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Teaching Modeling and Quantitative Cell Biology R.M. Holmes, A. Cowan, I. Moraru, J Schaff, B. Slepchenko, L.M.Loew

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Cell Biology Cell migration, adhesion, cell cycles, signaling Frogs, fruit flies, worms, plants, bacteria Differentiation, proliferation, morphogenesis… Wound healing, reproduction, angiogenesis Key question: Which particular factors and interactions are required or sufficient for a biological behavior?

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Measure quantitative parameters: concentrations, diffusion coefficients, kinetic constants. Microscopy Cell culture Molecular biology Pharmacological treatments Genetic manipulations

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Quantitative Cell Biology Predictions Dynamics of Cellular Structures and Molecules Simulation Hypothesis (Model) What are the initial concentrations, diffusion coefficients and locations of all the implicated molecules? What are the rate laws and rate constants for all the biochemical transformations? What are the membrane fluxes and how are they regulated? How are the forces controlling cytoskeletal mechanics regulated? Experiment Trends in Cell Biology 13:570-576 (2003)

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Curricular Questions for QCB What topics? –Computing: Applications? Programming? Software Design? –Mathematics Statistics? Algebra? Discrete math? Topology? –Biology Molecular? Cellular?... Multiple answers

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Depend on educational goals Undergraduate: concepts in biology –What is a cell? What are organelles? How does the cell know when to divide? Graduate: methods and tools for research –What questions can be addressed with…, –what tools are available, how do they work?

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The Classrooms Undergraduate Course: Cellular, Developmental Biology Research project on Computer Modeling Cell Cycle Stella, Basic kinetics Concepts of cell cycle Evaluation: Presentation of model, interpretation of results Survey Graduate Courses: Cell Biology, Biochemistry Lecture and Homework –Using VCell to create model and analyze FRAP –Using VCell model to explore biology Evaluation: Model creation, correct simulation result.

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Common Approach Three different faculty and contexts Use published research literature –e.g. Cell Cycle, PIP2 signaling, Nuclear Transport Use simulation software –Stella, Virtual Cell Work with basic reaction kinetics

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Undergraduate From Concepts to Concept Maps and Kinetic Reactions

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Walking through a Computational Model Concept Map Factors and relationships between factors Describe relationships mathematically Solve equations: using computer tools View and interpret results

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The Cell Cycle logic Kohn, 1999

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Cell Cycle Diagrams Draw flow diagrams/concept map for the statements provided below. Keep your hand drawings and turn them in. 1. System statements –inactive MPF becomes active MPF –Active MPF becomes inactive MPF 2. System statements –Cyclin is synthesized and degraded –Cyclin stimulates inactive MPF to become active MPF First Exercise

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V1=constant V4=k*MPF V2=k*Cyclin*X V5=k*MPF*iX V3=k*iMPF*Cyclin V6=k*X Mass Action Rate Equations

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Evaluation In the models Constructing correct relationships between biological factors Ability to write kinetic equations Describe and interpret graphed results Examinations Answer questions about biology and/or modeling

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Student models 2.3log [S] 0 /[S] = kt S=Substrate k=Rate Constant t=Time Ex. Wee1 activation constant [S]= 100 [S] = 50 t = 7.5 2.3log (100/50) = 7.5k k = 0.092 nM -1 min -1 Figure 2. Wee1 model Eq. 1 Wee1 and Cdc25 regulation of Cell Cycle Chung, Morgan-Wesiburg and Murphy

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Student models We believe that our results support our hypothesis that the cycin-cdc2 binding rate affects the cell cycle. As binding rate increases in relation to dissociation rate, oscillation frequency and amplitude increases; the reverse is true when dissociation rate is greater. Effect of cyclin-cdc2 binding rates on cell cycle progression

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1. Proteins in the cell cycle are regulated by phosphorylation and the formation of protein-protein complexes. 2. Cyclin degradation is required for cell cycle progression. Biological Concepts

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All known interacting proteins 3. The following are needed to make a mathematical model of the cell cycle: Feedback loop Rate equationsD. Differential equations

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Summary 1 Creating models of well described biological systems –Learn key biological concepts –Learn basics of creating numerical models –Work with basic reaction kinetics –Familiar with simulation tool What was missing –Stronger ties to data generation Image analysis Cell population growth

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Graduate Classes Ann Cowan

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Designed to be used interactively with experiment Enables construction and testing of complex models or rapid investigation of simple hypotheses Geometry from experimental images Math, physics, and numerics are transparent to an experimentalist while fully accessible to a theorist Collaborative distributed database and problem solving environment http://vcell.org

