Entering the Era of Computationally Driven Drug Development

Originally published in Drug Metabolism Reviews

The cost of successfully developing one marketed drug is estimated to be about $2.87 billion (DiMasi et al. 2016). In recent years, the probable causes of high attrition and low success rate of investigational therapies have been poor drug exposure and response predictions that ultimately lead to safety and efficacy related failures (Hay et al. 2014; Waring et al. 2015). Increasing drug development costs and rising attrition rates limit
the development of novel drug therapies, resulting in a detrimental impact on public health and welfare (Mahajan and Gupta 2010). Traditional drug development approaches involve preclinical testing in multiple animal species—rats, mice, dogs, monkeys, etc.—to secure critical safety and efficacy considerations in humans such as first-in-human dosing, therapeutic window, and toxicological assessments. In 2004, the Food and Drug Administration (FDA) released a white paper estimating the traditional preclinical screening and evaluation of drugs to have only an 8% chance of
reaching the market, highlighting the stagnation and inefficiency associated with this traditional approach (Mahajan and Gupta 2010). While there is some consensus around the analysis of overall success rates in drug development, this should not obscure the increased breadth of chemical space, modalities and targets prosecuted in modern drug development. Use of preclinical animal testing for human Absorption, Distribution,
Metabolism, and Excretion (ADME), pharmacology, and safety predictions faces several issues related to animal procurement, stringent experimental regulations and ethical considerations pertaining to their use. Animal models have demonstrated utility in specific areas of
drug development (e.g. predicting some hepatotoxicity mechanisms); however, many datasets generated with these subjects tend to translate poorly to human outcomes, especially when investigating more complex biosystems (e.g. brain uptake, neurotoxicity, various
oncology conditions) (Bracken 2009).

In the past few decades, in silico modeling and simu-
lation has emerged as a pivotal tool in the field of drug

discovery and development. According to a recent mar-
ket research report, the global biosimulation market is

estimated to increase from $1.65 billion USD in 2018 to

$4.58 billion USD by 2025 (Zion Market Research 2019).

These novel computational approaches leverage exist-
ing data and provide valuable insights to inform clinical

trial design and predict pharmacokinetic or pharmaco-
dynamic (PK/PD) outcomes (Kim et al. 2018). Given their

ability to forecast outcomes with fewer available data-
sets, they can be useful in predicting potential failures

earlier in drug development, effectively reducing the
attrition rates in the later, more costly stages of
research and testing.
Machine learning and artificial intelligence
approaches (ML/AI) have also increasingly been applied

to this space because of their utility in analyzing differ-
ent types of data and applicability to large datasets. In

recent years, efforts have been made to combine trad-
itional physiological models with machine learning

approaches to benefit from the valuable datasets gen-
erated through standardized and robust experimental

methodologies. Regulatory bodies such as FDA and
EMA strongly encourage the use of model-informed
drug development (MIDD) to facilitate efficient drug

development and enable rapid regulatory decision-
making (Jain et al. 2019). Recently, under the

Prescription Drug User Fee Amendments of 2017
(PDUFA VI), FDA aims at integrating MIDD into more
drug applications to lower uncertainty, failure rates,
and reduce redundant and expensive experimental
work (Jain et al. 2019). Given the increasing popularity
and utility of biosimulation framework, this article
focuses on reviewing some of the major modeling
approaches currently employed, and provides expert
opinion on the integration of existing computational
models with machine learning techniques to further
reduce, refine, and replace animal testing.
Current approaches for in silico
ADME modeling
In silico modeling approaches aid in understanding and
interpreting the complex interplay between xenobiotics

and physiological processes in the body. Different mod-
eling techniques are associated with distinct advan-
tages and limitations that will be discussed in the

sections below.
Quantitative structure–activity relationship
(QSAR) models

QSAR analysis involves instituting quantitative relation-
ships between compound structures and their bio-
logical activity by employing statistical and

mathematical approaches. The relationship is frequently

expressed as:
Biological property of xenobiotic
1⁄4 Function ðphysico  chemical propertiesÞ
1⁄4 Function ðchemical structureÞ (5)
The major steps involved in QSAR modeling are
the following.
Data collection
This step involves identifying the biological target and
securing large datasets of drug-like compounds with

information on their molecular descriptors (e.g. topo-
logical polar surface area, octanol–water partition coef-
ficients, pKa) and biological activity measures (e.g.

inhibition potency IC50, binding potency Kd). An import-
ant part of data collection is data curation, where the

collected dataset is analyzed to ensure that the data is
obtained using a standardized experimental protocol,
there is no redundant or confounding data present;
depending on the preset exclusion criteria and the
intended application of the QSAR model, this can lead
to the exclusion of duplicates of the same compound
(e.g. isomers in 2 D descriptors), molecular descriptors

with the same values across all compounds, com-
pounds with chemically incorrect structures or discon-
nected parts, salts of the active drug moiety, and other

outliers (Cherkasov et al. 2014). Multiple tools are avail-
able for the calculation of descriptors and data curation,

including but not limited to Dalton, Dragon, Gaussian,
Chemistry Development kit (CDK), RD kit, PADEL, ISIDA
fragments, molecular operating environment (MOE),
ChemAxon and OpenBabel (Golbraikh et al. 2017).
Model development
QSAR models can be classified as continuous (activity
can assume multiple values from a predefined range),

categorical (biological activity assigned rank), or classifi-
cation (activities that cannot be ordered, e.g. different

types of biological properties), based on the nature of
biological activity being modeled (Tropsha 2010;

Golbraikh et al. 2017). QSAR models utilize a wide var-
iety of multidimensional linear or nonlinear data meth-
ods, often combining machine learning approaches

from various research disciplines. As the name suggests,
linear methods are characterized by direct relationships

correlating the biological activity with chemical descrip-
tors while the nonlinear methods employ more compli-
cated approaches when defining the relationship

between the predictors and associated biological activ-
ities. Frequently used linear methods include Multiple

Linear Regression, Partial Least Squares, and Principal

Component Regression, while the more common non-
linear methods are Support Vector Machines (SVM),

Artificial Neural Networks (ANN), Decision Trees, and
Bayesian Classifiers (Tropsha and Golbraikh 2007;
Tropsha 2010; Golbraikh et al. 2017).
Model validation
A critical part of model validation is establishing the
domain of applicability. It defines the limitations of the
QSAR model predictions with respect to its chemical

domain and biological response space. External com-
pounds beyond the specified scope of the applicability

domain are associated with a high likelihood of inaccur-
ate predictions (Tropsha 2010). Several techniques are

published in the literature to define applicability
domain of QSAR models based on range, distance,
probability density distribution, decision trees, and
others as aptly summarized (Netzeva et al. 2005). The

predictive potential of a QSAR model can be demon-
strated by allocating a subset of data for training to

build the model and utilizing separate datasets not
included in model development for validation. Some of

the widely used validation criteria include Pearson cor-
relation coefficient (r

), leave-one-out cross-validated

), Y-randomization, and bootstrapping. A detailed
discussion of these validation criteria, different methods
to validate, and assess the extrapolatability of QSAR
models is beyond the scope of this article and can be
found in the detailed reviews here (Sprous et al. 2010;
Tropsha 2010; Sheridan 2013).
QSAR models have widespread applicability in drug
discovery and development. In the pharmaceutical
industry, QSAR models are routinely used to perform

high-throughput screening for identification of hit com-
pounds and optimization of hit-to-lead candidates.

QSAR approaches are commonly used for prediction of
quintessential physicochemical properties like logP,
pKa, aqueous, and biorelevant solubilities, in vitro
ADME properties including metabolic stability, passive
and active permeability, inhibition, and induction

potency. Gozalbes and Pineda-Lucena (2010) demon-
strated this by building a QSAR model to predict the

water solubility of a wide range of poor, medium and
highly soluble xenobiotics using simple 1D and 2D

molecular descriptors and identified log P as having sig-
nificant impact on the estimation of solubility. The pre-
diction of complex clinical endpoints in drug

development including oral bioavailability, drug

distribution, dominant metabolic pathways, and

involvement of drug transporters can also be accom-
plished using QSAR methods. Lombardo et al. (2006)

developed a distribution model to predict steady-state
volume of distribution (Vdss) with less than two-fold
error using a comprehensive dataset, vital 1D, 2D, and
3D molecular descriptors and the random forest

method. QSAR techniques can also be applied to pre-
dict compounds with desirable biological activities and

to provide insights on molecular interaction between
xenobiotics and biological targets. Zhang et al. (2011)
constructed an in silico model using Dragon descriptors,
ISIDA-2D fragments, and SVM methods to identify 176

compounds with putative antimalarial activity and pro-
vided novel chemical scaffolds to guide further devel-
opment of compounds against Plasmodium falciparum.

