Mathworks SIMBIOLOGY 3 user guide

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SimBiology

User’s Guide

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SimBiology

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User’s Guide

Revision History

September 2005 O nline 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 O nline 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 O nline only Updated for Version 3.1 (Release 2009b) March 2010 Online only Updated for Version 3.2 (Release 2010a)

Modeling

SimBiology Model Components ..................... 1-3

Organization of SimBiology Objects Model Compartment Species Reaction Kinetic Law Parameters Rules Events Configuration Sets Variants Simulation Data

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Contents

Defining Reaction Rates with Mass Action Kinetics

Definition of Mass Action Kinetics Zero-Order Reactions First-Order Reactions Second-Order Reactions Reversible Mass Action

Defining Reaction Rates with Enzyme Kinetics

Simple Model for Single Substrate Catalyzed Reactions Enzyme Reactions with Differential Rate Equations Enzyme Reactions with Mass Action Kinetics Enzyme Reactions with Irreversible

Henri-Michaelis-Menten Kinetics

Evaluation of Reaction Rate

Reaction Rate Dimensions Reactions Spanning Multiple Compartments Examples

........................................ 1-25

.............................. 1-14

.............................. 1-16

............................ 1-17

............................. 1-19

.......................... 1-25

.................... 1-14

....... 1-20

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.................. 1-23

........................ 1-25

.......... 1-25

... 1-13

.. 1-20

..... 1-20

Using Constant Amount and Boundary Condition for

Species

Definition of Constant and Boundary Properties Changing Species Amounts with Reactions or Rules Keeping Species Amount Unchanged Constant = NO, Boundary = YES Constant = YES, Boundary = YES Model Edges

Scoping Parameters for Reactions, Rules, and

Events

Definition of Parameter Scope Using a Parameter in Events and Rules Changing the Scope of a Parameter

......................................... 1-27

........ 1-27

..... 1-28

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..................... 1-29

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................... 1-33

Changing Model Component Values Using Rules

What Is a Rule? What Is an initialAssignment Rule? What Is a repeatedAssignment Rule? What Is an Algebraic Rule? What Is a Rate Rule? Typical Uses of Rate Rules

Changing Model Component Values Using Events

What Is an Event? How Events Are Evaluated Evaluation of Simultaneous Events Evaluation of Multiple Event Functions When O n e Event Trig ge rs Another Event Cyclical Events

Desktop Example — Changing Species Amounts Using

an Event

Overview Prerequisites Adding an Event to the Example Model Simulating the Modified Model

................................... 1-34

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..... 1-34

.... 1-42

vi Contents

Storing and Applying Alternate Model Values Using

Variants

What Are Variants? Using Variants

........................................ 1-58

............................... 1-58

................................... 1-59

Applying Multiple Variants in a Model ................ 1-60

Desktop Example — Applying Changes to Parameter

Value Using a V ariant

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

........................................ 1-61

..................................... 1-62

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............. 1-63

... 1-63

Verifying that a Model Has No Warn ing s or Errors

Verifying a Model in the SimBiology Desktop Verifying the Model at the Command Line

Desktop Example — Using User-Defined Functions in

Expressions

Prerequisites Overview Creating a Function Calling the Function in a Rule Expression See Also

Importing and Exporting Model Component Data

Importing Model Component Data Exporting M odel Component Data

..................................... 1-69

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Simulation

Performing Simulations ............................ 2-2

Performing Simulations at the Command Line Performing Simulations in the SimBiology Desktop

......... 2-2

... 1-66

.... 1-78

..... 2-2

About Simulation Solvers

How Solvers Work Stiff Versus Nonstiff Models Selecting a Solver

Nonstiff Determ inistic Solvers

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

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vii

When to Use No nstiff Deterministic Solv ers ............ 2-8

ode45 (Dormand-Prince) ode23 (Bogacki-Shampine) ode113 (Adams) See Also

......................................... 2-9

................................... 2-8

............................ 2-8

.......................... 2-8

Stiff Deterministic Solvers

When to Use Stiff Deterministic Solvers ode15s (stiff/NDF) ode23s (stiff/Mod. Rosenbrock) ode23t (Mode. stiff/Trapezoidal) ode23tb (stiff/TR-BDF2) See Also

Stochastic Solvers

When to Use Stochastic Solvers Stochastic Simulation Algorithm (SSA) Explicit Tau-Leaping Algorithm Implicit Tau-Leaping Algorithm Ensemble Runs of Stochastic Simulations References

Sundials Solvers

Accelerating Simulations

Prerequisites for Accelerating Simulations When to Accelerate Simulations Accelerating Simulations at the Command Line Accelerating Simulations in the SimBiology Desktop Troubleshooting

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viii Contents

Scanning Analysis ................................. 3-2

Scanning Overview Creating a Scan Task Setting Options to Scan Using User-Defined Values Options For Monte Carlo Methods

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

.............................. 3-3

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

Analysis

..... 3-3

Setting Options to Scan Using Monte C arlo Methods .... 3-7

Desktop Example — Scanning

Overview Prerequisites Setting Options to Scan with One Parameter Results of Scanning with One Parameter Scanning with Multiple Parameters Results of Scanning with Multiple Parameters References

Sensitivity Analysis

About S ensitivity Analysis Performing Sensitivity Analysis Using the Command

Line Performing Sensitivity Analysis Using the Desktop Reference

Desktop E xam ple — Calculating Sensitivities

Overview Prerequisites Setting Options for Sensitivity Analysis Getting Results for Sensitivity Analysis References

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

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

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Command-Line Example — Calculating Sensitivities

Overview Loading and Configuring the Model for Sensitivity

Analysis Performing Sensitivity Analysis Extracting and Plotting Sensitivity Data See Also

Parameter Estimation

About Parameter Estimation SimBiology Parameter Estimation

Command-Line E x am ple — Parameter Estimation

About the Example Model Importing Target Experimental Data Simulating the G Protein Model

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.. 3-36

.... 3-43

Estimating a Parameter (kGd) in the G Protein Model ... 3-47 Simulating and Plotting Results U sing the Estimated

Parameter

Estimating Other Parameters in the G Protein Model

..................................... 3-50

.... 3-51

Moiety Conservation

Introduction to Moiety C onserv ation Algorithms for Conserved Cycle Calculations

Command-Line Examples — D eterm ining Conserved

Moieties

GProteinExample Mitotic Oscillator Example

Desktop E xam ple — Creating Custom Analysis

About Custom Analysis Open the Example Project Setting Up a Custom Task Parameter Estimation Using Custom Task

Visualizing Results Using Plot Types

AboutPlotTypes How Plot Types Work Summary of Built-In Plot Types When to Use User-Defined Plot-Types

Desktop Example — Creating and Using Plot Types

Goal Workflow Why Use User-Defined Plot Types? Creating a User-Defined Plot Type in the Library

Explorer

Using the Plot Type in a Task

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.. 3-78

x Contents

Pharmacokinetic Modeling

Pharmacokinetic Modeling Functionality ............ 4-2

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

Required and Recommended Software for Pharmacokinetic

Modeling How This Product Supports Pharmacokinetic Modeling Using the Command Line Versus the SimBiology

Desktop Accessing a Pharmacokinetic Modeling Demo Acknowledgements: Tobramycin Data Set

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

.. 4-4

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.......... 4-6

............. 4-6

Importing Data — Supported Files and Data Types

Supported Files and Data Types Support for Importing NONMEM Formatted Files Creating a Data File with SimBiology Definitions

Importing D ata at the Command Line

Importing Data From NONMEM Formatted Files Importing Data Using the dataset function Other Resources for Importing Data

ImportingDataintotheSimBiologyDesktop

Data Import Using the SimBiology Desktop Importing Data from a File to the SimBiology Desktop Importing Data from the MATLAB Workspace to the

SimBiology Desktop Column Heading Classification for NONMEM

Interpretation of Headers Resources for Working with Imported Data

Working with Imported Data and the SimBiology

Desktop

Accessing Imported Data Specifying Units and Identifying Group and Independent

Variables in the Data Plotting Da ta Excluding Rows of Data Creating Additional Data Columns Using Derived Data Calculating Statistics for Imported Data Creating Dose Schedules Using Imported Data Saving Your Work as a SimBiology Project File

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...... 4-8

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... 4-8

... 4-19

.. 4-39

Creating Pharmacok inetic Models

Overview

........................................ 4-43

.................. 4-43

How SimBiology Models Represent Pharmacokinetic

Models Creating PK Models at the Command Line Creating PK Models in the SimBiology Desktop Using a

Wizard About Dosing Types About Elimination Types About Intercompartmental Clearance Unit Conversion for Imported Data and the Model Prerequisites for Using Custom SimBiology Models in

Parameter Fitting

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............. 4-45

........................................ 4-47

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...... 4-54

............................... 4-55

Parameter Fitting in Pharmacokinetic Mod els

Parameter Fitting Functionality Prerequisites for Parameter Fitting

Fitting Pharmacokinetic Model Parameters at the

Command Line

Fitting Parameters Specifying and Classifying the Data to Fit Setting Initial Estimates Specifying the Covariance Pattern of Random Effects and a

Covariate Model Specifying an Error Model Specifying Parameter Transformations Performing Population Fitting Using sbionlmefit or

sbionlmefitsa Performing Individual Fitting Using sbionlinfit About Simulation Settings and Specifying Alternate Values

for Initial Estimates

Fitting Pharmacokinetic Model Parameters in the

SimBiology Desktop

Fitting Parameters Opening a SimBiology Project Adding a Model Task to Fit Parameters Performing Population Fitting Performing Individual Fitting About Simulation Settings and Specifying Alternate Values

for Initial Estimates Visualizing Parameter Fitting Results and Generating

Diagnostic Plots

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xii Contents

Index

xiii

xiv Contents

Modeling

This chapter is a collection of topics relevant to modeling in general, but is presented in the context of using SimBiology biological processes.

