Marcus Tindall

Teaching Modelling Using

Simulation Tools: Examples

using Copasi and Matlab

RCUK Fellow in Emerging Technologies for Systems Biology

School of Biological Sciences,

Department of Mathematics & Statistics,

Institute for Cardiovascular and Metabolic Research and

University of Reading.

E-mail: m.tindall@reading.ac.uk.

Modelling Protein-Protein Interactions

• Both software packages can be utilised to model systems of

reaction equations, e.g

EPESESkk

k

21

1

• Consider the advantages and disadvantages of using Copasi and

Matlab to understand how such a “system” functions and thereby

teach the modelling process.

The Mathematical Modelling Process

Identify the problem.

Detail the attributes of the system (variables and parameters). Consider available data (if any).

Decide on modelling approach (discrete vs. continuous, temporal

and/or spatial)

Write down a model.

Solve it (computationally or analytically).

Test model outcomes with data or known practice.

Revise and improve the model.

STEP

1

STEP

2

STEP

3

STEP

4

Important – Use an example students can relate to!

• We will consider

.CBAk

Copasi

• Freely available– www.copasi.org.

• Can be used on a range of platforms – Windows, Mac, Linux.

• 3 things required to model protein reaction systems:

(i) details of the protein-protein interactions;

(ii) kinetic rate and concentration data;

(iii) simple understanding of how simulations tools

work.

• Does not require that the user understands how the underlying

mathematical model is derived – pros and cons to this in teaching

modelling.

Copasi

Copasi

• Can handle more complex tasks such as sensitivity analysis and

parameter estimation. Useful, but one should understand how

these methods work which requires more in depth study of what

each is trying to achieve.

• Disadvantages

-> Can not model other problems, e.g. Population growth,

ecology, etc. How do we get the Zoologists involved??!!

-> Mathematical Modelling process is a bit of a black box.

-> Limited by what features the program includes.

-> Modelling large networks can be time consuming.

Matlab

• Licenced software which is widely used in mathematical

modelling communities (e.g. Engineering, Applied Mathematics,

Physics)

• Can be used on a range of platforms – Windows, Mac, Linux.

• 3 things required to model protein reaction systems:

(i) details of the protein-protein interactions;

(ii) kinetic rate and concentration data;

(iii) more detailed understanding of mathematical

manipulation and theory including matrix

algebra, differential equations.

Matlab

• Good as the “next step up” tool for solving problems

computationally.

• Need to become familiar with the Matlab programming

language.

% Simple irreversible reaction sequence example % % A + B -> C % clear all; % Rate constants and initial concentrations k = 0.1; a0=1; b0=2; c0=0; % Solve the system of ODEs and plot the solution [t,y]=ode45(@simpreactodes, [0 50], [a0 b0 c0],'', k); plot(t,y(:,1),t,y(:,2),'r--',t,y(:,3),'g.-') xlabel('Time (seconds)'); ylabel('Concentration (mM)'); legend('a=[A]','b=[B]','c=[C]')

Matlab - Example

function simpreactodes = f(t, y, k) simpreactodes = [-k*y(1)*y(2), % a -k*y(1)*y(2) , % b k*y(1)*y(2) ]; % c

Main File Equation file

Confidence Building

• Start with a simple example students can relate to, e.g. Genetics

for Geneticists, population dynamics for Zoologists, etc..

• Make sure each part of the process is explained clearly either

beforehand or during the practical, e.g. handout, clear notes on

the web.

• Build on the initial model, e.g. Non-reversible to reversible

reactions, simple stoichometry to more complex stoichometry.

• Build in simple exercises that students can work on to gain

confidence away from the computer.

Confidence Building

• Get students thinking about the modelling process and asking

questions about what they are doing.

• Think about checking the model for “realism”, e.g. If one

reaction rate is zero and you still get the product from it, can that

be right???!!!

• Warn students about Garbage In Garbage Out (GIGO), i.e. just

believing the computer without thinking about what is going on.