However, despite their widespread utility, QSAR

models suffer from several limitations rooted in differ-
ences between biological activity landscapes and chem-
ical spaces, false correlations caused by a significant

reliance on inherently variable biological data, cross-
dependence of molecular descriptors, presence of out-
liers, use of small datasets, and lack of rigorous valid-
ation strategies. An editorial letter by Maggiora (2006)

provides a succinct summary of the major reasons asso-
ciated with failures of QSAR models. In cases where the

prediction of clinically relevant PK outputs is required,
these drawbacks frequently necessitate the application

of modeling approaches that utilize data beyond com-
pound physicochemical properties to make an assess-
ment of drug disposition.

Pharmacokinetic models
The biofate of compounds can also be predicted using

drug concentration–time profiles, drug biological prop-
erties, and species-specific physiological properties

through the application of different analytical techni-
ques, such as noncompartmental analysis (NCA), com-
partmental, and PBPK models. Accurate prediction of

PK profile of a drug is extremely critical as exposure
drives drug interaction with the biological target, which
ultimately determines the efficacy of the xenobiotic.
These PK modeling approaches will be discussed in the
sections below.
Noncompartmental analysis
Unlike QSAR models, which rely on a wealth of data to
predict vital ADME outputs, NCA enables parameter
prediction using only in vivo time course and measured
drug concentration data at a given dose. NCA, often

referred to as the model-independent approach, utilizes
simple algebraic equations to estimate important PK
parameters, and establishes initial exposure metrics

using preclinical data. This approach makes no assump-
tions about the number of in vivo compartments, and

hence is less subjective and can be more time-/cost-effi-
cient when compared with compartmental models.

NCA does make some basic simplifying assumptions
including linear PK, elimination from a systemic pool
and no time-dependence for disposition parameters
(Gabrielsson and Weiner 2012). These assumptions are
often related to the observed drug behavior and can be
readily assessed through experimental investigations. A

detailed comparison of compartmental and noncom-
partmental models and NCA equations is provided by

Gillespie (1991).
NCA involves the use of simple algebraic equations to
determine exposure metrics (e.g. AUC, Cmax, Tmax) and
other important PK parameters (clearance, terminal
half-life, mean residence time) of a drug from the time
course of measured drug concentrations. Gabrielsson

and Weiner (2012) provide a summary of the funda-
mental equations routinely used for conducting NCA

following IV and oral administration.

NCA forms a routine part of PK analysis in drug devel-
opment, especially for richly sampled clinical PK studies

that are utilized when conducting bioequivalence stud-
ies or evaluating the performance of compartmental

models. NCA is vital for characterizing PK within a single

study and is often used for making time-sensitive deci-
sions such as dosing regimens and dose escalation

studies following single and multiple dosing in phase I
trials. Commercial software products like MATLAB,
WinNonlin, and SAAM II can be used to perform linear
and nonlinear regression for numerical analysis using a
noncompartmental approach (Bulitta and Holford

2014). A typical example of the utility of NCA is the esti-
mation of area under the plasma-time curve using trap-
ezoidal rule. As shown in Figure 1, noncompartmental

observed AUC0-t calculation approximates integration
across the compound exposure time-course as the sum
of trapezoidal areas. This area can be extrapolated from
the last sampling point t to infinity (AUCt-1) by taking a

ratio of the last measurable nonzero plasma concentra-
tion and the terminal slope on a log scale (Figures 1

and 2) (Gabrielsson and Weiner 2012). AUC0-1 can

Figure 1. Estimation of AUC by NCA using trapezoidal rule
adapted with minor modifications from Gabrielsson and
Weiner (2012).
Figure 2. Estimation of terminal slope through log-linear
regression on the terminal data points adapted with minor
modifications from Gabrielsson and Weiner (2012).

therefore be determined as a sum of (observed) AUC0-t
and (extrapolated) AUCt-1. The total clearance can then
be calculated as ratio of administered dose and
AUC0-1. In comparison to compartmental or complex
physiologically based models, NCA suffers from certain
limitations due to the complete lack of physiological or
mechanistic relevance. The accuracy of NCA decreases
significantly when applied to sparse datasets, complex

study designs/dosing regimens, or when the aforemen-
tioned assumptions are invalid.

Compartmental PK analysis
Compartmental analysis involves dividing the body into
one or more ‘compartments’ to describe the disposition

of a drug. Each compartment is a mathematical repre-
sentation of ADME processes occurring in multiple

organs, and the individual compartments are frequently
assumed to exhibit homogeneous kinetics. Although

grounded in some fundamental physiological under-
standing, the simpler versions of compartmental mod-
els do not recapitulate specific organs or physiological

systems (such as organ-level composition, volumes,

flow rates, etc.) unlike the compartments in PBPK mod-
els (Gillespie 1991; Aarons 2005).

Typical workflows for compartmental analysis involve
selecting a compartmental model to best fit observed
data using nonlinear regression and initial parameter
estimation followed determination of PK parameters
using a computational tool. The last step undergoes
multiple iterations using different initial value estimates
until the simulation converges at a global minimum.
The prediction accuracy and precision is then assessed
using predefined statistical criterion (e.g. r
, residual
analysis, Akaike Information Criterion) or through
visual analysis in cases where quantitative metrics are
less representative of accuracy (Gillespie 1991;
Bassingthwaighte et al. 2012).

Compartmental models are extremely useful in predict-
ing pivotal PK parameters in food-effect studies, bio-
availability, and bioequivalence studies, and PK

interaction studies with minimal plasma concentra-
tion–time data. In contrast to NCA, compartmental

models are more mechanistic and allow flexibility in
modeling different ADME processes. Compartmental
PK models can be combined with population PK
approaches for characterizing PK of a drug when only
sparsely sampled data is available. Wade et al. (2008)
developed a one-compartment population-PK model to

describe the PK of fluconazole in neonates. This popula-
tion-PK model allowed the identification of dose adjust-
ment needed in neonates based on gestational age at

birth, postnatal age, and serum creatinine clearance.
This case study highlights the utility of compartmental
models over NCA specifically for sparse data sampling
and in special populations with ethical limitations on
conducting clinical trials.
Commercial software products like Winonlin, Matlab,
and PKSIM can be used to efficiently perform this type

of compartmental modeling. A major limitation of com-
partmental PK analysis comes from the fact that the

individual compartments are not entirely physiologic-
ally relevant and therefore cannot provide mechanistic

insights (Gillespie 1991). For example, there is no dis-
tinction between arterial and venous blood in circula-
tory systems and highly perfused organs are lumped

together in the central compartments. Thus, when
applied to prediction compartmental models require

integration of additional complexity and more physio-
logical inputs to become physiologically meaningful.

PBPK models
PBPK models integrate physicochemical, physiological,
preclinical, and clinical data to predict PKs and overall
drug disposition of novel molecular entities (Sager et al.
2015; Kuepfer et al. 2016). They divide the human body

into compartments corresponding to different physio-
logical organs or tissues, usually linked together by a

circulatory system. These types of models integrate

more physiological complexity when compared to com-
partmental or noncompartmental models. However, it

is important to maintain a balance between the degree
of complexity and scalability of the model; although

intuitively the integration of more equations and phys-
ics should correlate with better predictive performance,

the addition of novel, less-characterized input parame-
ters, and mechanisms will frequently introduce variabil-
ity into the model outputs when tested on large

compound datasets.

A whole-body PBPK model includes physiological repre-
sentation of organs that are most important for the

absorption, distribution, metabolism, and excretion of
xenobiotics by virtue of their physiological activity
(Kuepfer et al. 2016). Typically, the compartments
included are liver, intestine, heart, thymus, kidney, lung,
brain, skin, adipose, stomach, spleen, pancreas, gonads,
muscle, and bone and are linked by the blood (venous
and arterial) compartments (Kuepfer et al. 2016). Each
organ is assigned a blood flow rate, tissue volume, and
composition to capture the behavior that reflects its in
situ function relevant to the desired species. A model
can be expanded to include specific ADME processes or
subcompartments (e.g. intestinal segments) to closely
mimic the physiological interactions occurring in the
human or animal body. However, a simplified model
with fewer organs can also be used depending on the
research question to be answered.

In general, a PBPK model has three principal compo-
nents (Kuepfer et al. 2016).

Drug-specific parameters
This includes physicochemical and drug–biological
properties that help capture the overall drug behavior

and disposition. These parameters are mostly experi-
mentally derived using in vitro, in vivo, or in situ

systems. Some common examples include solubility,

drug-tissue partition coefficients, plasma protein bind-
ing, and in vitro microsomal clearance.