• “SimBiology Model Components” on page 1-3

software to model

• “Defining Reaction Rates with Mass A ction Kinetics” on page 1-13

• “Defining Reaction Rates with Enzyme Kinetics” on page 1-20

• “Evaluation of Reaction Rate” on page 1-25

• “Using Constant Amount and Boundary Condition for Species” on page 1-27

• “Scoping Parameters for Reactions, Rules, and Events” on page 1-32

• “Changing Model Component Values Using Rules” on page 1-34

• “Changing Model Component Values Using Events” on page 1-42

• “Desktop Example — Changing Species Amounts Using an Event” on page

1-51

• “Storing and Applying Alternate Model Values Us in g Variants” on page

1-58

• “Desktop Example — Applying Changes to Parameter Value Using a

Variant” on page 1-61

• “Verifying that a Model Has No Warnings or Errors” on page 1-66

1 Modeling

• “Desktop Example — Using User-Defined Functions in Expressions” on

page 1-69

• “Importing and Exporting Model Component Data” on page 1-78

1-2

SimBiology Model Components

In this section...

“Organization of SimBiology Objects” on page 1-3

“Model” on page 1-6

“Compartment” on page 1-6

“Species” on page 1-6

“Reaction” on page 1-7

“Kinetic Law” on page 1-7

“Parameters” on page 1-8

“Rules” on page 1-9

“Events” on page 1-10

“Configuration Sets” on page 1-10

“Variants” on page 1-11

SimBiology®Model Components

“Simulation Data” on page 1-12

Organization of SimBiology Objects

IfyouplantoworkmainlyfromtheSimBiologydesktopGUI,youcanskip this section and go to “Model” on page 1-6. The GUI allows you to interactively work with SimBiology model components without having prior k nowledge of object-oriented programming, or the object implementation thereof in the software product.

If you plan on using the product at the command line or have workflows that span the desktop and the command line, it is useful understand the hierarchical organization of SimBiology objects.

SimBiology objects are organized as a hierarchical list of objects under one

root object. Models and each model component are represented as objects.

Further, there are objects to store simulation settings ( data from simulation and analysis tasks ( the command line or the SimBiology desktop are contained in the

SimData object). Objects created at

configset object) and

root obje ct.

1-3

1 Modeling

Models must contain at least one species object and one compartment object. The hierarchy of objects in models is as follows:

Model

Compartment

Species Parameters Reaction

Kinetic Law

Parameters Rules Events Variant Configset

SimData

Parameters can be scoped to a kinetic law or the model.

1-4

The function

sbioreset deletes all model and simulation objects at the root

level. You should remove the objects from the workspace with the function

clear. If the SimBiology desktop is open, note that calling sbioreset at the

command line also deletes model and data objects that are open in the desktop.

All SimBiology objects are all handle objects. A handle is a reference to an object. If you copy an object’s handle, MATLAB

copies only the handle and both the original and copy refer to the same object data. If a function modifies a handle object passed as an input argument, the modification affects the original object. For example,

%Create a model Mobj = sbiomodel('cell')

SimBiology Model - cell

Model Components:

Compartments: 0 Events: 0 Parameters: 0 Reactions: 0

SimBiology®Model Components

Rules: 0 Species: 0

%Assign the model object to another variable newMobj = Mobj; % Modify the new variabl compObj = addcompartment(newMobj, 'contents'); set(newMobj, 'Name', 'newcell') % The new variable has a compartment and a new name newMobj

SimBiology Model - newcell

Model Components:

Compartments: 1 Events: 0 Parameters: 0 Reactions: 0 Rules: 0 Species: 0

% The change is reflected in the original variable Mobj

SimBiology Model - newcell

Model Components:

Compartments: 1 Events: 0 Parameters: 0 Reactions: 0 Rules: 0 Species: 0

The recommended method to store your SimBiology models is to create and store project files.

1-5

1 Modeling

Model

ASimBiologymod events that tran are compartmen creating a mode define a kinet

sform, transport, and bind species. The model components ts, species, reactions, parameters, rules, and events. After

l, add a compartment, then you can add reactions to the model,

ic law for each reaction, and add the parameters for the reaction.

el is a collection of interrelated reactions, rules, and

Properties de object inclu species, par properties i list object

Compartme

A compartm regions.

Since com to compar the mode

All mode must be a anothe model. SimBio

Speci

A spec

DNA, (MAP

ies is a chemical or entity that participates in reactions, for example,

ATP, Pi, creatine , G-Protein,orMitogen-Activated Protein Kinase K)

fine the characteristics of an object. For example, a reactio n

des properties for reactions, reaction rates, and links to associated

ameters, and kinetic laws. Y ou can interactively change object n the graphical user interface. Use the

properties and change their values at the command line.

get and set commands to

ent allows you to associate pools of species to physically isolated

partments define physically isolated regions, species are assigned tments. Reactions, rules, events, and parameters are assigned to

ls m ust have at least one compartment and all species in a model

ssigned to a compartment. You can create a compartment within

r compartment, but compartment names must be unique within a

For information on specifying names of compartments, see logy Reference documentation.

. Species amounts can vary or remain constant during a simulation.

Name in the

1-6

nformation on specifying names of species, see

For i

erence documentation.

Ref

Name in the SimBiology

SimBiology®Model Components

Reaction

A reaction describes a transformation, transport, or binding process that changes one or more species. Typically, the change is the amount of a species.

Examples:

Creatine + ATP <-> ADP + phosphocreatine glucose + 2 ADP + 2 Pi -> 2 lactic acid + 2 AT cytoplasm.A -> nucleus.A [compartment 1].[species A] -> [compa

rtment 2].[species A]

Spaces are required before and after species names and stoichiometric values. Stoichiometry values must be greater than zero. If the stoichiometry value is not sp eci fi ed it is assumed to be 1. In a model with a single compartment, the species is specified using its name. In a model with multiple compartments, the species must be specified as

compartmentName.speciesName.Enclose

names with non-alphanumeric characters in brackets.

P+2H2O

Kinetic Law

A kinetic law pr ovides a mechanism for applying a specific rate law to multiple reactions. It acts as a templateforthereactionrate. Thekinetic law is defined by an expression, and the species and parameter variables used in the expression.

The

ReactionRate is the result of defining the names of parameters and

species variables in a rate law. To get and parameter variables that participate in the reaction rate should be clearly assigned in the Project Settings-Reactions pane on the Kinetic Law tab.

Forexample,thekineticlaw

Henri-Michaelis-Menten is expressed in the

software as

VSK S

*/( )+

where Vm and Km are defined as parameters and S is defined as a species. (To see p arameter and species definitions for a kinetic law, access the Kinetic Law Manager from the Desktop menu.)

By applying the kinetic law

Henri-Michaelis-Menten to a reaction

ReactionRate, the species variables

1-7

1 Modeling

A->B with Vm = Va and Km = Ka andS=A

the rate equation is

Va*A/(Ka + A)

A, Va,andKa are defined in the Kinetic Law tab.

Reaction Rate Equation

The reaction rate equation is a mathematical expression that describes the rate at which the reactants combine to form products.

For a reaction following Mass Action kinetics,

Creatine + ATP <-> ADP + phosphocreatine

1-8

the rate equation is written as

K*Creatine*ATP - Krev*ADP*phosphocreatine

Parameters

A parameter is a quantity that can change or can be constant. Parameters are generallyusedtodefinerateconstants. But,youcouldalsouseparametersas constants to modify model component values in rules and events.

