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New Simulation Methods to Facilitate Achieving a MechanisticUnderstanding of Basic Pharmacology Principles

in the Classroom

Anita Grover Æ Tai Ning Lam Æ C. Anthony Hunt

Published online: 3 April 2008

Ó Springer Science+Business Media, LLC 2008

Abstract We present a simulation tool to aid the study of 

basic pharmacology principles. By taking advantage of theproperties of agent-based modeling, the tool facilitates

taking a mechanistic approach to learning basic concepts,

in contrast to the traditional empirical methods. Pharma-

codynamics 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 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 scien-

tific inquiry. We present results of two simulation

experiments that validate against data taken from current

literature. We follow with a classroom example demon-

strating how this tool can be seamlessly integrated within

the traditional pharmacology learning experience.

Keywords Education Á Pharmacology Á Systems biology Á

In silicoÁ

ModelÁ

SimulationÁ

Mechanism

Motivation

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 com-

ponent interactions within biology to create the dose–

response and time–course curves scattered throughout

textbooks and the pharmacology literature.

Achieving a mechanistic understanding is expected to

provide insights into the biology and experimental methods

that is often not achieved when following the traditional

data-based, empirical teaching approach. For example,

students in an introductory pharmacology course are often

taught the E max model of the concentration–response

relationship. The model uses the Hill function [a common

form is E  = E maxC a /(EC50 + C 

a)] to describe idealized

experimental data. The equation is used to predict the

effect of a drug, E , given its concentration, C , the maxi-

mum effect (E max), concentration at half the maximum

effect (EC50), several assumptions about the experimental

system, and an elusive parameter a known as the steepness

factor or Hill coefficient. Although aspects of the mecha-

nism are typically discussed and sketched, student

experience with the actual experimental details and data to

which of these parameters are expected to map is rare.

Often, students are expected to understand only how to use

this equation for its basic predictive properties.

Providing a comprehensive wet-lab experience to gen-

erate an appreciation for science and experimental methods

and to thereby provide a foundation for mechanistic under-

standing is problematic at the student level. There are

several delimiting and demotivating considerations.

A. Grover Á T. N. Lam Á C. A. Hunt (&)

The Biosystems Group, Department of Bioengineering

and Therapeutic Sciences, The University of California,

513 Parnassus Ave., S-926, San Francisco,

CA 94143-0912, USA

e-mail: a.hunt@ucsf.edu

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J Sci Educ Technol (2008) 17:366–372

DOI 10.1007/s10956-008-9106-6

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Providing such experiences would require that a time-

intensive and costly laboratory component accompany the

introductory pharmacology course. Even when the living

components of experiments behave reliably, the significant

variability associated with conducting wet-lab experiments

and accumulating sufficient data within a limited time frame

can complicate the experience and its interpretation for the

novice.The method of mechanism based in silico simulation

used here is one of several methods referred to collectively

as executable biology (Fisher and Henzinger 2007). The

method emerges as a potential solution to the above

problem. In particular, simulation of the type described

below offers an alternative that can be both cost and time

effective. It provides a world in which experiments always

‘‘work,’’ although outcomes can differ from expectations.

Through the visualizations afforded by the simulation, a

student can observe mechanisms in operation and thereby

develop and understanding of what effect changing bio-

logically rooted characteristics might have on theaccumulated data and empirically derived parameters.

The development of such pharmacodynamic simulations

has at its basis two significant motivations.

• Towards the understanding of how the interplay of 

various drug and biological system characteristics can

affect dose–response and time–course relationships.

• Reciprocally, towards the understanding of how various

observed phenomena can be understood mechanisti-

cally through manipulation of key drug and biological

system characteristics.

Simulation

The simulation was created using the agent-based model-

ing framework Net-Logo (Wilensky 1999). In this context,

an agent-based model (ABM) is an analogue of a referent,

wet-lab system created from software components. It is

created using a set of entities, called ‘‘agents’’; an inter-

active version is available (Grover and Tang 2008). During

a simulation, the agents interact with each other and their

environment according to rules (principles of operation)

defined by the programmer and, to some degree, by the

user. Those principles of operation are expected to have

biological counterparts, although they may not be fully

understood. In the analogue described below, there are two

types of agents: one maps to drug molecules and the other

maps to target macromolecules or sites in the referent

system. For simplicity, all other aspects of the referent

biological system are conflated and pushed into an inactive

background (but not forgotten). To distinguish clearly in

silico components and processes from corresponding

biological components and processes, we hereafter use

SMALL CAPS when referring to the former. The analogue

system, or ‘‘world,’’ is visualized with stationary TARGETS

and mobile DRUGS that move through the system. That

movement can map to perfusion of drug through a bio-

logical system in vitro. When a DRUG and TARGET contact

each other, they can bind to produce a measurable EFFECT.

