This example shows how to assess the efficacy and toxicity of various dose amounts in the SimBiology Model Analyzer app by using the target (receptor) occupancy as a biomarker. The example uses the target-mediated drug disposition (TMDD) model  with slight modifications.
Target-mediated drug disposition (TMDD) is a phenomenon in which a drug binds with high affinity to its pharmacologic target site, such as a receptor or enzyme, in an interaction that is reflected in the pharmacokinetic characteristics of the drug.
This example uses a modified TMDD model based on the model used by Mager and Jusko  with a minor adjustment. The
authors proposed a generic TMDD model that accounted for saturable drug-target binding and
target (or receptor) mediated elimination.
Drug in the
Plasma reversibly binds with the unbound
Target to form
Complex. kon and koff
are the association and dissociation rate constants, respectively. Clearance of free
Complex from the
described by first-order processes with rate constants — kel and
km, respectively. Free target turnover is described by the zero-order
synthesis rate ksyn and a first-order elimination (the rate constant,
kdeg). Variants of the TMDD model have been since used to characterize the
pharmacokinetics of numerous drugs.
The adjustment made to the model presented by Mager and Jusko, is as follows.
Target occupancy (TO) is modeled as
Complex), where TO is a parameter and
Complex and Target are species.
Investigate the model response on the target occupancy (TO) using different dose amounts.
At the MATLAB® command line, load the model (m1) by entering:
Open the SimBiology Model Analyzer app by typing
simBiologyModelAnalyzer at the command line or by clicking
SimBiology Model Analyzer on the Apps tab.
On the Home tab, select Model >
Import Model from MATLAB. Select
First, create a program to generate an array of doses with different dose amounts ranging from 0 to 300 nanomoles.
Select Program > Generate Samples.
In the Generate Samples step, double-click the empty cell under Component Name and enter Daily Dose.Amount.
Daily Dose.Amount, set Type to
MATLAB Code, and set Code to
linspace(0,300,31). This code specifies the generation of 31 doses with
amounts ranging from 0 to 300 nanomoles.
Disable the plotting of dose samples by clicking the plot button, as shown in the figure.
Add a simulation step to simulate the model using the defined doses. Click the (+) icon at the upper left of the program and select Simulation. A Simulation step appears following the Generate Samples step.
In the Model step, click States to Log. Select TO as the only state to log by clearing all other check boxes.
On the Home tab, click Run.
Once the simulation is complete, the program plots the results in Plot1, which shows the time course of the model response (TO) given different dose amounts.
Plots are backed by data that are currently present in the app workspace. Plots are not snapshots. When the data (either experimental data or simulation results) is removed or changed, the plots are also updated according to the changes in the underlying data.
Investigate which dose amounts correspond to the TO responses that lie
within the safety (
TO = 0.85) and efficacy (
TO = 0.15)
thresholds. One approach is to add two (horizontal) threshold lines to the
TO response plot.
On the Home tab, in the Project section, click New Datasheet.
In the Browser pane, expand the Program1 folder, then expand the LastRun folder.
Drag results into the new datasheet. The datasheet now shows time and TO columns with their corresponding values.
Point to the table and add an expression by clicking the (+) icon that appears at the top right.
Anytime you add an expression to a datasheet containing results from
LastRun, the expression is added as an
to the model. In addition, the Postprocessing: Calculate Observables
step is also added to the corresponding program that generated the
Double-click Name1 and rename it EfficacyThreshold.
Double-click UNITS and enter
Double-click the Expression cell and enter
0.15. The expression fills the column with the same constant value (0.15)
for every time point.
Similarly, add another expression column named SafetyThreshold
with the expression
0.85. Expand results in the
LastRun folder. The values from these two expression columns are
now stored in the table named scalars under
You can now plot the maximum and minimum thresholds along with the simulation data. On the Home tab, click New Plot.
Press Ctrl and select the TO, EfficacyThreshold, and SafetyThreshold variables from the Browser pane. Drag them into the plot. The plot now shows TO profiles along with the efficacy and safety threshold lines.
The plot shows that certain TO responses either exceed the safety threshold or dip below the efficacy threshold. To better visualize this observation, you can customize the plot to see each dose amount and the corresponding TO response on separate axes.
In the Property Editor of the plot, in the Slice
Data table, set Responses to
Color and Scenarios to
Click Plot Settings. For Plot YLabel, enter
TO as the value.
In the Axes Limits section, select Link Y-Axis to show the same set of labels on the y-axis for all subplots.
In addition to visually inspecting each response plot on separate axes, you can add a postprocessing step to query exactly which dose amounts stay within the thresholds.
Click the Program1 tab. In the Postprocessing: Calculate
Observables step, double-click the first empty cell in the
Name column and enter:
In the Expression column, enter
max(TO) < 0.85 &
min(TO) > 0.15. Set unit to
Anytime you add an expression to the Observables table in the step, the expression is automatically added as an
observable object to the corresponding model.
stat1 as the only observable. Clear
stat1, run just the simulation step by clicking the run
button at the top of the Simulation step.
Running the program step generates the following figure. Display both the x-grid and y-grid by clicking both in the Grid section. The x-axis represents the dose amounts and the y-axis represents whether the dose amount generates a TO response that stays within the safety and efficacy thresholds (with a value of 1) or not (with a value of 0).
The plot shows that dose amounts ranging from
180 nanomoles provide TO responses that lie within the
desired efficacy and safety thresholds.
 Marger, D., and W. Jusko. 2001. General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. Journal of Pharmacokinetics and Pharmacodynamics. 28: 507–532.