# Documentation

## Create and Simulate a Simple Model

This example shows how to create and simulate a simple model of receptor-ligand kinetics using the SimBiology Desktop.

Receptor-Ligand Kinetics

In this model, ligand `L` and receptor `R` species form receptor-ligand complexes through reversible binding reactions. Using the mass action kinetics, the kinetic rate equation for the rate of change in concentration of receptor-ligand complex can be defined as $\frac{dC}{dt}={k}_{on}\cdot L\cdot R-{k}_{off}\cdot C$, where kon and koff are forward and reverse rate constants, `L`, `R`, and `C` are the concentrations of ligand, receptor, and receptor-ligand complex respectively. The objective of this simulation is to find the concentrations of all three species (`L`, `R`, and `C`) as the reaction progresses given initial amounts of species and rate constants.

Create a Model

Open the SimBiology® desktop by typing `simbiology` in the MATLAB® Command Window or clicking SimBiology on the Apps tab.

On the Home tab, select Add Model > Create New Blank Model. Name the model as `m1` when prompted.

Select Open > Diagram to open the diagram view.

Rename the compartment to `cell` by double-clicking the text `unnamed`.

Drag and drop three species blocks and one reaction block inside the `cell` compartment.

Rename the species to `L` , `R`, and `C` as follows.

Connect the Species and Reaction Blocks

To connect the ligand species block to the reaction block, press and hold the Ctrl key (Windows® and Linux®) or the Option key (Macintosh®), click the `L` species block, and drag the line to `reaction_1`. Similarly connect `R` to `reaction_1` and `reaction_1` to `C`.

Update the Reaction Properties and Initial Amounts of the Reactant Species

Update the `reaction_1` properties to set the reaction as a reversible reaction, select mass action as kinetic law, and define the forward and reverse rate parameters:

• Double-click the `reaction_1` block to open the Reaction Properties dialog box.

• On the Settings tab, select Reversible.

• From KineticLaw drop-down list, select MassAction.

• Under Quantities Used by Reaction, enter `kon` as the name and `2.0E6` as the value for Forward Rate Parameter, and `koff` and `1E-4` for Reverse Rate Parameter.

Update the initial amounts of reactant species by entering `5E-9` and `1E-8` as `R` and `L` species values respectively. Click Close.

On the Model tab, select Add Task > Simulate model. This opens a new window called Task Editor, where you can edit and run the task. Given the previous initial amounts and rate parameters, the reaction reaches a saturated state after 300 seconds. Therefore, set the simulation stop time to 300 seconds instead of 10 seconds, which is the default stop time. To do so, expand the Task Stop Time section, select Use a Stop Time specific to this task only, and enter 300.

Simulate the Model

To simulate the model, click the Run button.

Once the simulation is finished, the Live Plots section shows the States versus Time plot for each species.