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Applications Topology Geometry, Initial Conditions, Boundary Conditions, Diffusion Coefficients, Pseudo-steady, Enable/Disable Reactions Images Applications Topology Geometry, Initial Conditions, Boundary Conditions, Diffusion Coefficients, Pseudo-steady, Enable/Disable Reactions Images Applications Topology Geometry, Initial Conditions, Boundary Conditions, Diffusion Coefficients, Pseudo-steady, Enable/Disable Reactions Images Applications Topology Geometry, Initial Conditions, Boundary Conditions, Diffusion Coefficients, Pseudo-steady, Enable/Disable Reactions Electrophysiology Protocols Images Math Description VCMDL Simulations Timestep, Mesh Size, Parameter Searches, Sensitivity Results Simulations Timestep, Mesh Size, Parameter Searches, Sensitivity Results Simulations Timestep, Mesh Size, Parameter Searches, Sensitivity Results Simulations Timestep, Mesh Size, Parameter Searches, Sensitivity Results Physiology Molecular Species Compartment Topology Reactions and Fluxes

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VCDB

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1.Examine simulation results for injection applications of importin alpha cargo and importin beta cargo models. Which cargo is imported into the nucleus faster? 2.Predict the effects of a mutation in Ran that prevents GTP hydrolysis on the nuclear transport system. How would you introduce this mutation into the model. 3. Propose a specific change in one of the reactions in the nuclear transport model. Predict the effects of the proposed change on the nuclear transport system. Class: Logic of Modern Biology

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Exercise: Fluorescence Redistribution After Photobleaching - FRAP

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Average Intensity in bleached region (background subtracted) APC1eAPC1APC1bAPC1a size of bleach region (msq)309.7677.4419.364.84 averaged prebleach intensityF(-)104.007384.25763109.4107.942 t (secs) -2.5103.94584.12125110.4375107.6 -2104.171984.37938109.7108.05 -1.5104.114284.34110.0925108.44 104.01284.17938108.365108.37 -0.5103.793684.26813108.405107.25 06.32343812.2518833.5561.75 0.59.9887523.0143857.61581.88 112.9006330.7968.57589.41 1.515.3634436.5687575.727591.16 217.6376640.7143879.66593.65 2.519.6168844.2556383.21595.2 321.3054746.68585.29596.53 Fluorescent Intensity Measures

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Photobleaching of cytoplasmic components Methods for analyzing the data start with an appropriate model of the biology

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Fluorescent Recovery After Photobleaching There is no universal protocol for FRAP experiments since the design of a FRAP experiment always has to take into account the geometry of the experiment and the bleaching and redistribution characteristics of the molecule under investigation. I.e. no good way to get D from previous curve. –Can from simulation.

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Analysis of Photobleaching using computational modeling First define a physiological model – start with a single compartment and single diffusing species.

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Analysis of Photobleaching using computational modeling Import 2D or 3D geometry from microscope images

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Analysis of Photobleaching using computational modeling Create an Application In this case, the initial concentration of APC is set to 10μM except in bleached region, a 6 X 9 μm rectangle.

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Analysis of Photobleaching using computational modeling Create and run a simulation (movie)

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Analysis of Photobleaching using computational modeling Compare simulation results with actual experiment D = 5 um 2 /s

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Homework 1. Plot 4 sets of data with different bleach sizes on one plot: Normalize the data to vs. (t/msqi), where Fi(t) is the fluorescence as a function of time t. 2. Construct model in VCell of diffusing species.

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Evaluation Proper calculations Running Simulation Appropriate construction of model Interpretation of results

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Conclusions Graduate Courses –Use of complex models enable students to examine multiple relationships within accepted biological model –Simple experimental frameworks can provide rich in quantitative data –Simple models can be used to obtain parameter values (D and mobile fraction) from experimentts Overall –Classes of 10-20 –Creating and exploring models Better understand molecular interactions Appreciation for quantitation, kinetics and behaviors Appreciation for modeling process

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Resources http://nrcam.uchc.edu/education/ Exercises available 12/6/07 Available 12/21/07 Published Models http://vcell.org

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The Virtual Cell Project John Carson Yung-Sze Choi Ann Cowan Fei Gao Susan Krueger Anu Lakshminarayana Frank Morgan Igor Novak Diana Resasco Li Ye Rashad Badrawi* Nick Hernjak* Daniel Lucio* John Wagner* (*alumni)

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