Imperial College/Courses/2010/Synthetic Biology/Computer Modelling Practicals/Design

Complementary Session: Introduction to the Design of Biological circuits

Objectives:

This page includes extra material for the course of synthetic biology. The material presented in this session is not part of your coursework. It is however, useful (very useful) for the rest of the course, especially the mini-iGEM project.

Computer-Assisted Design of synthetic biological pathways is in general a very complicated affair. You must, by now, be aware of some of the reasons for this.

• the behaviour depends on the parameters of the system
  • there may be many
  • we may not know them with enough accuracy - sometimes not at all
  • a small change in a parameter may lead to a totally different behaviour (bifurcation)
• initial conditions are also liable to have an influence (the arguments regarding the parameters mostly apply to the initial conditions too)

As you must have seen with the case of the repressilator, 3 genes are enough to generate a pathway with 'interesting' properties.

The situation is unfortunately worse. Even if there is a combination of parameters that

• some basic properties of the cell have a significant impact on the effective dynamics of pathways. Take for instance the growth rate:
  • it appears in the dilution term of proteins (easy to incorporate into the model)
  • but is also affects in a highly nonlinear way the gene copy number
  • it affects the concentration of free and bound RNAp and therefore the level of transcription etc..
• some modules in your system may be very hard to model (if at all possible)
  • for instance transport of molecules through a membrane and diffusion phenomena can be modelled but it becomes complicated fast
  • in a model, errors pile up so much so that after a while the predictive power of your model is negligible.
• your synthetic pathway may 'cross-talk' with natural pathways; since we are not able to model the whole metabolism of the cell this crosstalk effect can not be assessed.

Fortunately, designing simple pathways with predictable properties/functions is possible, even without the extensive use of software. This session aims at introducing to you the basic tools and techniques of design (without which no computer-assisted design is possible. Remember: in practice it gets very complicated, very fast...

Preliminary Simplifications

Download this File, and Open it with CellDesigner.

Model	CellDesigner Instructions
It can be shown that after some normalisation the ODE system can be written as: [math]\displaystyle{ \begin{alignat}{1} \frac{d[mRNA]_{i}}{dt} & = \frac{a}{1+{[Protein]_{j}}^n} - [mRNA]_{i} \\ \frac{d[Protein]_{i}}{dt} & = b[mRNA]_{i} - b[Protein]_{i} \\ \ i=1,2,3; \\ \ j=3,1,2; \\ \end{alignat} }[/math]

Negative Auto-Regulation

Model	The basic delay
It can be shown that after some normalisation the ODE system can be written as: [math]\displaystyle{ \begin{alignat}{1} \frac{d[mRNA]}{dt} & = \frac{a}{1+{[Protein]}^n} - [mRNA] \\ \frac{d[Protein]}{dt} & = b[mRNA] - b[Protein] \\ \end{alignat} }[/math]

The following questions constiture the last part of your coursework (Section E):