The document summarizes a RESOLVE workshop on computational biology held at Eindhoven University of Technology in the Netherlands. It provides information about the university, including its research focus areas and departments. Specifically, it describes the Biomedical Engineering department and its Computational Biology group. It then outlines the workshop's schedule over two days, including lectures on modelling biochemical systems with differential equations and computer practical sessions on simulation and parameter estimation. The workshop aims to help participants model and analyze biological data using computational approaches.

1. RESOLVE workshop
May 15, 2013
Natal van Riel, Christian Tiemann, Fianne Sips
Eindhoven University of Technology, the Netherlands
Dept. of Biomedical Engineering, n.a.w.v.riel@tue.nl
Systems Medicine and Metabolic Diseases

2. The university
• A research university specializing
in engineering science & technology
• 9 departments
• Biomedical Engineering • Built Environment
• Electrical Engineering • Industrial Design
• Industrial Eng. & Innovation Sciences • Chemical Eng. and Chemistry
• Applied Physics • Mechanical Engineering
• Mathematics and Computer Science
• Students
• 4,800 BSc students
• 2,800 MSc students
• 200 technological designers (PDEng)
• 1,100 doctoral candidates (PhD)
• Strategic Research Areas
• Energy
• Health
• Smart Mobility
/ biomedical engineering PAGE 216-8-2013

3. The Biomedical Engineering department
• 8 groups
• Soft tissue biomech. & eng. (Baaijens
& Bouten)
• Cardiovasculair biomechanics (van
de Vosse)
• Orthopaedic biomechanics (Ito)
• Chemical biology (Brunsveld)
• Biomedical chemistry (Meijer)
• Biomedical NMR (Nicolaij)
• Biomedical image analysis (ter Haar-
Romeny)
• Computational biology (Hilbers)
• Bachelor
• Biomedical Engineering
• Medical Sciences and
Technology (Sept. 2012)
• Master
• Biomedical Engineering
• Medical Engineering
• 3 thematic research programs
• Regenerative Medicine
• Molecular Imaging
• Systems Medicine
/ biomedical engineering PAGE 38/16/2013

4. The Computational Biology group
Understanding complex dynamic biochemical systems
/ biomedical engineering PAGE 416-8-2013
Systems
biology
Molecular
modeling

5. Program
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Day 1 (Wed. May 15, 2013)
• 10:00 Opening
• 10:15 Lecture 1: Modelling with differential equations
• 11:10 Coffee break
• 11:30 Computer practical 1: Modelling and simulation of pathways
• 13:00 lunch
• 14:00 Lecture 2: Parameter estimation
• 15:00 Computer practical 2: Parameter estimation in practice
• 16:15 Pitch talks by participants
• 16:45 Discussion about possibilities to model data provided by the participants.
Select cases that are interesting to be explored in more detail.
• 17:30 Drinks
• 19:00 Workshop dinner

6. Program
Day 2 (Thu. May 16, 2013)
• 9:00 Inquiry of observations and (remaining) questions of day 1
• 9:15 Lecture 3: Introducing ADAPT
• 10:10 Coffee break
• 10:30 Computer practical 3: ADAPT
• 12:30 lunch
• 13:30 Computer practical 4:
• Option 1 Work with your own data
• Option 2 Continue working on previous practicals
• 15:30 Wrap-up discussion
• 16:00 Closure
/ biomedical engineering PAGE 616-8-2013

7. / biomedical engineering PAGE 716-8-2013
Lecture 1: Modelling with
differential equations

8. Contents
• Models
• Nomenclature
• Differential Equations
• decay reaction
• Simulation
• numbers required
• decay reaction in Excel
and Matlab
• Computer practical 1:
• modelling and simulation of pathways
• irreversible enzymatic reaction
/ biomedical engineering PAGE 816-8-2013

9. Convergence of Life Sciences, Physical Sciences and
Engineering
• The Three Revolutions
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Models and modeling

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M.C. Escher
Karl Popper
(1902 – 1994)
George Box (1919 - 2013)

12. Mathematical models in systems biology
TOP-DOWN
• Bioinformatics
• ‘omics’-based
• Statistics / statistical models
• Hypothesis driven
• Targeted measurements
• Differential equations
BOTTOM-UP
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13. / biomedical engineering PAGE 1316-8-2013
Nomenclature
Processinput output

14. Nomenclature and definitions
Dynamic systems with input(s) and output(s)
• (State) variables: x, dynamics x(t)
• (Independent) input: u, u(t)
• Output: y, y(x,u,t)
• 0, , ,x u y t 
model
f(x,u,t)
u(t) y(t)
ENVIRONMENT
input
• experimental
perturbations
output process
• observations
• measurements
output model
process

15. Nomenclature and definitions
• Derivative:
• Scalar, vector:
• Parameters:
'( )x t x
( )
,
dx t dx
dt dt
2
2
, "( ),
d x
x t x
dt