For information on specifying names of parameters see Reference documentation.

Scope refers to the definition of a parameter at the model (global) level or kinetic law (local) level.

If the scope of the parameter is global in the model, it can be used by any rule, event, or by any reaction rate in the model. If the scope of the parameter is at the kinetic law level, it can be used only by the kinetic law in the reaction for which it was defined.

Name in the S imBiology

SimBiology®Model Components

How to Use Scope

For reaction rate, SimBiology hierarchically uses the value of the parameter with scope at the kinetic law level first. If there is no such parameter at the kinetic law level, SimBiology looks for the parameter with scope at the model level.

If there are two parameters with the same name, one at the model level and the other at the kinetic law level, the software uses the value of the parameter at the kinetic law level for the reaction rate. The software uses the value of the parameter at the m o del level for any rules or events that reference the parameter.

Rules

A rule is a mathematical expression that modifies a species amount, compartment capacity, or a parameter value. There are four types of SimBiology rules:

•

algebraic — Algebraic rules are evaluated continuously during a

simulation. An algebraic rule takes the form rule is specified as the conservation ex pression such as

Expression. For example, you could write a mass

species_total = species1 + species2

0 = Expression and the

where species_total is the independent variab le . In SimBiology, write theruleas

initialAssignment — initialAssignment rules are evaluated

•

once at the beginning of a simulation. expressed as

initialAssignment rule to set the amount of species1 to be proportional

species2.

species1 = k/species2

species1 + species2 - species_total.

initialAssignment rules are

Variable = Expression. For example, you could write an

• repeatedAssignment — repeatedAssignment rules are evaluated at every

time-step during a simulation. as

Variable = Expression. F or example, you could use the rule to specify

the amount of

species1 = k/species2

species1 to always be proportional to species2.

repeatedAssignment rules are expressed

1-9

1 Modeling

• rate — R ate rules are evaluated continuously during a simulation. Rate

rules are determined by in the software as rate of change in the q uantity of in the software as:

species3 = k * (species1 + species2)

Oneexampleofarateruleiswhenspecies1 is at the boundary of the system, but the rate of input of by a rate rule.

Tip Ifyouplantouseaparameterinarule,remembertosettheScope of the parameter to rule to vary the value of a parameter during the simulation, clear the

ConstantValue check box for the parameter in the Parameters pane, Settings tab.

dVariable/dt = Expression, which is expressed

Variable = Expression. For example, to define the

species3 (dspecies3/dt),writetherule

species1 to the system can be determined

model. Further, if you are using an algebraic or rate

1-10

For more information, see “Changing Model Component Values Using Rules” on page 1-34 in the SimBiology U ser’s Guide.

Events

Events are used to describe sudden changes in model behavior. An event lets you specify discrete transitions in model component values that occur when a user-specified condition become true. You can specify that the event occurs at a particular time, or spe c if y a time-independent condition. For example, you can use events to activate or deactivate ce rtain species (activator or inhibitor species), change parameter values, change reaction rates in response to addition or removal of species. For more inf ormation about events, evaluation of events, and examples, see “Changing Model Component Values Using Events” on page 1-42 in the SimBiology User’s Guide.

Configuration Sets

Configuration sets contain the options that the solver uses during simulation of a model. To add, view or edit configuration sets associated with a model, in

SimBiology®Model Components

the Project Explorer,clickConfiguration Settings. The configuration set contains the following options for you to choose:

• Type of solver

• Data to record (Data Logging tab)

• Stop time for the simulation

• Solver error tolerances, and for ode solvers – the maximum time step the

solver should take

• Whether to perform sensitivity analysis during simulation

• Whether to perform dimensional analysis and unit conversion during

simulation

• Species and parameter input and output factors for sensitivity analysis

For more information see “Performing Simulations” on page 2-2 in the SimBiology User’s Guide.

Variants

Variants let you store the names and values of model components and allow you to use the values stored in the variant as the alternate value to be applied during a simulation. To add, view or edit variants associated with a model, in the Project Explorer,clickVariants. You can store values for species

InitialAmount,parameterValue,andcompartmentCapacity,invariants.

Using one or more variants associated with a model allows you to evaluate model behavior during simulation, with different values for the various model components without having to search and replace these values, or having to create additional models with these values. If you determine that the values in a variant accurately define your model, you ca n permanently replace the values in your model with the values stored in the variant object by clicking Commit.

For more information see “Storing and Applying Alternate Model Values Using Variants” on page 1-58in the SimBiology User’s Guide.

1-11

1 Modeling

Simulation Data

The SimBiology S holds time and st for the logged s more informati

imData

ate data as well as metadata, such as the types and names

tates, or the configuration set used during simulation. For

on see

object contains simulation data. The SimData object

SimData object.

1-12

Defining Reaction Rates with Mass Action Kinetics

In this section...

“Definition of Mass Action Kinetics” on page 1-14

“Zero-Order Reactions” on page 1-14

“First-Order Reactions” on page 1-16

“Second-Order Reactions” on page 1-17

“Reversible Mass A ction ” on page 1-19

1-13

1 Modeling

Definition of Mass Action Kinetics

Mass action describes the be havio r of reactants and products in an eleme ntary chemical reaction . Mass a ction kinetics describes this behavior as an equation where the velocity or rate of a chemical reaction is directly proportional to the concentration of the reactants.

Zero-Order Reactions

With a zero-order reaction, the reaction rate does not depend on the concentration of reactants. Ex am ples of zero-order reactions are synthesis from a at a specified rate.

null species, and modeling a source species that is added to the system

reaction: null -> P

reaction rate: k mole/second

species: P = 0 mole

parameters: k = 1 mole/second

1-14

Note When specifying a null species, the reaction rate must be defined in units of amount per unit time not concentration per unit time.

Entering the reaction above into the software and simulating produces the following result:

Zero-Order Mass Action Kinetics

Defining Reaction Rates with Mass Action Kinetics

Note If the amount of a reactant with zero-order kinetics reaches zero before the end of a simulation, then the amount of reactant can go below zero regardless of the solver or tolerances you set.

1-15

1 Modeling

First-Order Rea

With a first-ord concentration o radioactive de

reaction: R -> P

reaction rate: k*R mole/(liter*second)

parameters: k = 1 1/second

Entering th following r

er reaction, the reaction rate is proportional to the

f a single reactant. An example of a first-order reaction is

cay.

species: R = 10 mole/liter

e reaction above into the software and simulating produces the

esults:

ctions

P = 0 mole/liter

1-16

First-Order Mass Action Kinetics

Defining Reaction Rates with Mass Action Kinetics

Second-Order Re

A second-order r or the concentra Notice the spac reactant. With

reaction: 2 R -> P

reaction rate: k*R^2 mole/(liter*second)

parameters: k = 1 liter/(mole*second)

Entering th following r

eaction h as a reaction rate that is proportional to the square tion of a single reactant or proportional to two reactants.

e between the reactant coe fficient and the name of the

out the space,

species: R = 10 mole/liter

e reaction above into the software and simulating produces the

esults:

actions

2R would be considered the name of a species.

P = 0 mole/liter

Second-Order Kinetics with Single Reactant

With two reactants, the reaction rate depends on the concentration of two of the reactants.

reaction: R1 + R2 -> P

reaction rate: k*R1*R2 mole/(liter*second)

1-17

1 Modeling

species: R1 = 10 mole/liter

R2 = 8 mole/liter

P = 0 mole/liter

parameters: k = 1 liter/(mole*second)

Enter the reaction above into the software and simulating produces the following results. There is a difference in the final values because the initial amount of one of the reactants is low er than the other. After the f irst reactant is used up, the reaction stops.

1-18

d-Order Kinetics with Two Reactants

Secon

Defining Reaction Rates with Mass Action Kinetics

Reversible Mass

You can model rev reaction. With a and reverse rea brackets befor

reaction: R <-> P

reaction rate: kf*R - kr*P mole/(liter*second)

species: R = 10 mole/liter

parameters: kf = 1 1/second

Entering th following the revers

results. At equilibrium when the rate of the forward reaction equals

ereaction,

single reversible reaction, the reaction rates for the forward

ctions are combined into one expression. Notice the angle

e and after the hyphen to represent a reversible reaction.

e reaction above into the software and simulating produces the

Action

ersible reactions with two s eparate reactions or with one

P = 0 mole/liter

kr = 0.2 1/second

v = kf*R - kr*P = 0 and P/R = kf/kr.

1-19

1 Modeling

Defining Reaction Rates with Enzyme Kinetics

In this section...