The 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.

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. They are ELIMINATED at the bottom

(exceptions are bolus time-course simulations,

detailed in Table 1). The input of drug can follow one of 

four patterns, detailed as simulationTypes in Table 1.

The events occurring in the analogue system during sim-ulations can be imagined as representing flow of drug

through a single cell, where the blood supply is at the top of 

the cell. In such a referent, drug would interact with

receptors within the cell on its way through. However, as

described in the examples below, the same analogue can

represent a number of other in vitro systems equally well.

TIME in an agent-based simulation progresses in discrete

steps. Each time step is a simulation cycle. During a sim-

ulation cycle, each active agent is given an opportunity to

update itself (e.g., apply its rules). During each time step,

DRUG has an opportunity to move (or not) into and adjacent

space. We define an experiment as a simulation in which

all DRUGS comprising a dose have an opportunity to move

through the WORLD.

The user has the option of changing a number of variables

associated with the system. The screen shot in Fig. 1 shows

various user interfaces and the location of the sliders used to

changevariable values.The variables are describedin Table 1.

Reproducibility

The first test of the analogue was to document the repro-

ducibility of the results. We ran seven experiments usingthe same parameter values. We plotted the mean and range

of the number of TARGETS remaining at the end of each time

step in Fig. 2 along with the DRUG input profile. The results

attest to the reliability of the simulations.

Validation 1

Delacher et al. studied the time–course relationship of 

bacteria to ciprofloxacin, an antibiotic drug. At the

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concentrations studied ciprofloxacin is bactericidal: it kills

bacteria. The group first studied human interstitial con-

centration data to determine the pharmacokinetic time

profile of drug at the active site. They successfully descri-

bed that profile using a two-exponential hysteresis model

(we had provided the same model as an input option).

Delacher et al. then performed an in vitro experiment using

cultured bacteria. They added drug to the culture according

to the hysteresis input model and measured the remaining

number of viable bacteria using a colony count method. The

extracted data is graphed in Fig. 3a.

To simulate the preceding in vitro experiments, we

applied the two-exponential hysteresis input option. The

TARGET agents now represent one or more bacteria, and the

DRUG agents represent ciprofloxacin. We defined effect in

this analogue as an observed DRUG–TARGET pair. We obtained

an acceptable match by assuming bacteria would die within

one time step following contact by at least one DRUG.

Table 1 User controlled variables

a. 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.

b. simType: The drop-down menu offers four choices for the manner in which DRUG will be delivered to the WORLD:

c. 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.

d. 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.

e. 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.

f. 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.

g. 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.

h. initialTargetMols The amount of TARGET molecules created at the start of simulation; the amount of  TARGET molecules will

change depending on targetRegulation and growthRate.

i. maxDrugMols The maximum number of  DRUGS to enter the WORLD in the experiment.

 j. bindingAffinity The probability a DRUG and TARGET at the same location in the WORLD will bind.

k. dissociation The probability a DRUG bound to a TARGET will dissociate from the TARGET.

l. efficacy The probability the bound DRUG-TARGET will create an EFFECT.

m. timeDelay Number of steps in delay between when the DRUG binds to the TARGET and the EFFECT can be seen.

n. 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.

o. growthRate (per 100 turns) Regardless of DRUG binding, how the numbers of  TARGETS change overtime.

p. Visualization Slider Slide to adjust the speed of the animation.

q. Visualization ON/OFF Turn the visualization screen ON or OFF. Turning the screen off may allow the simulation to run faster.

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We achieved that by having targetRegulation

= –100. The results are graphed in Fig. 3b.

The dramatic initial decrease in bacterial numbers with a

slight terminal fall off is evident in both plots. Because the

TARGETS die upon binding with the DRUG, there are never any

active DRUG–TARGET complexes, as evidenced by the

effect line consistently at 0 through the run. This plot also

shows the input of DRUG according to thehysteresis input type

described above.The quantitative numbers of TARGETS, DRUG,

and TIME will not necessarily be equivalent between the wet-

lab and simulation experiments, in the same manner that

results between in vitro and in vivo representations of a

system might not be quantitatively equal. The simulation

aims to develop an understanding of how the plot in the

literature might develop, and the associated visualizations of 

this simulation run quickly provide this understanding.