System- or species-specific parameters
This part of the PBPK model incorporates physiological

features (organ volume, weight, flow rate, tissue com-
position, in some cases concentration of enzyme and

transporter proteins) of the species of interest. It can

also include other physiological features specific to dis-
ease states, ethnicities, or special populations.

Study protocol
This captures the specific information on study design,
dosing route, and regimen, parameter variability in a

study population (dependent on factors such as ethni-
city, disease state, gender ratio), and any other experi-
mental considerations (presence of food, exercise,

formulation) of an in vivo or clinical study.
Detailed information on PBPK model development
can be found in the reviews by Kuepfer et al. (2016),
Sager et al. (2015), and Zhuang and Lu (2016).
PBPK models can be utilized to test the mechanistic
underpinnings of physiological processes that impact

compound ADME, and to enable a more accurate pre-
diction of drug disposition based on diverse population

factors, such as ethnicity, age, and disease condition to
identify ideal dosing regimens for first-in-human studies
and toxicological assessments (Sager et al. 2015).
SimCYP, GastroPlus, and PK-SIM are some of the widely
used commercial products for building PBPK models.
Indeed, there are several examples of the use of PBPK

models in regulatory submissions and labeling recom-
mendations for novel compounds as outlined in the

review by Yoshida et al. (2017). PBPK models are also

extensively used to predict putative drug–drug interac-
tions (DDI) (Yoshida et al. 2017). An excellent study by

Chen et al. elaborates on the use of PBPK model to

evaluate a complex DDI involving a circulating inhibi-
tory metabolite (mono-desethyl-amiodarone, MDEA), of

the perpetrator drug amiodarone and their effect on
the exposure of a victim drug simvastatin (Chen et al.
2015). The authors use a combination of bottom-up
and top-down approach to simulate the plasma-time

profiles of amiodarone and MDEA and the accumula-
tion of these chemical entities following chronic admin-
istration. The model successfully predicted CYP450

inhibition of several CYP substrates (simvastatin, dextro-
methorphan, and warfarin) mediated by amiodarone

and its metabolite. The authors further extend the
application of the mixed bottom-up and top-down
modeling approach to predict the interaction potential

of an antibody-conjugated cytotoxic agent—mono-
methyl auristatin E (Chen et al. 2015). Thus, the utility

of PBPK modeling is no longer limited to the conven-
tional small molecules but can be successfully applied

to large molecule PK predictions.

In comparison to QSAR, noncompartmental or sim-
plified compartmental methods, PBPK models are more

data intensive when it comes to physicochemical, bio-
logical, and biochemical parameterization. Often times

these data are secured from multiple sources using dif-
ferent experimental protocols that introduce significant

variability in model predictions. Unavailability of drug-
related or species-related data can lead to poor charac-
terization of PK and PD processes and can lead to incor-
rect predictions, specifically for complex models that

need a wealth of information to be built. PBPK models

are often unscalable and cannot be extrapolated accur-
ately to make clinical predictions for close struc-
tural analogs.

Pharmacodynamic models
Like the term PK describes the relationship between

the drug dose and observed plasma or tissue concen-
trations, PD attempts to identify the drug and species-
specific properties that control pharmacological

responses to xenobiotics. PD models develop mathem-
atical relationships to describe the interaction between

drug and its biological target and characterize the
mechanisms involved (Mager et al. 2003). This modeling
approach allows the integration of known information
on system-related parameters, evaluate mechanisms of
interaction between drug and target under different
test conditions and ultimately predict the system
related parameters that cannot be experimentally
determined (Mager et al. 2003). The widely used PD
models employed to capture the varying physiological
complexity in drug–target interaction will be discussed
in the following sections.
Simple direct effects models
The simple direct effects model represents one of the
simplest PD models, which assumes instantaneous

equilibration between plasma and biophase concentra-
tions and that the biophase drug concentrations drive

the PD effect. Thus, a linear relationship can be

constructed between the pharmacological effect of the
drug and its plasma concentrations, expressed as:
E 1⁄4 E06 m  log Cp (1)

where E gives the magnitude of the drug effect, E0 rep-
resents baseline effect (control), Cp indicates drug

plasma concentration, and m is the slope of the E-log
Cp relationship (Mager et al. 2003). While this equation

enables early estimation of PD relationships using sim-
ple linear regression, it holds true only when the effect

ranges between 20 and 80% (log-linear) of the max-
imum effect (Emax) or the effect is less than 20% of Emax

(Mager et al. 2003; Felmlee et al. 2012). To overcome
these shortcomings, Wagner recommended the use of

the Hill equation (Eq. 2) to better explain the dose–res-
ponse relationship (Wagner 1968):

E 1⁄4 E06
Emax  Cc
EC50 þ Cc


Equation 2 is also called the full Hill model or sig-
moidal Emax model (Mager et al. 2003). where Emax is

the maximum observed effect, EC50 represents drug
concentration at which half of maximal effect (0.5

Emax) is observed, and c is the Hill coefficient that indi-
cates the steepness of the drug concentration–effect

relationship. Hill coefficients less than 1 produce shal-
low slopes, however as the coefficients cross 1 they are

believed to produce an all or none type response
(Felmlee et al. 2012). Hill coefficients are also thought
be indicative of positive (c > 1) or negative (c < 1)
cooperativity in drug–receptor interaction. A distinct
advantage of the direct effects model is that it operates
under steady-state conditions, allowing assumptions
such as (Wright et al. 2011):
1. rapid binding equilibrium between drug and
receptor, and
2. same unbound drug concentrations in all tissue

water and tissues, thus enabling the use of plas-
ma–water concentrations as a surrogate.

Simple direct effects are commonly observed when
the target (e.g. enzyme activity) is measured in blood
(Wright et al. 2011). This is demonstrated in the study
by Toutain et al. (2000), which successfully explained
the relationship between the disposition kinetics of

benazeprilat and its inhibitory interaction with angio-
tensin-converting enzyme (ACE) using the Emax model.

The simplistic nature of this model often turns into a
major disadvantage when the clinically observed effects
exhibit a time-lag between time to appear in plasma

and to produce the intended effect leading to hyster-
esis in dose–response plots (Wright et al. 2011).

A model that incorporates the kinetics of drug distribu-
tion from systemic circulation to biophase can over-
come this limitation and will be discussed below.

Biophase distribution model
The pharmacological target of the majority of drugs is
distal to the systemic circulation and distribution to the
site of action can be the rate-limiting step that would
explain the time lag in drug effect (Mager et al. 2003;
Felmlee et al. 2012). This effect compartment mimics
the distribution characteristics of the drug’s true site of
action, also known as the biophase. The delay in effect
is attributed to the time taken by the drug to distribute

from the effect compartment to the biophase, a con-
cept popularized by Sheiner et al. (1979). Typically, a PK

model is developed to explain drug distribution into
the effect compartment, while a simple Emax model is
used to capture PD effects using the equation below:

E tð Þ 1⁄4 Emax
Ce ðtÞ
Ce ðtÞ þ EC50

where Ce represents drug concentrations in biophase
(Felmlee et al. 2012). Biophase distribution models are
widely used due to their simplicity. Yassen et al. (2007)
conducted a study to characterize the relationship of
fentanyl plasma concentrations and its respiratory

depressant effect in healthy subjects. The biophase dis-
tribution model successfully explained the hysteresis

shown by fentanyl.
Owing to its intuitive simplicity, this modeling

approach is applicable only in situations where distribu-
tion of drug to the biophase is the rate-limiting step in

the time course of drug response (Mager et al. 2003).
Since the biophase model was the first to explain the

time delays observed in drug response, it was occasion-
ally applied incorrectly until it was recognized that

processes such as slow receptor binding or indirect
effects caused by time-dependent interaction with
endogenous substances are more likely to cause time
lag in drug effects (Mager et al. 2003). Hence, there is a

need for a model that accounts for the impact of xeno-
biotics on endogenous substances and the indirect

effects mediated by these compounds.
Basic indirect response model
A drug can mediate its effect not just through direct
interaction with receptors or enzymes but indirectly by
influencing endogenous compounds that subsequently
exert the intended pharmacological effect. These
endogenous substances follow their own physiological
time course and can become the rate-limiting step in

Figure 3. Indirect response models figure adapted with minor
modifications from Mager et al. (2003).

the time required for producing drug effects. Dayneka
et al. (1993) proposed the four basic indirect response
models to account for the impact of reversible drug–
receptor interactions on stimulation or inhibition of
production or loss of biomarker response variables as
depicted in Figure 3.
The general equation of the indirect response model
can be expressed as:
dt 1⁄4 kin  1⁄2  1 6 H1ð Þ Cp  kout  1⁄2  1 6 H2ð Þ Cp  R

