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

Teaching Modeling and Quantitative Cell Biology

R.M. Holmes, A. Cowan, I. Moraru, J Schaff, B. Slepchenko, L.M.Loew

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?

Measure quantitative parameters: concentrations, diffusion coefficients, kinetic constants.

Microscopy

Cell culture

Molecular biology

Pharmacological treatments

Genetic manipulations

Quantitative Cell BiologyQuantitative 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?

ExperimentExperiment

Trends in Cell Biology 13:570-576 (2003)

Curricular Questions for QCB

• What topics?– Computing:

• Applications? Programming? Software Design?

– Mathematics• Statistics? Algebra? Discrete math? Topology?

– Biology• Molecular? Cellular?...

Multiple answers

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?

The Classrooms

UndergraduateCourse: 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.

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

Undergraduate

From Concepts to Concept Maps and Kinetic Reactions

Walking through a Computational Model

• Concept Map

• Factors and relationships between factors

• Describe relationships mathematically

• Solve equations: using computer tools

• View and interpret results

The Cell Cycle “logic”

Kohn, 1999

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

V1=constant V4=k*MPF V2=k*Cyclin*X V5=k*MPF*iX V3=k*iMPF*Cyclin V6=k*X

Mass Action Rate Equations

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

Student models

2.3log [S]0/[S] = kt

 S=Substratek=Rate Constantt=Time Ex. Wee1 activation constant[S]= 100 [S] = 50 t = 7.52.3log (100/50) = 7.5kk = 0.092 nM-1 min-1

Figure 2. Wee1 model 

Eq. 1

Wee1 and Cdc25 regulation of Cell Cycle

Chung, Morgan-Wesiburg and Murphy

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

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.

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All known interacting proteins

3. The following are needed to make a mathematical model of the cell cycle:

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Feedback loop

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Rate equations D. Differential equations

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

Graduate Classes

Ann Cowan

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.orghttp://vcell.org

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 DescriptionMath DescriptionMath Description

VCMDL

Simulations

Timestep,Mesh Size,ParameterSearches,Sensitivity Results

Simulations

Timestep,Mesh Size,ParameterSearches,Sensitivity Results

Simulations

Timestep,Mesh Size,ParameterSearches,Sensitivity Results

Simulations

Timestep,Mesh Size,ParameterSearches,Sensitivity Results

Physiology

Molecular SpeciesCompartment Topology

Reactions and Fluxes

VCDB

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

Exercise: Fluorescence Redistribution After Photobleaching - FRAP

Average Intensity in bleached region (background subtracted)

APC1e APC1 APC1b APC1a

size of bleach region (msq) 309.76 77.44 19.36 4.84

averaged prebleach intensityF(-) 104.0073 84.25763 109.4 107.942

t (secs)        

-2.5 103.945 84.12125 110.4375 107.6

-2 104.1719 84.37938 109.7 108.05

-1.5 104.1142 84.34 110.0925 108.44

-1 104.012 84.17938 108.365 108.37

-0.5 103.7936 84.26813 108.405 107.25

0 6.323438 12.25188 33.55 61.75

0.5 9.98875 23.01438 57.615 81.88

1 12.90063 30.79 68.575 89.41

1.5 15.36344 36.56875 75.7275 91.16

2 17.63766 40.71438 79.665 93.65

2.5 19.61688 44.25563 83.215 95.2

3 21.30547 46.685 85.295 96.53

Fluorescent Intensity Measures

Photobleaching of cytoplasmic components

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Whole cell

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

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.

Analysis of Photobleaching using computational modeling

First define a physiological model – start with a single compartment and single diffusing species.

Analysis of Photobleaching using computational modeling

Import 2D or 3D geometry from microscope images

Analysis of Photobleaching using computational modeling

Create an ApplicationIn this case, the initial concentration of APC is set to 10μM except in bleached region, a 6 X 9 μm rectangle.

Analysis of Photobleaching using computational modeling

Create and run a simulation (movie)

Analysis of Photobleaching using computational modeling

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Cell Data

VCell data

Compare simulation results with actual experiment

D = 5 um2/s

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.

)0()(

)0()()(

ii

iii FF

FtFtf

Evaluation

• Proper calculations

• Running Simulation

• Appropriate construction of model

• Interpretation of results

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

Resources

http://nrcam.uchc.edu/education/

Exercises available 12/6/07

Available 12/21/07

Published Models

http://vcell.org

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)