Mathworks SIMBIOLOGY 3 Model Reference

Download

SimBiology

Model Reference

How to Contact The MathWorks

www.mathworks. comp.soft-sys.matlab Newsgroup www.mathworks.com/contact_TS.html T echnical Support

suggest@mathworks.com Product enhancement suggestions

bugs@mathwo doc@mathworks.com Documentation error reports service@mathworks.com Order status, license renewals, passcodes

info@mathwo

com

rks.com

Web

Bug reports

Sales, prici

ng, and general information

508-647-7000 (Phone)

508-647-7001 (Fax)

The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098

For contact information about worldwide offices, see the MathWorks Web site.

SimBiology

The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathW orks, Inc.

FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. By accepting delivery of the Program or Documentation, the government hereby agrees that this software or documentation qualifies as commercial computer software or commercial computer software documentation as such terms are used or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and govern theuse,modification,reproduction,release,performance,display,anddisclosureoftheProgramand Documentation by the federal government (or other entity acquiring for or through the federal government) and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the government’s needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Docu mentation, unused, to The MathWorks, Inc.

Trademarks

MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See

www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand

names may be trademarks or registered trademarks of their respective holders.

Patents

The MathWorks products are protected by one or more U.S. patents. Please see

www.mathworks.com/patents for more information.

Model Reference

Revision History

September 2005 Online only New for Version 1.0 ( Release 14SP3+) March 2006 Online only Updated for Version 1.0.1 (Release 2006a) May 2006 Online only Updated for Version 2.0 (Release 2006a+) September 2006 Online only Updated for Version 2.0.1 (Release 2006b) March 2007 Online only Rereleased for Version 2.1.1 (Release 2007a) September 2007 Online only Rereleased for Version 2.1.2 (Release 2007b) October 2007 Online only Updated for Version 2.2 (Release 2007b+) March 2008 Online only Updated for Version 2.3 (Release 2008a) October 2008 Online only Updated for Version 2.4 (Release 2008b) March 2009 Online only Updated for Version 3.0 (Release 2009a) September 2009 Online only Updated for Version 3.1 (Release 2009b) March 2010 Online only Updated for Version 3.2 (Release 2010a)

Minimal Cascade Model for a Mitotic Oscillator

Goldbeter Model ................................... 1-2

About the Goldbeter M odel Reaction De scriptions and Model Assum ptions Mathematical Model

.......................... 1-2

......... 1-3

............................... 1-4

Contents

SimBiology Model with Rate Rules

SimBiology Model with Rules SimBiology Simulation with Rules

SimBiology Model with Reactions

Converting Differential Rate Equations to Reactions Calculating Initial Values for Reactions SimBiology Simulation with Reactions

References

........................................ 1-21

........................ 1-6

.................. 1-6

................... 1-9

................... 1-10

............... 1-12

................ 1-20

Model of the Yeast Heterotrimeric G Protein

Objectives ........................................ 2-2

Background on G Protein Cycles

GProteins G Proteins and Pheromone Response

....................................... 2-3

.................... 2-3

................. 2-4

..... 1-10

Cycle

Modeling a G Protein Cycle

Reactions Overview Assumptions, Experimental Data, and Units in the G

Protein Model

................................ 2-5

.................................. 2-7

......................... 2-5

Building the G Protein Cycle Model ................. 2-10

Tutorial Goals Opening the SimBiology Desktop Saving Your Work as a SimBiology Project File Adding a Reaction to the SimBiology Model Determining the Reaction Rate Equation Setting the Compartment Name Setting Initial Amounts of Species

.................................... 2-10

..................... 2-11

......... 2-12

............ 2-13

.............. 2-15

..................... 2-17

.................... 2-18

Completing the SimBiology Model

Reactions Alternative Ways to Build Reactions in the Desktop Parameters Species Creating a Rule for the G Protein Model Verifying the Model

Simulating the G Protein Cycle Model

Setting Conditions Before Simulating the G Protein

Model

Simulation Results for the Wild-Type Strain Model

Creating the Mutant Strain Using a Variant

Modeling the Mutant Strain Applying Alternate Values Using Variants Simulation Results for the Model of the Mutant Strain

Creating a Custom Plot-Type to View Simulation

Results

Creating a Custom Plot Visualizing Results for the Mutant Strain Using a Custom

Plot

........................................ 2-19

...................................... 2-22

.......................................... 2-23

................................ 2-26

......................................... 2-27

......................... 2-34

......................................... 2-37

............................ 2-37

........................................... 2-42

.................. 2-19

............... 2-25

............... 2-27

.......... 2-34

............. 2-34

..... 2-20

...... 2-31

... 2-35

vi Contents

Plotting Species from Two Different Data Sets

Procedures De scribed in This Section Plotting the Active G Protein Fraction from the Wild-Type

Strain Model Creating a Custom Plot to Compare the Data Plotting the Active G Protein Fraction from the Model of

the Mutant Strain

................................... 2-44

............................... 2-46

................. 2-44

....... 2-44

........... 2-45

Plotting Experimental Data with Simulation Data .... 2-48

About the Experimental Data Creating a Custom Plot for Experimental Data Plotting the Data

.................................. 2-49

....................... 2-48

......... 2-48

References

........................................ 2-52

M-Phase Control in Xenopus Oocyte Extracts

M-Phase Control Model ............................ 3-2

Synthesis Reactions Regulation Reactions with Active MPF

M-Phase Control Equations

About the Rate Equations in This Example Converting Differential Equations to Reactions Equation 1, Cyclin B Equation 2, M-Phase Promoting Factor Equation 3, Inhibited M-Phase Promoting Factor Equation 4, Inhibited and Activated M-Phase Promoting

Factor Equation 5, Activated M-Phase Promoting Factor Equation 11, Cell Division Control 25 Equation 12, Wee1 Activation/Deactivation Equation 13, Intermediate Enzyme

Activation/Deactivation Equation 14, APC Activation/Deactivation Equation 17, Rate Parameter K2 Equation 18, Rate Parameter Kcdc25 Equation 19, Rate Parameter Kwee1

......................................... 3-8

............................... 3-2

................ 3-2

......................... 3-4

............ 3-4

......... 3-4

............................... 3-6

............... 3-6

....... 3-7

....... 3-8

................. 3-9

............ 3-10

.......................... 3-10

............. 3-11

..................... 3-11

................. 3-12

.................. 3-12

SimBiology Model with Rate and Algebraic Rules

Overview Writing Differential Rate Equations as Rate Rules Species Parameters Rate Rule 1, Cyclin B (CycB) Rate Rule 2, M-Phase Promoting Factor (MPF)

........................................ 3-13

.......................................... 3-14

...................................... 3-15

........................ 3-16

......... 3-17

.... 3-13

...... 3-14

vii

Rate Rule 3, Inhibited M-Phase Promoting Factor

(pMPF)

Rate Rule 4, Activated but Inhibited M-Phase Promoting

Factor (pMPFp)

Rate Rule 5, Activated M-Phase Promoting Factor

(MPFp) Rate Rule 11, Activated Cdc25 (Cdc25p) Rate Rule 12, Inhibited Wee1 (Wee1p) Rate Rule 13, Activated Intermediate Enzyme (IEp) Rate Rule 14, Activated APC (APCa) Algebraic Rule 17, Rate Parameter K2 Algebraic Rule 18, Rate Parameter Kcdc25 Algebraic Rule 19, Rate Parameter Kwee1 Simulation of the M-Phase Control Model with Rules

SimBiology Model with Reactions and Algebraic

Rules

Overview Reaction 1, Synthesis of Cyclin B Reaction 2, Degradation of Cyclin B Reaction 3, Dimerization of Cyclin B with Cdc2 Kinase Reaction 4, Degradation of Cyclin B on MPF Reaction 5, Deactivation of Active MPF Reaction 6, Activation of MPF Reaction 7, Remove Inhibiting Phosphate from Inhibited

MPF Reaction 8, Inhibition of MPF by Phosphorylation Reaction 11, Degradation of Cyclin B on Inhibited MPF Reaction 12, Deactivation of M PF to Inhibited MPF Reaction 13, Activation of Inhibited MPF Reaction 15, Degradation of Cyclin B on Active but

Inhibited MPF Reaction 16, Inhibit MPF by Phosphorylation Reaction 17, Remove Inhibiting Phosphate from Activated

MPF Reaction 19, Degradation of Cyclin B on Activated MP F Reaction 36, Activation of Cdc25 by Activated MPF Reaction 37, Deactivation of Cdc25 Reaction 38, Deactivation of Wee1 by Active MPF Reaction 39, Activation of Wee1 Reaction 40, Activation o f Intermediate Enzyme by Active

MPF Reaction 41, Deactivation of IE Reaction 42, APC Activation by IEp

........................................ 3-17

................................. 3-18

........................................ 3-18

............... 3-18

................ 3-18

.................. 3-18

................ 3-19

............. 3-19

........................................... 3-21

........................................ 3-22

.................... 3-22

.................. 3-23

........... 3-25

............... 3-26

....................... 3-27

.......................................... 3-28

....... 3-29

.............. 3-31

.................................. 3-32

.......... 3-32

.......................................... 3-33

................... 3-34

....... 3-34

...................... 3-34

......................................... 3-35

...................... 3-35

.................. 3-35

..... 3-18

.... 3-19

... 3-24

.. 3-31

..... 3-31

.. 3-33

...... 3-33

viii Contents

Reaction 43, APC Deactivation ...................... 3-35

Block Diagram of the M-Phase C ontrol Model with

Reactions

Simulation of the M-Phase Control Model with

Reactions

...................................... 3-36

...................................... 3-38

References

........................................ 3-39

Index

x Contents

Minimal Cascade Model for a Mitotic Oscillator

Albert Goldbeter modified a model with enzy me cascades [Goldbeter and Koshland 1981] to fit cell cycle data from studies with embryonic cells [Goldbeter 1991]. He used this model to demonstrate thresholds with enzyme cascades and periodic behavior caused by negative feedback.

TherearetwoSimBiology first model uses the differential rate e quations directly from Goldbeter’s paper. The second model is built with reactions using Henri-Michaelis-Menten kinetics.

• “Goldbeter Model” on page 1-2

• “SimBiology Model w ith Rate Rules” on page 1-6

• “SimBiology Model with Reactions” on page 1-10

• “References” on page 1-21

model variations using Goldbeter’s model. The

1 Minimal Cascade Model for a Mitotic Oscillator

Goldbeter Model

In this section...

“About the Goldbeter Model” on page 1-2

“Reaction D escriptions and Model Assumptions” on page 1-3

“Mathematical Model” on page 1-4

About the Goldbeter Model

Albert Goldbeter created a simple c ell division model from studies w ith embryonic cells [Goldbeter 1991]. This model demonstrates thresholds with enzyme cascades and periodic behavior caused by negative feedback.

There are six species in Goldbeter’s minimal mitotic oscillator model [Goldbeter 1991].

• C — Cyclin. The periodic behavior of cyclin activates and deactivates an

enzyme cascade.

1-2

• M+, M — Inactive (phosphorylated) and active form s of cdc2 kinase.

Kinases catalyze the addition of phosphate groups onto amino acid residues.

• X+, X — Inactive and active (phosphorylated) forms of a cyclin protease.

Proteases degrade proteins by breaking peptide bonds.

The reactions are labeled

r1 to r7 on the following diagram.

This model shows:

• How thresholds with cdc2 kinase activation (M+ -> M) and protease

activation (X+ -> X) can occur as the result of covalent modification (for example, phosphorylation or dephosphorylation), but without the need for positive feedback.

Goldbeter Model

• How periodic behavior with cdc2 kinase activation can occur with negative

feedback and the time delay associated with activation/deactivation enzyme cascades.

