Simulation Method for Basic Pharmacodynamics

Created by Anita Grover (Anita.Grover[at]ucsf.edu) and Jonathan Tang; Last updated: March 17, 2008.

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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.

simType:

The drop-down menu offers four choices for the manner in which drug will be delivered to the world:

 

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

 

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.

 

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.

 

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.

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.

initialTargetMols

The amount of target molecules created at the start of simulation; the amount of target molecules will change depending on targetRegulation and growthRate.

maxDrugMols

The maximum number of drugs to enter the world in the experiment.

bindingAffinity

The probability a drug and target at the same location in the world will bind.

dissociation

The probability a drug bound to a target will dissociate from the target

efficacy

The probability the bound drug-target will create an effect.

timeDelay

Number of steps in delay between when the drug binds to the target and the effect can be seen.

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.

growthRate

(per 100 turns)

Regardless of drug binding, how the numbers of targets change overtime.

Visualization Slider

Slide to adjust the speed of the animation.

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 University of California, San Francisco, CA

 

Correspondence: C. Anthony Hunt

Department of Bioengineering and Therapeutic Sciences

513 Parnassus Ave., S-926

University of California

San Francisco, CA 94143-0912

P: 415-476-2455

F: 415-514-2008

E: a.hunt[at]ucsf.edu