Where kin and kout are the apparent zero-order pro-
duction rate constant and first-order elimination rate

constant, respectively, and R is the intended drug
response. Depending on the model chosen, the term
Hn(Cp) (n 1⁄4 1 or 2) can be formulated as one of the four
equations stated below (Felmlee et al. 2012):
Model 1: Inhibition of production
dt 1⁄4 kin  1  Imax  Cp
IC50 þ Cp
  kout  R (5)

Model 2: Inhibition of dissipation
dt 1⁄4 kin  kout  1  Imax  Cp
IC50 þ Cp
  R (6)

Model 3: Stimulation of production
dt 1⁄4 kin  1 þ

Smax  Cp
SC50 þ Cp
  kout  R (7)

Model 4: Stimulation of dissipation
dt 1⁄4 kin  kout  1 þ

Smax  Cp
SC50 þ Cp
  R (8)

where Smax and Imax are analogous to Emax but rede-
fined as the maximum fractional factors of stimulation

(Smax > 0) or of inhibition (0 < Imax  1), while SC50 and
IC50 are comparable to EC50 (i.e. the concentration at

0.5Smax or 0.5Imax, respectively). The time–response pro-
files of above models typically exhibit a gradual rise or

fall in the endogenous biomarkers to a maximum peak
response followed by a slow return to baseline levels as
the drug concentrations decline below the IC50 or SC50

concentrations. A classic example of this indirect effect
is the PD respond to warfarin (Holford 1986). As the
warfarin levels increase, the synthesis of prothrombin is
inhibited, which subsequently leads to anticoagulant

effects. In this example, there is a clear temporal separ-
ation between PD effect and the action of drug; thus, it

is best explained by the indirect effects model. Indirect
response models have been extensively applied to a

wide range of compounds that alter the natural dissipa-
tion or turnover of endogenous compounds.

The basic indirect effects model has also been

extended to include precursor compartments that fur-
ther capture the influence of physiological intermedi-
ates on the delayed observed in drug effects (Sharma

et al. 1998). Often, time-lag in pharmacological effect

may be attributed to a cascade of multiple time-
dependent steps that occur between binding of drug-
to-target and the final PD effect. In such instances, a

more complex model that can simultaneously describe

multiple in vivo interactions is needed, such as the sig-
nal transduction model. A detailed discussion of this

extended approach has been published previously and
is beyond the scope of this article (Sharma et al. 1998;

Sun and Jusko 1998). The modeling approaches dis-
cussed thus far assume reversible binding between the

drug and the target receptor/enzyme. However, xenobi-
otics can exhibit irreversible binding kinetics to their

biomolecular targets and require specific models that
can capture these types of effects.
Irreversible effects model
The irreversible effects model aids in describing the PD
of several antimicrobial and anticancer agents, and can
be applied to enzyme inhibitors that exhibit irreversible
interactions with their biological targets. Jusko (1971)

described a basic approach to capture the effect of che-
motherapeutic drugs on non-proliferating (Eq. 9) and

proliferating (Eq. 10) cell populations as follows:

dt 1⁄4  k  C  R (9)
dt 1⁄4 ks  R  k  C  R (10)

where R indicates the number of target cells or recep-
tors, C represents drug concentration in plasma (Cp), or

biophase (Ce), k is the second-order cell-kill rate con-
stant, and ks is the first-order growth rate constant.

Baseline control conditions (R0) obtained from placebo

treatments are recorded for calculation of survival frac-
tion. This model can also be extended to include pro-
duction or dissipation of biomarkers to build an

irreversible indirect turnover model (Abelo et al. 2000).

Figure 4. Basic components of PK/PD models adapted with minor modifications from Jusko et al. (1995).

There are numerous examples of application of irrevers-
ible effects approach to model PD effects of chemother-
apeutic and anti-infective agents. Jusko (1973)

successfully described the pharmacological effect of
anticancer agent vincristine on lymphoma cells using
this method.
PD models characterize the dynamics of drug–target
relationships, while PK models give insights into the
disposition of drug in the body. The rate and extent of
drug exposure (PK) govern the concentration of drug at

the site of action, which drives the intended pharmaco-
logical effect and ultimately determines the therapeutic

potential of a drug. Thus, when combined these com-
plementary PK and PD modeling approaches help in

predicting the safety and efficacy of a xenobiotic. PK/
PD modeling has emerged as a broad discipline that
quantitatively integrates PK with physiological and
pharmacological processes to dynamically estimate the
potency of biological effects of drugs on the body
(Jusko 2013).
Integration of PK and PD modeling
In the 1960s, Gerhard Levy pioneered the research that
mathematically linked PK and the time course of
pharmacological response (Jusko 2013). This scientific
breakthrough led to evolution of mechanistic PK/PD
modeling to quantitatively characterize the temporal
nature of drug responses by studying the underlying
mechanism of drug–biological system interaction.
Mechanism-based PK–PD models allow quantitative
characterization of multiple biological processes that
occur between drug administration and its PD effect.

These processes include drug–target receptor/enzyme
binding and activation, distribution to the site of action,
influence on intermediate biomarkers or endogenous
substances and transduction mechanisms (Danhof et al.
2008). A PK/PD model with typical components is
shown in Figure 4 (Jusko et al. 1995).
The PK component provides the time course of
measured drug concentrations usually in plasma (Cp)
and PK models can be used to model the disposition
kinetics. A suitable mathematical function describes the
relationship between drug concentration in plasma and
the tissue of interest (Ce, biophase concentration)
(Jusko et al. 1995; Wright et al. 2011). The biophase
drug levels are believed to be the driving force for the

pharmacological effects (Mager et al. 2003). Drug mole-
cules at the site of action interact with the biological

target, usually a receptor or an enzyme. The biophase
sensor process encompasses the kinetics of reversible

or irreversible binding and dissociation of drug–recep-
tor or drug–enzyme complexes (Jusko et al. 1995;

Wright et al. 2011). These drug–biological target inter-
actions may directly or indirectly increase or reduce the

production (kin) or dissipation (kout) of endogenous sub-
stances, which may represent the desired PD effect

(Jusko et al. 1995; Mager et al. 2003). Often, however,
the altered levels of endogenous substrates trigger a
further dynamic transduction process ultimately leading
to an acute or long-lasting pharmacological effect (E)

(Mager et al. 2003). PK/PD modeling enables mathemat-
ical characterization of the relationship between PK and

PD and hence is applied to all stages of drug

Applications of PK/PD modeling

Predicting the drug exposure–response (PK–PD) rela-
tionship is central to any safety and efficacy evaluations

of xenobiotics. In recent years, there has been a sub-
stantial increase in application of PK/PD modeling prac-
tices in preclinical and clinical phases of drug

development, prompting regulatory bodies to publish
guidance documents on best practices for assessing
drug exposure-response relationships (U.S. Food & Drug
Administration 2003). PK/PD models provide a basis for
optimization of doses and dosing regimens to achieve
and maintain the intended clinical effect (Park 2017). A

quintessential application of this feature is the model-
informed dosing optimization of antimicrobial agents.

One of the leading factors responsible for the develop-
ment of drug resistance is suboptimal dosing, which

results in lower drug concentrations in the body and
ultimately undermines the overall bactericidal effect of
the antibiotic (Asin-Prieto et al. 2015). Mechanistic PK/

PD models can help in addressing this issue as demon-
strated in the study conducted by Safdar et al. (2004)

investigating the in vivo PD activity of daptomycin. The
authors used a standard NCA to determine the rate and
extent of drug exposure. Sigmoidal Emax model was
used to characterize the antimicrobial (bacteriostatic
and bactericidal) effect of daptomycin in Swiss mice.

The study revealed that daptomycin exhibits concentra-
tion-dependent antimicrobial activity and once-daily

administration appears to maintain its bactericidal
effect better than two, four or eight doses administered
over 24 h. This case study emphasizes the vital role of

PK/PD modeling to improve success rates of antimicro-
bial therapy, reduce emergence of resistance, and inci-
dences of adverse effects. The usefulness of this

modeling approach is not limited to small molecule

drugs but also extends to large molecule drug candi-
dates. Wu et al. (2006) developed a mixed-effect mech-
anistic PK/PD model for muM17, an anti-mouse CD11a

monoclonal antibody used as a surrogate for evaluation
of human reproductive toxicity potential of efalizumab.