Reaction Descriptions and Model Assumptions

The following list describes each of the reactions in Goldbeter’s minimal mitotic oscillator with some of the simplifying assumptions. For a more detailed explanation of the model, see [Goldbeter 1991].

• Cyclin (

rate (r2).

• Cyclin (

the phosphatase that activates the kinase. Inactive cdc2 kinase ( activated by removing inhibiting phosphate groups (r4).

C) is synthesized at a constant rate (r1) and degraded at a constant

C) does not complex with cdc2 kinase (M).

C) activates cdc2 kinase (M+ -> M) by increasing the velocity of

M+)is

1-3

1 Minimal Cascade Model for a Mitotic Oscillator

• The amount of deactivating kinase (not modeled) for the cdc2 kinase (M)

is constant. Active cdc2 kinase (M) is deactivated by adding inhibiting phosphate group (r5).

• The activation of cyclin protease (

direct without other intervening cascades. Cyclin protease (

X+ -> X) by the active cdc2 kinase (M)is

X)isactivated

by adding phosphate groups (r6).

• The amount of deactivating phosphatase (not modeled) for the cyclin

protease (X) is constant. Active cyclin protease (

X) is deactivated by

removing the activating phosphate groups (r7).

• The three species of interest are cyclin (

kinase (

+M+

M), and active phosphorylated protease (X). The total amounts of (M

)and(X + X+) are constant.

C), active depho s ph orylated cdc2

Mathematical Model

Goldbeter’s minimal mitotic oscillator model is defined with three differential rate equations and two algebraic equations that define changing parameters intherateequations.

Differential Rate Equation 1, Cyclin (C)

The following differential rate equation is from [G oldbeter 1991] for cyc lin (C).

vvX

Differential Rate Equation 2, Kinase (M)

The follow ing differential rate equation is for cdc2 kinase (M). Notice that (1-

) is the amount of inactive (phosphorylated) cdc2 kinase (M+).

−

d=−

1-4

11=

−

VM C Kc C

11()

+−

()

[]

−

Goldbeter Model

Differential Rate Equation 3, Protease (X)

Differential rate equations for cyclin protease (X). Notice that (1-X)is the amount of inactive (unphosphorylated) cyclin protease (

X+).

−

()

+−

()

VVMM33= []

−

1-5

1 Minimal Cascade Model for a Mitotic Oscillator

SimBiology Model with Rate Rules

In this section...

“SimBiology Model with Rules” on page 1-6

“SimBiology Simulation with Rules” on page 1-9

SimBiology Model with Rules

In the literature, many biological models are defined using differential rate and algebraic equations. With SimBiology software, you can enter the equations directly as SBML rules. The example in this section uses Goldbeter’s mitotic oscillator to illustrate this point.

Writing differential rate equations in an unambiguous format that a software program can understand is a fairly simple pro cess.

• Use an a sterisk to indicate multiplication. For example,

k*a.

• Remove square brackets that indicate concentration from around

species. The units associated with the species will indicate concentration (

moles/liter) or amount (moles, molecules).

SimBiology software uses square brackets around species and parameter name to allow names that are not valid MATLAB For example, you could have a species named

dehydrogenase

rate and rule equations.

• Use parentheses to clarify the order of evaluation for mathematical

operations. For example, do not write a Henri-Michaelis-Menten rate as

Vm*C/Kd + C,becauseVm*C is divided by Kd before adding C,andthenC is

added to the result.

The following equation is the rate rule for “Differential Rate Equation 1, Cyclin (C)” on page 1-4:

dC/dt = vi - (vd*X*C)/(Kd + C) - kd*C

but you need to add brackets around the name in reaction

glucose-6-phosphate

k[a] is written

variable names.

1-6

SimBiology®Model with R ate Rules

The following equations are the rate and repeatedAssignment rules for “Differential Rate Equation 2, Kinase (M)” on page 1-4:

dM/dt = (V1*Mplus)/(K1 + Mplus) - (V2*M)/(K2 + M) V1 = (VM1*C)/(Kc + C) Mplus = Mt - M

The following equations are the rate and repeatedAssignment rules for “Differential Rate Equation 3, Protease (X)” on page 1-5:

dX/dt = (V3*Xplus)/(K3 + Xplus) - (V4*X)/(K4 + X) V3 = VM3*M Xplus = Xt - X

Species

The following table is a list of species in the model with their in iti al amounts.

The two parameters parameters in the parameter table with the

V1 and V3 are in the species list. You could enter the

ConstantAmount check box es

cleared. Here, the parameters are modeled as species but without reactions .

Parameters

The following table is a list of parameters in the model with their initial values. The ConstantValue property is selected for all the parameters.

1-7

1 Minimal Cascade Model for a Mitotic Oscillator

1-8

Rules

Theactive(M)andinactive(Mplus) forms of the kinase are assumed to be part of a conserved cycle with the total concentration (Mt) remaining constant during the simulation. You need only one differential rate equation with a mass balance equation to define the amounts of both species. Similarly, theactive( conserved cycle.

In the SimBiology desktop, you enter rate rules of the form

Expression Expression"

youcansolveforthevariable,usea algebraic rule. See “What Is a repeatedAssignment Rule?” in the SimBiology documentation.

X)andinactive(Xplus) forms of the protease are part of a second

dX/dt =

as X = Expression, and algebraic rules of the form "X =

, where X is the independent variable, as Expression - X.If

repeatedAssignment rule instead of an

SimBiology®Model with R ate Rules

SimBiology Simulation with Rules

This is a simulation of Goldbeter’s minimal mitotic oscillator using differential rate and algebraic equations. Simulate with the species with Rules” on page 1-6.

C, M,andX. For a d escription of the model, see “SimBiology Model

sundials solver and plot

1-9

1 Minimal Cascade Model for a Mitotic Oscillator

SimBiology Model with Reactions

In this section...

“Converting Differential Rate Equations to Reactions” on page 1-10

“Calculating Initial Values for Reactions” on page 1-12

“SimBiology Simulation with Reactions ” on page 1-20

Converting Differential Rate Equations to Reactions

In the literature, many models are defined with differential rate equations. With SimBiology software, creating the differential equations from reactions is unnecessary; you can enter the reactions and let the software calculate the equations.

Some models are defined with differential rate equations, and you might need the reactions to be compatible with your model. Two rules you can use to convert differential rate equations to reactions are:

1-10

• For a positive term — The species described by the equation is placed

on the right as a product, and the species in the term are placed on the left as reactants.

• For a negative term — The species describe d by the equation is placed

on the left as a product, and the species in the term are also placed on the left as reactants.

You need to determine the products using additional information, for example, a reaction diagram, a description of the model, or an understanding of a reaction. If a reaction is catalyzed by a kinase, then you can conclude that the product has one or more additional phosphate groups.

A simple first-order reaction has differential rate equation

- kf[R]

unknown product. The positive term identifies the product and completes the reaction,

. The negative term implies that the reaction is R->?with an

R<->P.

dR/dt = +kr[P]

SimBiology®Model with Reactions

Reactions R1 to R3 from Equation E1

The differential rate equation 1 is repeated here for comparison with the reactions. See “Differential Rate Equation 1, Cyclin (C)” on page 1-4.

vvX

−

d=−

The reaction and reaction rate equations from the differential rate equation E1 are given below:

r1 reaction: null -> C

reaction rate: vi

r2 reaction: C -> null

reaction rate: kd*C

r3 reaction: C -> null

reaction rate: (vd*X*C)/(Kd + C)

Reactions R4 and R5 from Equation E2

The differential rate equation 2 and algebraic equation 2 are repeated here for comparison with the reactions. See “Differential Rate Equation 2, Kinase (M)” on page 1-4.

−

11()

+−

()

−

VM C

11=

[]

Kc C

[]

The reaction and reaction rate equations from the differential rate equation E2 are given below:

r4 reaction: Mplus -> M

reaction rate: V1*Mplus/(K1 + Mplus)

repeatedAssignment rule: V1 = VM1*C/(Kc + C)

r5 reaction: M -> Mplus

1-11

1 Minimal Cascade Model for a Mitotic Oscillator

reaction rate: V2*M/(K2 + M)

Reactions R6 and R7 from Equation E3

The differential rate equation for equation 3 and algebraic equation 3 is repeated here for comparisonwiththereactions.

−

V3 = VM3*[M]

The reaction and reaction rate equations from the differential rate equation E3 are given below:

r6 reaction: Xplus -> X

repeatedAssignment rule: V3 = VM3*M

r7 reaction: X -> Xplus

reaction rate: V4*X/(K4 + X)

()

+−

()

reaction rate: V3*Xplus]/(K3 + Xplus)

−

Calculating Initial Values for Reactions

After you converted the differential rate equations to the reactions and reaction rate equations, you can start to fill in initial values for the species (reactants and products) and parameters.

The initial values for parameters and amounts for species are listed with four different units in the same dimension:

• A — Original units in the Goldbeter 1991 paper.

1-12

• B — Units of concentration with time converted to second. When converting

atob,use

X uM

minute

• C — Units of amount as moles. When converting concentration to moles,

use a cell volume of

1 minute = 60 second for parameters.

1e-6 mole/liter

1 uM

1e-12 liter and assume that volume does not change.

1 minute

60 second

liter*second

mole

SimBiology®Model with Reactions

Y mole

liter*second

• D — Units of amount as molecules. When converting amount as m oles to

molecules, use

Z mole second

With dimensional analysis on and unit conversion off, select all of the units for one letter. For example, select all of the As. If dimensional analysis and unit conversion are on, you can mix and match letters and get the same answer.

1e-12 liter

6.022e23 molecules = 1 mole.

6.022e23 molecule 1 mole

Z mole second

N molecules

second

Reaction 1 Cyclin Synthesis

reaction

reaction rate vi

parameters

species

null -> C

Value

---- ----

----

0.025

4.167e-10

4.167e-22

205

0.01

1e-8

1.0e-20

6.022e+3

Units

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. molecule/second

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. molecule/second

A. uM

B. mole/liter

C. mole

D. molecule

1-13

1 Minimal Cascade Model for a Mitotic Oscillator

Reaction 2 Cyclin Undifferentiated Degradation

reaction

reaction rate

parameters kd

species

C -> null ---- ----

kd*C ----

Value

----

0.010

1.6667e-4

0.01

1e-8

1.0e-20

6.022e+3

Reaction 3 Cyclin Protease Degradation

reaction

reaction rate

parameter vd

parameter Kd

C -> null ---- ----

(vd*X*C)/(Kd + C) ----

Val ue

----

0.25

0.0042

0.02

2.0e-8

2.0e-020

Units

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. molecule/second

A. 1/minute

B, C, D. 1/second

A. uM

B. mole/liter

C. mole

D. molecule

Units

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. molecule/second

A. 1/minute

B, C, D. 1/second

A. uM

B. mole/liter

C. mole

1-14

SimBiology®Model with Reactions

Val ue

12044

species

C (substrate)

0.01

1e-8

1.0e-20

6.022e+3

species

X (enzyme)

0.01

1e-8

1.0e-20

6.022e+3

Reaction 4 Cdc2 Kinase Activation

reaction

reaction rate

repeatedAssignment

rule

parameter

Mplus -> M ---- ----

(V1*Mplus)/(K1 + Mplus)

V1 = (VM1*C)/(Kc +C)

V1 (variable by rule)

Val ue

----

0.00

Units

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

Units

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. molecule/second

A. uM/minute

parameter VM1

3.0

5.0e-8

B. mole/(liter*second)

C. mole/second

D. molecule/second

A. uM/minute

B. mole/(liter*second)

1-15

1 Minimal Cascade Model for a Mitotic Oscillator

parameter Kc

parameter K1

species

Mplus (inactive

substrate)

