Mendel® SBML Editor User Guide Table of Contents

Introduction...... 1

Mendel® SBML Editor overview ...... 1

Mendel® SBML Editor features ...... 1

Getting started ...... 2

Installation notes ...... 2

Basic tutorial: Describing Reaction Network of Dimerization ...... 3

Tasks ...... 13

Navigating the workbench ...... 13

Basics...... 14

Open existing SBML Model ...... 14

New SBML Model...... 15

Save SBML Model ...... 15

Save SBML Model graph as image...... 15

Adding and configuring Nodes ...... 15

Adding a Species, Reaction or Compartment ...... 16

Configuring a Species, Reaction or Compartment...... 16

Adding and configuring Relations ...... 17

Adding a Reactant, Modifier or Product ...... 17

Configuring a Reactant, Modifier or Product ...... 18

Adding and configuring Kinetic Laws ...... 18

Adding and configuring Function Definitions ...... 19

Adding and configuring Unit Definitions...... 19

Adding and configuring Parameters ...... 20

Adding and configuring Rules, Initial Assignments and Constraints ...... 20

Adding and configuring Events ...... 21

Adding Notes ...... 22

Deleting elements...... 22

Reference ...... 24

Graphical User Interface overview ...... 24

Menu Bar ...... 24

File Menu Actions ...... 24

Edit Menu Actions ...... 25

Diagram Menu Actions...... 26

Window Menu Actions...... 27

Help Menu Actions ...... 27

Toolbar ...... 28

Model outline tab ...... 29

Graphical overview tab ...... 30 Graphical Editor tab ...... 31

Properties tab ...... 32

Nodes ...... 32

Species ...... 32

Reactions ...... 33

Compartment ...... 33

Relations ...... 34

Kinetic Laws ...... 34

Function Definitions ...... 34

Unit Definitions ...... 35

Parameters ...... 35

Initial Assignments ...... 35

Rules ...... 36

Algebraic Rules ...... 36

Assignment Rules ...... 36

Rate Rules ...... 36

Constraints ...... 36

Events ...... 37

Notes...... 37

Shared Properties ...... 37

Palette tab ...... 38

Tutorials ...... 40

Irreversible Michaelis-Menten Model...... 40

Appendix ...... 46

Concepts ...... 46

(Dynamic) Biological models ...... 46

Michaelis-Menten Kinetics ...... 47

Systems Biology Markup Language (SBML) ...... 48

Mendel® SBML Editor overview

The Mendel® SBML Editor is a fast, lightweight, stand-alone graphical SBML editor, helping you to graphically capture and represent your mechanistic bio-chemical models. It is platform- independent and free for personal use, allowing you to first build your SBML model and then save it as an image or SBML file. To simulate your model, just import the SBML file into an SBML- compatible simulation software of your choice (e.g. COPASI, PET).

The Mendel® SBML Editor was built on the Eclipse platform infrastructure, is plug-in based and written in Java. It is distributed under the Eclipse Public Licence (EPL) and uses the platform- independent and open-source Java library JSBML to provide methods to read, write, evaluate and manipulate the content of SBML documents.

Mendel® SBML Editor features

Features include:

• graphically build your model

• save your model as validated SBML Level 3 Version 1 Core Release 1 file

• save your model as image file (GIF, BMP, JPEG, JPG, SVG, PNG, PDF)

• open and edit any SBML model of any given SBML level and version

• wide array of styling and arrangement options for your model

• build-in MathML editor for easy creation of your formulas

1 Getting started

Installation notes

Versions of Mendel® SBML Editor for Windows, Linux, and Mac OS X can be downloaded from sbml-editor.org. There are 32-bit and 64-bit versions available (depending on your operating system).

Before installation, make sure you meet the minimal requirements:

1. at least 200 MB available hard disk space

2. you need a working installation of Java 7 or newer. Please check the Oracle website for more information

Depending on your operating system, please check the corresponding step-by-step instructions.

Microsoft Windows 1. If you are unsure which Windows version (32-bit or 64-bit) you have, press Windows logo key + Pause to open your system properties window.

2. Download the corresponding version of the Mendel® SBML Editor software (see above).

3. Extract the zip file to a directory of your choice, e.g. C:\SBMLEditor.

4. Locate the SBML-Editor.exe in this directory and double click to start the SBML editor.

If you receive a Windows Smart Screen warning (only Windows 8 and later),  click on More Info instead of the highlighted OK. Then choose the Run Anyway button to execute the program.

 If at any time your antivirus or firewall software prompts you, allow the request.

 If the User Account Control dialog shows, click Yes to continue the installation.

GNU/Linux 1. Download the corresponding version of the Mendel® SBML Editor software (see above).

2. Extract the tar.gz file to a directory of your choice, e.g. $HOME/SBML-Editor.

3. Locate the SBML-Editor in this directory and double click to start the SBML editor.

Mac OS 1. Download the corresponding version of the Mendel® SBML Editor software (see above).

2. Extract the zip file to a directory of your choice, e.g. $HOME/SBML-Editor.

3. Locate the SBML-Editor.app in this directory and double click to start the SBML editor. If macOS refuses to open it please follow the instructions at Apple for the first start.

2 Basic tutorial: Describing Reaction Network of Dimerization

Any chemical reaction in which two monomers react to form a dimer is called a dimerization. This may be represented schematically as

Based on this, the single reaction and rate laws look like this:

(R1) Forward Reaction

Mass-Action Kinetics

(R2) Backward Reaction

Mass-Action Kinetics

represents a Monomer and a Dimer.

The following step-by-step tutorial shows you how to create a Dimerization Model using the SBML editor.

1. Start by opening the SBML editor. You will see this:

3 Figure 1. Just opened SBML editor

2. Then create a new SBML model by going to Menu Bar > File > New > SBML Model. In the appearing dialog window, choose the location of your SBML editor workspace (the file directory where your model will be stored) and the name of your model, then confirm by clicking on Finish. Your workbench should now look like this:

4 Figure 2. SBML editor with new model opened

3. In the Properties Tab, name your model by putting the desired name in the Name field, for example Dimerization Reversible.

4. In the Outline Tab, expand the tree view of your model by left-clicking on the small triangle beside the root element.

5. Select Compartment Cell by left-clicking on it. In the Properties Tab, set the Size to 0.0001. Make sure that the box Constant is checked and that Spatial Dimensions is set to 3. Leave everything else untouched.

