Developing Models in Virtual Cell

Susana Neves, Ph.D.

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• Part 1: Compartmental Models (ODE models)• Compartments• Components and Reactions• Kinetics• Applications

• Part 2: Spatial Models (PDE models)• Geometries• Diffusion Coefficients

– Experimental approaches» FRAP» FCS

– Estimation of Diffusion coefficents• Reactions

– FRET

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Vcell Requirements

• Registration• Java

• Version 1.5 or later

• Internet connection• Vcell.org

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Steps to Develop A Kinetic Model

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Time course Dose response

Vcell Organization

BioModelrepresentation of the model: compartments, molecules, connectivity map, kinetics

Applications initial conditions: initial concentrations, diffusion coefficients, actual morphologies, electrical protocols, etc.

Simulations time length, time step, sampling rate, resolution, solvers to use, parameter overrides, etc.

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BioModels

compartments

molecules

biomodels Applications

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Compartments

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Compartments

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Molecules

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Molecules

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Reactions

reactions

fluxes

connectors

Right click on compartment of interest and select reactions

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Reactions

Reactants connect to the left of the reaction icon, products to the right

Enzymes connect to the center of the reaction icon

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Reactions

• Kinetic Type:– General– Mass Action– Henri Michaelis-Menten (irreversible)– Henri Michaelis-Menten (reversible)

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Mass ActionRight click on reaction icon; select properties

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Enzymatic

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ODE applicationRight click on Biomodel icon in the application box; select create deterministic application

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ODE applicationInput the volume and surface of your compartment. In this case we assume cytosol to be a sphere with a radius of 10 um

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ODE application

Select the “initial concentrations” tab. Input the initial concentrations of your molecules. Cytosolic molecules have units of uM. Membrane molecules have units of molecules/um2

Select “clamped” if the molecule of interest is supposed to be buffered (not limiting, endless supply).

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ODE applicationFor each application, it is possible to disable specific reactions under the “reaction mapping tab”

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ODE applicationSelect ”Simulation” tab and click on New, and then edit

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ODE applicationUnder the parameters tab, there will be a list of all the parameters in your application/biomodel (initial concentrations, kinetic parameters, etc).By selecting “scan” you can run several simulations simultaneously with different combinations of parameters.

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ODE applicationUnder the task tab, input the length of the simulation (in seconds), and the sampling rate (how many time samples you want to retrieve in your results)

Under the advanced tab, select solver (either variable time step or fixed time step)

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ODE applicationUpon completion, view graph results by selecting variable of interest; multiple variables can be selected by holding the ctrl key.

Right clicking on graph will allow you to change the scale of the graph.

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ODE application

Results can also be viewed in a table format. To copy data, right click25

ODE applicationTo export multiple variables, click on export tab, and select time interval and variables of interest. You will get a zipped comma-delimited ASCII file that you can open in Excel.

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Part 2

• Part 2: Spatial Models (PDE models)• Geometries• Diffusion Coefficients

– Experimental approaches» FRAP» FCS

– Estimation of Diffusion coefficents

• Reactions– FRET

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PDE Application

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Upload geometry

File->New-> Geometry -> from image -> from file

Image•Tiff format•Grayscale 8 bit•Each compartment should have its own gray-scale coloring

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Geometry

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Geometry

((x*x+y*y)<100.0)

File>New>Geometry>Analytic>2-D

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Virtual Cell

ΔV volume elementΔS surface delineating

the volume element

10 x 10 elements

The more intricate the geometry, the smaller the mesh (more elements per unit area)

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Spatial Models

Assuming that the volume element ΔV, is small enough to ignore any spatial changes within it,

net flux of the species X across the surface ΔS, delineating the volume element; jn,X is the flux density

reaction term, sum of all the reaction rates vX that affect the species X.

Slepchenko BM. et al., Trends in Cell Bio 13:570 (2003)35

PDE Application

Rate = (J_MEK_activates_MAPK - J_PP2A_MAPK - J_PTP - J_PTP_PKA)

J_MEK_activates_MAPK = (Vmax_MEK_activates_MAPK * MAPK_cyto / (Km_MEK_activates_MAPK + MAPK_cyto)

J_PTP = (Vmax_PTP * MAPK_active_cyto / (Km_PTP + MAPK_active_cyto) J_PTP_PKA = (Vmax_PTP_PKA * MAPK_active_cyto / (Km_PTP_PKA + MAPK_active_cyto) J_PP2A_MAPK = (Vmax_PP2A_MAPK * MAPK_active_cyto / (Km_PP2A_MAPK + MAPK_active_cyto)

PdeEquation MAPK_active Rate (J_MEK_activates_MAPK - J_PPase_MAPK - J_PTP - J_PTP_PKA);Diffusion MAPK_active_cyto_diffusionRate;Initial MAPK_active_cyto_init;

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Geometry reconstructed from serial stacks of purkinje neuron

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PDE application

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PDE Application

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PDE Application

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PDE Application

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FRAP

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http://vcell.org/vcell_software/user_materials.html

FRAP tutorial

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FCS

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Diffusion coefficent

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GFPGFP

MW

MWD D

Where DGFP = 25 m2/s,

and MWGFP = 27 kDa.

FRET

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Comparing simulations to FRET imaging experiments

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Modifiers

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Modifiers

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Modifiers

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Modifiers

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Parameter Estimation

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Parameter Estimation

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Parameter Estimation

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PDE model of PIP2 in spines

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Brown SA, et al.,. Analysis of phosphatidylinositol-4,5-bisphosphate signaling in cerebellar Purkinje spines. Biophys J. 2008 Aug;95(4):1795-812.

PDE model of Ca++ in neuroblastoma cells

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Fink CC, Slepchenko B, Moraru II, Watras J, Schaff JC, Loew LM. An image-based model of calcium waves in differentiated neuroblastoma cells. Biophys J. 2000 Jul;79(1):163-83.

PDE model of nuclear Ran transport

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Smith AE, Slepchenko BM, Schaff JC, Loew LM, Macara IG. Systems analysis of Ran transport. Science. 2002 Jan 18;295(5554):488-91

PDE model of signaling microdomains

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Neves SR, Tsokas P, Sarkar A, Grace EA, Rangamani P, Taubenfeld SM, Alberini CM, Schaff JC, Blitzer RD, Moraru II, Iyengar R. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell. 2008 May 16;133(4):666-80

www.sciencesignaling.org

Slides from a lecture in the course Systems Biology—Biomedical Modeling

Citation: S. R. Neves, Developing models in Virtual Cell. Sci. Signal. 4, tr12 (2011).