Simulation Method for Basic Pharmacodynamics
Created by Anita Grover (Anita.Grover[at]ucsf.edu) and
Jonathan Tang; Last updated:
created with NetLogo
INTRODUCTION
The field of
pharmacodynamics encompasses the study of the time course of a drug effect at
target site within a living system.
There are numerous, intertwining concepts associated with the field: it
is often hard for the new student to comprehend how these concepts emerge from
biological experiments, and how these concepts relate to the component
interactions within biology to create the dose-response and time-course curves
scattered throughout textbooks and the pharmacology literature.
We present a simulation
tool to aid the study of basic pharmacology principles. By taking advantage of the properties of
agent-based modeling, the tool facilitates taking a mechanistic approach to
learning basic concepts, in contrast to the traditional empirical methods. Pharmacodynamics is a particular aspect
of pharmacology that can benefit from use of such a tool: students are often
taught a list of concepts and a separate list of parameters for mathematical
equations. The link between the two
can be elusive. While
wet-lab experimentation is the proven approach to developing this link, in silico simulation can provide a means
of acquiring important insight and understanding within a time frame and at a
cost that cannot be achieved otherwise. We suggest that such simulations and
their representation of laboratory experiments in the classroom can become a
key component in student achievement by helping to develop a student’s
positive attitude towards science and his or her creativity in scientific
inquiry.
HOW IT WORKS
At
the start of a simulation, the TARGETS are distributed randomly through the
WORLD. In most cases, DRUGS are
distributed randomly within the top of the WORLD. DRUGS PERFUSE down the world using a
random walk that is biased in the x-direction. The input of DRUG can follow one of four
patterns, detailed as simulationTypes in User Controlled Variables. They are ELIMINATED at the bottom
(exceptions are bolus
time-course simulations).
When a DRUG and TARGET
contact
each other, they can bind to produce a measurable EFFECT. This EFFECT, along with
the numbers of TARGET and DRUG, are plotted
against TIME in the Time-Course graph; the EFFECT
and
the TARGET are plotted against the number of DRUGS
in
the Dose-Response graph.
This EFFECT can be altered by a number of biological
phenomena, including concepts such as the binding affinity or dissociation
probability for the drug and target.
These phenomena are incorporated as “sliders” in the
simulation program, able to be controlled by the user to tailor the simulation
run to his or her needs, as also listed in User
Controlled Variables.
USER CONTROLLED VARIABLES
|
start & Start/Stop |
The
Start/Stop switch must be
turned to On to run
the simulation. Click start to begin.
To stop the simulation at any time while it is running, turn the Start/Stop switch to Off. |
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|
simType: |
The
drop-down menu offers four choices for the manner in which drug will be delivered to the world: |
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dose-response
|
To
create a standard dose-response curve: at each turn, more drug will enter the world in a linear
fashion until the maxDrugMols have been delivered |
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|
bolus
time-course
|
To
understand how a bolus dose of drug
will affect target, the maxDrugMols amount of drugs will circulate through the world until simLength time is reached. In this case, drugs are initially distributed and move randomly through
the world (not necessarily towards
the bottom) at each step. |
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steady-state
|
Towards
a situation where the effect site is different from the administration site,
where concentration is slow to rise but reaches a plateau at the maxDrugMols amount. At each turn, an
amount of drug will enter the world according to a standard hill
function, until a plateau has been significantly established. |
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hysteresis
|
Towards another situation where the effect site is
different from the administration site, where the concentration rises and
falls to produce a hysteresis type dose-response curve. At
each turn, an amount of drug
will enter the world according to a two-exponential function, until the drug amount has fallen to 0. |
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|
simLength (applies only to bolus time-course) |
Slider
to specify the amount of time steps the simulation will run in the bolus time-course simType. |
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initialTargetMols |
The
amount of target molecules
created at the start of simulation; the amount of target molecules will change depending on targetRegulation and growthRate. |
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maxDrugMols |
The maximum number of drugs to enter the world
in the experiment. |
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|
bindingAffinity |
The
probability a drug and target at the same location in the world will bind. |
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dissociation |
The
probability a drug bound to a target will dissociate from the target |
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|
efficacy |
The
probability the bound drug-target
will create an effect. |
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|
timeDelay |
Number
of steps in delay between when the drug
binds to the target and the effect can be seen. |
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targetRegulation |
Probability
the drug binding to the target will: targetRegulation < 0: kill the target. targetRegulation > 0: cause the target
to replicate, creating a new target
adjacent to the bound target. |
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|
growthRate (per 100 turns) |
Regardless
of drug binding, how the numbers
of targets change overtime. |
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|
Visualization Slider |
Slide
to adjust the speed of the animation. |
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|
Visualization ON/OFF |
Turn
the visualization screen ON
or OFF. Turning the screen off may allow the
simulation to run faster. |
An Example
A typical
question an introductory pharmacology student would be exposed to might be
along the lines of:
Given the following two drugs:
1. Drug A
binds tightly—essentially irreversibly—to the target receptors, but
its intrinsic efficacy is qualitatively low.
2. Drug B has a slight probability of
dissociating from the receptor after binding, and its
intrinsic efficacy is twice that of drug A. Once the drug dissociates, the target is
fully active: it is the same as if it had never been bound.
Is drug A or drug B is more potent in
activating a key target molecule in an essential regulatory system?
In empirical pharmacological terms,
which drug has a lower EC50, the concentration at which half the maximum effect
is reached?
We can use
the simulation to quickly solve this question:
§ Because we are interested in
determining potency, choose the dose-response simulation setting to solve this
problem. Under this simulationType, at each turn, more DRUG will enter the world in a linear fashion until the maxDrugMols have been delivered. In doing so, we can
measure the EFFECT at each dose, and so determine the potency and a good
quantitative estimate of the EC50.
§ To get a good range of doses, set maxDrugMols to 200. Somewhat
arbitrarily, set initialTargetMols to 40.
§ There are two drug characteristics
under consideration in this example:
dissociation probability and intrinsic efficacy. For drug A, because the drug molecule
does not dissociate once bound to target, we set dissociation to 0. For drug B, however, because there is a
slight probability the drug will dissociate from bound target, we set dissociation to 3. Similarly, the intrinsic efficacy of
drug A is half as great as that of drug B.
Therefore, we set the efficacy of drug A to 50, and the efficacy of drug B to 100.
§ Ensure that the Start/Stop switch is turned to on, and click Start to begin.
Below are the sample graphs from running the above simulation:
|
Drug A |
Drug B |
|
observed Emax:
21 final effect: 17 percent targets remaining: 57.5% |
observed Emax:
8 final effect: 0 percent targets remaining: 100.0% |
Overlaid on the graph are lines to
signify the trend of the simulation lines.
Through these lines, the significantly higher Emax
and lower EC50 are evident for drug A even though the dissociation probability
was small. Therefore, drug A is the
more potent drug.
Working with simulations and problems
such as this helps a student develop an intuition for, and an understanding of
how the system responds to two different drug interventions.
Anita Grover, Tai Ning Lam, and C. Anthony Hunt
The Biosystems
Group, Department of Bioengineering and Therapeutic Sciences,
The
Correspondence: C. Anthony
Hunt
Department of
Bioengineering and Therapeutic Sciences
513 Parnassus Ave., S-926
San Francisco, CA
94143-0912
P: 415-476-2455
F: 415-514-2008
E:
a.hunt[at]ucsf.edu