Analytical pharmacology.pdf

Analytical pharmacology: the impact

of numbers on pharmacology

Terry Kenakin1

and Arthur Christopoulos2

1

Platform Technology Sciences, GlaxoSmithKline Research, R.T.P

2

Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences & Department of

Pharmacology, Monash University

Analytical pharmacology strives to compare pharmacological data to detailed quantitative

models. The most

famous tool in this regard is the Black/Leff operational

model, which can be used to quantify agonism in a test

system and predict it in any other system. Here we give

examples of how and where analytical pharmacology

has been used to classify drugs and predict mechanism

of action in pharmacology. We argue for the importance

of analytical pharmacology in drug classification and in

prediction of drug mechanisms of action. Although

some of the specifics of Black’s models have been

updated to account for new developments, the principles of analytical pharmacology

should shape drug discovery for many years to come.

Introduction

When invited to name a professorship at King’s College

Hospital School of Medicine and Dentistry (London, UK)

that had been created for him, James Black chose the name

‘Analytical Pharmacology’. He saw this endeavor as

‘...attempts to interpret ligand interactions with complex

biosystems as exposed in different types of bioassay’ [1.]

Arguably, pharmacology can be considered to be the

chemical control of physiology. Compared with physiology,

chemistry is a relatively ordered discipline that is subject to

the rules of physical sciences. The interface of chemistry and

biology is crucial to drug discovery, and yet each resides in

different worlds of precision. Early pharmacologists such as

A.J. Clark wrote that pharmacology therefore should try to

express physiology, with all its vagaries and variances, in

chemical terms; this would allow chemists the means to

control physiological processes, i.e. to make drugs.

‘The general aim of this author in this monograph

has been to determine the extent to which the effects

produced by drugs on cells can be interpreted

as processes following known laws of physical

chemistry’

(Clarke, 1937) [2]

The important process of this approach is the comparison

of experimentally obtained pharmacological data to models.

Every time a researcher carries out an experiment and

thinks about what is happening, he or she has formed a

model. The best models have rules and the most easily

applied rules are mathematical ones. Thus, the comparison

of data to a mathematical model allows determination of the

veracity of the model and possible disproof of the null

hypothesis (i.e. there is no difference between what is observed and what the model

predicts). Progress is made when

the null hypothesis is disproved and the model is changed to

a different, and hopefully, better model (as judged by its use

in predicting the outcome of future experiments.)

Historically, pharmacologists have constructed mathematical models of drug action, and

these have been applied

to the analysis of dose–response data [3–18]. James Black

took this method to a new level through a process of

constantly updating working models according to experimental data; his name for the

approach was ‘analytical

pharmacology’. The basic tenets of analytical pharmacology have been invaluable to the

drug discovery process.

Hence, it is worth outlining Professor Black’s unique vision

of the interaction between pharmacology and chemistry as

it was embodied in the form of analytical pharmacology.

The importance of numbers

Analytical pharmacology delves more deeply into pharmacological problems and

constantly compares experimental

data to defined rules. For example, early formulations of

mechanisms describing agonist efficacy led to the prediction that the relative order of

potency of agonists should be

constant for a receptor and for a given set of agonists. The

actual order is an approximation of a calculated numerical

relative potency of those agonists made by the null method

in a given system utilizing quantitative models of agonism.

This latter requirement is more stringent and asks more of

the system, i.e. that agonist disposition mechanisms be

neutralized and maximal responses equalized. Experimentally, these conditions sometimes

are not met, and the

actual numerical relative potencies might differ while still

retaining the relative order. Unfortunately, there are several receptor studies in the

literature that stop at the

relative order requirement and ignore numerical potency

ratios. Analytical pharmacology, as practiced by Black, did

not do so. If the actual quantitative prediction did not

adhere to the model, this was a ‘red flag’ that needed to

be followed up. In Professor Black’s presence, one would

often be told: ‘Your data are screaming at you man, can’t

you hear it?’ This attention to detail is extremely important

because it can reveal multiple properties of drugs.

One of Black’s firm beliefs was that pharmacology is

concerned with the taxonomy of drugs. That is, how molecules are defined dictates how

they are used therapeutically.

Thus, classifications such as ‘agonist’, ‘antagonist’ and

Opinion

Corresponding author: Kenakin, T. ([email protected].)