6. Add your first species by right-clicking on Compartment Cell in the tree-view, then Add to this node > Species. Repeat to add a second species.

You can also add nodes and relations by using the Palette Tab and placing them  directly at the wanted location in the Graphical Editor Tab.

Since you have not yet named the species, their automatically generated  unique id will be shown instead.

7. To name your first species and set its properties, select one of your species by left-clicking on it in the tree-view. In the Properties Tab, put the name M for the monomer in the Name field. Check the box Has Only Substance Units. Also set Initial Concentration to 3000000.0. Leave everything else alone.

8. Now do the same for the dimer naming it D. Also check the box Has Only Substance Units. Make sure the Initial Concentration is set to 0.0. Leave everything else alone.

5 9. Add a parameter by right-clicking on the root-element in the tree-view, then Add to this node > Parameter. Select the newly added parameter in the tree-view and name it k1 in its Properties Tab. Check the box Constant and set the field Value to 0.2. Leave everything else untouched.

10. To add the needed reaction, right-click on Compartment Cell in the tree-view, then Add to this node > Reaction. Name the newly added reaction by selecting it in the tree-view and naming it dimerization in its Properties Tab. Check the box Reversible and leave everything else alone. By now, your workbench should look like this:

Figure 3. SBML editor with added nodes, parameter and reactions

For nicer optics, drag the species and the reaction into a more ordered form in  the Graphical Editor Tab. Also adjust the size of the reaction node to make it better readable by selecting it and dragging it bigger.

11. To add the relations, choose Reactant in the Palette Tab. In the Graphical Editor Tab, click then on the node M and drag the appearing relation over to the reaction dimerization where you let go. Do the same again, but this time choose Product in the Palette Tab and drag the relation from the reaction dimerization to the species node D.

You can only add the relations directly via the Palette Tab, adding them in the  tree-view is not possible.

You will now see two newly added relations under your reaction in the tree-  view, Reactant M and Product D.

12. Select Reactant M in the tree-view and in its properties tab, set Stoichiometry to 2.0, check the

6 Constant box and leave the rest untouched. Also leave all settings of Product D alone.

13. Add a kinetic law by right-clicking Reaction dimerization in the tree-view and then Add To This Node > Kinetic Law. Now add the corresponding mathematical formula to the kinetic law by adding k1 * M^2 to the Math field in the Properties Tab of the kinetic law. Your workbench now should look like this:

Figure 4. Finished model in the SBML editor

You can also use the formula editor to add the mathematical formula by  clicking on the three dots right beside the Math field in the properties tab of the kinetic law.

Your SBML model is now complete. The SBML file looks like this:

8 $parameter_giuYlkGjEeiadJA0_3qQfA species_UXS9gUGjEeiadJA0_3qQfA 2$

You can also fully simulate your SBML editor model in an SBML-compatible simulator of your choosing (e.g. COPASI) by importing the SBML-file into it. For example, if you want to simulate your model in COPASI, follow these steps:

If you need more in-depth information than given in the steps below on how to use  COPASI, please check the COPASI homepage on http://copasi.org/.

1. Open COPASI. Your COPASI workbench should look like this:

Figure 5. Just opened COPASI workbench

2. Now import your SBML model created in the SBML editor by doing this:

a. Go to Menu Bar > File > Import SBML.

b. In the appearing window, navigate to the destination of your SBML model via the tree view shown on the left.

Make sure you are shown all files and not just the XML files (COPASI  default) by choosing All files (*) instead of XML files (*.xml) in the corresponding drop-down menu.

10 c. Choose your SBML model out of the file list shown on the right.

d. Open the model by clicking Open or abort the action by clicking Abort. By now, your workbench should look like this after expanding part of the tree structure on the left:

Figure 6. COPASI workbench with imported SBML model

3. Then navigate to COPASI > Tasks > Time Course in the tree view on the left and expand it by right-clicking to set the simulation parameters:

a. Duration (s): 1

b. Interval Size (s): 0.01

c. Intervals: 100

d. Leave the rest alone

e. Click on the button Output Assistant and choose Particle Numbers, Volumes, and Global Quantity Values as a plot output. Confirm by clicking Create or abort by clicking Cancel.

4. Finally simulate your model by clicking Run in the Time Course window. Your simulation plot will look like this:

11 Figure 7. COPASI simulation of your SBML model

12 Tasks

In this chapter, you will find short directions on how to perform certain tasks with the SBML editor. For more detailed examples with screenshots, you might want to check out chapters Basic tutorial: Describing Reaction Network of Dimerization and Tutorials.

Navigating the workbench

The following section describes the elements of the workbench and gives you a short overview what you can do with them. The image SBML editor Graphical User Interface below is a screenshot of the SBML editor workbench, this is how it looks like just after you started the SBML editor and opened a new SBML Model (for information on how to do this, see section New SBML Model).

Figure 8. SBML editor Graphical User Interface

Menu Bar Provides access via drop down menus to common functions concerning files (open, close, save, print, …), editing (undo, redo, copy, paste,…), diagram appearance (font, color, line properties, alignment, …), windows and help.

Toolbar Quick access to important functions via toolbar buttons.

Model Outline Tab Displays a tree view of your complete SBML Model. Navigating the tree, adding, editing and

13 deleting elements is possible.

Graphical Overview Tab Displays an overview of your complete SBML Model, helpful for navigating your model if it is bigger than your Graphical Editor Tab.

Graphical Editor Tab Shows your SBML Model as graph, fully editable.

Properties Tab Displays properties of SBML Model elements.

Palette Tab Provides quick access to function like adding nodes and relations, zooming.

You can always minimize the tabs you do not need and, if you change your mind  later, restore them again via the minimize ( ) and restore ( ) buttons.

If you need more information on the workbench elements, please refer to the Reference-Section and its corresponding subsections:

• Reference

• Graphical User Interface overview

• Menu Bar

• Toolbar

• Model outline tab

• Graphical overview tab

• Graphical Editor tab

• Properties tab

• Palette tab

Basics

In this section, we will start by describing how you can perform some basic tasks in the SBML editor.

Open existing SBML Model

To open an existing SBML Model, do the following:

1. Go to the menu bar, then click File > Open

2. Navigate to the directory where the existing SBML Model is located and select it

3. Click Open

14 You can open more than one model. Each model will then reside in its own SBML  Graphical Editor tab.

New SBML Model

If you do not want to open an existing SBML Model, but to create a new SBML Model:

1. Go to the menu bar, then click File > New > SBML Model

2. In the dialog box, enter the file destination and a file name for your new SBML model

3. Click Finish to confirm or Cancel to abort the action

Save SBML Model

To save your SBML Model and any changes done to it:

• Go to the menu bar, then click File > Save or alternatively

• Go to the Toolbar and click

If you are working on more than one SBML Model simultaneously and therefore have different tabs open, you can save all changes in all SBML Models at once by going to the Menu Bar > Save All.

