Introduction to Biological odeling Lecture : odeling dynamics Sept. 9, 010 Steve Andrews Brent lab, Basic Sciences Division, FHCRC Last week Why model biology? Example: E. coli chemotaxis Typical modeling progression Think about What aspects of your research are ready for modeling? What might you learn from it? Reading Tyson, Chen, and Novak Sniffers, buzzers, toggles, and blinkers: dynamics of regulatory and signaling pathways in the cell Current Opinion in Cell Biology 15:1-31, 003. 1 Dynamic cells Tyson, 1991 initial good model of eukaryotic cell cycle All cell systems are dynamic cell cycle circadian rhythms signaling development cell motility apoptosis metabolism* 3 4 Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 5 Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 6
Eukaryotic cell cycle Cell cycle checkpoints mitosis Cycle times gap gap 1 8 min. in fly embryo 30 min. in Xenopus early embryo 1 hours in fast growing mammalian tissues year or longer in mammalian liver stopped in human neurons and skeletal muscles DNA synthesis 7 Cell cycle checkpoints 8 Cyclins and Cdk Cdk = cyclin dependent kinase p34, from mol. weight Cdc8 in budding yeast Cdk1 in human cdc in fission yeast Question How does the controller work? cyclin lots of different cyclins Cdk + cyclin = Start kinase 9 Xenopus life cycle 1st round of meiosis stops at G checkpoint cycling stopped egg travels down oviduct rapid cell divisions and is laid without growth nd round of meiosis stops at metaphase arrest fertilization 10 and cyclin in early embryo cell divisions depend on growth midblastula transition 11 1
Cell cycle network Step Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 13 Credit: http://satyaprakashnayak.com/projects.html, which says it s from Tyson and Novak. 14 Tyson s model (1991) Tyson s model (1991) P P includes core cdc-cyclin interactions P P aa = amino acids ignores cdc phosphorylation at T167 attributes cyclin degradation to phosphate, not ubiquitin enhancement of cyclin degradation cell size control, wee1, and cdc5 downstream effects assumptions total amount of cdc is fixed phosphorylation in rxn 3 is much faster than dimerization several parameter relations... Credit: Alberts, et al. olecular Biology of the Cell, 3rd ed., 1994; Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 15 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 16 Tyson s model (1991) Step Step 3 * [CT] = total cdc Note any parameters don t matter, and so are set to 0, or >>k? Fewer parameters are needed by grouping multiple unknowns together, e.g. k 1 [aa]/[ct] The model is explored with respect to the adjustable parameters. Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 17 Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 18
From reactions to equations From reactions to equations YP ass action kinetics: reaction ~ reactant concentrations C YP ass action kinetics: reaction ~ reactant concentrations C p Y CP p Y CP All straight-forward, except reaction 4 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 19 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 0 p Reaction 4: positive feedback F With feedback = [ p ]F([ ]) d No feedback d ([ ]) =! = k 4 [ p ] " % k 4 + k 4 CT & ' production positive feedback no feedback limited by p p Positive feedback can cause bistability Add in reaction 5 d production " " % % = [ p ] k 4! + k 4 [ CT ]& ' & ' ( k ~ P 5 loss [ ] * [CT] = total cdc, which is constant in this model Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 1 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. p Positive feedback can cause bistability Add in reaction 5 d production " " % % = [ p ] k 4! + k 4 [ CT ]& ' & ' ( k ~ P 5 loss [ ] fixed points production = loss d[]/ = 0 p Positive feedback can cause bistability Add in reaction 5 d production " " % % = [ p ] k 4! + k 4 [ CT ]& ' & ' ( k ~ P 5 loss [ ] fixed points production = loss d[]/ = 0 stable points, 1 unstable point Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 3 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 4
