SPATIO-TEMPORAL MODELLING IN BIOLOGY

Transcription

1 SPATIO-TEMPORAL MODELLING IN BIOLOGY Prof Dagmar Iber, PhD DPhil ((Vorname Nachname)) 04/10/16 1

2 Challenge: Integration across scales Butcher et al (2004) Nat Biotech, 22,

3 INTERDISCIPLINARY WORK BIOLOGISTS DATABASE CURATORS DATABASE SPECIALISTS Databases s Expert Knowledge by Biologists MATHEMATICIANS PHYSICISTS / ENGINEERS COMPUTER SCIENTISTS Tools & Concepts for efficient model building Experiments Data Analysis Image Analysis Machine Learning GOALS:! Understanding! In silico Genetics! Bioengineering! Evolution!! Efficient algorithms for multi-scale simulations BIOLOGISTS COMPUTER SCIENTISTS Iber and Zeller (2012) Curr Opin Genet & Development NUMERICAL ANALYSTS COMPUTER SCIENTISTS

4 Spatio-Temporal Modelling in Biology 28/9 Introduction to Spatial Modelling: Biochemical Reaction Modelling 5/10 Morphogen Gradients 12/10 Patterning on Growing Domains & Pattern Scaling 19/10 Turing Pattern 26/10 Travelling Waves, Wave Pinning & Shuttling 2/11 Single-Cell Behaviour: Chemotaxis & Notch-Delta Patterning 9/11 Tissue Mechanics 16/11 Cell-based Simulation Frameworks (Anna Stopka) 23/11 Image-Based Modelling; Case Study I: Branching Processes 30/11 Parameter Estimation & Model Selection 7/12 Case Study II: Modelling the Limb 14/12 Growth Control 21/12 Evolution of Patterning: Summary & Conclusion Computational Biology (CoBi), D-BSSE Tuesday 4 October 164

5 LITERATURE Murray, Mathematical Biology, Springer Keener and Sneyd, Mathematical Physiology, Springer Fall et al, Computational Cell Biology, Springer Forgacs and Newman, Biological Physics of the Developing Embryo, CUP Kreyszig, Engineering Mathematics, Wiley Our Web-Resource: Computational Biology (CoBi), D-BSSE Tuesday 4 October 165

6 Tutorials: weekly Wed pm, HG D3.1 Tutorial I Morphogen Gradients Tutorial II Turing Patterns & Travelling Waves Tutorial III Tissue Mechanics & Cell-based Tissue Modelling Tutorial IV Image-based Modelling Tutorial V Organogenesis Tutorial VI Revision Problem sheets will be given out every week. Your tutor is Christine Lange (christine.lange@bsse.ethz.ch). STUDY SUPPORT:!! Use the script Do the exercises YOURSELVES discuss with your colleagues!!! Do the exercises BEFORE the tutorials ask questions in the tutorials Computational Biology (CoBi), D-BSSE Tuesday 4 October 166

7 Work Load and Management Course gives 6 credit points = 180 hours of work (1 ECTS Credit Point = 30 learning hours) 13 x 2h lectures = 26 hours 13 x 1h tutorials = 13 hours > self-study= 141 hours > 10 hours per week Questions at end of lectures to help you revise and focus: please download EduApp ( on your smartphones Working in groups can help you to understand better & faster everyone needs to hand in their own (distinct!) solution. Solving problems is the only way to learn! consider it lab work 7

8 Tutorial: NUMERICAL METHODS!! Finite Difference Methods (pdepe in MATLAB)!! Finite Element Methods (COMSOL)!! Lattice-Boltzmann!! Particle Methods! Look at material on our website!! Tuesday 4 October 168

9 INTRODUCTORY MATERIAL Lecture 1 Dagmar Iber 04/10/16 9

10 TRANSPORT MECHANISMS Diffusion Active transport ( cytonemes ) Cell-cell interaction Cell-linked transport (migration) Dagmar Iber 04/10/16 10

11 THE DIFFUSION EQUATION Computational Biology (CoBi), D-BSSE Tuesday 4 October 1611

12 REACTION-DIFFUSION EQUATIONS In chemical processes compounds not only diffuse but also react. We then have: c t = D 2 c x 2 + R(c) where the function R(c) describes the chemical reaction terms Computational Biology (CoBi), D-BSSE Tuesday 4 October 1612

13 Reaction-Diffusion PDEs Reaction diffusion equation based Simplest reaction is decay Often! Often we have we have complex complex dynamics dynamics 1 REGULATION: activation & inhibition 1/2 K X

14 How to formulate a mechanistic model?!! Understand the biological problem!! Describe the reaction kinetics!! Formulation!! Parameter Estimation!! Validation!! Describe the reaction domain!! Analyse the model!! Analytic approaches!! Computational approaches Negative Feedback Gene 1 Competition Crossregulation Gene 3 Gene 2 Cross-activation

15 BASIC REACTION TYPES Computational Biology (CoBi), D-BSSE Tuesday 4 October 1615

16 COMPOSITE REACTIONS

17 REGULATORY REACTIONS

18 Qualitative Analysis I. Steady State Analysis: Response Types II. Phase Plane III. Linear Stability Analysis IV. Dynamic Response Types V. Signaling Kinetics in Cascades

19 PHASE PLANE ANALYSIS

20 LINEAR STABILITY ANALYSIS

21 Feedback Control

22 Switches

23 THANKS FOR YOUR ATTENTION! Slides for this lecture are available at: Mathematical Modelling in Systems Biology Prof Dagmar Iber Computational Biology (CoBI), D-BSSE, ETHZ Computational Biology (CoBi), D-BSSE Tuesday 4 October 1623

24 THANKS!!