I Systems Microbiology (13 Lectures) ‘The cell as a well-stirred biochemical reactor’ L1 Introduction L2 Chemical kinetics, Equilibrium binding, cooperativity L3 Lambda phage L4 Stability analysis L5-6 Genetic switches L7-9 E. coli chemotaxis L10-11 Genetic oscillators L12-13 Stochastic chemical kinetics 1 II Systems Cell Biology (9 Lectures) ‘The cell as a compartmentalized system with concentration gradients’ L15 Diffusion, Fick’s equations, boundary and initial conditions L16-17 Local excitation, global inhibition theory L18-19 Models for eukaryotic gradient sensing L20-21 Center finding algorithms L22-23 Modeling cytoskeleton dynamics 2 III Systems Developmental Biology (2 Lectures) ‘The cell in a social context communicating with neighboring cells’ L23 Quorum sensing L25 Drosophila development 3 Main take home messages from this course: 4 1. translate the biology into a quantitative model: given the biology set up the coupled differential equations that capture the essence of the biological phenomena (not trivial since 4 papers came up with a different model given the same biological phenomenon, which assumptions to make is critical) 2. analysis of the system of differential equations stability analysis (both in space and time) 3. interpretation of the mathematical analysis, what are the biological conclusions ? e.g. if the imaginary part of the eigenvalue is non zero, what does this mean for the underlying biology? 4. develop a taste for the potential of these systems approaches for biological problems that you may encounter in the future Developmental Systems Biology ‘Building an organism starting from a single cell’ Introducing: Drosophila melanogaster (or the fruitfly) Great book: ‘The making of the fly’ by Peter Lawrence 5 major advantage of Drosphila: each stripe in the embryo corresponds to certain body parts in adult fly Image removed due to copyright considerations. 6 MOVIE ! http://flymove.uni-muenster.de Image removed due to copyright considerations. 7 Pioneering experiments by Klaus Sander (1958) on leaf-hoppers Image removed due to copyright considerations. 8 ligation and transplantation experiments indicate the presence of morphogens created/destroyed at the poles of the embryo Image removed due to copyright considerations. 9 First morphogen: bicoid (true maternal) transplantation of bicoid can rescue cells Image removed due to copyright considerations. head fold shift to right for increasing number of gene copies in mother 10 interpreting the bicoid gradient (created by maternal effects) by zygotic effect (gene expression by embryo itself) Image removed due to copyright considerations. 11 Image removed due to copyright considerations. hunchback reads the bicoid gradient 12 recent experimental paper explores relation between bicoid and hunchback quantitatively: Houchmandzadeh et al. Nature 415, 798 (2002). Image removed due to copyright considerations. 13 How can you make a steep step in hunchback exactly in the middle of the embryo from a noisy bicoid gradient ? Nobody knows ... Second example: Robustness of Drosophila patterning Eldar et al., Nature 419, 304 (2002) 14 remember robustness of chemotaxis (L9-10): Image removed due to copyright considerations. 15 explore robustness in Drosophila patterning Image removed due to copyright considerations. 16 main molecules of interest: Scw: BMP (bone morphogenic protein) ligand Sog: a BMP inhibitor Tld: protease (cleaves Sog) 17 simple reaction-diffusion model: ]][[][]][[ ][][ ]][[][]][[ ][][ ]][[][]][[ ][][ 2 2 2 2 2 2 ScwSogTldScwSogkScwSogk x ScwSog D t ScwSog ScwSogTldScwSogkScwSogk x Scw D t Scw SogTldScwSogkScwSogk x Sog D t Sog bbC bbBMP bbS ????+ ? ?? = ? ?? ?+?+? ? ? = ? ? ??+? ? ? = ? ? ? ? ? λ λ α what does this mean ? 18 robustness analysis 19 Image removed due to copyright considerations. ]][[][]][[ ][][ ]][[][]][[ ][][ ]][[][]][[ ][][ 2 2 2 2 2 2 ScwSogTldScwSogkScwSogk x ScwSog D t ScwSog ScwSogTldScwSogkScwSogk x Scw D t Scw SogTldScwSogkScwSogk x Sog D t Sog bbC bbBMP bbS ????+ ? ?? = ? ?? ?+?+? ? ? = ? ? ??+? ? ? = ? ? ? ? ? λ λ α why robust, ideal model: D BMP =0, α=0, k -b =0 ]][[]][[ ][ 0 ]][[]][[00 ]][[ ][ 0 2 2 2 2 ScwSogTldScwSogk x ScwSog D ScwSogTldScwSogk ScwSogk x Sog D bC b bS ??+ ? ?? = ?+?= ? ? ? = λ λ S b D k Scwx = ? ? ][ 1 2 2 20