Spatiotemporal Modeling and Simulation

01 - Introduction

Ivo F. SbalzariniMOSAIC Group, CSBD, TUD & MPI-CBG

Topic

1. Modeling in Biology: where and why?

2. Diffusion in a complex-shaped cell organelle

3. Other examples4. Summary

2

Outline

Overview of spatio-temporal modeling and simulation in biology

Where and Why?

Modeling in Biology

Modeling in Biology

4

Computer science will be for 2020 biology what

mathematics is for today’s physics.

Microsoft Report “2020 Science”

1. Modeling in Biology

5

Images: Wikipedia

Life

• Highly organized

• Regulated

• Complex shapes

• Non-equilibrium

• Nonlinear

• Coupled

Goal: System dynamicsSo far: Description

1. Modeling in Biology

Life in space AND time

6

Mol

ecul

es

Org

anel

les

Cel

ls

Org

ans

Org

anis

ms

Ecos

yste

ms

Wolters et al., IJBEM 7:203, 2005

1. Modeling in Biology

Genotype / Phenotype7

Bilder: Wikipedia

???

1. Modeling in Biology

What is the connection?8

In order to understand how genotype and phenotype are

connected, we also have to consider:

• Spatial organization and compartmentalization

• Temporal plasticity and dynamics

• Environmental influences

• Physics of interactions

• Regulatory mechanisms

1. Modeling in Biology

Computational Biology9

Data analysis

Model

Simulation

Comparison

Prediction

Experiments

• Physics as the basis of function of biological systems

• Understanding of function with minimal assumptions

• Data analysis and modeling using computers

1. Modeling in Biology

Why Computers ?10

Amount of data / Reproducibility

Manual evaluation too slow or too unreliable

Complexity System behavior not apparent from description

Controllability Variables controllable

Observability Variables measureable

Ethics No living beings involved

Time/length scales Too big/small, slow/fast for experimental measurement

1. Modeling in Biology

Interdisciplinary work

11

experiment analysis

interpretation

raw data

processed

data

knowledge

Cell Biologists Computer Scientists

Cell Biology with and versus Computer Science

modelling

and simulation

interpretation

Biology Computer Science

1. Modeling in Biology

Diffusion in a complex-shaped cell organelle

2. Example

Synthesis plant for proteins and lipids in eucaryotic cells.

Enclosed by a contiguous membrane.

132. Diffusion in the ER

Membrane

Figure: De Duve, Une visite guidée de la cellule vivante, 1987.

Figur: D. Kunkel, (c) www.DennisKunkel.com

Figure: Purves et al., Life: The Science of Biology, W.H. Freeman.

LumenThe Endoplasmic Reticulum (ER)

0 1 2 3 4 5 6 7 8 9 10Time [s]

0

0.2

0.4

0.6

0.8

1

FRA

P [

-]

• Protein fluorescently tagged

• Region Of Interest (ROI) bleached with laser

• recovery of fluorescence monitored over time

pre-bleach

t=0 min

t=2 min

14

FRAP: Fluorescence Recovery After Photobleaching

10µmHelenius group

Diffusion

2. Diffusion in the ER

Original task

15

Identification of diffusion constants from fluorescence

recovery curves.

2. Diffusion in the ER

• Bleached region is larger than ER structures

• Separation of scales: Observation summed (or averaged) over bleached region

• 2D projection (or slice) of a 3D object

Why this is not easy

16

Have to be corrected, but are not controllable in the experiment ... Modeling and simulation!

2. Diffusion in the ER

D =Dsim

ts

17

FRAP experiment

Experimental FRAP curve

Simulation

Simulated FRAP curve

Micrograph sections of the same organelle

3D reconstruction

Fit in time

Time unit tsMolecular diffusion

constant

Dsim

0 1 2 3 4 5 6 7 8 9 10

Time [s]

0

0.2

0.4

0.6

0.8

1

FR

AP

[

-]

2. Diffusion in the ER

Parallel sections from confocal imaging of fluorescently stained ER.

Movie: Helenius group, D-BIOL, ETHZ

Reconstruction of the real ER geometry

182. Diffusion in the ER

• Threshold

• Resolution of the microscope

19

19

Figure 5: Supplementary Material, Sbalzarini et. al.