Save SBML Model graph as image

Besides saving your work as SBML Model, you can also save the SBML Model directly as an image file:

1. Place a right-click somewhere into the free space of the Graphical Editor Tab

2. In the Right-click Menu click File > Save As Image

3. Choose the destination folder and a name for the image in the dialog box

4. Also choose the format in which the image will be saved

If the image format is JPEG you can specify the image quality. The lower you set  the quality, the smaller the file size of the image will be.

5. Optionally, check the corresponding boxes if you want to overwrite the existing file without further warning or export it to HTML

6. Click OK to confirm or Cancel to abort the action

Adding and configuring Nodes

In this section, you will learn how to add nodes to your SBML Model and configure them. There are three different kind of nodes possible in your model:

• Species

15 • Reaction

• Compartment

After adding the nodes you can configure node-specific properties.

Adding a Species, Reaction or Compartment

There are two ways to add a node to your SBML Model, and the process is the same for all three types of nodes (Species, Reaction, Compartment). The easiest way to do it, also giving you direct control over the placement of the node, is as follows:

1. To add a node, navigate to

a. Nodes > Species in the Palette Tab, if you want to add a Species node.

b. Nodes > Reaction in the Palette Tab, if you want to add a Reaction node.

c. Nodes > Compartment in the Palette Tab, if you want to add a Compartment node.

2. Left-click on

a. Species for a new Species node

b. Reaction for a new Reaction node

c. Compartment for a new Compartment node

3. Place your node via a left-click at its destination inside the Graphical Editor Tab

4. Right after placing the node you can directly name it in the appearing input field

If positioning the node at an exact point is not that important for you at the moment (the nodes will be automatically positioned by the program), then this is the way to go:

1. In the Outline Tab, right-click either on the root element of the tree structure if you want the node positioned outside of a compartment. To place a node inside the compartment, navigate to the Compartment cell in the tree structure and place a right-click on there.

2. In the right-click menu, go to

a. Add to this node > Species to add a Species node

b. Add to this node > Reaction to add a Reaction node

c. Add to this node > Compartment to add a Compartment node

With this method there will be no automatically appearing input field for  the name of the node. You will have to name the node manually at a later time.

Configuring a Species, Reaction or Compartment

Once you have added a Species, Reaction or Compartment node, you can configure its properties:

1. Mark the node by left-clicking on it. This will show you its properties in the Properties Tab.

16 Alternatively, you can also view and edit the corresponding properties of a  node by navigating to the desired node in the tree view in the Outline Tab. The properties will also be displayed in the Properties Tab.

2. Set the properties as desired. As soon as you leave the Properties Tab the new properties will take effect.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Nodes

• Species

• Reactions

• Compartment

Adding and configuring Relations

A Relation describes the relationship between a Species node and a Reaction node. Therefore, before you can add a Relation to your SBML Model, you need to have at least one Species node and one Reaction node. For further information on how to do this please refer to the corresponding subsections:

• Adding a Species, Reaction or Compartment

• Configuring a Species, Reaction or Compartment

There are three types of relations:

• Reactant

• Modifier

• Product

How you add and configure relations is described in the following sections.

Adding a Reactant, Modifier or Product

Adding a relation is similar to adding a node to your SBML Model, the process is the same for all three types of relations (Reactant, Modifier or Product). To add a relation, do the following:

1. Navigate to

a. Relations > Reactant in the Palette Tab, if you want to add a Reactant relation.

b. Relations > Modifier in the Palette Tab, if you want to add a Modifier relation.

c. Relations > Product in the Palette Tab, if you want to add a Product relation.

17 2. Left-click on

a. Reactant for a new Reactant relation

b. Modifier for a new Modifier relation

c. Product for a new Product relation

3. Place your relation:

a. Left-click on the relation’s starting node inside the Graphical Editor Tab, this can be either a Species node or a Reaction node inside the Graphical Editor Tab.

You cannot choose invalid starting or ending points. A valid point is shown to you by a hovering arrow over the node when you move the mouse  cursor over it. Otherwise you will see an arrow with a prohibited sign below it, and you will not be able to select it as starting or ending point of your relation.

b. Now drag the appearing arrow (without letting go of the left-click) from the starting node to the ending node of your relation.

c. Once the dragged arrow is over a valid and desired ending node, release the left-click.

4. Right after placing the relation you can directly name it in the appearing input field.

Configuring a Reactant, Modifier or Product

Once you have added a Reactant, Modifier or Product relation, you can configure its properties:

1. Mark the relation by left-clicking on it. This will show you its properties in the Properties Tab.

Alternatively, you can view and edit the corresponding properties of a relation by navigating to the desired relation in the tree view in the Outline Tab. The  properties will also be displayed in the Properties Tab. In the tree view, relations are always subelements of Reaction elements.

2. Set the properties as desired. As soon as you leave the Properties Tab the new properties will take effect.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Relations

Adding and configuring Kinetic Laws

To add a kinetic law to your reaction:

1. In the Outline Tab, navigate in the tree view to the reaction you want to add a kinetic law to

18 2. Right-click to access the context menu

3. In the context-menu, go to Add to this node > Kinetic Law

4. A left-click will add a new kinetic law to your reaction. It will appear in the tree view under said reaction.

You can access the kinetic law you just created via the tree view in the Outline Tab  by placing a left-click on it. This will show you its properties in the Property Tab where you can edit them.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Kinetic Laws

Adding and configuring Function Definitions

If you want to add a Function Definition:

1. Right-Click on the root element of the tree view in the Outline Tab to access the context menu

2. In the context-menu, go to Add to this node > Function Definition

3. Left-click to add a new function definition to your SBML Model. It will appear in the tree view under the root element.