“Simple Model for Single Substrate Catalyzed Reactions” on page 1-20

“Enzyme Reactions with Differential Rate Equations” on page 1-20

“Enzyme Reactions with Mass Action Kinetics” on page 1-22

“Enzyme Reactions with Irreversible Henri-Michaelis-Menten Kinetics” on page 1-23

Simple Model for Single Substrate Catalyzed Reactions

A simple model for enzyme-catalyzed reactions starts a substrate S reversibly binding with an enzyme complex is converted to product

E. Some of the substrate in the substrate/enzyme

P w ith the release of the enzyme.

⎯→⎯⎯

S + E ES E + P

←⎯⎯⎯

k1r

v = k [S][E], v = k [ES], v = k [ES]

1 1 1r 1r 2 2

This simple model can be defined with

• Differential rate equations. See “Enzyme Reactions w ith Differential Rate

Equations” on page 1-20.

• Reactions with mass action kinetics. See “Enzyme Reactions with Mass

Action Kinetics” on page 1-22.

• Reactions with H enri-Michaelis-Menten kinetics. See “Enzyme Reactions

with Irreversible Henri-Michaelis-Menten Kinetics” on page 1-23.

⎯→⎯⎯

Enzyme Reactions with Differential Rate Equations

The reactions for a single-substrate enzyme reaction mechanism (see “Simple Model for Single Substrate Catalyzed Reactions” on page 1-20) can be described with differential rate equations. You can enter the differential rate equations into the software as rate rules.

reactions: none

1-20

Defining Reaction Rates with Enzyme Kinetics

reaction rate: none

rate rules: dS/dt = k1r*ES - k1*S*E

dE/dt = k1r*ES + k2*ES - k1*S*E dES/dt = k1*S*E - k1r*ES - k2*ES dP/dt = k2*ES

species: S = 8 mole

E = 4 mole

ES = 0 mole

P = 0 mole

parameters: k1 = 2 1/(mole*second)

k1r = 1 1/second

k2 = 1.5 1/second

Remember that the rate rule dS/dt = f(x) is written in a SimBiology rate rule expression as

S = f(x). For more information about rate rules see

“What Is a Rate Rule?” on page 1-37.

Alternatively,youcouldremovetherateruleforES,addanewspeciesEtotal for the total amount of enzyme, and add an algebraic rule 0 = Etotal - E -

, w here the initial amounts for Etotal and E are equal.

1-21

1 Modeling

reactions: none

reaction rate: none

rate rules: dS/dt = k1r*ES - k1*S*E

dE/dt = k1r*ES + k2*ES - k1*S*E dP/dt = k2*ES

algebraic rule: 0 = Etotal - E - ES

species: S = 8 mole

E = 4 mole

ES = 0 mole

P = 0 mole

Etotal = 4 mole

parameters: k1 = 2 1/(mole*second)

k1r = 1 1/second

k2 = 1.5 1/second

Enzyme Reactions with Mass Action Kinetics

Determining the differential rate equations for the reactions in a model is a time-consuming process. A better way is to enter the reactions for a single substrate enzyme reaction mechanism directly into the software. The following example using models an enzyme catalyzed reaction with mass action kinetics. For a description of the reaction model, see “Simple Model for Single Substrate Catalyzed Reactions” on page 1-20.

1-22

reaction: S + E -> ES

reaction rate: k1*S*E (binding)

reaction: ES -> S + E

reaction rate: k1r*ES (unbinding)

reaction: ES -> E + P

reaction rate: k2*ES (transformation)

species: S = 8 mole

E= 4 mole

ES = 0 mole

P= 0 mole

parameters: k1 = 2 1/(mole*second)

k1r = 1 1/second k2 = 1.5 1/second

Defining Reaction Rates with Enzyme Kinetics

The results for a sim u lation using reactions are identical to the r esu lts from using differential rate equations.

Enzyme Reactions with Irreversible Henri-Michaelis-Menten Kinetics

Representing an enzyme-catalyzed reaction with mass action kinetics requires you to know the rate constants constants are rarely reported in the literature. It is more common to give the rate constants for Henri-Michaelis-Menten kinetics with the maximum velocity a single substrate enzyme reaction using Henri-Michaelis-Menten kinetics is given below. For information about the model, see “Simple Model for Single Substrate Catalyzed Reactions” on page 1-20.

Vm=k2*E and the constant Km = (k1r + k2)/k1. The reaction rate for

Vmax[S]

v =

Km + [S]

k1, k1r,andk2. However, these rate

1-23

1 Modeling

The following example models an enzyme catalyzed reaction using Henri-Michaelis-Menten kinetics with a single reaction and reaction rate equation. Enter the reaction defined below into the software and simulate.

reaction: S -> P

reaction rate: Vmax*S/(Km + S)

species: S = 8 mole

P = 0 mole

parameters: Vmax = 6 mole/second

Km = 1.25 mole

The results show a plot slightly different from the plot using mass action kinetics. The differences are due to assumptions made when deriving the Michaelis-Menten rate equation.

1-24

Evaluation of Reaction Rate

Reaction Rate Dimensions

When calculating species fluxes, SimBiology must determine whether you specified reaction rates in dimensions of amount/time or concentration/time. When all compartments in a model have a capacity of one unit, amount and concentration are numerically equivalent.

For all other models, the numerical results of the simulation depend on which interpretation SimBiology selects. SimBiology determines whether a reaction rate is in dimensions of amount/time or concentration/time via dimensional analysis of dimensional analysis always occurs, even when

UnitConversion are off.

The

DefaultSpeciesDimension property defines the dimensions of species

appearing in a reaction rate. SimBiology infers the dimensions of parameters appearing in a reaction rate from their parameters appearing in a reaction rate expression do not have units, SimBiology interprets the reaction rate in dimensions of amount/time. Therefore, the only way to specify that a reaction rate has dimensions of concentration/time is to assign appropriate units to all parameters.

ReactionRate expressions. This minimum level of

Evaluation of Reaction Rate

DimensionalAnalysis and

ValueUnits property. If any

Reactions Spanning Multiple Compartments

Specify reactions that span compartments using the syntax

compartment1Name.species1Name –> compartment2Name.species2Name.

The reaction rate dimensions must resolve to amount/time whe n:

• Species span multiple compartments.

• The reaction is reversible mass action and the products a re in multiple

compartments.

Examples

Consider a reaction a+b >c. Using mass action kinetics, the reaction rate is

k*a*b,wherek is the rate constant of the reaction. If you specify that initial

amounts of then the reaction rate is in concentration/time (and units of

a and b are 0.01 molarity and 0.005 molarity respectively,

molarity/second)

1-25

1 Modeling

if the units of k are 1/(molarity*second).Ifyouspecifyk with another equivalent unit definition, for example,

1/((moles/liter)*second),

SimBiology checks whether the physical quantities match. If the physical quantities do not match, you see an error and the model is not simulated.

If, in the previous example, you specify that initial amounts of

0.01 and 0.005 respectively, without specifying units, SimBiology checks

whether

DefaultSpeciesDimension is concentration, and you set units on the rate

DefaultSpeciesDimension is substance or concentration.If

a and b are

constant such that the reaction rate dimensions resolve to concentration/time, SimBiology scales the species amounts for compartment capacity, and returns the species va lues in concentration.

If you specify initial amounts of

respectively, include the volume scaling for b in the reaction rate

mole

a and b as 0.01 molarity and 0.005

expression. Include volume scaling in the rate constant, and set the units of the rate constant accordingly (

1/(molarity*second) for amount/time).

1/(mole*second) for concentration/time, or

1-26

Using Constant Amount and Boundary Condition for Species

In this section...

“Definition of Constant and Boundary Properties” on page 1-27

“Changing Species Amounts with Reactions or Rules ” on page 1-28

“Keeping Species Amount Unchanged” on page 1-28

“Constant = NO, Boundary = YES” on page 1-29

“Constant = YES, Boundary = YES” on page 1-30

“Model Edges” o n page 1-31

Definition of Constant and Boundary Properties

There are two properties (constant amount, boundary condition) to specify how the amount of a species changes or does not change during a simulation. Based on the conditions of your model you can decide how to use these properties.

The SBML specification (Level 2, Version 1) added the property

BoundaryCondition to the model definition.

Species with BoundaryCondition = Yes — The species amount is either constant or determined by a rule, but in either case the amount is not determined by a chemical reaction. In other w ords, the simulation does not create a differential rate term from the reactions for this species even if it is in a reaction, but it can have a differential rate term created from a rule.

Species with ConstantAmount = No — The species amount is determined by a reaction or a rule, but not both.

Species with C onstantAmount = Yes — The species amount does not change during a simulation. The species can be in a reaction or rule, but it cannot have a rule that changes its amount.

