"
Team:Edinburgh/Model Comparison
From 2011.igem.org
Model Comparison
Contents |
The approaches
- MATLAB - Within the reactor tasked with degrading cellulose into glucose in the biorefinery, temperature, enzyme concentration, substrate reactivity as well as xylose, cellobiose and glucose inhibition all govern the amount of glucose product. Deterministic modelling using a set of ordinary differential equations highlights the essential kinetic relationship among the enzymes, exo/endo-glucanase and β-glucosidase. By solving these governing equations using the numerical tool MATLAB the level of degradation is qualitatively predicted.
- C model - The system was represented using a simple grid, and enzyme movement using Brownian motion, implemented by ourselves.
- Kappa - As an alternative, stochastic models were created using the Kappa language. The system is defined in terms of many discrete agents and rules of their interaction. The Kappa simulator then uses probabilistic equations to simulate the evolution of the system, incorporating an indeterministic element into the system.
- Spatial kappa - Because of problems with the Kappa language, we decided to use a spatial extension developed by Team Edinburgh 2010. This adds extra functionality to the language by introducing the concept of space.
Steady state
We found that the equations used for the deterministic modelling only gave sensible answers when the model parameters remained within certain limits. Outside those limits, results could be physically impossible; e.g. producing negative amounts of cellobiose therefore breaking the law of conservation of mass. The deterministic model always had reactants available, i.e cellulose able for every reaction, ensuing it would never reach zero. A 'stress test' was carried out simulating the model over one hundred thousand hours confirming this. Therefore, within the limits of differential equation based modelling, it will unlikely reach a mathematical steady state. An engineer defines steady state when 99% of the initial value of cellulose has been degraded, which was found to occur after 8000 hours. It can be seen from Figure 3, that the 'stress test' revealed neither a mathematical nor engineering steady state will be reached for cellobiose and glucose in the MATLAB model.
Whereas with the C model and Kappa model cellulose, glucose and cellobiose all reach steady state within the iteration time limit. Analysing steady state is important to find out whether a system accumulates excess mass or energy over the time period of interest. Looking at the MATLAB model one asks, is the system inherently thermodynamically unstable or is there a flaw with the model?