A left-click in the tree view on the newly added function definition will allow you  to set or edit its properties via the Properties Tab.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Function Definitions

Adding and configuring Unit Definitions

To add a Unit Definition, follow these steps:

1. Right-Click on the root element of the tree view in the Outline Tab to access the context menu

2. In the context-menu, go to Add to this node > Unit Definition

3. Left-click to add a new unit definition to your SBML Model. It will appear in the tree view under the root element.

19 You can set or edit its properties via the Properties Tab by placing a left-click in the  tree view on the newly added unit definition.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Unit Definitions

Adding and configuring Parameters

You can add a Parameter, by doing this:

1. Right-Click on the root element of the tree view in the Outline Tab to access the context menu.

2. In the context-menu, go to Add to this node > Parameter to add a new parameter to your SBML Model.

3. Left-click to add it to your SBML Model. It will appear in the tree view under the root element.

A left-click in the tree view on the newly added parameter will allow you to set or  edit its properties via the Properties Tab.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Parameters

Adding and configuring Rules, Initial Assignments and Constraints

There are three different kind of rules you can add to your SBML Model:

• Algebraic Rules

• Assignment Rules

• Rate rules

Besides, you can also add initial assignments and constraints to your SBML Model.

To add a rule, initial assignment or constraint, follow these steps:

1. Right-Click on the root element of the tree view in the Outline Tab to access the context menu

2. In the context-menu, depending on what you want to add, go to:

20 a. Add to this node > Algebraic Rule to add a new algebraic rule to your SBML Model

b. Add to this node > Assignment Rule to add a new assignment rule to your SBML Model

c. Add to this node > Rate Rule to add a new rate rule to your SBML Model

d. Add to this node > Initial Assignment to add a new initial assignment to your SBML Model

e. Add to this node > Constraint to add a new Constraint to your SBML Model

3. Left-click to add it to your SBML Model. It will appear in the tree view under the root element.

A left-click in the tree view on the newly added rule, initial assignment or  constraint will allow you to set or edit its properties via the Properties Tab.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Parameters

• Rules

• Algebraic Rules

• Assignment Rules

• Rate Rules

• Initial Assignments

• Constraints

Adding and configuring Events

If you want to add an Event to your SBML Model, do the following:

1. Right-Click on the root element of the tree view in the Outline Tab to access the context menu.

2. In the context-menu, go to Add to this node > Event to add a new event to your SBML Model.

3. Left-click to add it to your SBML Model. It will appear in the tree view under the root element.

A left-click in the tree view on the newly added event will allow you to set or edit  its properties via the Properties Tab.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Parameters

• Events

21 Adding Notes

You can add notes to every element in you SBML Model by doing this:

1. In the tree view of your SBML Model in the Outline Tab, navigate to the element you want to add a note to.

2. Right-Click on this element to access the context menu.

3. In the context-menu, go to Add to this node > Note to add a new note specifically to this element.

4. Left-click to add it to your SBML Model. It will appear in the tree view under the element you chose to attach it to.

You can also add a note by left-clicking on the element you want the note attached  to in the Graphical Editor Tab, and then selecting Add note in the appearing context menu.

A left-click in the tree view on the newly added note will allow you to set or edit its  properties via the Properties Tab. In this case you only have a text field in the properties tab where you can add the content of your note.

For more information on the property fields in the Property Tab, please refer to the Reference- Section and its corresponding subsections:

• Reference

• Properties tab

• Parameters

• Notes

Deleting elements

If you want to delete an element from your SBML Model, you can do this in two different ways. The first one is to go via the Graphical Editor Tab:

1. Place a left-click on the element you want to remove.

2. In the now appearing context menu, select Delete from Model

Alternatively, you can remove an element using the Outline Tab:

1. In the tree view in the Outline Tab, navigate to the element you want to remove from your SBML Model.

2. Right-Click on this element to access the context menu.

3. In the context-menu, choose Delete to remove the desired element.

22 There will be no further confirmation window before the delete where you can  abort the action. If you delete an element by accident, you can always undo the action by navigating to Menu bar > Edit > Undo.

23 Reference

In this section you will find detailed descriptions of all GUI and menu elements of the SBML editor including their functions and keyboard shortcuts.

Graphical User Interface overview

The graphical user interface looks like this after you started the SBML editor and opened a new SBML Model:

Figure 9. SBML editor Graphical User Interface

Menu Bar

File Menu Actions

Table 1. File menu commands

Name Function Keyboard Shortcut New Create a new SBML model. none Configure which file will contain the model and where it is located in the dialog showing up.

24 Name Function Keyboard Shortcut Open Opens a file from the file system Ctrl + O in an SBML editor. Open URI Load a resource by Uniform Ctrl + U Resource Identifier (URI). Open File Opens a file from the file system none in an SBML editor. Convert Line Delimiters To Convert the line delimiters of none all the text files in the selection to the selected delimiter kind. Close Close the current SBML model. Ctrl + W If the model contains unsaved data, a save request dialog will be shown. Close All Close all SBML models. If any of Ctrl + Shift + W the models contain unsaved data, a save request dialog will be shown. Save Save the content of the current Ctrl + S SBML model. Disabled if the model does not contain unsaved changes. Save As Save the content of the current none SBML model under a new name. Save All Save the content of all ABML Ctrl + Shift + S models with unsaved changes. Disabled if no model contains unsaved changes. Print Preview Shows a print preview of the none current SBML model. Enabled when a model has the focus. Exit Exit the SBML editor. none Page Setup Set the page properties. Either none use the global workspace settings or the diagram settings.

Edit Menu Actions

Table 2. Edit menu commands

Name Function Keyboard Shortcut Undo Revert the last change in the Ctrl + Z SBML model. Redo Revert an undone change. Ctrl + Y

25 Name Function Keyboard Shortcut Cut Copies the currently selected Ctrl + X text or element to the clipboard and removes the element. Copy Copies the currently selected Ctrl + C text or elements to the clipboard. Paste Paste the current content as text Ctrl + V to the editor, or as a sibling or child element to the a currently selected element. Delete Delete the current text or Delete element selection. Select All Select all the SBML editor Ctrl + A content. Validate Validate the SBML model? none

Diagram Menu Actions

Table 3. Diagram menu commands

Name Function Keyboard Shortcut Font Set the font and its properties none used for an element in an SBML editor. Fill Color Set the fill color of an none compartment in an SBML editor. Line Color Set the line color of an none compartment in an SBML editor. Line Type Set the line type of ? in an SBML none editor. Line Width Set the line width of ? in an none SBML editor. Arrow Type Set the arrow type of ? in an none SBML editor. Line Style Set the line style of a relation none element in an SBML editor (rectilinear or oblique routing). Select Select certain elements in an none SBML editor (all, all shapes or all connectors). Arrange Arrange either all or a selection none of the elements in an SBML editor.

