These parameters control at what speed each reaction takes place & would someday be calculated by experimentally finding the amount of polysaccharide produced at any given time. A seemingly huge task, however this model serves as a proof of principle that such a ranking system could be introduced to GlycoWeb.

Demonstrated here is a number of variations of parameter conditions to demonstrate the outputs of the model under for different polysaccharide combinations. Noting that the parameters are control the rate at which each reaction takes place and is particular to each combination of enzymes & sugars.

Read the report on The Enzyme-Kinetic Model Of The e-candi System

Some helpful MATLAB Scripts used in the development of this model can be found:

Here(1) and Here(2).