1-27

1 Modeling

Changing Specie

Set Constant = NO

The value of a sp or rule, but not

Constant

NO NO YES NO

NO NO NO YES

Example 1 —S equation. This is the the specie

reaction rate: k*A

Example 2 —SpeciesE is not in the reaction, but it is in the reaction rate equation. E varies with another reaction or rule.

reaction rate: kcat*E*S/(Km + S)

The spe cies amount or concentration is determined by the reaction.

s is created from the reactions.

reaction: A -> B

reaction: S -> P

ecies can change, and it can change with either a reaction

both

Boundary

pecies A is in a reaction, and it is in the reaction rate

most common category of a species. A differential rate equation for

s Amounts with Reactions or Rules

, Boundary = NO

Reaction

Rule Changed By

Reaction

Rule

1-28

Example 3 —SpeciesG is not in a reaction, and it is not in a rate equation. G varies with an algebraic rule or rate rule.

rate rule: dG/dt = k

Keeping Species Amount Unchanged

Set Constant = YES, Boundary = NO

The value of a species cannot change. When a species has its selected and BoundaryCondition not s elected, it acts like a parameter. It cannot be in a reaction and it cannot be varied by a rule.

Constant

YES NO NO NO

Boundary

Reaction

Rule Changed By

Never

ConstantValue

Using Constant Amount and Boundary Condition for Species

Example —SpeciesE is not in the reaction, but it is in the reaction rate equation. E is constant and could be replaced with the constant

reaction: S -> P

reaction rate: kcat*E*S/(Km + S)

Vm = k2*E.

Constant = NO, Boundary = YES

The value of a species can change, and it is in a reaction, but a differential rate term from the reaction is not created. The value of the species change with a rule and a d ifferential rate term is created from the rule.

Constant

Boundary

NO YES YES YES

Reaction

Rule Changed By

Rule

From the SBML specification (Lev el 2, Version 1), “By default, when a species is a product or reactant of one or more reactions, its concentration is determined by those reactions. In SBML,itispossibletoindicatethata given species’ concentration is not determined by the set of reactions even when that species occurs as a product or reactant; i.e., the species is on the boundary of the reaction system but is a component of the rest of the model.”

Example 1 —SpeciesA is not changed by the rate equation, but changes according to a rate rule. However, A could be in the rate equation that changes other species in the reaction.

reaction: A -> B

reaction rate: k1 or k1*A

rate rule: dA/dt = k2*A (solution is

(enter in SimBiology as

A=k2*t)

A = k2*A)

Example 2 —SpeciesA is not in t he rate equation, but changes according to an algebraic rule.

reaction: A -> B + C

reaction rate: k or k*A

algebraic rule: A =2*C

(enter in SimBiology as

2*C - A)

1-29

1 Modeling

Constant = YES, B

Thevalueofthes rate term is not c created from a r

Constant

pecies cannot change. It is in a reaction, but a differential

reated from the reaction. The differential rate term is

ule.

Boundary

oundary = YES

Reaction

YES YES YES NO

During simul

dSpecies/dt

Example 1 — A increases refers to a

reaction rate: k or k*A

Example 2

and

sink

is subtr

reaction rate: k*B

ation, a differential rate equation is not created for the species.

does not exist.

is a

infinite source and its amount does not change. B

with a zero order rate (

k and k*A are both constants). A source

species where mass is added to the system.

reaction: A -> B

— B decreases with a first-order rate, but A is an

its amount does not change. A

sink refers to a species where mass

acted from the system.

reaction: B -> A

Rule Changed By

Never

infinite

1-30

Exampl

sourc

Exa

but

e3—Thenull species is a reserved species name that can act as a

eorasink.

reaction: null -> B

reaction rate: k

reaction: B -> null

reaction rate: k*B

mple 4 — ATP and ADP are in the reaction and have constant values,

they are not in the reaction rate equation.

reaction: S + ATP -> P + ADP

reaction rate: Vm*S/(Km + S)

Model Edges

As you build comp model that you ne the model edges constant or unr concept of a mo

are located is important because a species that is initially

egulated can later vary as you add details to your model. The

del edge overlaps with SBML boundaries, but not always.

Using Constant Amount and Boundary Condition for Species

lex m odels from simpler pathways, there are edges in the

ed to define before simulating the model. Knowing where

Model edge — Sp modeled in th

NAD

, ATP, an

Model edge — For example parameter a remains co

nstant.

V [Substrate]

max*

K+ [Substrate]

You may w the amou adding

Mode cons

nt of enzyme is constant, then this species is a model edge. After

the reaction(s) that change the amount of the enzyme,

k*[ ]*[Substrate]

Enzyme

l edge — Null or source species that synthesizes another species at a

tant rate (zero o rder reaction). M ass is added to the system.

ecieswithconstantamountsthatmightormightnotbe

e reaction and reaction rate equations. Examples are cofactors,

dDNA.

Enzymes with constant amounts that are not regulated.

, a Michaelis-Menten rate equation with

Vmax specified as a

ssumes that the amount of enzyme catalyzing the reaction

ant to temporarily model a regulated enzyme in a rate equation. If

K+ [Substrate]

el edge — Degradation of a species to a null or sink species (first-order

Mod

ction). Mass is taken away from the system.

rea

1-31

1 Modeling

Scoping Parameters for Reactions, Rules, and Events

In this section...

“Definition of Parameter Scope” on page 1-32

“Using a Parameter in Events and Rules” on page 1-33

“Changing the Scope of a Parameter” on page 1-33

Definition of Parameter Scope

Parameters are quantities used to define the behavior of a modeled system. Parameters can either be constant or change over time. SimBiology parameters are generally used to define rate constants.

A SimBiology parameter is defined either globally at the model level or locally at the kinetic law level. Scope refers to this definition of the parameter at the model or kinetic law level.

1-32

• If the scope of the parameter is global in the model, it can be used by any

event o r rule, or by any reaction rate expression in the model.

• If the scope of the parameter is at the kinetic law level, it can be used only

by the reaction rate expression for which it was defined.

If you create a new parameter in the Project Settings-Parameters pane, the scope is set by default to the define a reaction rate equation in the Project Settings-Reactions pane’s Kinetic Law tab, you can choose whether to assign the parameter locally to the kinetic law or globally to the model.

SimBiology parameters are resolved hierarchically:

• For reaction rate, the software hierarchically uses the value of the

parameter at the kinetic law level first. If no such parameter is at the kinetic law level, the software looks fortheparameteratthemodellevel.

• If two parameters have the same name, one at the model level and the

other at the kinetic law level, the software uses the value of the parameter at the kinetic law level for the reaction rate. The software uses the value

model. When you create a new parameter to

Scoping Parameters for Reactions, Rules, and Events

of the parameter at the model level for any rules or events that reference the parameter.

Note Ifyouwanttovaryaparameterthatis being referenced in a reaction rate equation, that parameter must have a unique name, and have scope at the model level.

Using a Parameter in Events and Rules

When you want to refer to a parameter in an event or rule expression, or inmorethanonereactionrateequation,theparameterscopemustbeat the model level.

Ifyouwanttovaryaparameterthatisbeing referenced in a reaction rate equation, that parameter must have a unique name, and have s cope at the model level. See “Definition of Parameter Scope” on page 1-32 for more information.

Note Tovaryaparameterwitharuleoranevent,cleartheConstan tValue check box in the Project Settings-Parameters pane, Settings tab.

Changing the Scope of a Parameter

When you want to refer to a parameter in an expression for a rule, or in more than one reaction rate equation, the parameter scope must be at the model level.

To change the scope of a parameter in the SimBiology desktop:

1 In the Project Explorer,clickParameters,toopentheParameters

pane.

2 In the Parameters table, right-click a parameter row select Change

Parameter Scope to change the scope of the selected parameter from

kinetic law to model, or the reverse.

1-33

1 Modeling

Changing Model Component Values Using Rules

In this section...

“What Is a Rule?” on page 1-34

“What Is an initialAssignment Rule?” on page 1-35

“What Is a repeatedAssignment Rule?” on page 1-35

“What Is an Algebraic Rule?” on page 1-36

“What Is a Rate Rule?” on page 1-37

“Typical Uses of Rate Rules” on page 1-37

What Is a Rule?

A rule is a model component that specifies a mathematical relationship between model component values during a simulation. Rules let you specify mathematical relationships involving the following model components values:

1-34

• parameter value

• species amount

• compartment capacity

Examples of using a rule include:

• Specify values for model components that are required for comparison w ith

experimental data. For example, specify the active fraction of total protein.

• Assign values to model components based on the values of other

components in the model. For example, define a parameter’s value as being proportional to a species or another parameter.

• Define mass balance equations.

• For species, use rate rules as an alternative to the differential rate

expression generated from reactions.