26 Name Function Keyboard Shortcut Align Align elements vertically and none horizontally. Text Alignment Align text horizontally. none Order Order the elements in an SBML none editor by bringing them forward or backward compared to others. Auto Size Automatically size the content none of the SBML editor? Make Same Size Make selected elements of an none SBML editor the same size in height or width or both. Filters Apply filters to the SBML model none like sorting and filtering compartment items and toggling visibility of compartments? View Show a grid, rulers, page breaks none in the SBML editor. Additionally choose if diagram gets snapped to the grid. Zoom Offers different zooming views none of the content of an SBML editor. Apply Appearance Properties Apply the applicable none appearance of the first selected shape to the other selected shapes.

Window Menu Actions

Table 4. Window menu commands

Name Function Keyboard Shortcut Open In New Window Opens a new SBML editor none window.

Help Menu Actions

Table 5. Help menu commands

Name Function Keyboard Shortcut SBML editor About Short information about the none SBML editor and current version number.

27 Name Function Keyboard Shortcut Key Assist Opens a list of available key Ctrl + Shift + E bindings in the SBML editor.

Toolbar

Table 6. Toolbar actions available

Toolbar Button Command Description Save Save your SBML model.

Print Print your SBML model.

Next Annotation Jumps to the next annotation of? Previous Annotation Jumps to the previous annotation of? Last Edit Location NOT WORKING

Font Choose your font.

Font Size Choose your font size.

Bold Font Style Set your font style to bold.

Italic Font Style Set your font style to italic.

Font Color Choose your font color.

Fill Color Choose a fill color.

Line Color Choose a line color.

Line Style Choose a line style for the routing of relations (rectilinear, oblique or tree style). Apply the applicable Apply the applicable appearance properties of the appearance properties of the first selected shape to the other first selected shape to the other selected shapes selected shapes. Select All Select elements (all, all shapes or all connectors). Arrange All Arrange elements (all or a selection of them).

28 Toolbar Button Command Description Align Align elements (left, center, right, top, middle or bottom). Auto Size Auto size your SBML model?

All Connector Labels Show all connector labels.

No Connector Labels Show no connector labels.

Show/Hide Compartment Show your compartments (all compartments or name compartment only). Zoom Choose a zoom (zoom in, zoom out, zoom to fit, fit to width, fit to height, fit to selection or choose between different percentages).

Model outline tab

Table 7. TabBar Actions

Tab Bar Button Command Description Collapse All Collapse the model outline tab and the space it is inhabiting. Link With Editor Links the Model Outline Tab to the SBML Model Editor Tab. Show Navigator Show only the Navigator Pane in the Model Outline Tab. Show Overview Show only the Overview Pane in the Model Outline Tab. Show Both Show the Overview Pane and the Navigator Pane in the Model Outline Tab. type filter text Filter the results in the tree view of your SBML model by typing in text.

Table 8. Context Menu commands

Name Function Add to this node Add a new element to this node. Possible choices are presented to you in a submenu. Add to parent node Add a new element to the parent node of the current node. Possible choices are presented to you in a submenu.

29 Name Function Notes Attach a note to the selected element. Reaction Add a reaction to your SBML model. Species Add a species to your SBML model. Function Definition Add a function definition to your SBML model. Kinetic Law Add a kinetic law to a reaction of your SBML model. Unit Definition Add a unit definition to your SBML model. Compartment Add a compartment to your SBML model. Parameter Add a parameter to your SBML model. Initial Assignment Add an initial assignment to your SBML model. Algebraic Rule Add an algebraic rule to your SBML model. Assignment Rule Add an assignment rule to your SBML model. Rate Rule Add a rate rule to your SBML model. Constraint Add a constraint to your SBML model. Event Add an event to your SBML model. Undo New Notes Revert the adding of new notes. Redo Revert an undone change. Cut Copies the currently selected text or element to the clipboard and removes the element. Copy Copies the currently selected text or elements to the clipboard. Paste Paste the current content as text to the editor, or as a sibling or child element to the a currently selected element. Delete Delete element from the SBML model.

Not all context menu commands are available for each element of your SBML  model.

For specific information on how to set the properties of the added elements and  possible constraints regarding the input fields, please refer to the section Properties tab.

Graphical overview tab

The Graphical Overview tab shows you an overview of your complete SBML model, even if it is bigger than your Graphical Editor tab. The blue overlay shows you the part of your model currently visible in the Graphical Editor tab. The Graphical Overview tab is synchronized to your Graphical Editor tab. Therefore, left-clicking on the overlay and dragging it to a new position will show you its new content in the Graphical Editor tab.

30 Figure 10. Graphical Overview tab with blue overlay showing part of model visible in Graphical Editor tab

Graphical Editor tab

Table 9. Context Menu commands in the Graphical Editor Tab

Name Function Add Add a new element to this node. Possible choices (Note or Text) are presented to you in a submenu. Navigate ? File Lets you save the file as image file or print it. Possible choices are presented to you in a submenu. Edit Edit your actions (Undo, Redo, Cut, Copy or Paste are found in the submenu). Delete from Model Delete a selected element from your model. Select Select elements of your model (All, All Shapes or All Connections). Possible choices are presented to you in a submenu. Arrange All Arrange all the elements in your model (All or Selection). Possible choices are presented to you in a submenu.

31 Name Function Filters Lets you toggle the showing of connector labels (All Connector Labels or No Connector Labels). Possible choices are presented to you in a submenu. View Choose additional viewing options (Grid, Rulers, Page Breaks, Recalculate Page Breaks or Snap TO Grid). Possible choices are presented to you in a submenu. Zoom Zoom your model (Zoom In, Zoom Out, Zoom to 100%, Zoom to fit, Fit To Width, Fit To Height or Fit To Selection). Possible choices are presented to you in a submenu. Edit Properties Edit the properties of a selected element of your model. Load Resource Load Resource URIs. Add Note Add a note to an element in your model. Format Choose styling options (Font, Fill Color, Line Color, Line Width, Line Type, Arrow Type, Arrange, Align, Text Alignment, Order, Auto Size or Apply Appearance Properties). Possible choices are presented to you in a submenu.

Not all context menu commands are available for each element of your SBML  model.

Properties tab

Nodes

Species

Table 10. Input controls for a Species in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the species. Name Set the name of the species. Boundary Condition Check box if boundary condition exists, otherwise leave unchecked. Charge Check box if the species is charged, otherwise leave unchecked. For more information on deprecation, please see this link. Constant Check box if the species is constant, otherwise leave unchecked.