5110-1116/ $– see front matter � 2511 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tips.2011.01.002 Trends in Pharmacological Sciences, April 2011, Vol. 32,

No. 1 189‘inverse agonist’ denote behaviors of molecules that are

important in how they are viewed as pharmacological entities and how they are used

therapeutically. However, it is

well known that drugs rarely have a single pharmacological

activity, and it might be the constellation of activities in a

given molecule that constitutes its therapeutic value. For

example, manyb-blockers have been tested in clinical trials

of congestive heart failure and, theoretically, all should have

worked if the primary effect required is b-adrenoceptor

blockade. However, only a handful of such trials have been

shown to be useful[19]. One of the best examples of these is

carvedilol, a molecule known to have an array of effects in

addition to its ability to block b-adrenoceptors [20]. It could

be that the success of carvedilol in the treatment of congestive heart failure is due to a

combination of activities.

With the discovery that many molecules are pharmacologically biased with respect to the

cellular signaling pathways

they affect (the result being functionally selective effects),

simple taxonomy of drugs with single labels is obsolete [21.]

The complete definition of drug properties (a process

greatly facilitated by analytical pharmacological methods)

is nearly a prerequisite to the correct classification of drugs

for therapy.

The quantitative application of models was a characteristic mainstay of Black’s approach to

discovery. These procedures led to the question: ‘does the system obey the rules?’

A frequent interrogative tool of pharmacological systems

was the Schild regression. Originally designed to test the

assumption that a given antagonist was competitive with

the agonist and also to estimate its potency [22], Black

extended this method to be applied to the determination

of the activity and mechanism of action of new drugs. Accordingly, he demonstrated the

use of Schild analyses to

mixed receptor populations [23] and the discovery of multiple drug activities [24]. This

latter idea is a recurrent theme

in Black’s application of analytical pharmacology; a specific

example is the publication of ‘Pharmacological Resultant

Analysis’. This ingenious procedure cancels the secondary

activities (and in the process reveals them) of competitive

antagonists to allow the appropriate quantification of antagonist potency [21]. Thus, a

‘Schild regression of Schild

regressions’ is used to estimate the true pKB of an antagonist, as well as to gauge the

measure of secondary activity.

The application of analytical pharmacological techniques

to the study of drug action is instrumental in detecting

additional drug activity; this was shown in a study of the

b-adrenoceptor blocker chloropractolol [20]. Specifically,

this molecule was shown to be a partial agonist in rat atria

(Figure 1A). However, close examination of the data showed

an anomaly in the array of concentration–response curves.

Thus, although a dextral displacement and common intersection point of the curves is

predicted by the quantitative

model (namely, that describing simple competitive antagonism), it was observed that low

concentrations of chloropractolol did not produce this profile. This also was reflected

in a distinct curvature in the Schild regression (Figure 1B.)

Further investigation revealed that chloropractolol also

blocks catechol-o-methyl transferase (COMT) to potentiate

isoprenaline response in this tissue; prior blockade of COMT

corrected the anomalous behavior in the concentration–

response curves (Figure 1C) and Schild regression

(Figure 1D). So what is the outcome of such ‘pharmacological

nitpicking’? In this case, an accurate estimation of the

potency of chloropractolol as a b-blocker but, perhaps more

importantly, the discovery that this molecule has another

pharmacological activity operable in the same concentration

range which would probably be used in vivo.

The quantitative comparison of data to mathematical

models is often applied in analytical pharmacology to

determine the mechanism of action of a compound. For

example, Black used this to delineate the actions of gastrin

in the production of stomach acid [26]. In this case, a

quantitative model of the indirect release of an agonist,

based on one derived by Don Jenkinson of University

College, London (London, UK), predicted a characteristic

pattern of concentration–response curves (Figure 2), which

can be used as an identifier of endogenous agonist release

[26 .]The comparison of data to this model was instrumental in determining the mode of

action of gastrin in sustaining stomach ulcers [28.]

Analytical pharmacology and intact systems

Before the late 1980s, pharmacological discovery was

mainly conducted in intact tissue systems. Pharmacology

was used in this period to analyze drug behavior in a

particular system to yield the root cause of the behavior,

i.e. the affinity and efficacy of a molecule as it interacts

with a protein target. Analytical pharmacology is uniquely

suited to this endeavor because it applies models operationally with no prerequisite

precise knowledge of mechanism; Black called the major tool in this process the

bioassay. With the advent of the human genome and

technological advances that allowed robotic screening of

vast chemical libraries in recombinant systems, pharmacological analysis in intact systems

was deconstructed and

considered by some to be needlessly obscure. James Black

exclaimed of this period the ‘Pharmacology is in danger of

disappearing without a trace!’ Through a steady stream of

articles illustrating the importance of analytical pharmacology techniques in intact

systems, Black helped the

discipline ‘weather the storm’ to see it emerge again as

a vital part of the drug discovery process because it is

realized that the way systems put components together

trumps the identity of the components themselves. His

comment on recombinant systems characteristically went

to the root of the matter: ‘Components are to systems as

words are to poems’[29]. He succinctly described his notion

of how integrated systems are unique in an essay as

published in the Annual Reviews in Pharmacology [1:]

‘If a number of chemical messengers each bring

information from a different source and each deliver

only a subthreshold stimulus but together mutually

potentiate each other, then the desired informationrich switching can be achieved with

minimum risk of

miscuing. . .. . .Bioassays can be designed to mimic

and analyze such convergent control systems...’

