Biological Systems
Modeling & Simulation

Dr. Werner Van Belle

werner.van.belle@itek.norut.no

werner.van.belle@fagmed.uit.no

+47 776 29 404

A national institute for applied research

Performs technology transfer

Educate at both pre- and post doctoral level

Contributes to national innovation

Technological focus

Earth Observations, Remote Sensing

Network Systems, Distributed Systems, IT

Bioinformatics

Presentation Outline

Theoretical Models

Model Execution

Model Invertion

Simulation

Maldi Tof Analysis

Visualisation Demonstration

Theoretical Models

Science

Reality

Prediction

Simulation

Experiments

Theoretical

Model Building

Model Invertion

Modeling

A model describes the causal relation between variables of a system under investigation

a chemical pathway

under the presence of protein (x), protein (y) will be activated

a proteome

specific protein function

inhibitor (i), activator (a) relates to protein (x)

dynamics: protein (x) oscillates over time (t)

subcellular protein location: protein (x) is located at position (y)

protein (x) interacts with protein (y)

kinetics: protein (x) moves from (a,b) to (c,d)

Modeling

A model can be expressed in different ways

Data Approximation

Deterministic

Stochastic

Differential equations

Modeling – Differential Equations

When the 'speed' of an event depends on its own state

E.g: the rate of change depends on the concentration

A → B

Modeling – Differential Equations

If you know the concentration at two times, you can calculate it for any other time

Modeling – Differential Equations

Equilibrium

Modeling – Differential Equations

Irreversible two molecule interaction

A+B→C

Modeling – Differential Equations

A step in a metabolic pathway

A→B←→C+D

-1

1

0

D

-1

1

0

C

1

-1

1

B

0

0

-1

A

k3

k2

k1

Modeling – Differential Equations

A step in a metabolic pathway

A→B←→C+D

-1

1

0

D

-1

1

0

C

1

-1

1

B

0

0

-1

A

k3

k2

k1

-k3[C][D]

+k2[B]

[D]

-k3[C][D]

+k2[B]

[C]

+k3[C][D]

-k2[B]

+k1[A]

[B]

-k1[A]

[A]

reverse

forward

decay

d/dt

Modeling – Differential Equations

Regulation of the Ras/Raf/MEK/ERK signaling network; solid lines represent direct effects on activity. The broken line indicates that PAK phosphorylation enhances the binding of MEK to Raf-1 and hence facilitates MEK activation indirectly. Abbreviations: PI-3 K, phosphoinositide 3-kinase; PTP, protein tyrosine phosphatase; MKP, MAPK phosphatase

Modeling – Differential Equations

The Raf-1/RKIP/ERK pathway

k1 = 0.53;

k2 = 0.0072;

k3 = 0.625;

k4 = 0.00245;

k5 = 0.0315;

k6 = 0.8;

k7 = 0.0075;

k8 = 0.071;

k9 = 0.92;

k10 = 0.00122;

k11 = 0.87;

Modeling – Differential Equations

Enzyme Kinetics

Model Execution

Differential Equations

Analytically solving

specific and efficient solutions exist. E.g;

Drawbacks

Requires analytic analysis

useful analytical solutions not necessarily exit

multi-stability

Differential Equations

Numerically solving f(t) – f'(t): Euler

Differential Equations

Resolution/scale

Simulation – Differential Equations

Numerically solving f(x,t) – f(x',t'): Lax method

Differential Equations

Optimalisations

use of location independence

approximate subsystems

transfer information between cells

symmetry

Differential Equations

Step/Scale Analysis

Fourier: detects frequency content

Wavelets: detects locations of fronts

Model Invertion

System Modeling

Small Models

all factors can be easily understood

model parameters can be obtained by simple experiments

DANGER !

Dissociation: small models not necessarily compatible

Very localized view

Integrated Models

System Modeling

System of Differential Equations

Models & Simulation

Integrated models = system models

large number of parameters

few known and probably incorrect in the total picture

Model Invertion

In order to make models useful the unknown parameters must be known

Experiments needs to be retrofitted to the model

Experiment

Synchronized cells, microarray experiment

Analysis

Resolution/Scale of events

Analysis

Correlation / Clustering

Information

The availability of a protein interaction map

Mathematically Speaking

Measured

Modelled based on correlation measures

Mathematically Speaking

We have

a function (set of differential equations)

a function (based on measurements)

What we want
function minimalisation problem

Techniques

Many techniques exists

Swarm Intelligence / Particle Systems / Parallel Searching

Learning algorithms / Neural networks

Singular Value Decomposition

Iterative methods: Levenberg-Marquardt

Predictive methods using signal processing

Norut => Experience in model invertion

Pragmatism

depends very much on the experiments performed

understanding of the experiments is necessary

Simulation

Simulation

Integration of

input/modify models

algorithms to execute models

input experiments

data analysis of experiments

data mining external sources

visualisation of execution/analysis/models

Summary

Impossible to simulate what is not modeled !

It is possible to model what is not entirely understood

A simulation should always be targeted towards its goal

Strong interaction between mathematical modeling and algorithmic execution

Software tool support necessary

Summary

Advantages

Backward Reasoning

Verification of hypotheses

Finding of 'interesting' phenomena

Cheaper & faster

Holistic/integrated models

Can guide experiments

Inside-the-cell view

Related Work

http://www.ipam.ucla.edu/programs/prot2004/ Proteomics - a past conference on proteomics. Some of the talks summarized

Prediction, determination and understanding of structures via global exploration of their energy landscapes.