32 Name Function Has Only Substance Units Check box if the species only has substance units, otherwise leave unchecked. Initial Concentration Set the concentration of the species at the beginning of simulation. Initial Amount Set the amount of species at the beginning of simulation. Substance Units Choose the substance units. Conversion Factor Choose the conversion factor.

For more information about the Input controls in the SBase and Appearance  subtabs, please refer to the tables Input controls in the SBase subtab and Input controls in the Appearance subtab.

Reactions

Table 11. Input controls for a Reaction in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the reaction. Name Set the name of the reaction. Fast Check box if the reaction is fast, otherwise leave unchecked. Reversible Check box if the reaction is reversible, otherwise leave unchecked.

For more information about the Input controls in the SBase and Appearance  subtabs, please refer to the tables Input controls in the SBase subtab and Input controls in the Appearance subtab.

Compartment

Table 12. Input controls for a Compartment in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the compartment. Name Set the name of the compartment. Constant Check box if the compartment is constant, otherwise leave unchecked. Spatial Dimension Choose the number of spatial dimensions. Size Choose the size of the compartment. Units Choose the units of the compartment.

33 For more information about the Input controls in the SBase and Appearance  subtabs, please refer to the tables Input controls in the SBase subtab and Input controls in the Appearance subtab.

Relations

Table 13. Input controls for a Relation (Reactant, Product or Modifier) in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the relation. Name Set the name of the compartment. Species Shows the species the relation belongs to. Stoichiometry Set the stoichiometry factor. This option is only available for reactant or product. Constant Check the box if the relation is constant, otherwise leave unchecked. This option is only available for reactant or product.

For more information about the Input controls in the SBase and Appearance  subtabs, please refer to the tables Input controls in the SBase subtab and Input controls in the Appearance subtab.

Kinetic Laws

Table 14. Input controls for a Kinetic Law in the Node tab of the Properties tab

Name Function Local Parameter Add a local parameter. Math Add a mathematical formula describing the kinetic law.

For more information about the Input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Function Definitions

Table 15. Input controls for a Function Definition in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the function definition. Name Set the name of the function definition. Math Add a mathematical formula describing the function definition.

34 For more information about the Input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Unit Definitions

Table 16. Input controls for a Unit Definition in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the unit definition. Name Set the name of the unit definition. Units List the units used for the unit definition and also lets you edit their properties (double-click on it).

For more information about the Input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Parameters

Table 17. Input controls for a Parameter in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the parameter. Name Set the name of the parameter. Constant Check the box if the parameter is constant, otherwise leave unchecked. Value Set the value of the parameter, positive and negative values are allowed. Units List the units used for the parameter and also lets you edit their properties (double-click on it).

For more information about the Input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Initial Assignments

Table 18. Input controls for an Initial Assignment in the Node tab of the Properties tab

Name Function Symbol Select an existing element as symbol. Math Add a mathematical formula describing the initial assignment.

35 For more information about the input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Rules

Algebraic Rules

No input controls for an Algebraic Rule in the Node tab of the Properties tab available. ?

For more information about the input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Assignment Rules

Table 19. Input controls for an Assignment Rule in the Node tab of the Properties tab

Name Function Variable Select an existing element as variable. Math Add a mathematical formula describing the assignment rule.

For more information about the input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Rate Rules

Table 20. Input controls for a Rate Rule in the Node tab of the Properties tab

Name Function Variable Select an existing element as variable. Math Add a mathematical formula describing the rate rule.

For more information about the input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Constraints

Table 21. Input controls for a Constraint in the Node tab of the Properties tab

Name Function Math Add a mathematical formula describing the constraint.

For more information about the input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

36 Events

Table 22. Input controls for an Event in the Node tab of the Properties tab

Name Function Id Shows the automatically generated unique identification string of the event. Name Set the name of the event. Use Values From Trigger Time Check the box if you want to use the values from trigger time, otherwise leave unchecked. EventAssignment Define how variables are affected by an Event. Priority Add a mathematical formula describing the priority. Delay Add a mathematical formula describing the delay.

For more information about the input controls in the SBase subtab, please refer to  the table Input controls in the SBase subtab.

Notes

Table 23. Input controls for a Note in the Node tab of the Properties tab

Name Function Text Add the text your note should contain here.

Shared Properties

All elements of your SBML Model show under their Properties tab an SBase subtab, and additionally some of them also show an Appearance subtab. Since the input controls greatly overlap, they are listed in this separate subsection and not repeated under each corresponding element section.

Table 24. Input controls in the SBase subtab

Name Function Metaid For metadata annotations using RDF (Resource Description Format). Each 'metaid' value must be globally unique within an SBML file. SboTerm Adds support of the use of the Systems Biology Ontology. Annotation Container for optional software-generated content not meant to be shown to humans.

In the Appearance subtab, not all Input controls are available for each of your  elements in your SBML model.

37 Table 25. Input controls in the Appearance subtab

Name Function Fonts and Colors Choose the font, font style, font size, font color, fill color and line color. Lines And Arrows Choose the line type, line width and arrow type. Smoothness Set the level of smoothness of the relation (none, normal, less or more). Routing Set the line style for the routing of the relation (oblique, rectilinear or tree). Jump Links Set the status (none, all, below or above) and the type (semi-circle, square or chamfered) for jumping links. Check the box Reverse jump links if needed otherwise leave unchecked.

Palette tab

Table 26. Palette Toolbar Actions

Tab Bar Button Command Description Hide Palette Hide the Palette tab.

Show Palette Show the Palette tab. Only visible if the Palette tab was hidden before. Select Selection tool for selecting, moving or placing elements in the Graphical Editor Tab. Zoom In Zoom in on elements in the Graphical Editor Tab. Zoom Out Zoom out on elements in the Graphical Editor Tab. Pin Open ?

Unpin ?

Create New Compartment Creates new compartment, place it with a left mouse-click at desired position in the Graphical Editor Tab. Create New Species Creates new species, place it with a left mouse-click at desired position in the Graphical Editor Tab.

38 Tab Bar Button Command Description Create New Reaction Creates new reaction, place it with a left mouse-click at desired position in the Graphical Editor Tab. Create New Reactant Creates new reactant, place it by left-clicking on the starting element and dragging the appearing line to the finish element. Create New Modifier Creates new modifier, place it by left-clicking on the starting element and dragging the appearing line to the finish element. Create New Product Creates new product, place it by left-clicking on the starting element and dragging the appearing line to the finish element.