M (active product)

Val ue

5.0000e-020

30110

0.5

5.0000e-7

5.0e-19

3.011e+5

0.005

5e-9

5e-21

3.011e+3

0.99

9.9e-7

9.9e-19

5.962e+5

0.01

1e-8

1.0e-20

6.022e+3

0.01

1e-8

1.0e-20

6.022e+3

Units

C. mole/second

D. molecule/second

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

1-16

Reaction 5 Cdc2 Kinase Deactivation

SimBiology®Model with Reactions

reaction

reaction rate

M -> M_plus ---- ----

(V2*M)/(K2 + M) ----

parameter V2

parameter K2

species

Mplus (inactive)

M (active)

Value

----

1.5

2.5000e-008

2.5000e-020

15055

0.005

5.0000e-009

5.0000e-021

3011

1.0e-20

0.99

9.9e-7

9.9e-19

5.962e+5

0.01

1e-8

1.0e-20

6.022e+3

Units

A. uM/minute

B. (mole/liter-second)

C. mole/second

D. molecule/second

A. uM/minute

B. mole /liter-second

C. mole/second

D. molecule/second

A. uM

B. mole/liter

C. mole

D. molecule

C. mole

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

1-17

1 Minimal Cascade Model for a Mitotic Oscillator

Reaction 6 Protease Activation

reaction

reaction rate

repeatedAssignment

Xplus -> X ---- ----

(V3*Xplus)/(K3 + Xplus)

V3 = VM3*M ----

rule

parameter

V3 (variable by rule) A. uM/minute

parameter VM3

parameter K3

species

Xplus (inactive

substrate)

species

X (active product)

Value

----

1.0

0.0167

0.005

5e-9

5e-21

3.011e+3

0.99

9.9e-7

9.9e-19

5.962e+5

0.01

1e-8

1.0e-20

Units

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. mo le cule/second

B. mole/liter-seco n d

C. mole/second

D. mo le cule/second

A. 1/minute

B, C, D. 1/second

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

1-18

SimBiology®Model with Reactions

species

M (enzyme)

Reaction 7 Protease Deactivation

reaction

reaction rate

parameter V4

parameter K4

species

X -> X_plus ---- ----

(V4*X)/(K4 + X) ----

Xplus (inactive)

X (active)

Value

6.022e+3

0.01

1e-8

1.0e-20

6.022e+3

Value

----

0.5

8.3333e-009

8.3333e-021

5.0183e+003

0.005

5e-9

5e-21

3011

0.99

9.9e-7

9.9e-19

5.962e+5

0.01

Units

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

Units

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. mo lecule/s econd

A. uM/minute

B. mole/(liter*second)

C. mole/second

D. mo lecule/s econd

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

B. mole/liter

C. mole

D. molecule

A. uM

1-19

1 Minimal Cascade Model for a Mitotic Oscillator

Value

1e-8

1.0e-20

6.022e+3

Units

B. mole/liter

C. mole

D. molecule

SimBiology Simulation with Reactions

This is a simulation of Goldbeter’s minimal mitotic oscillator with rate and algebraic equations. Simulate with the and

X. For a d escription of the model, see “SimBiology Model with Reactions”

on page 1-10.

sundials solver and plot species C, M,

1-20

References

[1] Goldbeter A. (1991), “A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase,” Proceedings of the National Academy of Sciences USA, 88:9107-9111.

[2] Goldbeter A., K oshland D. (1981), “An amplified sensitivity arising from covalent modification in biological systems,” Proceedings of the National Academy of Sciences USA, 78:6840-6844.

[3] Goldbeter A., Koshland D. (1984), “Ultrasensitivity in biochemical systems controlled by covalent modification,” The Journal of Biological Chemistry, 259:14441-14447.

[4] Goldbeter A., home page on the Web,

http://www.ulb.ac.be/sciences/utc/GOLDBETER/agoldbet.html

[5] Murray A.W., Kirschner M.W. (1989), “Cyclin synthesis drives the early embryonic cell cycle,” Nature, 339:275-280.

1-21

1 Minimal Cascade Model for a Mitotic Oscillator

1-22

ModeloftheYeast Heterotrimeric G Protein Cycle

• “Objectives” on page 2-2

• “Background on G Protein Cycles” on page 2-3

• “Modeling a G Protein Cycle” on page 2-5

• “Building the G Protein Cycle Model” on page 2-10

• “Completing the SimBiology Model” on page 2-19

• “Simulating the G Protein Cycle Model” on page 2-27

• “Creating the Mutant Strain Using a Variant” on page 2-34

• “Creating a Custom Plot-Type to View Simulation Results” on page 2-37

• “Plotting Species from Two Different Data Sets” on page 2-44

• “Plotting Experimental Data with Simulation Data” on page 2-48

• “References” on page 2-52

2 Model of the Yeast Heterotrimeric G Protein Cycle

Objectives

SimBiology software lets you build a model using a conceptual framework of biochemical reactions that describe a biological proces s. You can plot experimental data on top of your model’s simulation results to investigate the validity of your model, make predictions based on the model, and test your hypotheses.

Using concepts and data from the published work of Yi and colleagues [Yi et al. 2003], this tutorial shows you how to:

1 Build a model using the SimBiology graphical user interface (GUI).

2 Apply an alternate value during simulation to create a variation of the

model (for example, wild-type versus mutan t ) .

3 Simulate a

4 Compare the two simulations.

5 Compare the simulation results with the experimental data.

nd save the data from the two models.

2-2

Background on G Protein Cycles

In this section...

“G Proteins” on page 2-3

“G Proteins and Pheromone Response” on page 2-4

G Proteins

Cells rely on signal transduction systems to communicate with each other and to regulate cellular processes. G proteins are GTP-binding proteins that are involved in the regulation of many cellular processes. There are tw o known classes of G proteins: the monomeric G prote ins (one GTPase), and the heterotrimeric G proteins (three different monomers). The G proteins usually facilitate a step requirin g energy. This energy is supplied by the hydrolysis of GTP by a GTPase activating protein (GAP). The exchange of GDP for GTP is catalyzed by a guanine nucleotide releasing pro tein (GNRP) [Alberts et al. 1994].

Background on G Protein Cycles

GAP

Gprotein GTP Gprotein GDP

G protein-coupled receptors (G PCR s) are the targets of many pharmaceutical agents. Some estimates suggest that 40 to 50% of currently marketed drugs target GPCRs and that 40% of current drug discovery focus is on GPCR targets. Some examples include those for reducing stomach acid (ranitidine which targets histamine H2 receptor), migraine (sumatriptan, which targets a serotonin receptor subtype), schizophrenia (olanzapine, which targets serotonin and dopamine receptors), allergies (desloratadine, which targets histaminereceptors). Oneapproachin pharmaceutical research is to model signaling pathways to analyze and predict both downstream effects and effects in related pathways. This tutorial examines model building and analysis of the G protein cycle in the yeast pheromone response pathway using the SimBiology desktop.

⎯→⎯⎯⎯ ←⎯⎯⎯⎯

GNRP

2-3

2 Model of the Yeast Heterotrimeric G Protein Cycle

G Proteins and Ph

In the yeast Sacc response is a wel secreted by alp (Ste2p) in a cel arrest and syn a quantitativ activation in that confer s of cell-cycl developed a m estimate ra

e arrest and pheromone-induced transcriptional activation and

haromyces cerevisiae, G protein signaling in pheromone

l characterized signal transduction pathway. The pheromone

ha cells a ctivates the G protein-coupled α-factor receptor ls which results in a variety of cell respon ses including cell-cycle thesis of new proteins. The authors of the study performed

e analysis of this cycle, compared the regulation of G protein

wild-type y east haploid a cells with cel ls containing mutations

upersensitivity to α-factor. They analyzed the data in the context

athematical model of the G protein cycle that they used to

tes of activation and deactivation of active G protein in the cell.

eromone Response

2-4

Modeling a G Protein Cycle

In this section...

“Reactions Overview” on page 2-5

“Assumptions, Experimental Data, and Units in the G Protein Model” on page 2-7

Reactions Overview

Systems biologists represent biological pathwa ys and processes as reactions with reaction rates, and treat the components of these pathways as individual species.

The G protein cycle in the yeast pheromone-response pathway can be condensed into a set of biochemical reactions. These reactions are complex formation, transformation, or disassociation reactions that Yi and colleagues [Yi et al. 2003] use to simplify and describe the system. In this example, α-factor, α-factor receptor, and the G protein subunits are all treated as species participating in reactions. The system can be graphically represented as follows.

Modeling a G Protein Cycle

2-5

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-6

The following table shows you the reactions used to model the G protein cycle and the corresponding rate constants (rate parameters) for each reaction. For reversible reactions, the forward rate parameter is listed first.

No. Name

Receptor-ligand

ion

React

L+R<

-> RL

Rate Param

kRLm

kRL,

eters

interaction

Heterotrimeric G protein

Gd + Gbg -> G kG1

formation

G protein activation

RL+G->Ga+Gbg+RLkGa

Modeling a G Protein Cycle

No. Name

Receptor synthesis and degradation

Receptor-ligand degradation

G protein inactivation

Note that in reaction 3 (G protein activation), RL appears on both sides of the reaction. This is because assumes that there is no synthesis or consumption of

The a uthors use a set of ordinary differential equations (ODEs) to describe the system. In the software, you can represent the biological pathway as a system of biochemical reactions and the s oftwa re creates the ODEs for you. Alternatively, if you have a set of ODEs that describe your system you can enter these as rate rules. For an example of modeling using rate rules, see “SimBiology Model with Rate Rules” on page 1-6.

RL is treated as a modifier or catalyst, and the model

Reaction

R <-> null kRdo, kRs

RL -> null kRD1

Ga -> Gd kGd

RL in this reaction.

Rate Parameters

Assumptions, Experimental Data, and Units in the G Protein Model

The authors have obtained experimental data either through their own measurements or through published literature. As with any other model, the G protein cycle model simplifies the biological process while also trying to reconcile the experimental data. Consider these points:

• Reaction 2 — Binding and formation of the heterotrimeric G protein

complex is treated as a single-step reaction.

• Reaction 3 — Activation of G protein is modeled as a single-step. Guanine

nucleotide exchange factors (GEFs) are not modeled.

• Reactions 3 and 6 — The parameters for the rate of G protein activation

and deactivation ( response curves in the reference paper. The SimBiology model being built in this tutorial directly uses those values.

kGa and kGd) have been estimated based on the dose

2-7

2 Model of the Yeast Heterotrimeric G Protein Cycle

• Reactions 4 and 5 — Receptor synthesis and deg radation are handled

purely as two simple reaction steps.

• Reaction 6 — Deactivation of G protein by the regulator of G protein

signaling (RGS) protein Sst2p is modeled as a single step. Sst2p is not modeled.

The reaction is modeled with an estimated reaction rate of the Sst2p containing wild-type strain. The uncatalyzed reaction rate is estimated to be mutant strain).

• Free GDP, GTP, and Pi are not included in the model.

This tutorial shows you how to plot the experimental data over the simulation plot of the active G protein fraction. You can estimate the values of the experimental data of interest for this example from the coordinates of the plots found in Figure 5 of the reference paper [Yi et al. 2003]. The following values were obtained by comparing the coordinates of the standards with those of the unknowns in the figure.