40 50 60 70 80 90 100 110 120 130 140 1500

0.5

1

1.5

2

2.5

Threshold

Re

lative

err

or

anisotropy 8

anisotropy 6

anisotropy 4anisotropy 3

anisotropy 2

anisotropy 1

Figure 6: Supplementary Material, Sbalzarini et. al.

18

a: Whole network, anisotropy 3

b: 4 × 4 × 3 closeup, anisotropy 1

Figure 4: Supplementary Material, Sbalzarini et. al.

Reconstruction error determined by:

Find optimal threshold in the computer

5.3 Calculations done with small, smallRAD and smallMU 49

80 90 100 110 120 130 140 150 160 1700

0.2

0.4

0.6

0.8

1

1.2

1.4smallMU: anisotropy = 2

Threshold used in imaris

Rela

tive e

rrors

Vol reconstrhitsmissedexcesstotal error

Figure 5.47: Plot of errors for smallMU, = 2

threshold total error hits missed excess disconnected objects

90.43 0.3782 0.9699 0.0301 0.3482 1

100.04 0.3248 0.9218 0.0782 0.2465 3

120.14 0.3000 0.7922 0.2078 0.0922 1

140.23 0.4547 0.5820 0.4180 0.0367 1

160.33 0.6405 0.3719 0.6281 0.0124 1

Table 5.14: Error listing

Figure 5.48: Three reconstructions with thresholds: 90, 110, 120

3D reconstruction

2. Diffusion in the ER

202. Diffusion in the ER

Computer simulation

21

1. Mathematical description of the process

2. Discretization of the model

4. Simulation

3. Programming in the computer

5. Validation of the correctness of the results

6. Evaluation and interpretation of the results

2. Diffusion in the ER

1. Mathematical description

22

hu(x, t)i =1

|ROI|

Z

ROI

u(y, t) d3y

@u(x, t)@t

= r · (D(x, t)ru(x, t))

Physical process: transport by diffusion

Dynamics of the observed (measurement) quantity

@thu(x, t)i = r · (Dapprhu(x, t)i)

Dapp =D +

1|ROI|

Z

@ROI

b(x, t)>· n dA

�

2. Diffusion in the ER

2. Discretization

23

Fill geometry with interacting particles.

Interaction such that the mathematical model is solved.

Particle methods

2. Diffusion in the ER

24

For (anisotropic) diffusion:

Degond & Mas-Gallic, Math. Comput. 53:509. 1989.

dup

dt=

X

q 6=p

�✏(xp,xq,D, t)(uq � up)Vq

Eldredge et al., J. Comp. Phys. 180:686. 2002.

Extension to any differential operator:

L�hf(xp) ⇡

1✏|�|

X

q

Vq (f(xq)± f(xp)) ⌘�✏ (xp � xq)

Diffusion in space

Formulation of the diffusion operator on particles

2. Diffusion in the ER

25

ER lumen

Sbalzarini et al., Biophys. J. 89(3):1482. 2005.

2. Diffusion in the ER

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5

FRAP

[-

]

time [s]

5. Validation of results

Comparison withcontrol experiments.

Simulation and experiment in the same ER

Simulation

Experiment

26

Sbalzarini et al., Biophys. J. 89(3):1482. 2005.

2. Diffusion in the ER

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20

FRAP

[-

]

time [100 δt]

6. Interpretation of resultsFRAP simulationsin the lumen ofdifferent ER

All simulation use the same diffusion constant

Influence (artifact) of geometry: 250%

27

Sbalzarini et al., Biophys. J. 89(3):1482. 2005.

2. Diffusion in the ER

Examples from outside MOSAIC

3. Other examples

Kaandorp et al., Amsterdam293. Other examples

Coral growthusing reaction-diffusion model

Alfio Quarteroni, EPFL

303. Other examples

Simulations of bloodflow in sclerotic arteries and bypasses.

Marc Thiriet, INRIA

313. Other examples

Cerebral aneurisms

M. Gobbert, U. Maryland

323. Other examples

Calcium activation waves in a muscle fiber

Bioengineering, U. Auckland333. Other examples

Growth of coronary vessels in the human heart

Summary

35

A symbiosis• Computer modeling and simulation enables larger

amounts of data and model complexities

• Observation and control of processes that are not observable/controllable in the experiment

• New algorithms and programming techniques are inspired or required

• Direct links to many areas in core CS

• New knowledge on both sides

4. Summary

Common goal: understand systems