39 Tutorials

Irreversible Michaelis-Menten Model

In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. The mathematical model of the reaction involves an enzyme E binding to a substrate S to form a ES complex, which in turn is converted into a product P and the enzyme E. This may be represented schematically as

The Michaelis–Menten equation describes the rate of enzymatic reactions, by relating reaction rate to , the concentration of a substrate :

represents the maximum rate achieved by the system, at maximum saturation of the substrate concentration. The Michaelis constant is the substrate concentration at which the reaction rate is half of .

Based on this, the single reaction and rate laws look like this:

(R1) Single Reaction

Mass-Action Kinetics

(R2) Single Reaction

Mass-Action Kinetics

(R3) Single Reaction

Mass-Action Kinetics

E stands for Enzyme, S for Substrate, ES for Enzyme-Substrate-Complex and P for Product. Reaction R1 and R2 describe the reversible nature of the reaction, therefore you will only need R1 later in

40 the SBML editor as long as you mark it as reversible.

The following is a step-by-step tutorial on how to create your Irreversible Michaelis-Menten Model.

1. Start by opening the SBML editor. You will see this:

Figure 11. Just opened SBML editor

2. Then create a new SBML model by going to Menu Bar > File > New > SBML Model. In the appearing dialog window, choose the location of your SBML editor workspace and the name of you model, then confirm by clicking on Finish. Your workbench should now look like this:

41 Figure 12. SBML editor with new model opened

3. In the Properties Tab, name your model by putting the desired name in the Name field, for example Michaelis-Menten Irreversible.

4. In the Outline Tab, expand the tree view of your model by left-clicking on the small triangle beside the root element.

6. Add your first species by right-clicking on Compartment Cell in the tree-view, then Add to this node > Species. Repeat three times to add the second to fourth species.

You can also add nodes and relations by using the Palette Tab and placing them  directly at the wanted location in the Graphical Editor Tab.

Since you have not yet named the species, their automatically generated  unique id will be shown instead.

7. To name your first species and set its properties, select one of your species by left-clicking on it in the tree-view. In the Properties Tab, put the name E in the Name field. Check the box Has Only Substance Units. Also set Initial Amount to 100.0. Leave everything else alone.

8. Now do the same for the second species naming it S. Also check the box Has Only Substance Units and set the Initial Amount to 100.0. Leave everything else alone.

9. Name the two remaining species ES and P. For each of those two species, check the box Has

42 Only Substance Units and set Initial Amount to 0.0. Leave everything else alone.

10. Add a parameter by right-clicking on the root-element in the tree-view, then Add to this node > Parameter. Repeat to add a second parameter.

11. Select one of the newly added parameters in the tree-view and name it k1 in its Properties Tab. Check the box Constant and set the field Value to 0.2. Leave everything else untouched.

12. Do the same for the second parameter naming it k2. Again, check the box Constant and set the field Value to 0.2. Leave everything else untouched.

13. To add the first of the two needed reactions, right-click on Compartment Cell in the tree-view, then Add to this node > Reaction. Repeat to add the second reaction.

14. Select one of the newly added reactions in the tree-view and name it R1 in its Properties Tab. Check the box Reversible and leave everything else alone.

15. Do the same for the second reaction naming it R2. Leave the box Reversible and leave everything else alone. By now, your workbench should look like this:

Figure 13. SBML editor with added nodes, parameter and reactions

16. To add the relations Reactant, choose Reactant in the Palette Tab. In the Graphical Editor Tab, click then on the node E and drag the appearing relation over to the reaction R1 where you let go. Do the same again, starting at the node S and ending again at the reaction R1. Now repeat one last time, beginning at node ES and ending at reaction R2.

43 17. To add the relations Product, choose Product in the Palette Tab and drag the relation from the reaction R1 to the node ES. Repeat, starting at the reaction R2 and ending at the node E. Do the same a last time beginning at the reaction R2 and ending at the node P.

You can only add the relations directly via the Palette Tab, adding them in the  tree-view is not possible.

You will now see the newly added relations under your reactions in the tree- view. Under Reaction R1, you should see Reactant E, Reactant S and Product  ES. Under Reaction R2 you should find Reactant ES, Product P and Product E.

18. Leave the properties settings of all relations unchanged.

19. Add a kinetic law to your first reaction by right-clicking Reaction R1 in the tree-view and then Add To This Node > Kinetic Law. Now add the corresponding mathematical formula to the kinetic law by adding k1 * E * S to the Math field in the Properties Tab of the kinetic law.

20. Now add a kinetic law to your second reaction by right-clicking Reaction R2 in the tree-view and then Add To This Node > Kinetic Law. Add the corresponding mathematical formula to the kinetic law by adding k2 * ES to the Math field in the Properties Tab of the kinetic law. Your workbench now should look like this:

Figure 14. Finished model in the SBML editor

44 You can also use the formula editor to add the mathematical formula by  clicking on the three dots right beside the Math field in the properties tab of the kinetic law.

Your SBML model is now complete. You can also fully simulate your SBML editor model in an SBML-compatible simulator of your choosing (e.g. COPASI) by importing the SBML-file into it. For steps on how to simulate your model in COPASI, please see the corresponding part in Basic tutorial: Describing Reaction Network of Dimerization.

If you need more in-depth information than given in the steps below on how to use  COPASI, please check the COPASI homepage on http://copasi.org/.

45 Appendix

Concepts

(Dynamic) Biological models

Mathematical models can be used to help explain biological systems and to study the effects of different components, and even to make predictions about behaviour. They are usually composed of relationships described by operators (algebraic operators, functions, differential operators, etc.) and variables which are quantifiable abstractions of system parameters of interest. Several classification critera can be used for mathematical models according to their structure:

• Linear vs. nonlinear: A mathematical model is defined as linear if all the operators in a mathematical model exhibit linearity, otherwise it is considered to be nonlinear.

• Dynamic vs. static: A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations.

• Explicit vs. implicit: If all of the input parameters are known and the output parameters of the model can be calculated by a finite series of computations, the model is called explicit. If, on the other hand, only the output parameters are known, and the corresponding inputs must be solved for by an iterative procedure (e.g. Newton’s method or Broyden’s method), the model is called implicit.

• Discrete vs. continuous: A discrete model treats objects as discrete, whereas a continuous model represents the objects in a continuous manner.