0.004 s

0.11 s

-1

in a strain with a del etion of SST2 (sst2Δ,

-1

)in

2-8

Time

Fraction of Active Ga (Experimental)

00.00

10 0.35

30 0.40

60 0.36

110 0.39

210 0.33

300 0.24

450 0.17

600 0.20

Modeling a G Protein Cycle

Note The SimBiology Dimensional Analysis feature is not used in this tutorial. For this tutorial, the values of all species are converted to have the unit

molecule, and all rate parameters are converted to have either the unit

1/second or the units 1/(molecule*second), depending on whether the

reaction is first or second order. You should leave the InitialAmountUnits box for species and the ValueUnits box for rate parameters empty for the models in this tutorial.

2-9

2 Model of the Yeast Heterotrimeric G Protein Cycle

Building the G Protein Cycle Model

In this section...

“Tutorial Goals” on page 2-10

“Opening the SimBiology Desktop” on page 2-11

“Saving Your Work as a SimBiology Project File” on page 2-12

“Adding a Reaction to the SimBiology Model” on page 2-13

“Determining the Reaction Rate Equation” on page 2-15

“Setting the Compartment Name” on page 2-17

“Setting Initial Amounts of Species” on page 2-18

Tutorial Goals

This section shows you how to build the example yeast heterotrimeric G protein m odels using the SimBiology desktop GUI (graphical user interface). For an overview of the SimBiolog y desktop, click here. The SimBiology desktop is also called “the desktop” in the SimBiology documentation.

2-10

This section assumes that you are starting with an untitled default

If you are running the tutorial, see “Simulating the G Protein Cycle Model” on page 2-27 for details about the simulation and analysis of these models.

This example uses the yeast G protein cy cle [Yi et al. 2003] to illustrate model building and analysis. The goals of this tutorial are the following:

1 Build a model of the wild-type strain (TMY101) that has the SST2 gene.

2 Store alternate values in a Variant to create a different model for the

Untitled Model Session in the SimBiology desktop.

gprotein.sbproj file that contains the models in this

This strain shows a catalyzed rate of deactivation of Gα.Gα is represented as Ga in the model.

mutant strain (sst2Δ , TMY111) that shows an uncatalyzed rate of G-Protein inactivation.

Project and a

Building the G Protein Cycle Model

3 Simulate and save the data from the two models.

4 Compare the active G protein fractions in the two simulations.

5 Compare the simulation results for active G protein fractions with

experimental data.

For additional help in each procedure, select Help > SimBiology Desktop Help.

Opening the SimBiology Desktop

The procedures in this tutorial are performed in the SimBiology desktop. The desktop provides access to command-line functionality through a graphical user interface. Yo u can open the desktop from the MATLAB Command Window.

1 In the MATLAB Command Window, type:

simbiology

The SimBiology desktop opens.

2 Select File > New Project. The New Project Wizard opens.

3 Skip the Add Data step for this example and select Add Model.

4 In the Add Model pane, from the Select a model to add list, select

Create a new blank model. This selection creates a Model Session

containing one compartment (at least one compartment is required for all models). You will later add model components such as species, reactions, rules, and events to the model.

2-11

2 Model of the Yeast Heterotrimeric G Protein Cycle

5 In the Model Name box, type the name for your model.

Yeast_G_Protein_wt

2-12

6 Click Next.

7 In the Choose Analysis pane, leave the default selection (Simulate

model) selected for the analysis tasks to add to the model and click Finish.

Anewpr

Saving

Proje Proje model

Save

1 Sele

box.

2 Browse to the folder in which you want to save your projects, enter a name

for the project file, and then click Save.

oject with the selected specifications opens.

Your Work as a SimBiology Project File

ct (

.sbproj) is the file format used to save one or more model sessions.

cts l et you save custom settings, notes, and data a ssociated with your

your work as a project now so that you can access this file later.

ct File > Save Project As to open the Save SimBiology Project dialog

Building the G Protein Cycle Model

yeast_g_protein_cycle.sbproj

Adding a Reaction to the SimBiology Model

The next steps show how to add a reaction and determine the reaction rate equation for your model.

This example shows the first reaction.

Name

Receptor-ligand interaction

1 In the Project Explorer,expandSimBiology Model and click Reactions

Reaction

L+R<->RL

Rate Parameters

kRL, kRLm

to open the Reactions pane.

2 Enter the reaction in the Enter Reaction box, and click Add.

L+R<->RL

A r ed indicator appears to the right of the table. Move the pointer over the indicator for the reaction, to get more information about the reason for the indicator. In this case, the indicator shows that the reaction rate is invalid. The next section shows h ow to define the reaction rate.

3 Double-click the Name box, and type the name for your reaction. For

example:

Receptor-Ligand Interaction

4 In the reaction table, from the KineticLaw list, select MassAction.

Your screen should now resemble the following figure.

2-13

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-14

Notice

• Because this reaction is reversible, the Reversible check box is selected

• All the reactions in this example model are included in the simulation

the following in the Settings tab:

by default when you enter the reaction.

and, therefore, have the Active check b ox selected. By default, the Active check box is selected.

Building the G Protein Cycle Model

Tip You must use spaces between the species and the characters in the reaction. If you have a reaction with different stoichiometry, for example,

2A+B<->3AB, you must have a space between the stoichiometric

coefficient and the species name for the reaction rate to be accurately determined. Otherwise, the coefficients are considered as part of the species name.

Determining the Reaction Rate Equation

The desktop populates the reaction rate column after you specify the kinetic lawandtherateparametersofthereaction.

To assign and configure the kinetic law and the rate parameters, do the following in the Reactions pane:

1 In the Map between KineticLaw Parameters and Parameter Names

section, locate the Forward Rate Parameter row, double-click the Parameter Name cell, type

kRL and press Enter.

2 In the Reverse Rate Parameter row, double-click the Parameter Name

cell, type

kRLm and press Enter.

2-15

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-16

• The desktop updates the ReactionRate column to show kRL*L*R -

kRLm*RL

completely defined.

• For this example, Scope of all the parameters is at the kinetic law level.

The desktop displays the reaction in the Scope box.

• The desktop automatically sele c ts the species when you select

MassAction kinetic law. For other kinetic laws, you should ente r the

species to be included in the rate equation.

3 In th

kRL = 3.32E-18 and kRLm = 0.01

, and the indicator is now green showing that this reaction is

e Value cell, enter the follow ing parameter values:

Building the G Protein Cycle Model

Setting the Compartment Name

All models created in the desktop contain a compartment by default. The process of adding a reaction automatically adds the reaction species to a compartment in the model. If there are multiple compartments in the model, you must specify the reactants and products using qualified names (

compartmentName.speciesName). For example, nucleus.DNA denotes the

species

DNA in the compartment nucleus.

This example contains only one compartment. To rename the compartment:

1 In the Project Explorer,clickCompartments.

2 In the N

then pr

The c

Use t

Why

• Own

com

ame cell, double-click and type a nameforthecompartment,and

ess Enter.

yeast_cell

ompartment table updates with the new name.

he default values for the Owner, Capacity,andCapacityUnits cells.

Use Default Values

er lets you define whether the compartment is within another

partment. This model has only one com partment within which you

2-17

2 Model of the Yeast Heterotrimeric G Protein Cycle

define all the species. No Owner means that the compartment is a top-level compartment.

• Capacity lets you enter the compartment size, such as volume, length,

or area. In this model, species are defined in amounts, the reaction rate dimensions are amount/time, and the model assumes that compartment volume is constant. Thus, all the values and the units are internally consistent with each other and the compartment volume can use the default value of

• CapacityUnits lets you specify the units for Capacity,whicharenot

needed for this example.

Setting Initial Amounts of Species

You can set the initial amounts of all the model species in the Species pane.

1.0.

Name

L 6.022E17

R 10000.0

RL 0.0

1 In the Project Explorer,expandCompartments and click yeast_cell

Species.

2 In the Species pane, double-click in each InitialAmount cell and enter

the preceding values.

Notice that the Scope column lists the name of the compartment containing the species.

You n ow have a complete reactio n with a ll components added and defined.

InitialAmount

2-18

Completing the SimBiology Model

In this section...

“Reactions” on page 2-19

“Alternative Ways to Build Reactions in the D esktop” on p age 2-20

“Parameters” on page 2-22

“Species” on page 2-23

“Creating a Rule for the G Protein Model” on page 2-25

“Verifying the Model” on page 2-26

Reactions

The previous sections showed you how to the enter the first reaction for the yeast G protein cycle model and configure the reaction rate equation. Repeat the procedures to add the rest of the reactions, parameters, and species values as described in the previous sections, and create a rule to specify the ratio of active G protein that corresponds to the ratio determined experimentally in the referenced study [Yi et al. 2003].

Completing the SimBiology®Model

Add reactions 2 to 6 listed in this table, set the kinetic law for each reaction to

MassAction, create parameters, and configure the reaction rate using the

procedure for “Determining the Reaction Rate Equation” on page 2-15.

No. Name

Receptor-ligand

ion

React

L+R<

-> RL

Rate P

kRL,

arameters

kRLm

interaction

Heterotrimeric G

Gd + Gbg -> G kG1

protein formation

Gprotein activation

Receptor synthesis

RL + G -> Ga + Gbg + RL

R <-> null kRdo, kRs

kGa

and degradation

2-19

2 Model of the Yeast Heterotrimeric G Protein Cycle

No. Name

Receptor-ligand degradation

Gprotein inactivation

Your reaction table should resemble the following figure.

The nex t section describes other ways you can build reactions in the desktop. If you want to continue building the model, skip the next section and go to “Parameters” on page 2-22.

Reaction

RL -> null kRD1

Ga -> Gd kGd

Rate Parameters

2-20

Alternative Ways to Build Reactions in the Desktop

This optional section shows you some alternative methods to build a reaction in the Reactions pane. Use the exam ples above to try out these methods. If you have finished entering the reactions for the model, proceed to “Parameters” on page 2-22.

The Reactions pane has several dialog boxes that are convenient for building reactions.

Building a Reaction

You can graphically build a reaction using the Reaction Builder.

1 If you are not already in the Reactions pane, in the Project Explorer

click Reactions.

Completing the SimBiology®Model

2 Click Build to open the Reaction Builder dialog box.

3 Select a species from the Available Species list and click the Reactant

or Product button.

4 To edit stoichiometric relationships, click in the Stoich column and type.

5 Select the Reversible check box if the reaction i s reversible.

6 Click Add to continue editing within the Reaction Builder. Click OK to

finish and return to the Reactions pane.

Creating a Binding Reaction

Use the Bind button to create a bound product from two reactant species.

1 If you are not already in the Reactions pane, in the Project Explorer

click Reactions.

2 In the Enter Reaction box, enter the reactant species.

lactose + lactase

3 Click the button. The software writes the product as a compound

name, w ith a colon between reactant names to indicate binding.

lactose:lactase

Creating an Unbinding Reaction

Use the Unbind button to create two product species from a bound reactant.

1 If you are not already in the Reactions pane, in the Project Explorer

click Reactions.

2 In the Enter Reaction box, enter the reactant species.

lactose:lactase

3 Click . The software writes the product names with a + between

them to indicate unbinding.

2-21

2 Model of the Yeast Heterotrimeric G Protein Cycle

lactose + lactase

Parameters

In the Reactions pane, after you create parameters in the S ettings tab, you can set the value of the parameter in the parameters table.

Alternatively, you can set all the parameters in the Parameters pane. In the Project Explorer,clickParameters to open the Parameters pane.

Use the following values for rate parameters.

Parameter Value Table

Name

kRLm 0.01

kRL 3.32E-18

kRdo 4.0E-4

kRs 4.0

kRD1 0.0040

kG1 1.0

kGa 1.0E-5

kGd 0.11

Value

To be consistent with units for kRL, RL and L,thevalueforkRL is converted from the published value,

1/(molecule*second) (assuming a volume of unity).