The model successfully linked muM17 with the expres-
sion pattern of CD11a and enabled dose selection of

muM17 through multi-dose simulated PK/PD studies, to
ultimately establish dose equivalency of muM17 in
mice to efalizumab in humans (Wu et al. 2006). Such

modeling approaches can be further applied to deter-
mine clinically applicable doses of surrogate molecules

for other protein drugs, where PD studies of adverse

effects are limited by ethical reasons. Despite the obvi-
ous advantages of PK/PD models, their use is limited by

the data-intensive nature. This approach requires the
availability of drug concentration-time data in biophase,

but often exposure data is only collected in plasma.
Owing to practical limitations, PK and PD data are often
collected in separate human or animal subjects when
they should be collected from the same subjects. While
several commercial platforms support PK/PD model
development, these softwares fail to provide means of
effectively performing data optimization to fill-in the
knowledge and data gaps (Hsieh et al. 2018).
Frequently, only a limited number of missing or variable
parameters can be optimized that restricts the use of
these softwares to build accurate and scalable PK/PD
model. There is a clear need for the integration of two
or more modeling approaches spanning different scales
to effectively mitigate the issues raised above.
Multiscale physiologically based PK and PK/
PD approaches
Multiscale models integrate multiple tiers of biological

complexity (e.g. organelles to cells, cells to organs/tis-
sue and organs to the whole body) and population dif-
ferences (Deisboeck et al. 2011). They offer an

opportunity to merge PK/PD, systems biology and sys-
tems pharmacology approaches to further model-
informed drug development. Hence, these models are

uniquely suited for optimizing and advancing several
steps in the drug discovery and development pipeline.
The model development, validation, and verification of
multiscale models varies drastically based on their

intended applications. Even the basic definitions of bio-
logical scales differ in different life sciences fields as

aptly discussed by Hunter et al. (2008). This makes it dif-
ficult to identify and elaborate on a standard or semi-
standard workflow for building multiscale models.

However, typically multiscale models comprise the use
of discrete, continuum, or a combination of discrete
and continuum methods (Deisboeck et al. 2011).

Discrete models afford incorporation of biological data-
driven assumptions describing interactions at cellular

level. Their biggest limitation is the significant compu-
tational power required to capture the minute bio-
logical details of the cell physiology. Continuum models

are computationally less demanding as they capture

more global physiological information. However, con-
tinuum models cannot be used when individual cellular

processes in different types of cells or at different
stages of disease development need to be captured
closely. Hence, often researchers opt for a combination

of continuum and discrete models to overcome the lim-
itations associated with the individual methods

(Deisboeck et al. 2011). A typical example of composite
discrete-continuum models can be found in the study

conducted by Zheng et al. (2005) to develop coupled
tumor growth and angiogenesis models. The study
used a continuum model to capture tumor growth
while using a discrete model for angiogenesis. The

model was able to describe the morphological instabil-
ity of tumor-affected region, the impact of physiological

mechanics like surface tension, mechanical pressure,
and other fluid dynamics on the tumor affected area
and estimate the trend of tumor growth. Another good
example of multiscale models can be seen in the study

conducted by Cordes et al. (2018) that integrates gen-
ome-scale metabolic networks with whole-body PBPK

models to predict drug-induced metabolic injuries. The
study illustrates the application of the multi-scale
model using isoniazid, an anti-tuberculosis drug that is

associated with drug-induced liver injury. The com-
bined genome scale-whole body PBPK model was able

to accurately predict the disposition of isoniazid and

the cellular responses and changes in the liver metabo-
lome observed after administration of isoniazid. A study

conducted by Singh and Shah (2017), highlights the
utility of multiscale PK/PD models in clinical translation
of antibody–drug conjugate—Trastuzumab emtansine
from preclinical tumor models to clinical tumors. The

preclinical PK and in vivo efficacy data collected in mon-
keys was incorporated into a clinical PK–PD model to

predict the efficacy parameters, tumor volume, and
growth parameters for breast cancer in humans. The
clinical trials simulated using this model were able to
predict progression-free survival and objective response
rates in close agreement to the data observed in clinical
trials of Trastuzumab emtansine. This case study further
emphasizes the applicability of multiscale models in

predicting clinical efficacy of xenobiotics. Above exam-
ples clearly illustrate the inadequacy of single models

and the need for multiscale approaches to effectively

address complex problems encountered in drug discov-
ery and development. Despite the obvious advantages

of multiscale models, their applicability is severely
restricted by the availability of rich in vitro, in vivo, and

clinical datasets at different scales to build robust mod-
els with fairly accurate predictions. Another significant

limitation is the presence of multiple parameters that
makes parameter estimation a difficult task. Often,

model calibration is performed by selecting a small sub-
set of parameters based on ‘expert opinion’ in the field

with no statistical evaluation to support the judgement
(Hsieh et al. 2018). Furthermore, even with this small
subset of parameters, simultaneous optimization of
multiple parameters can be seldom achieved due to
computational restrictions. These limitations often lead
to model overfitting which can have a detrimental

impact on the performance of the model. The complex
nature of multiscale models also makes it difficult to
extrapolate observations between different species thus
lowering their efficiency and broad applicability. There
is a demonstrated need for a novel software product

that integrates multiscale models with machine learn-
ing tools to address the scalability, extrapolation and

applicability issues highlighted above.
Application of machine learning in drug
Machine learning utilizes algorithms that can self-learn
and improve the efficiency of the process over time.

Frequently, ML techniques are categorized as super-
vised or unsupervised learning. Supervised learning

uses algorithms that determine a predictive model
using data points with known outputs; this type of data
is usually referred to as ‘labeled data’. The learning
occurs by training the models through a supervised
algorithm (e.g. linear regression, random forest, or

neural network) that optimizes and self-corrects to min-
imize the value of an error. In contrast, unsupervised

learning trains the model using inputs that are not
labeled, allowing the algorithm to learn insights from
the dataset and make predictions. These methods can
be used to predict missing biological or drug-related
data, and to perform complex trend analysis to identify

consistent input–output patterns. As stated earlier, bio-
logical datasets are often incomplete and riddled with

experimental and physiological variability, which can
significantly impact the predictive power of single and

multiscale models. ML algorithms trained on well-
sampled and diverse data can be used to complete

these missing datasets. In vitro and in vivo assay proto-
cols continue to be developed for faster and more

accurate results. This restricts the utility of data

obtained from these nonstandardized and ever-chang-
ing methodologies in making meaningful predictions.

Transfer learning ML approaches can prove vital in such

instances to integrate data obtained by employing dif-
ferent techniques to gain better insight into drug

behavior. Insights learned from either a single or a

batch of compounds can be extended to other structur-
ally similar analogs of interest or other compounds that

share the parent structure using ML methods (Bhhatarai
et al. 2019). A classic example of the utility of ML in
drug development can be found in a study conducted
by Perryman et al. (2016). The authors integrated a
Bayesian ML model with a QSAR model built using nine

distinct molecular descriptors to predict metabolic sta-
bility of drugs in mouse liver microsomes. The

combined model was associated with high prediction
accuracy for clearance in mouse liver microsomes as

confirmed using a comprehensive dataset of 571 com-
pounds. Another good example can be found in the

study conducted by Krauss et al. (2013) which com-
bined Bayesian statistical approaches with a mechanis-
tic PBPK model, using pravastatin as a case study.

Pravastatin is associated with high interindividual vari-
ability in its clinical PK and hence authors used Markov

chain Monte Carlo algorithm to separately consider the

species-related and drug-related parameter distribu-
tions. This Bayesian-PBPK model successfully character-
ized the interindividual variability in pravastatin PK by

combining previous knowledge with new experimental

data. The model also exhibited potential for extrapola-
tion to other structurally similar drugs and performing

similar assessment in diverse populations. Similarly, the

utility of ML integrated with PK/PD models was demon-
strated by Zhou et al. (2017). The authors developed

ANN model to successfully characterize the exposure
and efficacy of the major components of two varieties
of Zingiber rhizome commonly used in traditional

Chinese medicine. Most of the traditional Chinese medi-
cines are mixtures containing a plethora of biologically

active compounds interacting with several in vivo tar-
gets, making their model development quite a chal-
lenging task (Maharao et al. 2017; 2019). In such

instances, the attributes of ANN such as ability to cap-
ture nonlinearities, iterative analysis and potential to

characterize the relationship between input and output
data can prove invaluable (Zhou et al. 2017). Above

case studies highlight the need and benefits of combin-
ing machine learning with traditional models to

improve the prediction accuracy and efficient by leaps
and bounds.

Animal models continue to be widely used for perform-
ing preclinical testing in the drug development pipe-
line. While animal studies have a major contribution in

advancing our understanding of disease conditions,
their utility in predicting clinically relevant treatment

strategies remains questionable (Pound and Ritskes-
Hoitinga 2018). There is a strong and weakly tested

assumption in the biomedical discipline that major

developmental functions and genetic makeup are con-
served between different species including humans

(van der Worp et al. 2010). Often the animal models are

used to emphasize the similarities in humans and ani-
mals without due recognition of the significant differen-
ces and their impact on interpretation of clinical

outcomes (van der Worp et al. 2010). The impact of this
oversimplified assumption on the accuracy of clinical
prediction differs for different diseases depending on
the complexity of the underlying pathophysiology.