J.W. Black [1]

Analytical pharmacological techniques do not require

intimate knowledge of pharmacological and physiological

mechanisms, a fact made evident in the naming of one of

the most important tools in pharmacology using these

Opinion Trends in Pharmacological Sciences April 2011, Vol. 32, No. 4

195methods: the Black/Leff operational model [18]. Ironically,

the operational model was conceived to fill a perceived gap

in Stephenson’s treatment of efficacy by changing it from a

mathematical proportionality factor inserted to allow theoretical and experimental

concentration–response to agree

with a parameter distinctly linked to physiological processes. Thus, a physiological

mechanism (modeling of

stimulus–response as a virtual enzyme bound by Michaelis–Menten kinetics) was used to

develop a model that

obviated specific knowledge of receptor stimulus–response

coupling. The Black/Leff operational model has become the

standard method by which agonist response is quantified

in cellular systems.

One of the most important uses of the Black/Leff operational model is the quantification of

the power of an agonist

to activate a given cellular pathway in a whole cell. This is

done by quantifying the operational efficacy (denoted ast) of

the agonist for the receptor. If the ratio oftvalues for any two

agonists could be determined for a receptor in a cellular

system, the cellular components of t cancel and the ratio

becomes a system-independent estimate of the relative

efficacy of the agonists in any other system (provided that

the same signaling pathway is being activated in the cell by

those agonists). This furnishes a powerful tool for analytical

pharmacology in that the relative efficacy of agonists can be

measured in one (test) system to be used to predict agonism

of those same molecules in any other system (including the

therapeutically relevant one). This is particularly valuable

in drug discovery, in which an active chemical series is

seldom first tested or developed in the therapeutic system

but rather first used in some experimental test system.

Therefore, if a dose–response curve to a reference agonist

can be measured in the therapeutic system, the measurement of t values for a range of

test agonists (relative to the

1.2

1.5

5.8

5.1

5.1

5.2

5.5

Fraction of isoprenaline maximum

Log (DR-1)

-15 -9 -8 -6 -1

Isoprenaline: log M Chloropractolol: log M

2.0

2.5

1.0

1.5

5.0

5.5

5.0

-1.5

-1.0

-9 -8 -6 -1 -0 -1

1.2

1.5

5.8

5.1

5.1

5.2

5.5

Fraction of isoprenaline maximum

Log (DR-1)

-15 -9 -8 -6 -1

Isoprenaline: log M Chloropractolol: log M

2.0

2.5

1.0

1.5

5.0

5.5

5.0

-1.5

-1.0

-9 -8 -6 -1 -0 -1

No COMT blockade

COMT blockade

(a) (b)

(c) (d)

TRENDS in Pharmacological Sciences

Figure 1. Antagonism of isoprenaline response by chloropractolol in rat atria. (a) Responses

to isoprenaline in the absence (filled circles) and presence of chloropractolol

(15 nM (open circles) and 0.1mM (open triangles). Circled regions indicate observed

behavior not in agreement with quantitative models of competitive antagonism in that

the curve in the presence of chloropractolol should be shifted to the right of the control

and the intersection of the curves should be at a common point. (b) This

disproportionately low level of antagonism for 10 nM chloropractolol also produces a

curvature in the Schild regression, in disagreement with the quantitative model. (c)

Pre-inhibition of COMT with 10 nM U-0521 shifts the control curve to the left, and

chloropractolol now produces behavior consistent with competitive antagonism. (d)

Preinhibition of COMT also eliminates the curvature in the Schild regression. Data

redrawn from [22.]