2.0E6M-1s

-1

,to3.32E-18 with units

2-22

Completing the SimBiology®Model

Species

Set t he species amounts in the Species pane. In the Project Explorer,click yeast_cell Species to access this pane.

• Note that the process of adding reactions resulted in species automatically

being added to the species list, with default amounts set to

0.0.Double-click

each InitialAmount cell to change the values to those given in the table.

• The amount of

when converted to This is now internally consistent with the units for the species, the parameter,

L (α-factor) used in the experiments is 1M. This value

molecule (assuming a volume of unity) is 6.022E17.

RL,and

kRL.

Species Initial Amounts

Name

L 6.022E17

R 10000.0

G 7000.0

Gd 3000.0

Gbg 3000.0

InitialAmount (Molecule)

2-23

2 Model of the Yeast Heterotrimeric G Protein Cycle

Species Initial Amounts (Continued)

Name

Ga 0.0

RL 0.0

InitialAmount (Molecule)

To replicate the published results, the model needs the definition of the ratio of active G protein. Call this ratio active G protein (Gα-GTP) and

Ga_frac. Ga_frac is Ga/Gt,whereGa is

Gt is the total amount of G protein in a cell.

This relationship is defined using a rule, and the procedure to create this rule is described in “Creating a Rule for the G Protein Model” on page 2-25.

Define two additional species, called

Ga_frac and Gt.

Additional Species

Name

Ga_frac 0.0

Gt 10000.0

InitialAmount (Molecule)

To add a new species:

1 In the Project Explorer,clickyeast_cell Species to open the Species

pane.

2-24

2 In the Enter name box, enter the name of a new species, and then click

Add or press Enter.

Ga_frac

The species table updates with the new entry and its row is selected. Note that the species is now available in the Settings tab.

3 In the Initial Amount cell, enter a value for the amount of the species.

For

Ga_frac, leave this at the default value (0.0).

4 Repeat steps 1 to 3 for Gt. InitialAmount is 10000.0.

Completing the SimBiology®Model

5 In the Settings tab, select the ConstantAmount check box only for Gt,

because the amount of

Gt does not vary during the simulation.

Your species table should resemble this.

Notice the yellow indicator; move your pointer over the indicator to see the warning message. The message shows that the species is never used, be cau se

Ga_frac and Gt are not yet defined in a rule. After you define the rule as

described in the next section, the indicator shows one green square.

For additional help in each procedure, select Help > SimBiology Desktop Help for context-sensitive help.

Creating a Rule for the G Protein Model

A SimBiology rule is a mathematical expression that modifies a species amount, compartment volume, or a parameter value. U se a repeatedAssignment rule to define the value of the species model.

1 In the Project Explorer,clickRules to open the Rules pane.

2 In the Enter Rule box, type the expression, and then click Add or press

Enter.

Ga_frac in the

2-25

2 Model of the Yeast Heterotrimeric G Protein Cycle

Ga_frac = Ga/Gt

3 From the RuleType list select repeatedAssignment.

4 (Optional) Give your rule a name. Double-click and type the following in

the Name box:

Ga_frac_rule

This completes the section on building the G protein cycle model for the wild-type strain.

2-26

Verifying the Model

While you are building your model in the SimBiology desktop, you can click

at any time to generate a list of any errors and warnings in the model. The errors and warnings appear in the Errors and W arnings pane. For more information about verification see “Verifying that a Model Has No Warnings or Errors” in the SimBiology User’s Guide.

Simulating the G Protein Cycle Model

In this section...

“Setting Conditions Before Simulating the G Protein Model” on page 2-27

“Simulation Results for the Wild-Type Strain Model” o n page 2-31

Setting Conditions Before Simulating the G Protein Model

In previous sections, this tutorial described building a model for a G protein cycle. This model uses the G protein cycle in the yeast pheromone response pathway. This section describes conditions for simulation and the simulation results for this model.

Consider the following points about simulating this model:

Simulating the G Protein Cycle Model

• Yi. et al. show data up to

replicate these results, change the simulation settings from the default

second

you change it back to the default.

• The ligand species

many of the other species. Don’t log data for can enable instant visualization of the other species through proper scaling of plots. To do this, define Data Logging to stop logging data for

The first procedure (below) describes how to change the simulation stop time. The second procedure is about recording a subset of data (“Specifying Which Data Is Recorded” on page 2-29).

to 600 second. This change remains active for this model unless

'L' has values that are magnitudes higher than those of

600s for the active G protein time course. To

'L' so that while plotting you

'L'.

Adding a Simulation Task

When you created a n ew project as shown in “Opening the SimBiology Desktop” on page 2-11, the option chosen added a Simulation task to the project. You can skip to “Changing the Simulation Stop Tim e” on page 2-28.

If you have a project without a Simulation task, do the following to add a

Simulation task:

2-27

2 Model of the Yeast Heterotrimeric G Protein Cycle

• In the Task menu, select Add Model Task to

Yeast_G_Protein_wt > Simulate model.

The S imB iology desktop adds the task to the Project Explorer,opensthe task pane, and highlights the new task.

2-28

Changing the Simulation Stop Time

Changethestoptimetoreplicatethesimulationusedinthereferencepaper [Yi et al. 2003], and to facilitate comparison with the experimental results presented in the study.

You will modify the modify the default in your models, you can add another configuration set that you can then modify.

1 In the Project Explorer,clickConfigura t ion Settings.

2 In the Settings tab, enter the stop time in the Stop box an d press Enter.

600.0

Leave the following properties as the default (you may have to scroll to see some of the properties mentioned below):

• SolverType(

default settings for this example. If you do not want to

sundials)

• AbsoluteTolerance ( 1.0E-6)

Simulating the G Protein Cycle Model

• RelativeTolerance (

• MaxStep (

[])

0.0010)

• DimensionalAnalysis (check box selected)

• UnitConversion (check box clear)

• DefaultSpeciesDimension (

concentration). This value is important if

you are accounting for volume in your model. This example i gn ores vol u me and thus the value assigned to this property is not rele vant.

Youcanalsochangethesolvertypetouseandthestoptimeforthesimulation in the SimBiology toolbar. The desktop changes the setting of the

Active

configuration set when you change s ettings in the Toolbar.

Specifying Which Data Is Recorded

You can specify the species names for which SimBiology should log,thatis, record the simulation data.

As mentioned in the previous section, you will modify the this example. If you do not want to modify the default in your models, you can add another configuration set that you can then modify.

1 In the Con figuration Settings pane, click the Data Logging tab.

default settings for

2 Select the check boxes for the species to log. Because, all the species check

boxes are selected by default, clear the check box for

'L'.Theorderofthe

species in the figure below may not exactly match the order on your screen.

2-29

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-30

Tips for Use and Points to Consider

• You can save all these simulation settings as one custom simulation

setting. See the context-sensitive help for Simulation Settings. To access context-sensitive help, select Help > SimBiology Desktop Help.

• The default

pathways. You might, however, need a different solver for some models. For more information on choosing solver types, see “Selecting a Solver” in the SimbBiology User’s Guide documentation.

• You can choose from three stochastic solvers:

,andexplicit tau. Try one of the stochastic solvers with this model

tau

and see how it compares with Solvers” in the SimBiology User’s Guide documentation. You can also see how the stochastic solvers compare with each other.

• For a counter that tracks the simulation, look in the lower-right corner

of the SimBiology desktop.

sundials is adequate for modeling of many biological

stochastic (SSA), implicit

sundials. For information, see “Stochastic

Simulating the G Protein Cycle Model

• Click the following links to learn more about absolute and relative

tolerance. These are links to SimBiology reference pages with definitions for

AbsoluteTolerance and RelativeTolerance.

Simulation Results for the Wild-Type Strain Model

Simulate the model you have built and see your results. To simulate the model:

1 In the Project E xp lorer, under Model Tasks,clicktheSimulation task

to open the Simulation pane.

2 Click (Run).

Your plot should resemble the following figure:

2-31

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-32

Saving Simulation Data

You can optionally save the data from the mos t recent simulation run. Unless yousavethedataforeachsimulationrun,itisoverwrittenbythedatafor the next run.

1 In the Project Explorer, under Simulation,clickData for the wild-type

model.

2 In the Data pane, click Save to open the Save Data dialog box.

Simulating the G Protein Cycle Model

3 Specify a name for your data, and then click Save.

wt_model_run1

The desktop adds the saved data under the Simulation task in the Project Explorer.

2-33

2 Model of the Yeast Heterotrimeric G Protein Cycle

Creating the Mutant Strain Using a Variant

In this section...

“Modeling the Mutant Strain” o n page 2-34

“Applying Alternate Values Using Variants” on page 2-34

“Simulation Results for the Model of the Mutant Strain” on page 2-35

Modeling the Mutant Strain

The d eletio n in SST2 results in uncatalyzed G protein deactivation (Reaction 6;

Ga -> Gd). From a modeling perspective, this means a change in the rate of

the reaction. This section shows you how represent the value for the mutant strain in a Variant and simulate the model using the variant value.

Note An additional simplifying assumption of this model is that there are no changes in the initial amounts of s pecies or the rate of any other reaction.

2-34

Applying Alternate Values Using Variants

1 In the Project Explorer,clickVariants to open the Variants pane.

2 In the Enter Name box, type a name for the variant, and then click Add

or press Enter. For example:

alue

mut_v

3 Add content to the variant:

a In the Settings tab, from the Type list, select parameter.The

Property list updates to show the property available for changing.

b Double-click the Component Name cell and type the name of the

component.

rotein Inactivation.kGd

Creating the Mutant S train Using a Variant

Tip Alternatively, double-click the Component Name cell, press the down arrow, and select

Gprotein Inactivation.kGd from the list and

press Enter.

The parameter kGd is at the kinetic law level, and not the mo del level. Thus, you must specify the parameter in the format

ReactionName.ParameterName.

c In the Value cell,typeavaluetoapplyusingthevariant.

0.004

Simulation Results for the Model of the Mutant Strain

To simulate the model of the mutant strain, apply the variant and simulate as follows:

1 If the Simulation pane is not already open, in the Project Explorer

select Simulation to open the pane.

2 In the Variants table, select the Use in Task check box for mut_value.

3 Click (Run). Your plot should resemble the following figure.

2-35

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-36

4 In the Data pane for the latest simulation, click Save to open the Save

Data dialog box.

5 Specify a name for your data, and then click Save.

mut_model_run1

The desktop adds the saved data under the Simulation task in the Project Explorer.

The simulation results for the wild-type strain are described in “Simulation Results for the Wild-Type Strain Model” on page 2-31.

Creating a Custom Plot-Type to View Simulation Results

In this section...

“Creating a Custom Plot” on page 2-37

“Visualizing R esults for the Mutant Strain Using a Custom Plot” on page 2-42

Creating a Custom Plot

To keep data plots from each model simulation distinct and to facilitate comparison, you can use customized plots. This example shows how to create and save a custom plot in the Plot Types library for use in plotting the simulation data with a different line style (dashed lines).

1 Select Library > Show Library Explorer.TheLibrary Explorer opens.

2 In the Library Explorer,clickPlots Types.ThePlot Types pane opens.

3 In the En

ter Nam e box, type a name for the custom plot and press Enter.

Time plot line style

The des

4 In the Enter Plot Type code below or copy Plot Type code from

ktop adds the new plot to the plot types table.

section, replace the code in the editor window with the following:

function Time(tobj, y, lstyle)

%TIME Plots states versus time.

% Plot the results of the simulation for the species with the specified

% names versus time. Data from each run is plotted into one axes. The

% string '<all>' can be used to indicate that all species should be

% plotted. LStyle specifies the line style that can be used.