Animal models have been extremely effective in decod-
ing the pathogenesis of venous thrombosis and have

positively contributed to optimal management of this
disorder (Levi et al. 2001; Monroe and Hoffman 2014;
Gailani et al. 2015) as well as predicting certain cellular
toxicities (Boelsterli 2003). Similarly, animal models
have had huge success in the development and dosing
optimization of antimicrobial agents in humans (Zhao
et al. 2016). Unfortunately, the clinical translatability
achieved in the above examples drastically weakens
when animals are employed to treat neurodegenerative
diseases such as Alzheimers, Parkinson’s disease,
dementia, and multiple sclerosis (Institute of Medicine

2013; Bailey and Taylor 2016; Sjoberg 2017). An excel-
lent review by Ransohoff (2018) presents a detailed

analysis of inefficiencies of using preclinical animal
models in neurodegeneration drug development. To
improve the ‘human-likeness’ of animal models,

patient-derived xenograft (PDX) models were devel-
oped, a methodology widely adopted in immuno-
oncology studies (Collins and Lang 2018). The PDX

models allow for partial assessment of human systems

in animals, however they suffer from severe disadvan-
tages (Lai et al. 2017; Collins and Lang 2018). For

instance, in tumor growth studies, the tumor cells are
often transplanted subcutaneously or intraperitoneally
in murine xenograft models instead of mirroring the
true location of the tumors found in humans. Under

these test conditions, the tumor growth occurs in mur-
ine microenvironment (e.g. vascular perfusion pattern

and cellular systems), which is clearly distinct from
humans (Lai et al. 2017; Collins and Lang 2018).
Unsurprisingly, the majority of murine PDX models fail
to reliably predict anticancer activity in the clinics due
to significant discord in animal and human physiology
as evidenced through dissimilar expression pattern of
cellular biomarkers and overall histopathology (Lai et al.

2017). There is a resistance to acknowledging these ani-
mal–human species differences because this entails

considering the possibility that preclinical animal

research has not a lot to offer to further drug develop-
ment (Pound and Ritskes-Hoitinga 2018; Ransohoff

2018). It is high time that research efforts focus on
humanizing the biomedical science. There have been
significant efforts toward developing better testing
platforms, such as organoids and organs-on-chips, that
recapitulate human organ systems in a testing platform
(Kaushik et al. 2018; Wagar et al. 2018; Montes-Olivas

et al. 2019; Tuveson and Clevers 2019). However, these
systems are still in their infancy, and while they may

prove useful for gaining insight into specific physio-
logical mechanisms important to therapeutic develop-
ment, when used in isolation they fail to capture the

complex interplays that can occur between different
pathways and interactions in vivo. Biosimulation models

offer a cost and time-efficient alternative to animal test-
ing and can effectively leverage data from in vitro sys-
tems, thus demonstrating the need to be developed

and adopted globally through different stages of drug
discovery and development. Additionally, in silico-based
systems can gain widespread adoption and regulatory

acceptance at a much faster rate than previous techno-
logical advancements in pharmacology by using exist-
ing datasets as evidence; validation can come through

showcasing the prediction of well-characterized drug
failures/successes through retroactive data analysis.
The pharmaceutical industry relies on a plethora of
diverse methodologies in an attempt to drive down
costs associated with drug development. Amongst
these methodologies, advances in in silico approaches,
PK/PD and PBPK are notable and well-reviewed

(Lombardo et al. 2017; Yoshida et al. 2017; Loisios-
Konstantintinidis et al. 2019). All of the aforementioned

methods have their place in preclinical development

and will likely continue to be utilized in specific applica-
tions given the industry standards and the overall sim-
plicity of some of the approaches. However, the

majority of existing solutions tend to be soiled in appli-
cation; the existing paradigm for model development

relies on developing custom solutions for individual
compounds and, in some cases, even to the level of

individual experiments. This granularity of customiza-
tion inevitably leads to a multitude of models and mod-
eling approaches that are overfitted for their target

datasets; in other words, these models simply do not
translate to additional compounds and compound

datasets and in effect cannot be used for effective pre-
clinical prediction in cases where experimental data

is sparse.
Multiscale models carry the greatest promise when it

comes to the establishment of a comprehensive model-
ing system with the capacity to incorporate increasing

mechanistic complexity and scale throughput without

sacrificing predictive accuracy as the amount of gener-
ated input data grows in number and in dimension.

The simpler, core modeling approaches defined
above—QSAR, NCA, compartmental, PBPK, and PK/

PD—act as sources of inspiration for this holistic devel-
opment framework. Noncompartmental analysis will

continue to be the standard benchmark by which

clinical in vivo studies are calculated; these simpler
methods can continue to be utilized for assessing the
predictive affinity of models. Compartmental, PBPK and
PK/PD models are still at the root core of the multiscale
approach, as they provide functional ‘building blocks’

for a whole-system model and are the minimal struc-
tures required for adding physical, physiological or

functional complexity to in silico computational models

of living organisms and their interaction with xenobiot-
ics. Finally, leveraging the available data for effective

computational learning requires conscious consider-
ation and addressing of the problems that plague train-
ing data used in preclinical pharmaceutical

development—variability in data collection, lack of clin-
ical translatability, large population variation, overall

inaccurate datasets—using data curation methods com-
monly encountered in QSAR modeling space. Relying

on self-learning algorithms, supervised or unsupervised,
allows for the development of tools that can cluster

‘negative data’ utilizing descriptors and mapping func-
tions that move beyond the manual data filtering tech-
niques currently in use.

With this data-processing foundation, the incorpor-
ation of data from both existing or novel in vitro and

in vivo assays is simplified and any subsequent model
development is accelerated. The ideal prediction model

ends up being semi-mechanistic; it combines mechanis-
tic PBPK or PK/PD in cases where the fundamental sci-
ence, biological interactions, and mathematical

relationships are well-understood, but can depend on
the machine learning optimization to converge on a
solution when experimental data inputs are missing.
This same methodology can be used prospectively for
prioritization of drug candidates or study designs and
retroactively to analyze experimental conditions in

studies with high uncertainty. Overall, employing multi-
scale models can offset the limitations of existing mod-
eling methods and enhance the utility of individual

models. Integration of ML with current PBPK or PK/PD
models and designing for scalability is the key to faster,
accurate and more cost-effective drug development.
In conclusion, it is worthwhile to speculate on the
nature of the impact that the integrated approaches
described here may have. Given the time scale (ca.
10 years) and current success rates (ca. 8%) of drug
development any effects on overall success rate will not
be evident for many years. Since global success rates
for drug development are influenced by many factors

external to the science of drug discovery and develop-
ment (e.g. business considerations, regulatory climate

etc), a simplistic comparison of apparent success rates

reflection of improvements in discrete portions of the
overall process. Rather, computationally driven
approaches are more likely to affect decision-making,

data visualization, and scenario planning within discov-
ery and development programs within companies and

the cumulative effect will result in improved internal
efficiencies. Typically these shifts within pharmaceutical
companies occur over a period of years as evidenced
by the experience with methods of in vitro–in vivo
extrapolation which are now considered fundamental
but were a significant shift from the common practice

at the time of publication (Obach et al. 1997). The inclu-
sion of AI-based approaches also overcomes a limita-
tion of highly parameterized models in that these

inherently capture events that are not built into the
structure of the model and their cooperative use with
systems-based approaches may provide a rational basis
for further experimentation. Finally, computational

approaches have advanced to the point where reason-
able a priori predictions can be made. This creates

the opportunity to take, for instance, PKs in early drug

discovery from an observational exercise to a hypoth-
esis-driven study and derive durable value from the

experimental data.
Disclosure statement
No potential conflict of interest was reported by
the author(s).

Aarons L. 2005. Physiologically based pharmacokinetic mod-
elling: a sound mechanistic basis is needed. Br J Clin

Pharmacol. 60:581–583.
Abelo A, Eriksson UG, Karisson MO, Larsson H, Gabrielsson J.
2000. A turnover model of irreversible inhibition of gastric
acid secretion by omeprazole in the dog. J Pharmacol Exp
Ther. 295:662–669.
Asin-Prieto E, Rodriguez-Gascon A, Isla A. 2015. Applications
of the pharmacokinetic/pharmacodynamic (PK/PD) analysis
of antimicrobial agents. J Infect Chemother. 21:319–329.
Bailey J, Taylor K. 2016. Non-human primates in neuroscience
research: the case against its scientific necessity. Altern
Lab Anim. 44:43–69.
Bassingthwaighte JB, Butterworth E, Jardine B, Raymond GM.