The types of rules in SimBiology are as follows:

Changing Model Component Values Using Rules

• initialAssignment — Lets you specify the initial value of a parameter,

species, or compartment capacity, as a function of othe r model component values in the model.

•

repeatedAssignment — Lets you specify a value that holds at all times

during simulation, and is a function of other model component values in the model.

•

algebraic — Lets you specify mathematical constraints on one or more

parameters, species, or compartments that must hold during a simulation.

•

rate — Lets you specify the time derivative of a parameter value, species

amount, or com partment capacity.

What Is an initialAssignment Rule?

initialAssignment rules are evaluated once at the beginning of a simulation. initialAssignment rules are expressed as Variable = Expression.

Forexample,usetheruletosettheinitialamountof proportional to

species2. This lets you change the initial conditions for both

species1 to be

species by updating the value for one.

species1 = k*species2

What Is a repeatedAssignment Rule?

repeatedAssignment rules are evaluated at every time step during a

simulation.

Expression

For example, if you want the capacity of a compartment ( change in response to a change in the concentration of a species ( rule to set the capacity of

cytoplasm = k*x

Where k is a specified constant.

repeatedAssignment rules are mathematically equivalent to algebraic

rules, but result in exact solutions, compared to algebraic rules whose accuracy depends on the tolerance specifi ed in the configuration set used while performing simulations.

repeatedAssignment rules are expressed as Variable =

cytoplasm)to

x), use the

cytoplasm to be proportional to x.

1-35

1 Modeling

Tip

• Ifyoucansolveforthevariable,usea

of an

algebraic rule.

repeatedAssignment rules the cons trained variable is explicitly defined

• In

as the lef t-hand side, whereas in algebraic rules it is inferred from the degrees of freedom in the system of equations (see also, “Considerations When Imposing Constraints” on page 1-36 in the SimBiology User’s Guide.

repeatedAssignment rule instea d

What Is an Algebraic Rule?

An algebraic rule is a convenient way to define mathematical relationships between states. A model can consist of a combination of differential and algebraic relationships.

An algebraic rule is a constraint that is enforced by the solver during simulation. You can use algebraic rules to specify the dynamics for parameters, species, and compartments that are not driven by one or more reactions. The accuracy of the solution depends o n the tolerance specified in the configuration set used while performing simulations.

An algebraic rule is defined by the equation:

f(t,x)= 0

Where t is simulation time. The variable x is species amount, parameter value, or compartment capacity.

1-36

An example of an algebraic rule is,

x*log(x) - 3

Considerations When Imposing Constraints

Consider the mathematical constraint y = m*x - c. In the software this rule is written as of

y,thenm, x,andc must be variables or constants whose values are known

or determined by other equations. In general, the degree of freedom available must match the number of constraints. Therefore, you must ensure that the

m*x-c-y. If you want to use this rule to determine the value

Changing Model Component Values Using Rules

equation is not overconstrained or underconstrained. In this example, if the equation is underconstrained, it is unclear which variable is being determined by the expression.

What Is a Rate Rule?

Arateruleisdefinedbytheequation:

dx/dt = f(t,W)

The variable x can be a species amount, parameter value, or compartment capacity. The function

f(W) is an expression that can include other species

and parameters. Enter a rate rule using the form

x = f(t,W)

TypicalUsesofRateRules

WhentheRateofChangeIsConstant

You can increase or decrease the amount or concentration of a species by a constant value using a zero order rate rule. For example, suppose species increases by a constant rate k.

reaction: none

rate equation: none

rate rule: dc/dt = k

species : c = 10 mole(initial amount)

parameters: k = 1 mole/second

The analytical solution is c=kt+co,wherecois the initial amount or concentration of the species

Enter the rule described above as

rate, enter the values for c and k, and then simulate.

c=k.FromtheRuleType list, select

1-37

1 Modeling

Alternatively, you could model a constant increase in a species using Mass Action reaction

null -> C.

1-38

When the

You can change the amount of a species similartoafirst-orderreactionusinga first-orderraterule. Forexample,supposethespecies

The solution for the rate rule

Enter the rate rule described above and the simulate.

Rate of Change Is Exponential

dc/dt = -k*c is

c =

c decays exponentially.

-kt

Changing Model Component Values Using Rules

Notice that if the amount of a species c isdeterminedbyarateruleandcis also in a reaction, For example, with a reaction

BoundaryCondtion for c so that a differential rate term is not created from

the reaction. The amount of

c must have itsBoundaryCondition property set to true.

a->cand a rate rule dc/dt = k*c,selectthe

c is determined solely by a differential rate term

fromtheraterule.

If the boundary condition is not selec ted, you will get the following error message:

id rule variable 'in a reaction or another rule'.

Inval

When the Rate of Change Is Determined by Another Species

cies from one reaction can determine the rate of another reaction if it

Aspe

the s econd reaction rate equation. Similarly, a species from a reaction

is in

etermine the rate of another species if it is in the rate rule that defines

can d

t other species.

tha

reaction: a -> b

rate equation: v = -k1*a

rate rule: dc/dt = k2*a

1-39

1 Modeling

species: a = 10 mole

b = 0 mole c = 5 mole

parameters: k1 = 1 1/second

k2 = 1 1/second

The solution for the species in the reaction are:

-k1t

a=a e

b=a (1-e )

and

With the rate rule dc/dt = k

-k1t

2(ao

c=co+k2ao/k1(1 - e

), and the solution is:

-k1t

*a dependent on the reaction, dc/dt =

-k1t

)

Enter the reaction and rule described above and simulate.

1-40

Expressing Differential Rate Equations as Rules

Many mathematical models in the literature are described with differentia l rate equations for the species. You could manually convert the equations to

Changing Model Component Values Using Rules

reactions, or you could enter the equations as rate rules. For example, you could enter the following differential rate equation for a species

= v - v X

K + C

- k C

asarateruleinSimBiology:

C = vi - (vd*X*C)/(Kc + C) - kd*C

1-41

1 Modeling

Changing Model Component Values Using Events

In this section...

“What Is an Event?” on page 1-42

“How Events Are Evaluated” on page 1-43

“Evaluation of Simultaneous Events” on page 1-48

“Evaluation of Multiple Event Functions” on page 1-49

“When One Event Triggers Another Event” on page 1-49

“Cyclical Events” on page 1-50

What Is an Event?

1-42

For example, you can use events to activate or deactivate certain species (activator or inhibitor species), chan g e parameter values based on external signals, or change reaction rates i n response to addition or removal of species. You can also use an event in a model when you want to replicate an experimental condition, for example, to replicate the addition or removal of an activating agent (such as a drug) to a sample. This section describes events and how they are evaluated.

Use events to define events that occur when a condition becomes true. When you specify a condition in the should be executed when the condition becomes true. Typical triggers are:

• Cause an event to occur at a specific time during simulation — Specify that

the event must change the amounts or values of species or parameters. For example, at time = 5 s, increase the amount of an inhibitor species above the threshold to inhibit a given reaction.

• Cause an event to occur in response to state or changes in the system —

Change amounts/values of certain species/parameters in response to events that are not tied to any specific time. For example, when species

Trigger you are specifying that the event

A reaches

Changing Model Component Values Using Events

an amount of 30 molecules, double the value of reaction rate constant k;or when temperature reaches 42

C, inhibit a particular reaction by setting its

reaction rate to zero.

The event that is executed when the function (

EventFcn). Event functions could range from simple to complex, for

Trigger becomes true is called an event

example, an event function might:

• Change the values of com partments, species, or parameters.

• Double the value of a reaction rate constant.

To simulate SimBiology models containing events, use the deterministic

sundials solver or the stochastic ssa solver; other solvers do not support

events. See “Sundials Solvers” on page 2-17 and “Stochastic Solvers” on page 2-12 for more information.

Procedures

• For an example using events in the SimBiology desktop, see “Desktop

Example — Changing Species Amounts Using an Event” on page 1-51 in the SimBiology User’s Guide

• For an example of using events at the command line, see

addevent in the

SimBiology Reference

How Events Are Evaluated

Consider the example of a simple event where you specify that at 4s,youwant to assign a value of

10 to species A.

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1 Modeling

1-44

At time = 4 the trigger becomes true and the event is executed. In the figure above assuming that 0 is false and 1 is true, when the trigger becomes true, the amount of event would be executed exactly at

Species A is set to 10. In theory, with a perfect solver, the

time = 4.00. In practice there is a very

minute delay (for example you might notice that the event is executed at time = 4.00001 s). Thus, you must specify that the trigger can become true at or after

Trigg

time

4s,whichistime >= 4.