% See also GETDATA, SELECTBYNAME.

if (length(tobj) > 1)

sbioplot(tobj, @timeplotdata, [], y, lstyle);

2-37

2 Model of the Yeast Heterotrimeric G Protein Cycle

else

timeplotdata(tobj, [], y, lstyle);

end

%--------------------------------------------------------

function [handles, names] = timeplotdata(tobj, x, y, lstyle)

colors = get(gca, 'ColorOrder');

numColors = length(colors);

handles = [];

for i=1:length(tobj)

% Get the data from the next run.

nexttobj = tobj(i);

% Get the simulation data associated with the species

% specified in y.

if strcmpi(y, '<all>')

[time, data, names] = getdata(nexttobj);

else

[time, data, names] = selectbyname(nexttobj, y);

end

2-38

% Error checking.

if size(data,2) == 0

error('Species specified do not exist.');

end

% Plot data. If there is only one state use different colors for runs.

if(size(data,2) ==1)

hLine = plot(time, data, 'color',colors(mod(i-1,numColors)+1,:), 'LineStyle', lstyle);

else

hLine = plot(time, data, 'LineStyle', lstyle);

end

handles = [handles hLine];

end

% Label.

hold off;

xlabel('Time');

ylabel('States');

Creating a Custom Plot-Type to View Simulation Results

title('States versus Time');

if length(tobj) == 1

leg = legend(names, 'Location', 'NorthEastOutside');

set(leg, 'Interpreter', 'none');

end

Code Modifications for Line Style

This code uses the

Time plot type as a starting point and contains the

modifications highlighted next.

2-39

2 Model of the Yeast Heterotrimeric G Protein Cycle

2-40

Creating a Custom Plot-Type to View Simulation Results

5 Modifythecodetocustomizetheplot type, by typing in the section

containing the code. If you change the arguments, the desktop updates the List of Arguments Passed to Plot Type Code table with the new list.

6 Specify additional information for the lstyle argument by double-clicking

its row in the table. The Define Argument lstyle dialog box open s.

7 From the Define the values that the plot type argument can be

configured to list, select

Enumerations. Thisoptionletsyouspecifya

comma-separated list of supported values.

8 In the Comma separated list of supported values box, type the values

that can be entered for this plot type. The

Line Style argument takes

the following values:

-, --, -., :, none

9 From the Default value of the plot type argument lstyle list, select a

default value. For this example select

--. This list is populated with the

values entered in the Comma separated list of supported values box.

10 Click OK to close the Define Argument lstyle dialog box.

11 Double click the row contain in g the tobj argument. The Define Argument

tobj dialog box opens.

12 From the Define the values that the plot type argument can be

configured to list, select

13 Click OK to close the Define Argument tobj dialog box.

14 Double click the row containing the y argument. The Define Argument y

Data Source.

dialog box opens.

15 From the Define the values that the plot type argument can be

configured to list, select

tobj)

16 Select the State Names (what is being logged) check box. Leave the

Default value of the plot type argument y as

17 Click OK to close the Define Argument y dialog box.

Data Names, (the Data Source for this argument

<all>.

2-41

2 Model of the Yeast Heterotrimeric G Protein Cycle

18 Click Save Now to save your new plot type. Plot types are automatically

saved at regular time intervals. If Save Now is disabled, this means that the desktop has automatically saved the plot type.

This plot type is available for use with any task.

Visualizing Results for the Mutant Strain Using a Custom Plot

Plot the simulation data for the model of the mutant strain with dashed lines. If you have the example open and have simulated the model for the mutant strain you do not need to rerun the simulation. You can use the saved data from “Simulation Results for the Model of the Mutant Strain” on page 2-35. Follow the steps described in “Plotting the Results” on page 2-43.

If you do not hav e the example open do the following:

1 Load the example project by typing the following at the command lin e:

sbioloadproject gprotein

2-42

The model is stored in a variable called m1.

2 Open the SimBiology desktop with the model loaded by typing:

simbiology(m1)

The SimBiology desktop opens with Model Session-Heterotrimeric_G_Protein_wt.

3 Select File > Save Project As. The Save S imBiology Project dialog box

opens.

4 Specify a name (for example, gprotein_ex) and location for your project,

and click Save.

Simulate the model as shown in “Simulation Results for the Model of the Mutant Strain” on page 2-35, and then continue with the steps described in “Plotting the Results” on page 2-43.

Creating a Custom Plot-Type to View Simulation Results

Plotting the Results

1 In the Project Explorer, under the Simulation task, click

mut_model_run1.

2 In the Data pane , click the Plots tab.

3 From the Plot Type list, select Time plot line style and click Add

Plot Type.

4 Under Arguments, select -- from the lstyle list.

5 Intheplottypetable,cleartheCreate Plot check box for the Time plot.

6 Click Plot. Y our figure should resemble the following.

2-43

2 Model of the Yeast Heterotrimeric G Protein Cycle

Plotting Species from Two Different Data Sets

In this section...

“Procedures Described in This Section” on page 2-44

“Plotting the Active G Protein Fraction from the Wild-Ty pe Strain Model” on page 2-44

“Creating a Custom Plot to Compare the Data” on page 2-45

“Plotting the Active G Protein Fraction from the Model of the Mutant Strain” on page 2-46

Procedures Described in This Section

This section shows you the following:

• How to compare the active G protein fractions in the two simulations. The

procedures in this section show you how to create a plot showing s pe cies from the two data sets in this tutorial.

2-44

• Howtoplotthedatawithouthavingtorerunthesimulation,andmore

about how to generate custom plots.

Plotting the Active G Protein Fraction from the Wild-Type Strain Model

You can find the simulation data under Simulation task for the model. You canalsosavethedatafromprevioussimulations. See “Saving Simulation Data” on page 2-32 for more information.

Specify that the species

1 In the Project Explorer, under the Simulation task, click

wt_model_run1. The data saved for the wild-type strain opens.

2 In the Data pane, click the Plots tab.

3 From the Plot Type list, select the Time plot and click the Add Plot Type

button.

Ga_frac should be plotted for the wild-type model.

Plotting Species from Two Different Data Sets

4 In the Arguments

section, click

. The Select Values for y dialog box

opens.

5 Click Clear All.

6 Select yeast_cell.Ga_frac and click OK.

7 In the plot typ

and click Plot

Creating a Cu

Create a cus with dashed from wild-t

1 Select Lib

2 In the Library Explorer,clickPlots Types.ThePlot Types pane opens.

3 In the Enter Name box, type a nam e for the custom plot and press Enter.

Time plot for Ga_frac comparisons

The desktop adds the n ew

e table, clear the Create Plot check boxes for the o ther plots, . Leavethefigurewindowopen.

stom Plot to Compare the Data

tom plot that specifies that the species

lines for the sst2

ype (

Ga_frac_wt)andGa_frac from sst2

model, and ad d a legend indicating Ga_frac

rary > ShowLibrary Explorer.TheLibrary Explorer opens.

plot to the plot types table.

Ga_frac should be plotted

(Ga_frac_mut).

4 In the Enter Plot Type code below or copy Plot Type code from

section, from the list select

5 Click A pply. The Plot Types command w indow updates to show you the

code for the

6 Locate and change th

leg = legend(names, 'Location', 'NorthEastOutside'); set(leg, 'Interpreter', 'none');

Time plot line style plot.

Time plot line style.

e following li nes of code:

leg = legend({'Ga_frac_wt','Ga_frac_mut'}, 'Location', 'NorthEastOutside');

set(leg, 'Interpreter', 'none');

2-45

2 Model of the Yeast Heterotrimeric G Protein Cycle

7 Click Save Now.IfSave Now is not available (grayed out), this means

that the plot type has been automatically saved.

This plot type is availabl e for use with any task for this project.

Now you can plot from the sst2

Ga_frac data from the wild-type strain with Ga_frac data

Plotting the Active G Protein Fraction from the Model of the Mutant Strain

Plot the sst2

1 In the Project Explorer, under the Simulation task, click

mut_model_run1

2 In the Data pane , click the Plots tab.

3 From the Plot Type list, select the Time plot for Ga_frac comparisons

plot and click Add Plot Type.

4 In the Ar

opens.

5 Click Clear All.

6 Select yeast_cell.Ga_frac and click OK.

7 In the

Ga_frac data using dashed lines.

guments section, click

. The Select Values for y dialog box

plot type table, clear the Create Plot check boxes for the o ther plots.

2-46

8 For the newly added plot, from the Plot Behavior list, select Add to

current axes

and click Plot. Thisoptionletsyouadddatatothemost recently generate d plot. You must have the figure window open to exercise this option.

Plotting Species from Two Different Data Sets

2-47

2 Model of the Yeast Heterotrimeric G Protein Cycle

Plotting Experimental Data with Simulation Data

In this section...

“About the Experimental Data” on page 2-48

“Creating a Custom Plot for Experimental Data” on page 2-48

“Plotting the Data” on page 2 -49

About the Experimental Data

You can work with your experimental data and plot your data from the SimBiology desktop. T he section describes how to store the experimental data and use the custom plotting features to plot the data with your simulation data.

This example uses the yeast G protein model built in this tutorial, based on a reference paper published by Yi and colleagues [Yi et al. 2003]. The experimental data used here are a lso from the same reference paper.

2-48

Creating a Custom Plot for Experimental Data

1 Select Library > Library Explorer.TheLibrary Explorer opens.

2 In the Show Library Explorer,clickPlots Types.ThePlot Types

pane opens.

3 In the

The d

4 In the Plot Types pane, copy and add the following code into the plot

types editor window:

Enter Name box, type a name for the custom plot and press Enter.

Ga_frac Experimental Data Plot

esktop adds the new plot to the plot types table.

% 1. Store the time and state data %(Obtained from Fig. 5 of reference paper.)

x = [0 10 30 60 110 210 300 450 600]; y = [0 0.35 0.4 0.36 0.39 0.33 0.24 0.17 0.2];

Plotting Experimental Data with Simulation Data

% 2. Store the estimated error values. %(Obtained from Fig. 5 of reference paper.)

L = [0 0.0100 0 0.0100 0.0200 0.0200 0.0300 0.0200 0.0200]; U = [0 0.0100 0 0.0200 0.0100 0.0180 0.0350 0.0300 0.0100];

% 3. Plot the experimental data.

errorbar(x,y,L,U,'LineStyle','none', 'Marker', '.');

legH3 = legend('Ga_frac_sim','Ga_frac_exp' , 'Location','NorthEastOutside');

set(legH3, 'Interpreter','none')

% To make a better picture,

axis([0 600 0 0.5]);

Explanation of the Code

In step 1 you store the data as vectors in two variables, one for the experimental values of active G protein fractions ( time points (

y). By writing scripts in this command window, you can store

x), and the other for the

and process your experimental data before plotting.

In step 2 you store the estimated upper (U) and lower (L) bounds of the error values of each data point.

In step 3, the function bars

L(i)+U(i) long. x, y, L,andU must be the same size. When they are

errorbar enables you to plot x versus y with error

vectors, each error bar is a distance of L(i) below and U(i) above the point defined by (x(i),y(i)). For more information, see

errorbar.

The code also specifies legend location, marker style, line style, and axis scale. For more information , see

5 Click Save Now.IfSave Now is not available (grayed out), this means

legend and axis.

that the plot type has been automatically saved.

This plot type is availabl e for use with any task for this project.

Plotting the Data

You can add the new custom plot to the data plot for the model of the wild-type strain and plot the simulation data for

Ga_frac w ith the e xperimental data.

2-49

2 Model of the Yeast Heterotrimeric G Protein Cycle

1 In the Project Exp lo rer,clickData for the wild-type model

wt_model_run1)

2 In the Data pane, click the Plots tab.

3 From the Plot Type list, select the Ga_frac Experimental Data Plot

plot and click Add Plot Type.