The mathematical model Step YP C Step 4 Step 3 p Y CP Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 5 Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 6 Simulation tools Excel - surprisingly good for very simple models, Getting the Tyson 1991 model Cell Cycle Database: http://www.itb.cnr.it/cellcycle/ Lots of good cell cycle information atlab - excellent multi-purpose tool, lots of extensions, athematica - also excellent; better for analytical work, Copasi - designed for cell biology simulations, has GUI SBW - Systems Biology Workbench, front end to lots of simulators. lots of others... 7 8 odels section has 6 cell cycle models 14 in SBL 1 simulable modules Cell cycle database models SBL Systems Biology arkup Language XL language A computer-readable standard language that many simulators use. <reaction metaid="_000011" id="reaction" name="cdck phosphorylation" reversible="false"> <listofreactants> <speciesreference species="c"/> </listofreactants> <listofproducts> <speciesreference species="cp"/> </listofproducts> <kineticlaw> <math xmlns="http://www.w3.org/1998/ath/athl"> <apply> <times/> <ci> cell </ci> <ci> C </ci> <ci> k8notp </ci> </apply> </math> <listofparameters> <parameter metaid="_84013" id="k8notp" value="1000000"/> </listofparameters> </kineticlaw> </reaction> Bioodels database http://www.ebi.ac.uk/biomodels-main/ lots of published models, all written in SBL 9 30
Simulation results stable oscillations k4 = 180 min-1, k6 = 1 min-1 similar to early embryo oscillations total cyclin Get the model from either Cell Cycle Database and simulate its simulable module, or get it from Bioodels and simulate it with Copasi. 31 3 Credit: Alberts, et al. olecular Biology of the Cell, 3rd ed., 1994; Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. Simulation results Simulation results Phase diagram for system behaviors stable steady-state, but excitable k4 = 180 min-1, k6 = min-1 metaphase arrest similar to late embryo growth-limited cell cycle; sustained cycles excitable A a large enough perturbation triggers excitation Credit: Alberts, et al. olecular Biology of the Cell, 3rd ed., 1994; Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 33 B C 34 Credit: Alberts, et al. olecular Biology of the Cell, 3rd ed., 1994; Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. Simulation results Growth-limited cycles Phase diagram for system behaviors metaphase arrest cell volume increase lowers k6 lower k6 triggers mitosis DNA replication doubles k6 sustained cycles Step excitable Step 3 Step 4 Step 5 A B C Credit: Alberts, et al. olecular Biology of the Cell, 3rd ed., 1994; Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 35 Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 36
Summary of model results Good aspects biology is basically correct represents all 3 Xenopus cell cycle stages: metaphase arrest, early embryo, and growthlimited cycling and cyclin curves qualitatively agree with experiment Bad aspects roles of cdc5 and wee1 are not clear positive feedback F([]) is ad hoc k 6 oscillation in growth-limited cycling is speculative Step 5 Step 4 Step Step 3 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 37 Credit: Shaffer et al., ethods in olecular Biology, Systems Biology, (aly, ed.) 500:81, 009. 38 Step 6 A subst-depletion oscillator Sniffers, buzzers, toggles, and blinkers interpretation A subst-depletion oscillator Sniffers, buzzers, toggles, and blinkers interpretation Cdc5 inactive inactive Cdc5p Cdc5 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991; Tyson et al. Current Opinion in Cell Biology 15:1, 003. 39 Credit: Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991; Tyson et al. Current Opinion in Cell Biology 15:1, 003. 40 A subst-depletion oscillator Summary cyclin degraded cyclin Cell cycle overview odel development odel equations from reactions mass action kinetics Positive feedback can cause bistability Parameter choices few matter, group as possible, explore some Databases Cell cycle database, Bioodels Simulation tools Copasi Tyson s model results metaphase arrest, early embryo, growth-limited Generalizing results Credit: http://www.aspencountry.com/product.asp?dept_id=460&pfid=3519; Tyson, Proc. Natl. Acad. Sci. USA 88:738, 1991. 41 4
Homework Copasi Download Copasi (Google for copasi download and explore some of the examples that come with it. Read Covert, Schilling, Famili, Edwards, Goryanin, Palsson, etabolic modeling of microbial strains in silico TRENDS in Biochemical Sciences 6:179, 001. 43