Validation 2

The anticancer drug gefitinib inhibits cancer cell growth.

Sugimoto et al. studied growth inhibition of two types of 

gefitinib-treated human tumor cells: those that, following

transduction, expressed the transporter gene for breast

cancer resistance protein (BCRP), and control cells that

were not transduced. The BCRP transporter is believed to

pump various anticancer drug molecules, including gefiti-

nib, out of cells, thus limiting their effectiveness. To test

0

2

4

6

8

10

0 50 100 150 200 250

Time (min)

   B  a  c   t  e  r   i  a   (  c   f  u   /  m   l   *

   1   0   ^   8   )a

b

Fig. 3 (a) Data extracted from the literature Delacher et al. (2000).

Bacterial death in time in the presence of antibiotic; (b) Simulationresults of data extracted from (Delacher et al. 2000). The dashed

overlay follows the shape of the extracted data in Fig. 3a, serving as

validation of the simulation

Fig. 1 Screen shot of the

simulation program

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0 10 20 30 40 50

Time

   A  g  e  n   t  s

Fig. 2 Reproducibility: the upper graph shows the mean and range

(error bars) of number of targets remaining for seven experiments at

the end of each time step. The lower graph shows corresponding drug

input values

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this theory for both cell types, the authors measured cell

growth in the presence of different gefitinib concentrations.

They observed that growth over a 5-day period of the cells

transduced with the BCRP gene approached that of 

untreated controls (not shown). That result confirmed that

BCRP-transduction enabled cells to become resistant to the

drug. From the extracted data shown in Fig. 4a, it is clearthat gefitinib is more efficacious against the non-transduced

cells than it is against the transduced cells.

To mimic the data in Fig. 4a, using simulation, we note

that the resistance conferred by BCRP-transduction

increased the likelihood that the tumor cells growth after

5 days would be normal when cells are treated with gefi-

tinib. In the simulation TARGET agents represent control

numbers of tumor cells after 5 days of growth. DRUG agents

represent gefitinib. We conducted two simulations in the

dose-response mode. Only the targetRegula-

tion parameter was changed. A non-transduced cell fails

to grow once it has contacted and bound the drug agent, sotargetRegulation is set at –100. To demonstrate

resistance in transduced cells, we set this parameter to

larger values. The simulation results shown are for tar-

getRegulation = -20.

The bottom line in each plot shows the number of TARGETS

that fail to grow despite contacting and binding the DRUG.The

number is consistently 0 when targetRegulation =

-100. However, when targetRegulation = -20,

some TARGETS grow normally, even after treatment with the

DRUG. Note again that the scales on the simulation are not

intended to match quantitatively the scales used in the wet-

lab experiments. The key is that changing the response of 

targets to the drug had two consequences: it changed the

maximum effect over this dose range (E max) and it changed

the rate (effectively the EC50) at which an effect occurred.

The result was that the observed simulated effect mirroredthat from the wet-lab experiments.

Classroom Example

The previous two examples have been concerned with

understanding observed wet-lab experimental data. Recip-

rocally, simulation can be used to design, evaluate, and

build insight into experiments outside of the wet-lab.

For example, the student is asked to determine if drug A

or drug B is more potent in activating a key target molecule

in an essential regulatory system. Effect is caused by drugbinding to targets.

1. Drug A binds tightly—essentially irreversibly—to the

target receptors, but its intrinsic efficacy is qualita-

tively 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.

0

20

40

60

80

100

0 20 40 60 80 100 120 140

Drug Concentration (nM)

   C  e   l   l   N  u  m   b  e  r  s   (   %   o

   f   C  o  n   t  r  o   l   )a

b

Fig. 4 (a) Inhibition of BCRP-

transduction of human cancer

cells on the growth-inhibitory

effect of gefitinib. The data

were extracted from Sugimoto

et al. (2005). The values are

percent of untreated control cell

numbers after 5 days of growth

in increasing concentrations of 

gefitinib. Squares: cells were

BCRP-transduced; circles: cells

were not BCRP-transduced; (b)

measurements taken during

simulated experiments mimic

data extracted from Sugimoto

et al. Left: results from a

simulated experiment used

agents representing non-

transduced cells. Right: results

from a simulated experiment

used agents representing BCRP-

transduced cells. The

differences in the final percent

targets remaining are similar to

those extracted from the data,

which serves as validation

evidence

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The student’s task, in empirical pharmacological terms, is

to determine which drug has a lower EC50, the concentra-

tion at which half the maximum effect is reached?We choose the dose-response simulation setting to

solve this problem, and choose 40 initial TARGETS with a

maximum DRUG input of 200. In the first case, efficacy is

set to 50 and dissociation is set to 0. In the second,

efficacy is set to 100 and dissociation is set to 3.