Computational approaches for serum marker discovery

Estimating information quantities from biological data

Combining multiple genomic data sources into reliable predictions of protein complexes

The SMARTCELL Project - cell simulation by Brussels University in cooperation with Heidelberg.

Related Work

EMBL, Ellenberg Group - Uses an experimental and computational approach to the Functional dynamics of nuclear structure during the cell cycle.

Virtual Cell - The Virtual Cell is capable of handling a range of biological based models from the simple to the very complex. Computational modeling can be a useful tool for providing the answers to a variety of questions.

Is a hypothetical network complete and correct ? Do MS protein profiles match model prediction?

What are the critical components of a pathway? Virtual knockouts; evaluate drug targets.

Analyze quantitative microscopy experiments. FRAP, uncaging, probe translocation

Visualize species that can't be probed experimentally. Spatiotemporal patterns of post-translational modifications

Facilitate the sharing of models and the collaborative construction of 'supermodels'.

Related Work

http://www.e-cell.org/ [E-Cell] - an international research project aiming to model and reconstruct biological phenomena in silico, and developing necessary theoretical supports, technologies and software platforms to allow precise whole cell simulation. They have different projects running ranging from the very basic to the larger picture.

Mitochondrion - understand and control dynamics of mitochondrial metabolism through computer simulation in a whole organelle scale.

E-Neuron - aims at reproducing neural nerve behavior at a molecular level using kinetic equations.

E2coli - An energy metabolism model of Escherichia coli was constructed.

e-Rice - The complete genomic sequence of rice has been elucidated and its metabolism thoroughly researched, making rice an ideal prospect for modeling and simulation.

Related Work

Erythrocyte - A steady state computer model of the human erythrocyte has been constructed with three major metabolic pathways, glycolysis, the pentose phosphate pathway, nucleotide metabolism, and also ion transport systems.

Cell Signaling - two main threads: (i) implementing a stochastic module in the E-Cell Simulation Environment Version 3 , and (ii) modelling the bacterial chemotaxis signalling pathway.

Circadian rhythm - A gene regulatory network and signaling pathway of circadian rhythm in Synechococcus sp. PCC7942 was estimated.

Diabetes - construct a multi-organ diabetes model using the E-Cell Simulation Environment.

Mathematical Analysis - Simulation using E-CELL Simulation Environment often requires kinetic data of biochemical reactions. Investigate mathematical estimators.

Related Work

http://www.cellzome.com/ [Cellzome] - is a drug discovery company building a R&D pipeline in chronic diseases by leveraging its unique drug proteomics engine.

http://www.science.uva.nl/research/scs/CellMath/ - mathematical models of metabolic and regulatory networks including intrinsic spatial non-homogeneity.

System reduction techniques for ordinary differential equations (ODEs) of the type that arises in chemical networks (simplification and modularization in the chemical `dimension')

Particle-based methods for modelling of features with high spatial variability or low number of molecules

Multi-adaptive numerical methods for the efficient solving of reaction-diffusion PDEs with varying spatial and temporal scales, and space dependent chemical schemes

References

Paul T. Spellman, Gavin Sherlock, Michael Q. Zhang, Viswanath R. Iyer, Kirk Anders, Michael B. Eisen, Patrick O. Brown, David Botstein and Bruce Futcher; Comprehensive Identification of Cell Cycle-regulated Genes of the Yeast Saccharomyces cervisiae by Microarray Hybridization; Molecular Biology of the Cell, vol 9, 3273-3297, December 1998

Robert R. Klevecz; Dynamic Architecture of the yeast cell cycle uncovered by Wavelet Decomposition of expression Microarray data; Func. Integr. Genomics (2000); 1:186-192

L. Giot, J.S.Bader, C. Brouwer, A. Chaudhuri; A Protein Interaction Map of Drosophila Melanogaster; science vol 302, 5 december 2003

Rainer Breitling (R.Breitling@bio.gla.ac.uk); Modelling Biological Systems with Differential Equations; Bioinformatics Research Centre; February 2004

W. Kolch; Schematic representation of the structure of MAPK pathways; Biochemical journal 2000; volume 351

References

William H. Press, Saul A. Teukolsky, William T. Vetterling, Briand P. Flannery. Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press

Helmut Knaust; Numerical Techniques, Eulers Methods; Sep 17 1996: http://www.sosmath.com/

Maldi Tof

Maldi Tof – Signal Analysis

Maldi Tof – 90 % Denoised - Global

Maldi Tof – 90 % Denoised – Local View

Maldi Tof – Correlation Analysis

Visualisation Protein
Interaction Map

Protein Interaction Map

The End

Norut Itek

Expertise in data handling

Expertise in signal processing

Expertise in model invertion

Expertise in software development

Modality

Hourly based

Project partner

Contact

werner.van.belle@itek.norut.no

werner.van.belle@fagmed.uit.no

Extra Slides

Modeling Diffusion

Concentrations are different in different places

n = f(t,x,y,z)

Diffusion superimposed on chemical reactions:

Modeling Diffusion

Modeling Difusion

2004-07-08T11:57:46