Efficient%20and%20flexible%20modelling%20of%20dynamical%20biochemical%20systems

1
Efficient and flexible modelling ofdynamical
biochemical systems

• by Jan Bert van Klinkenand Davide Chiarugi

2

• A typical iteration of biological modelling
• 1. data gathering
• 2. formalising natural description
• 3. applying analysis methods
• 4. interpreting analysis results

3

• Problems encountered
• 1. kinetic coefficients difficult to obtain
• 2. loss of overview with large models
• 3. finding efficient and informative analysis
  methods
• 4. interpreting analysis results

4

• 4. interpreting analysis results

5

• What is our strategy to tackle these problems?
• --gt Listen well to biologists!
• --gt Realise a flexible interaction with the
  computer!

6

• What is our strategy to tackle these problems?
• --gt Realise a flexible interaction with the
  computer!

fast and many modelling iterations rapid
prototyping
7

• In order for this to happen, we need to adopt the
  right piece of software . . .
• our choice --gt the MATLAB environment

8

• MATLAB is
• 1. a technical computing language
• 2. an interactive environment for
• - algorithm development
• - data visualisation
• - data analysis
• - numerical computation
• from http//www.mathworks.com/products/matlab/

9
Now lets get practical!

• 1. data gathering
• 2. formalising natural description
• 3. applying analysis methods
• 4. interpreting analysis results

10
I. DATA GATHERING

• stoichiometric data --gt directly from literature
• initial concentrations--gt only look at pools and
  external substance concentrations
• kinetic coefficients

11
I. DATA GATHERING

• stoichiometric data --gt directly from literature
• initial concentrations--gt only look at pools and
  external substance concentrations
• kinetic coefficients--gt use Gibbs standard free
  energies!

12
I. DATA GATHERING

• A
  B
• kinetic coefficients--gt use Gibbs standard free
  energies!

13
I. DATA GATHERING

• A
  B
• kinetic coefficients--gt use Gibbs standard free
  energies!

14
I. DATA GATHERING

• A
  B
• kinetic coefficients--gt use Gibbs standard free
  energies!

often known for metabolites!
is determined intuitively
15
II. FORMALISING MODEL

• formal language--gt reduced p calculus (CCS)
• basal rates--gt kinetic coefficients
• a vector of initial values for simulation

16
II. FORMALISING MODEL

• formal language--gt reduced p calculus (CCS)
• basal rates--gt kinetic coefficients
• a vector of initial values for simulation
• NOW HOW CAN WE BE SUREWE FORMALISED CORRECTLY??

17

• A graph inferred from the process identities to
  gain insight into pathways and pools.

18

• A graph inferred from the process identities to
  gain insight into pathways and pools.

19

• A graph inferred from the process identities to
  gain insight into pathways and pools.

20

• The list of reactions corresponding to the CCS
  description.

21

• The list of reactions corresponding to the CCS
  description.
• external substances are replenished continuously

22
III. PERFORMING ANALYSES

• CCS is reducible to a matrix form--gt a reactant
  and stoichiometric matrix columns are reactions
  rows are participating substances
• R ( i , j ) r --gt r substances of type i react
  in reaction j
• S ( i , j ) s --gt substance type i reacting in
  j is updated xinew xiold s

23
III. PERFORMING ANALYSES

• such that we can write the set of ODEs as

24
III. PERFORMING ANALYSES

• such that we can write the set of ODEs as
• in MATLAB code
• dx Sv v diag(k)exp(Rlog(x))
• stochastic case uses similar computations

25
(No Transcript)
26
take 10000 times more stochastic noise
original Gillespie algorithm simulate for 100000
steps takes 16.8 seconds
plot substance concentrations
27
Substance quantities are reconverted into actual
concentrations!
28
deterministic Euler simulation with large
stepsize simulate for 100000 steps takes 9.0
seconds
plot also reaction flows (/fluxes)
29
(No Transcript)
30
III. PERFORMING ANALYSES

• Because of both process calculus and matrix
  representation, various other analysis methods
  could be applied --gt FBA, MCA, modelchecking
• Also, various system biology toolboxes for
  MATLAB are available on the internet

31
IV. INTERPRETING RESULTS

• MATLAB provides various ways for further analysis
  or visualisation of the simulation results . . .

32
IV. INTERPRETING RESULTS

• MATLAB provides various ways for further analysis
  or visualisation of the simulation results . . .
• For instance, if we want to check if all
  reactions are active, or if we want to get an
  idea of the stiffness of the system . . .

33

• type
• which calculates and plots the log10 activity of
  each reaction (i.e. log10(v1v-1))

There is a difference in activity of almost 20
orders of magnitude (1020) !!! So we have to do
with a very stiff system
34
IV. INTERPRETING RESULTS

• MATLAB provides various ways for further analysis
  or visualisation of the simulation results . . .
• Since the system is stiff, we would like to have
  an indication of how much time it will take to
  reach a steady state . . .

35

• Lets perform a deterministic simulation with
  implicit integration, and fix the timestep of a
  transition a priori to increase exponentially. .
  .

36

• Lets perform a deterministic simulation with
  implicit integration, and fix the timestep of a
  transition a priori to increase exponentially. .
  .
• Then plot both concentration and time on a log
  scale

Steady state is reached after about 1 second,
whereas the first observable changes already
happen after 10-11 seconds. Very stiff indeed!