• Deterministic vs. probabilistic (stochastic): If every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables, the model is called deterministic. Therefore, a deterministic model always performs the same way for a given set of initial conditions. If variable states are not described by unique values, but rather by probability distributions, the model is called stochastic.

• Deductive, inductive, or floating: A deductive model is a logical structure based on a theory, whereas an inductive model arises from empirical findings and generalization from them. A floating model rests on neither theory nor observation, but is merely the invocation of expected structure.

Depending on the modelled system, mathematical models can take many forms, including dynamical systems, statistical models or differential equations. These types of models can also overlap, creating a model involving a variety of abstract structures.

Modelling biological systems is a significant task of systems biology and mathematical biology. Some examples include:

• Cellular models (enzyme kinetics, signal transduction, gene regulatory networks, …)

• Epidemic models (SIR-Model, …)

• Protein folding, protein structure prediction (high importance in the designing of new drugs or enzymes)

46 • Human biological systems (Brain model, Virtual Liver, Model of the immune system)

• Population Growth models (Lotka–Volterra predator–prey model, …)

• Modelling of infectious diseases

• and many more

For more in-depth reading, please refer to the following links:

• https://en.wikipedia.org/wiki/Mathematical_model (Wikipedia: Mathematical model)

• https://en.wikipedia.org/wiki/Dynamical_system (Wikipedia: Dynamical system)

• https://en.wikipedia.org/wiki/Systems_biology (Wikipedia: Systems biology)

• https://en.wikipedia.org/wiki/Modelling_biological_systems (Wikipedia: Modelling biological systems)

• https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology (Wikipedia: Mathematical and theoretical biology)

• https://en.wikipedia.org/wiki/Enzyme_kinetics (Wikipedia: Enzyme Kinetics)

• https://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics (Wikipedia: Michaelis- Menten kinetics)

Michaelis-Menten Kinetics

Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. The model is described by the Michaelis–Menten equation describing the rate of enzymatic reactions, by relating reaction rate to , the concentration of a substrate :

represents the maximum rate achieved by the system, at maximum saturation of the substrate concentration. The Michaelis constant is the substrate concentration at which the reaction rate is half of . Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model’s underlying assumptions.

The mathematical model of the enzyme reaction involves an enzyme binding to a substrate to form a complex, which in turn is converted into a product and the enzyme . This may be represented schematically as

, , and represent the rate constants, and the double arrows between and indicate that the enzyme-substrate binding is a reversible process.

Assuming a much less enzyme concentration than substrate concentration the rate of product formation is given by

47 The reaction rate increases with increasing substrate concentration , asymptotically approaching its maximum rate , reaching the maximum when all enzyme is bound to substrate. Also, , where is the initial enzyme concentration. , the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second.

The Michaelis constant is the at which the reaction rate is at half-maximum. Therefore, it is an inverse measure of the substrate’s affinity for the enzyme. A small indicates high affinity, meaning that the rate will approach with lower than those reactions with a larger . The value of is dependent on both the enzyme and the substrate, as well as conditions such as temperature and pH.

The model is used in a variety of biochemical situations other than enzyme-substrate interaction, including antigen-antibody binding, DNA-DNA hybridization, and protein-protein interaction.

For more in-depth reading, please refer to the following links:

• Wikipedia: Enzyme Kinetics

• Wikipedia: Michaelis-Menten kinetics

Systems Biology Markup Language (SBML)

The Systems Biology Markup Language (SBML) is a representation format based on XML and is also the standard for representing computational models in systems biology today. It is used for communicating and storing computational models of biological processes, including metabolic networks, cell signaling pathways, regulatory networks, infectious diseases, and many others. In SBML, a biological model is a collection of chemical reactions where each reaction is then characterized by its reactants, products, modifiers, and kinetic laws.

To manage complexity in the evolution and enhancement of SBML, it is being developed in a series of levels. Each level adds new features and fixes problems with the previous level. The lowest- numbered levels provide fundamental features common to all biochemical network models, whereas higher-numbered levels add more features specific to particular classes of tools. Any level can be used as a standard for interchanging models.

SBML Level 3 is the most recent specification of SBML.

SBML is a modular language, with a core comprising a complete format that can  be used alone. Additional packages are layered on this core providing additional, optional features.

SBML Levels are intended to coexist, newer SBML Levels do not render older  levels obsolete. Therefore, models and software tools compatible with older levels are still used.

The top level of an SBML model definition consists of lists of the following components, with every list being optional:

Function definition • a named mathematical function

48 • usable throughout the rest of a model

Unit definition • a named definition of a new unit of measure, or a redefinition of an existing SBML default unit

Compartment Type (only in SBML Level 2) • a type of location where reacting entities such as chemical substances may be located

Species type (only in SBML Level 2) • a type of entity that can participate in reactions

• examples include ions such as Ca2+, molecules such as glucose or ATP, binding sites on a protein, and more.

Compartment • a well-stirred container of a particular type and finite size where SBML species may be located

• multiple compartments of the same compartment type possible in a model

• every species in a model must be located in a compartment

Species • a pool of entities of the same species type located in a specific compartment

Parameter • a quantity with a symbolic name

• in SBML used generically to refer to named quantities regardless of whether they are constants or variables in a model

• a parameter defined at the top level is global to a model

• it is also possible to define parameters that are local to a single reaction

Initial Assignment • a mathematical expression used to determine the initial conditions of a model

Rule • a mathematical expression added to the set of equations constructed based on the reactions defined in a model

• can be used to define how a variable’s value can be calculated from other variables

• can also be used to define the rate of change of a variable

• the set of rules in a model can be used with the reaction rate equations to determine the behaviour of the model with respect to time

• the set of rules constrains the model for the entire duration of simulated time.

Constraint • a means of detecting out-of-bounds conditions during a dynamical simulation (and optionally issuing diagnostic messages)

• defined by an arbitrary mathematical expression computing a true/false value from model

49 variables, parameters and constants

Reaction • statement describing some transformation, transport or binding process that can change the amount of one or more species

• have associated kinetic rate expressions describing how quickly they take place

• in SBML, the rate expressions can be arbitrary mathematical functions

Event • statement describing an instantaneous, discontinuous change in a set of variables of any type (species concentration, compartment size or parameter value) when a triggering condition is satisfied.

For more information on SBML, please refer to the following websites:

• SBML.org

• Wikipedia entry on SBML

50 Copyright and Trademark Notices

All other brands, product names, company names, trademarks, and service marks are the properties of their respective owners.