2012. Compartmental modeling in the analysis of bio-
logical systems. Methods Mol Biol. 929:391–438.

Bhhatarai B, Walters WP, Hop CE. C. A, Lanza G, Ekins S.

2019. Opportunities and challenges using artificial intelli-
gence in ADME/Tox. Nat Mater. 18:418–422.

Boelsterli UA. 2003. Animal models of human disease in drug
safety assessment. J Toxicol Sci. 28:109–121.

Bracken MB. 2009. Why animal studies are often poor predic-
tors of human reactions to exposure. J R Soc Med. 102:


Bulitta JB, Holford NHG. 2014. Non-compartmental analysis.
In: Balakrishnan N, Colton T, Everitt B, Piegorsch W,

Ruggeri F, Teugels JL, editors. Wiley StatsRef: statistics ref-
erence online. Hoboken (NJ): John Wiley & Sons.

Chen Y, Mao J, Hop CE. 2015. Physiologically based pharma-
cokinetic modeling to predict drug-drug interactions

involving inhibitory metabolite: a case study of amiodar-
one. Drug Metab Dispos. 43:182–189.

Chen Y, Samineni D, Mukadam S, Wong H, Shen B-Q, Lu D,
Girish S, Hop C, Jin JY, Li C, et al. 2015. Physiologically
based pharmacokinetic modeling as a tool to predict drug
interactions for antibody-drug conjugates. Clin
Pharmacokinet. 54:81–93.
Cherkasov A, Muratov EN, Fourches D, Varnek A, Baskin II,
Cronin M, Dearden J, Gramatica P, Martin YC, Todeschini
R, et al. 2014. QSAR modeling: where have you been?
Where are you going to? J Med Chem. 57:4977–5010.
Collins AT, Lang SH. 2018. A systematic review of the validity

of patient derived xenograft (PDX) models: the implica-
tions for translational research and personalised medicine.

PeerJ. 6:e5981.
Cordes H, Thiel C, Baier V, Blank LM, Kuepfer L. 2018.
Integration of genome-scale metabolic networks into
whole-body PBPK models shows phenotype-specific cases
of drug-induced metabolic perturbation. NPJ Syst Biol
Appl. 4:10.
Danhof M, Delange E, Dellapasqua O, Ploeger B, Voskuyl R.

2008. Mechanism-based pharmacokinetic-pharmacody-
namic (PK-PD) modeling in translational drug research.

Trends Pharmacol Sci. 29:186–191.
Dayneka NL, Garg V, Jusko WJ. 1993. Comparison of four
basic models of indirect pharmacodynamic responses.
J Pharmacokinet Biopharm. 21:457–478.
Deisboeck TS, Wang Z, Macklin P, Cristini V. 2011. Multiscale
cancer modeling. Annu Rev Biomed Eng. 13:127–155.
DiMasi JA, Grabowski HG, Hansen RW. 2016. Innovation in
the pharmaceutical industry: new estimates of R&D costs.
J Health Econ. 47:20–33.
Felmlee MA, Morris ME, Mager DE. 2012. Mechanism-based
pharmacodynamic modeling. Methods Mol Biol. 929:
Gabrielsson J, Weiner D. 2012. Non-compartmental analysis.
Methods Mol Biol. 929:377–389.
Gailani D, Cheng Q, Ivanov IS. 2015. Murine models in the
evaluation of heparan sulfate-based anticoagulants.
Methods Mol Biol. 1229:483–496.

Gillespie WR. 1991. Noncompartmental versus compartmen-
tal modelling in clinical pharmacokinetics. Clin

Pharmacokinet. 20:253–262.
Golbraikh A, Wang XS, Zhu H, Tropsha A. 2017. Predictive

QSAR modeling: methods and applications in drug discov-
ery and chemical risk assessment. In: Leszczynski J,

Kaczmarek-Kedziera A, Puzyn T, Papadopoulos MG, Reis H,
Shukla MK, editors. Handbook of computational chemistry.
Cham: Springer International Publishing; p. 2303–2340.
Gozalbes R, Pineda-Lucena A. 2010. QSAR-based solubility
model for drug-like compounds. Bioorg Med Chem. 18:
Hay M, Thomas DW, Craighead JL, Economides C, Rosenthal

J. 2014. Clinical development success rates for investiga-
tional drugs. Nat Biotechnol. 32:40–51.


Holford NH. 1986. Clinical pharmacokinetics and pharmaco-
dynamics of warfarin. Understanding the dose-effect rela-
tionship. Clin Pharmacokinet. 11:483–504.

Hsieh N-H, Reisfeld B, Bois FY, Chiu WA. 2018. Applying a

global sensitivity analysis workflow to improve the compu-
tational efficiencies in physiologically-based pharmacoki-
netic modeling. Front Pharmacol. 9:588.

Hunter PJ, Crampin EJ, Nielsen PM. 2008. Bioinformatics, mul-
tiscale modeling and the IUPS Physiome Project. Brief

Bioinform. 9:333–343.

Institute of Medicine. 2013. Improving the utility and transla-
tion of animal models for nervous system disorders.

Workshop Summary. Washington (DC): The National
Academies Press.
Jain L, Mehrotra N, Wenning L, Sinha V. 2019. PDUFA VI: it is
time to unleash the full potential of model-informed drug
development. CPT Pharmacometr Syst Pharmacol. 8:5–8.
Jusko WJ. 1971. Pharmacodynamics of chemotherapeutic

effects: dose-time-response relationships for phase-non-
specific agents. J Pharm Sci. 60:892–895.

Jusko WJ. 1973. A pharmacodynamic model for cell-cycle-
specific chemotherapeutic agents. J Pharmacokinet

Biopharm. 1:175–200.

Jusko WJ. 2013. Moving from basic toward systems pharma-
codynamic models. J Pharm Sci. 102:2930–2940.

Jusko WJ, Ko HC, Ebling WF. 1995. Convergence of direct
and indirect pharmacodynamic response models. J
Pharmacokinet Biopharm. 23:5–8.
Kaushik G, Ponnusamy MP, Batra SK. 2018. Concise review:

current status of three-dimensional organoids as preclin-
ical models. Stem Cells. 36:1329–1340.

Kim TH, Shin S, Shin BS. 2018. Model-based drug develop-
ment: application of modeling and simulation in drug

development. J Pharm Investig. 48:431–441.
Krauss M, Burghaus R, Lippert J, Niemi M, Neuvonen P,
Schuppert A, Willmann S, Kuepfer L, Gorlitz L. 2013. Using €
Bayesian-PBPK modeling for assessment of inter-individual
variability and subgroup stratification. In Silico Pharmacol.
Kuepfer L, Niederalt C, Wendl T, Schlender J-F, Willmann S,
Lippert J, Block M, Eissing T, Teutonico D. 2016. Applied
concepts in PBPK modeling: how to build a PBPK/PD
model. CPT Pharmacometr Syst Pharmacol. 5:516–531.
Lai Y, Wei X, Lin S, Qin L, Cheng L, Li P. 2017. Current status
and perspectives of patient-derived xenograft models in
cancer research. J Hematol Oncol. 10:106.
Levi M, Dorffle-Melly J, Johnson GJ, Drouet L, Badimon L; €
Subcommittee on Animal, Cellular, and Molecular Models
of Thrombosis and Haemostasis of the Scientific and
Standardization Committee of the International Society on

Thrombosis and Haemostasis. 2001. Usefulness and limita-
tions of animal models of venous thrombosis. Thromb

Haemost. 86:1331–1333.
Loisios-Konstantintinidis I, Paraiso RLM, Fotaki N, McAllister
M, Cristofoletti R, Dressman J. 2019. Application of the

relationship between pharmacokinetics and pharmaco-
dynamics in drug development and therapeutic equiva-
lence: a PEARRL review. J Pharm Pharmacol. 71:699–7223.

Lombardo F, Desai PV, Arimoto R, Desino KE, Fischer H,
Keefer CE, Petersson C, Winiwarter S, Broccatelli F. 2017. In
silico absorption, distribution, metabolism, excretion and
pharmacokinetics (ADME-PK): utility and best practices. An

industry perspective from the international consortium for

innovation through quality in pharmaceutical develop-
ment. J Med Chem. 60:9097–9113.

Lombardo F, Obach RS, DiCapua FM, Bakken GA, Lu J, Potter
DM, Gao F, Miller MD, Zhang Y. 2006. A hybrid mixture
discriminant analysis-random forest computational model
for the prediction of volume of distribution of drugs in
human. J Med Chem. 49:2262–2267.