4 Select the Create Plot check box for the following:

a For the Time plot in which only Ga is specified in the YArgumentslist,

select

New Figure from the Plot Behavior list.

b For the Ga_frac Experimental Data Plot, select Add to current

from the Plot Behavior list.

axes

5 Intheplottypetable,cleartheCreate Plot check boxes for the other

plots and click Plot.

2-50

Plotting Experimental Data with Simulation Data

Formoreinformationontheplotusedinstep4a,see“PlottingtheActiveG Protein Fraction from the Wild-Type Strain Model” on page 2-44.

2-51

2 Model of the Yeast Heterotrimeric G Protein Cycle

References

[1] Tau-M u Y i, Hiroaki Kitano, and Melvin I. Simon. A quantitative characterization of the yeast heterotrimeric G protein cycle. PNAS (2003) vol. 100, 10764-10769.

[2] Alberts,B.,Bray,D.,Lewis,J.,Raff,M.,Roberts,K.,andWatson,J.D. Molecular Biology of the Ce ll , 3rd edition, Garland Publishing, 1994.

2-52

M-Phase Control in Xenopus Oocyte Extracts

John Tyson’s Computational Cell Biology Lab created a mathematical model for M-phase control in Xenopus oocyte (frog egg) extracts [Marlovits et al. 1998]. The M-phase control model shows principles by which you can apply phosphorylation and regulatory loops in your own models. Publications typically list systems of ordinary differential equatio ns (ODEs) that represent a model system. This example shows you how to interpret these ODEs in the form of reaction pathways that are easier to represent and visualize in SimBiology software.

The model is centered around M-phase promoting factor (MPF). There are two positive feedback lo ops where MPF increases its synthesis and a negative feedback loop where MPF decreases its amount by increasing its degradation.

• “M-Phase Control Model” on page 3-2

• “M-Phase Control Equations” on page 3-4

• “SimBiology Model with Rate and Algebraic Rules” on page 3-13

• “SimBiology Model with Reactions and Algebraic Rules” on page 3-21

• “References” on page 3-39

3 M-Phase Control in Xenopus Oocyte Extracts

M-Phase Control Model

In this section...

“Synthesis Reactions” on page 3-2

“Regulation Reactions with Active MPF” on page 3-2

Synthesis Reactions

Cyclin B (CycB) dimerizes with Cdc2 kinase (Cdc2) to form M-phase promoting factor (MPF).

3-2

Regu

Posi Cdc wit deg

lation Reactions with Active MPF

tive feedback loops with M-p ha se promoting factor (MPF) activate the

25 phosphatase and deactivate the Wee1 kinase. A negative feedback loop

h MPF activates anaphase-promoting complex (APC) that regulates the

radation of the Cyclin B subunit.

M-Phase Control Model

3-3

3 M-Phase Control in Xenopus Oocyte Extracts

M-Phase Control Equations

In this section...

“About the Rate Equations in This Example” on page 3-4

“Converting Differential Equations to Reactions” on p age 3-4

“Equation 1, Cyclin B” on page 3-6

“Equation 2, M-Phase Promoting Factor” on page 3-6

“Equation 3, Inhibited M-Phase Promoting Factor” on page 3-7

“Equation 4, Inhibited and Activated M-Phase Promoting Factor” on page 3-8

“Equation 5, Activated M-Phase Promoting Factor” on page 3-8

“Equation 11, Cell Division Control 25” on page 3-9

“Equation 12, Wee1 Activation/Deactivation” on page 3-10

“Equation 13, Intermediate Enzyme Activation/Deactivation” on page 3-10

3-4

“Equation 14, APC Activation/Deactivation” on page 3-11

“Equation 17, Rate Parameter K2” on page 3-11

“Equation 18, Rate Parameter Kcdc25” on page 3-12

“Equation 19, Rate Parameter Kwee1” on page 3-12

About the Rate Equations in This Example

Models in systems biology are commonly described in the literature with differential rate equations. However, SimBiology software defines a model using reactions. This section shows you how to convert models published in the literature to a SimBiology format. The equation numbers match the published paper for this model [Marlovits et al. 1998]. Equations that are missing in the sequence involve the Cdk inhibitor (CKI) protein, which is not currently modeled in the SimBiology version.

Converting Differential Equations to Reactions

The rules for writing reaction and reaction rate equations from differential rate equations include not only the equations but also an understanding of

M-Phase Control Equations

the reactions. dx/dt refers to the species the differential rate eq u ation is defining.

kinetics refers to the species in the reaction rate.

• Positive terms: Rate species are placed on right side of the reactions;

reaction rate equation species are placed on the left.

kinetics

→

• Negative terms: Rate species are placed on the left side of the reaction

because the species are being used up in some w ay; reaction rate equation species are also placed on left. You need to deduce the products from additional information about the model.

kinetics or (

) products?→

The following table will help you deduce the products for a reaction. In this example, by convention, phosphate groups on the right side of a species name are a ctivating while phosphate groups on left are inhibiting.

Enzyme

wee1

Description Reaction

Kinase, add inhibiting phosphate

MPF —> P-MPF

group

cdc25

Phosphatase, remove inhibiting

P-MPF —> MPF + P

phosphate group

kcak

Kinase, add activating

MPF —> MPFp

phosphate group

kpp

Phosphatase, remove activating

MPF-P —> MPF + P

phosphate group

MPF

kir

Kinase, add activating or inhibiting phosphate group

Wee1/Cdc25/IE — > X-P or P-X

Add inhibiting Cki Cki + MPF —> Cki:MPF

Remove inhibiting Cki Cki:MPF —> Cki + MPF

3-5

3 M-Phase Control in Xenopus Oocyte Extracts

Equation 1, Cycl

Differential ra

ddt[CycB]

Rate rule usin a model using Rules” on pag

Rule 1 [CycB] = k1 - K2*[CycB] - k3*[Cdc2]*[CycB]

Reaction an equation. Reactions

Reaction 1 AA -> CycB v = k1 Reaction 2 CycB -> AA v = K2*[CycB] Reaction 3 Cdc2 + CycB -> MPF v = k3*[Cdc2]*[CycB]

Equatio

Differe 1998]. N change hetero

ntial rate equ a tion for M-phase promoting factor (MPF) [Marlovits

dto

dimer of cdc2 kinase and cyclin B.

te equation for cyclin B [Marlovits et al. 1998].

k1 -k2[CycB] -k3[Cdc2][CycB]=+

g SimBiology format for the differential rate equation 1. For

this rule, see “SimBiology Model with Rate and Algebraic

e3-13.

d reaction rate equations derived from the differential rate For a model using these reactions, see “SimBiology Model with and Algebraic Rules” on page 3-21.

n 2, M-Phase Promoting Factor

ote that the parameter name

kpp [Borisuk 1998] in the f ollowing reaction equations. MPF is a

in B

kcakr [Marlovits et al. 1998] is

3-6

ddt[MPF]

+kpp[MPF=pp] -kcak[MPF]

+Kcdc25[pMPF] -Kwee1[MPF]

+kir[Cki:MPF] -ki[MPF][Cki]

e rule using SimBiology format for the differential rate equation 1. For

Rat

del using this rule, see “SimBiology M odel with Rate and Algebraic

amo

es” on p age 3-13.

Rul

Rule 2 MPF = kpp*MPFp - (Kwee1 + kcak + K2)*MPF + Kcdc25*pMPF + k3*Cdc2*CycB

+k3[Cdc2][CycB] -K2[MPF]

M-Phase Control Equations

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” o n page 3-21. A reaction name in parentheses denotes a reaction repeated in another differential rate equation.

(Reaction 3) Cdc2 + CycB -> MPF v = k3*[Cdc2]*[CycB] Reaction 4 MPF -> Cdc2 + AA v = K2*[MPF] Reaction 5 MPFp -> MPF v = kpp*[MPFp] Reaction 6 MPF -> MPFp v = kcak*[MPF] Reaction 7 pMPF -> MPF v = Kcdc25*[pMPF] Reaction 8 MPF -> pMPF v = Kwee1*[MPF]

Equation 3, Inhibited M-Phase Promoting Factor

Differential rate equation for inhibited M -phas e promoting factor (pMPF) [Marlovits 1998].

ddt[pMPF]

K2[pMPF]

+kpp[pMPFp] -kcak[pM=−PPF]

+Kwee1[MPF] -Kcdc25[pMPF]

+kd[Cki:pMPF]

Rate rule using SimBiology format for the differential rate equ ation 3. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Rule 3 pMPF = Kwee1*MPF - (Kcdc25 + kcak + K2)*pMPF + kpp*pMPFp

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Reaction 11 pMPF -> Cdc2 + AA v = K2*[pMPF] Reaction 12 pMPFp -> pMPF v = kpp*[pMPFp] Reaction 13 pMPF -> pMPFp v = kcak*[pMPF] (Reaction 8) MPF -> pMPF v = Kwee1*[MPF] (Reaction 7) pMPF -> MPF v = Kcdc25*[pMPF]

3-7

3 M-Phase Control in Xenopus Oocyte Extracts

Equation 4, Inhi Promoting Facto

Differential ra factor (pMPFp)

ddt[pMPFp]

+kcak[pMPF] -kpp=[[pMPFp]

+Kwee1[MPFp] -Kcdc25[pMPFp]

+kd[Cki:pMPFp]

Rate rule using SimBiology format for the differential rate e qu ation. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Rule 4 pMPFp = Kwee1*MPFp - (kpp + Kcdc25 + K2)*pMPFp + kcak*pMPF

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Reaction 15 pMPFp -> Cdc2 + AA v = K2*[pMPFp] (Reaction 13) pMPF -> pMPFp v = kcak*[pMPF] (Reaction 12) pMPFp -> pMPF v = kpp*[pMPFp] Reaction 16 MPFp -> pMPFp v = Kwee1*[MPFp] Reaction 17 pMPFp -> MPFp v = Kcdc25*[pMPFp]

te equation for inhibited and activated M-phase promoting

[Marlovits 1998].

-K2[pMPFp]

bited and Activated M-Phase

3-8

Equation 5, Activated M-Phase Promoting Factor

Differential rate equation for activated M-phase promoting factor (MPFp) [Marlovits 1998].

ddt[MPFp]

+kcak[MPF] -kpp[MPFp]]

+Kcdc25[pMPFp] -Kwee1[MPFp]

+kir[CKI:MPFp] -ki[CKI][MPFp]

= -K2[MPFp]

M-Phase Control Equations

Rate rule using SimBiology format for the differential rate equ ation 1. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Rule 5 MPFp = kcak*MPF - (kpp + Kwee1 + K2)*MPFp + Kcdc25*pMPFp

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Reaction 19 MPFp -> MPF + AA v = K2*[MPFp] (Reaction 6) MPF -> MPFp v = kcak*[MPF] (Reaction 5) MPFp -> MPF v = kpp*[MPFp] (Reaction 17) pMPFp -> MPFp v = Kcdc25*[pMPFp] (Reaction 16) MPFp -> pMPFp v = Kwee1*[MPFp]

Equation 11, Cell Division Control 25

Differential rate equation for activating and deactivating Cdc25 [Marlovits 1998].

ddt[Cdc25p]

k25[MPFp][Cdc25]

= +

Km25+[Cdc25]

k25r[Cdc25p]

225r+[Cdc25p]

Rate rule in SimBiolog y format for the differential rate equation 1. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13. Note that since there isn’t a rate rule for written as

Rule 11 Cdc25p = (k25*MPFp*(TotalCdc25 - Cdc25p))/(Km25 + (TotalCdc25 - Cdc25p)) - (k25r*PPase*Cdc25p)/(Km25r + Cdc25p)

(TotalCdc25 - Cdc25p).