The results are shown in Fig. 5.

The dramatic variability observed during the single

simulations in Fig. 5 are typical of what one could

encounter during wet-lab experiments. Nevertheless, the

significantly lower E max and higher EC50 are evident in

the graph on the right even though the dissociation

probability was small. These results are not entirelyintuitive. Working with simulations helps one develop an

intuition for, and an understanding of how the system

responds to two different drug interventions. Such exer-

cises can give the student important mechanistic insight

into the origin of the elusive mathematical parameters of 

empirical, inductive models such as the Hill function

introduced previously.

Discussion

The three above examples combine to document theeffectiveness of the simulation method in achieving the

goals previously set forth.

• Towards the understanding of how the interplay of 

various drug and biological system characteristics can

affect dose–response and time–course relationships.

• Reciprocally, towards the understanding of how various

observed phenomena can be understood mechanisti-

cally through manipulation of key drug and biological

system characteristics.

Inclusion of traditional, hands-on, wet-lab experimentation

experiences within life science curricula is becoming

increasingly rare. That is because doing so is becomingmore costly and time-consuming. We suggest that ABM

simulations of the type described here can help fill the void.

The importance of providing laboratory experiences, as

part of life science coursework, is well documented. Most

notably, laboratory experiences have a positive effect on

secondary students’ attitudes towards science, and there is

a highly significant correlation between attitude and

achievement (Freedman 1997). A comprehensive review

of thoughts on the importance of laboratory experience

(Hofstein and Lunetta 2003) details a number of related

concepts. First, experimentation plays a critical role in

developing a student’s sense of inquiry, or his or her abilityto study systems in diverse and novel ways. This is

furthered when the laboratory activities are well integrated

with the non-laboratory portions of the class, and even

more so when the level of ‘‘open-endedness’’ of the

activity, or how well the activity promotes an open-ended

approach to research, is high. Hofstein and Lunetta also

allude to a number of studies focusing on the use of 

technology in the classroom—in particular, how computer

visualization provides unique benefits, and the technology

can afford a more complete understanding than other

teaching methods. These concepts are markedly repre-

sented in the above two goals.Building an intuitive understanding of the concepts

associated with pharmacology and pharmacodynamics is

important within many life science fields. However, it can

be hard for a student to develop, and can truly only be done

through experiences such as those traditionally provided by

laboratory activities. We posit that improved, more realistic

simulation methods of the type demonstrated could facili-

tate developing this understanding within students at all

levels. The approach described above affords this

a bFig. 5 Simulation results from

a hypothetical experiment

comparing the dose–effect

relationship of two hypothetical

drugs, A (left) and B (right).

Horizontal dotted lines:

maximum effect (E max); vertical

dotted lines: dose at which half 

maximal effect is achieved

(EC50)

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possibility by using simulation systems in which obser-

vable and measurable behaviors are a consequence of 

actual mechanisms: interacting components. These mech-

anisms, although in silico, can be sufficiently realistic so

that they behave during experiments analogously to how

biological systems behave.

In the traditional approach, the scientist offers an

abstract, inductive, mathematical model to explain sys-temic observations. Model parameters are used to describe

properties of the data believed to have been caused by the

underlying, but abstracted away, mechanisms. The simu-

lation approach described here builds a mechanism of 

interacting components. So doing allows one to observe the

emergence of the characteristics seen at the empirical level.

The two validation experiments demonstrate that it is

relatively straightforward to construct abstract in silico

systems that can exhibit behaviors that mimic those

observed in wet-lab experiments. The classroom example

demonstrates that interesting informative examples can be

created to learn how particular phenomena can arise. Wesuggest that such exercises can be easily integrated with

and used to supplement the traditional pharmacological

classroom practices.

Acknowledgments This research was funded in part by the CDH

Research Foundation (R21-CDH-00101). The software described

along with supporting documentation may be obtained without charge

from the corresponding author.

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