Modelling in Biology - WT/EBI course systems biology 2018

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The document discusses mathematical modeling in biology. It describes how the goals of modeling have evolved from describing systems in 1917 to explaining them in 1952 to predicting their behavior in 2000. It also discusses different ways mathematical models can represent biological systems, including how they represent time, space, granularity, stochasticity, and whether they use logic or numeric approaches.

Science

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
The many faces
of modelling in biology
Nicolas Le Novère, The Babraham Institute
n.lenovere@gmail.com

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is the goal of using mathematical models?
Describe
1917

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is the goal of using mathematical models?
Describe Explain
1917 1952

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is the goal of using mathematical models?
Describe Explain Predict
1917 1952 2000

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is a mathematical model?
Wikipedia (October 14th 2013): “A mathematical model is a description of a
system using mathematical concepts and language.”

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is a mathematical model?
What we want to know
or compare with experiments
variables
[x]
Vmax
Kd
EC50
length
t1/2
Wikipedia (May 31st 2018): “A mathematical model is a description of a
system using mathematical concepts and language.”

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is a mathematical model?
What we already know
or want to test
Wikipedia (May 31st 2018): “A mathematical model is a description of a
system using mathematical concepts and language.”
variables relationships
[x]
Vmax
Kd
EC50
length
t1/2
If
then

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
What is a mathematical model?
Wikipedia (May 31st 2018): “A mathematical model is a description of a
system using mathematical concepts and language.”
variables relationships constraints
[x]
Vmax
Kd
EC50
length
t1/2
If
then
[x]≥0
Energy conservation
Boundary conditions
(v < upper limit)
Objective functions
(maximise ATP)
Initial conditions
The context or what
we want to ignore

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
1952 1960 1969 1981
1973
1991
1993
1998
2000
2005 2012
Turing
morphogen
Hodgkin-Huxley
action potential
Chance
catalase
Chance
glycolysis
Noble
pacemaker
Kauffman
Boolean networks
Savageau
BST
Kacser
MCA
Thomas
logic models
Goldbeter
Koshland
ultrasensitive
covalent
cascades
Tyson
cell cycle
Bray
bacterial
chemotaxis
Karr et al
Whole
mycoplasma
McAdams, Arkin
Stochastic simulations
Kitano, Hood
Systems biology revival
Repressilator,
toggle switch
Synthetic biology
2013
Thiele et al
Recon 2
BioModels
1989
Palsson
Erythrocyte
metabolism

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Computer simulations Vs. mathematical models

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
One would like to be able to follow this more general process
mathematically also. The difculties are, however, such that one
cannot hope to have any very embracing theory of such processes,
beyond the statement of the equations. It might be possible,
however, to treat a few particular cases in detail with the aid of a
digital computer. This method has the advantage that it is not so
necessary to make simplifying assumptions as it is when doing a
more theoretical type of analysis.
Computer simulations Vs. mathematical models

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Birth of Computational Systems Biology

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
The Computational Systems Biology loop
“biological” model
mathematical model
computational model
simulation
parameterisation
validation

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Representation of time
No time: correlations, steady-states
Discrete time
Continuous time
Pseudo-time
(t4 – t0 is not 2 x t2 -t0): Logic models

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Variable granularity
Single particles Discrete populations
Continuous populations
Fields

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Spatial representation
No dimension Homogeneous
(well-stirred, isotropic)
Compartments
Cellular automata Finite elements Real space
[x]
[x]A
[x]B

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Stochasticity
Deterministic simulation
Stochastic differential equations
Ensemble models (distributions)
Probabilistic models
Initial conditions
Parameter values
Stochastic simulations
(SSA, “Gillespie”)

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Logic versus numeric

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Many other types of models
Multi-agents models (cellular potts)
Cable approximation
Matrix models

In Silico Systems Biology, EMBL-EBI, 03-08 June 2018

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Modelling in Biology - WT/EBI course systems biology 2018

1. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 The many faces of modelling in biology Nicolas Le Novère, The Babraham Institute n.lenovere@gmail.com

2. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is the goal of using mathematical models? Describe 1917

3. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is the goal of using mathematical models? Describe Explain 1917 1952

4. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is the goal of using mathematical models? Describe Explain Predict 1917 1952 2000

5. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is a mathematical model? Wikipedia (October 14th 2013): “A mathematical model is a description of a system using mathematical concepts and language.”

6. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is a mathematical model? What we want to know or compare with experiments variables [x] Vmax Kd EC50 length t1/2 Wikipedia (May 31st 2018): “A mathematical model is a description of a system using mathematical concepts and language.”

7. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is a mathematical model? What we already know or want to test Wikipedia (May 31st 2018): “A mathematical model is a description of a system using mathematical concepts and language.” variables relationships [x] Vmax Kd EC50 length t1/2 If then

8. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 What is a mathematical model? Wikipedia (May 31st 2018): “A mathematical model is a description of a system using mathematical concepts and language.” variables relationships constraints [x] Vmax Kd EC50 length t1/2 If then [x]≥0 Energy conservation Boundary conditions (v < upper limit) Objective functions (maximise ATP) Initial conditions The context or what we want to ignore

9. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 1952 1960 1969 1981 1973 1991 1993 1998 2000 2005 2012 Turing morphogen Hodgkin-Huxley action potential Chance catalase Chance glycolysis Noble pacemaker Kauffman Boolean networks Savageau BST Kacser MCA Thomas logic models Goldbeter Koshland ultrasensitive covalent cascades Tyson cell cycle Bray bacterial chemotaxis Karr et al Whole mycoplasma McAdams, Arkin Stochastic simulations Kitano, Hood Systems biology revival Repressilator, toggle switch Synthetic biology 2013 Thiele et al Recon 2 BioModels 1989 Palsson Erythrocyte metabolism

10. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Computer simulations Vs. mathematical models

11. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 One would like to be able to follow this more general process mathematically also. The difculties are, however, such that one cannot hope to have any very embracing theory of such processes, beyond the statement of the equations. It might be possible, however, to treat a few particular cases in detail with the aid of a digital computer. This method has the advantage that it is not so necessary to make simplifying assumptions as it is when doing a more theoretical type of analysis. Computer simulations Vs. mathematical models

12. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Birth of Computational Systems Biology

13. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Birth of Computational Systems Biology

14. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 The Computational Systems Biology loop “biological” model mathematical model computational model simulation parameterisation validation

15. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Representation of time No time: correlations, steady-states Discrete time Continuous time Pseudo-time (t4 – t0 is not 2 x t2 -t0): Logic models

16. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Representation of time No time: correlations, steady-states Discrete time Continuous time Pseudo-time (t4 – t0 is not 2 x t2 -t0): Logic models

17. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Variable granularity Single particles Discrete populations Continuous populations Fields

18. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Variable granularity Single particles Discrete populations Continuous populations Fields

19. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Spatial representation No dimension Homogeneous (well-stirred, isotropic) Compartments Cellular automata Finite elements Real space [x] [x]A [x]B

20. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Spatial representation No dimension Homogeneous (well-stirred, isotropic) Compartments Cellular automata Finite elements Real space [x] [x]A [x]B

21. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Stochasticity Deterministic simulation Stochastic differential equations Ensemble models (distributions) Probabilistic models Initial conditions Parameter values Stochastic simulations (SSA, “Gillespie”)

22. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Stochasticity Deterministic simulation Stochastic differential equations Ensemble models (distributions) Probabilistic models Initial conditions Parameter values Stochastic simulations (SSA, “Gillespie”)

23. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Logic versus numeric

24. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Logic versus numeric

25. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018 Many other types of models Multi-agents models (cellular potts) Cable approximation Matrix models

26. In Silico Systems Biology, EMBL-EBI, 03-08 June 2018

Modelling in Biology - WT/EBI course systems biology 2018

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