Cdc25, its amount is

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Reaction 36 Cdc25 -> Cdc25p, v = k25*[MPFp]*[Cdc25]/(Km25 + [Cdc25]) Reaction 37 Cdc25p -> Cdc25, v = k25r*[Cdc25p]/(Km25r + [Cdc25p])

3-9

3 M-Phase Control in Xenopus Oocyte Extracts

Equation 12, Wee

Differential ra [Marlovits 1998 its inactive fo by an unknown ph

dWee

[] [ ][]

Rate rule in SimBiolog y format for the differential rate equation 1. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Rule 12 Wee1p = (kw*MPFp*(TotalWee1 - Wee1p))/(Kmw + (TotalWee1 - Wee1p))

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

reaction 38 Wee1 -> Wee1p, v = (kw*[MPFp]*[Wee1])/(Kmw + [Wee1]) reaction 39 Wee1p -> Wee1, v = (kwr*[Wee1p])/(Kmwr + [Wee1p])

te equation for activating and deactivating Wee1 kinase

]. The kinase (MPFp) phosphorylates active Wee1 (Wee1) to

rm (Wee1p). The dephosphorylation of inactive Wee1 (Wee1p) is

osphatase.

kw MPFp Wee

=−

Kmw Wee

1 Activation/De activation

kwr Wee P

[]

Kmwr Wee P

- (kwr*Wee1p)/(Kmwr + Wee1p)

Equation 13, Intermediate Enzyme Activation/Deactivation

Differential rate equation for a ctivating and deactivating the intermediate enzyme (IE) [Marlovits 1998]. The active kinase (MPFp) phosphorylates the inactive intermediate enzyme (IE) to its active form (IEp).

3-10

dIEpdtkie MPFp IE

[] [ ][]

Kmie IE

e rule in SimBiology format for the differential rate equation 1. For a

Rat

el using this rule, see “SimBiology Model with Rate and Algebraic Rules”

mod

age 3-13.

on p

Rule 13 IEp = (kie*MPFp*(TotalIE - IEp))/(Kmie + (TotalIE - IEp))

[]

- (kier*IEp)/(Kmier + IEp)

kier IEp

−

[]

Kmier IEp

[]

M-Phase Control Equations

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

reaction 40 IE -> IEp, v = (kie*[MPFp]*[IE])/(Kmie + [IE]) reaction 41 IEp -> IE, v = (kier*[IEp])/(Kmier + [IEp])

Equation 14, APC Activation/Deactivation

Differential rate equation for [Marlovits 1998].

dAPCadtkap IEP APCi

[] [][]

Kmap APCi

[]

kapr APCa

−

Kmapr APCa

[]

[

]]

Rate rule in SimBiolog y format for the differential rate equation 1. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Rule 14 APCa = (kap*IEp*(TotalAPC - APCa))/(Kmap + (TotalAPC - APCa))

- (kapr*APCa)/(Kmapr + APCa)

Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Reaction 42 APCi -> APCa, v = (kap*[IEp]*[APCi])/(Kmap + [APCi]) Reaction 43 APCa -> APCi, v = (kapr*[APCa])/(Kmapr + [APCa])

Equation 17, Rate Parameter K2

Algebraic equation to define the rate parameter K2 [Marlovits 1998]. Inactive APC (APCi) is catalyzed by IE (intermediate enzyme) to active APC (APCa).

k2 = V ’[APC] + V ’’[APC’]22

Algebraic rule in SimBiology format for the algebraic equation 17. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Algebraic Rule 17 V2i*(TotalAPC - APCa) + V2a*APCa - K2

Algebraic rule when simulating with reactions. For a model using this rule with reactions, see “SimBiology Model with Reactions and Algebraic Rules”

3-11

3 M-Phase Control in Xenopus Oocyte Extracts

on page 3-21. V2' is renamed to V2i and V2 is renamed to V2a. APCi (APC) is the inactive form of the enzyme while APCa (APC’) is the active form. is the independent variable.

Algebraic Rule 1 (V2i*APCi) + (V2a*APCa) - K2

Equation 18, Rate Parameter Kcdc25

Algebraic equation to define the rate parameter Kcdc25 [Marlovits 1998]. Inactive Cdc25 (

kcdc25 = V ’[Cdc25] + V ’’[Cdc25p]25 25

Algebraic rule in SimBiology format for the algebraic equation 18. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Algebraic Rule 18 V25i*(TotalCdc25 - Cdc25p) + V25a*Cdc25p - Kcdc25

Algebraic rule when simulating with reactions. Kcdc25 is the independent variable. For a model using this rule with reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Cdc25) is phosphorylated by MPF to active Cdc25 (Cdc25p).

3-12

Algebraic Rule 2 (V25i*Cdc25) + (V25a*Cdc25p) - Kcdc25

Equation 19, Rate Parameter Kwee1

Algebraic equation to define the rate parameter [Marlovits 1998]. Active Wee1 (

Algebraic rule in SimBiology format for rate parameter equation 19. For a model using this rule, see “SimBiology Model with Rate and Algebraic Rules” on page 3-13.

Algebraic rule when simulating with reactions. Kwee1 is the independent variable. For a model using this rule with reactions, see “SimBiology Model with Reactions and Algebraic Rules” on page 3-21.

Wee1) is phosphorylated by MPF to inactive Wee1 (Wee1p).

k = V ’[Wee1p] + V ’’[Wee1]wee1 wee1 wee1

Algebraic Rule 19 Vwee1i*Wee1p + Vwee1a*(TotalWee1 - Wee1p) - Kwee1

Algebraic Rule 3 (Vwee1i*Wee1p) + (Vwee1a*Wee1) - Kwee1

SimBiology®Model with Rate and Algebraic Rules

SimBiology Model with Rate and Algebraic Rules

In this section...

“Overview” on page 3-13

“Writing Differential Rate EquationsasRateRules”onpage3-14

“Species” on page 3-14

“Parameters” on page 3-15

“RateRule1,CyclinB(CycB)”onpage3-16

“Rate Rule 2, M-Phase Promoting Factor (MPF)” on page 3-17

“Rate Rule 3, Inhibited M-Phase Promoting Factor (pMPF)” on page 3-17

“Rate Rule 4, Activated but Inhibited M-Phase Promoting Factor (pMPFp)” on page 3-18

“Rate Rule 5, Activated M-Phase Promoting Factor (MPFp)” on page 3-18

“Rate Rule 11, Activated Cdc25 (Cdc25p)” on page 3-18

“Rate Rule 12, Inhibited Wee1 (Wee1p)” on page 3-18

“RateRule13,ActivatedIntermediateEnzyme(IEp)”onpage3-18

“Rate Rule 14, Activated A PC (APCa)” on page 3-18

“Algebraic Rule 17, Rate Parameter K2” on page 3-19

“Algebraic Rule 18, Rate Parameter Kcdc25” on page 3-19

“Algebraic Rule 19, Rate Parameter Kwee1” on page 3-19

“Simulation of the M-Phase Control Model with Rules” on page 3-19

Overview

There is one rate rule for each equation defining a species and one algebraic rule for each variable parameter in the M-phase control model [Marlov its 1998]. For a lis t and description of the equations, see “M-Phase Control Equations” on page 3-4.

A basic model includes rate rules 1 to 5 and 11 to 14 with algebraic rules 17, 18, and 19.

3-13

3 M-Phase Control in Xenopus Oocyte Extracts

Writing Differential Rate Equations as Rate Rules

Writing differential rate equations in an unambiguous format that a software program can understand is a simple process when you follow the syntax rules for programming languages.

• Use an asterisk to ind ica t e multiplication. For example,

or k*[A]. The brackets around the species A do not indicate concentration.

• SimBiology uses square brackets around species and parameter name to

allow names that are not valid MATLAB variable names. For example, you could have a species named need to add brackets around the name inreactionrateandruleequations.

[glucose-6-phosphate dehydrogenase]

• Use parentheses to clarify the order of evaluation for mathematical

operations. For example, do not write Henri-Michaelis-Menten reaction rates as result. Instead, write this reaction rate as

Vm*C/Kd + C,becauseVm*C is divided by Kd before adding C to the

glucose-6-phosphate dehydrogenase but y ou

(Vm*C)/(Kd + C).

k[A] is w ri tte n k*A

Species

The following table lists species in the model with their in i tial amounts. There are three variable parameters modeled as species (

KWee1). You could also model the variable parameters as parameters with the

property ConstantAmount cleared.

K2, Kcdc25,and

3-14

SimBiology®Model with Rate and Algebraic Rules

Parameters

The following table lists parameters in the m odel with their initial values. The property ConstantValue is selected for all of the parameters.

3-15

3 M-Phase Control in Xenopus Oocyte Extracts

3-16

Rate Rule 1, Cyclin B (CycB)

Therateruleisfrom“Equation1,CyclinB”onpage3-6.

rate rule: CycB = k1 - K2*CycB - k3*Cdc2*CycB

Mathworks SIMBIOLOGY 3 Model Reference

Specifications and Main Features

Frequently Asked Questions

User Manual

Minimal Cascade Model for a Mitotic Oscillator

Goldbeter Model

About the Goldbeter Model

Reaction Descriptions and Model Assumptions

Mathematical Model

Differential Rate Equation 1, Cyclin (C)

Differential Rate Equation 2, Kinase (M)

Differential Rate Equation 3, Protease (X)

SimBiology Model with Rate Rules

SimBiology Model with Rules

Species

Parameters

Rules

SimBiology Simulation with Rules

SimBiology Model with Reactions

Converting Differential Rate Equations to Reactions

Reactions R1 to R3 from Equation E1

Reactions R4 and R5 from Equation E2

Reactions R6 and R7 from Equation E3

Calculating Initial Values for Reactions

Reaction 1 Cyclin Synthesis

Reaction 2 Cyclin Undifferentiated Degradation

Reaction 3 Cyclin Protease Degradation

Reaction 4 Cdc2 Kinase Activation

Reaction 5 Cdc2 Kinase Deactivation

Reaction 6 Protease Activation

Reaction 7 Protease Deactivation

SimBiology Simulation with Reactions

References

ModeloftheYeast Heterotrimeric G Protein Cycle

Objectives

Background on G Protein Cycles

G Proteins

Modeling a G Protein Cycle

Reactions Overview

Assumptions, Experimental Data, and Units in the G Protein Model

Building the G Protein Cycle Model

Tutorial Goals

Opening the SimBiology Desktop

Adding a Reaction to the SimBiology Model

Determining the Reaction Rate Equation

Setting the Compartment Name

Setting Initial Amounts of Species

Completing the SimBiology Model

Reactions

Alternative Ways to Build Reactions in the Desktop

Building a Reaction

Creating a Binding Reaction

Creating an Unbinding Reaction

Parameters

Parameter Value Table

Species

Species Initial Amounts

Additional Species

Creating a Rule for the G Protein Model

Verifying the Model

Simulating the G Protein Cycle Model

Setting Conditions Before Simulating the G Protein Model

Adding a Simulation Task

Changing the Simulation Stop Time

Specifying Which Data Is Recorded

Tips for Use and Points to Consider

Simulation Results for the Wild-Type Strain Model

Saving Simulation Data

Creating the Mutant Strain Using a Variant

Modeling the Mutant Strain

Applying Alternate Values Using Variants

See Also

Simulation Results for the Model of the Mutant Strain

Creating a Custom Plot-Type to View Simulation Results

Creating a Custom Plot

Code Modifications for Line Style

Visualizing Results for the Mutant Strain Using a Custom Plot

Plotting the Results

Plotting Species from Two Different Data Sets

Procedures Described in This Section