Mager DE, Wyska E, Jusko WJ. 2003. Diversity of mechanism-
based pharmacodynamic models. Drug Metab Dispos. 31:

Maggiora GM. 2006. On outliers and activity cliffs–why QSAR
often disappoints. J Chem Inf Model. 46:1535–1535.
Mahajan R, Gupta K. 2010. Food and drug administration’s

critical path initiative and innovations in drug develop-
ment paradigm: challenges, progress, and controversies.

J Pharm Bioall Sci. 2:307–313.

Maharao NV, Joshi AA, Gerk PM. 2017. Inhibition of glucuro-
nidation and oxidative metabolism of buprenorphine

using GRAS compounds or dietary constituents/supple-
ments: in vitro proof of concept. Biopharm Drug Dispos.


Maharao N, Venitz J, Gerk PM. 2019. Use of generally recog-
nized as safe or dietary compounds to inhibit buprenor-
phine metabolism: potential to improve buprenorphine

oral bioavailability. Biopharm Drug Dispos. 40:18–31.
Monroe DM, Hoffman M. 2014. A mouse bleeding model to
study oral anticoagulants. Thromb Res. 133:S6–S8.
Montes-Olivas S, Marucci L, Homer M. 2019. Mathematical
models of organoid cultures. Front Genet. 10:873.
Netzeva TI, Worth AP, Aldenberg T, Benigni R, Cronin MTD,
Gramatica P, Jaworska JS, Kahn S, Klopman G, Marchant
CA, et al. 2005. Current status of methods for defining the
applicability domain of (quantitative) structure-activity
relationships. The report and recommendations of ECVAM
Workshop 52. Altern Lab Anim. 33:155–173.
Obach RS, Baxter JG, Liston TE, Silber BM, Jones BC,
MacIntyre F, Rance DJ, Wastall P. 1997. The prediction of
human pharmacokinetic parameters from preclinical and
in vitro metabolsim data. J Pharmacol Exp Ther. 243:
Park K. 2017. A review of modeling approaches to predict
drug response in clinical oncology. Yonsei Med J. 58:1–8.
Perryman AL, Stratton TP, Ekins S, Freundlich JS. 2016.
Predicting mouse liver microsomal stability with “Pruned”
machine learning models and public data. Pharm Res. 33:
Pound P, Ritskes-Hoitinga M. 2018. Is it possible to overcome
issues of external validity in preclinical animal research?
Why most animal models are bound to fail. J Transl Med.

Ransohoff RM. 2018. All (animal) models (of neurodegenera-
tion) are wrong. Are they also useful? J Exp Med. 215:

Safdar N, Andes D, Craig WA. 2004. In vivo pharmacodynamic
activity of daptomycin. Antimicrob Agents Chemother. 48:
Sager JE, Yu J, Ragueneau-Majlessi I, Isoherranen N. 2015.
Physiologically based pharmacokinetic (PBPK) modeling

and simulation approaches: a systematic review of pub-
lished models, applications, and model verification. Drug

Metab Dispos. 43:1823–1837.


Sharma A, Ebling WF, Jusko WJ. 1998. Precursor-dependent
indirect pharmacodynamic response model for tolerance
and rebound phenomena. J Pharm Sci. 87:1577–1584.
Sheiner LB, Stanski DR, Vozeh S, Miller RD, Ham J. 1979.

Simultaneous modeling of pharmacokinetics and pharma-
codynamics: application to d-tubocurarine. Clin Pharmacol

Ther. 25:358–371.
Sheridan RP. 2013. Time-split cross-validation as a method
for estimating the goodness of prospective prediction.
J Chem Inf Model. 53:783–790.
Singh AP, Shah DK. 2017. Application of a PK-PD modeling
and simulation-based strategy for clinical translation of
antibody-drug conjugates: a case study with trastuzumab
emtansine (T-DM1). Aaps J. 19:1054–1070.
Sjoberg EA. 2017. Logical fallacies in animal model research.
Behav Brain Funct. 13:3.
Sprous DG, Palmer RK, Swanson JT, Lawless M. 2010. QSAR
in the pharmaceutical research setting: QSAR models for
broad, large problems. CTMC. 10:619–637.
Sun YN, Jusko WJ. 1998. Transit compartments versus
gamma distribution function to model signal transduction
processes in pharmacodynamics. J Pharm Sci. 87:732–737.

Toutain PL, Lefebvre HP, King JN. 2000. Benazeprilat dispos-
ition and effect in dogs revisited with a pharmacokinetic/

pharmacodynamic modeling approach. J Pharmacol Exp
Ther. 292:1087–1093.

Tropsha A. 2010. Best practices for QSAR model develop-
ment, validation, and exploitation. Mol Inf. 29:476–488.

Tropsha A, Golbraikh A. 2007. Predictive QSAR modeling

workflow, model applicability domains, and virtual screen-
ing. Curr Pharm Design. 13:3494–3504.

Tuveson D, Clevers H. 2019. Cancer modeling meets human
organoid technology. Science. 364:952–955.
U.S. Food & Drug Administration. 2003. FDA guidance for
industry: exposure-response relationships—study design,
data analysis, and regulatory applications. Rockville (MD):
van der Worp HB, Howells DW, Sena ES, Porritt MJ, Rewell S,

O’Collins V, Macleod MR. 2010. Can animal models of dis-
ease reliably inform human studies? PLoS Med. 7:

Wade KC, Wu D, Kaufman DA, Ward RM, Benjamin DK,
Sullivan JE, Ramey N, Jayaraman B, Hoppu K, Adamson PC,
et al. on behalf of the NICHD Pediatric Pharmacology
Research Unit Network. 2008. Population pharmacokinetics
of fluconazole in young infants. Antimicrob Agents
Chemother. 52:4043–4049.

Wagar LE, DiFazio RM, Davis MM. 2018. Advanced model sys-
tems and tools for basic and translational human immun-
ology. Genome Med. 10:73.

Wagner JG. 1968. Kinetics of pharmacologic response. I.
Proposed relationships between response and drug

concentration in the intact animal and man. J Theor Biol.
Waring MJ, Arrowsmith J, Leach AR, Leeson PD, Mandrell S,
Owen RM, Pairaudeau G, Pennie WD, Pickett SD, Wang J,
et al. 2015. An analysis of the attrition of drug candidates
from four major pharmaceutical companies. Nat Rev Drug
Discov. 14:475–486.
Wright DF, Winter HR, Duffull SB. 2011. Understanding the
time course of pharmacological effect: a PKPD approach.
Br J Clin Pharmacol. 71:815–823.

Wu B, Joshi A, Ren S, Ng C. 2006. The application of mechan-
ism-based PK/PD modeling in pharmacodynamic-based

dose selection of muM17, a surrogate monoclonal anti-
body for efalizumab. J Pharm Sci. 95:1258–1268.

Yassen A, Olofsen E, Romberg R, Sarton E, Teppema L,

Danhof M, Dahan A. 2007. Mechanism-based PK/PD mod-
eling of the respiratory depressant effect of buprenor-
phine and fentanyl in healthy volunteers. Clin Pharmacol

Ther. 81:50–58.
Yoshida K, Budha N, Jin JY. 2017. Impact of physiologically
based pharmacokinetic models on regulatory reviews and

product labels: frequent utilization in the field of oncol-
ogy. Clin Pharmacol Ther. 101:597–602.

Zhang X, Lionberger RA, Davit BM, Yu LX. 2011. Utility of

physiologically based absorption modeling in implement-
ing quality by design in drug development. Aaps J. 13:

Zhao M, Lepak AJ, Andes DR. 2016. Animal models in

the pharmacokinetic/pharmacodynamic evaluation of anti-
microbial agents. Bioorg Med Chem. 24:6390–6400.

Zheng X, Wise SM, Cristini V. 2005. Nonlinear simulation of
tumor necrosis, neo-vascularization and tissue invasion via
an adaptive finite-element/level-set method. Bull Math
Biol. 67:211–259.

Zhou S, Meng J, Liu B. 2017. Investigation into the pharma-
cokinetic–pharmacodynamic model of Zingiberis Rhizoma/

Zingiberis Rhizoma Carbonisata and contribution to their
therapeutic material basis using artificial neural networks.
RSC Adv. 7:25488–25496.
Zhuang X, Lu C. 2016. PBPK modeling and simulation in
drug research and development. Acta Pharm Sin B. 6:
Zion Market Research. 2019. Biosimulation Market by Product
(Software and Services), by Application (Drug

Development, Drug Discovery, and Others), and by End-
User (Pharmaceutical & Biotechnology Companies,

Contract Research Organizations, Regulatory Authorities,
and Academic Research Institutions): Global Industry
Perspective, Comprehensive Analysis, and Forecast,

Learn more about VeriSIM Life’s BIOiSIM platform and unique Translational Index™️ technology.