, ,x x x 1 2[ , ,..., ]nx x x x
1
2T
n
x
x
x
x

0
n
x 
, ,p p p

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Nomenclature and definitions
• Differential equations
• Ordinary Differential Equation (ODE)
• Only derivatives w.r.t. one of the independent variables
Here: time (dynamics)
• Partial DE (PDE)
E.g. also derivatives in space
• Autonomous
• Steady-state: rate of change = 0
• Stable / unstable
• Bistable
2
2
2
c
t x
heat equation
0ˆ
dx
dt
( ( ), ( ), )
dx
f x t u t p
dt
( ( ), )
dx
f x t p
dt

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Differential Equations
biology physics
model model
scheme equations

18. Differential Equations (DE)
• Mathematical framework to describe a deterministic relation
involving continuously varying quantities (modeled by
functions) and their rates of change in time and/or space
(expressed as derivatives)
Back to Sir Isaac Newton (classical mechanics)
• Newton's laws allow one to predict the unknown position of a body as a function
of time (trajectory) in relation to the position, velocity, acceleration and various
forces acting on the body
• DE’s can describe real world (physical, chemical, biological)
processes (that ‘live’ in continuous time)
• DE’s can capture mechanistic understanding
• DE’s play a prominent role in many areas of science and
technology (engineering, physics, economics, …)
/ biomedical engineering PAGE 1816-8-2013

19. / biomedical engineering PAGE 1916-8-2013
From a ‘wiring diagram’ to a set of ODEs
• Mass balance for each species
Change in concentration = (producing reactions) -
(consuming and degrading processes)
• Each mass balance will translate into a (1st order) differential
equation
• Species are coupled through interactions (biochemical
conversions)  network  system of coupled differential
equations
( )dx t
dt

20. An irreversible monomolecular reaction
• An irreversible monomolecular reaction
Autonomous system (chemistry: closed system)
• Law of mass action
• Model with y = [A]
• Initial condition
• Solution
• Required: values for parameter(s) and initial conditions
k
A
dy
ky
dt
(0) 5y1k
/ biomedical engineering PAGE 2016-8-2013
0
kt
y A e
0(0)y A

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Simulation of biochemical systems

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Simulation of 1st order ODE’s
Numerical: discretization (here equidistant)
• Taylor series expansion
• For small td the higher powers td
2, td
3, … are very small.
This suggests the crude approximation
• Forward Euler method (1st order fixed step method):
2
[ 1] [ ] '[ ] ''[ ] . . .
2
d
d
t
y i y i t y i y i H OT 
[ 1] [ ] '[ ] [ ] ( )d dy i y i t y i y i t f i
[ 1] [ ] ( , [ ])dy i y i t f i y i
'( ) ( ( ))y t f y t
y(0) = y0 td 2td0
[ ] ( ),dy i y it i 

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Forward Euler method
• A recurrence relation (Difference Equation)
i i+1
slope= f (y[i])
td
y[i]
y[i+1]
[ 1] [ ] ( , [ ])dy i y i t f i y i
Example:
molecular decay

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Effect of integration step td on accuracy
• exact solution
• td = 1
• td = 0.1
• td = 0.01
0 2 4 6 8 10
0
1
2
3
4
5
Euler integration k=1
-
( ) (0) 5kt t
y t y e e
y ky

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Using computers to simulate (bio)chemical kinetics
• A great number of computer tools is available for simulation of
systems of coupled DE’s
• Matlab Python
− Systems Biology Tlbx - PySCeS (Python Simulator
− for Cellular Systems)
• Supply a code that computes the time derivatives of the ‘state
variables’ (right-hand side of 1st order differential equations)
• Graphical modeling and simulation tools

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1st order fixed step method
• 1st order fixed step method
• Euler:
• In Matlab:
• t1, tend, td and x0 depend on the system and the simulation
• p is a vector with the model parameters
• x is matrix with different time points as the rows and the states in
the columns
[ 1] [ ] ( )dx i x i t f i
tspan=t1:td:tend;
x(1,:)=x0;
for i=1:length(tspan)-1
x(i+1,:)=x(i,:)+td*f(i,x(i,:),p);
end
function dx=f(i,x,p)
… %enter the ODE’s here
( ) ( ( ))x t f x t
x(0) = x0
autonomous system:

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Variable step integration methods
• Higher order, variable step method
• In Matlab:
• ‘options’ defines settings of the simulation algorithm and can be
changed using odeset; usually default (options=[]) is OK
• all input arguments of ode15s after ‘options’ are user defined; the
function with the ODE’s has to accept these as the 3rd (and so forth)
inputs
• t is determined by Matlab
tspan=[t1,tend];
[t,x]=ode15s(@f,tspan,x0,options, p); %see help ode15s
function dxdt=f(t,x, p)
… %enter the ODE’s here
dxdt=dxdt(:); %ode45 requires output to be a column
( ) ( ( ))x t f x t
x(0) = x0

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Computer practical 1: Modelling
and simulation of pathways

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