>= 4

Fcn

Event

A=10

The point at which the trigger becomes true is called a rising edge.SimBiology events execute the

The

Trigger is evaluated at every time step to check whether the condition

EventFcn only at rising e dges.

specified in the trigger tran siti on s from false to true. T he solver detects and tracks falling edges, which is when the trigger becomes false, so if another

Changing Model Component Values Using Events

rising edge is encountered, the event is executed again. If a trigger is already true before a simulation starts, then the event does not execute the at the start of the simulation . The event is not executed until the solver encounters a rising edge. Very rarely, the solver might miss a rising edge; one example of this is when a rising edge follows very quickly after a falling edge, and the step size results in the solver skipping over the transition p oint.

If the trigger becomes true exactly at the stop time of the simulation, the event may or may not execute. If you want the event to execute, increase the stop time.

Note Since the rising edge is instantaneous and changes the system state, therearetwovaluesforthestateatthesametime.Thesimulationdatathus contains the state before the event and after the event, but both points are atthesametimevalue. Thisleadstomultiple values of the system state at a single instant in time.

Specifying Event Triggers

A Trigger is a condition that must become true for an event to be executed. Typically, the condition uses a combination of relational and logical operators to build a trigger expression.

MATLAB uses specific operator precedence to evaluate trigger expressions. Precedence levels determine the order in which MATLAB evaluates an expression. Within each precedence level, operators have equal precedence and are evaluated from left to right. To find more information on how relational and logical operators are evaluated see “Operators” in the MATLAB Programming Fundamentals documentation.

Some examples of triggers are:

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1 Modeling

Trigger

'(time >=5) && (speciesA<1000)'

'(time >=5) || (speciesA<1000)'

'(s1 >=10.0) || (time>= 250) && (s2<5.0E17)'

Explanation

Execute the event when the following condition becomes true:Time is greater than or equal to

5,andspeciesA is less

than 1000.

Tip Using a && (instead of &)tells the software to evaluate the first part of the expression for wh ether the statement is true or false, and skip evaluating the second statement if this statement is f alse.

Execute the event when the following condition becomes true: Time is greater than or equal to

5,orifspeciesA is

less than 1000.

Execute the event when the following condition becomes true: Species, greaterthanorequalto

10.0 or, time

is greater than or e qual to species

s2 is less than 5.0E17.

s1 is

250 and

1-46

Because of operator precedence the expression is treated as if it were

'(s1 >=10.0) || ((time>= 250) && (s2<5.0E17))'

Thus, it is always a good idea to use parenthesis to explicitly specify the intended precedence of the statements.

Changing Model Component Values Using Events

Trigger

'((s1 >=10.0) || (time>=

250)) && (s2<5.0E17)'

'((s1 >=5000.0) && (time>=

250)) || (s2<5.0E17)'

Explanation

Execute the event when the time the following condition becomes true: Species,

10 or time is greater than or e qual to 250,andspeciess2 is less than 5.0E17.

s1 isgreaterthanorequalto

Execute the event when the time the following condition becomes true: Species, to equal to

5.0E17.

s1 isgreaterthanorequal

5000 and time is greater than or

250,orspeciess2 is less than

For more information on triggers see Trigger in the SimBiology Reference Guide.

Specifying Event Functions

The event that is executed when a Trigger condition has a rising edge is called an event function ( the value of a species or a parameter, or you can specify complex tasks by calling a user-defined function or script.

An event function is either a single valid MATLAB expression (without ’ the expression) or a cell-array of single valid MATLAB expressions . For more information see also examples of event functions include:

EventFcn). You can use an event function to change

;’in

EventFcns in the SimBiology Reference Guide. Some

EventFcn

'speciesA = speciesB'

'k = k/2'

Explanation

When the event is executed set the amount of

speciesB.

speciesA equal to that of

When the event is executed halve the value of the rate constant

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1 Modeling

EventFcn

{'speciesA = speciesB', 'k = k/2'}

'kC = my_func(A, B, kC)'

Explanation

When the event is executed set the amount of

speciesB, and halve the value of the

rate constant

speciesA equal to that of

When the event is execute d call the user-defined function

my_func().

This function takes 3 arguments: Thefirsttwoargumentsarethe current amounts o f two species (

and B) during simulation and the third argument is the current value of a parameter, returns the modified value of

kC. The function

kC as

its output.

Evaluation of Simultaneous Events

When two or more trigger conditions simultaneously become true, the solver executes the events in the order in which they are on the model. You can reorder events using the in the SimBiology desktop, arrange the rows of events in the order you desire, then right-click and select Reorder Events as Shown in Table. Forexample,consideracasewhere:

reorder method at the command-line. Alternatively,

1-48

Event

Trigger EventFcn

Number

1 SpeciesA >= 4 SpeciesB = 10

SpeciesC >= 15 SpeciesB = 25

The solver tries to find the rising edge for these events within a certain level of tolerance. If this results in the two events occurring simultaneously, then the value of be

25. If you reorder the events to reverse the event order then the value of

SpeciesB after the time step in which these two events occur will be 10.

SpeciesB after the time step in which these two events occur will

Changing Model Component Values Using Events

Consider an example in which you include event functions that change model components in a dependent fashion. For example, the event function in Event 2 b elow , stipulates that

SpeciesB takes the value of SpeciesC.

Event

Trigger EventFcn

Number

1 SpeciesA >= 4 SpeciesC = 10

time >= 15 SpeciesB = SpeciesC

Event 1 and Event 2 may or may not occur simultaneously.

• If Event 1 and E vent 2 do not occur simultaneously, when Event 2 is

triggered

SpeciesB is assigned the value that SpeciesC has at the time

of the event trigger.

• If Event 1 and Event 2 occur simultaneously, the solver store s the value of

SpeciesC at the rising edge, before any event functions are executed and

uses this stored value to assign if

SpeciesC = 15 when the events are triggered, after the events are

executed

SpeciesB = 15,andSpeciesC = 10.

SpeciesB its value. In the above example

Evaluation of Multiple Event Functions

Consider an event function in which you specify that the value of a model component ( (

SpeciesA), but SpeciesA also is changed by the ev ent function.

Trigger EventFcn

time >= 4 {'SpeciesA = 10, SpeciesB = SpeciesA'}

SpeciesB) is dependent on the value of model component

The solver stores the value of SpeciesA at the rising edge and before any event functions are executed and uses this stored value to assign

SpeciesB

its value. So in the above example if SpeciesA = 15 atthetimetheeventis triggered, after the event is executed,

SpeciesA = 10 and SpeciesB = 15.

When One Event Triggers Another Event

In the example below, Event 1 includes an expression in the event function that causes Event 2 to be triggered, (assuming that than

5 when Event 1 is executed).

SpeciesA has amount less

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1 Modeling

Event

Trigger EventFcn

Number

1 time >= 5 {'SpeciesA = 10, SpeciesB = 5'}

SpeciesA >= 5 SpeciesC = SpeciesB

When Event 1 is triggered, the solver evaluates and executes Event 1 with the result that Event 2 becomes true (assuming that executes the event function for E vent 2. Thus,

SpeciesA = 10,andSpeciesB = 5. Now, the trigger for

SpeciesA is be low 5)andthesolver

SpeciesC = 5 at the end of

this event execution.

You can thus have event cascades of arbitrary length, for example, Ev ent 1 triggers Event 2, which in turn triggers Event 3, and so on.

Cyclical Events

In some situations, a series of events can trigger a cascade that becomes cyclical. Once you trigger a cyclical set of events, the only way to stop the simulation is by pressing Ctrl+C. You lose any data acquired in the current simulation. An example of cyclical events is shown below. This example assumes that

Event Number

1 SpeciesA > 10 {SpeciesB = 5, SpeciesC =

Species B <= 4 at the start of the cycle.

Trigger EventFcn

1'}

SpeciesB > 4 {SpeciesC = 10, SpeciesA =

1'}

SpeciesC > 9 {SpeciesA = 15, SpeciesB =

1'}

1-50

Desktop Example — Changing Species Amounts Using an Event

In this section...

“Overview” on page 1-51

“Prerequisites” on page 1-52

“Adding a n Event to the Example Model” on page 1-52

“Simulating the Modified Model” on page 1-55

Overview

This examp time-bas “Changin

le shows you how to add an event to a model to trigger a

ed change. For information on events and how they are evaluated see

g M odel Component Value s Using Events” on page 1-42.

This exa (L), thu

mple shows you how to add an event that modifies amount of ligand

s modeling a delay in the addition of α-factor to the cell culture.

About the Example Model

This ex SimBio

This t corre rever

ample uses the model from “Mo deling a G Protein Cyc le” in the

logy Model Reference documentation.

able shows the reactions used to model the G protein cycle and the

sponding rate parameters (rate constants) for each reaction. For

sible reactions, the forward rate parameter is listed first.

No. Name

Receptor-ligand interaction

Heterotrimeric G protein formation

G protein activation

Reaction

L + R <-> RL kRL,kRLm

Gd + Gbg -> G kG1

RL + G -> Ga + Gbg + RLkGa

Rate Parameters

1-51

1 Modeling

No. Name

Reaction

Rate Parameters

Receptor synthesis and

R <-> null kRdo, kRs

degradation

Receptor-ligand

RL -> null kRD1

degradation

G protein inactivation

Ga -> Gd kGd

Prerequisites

Opening and Saving the Example Model

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

sbioloadproject gprotein

The model is stored in a variable called m1.

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

simbiology(m1)

1-52

The desktop opens w ith Model Session-Heterotrimeric_G_Protein_wt.

3 Save the project.

a Select File > Save Project As. The Save SimBiology Project dialog

box opens.

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

and click Save.

Adding an Event to the Example Model

1 In the Project Explorer expand SimBiology Model and click Events

to open the Events pane.

2 In the Enter Trigger box, type the following expression and press Enter:

Desktop Example — Changing Species Amounts Using an Event

time >= 100

3 In the EventFcns box, type the following expression and press Enter:

L = 6.022E17

In the Settings tab, under the SpeciesbeingusedbyEventsection, note that the species

4 In the row containing the species L, double-click the InitialAmount

L is available.

column, type 0,andthenpressEnter.

The InitialAmount of

L is set to be 0.0 when the simulation starts.

The E vents pane should now resemble the following:

1-53

1 Modeling

1-54

5 In the Project Explorer,clickConfiguration Settings to open the pane

that contains so lver settings.

6 Click the Data Logging tab.

7 Click Select All.

8 Save the project by selecting File > Save Project.

Desktop Example — Changing Species Amounts Using an Event

Simulating the Modified Model

1 Click Run.

The simulation runs to completion and plots the result in a figure. Notice that the plot shows that the ligand amount increases when the event is executed.

Theplotdoesnotshowthespeciesofinterestduetoawiderangeinspecies amounts. Follow the next steps to view the species of interest.

2 In the Project Explorer, under Simulation,right-clickData and select

Save Data. The Save Data dialog box opens.

1-55

1 Modeling

3 Specify a name for the saved data, for example, event_ex,andclickSave .

The Project Explorer shows a new item with the saved data name under Simulation.

4 In the Project Explorer, click the saved data, for example, event_ex,to

open the Data pane for the saved data.

5 Click the Plots tab.

6 From the Plot Type list, select Time and click Add Plot Type.

7 Select the n

The Select V

8 Clear the check boxes for the species L and Gbg.

9 Click OK.

10 (Optiona

11 Click Plot. Your plot should resemble the one below. Notice the increase in

activation of G protein (species at

time = 100 (simulation time).

ew plot (second row), and in the Arguments section, click

alues for y dialog box opens.

l) Clear the Create Plot check box for the first plo t.

Ga, shown in red) after ligand (L) is added

1-56

Desktop Example — Changing Species Amounts Using an Event

1-57

1 Modeling

Storing and Applying Alternate Model Values Using Variants

In this section...

“What Are Variants?” on page 1-58

“Using Variants” on page 1-59

“Applying M ultiple Variants in a Model” on page 1-60

What Are Var

Variants a represent asimulati for use of

• Store and

separat

• Store pa

several

• Store c

repres

Simul perma simul

• Spec

• Para

• Com

ng one or more variants associated with a model allows you to ev aluate

Usi

el behavior during simulation, with different values for the various model

mod

mponents without having to search and replace these v alues, or having to

eate additional models with these values. If you determine that the values

llow you to apply alternate values to model components to values for the components. The alternate values apply only during on and do not otherwise alter the model’s values. Som e examples

variants are:

apply parameter values for yeast and mouse models using two

evariants.

rameter estimates from differe n t experimental conditions in

variants and apply them to a model.

omponent values for mutant strains and apply the values to a model

enting the wild-type.

ating using a variant does not alter the model component values

nently. The values specified in the variant temporarily apply during

ation. You can store values for:

ies

InitialAmount

meter

partment

iants?

Value

Capacity

1-58

Storing and Applying Alternate Model Values Using Variants

in a variant accurately define your model, you ca n permanently replace the values in your model with the values stored in the variant object.

Using Variants

Creating and Using Variants at the Command Line

1 Create the variant and add it to the model using the addvariant method.

2 (Optional) Set the Active property to true if you always want the variant

to be applied before simulating the model.

3 Enter the variant object as an argument to sbiosimulate.Thisappliesthe

variant only for the current simulation and supersedes any active variant objects on the model.

If you followed step 2, simply calling

sbiosimulate on the model object

apples the variant.

For more information, see the following sources of information in the SimBiology Reference:

For information about...

Variant object methods and

See...

Variant object

properties

Example of creating and adding a

addvariant

variant

Appending contents to variants

Replacing model values permanently

addcontent

commit

with values from a variant

Creating and Using Variants in the SimBiology Desktop

For information about creating variants in the SimBiology desktop and applying them during a simulation, see the following:

1-59

1 Modeling

• The context-sensitive help (SimBiology Desktop Help) in the SimBiology

desktop for procedures. To access this help:

1 In the SimBiology desktop, from the Project Explorer, select Variants.

The desktop opens the Variants pane. The SimBiology Desktop Help updates to show you how to work with variants.

2 If the context-sensitive help is not open, select Help > SimBiology

Desktop Help.

• “Desktop Example — Applying Changes to Parameter Value Using a

Variant” on page 1-61

Applying Multiple Variants in a Model

When multiple variants are used during a simulation, and there are duplicate specifications for a property’s value, the last occurrence for the property value in the array of variants is used during simulation. You can find out which variant is applied last by looking at the indices of the variant objects stored on the model (at the command line) or the last variant created.

1-60

If you specify variants as argum ents to variants for the current simulation in the order that they are specified, and supersedes any active variant objects on the model.

Similarly, in th e variant contents ( specifications for a prope r ty’s value, the last occurrence for the property in the contents is used during simulation.

If you permanently replace values in a model with values from multiple variants using the Commit button in the desktop, the value committed in the model is the last occurrence of the value in the variants.

sbiosimulate,thisappliesthe

Content property), if there are duplicate

Desktop Example — Applying Changes to Parameter Value Using a Variant

Desktop Example — Applying Changes to Parameter Value Using a Var

In this section...

“Overview” on page 1-61

“Prerequisites” on page 1-62

“Applying Alternate Values Using Variants” on page 1-63

“Simulation Results for the Model of the Mutant Strain” on page 1-63

Overview

This examp wild-typ cycle in a the varia with the

iant

le shows you how to apply a variant to a model representing a

e strain. The variant represents a parameter value for a G protein

mutant strain. Thus, when the model is simulated without applying nt, you see results for the wild-type, and when the model is simulated variant you see results for the mutant.

About the Example Model

This ex SimBio

This t corre rever

ample uses the model from “Mo deling a G Protein Cyc le” in the

logy Model Reference documentation.

able shows the reactions used to model the G protein cycle and the

sponding rate parameters (rate constants) for each reaction. For

sible reactions, the forward rate parameter is listed first.

No. Name

Receptor-ligand interaction

Heterotrimeric G protein formation

G protein activation

eceptor synthesis and

egradation

Reaction

L + R <-> RL kRL,kRLm

Gd + Gbg -> G kG1

RL + G -> Ga + Gbg + RLkGa

R <-> null kRdo, kRs

Rate Parameters

1-61

1 Modeling

No. Name

Reaction

Rate Parameters

Receptor-ligand

RL -> null kRD1

degradation

G protein inactivation

Ga -> Gd kGd

About the Variant Created in This Example

The value of the parameter kGd is 0.11 for the wild-type and 0.004 for the mutant. To represent the mutant, the alternate value of the parameter stored as

0.004 in a variant and applied during simulation.

kGd is

For a description of variants, see “Storing and Applying Alternate Model Values Using Variants” on page 1-58.

Prerequisites

Opening and Saving the Example Model

1 Load the example project at the command line by typing

sbioloadproject gprotein_norules

1-62

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 Yeast_G_Protein_wt.

3 Save the project.

a Select File > Save Project As. The Save SimBiology Project dialog

box opens.

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

and click Save.

Desktop Example — Applying Changes to Parameter Value Using a Variant

Applying Altern

1 In the Project Ex

click Variants

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

ate Values Using Variants

plorer,underModel Session-Yeast_G_Protein_wt,

to open the Variants pane.

or press Enter. For example:

mut_value_ex

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.

Gprotein Inactivation.kGd

Tip Alternatively, double-click the Component Name cell, p ress the down arrow, 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

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