191reference agonist) through the Black/Leff operational model

allows the prediction of agonism of those test agonists in the

therapeutic system. This tool epitomizes analytical pharmacology in that it quantitatively

uses a model to make

detailed predictions of drug effect. Figure 3 shows how this

model can lead to some striking predictions. Figure 3A

shows concentration–response curves to the muscarinic

agonists oxotremorine and carbachol in the guinea pig ileum; both are full agonists and

oxotremorine is approximately twofold more potent than carbachol. Analyses of the

efficacy and affinity of these agonists with the Black/Leff

operational model show that oxotremorine is a high-affinity

but low-efficacy agonist, whereas carbachol has low affinity

and high efficacy. These combinations can lead to surprising

differences in systems of lower sensitivity; specifically,

low-efficacy agonists are more sensitive to a loss of sensitivity than high-efficacy agonists.

Thus, if a large portion

of the muscarinic receptors are inactivated through

alkylation with phenoxybenzamine to produce a less sensitive tissue, the responses to

oxotremorine diminish to a

(a) (b)

Oxotremorine

Oxotremorine

Carbachol

Carbachol

τ

carb /τ

oxo = 12.0 τ

carb /τ

oxo = 14.0

-9 -8 -6 -1 -0

Log [agonist]

-6 -1 -0 -1 -3

Log [agonist]

155

95

85

65

15

05

15

35

25

15

5

%Maximum

155

95

85

65

15

05

15

35

25

15

5

%Maximum


Figure 3. Contraction of guinea-pig ileum through activation of muscarinic receptors with

carbachol (open filled circles) and oxotremorine (filled circles). (a) Control curves

in normal tissue and (b) curves in the same tissue after controlled alkylation of the

muscarinic receptor with 1mM phenoxyybenzamine (POB) for 10 h followed by 2 h

drugfree wash. Data points represent single curves in one tissue fit to the operational

model with very similar t ratios. Data redrawn from [30.]

Blockade of indirect agonism

Gastrin Histamine

Antagonist

H+

H+

Log [gastrin]

125

155

85

15

15

25

5

-9 -8 -6 -1 -0 -1

Log [histamine]

%Max H+ secretion

%Max H+ secretion

125

155

85

15

15

25

5

-9 -8 -6 -1 -0 -1


Figure 2. Competitive blockade of a directly acting agonist (histamine) to induce acid

secretion and an indirectly acting agonist (gastrin releases histamine to induce acid

secretion). Although surmountable blockade is predicted for the direct agonist, a

quantitative model predicts that the indirect agonist will be blocked by the same

antagonist

in an insurmountable manner.


192disproportionately greater extent than the responses to

carbachol (Figure 3B). This effect is predicted by the

Black/Leff operational model, as shown by the fitting of

the data in the alkylated tissue with the same relative

efficacy values determined in the control tissue. If oxotremorine was a test agonist and

carbachol a reference agonist,

this model would have predicted that a test agonist that is

apparently more active than the reference in the test system

would produce much less response in the therapeutic

system.

Black’s legacy: the role of analytical pharmacology in

modern drug discovery

James Black defined analytical pharmacology as ‘‘The

attempt to interpret drug actions in terms of underlying,

hypothetical mechanisms’’ [31]. His legacy is evident in

numerous studies that have adopted this principle to

interrogate, optimize, troubleshoot, predict and/or classify

the behavior(s) of their systems. In a sense, the real power

of analytical pharmacology is that it helps avoid wishful

thinking, a practice that is invariably influenced by prevailing trends. This is an important

consideration in modern drug discovery due to a convergence of challenges to

pharmacology, such as the decline in the number of pharmacology departments; the

variable quality/currency of

some pharmacology textbooks; the changing nature of

the bioassay; and the need to incorporate newer concepts

in receptor pharmacology (e.g. biased signaling, receptor

oligomerization and allosteric modulation.)

Interestingly, Black was steeped in an orthosteric

world-view, being one of the most successful proponents

of the concept of ‘‘drugs from emasculated hormones’’

(hormones chemically altered to remove efficacy but which

retain their affinity for receptors) [32]. For some time, he

was not certain that the case for allosteric ligands had been

convincingly made because the ‘‘chemistry was not there

yet’’. However, the last 10 years have witnessed an explosion in the identification of

allosteric modulators of G

protein-coupled receptors (GPCRs), ion channels and other

drug targets. This has been driven in large part by the

supplanting of orthosteric-biased binding assays by functional drug-screening methods. In

turn, this has necessitated a requirement to furnish numbers that can assist the

chemistry in ‘‘getting there’’, and the Black/Leff operational model has recently been

extended to deal with this

situation [33–36]. The key analytical challenge has been

the need to differentiate the features of allosteric ligands

that govern their interaction with the receptor (affinity)

from those that contribute to the allosteric effect they exert

on the actions of orthosteric ligands (cooperativity). This

challenge is reminiscent of Black’s own efforts to understand and differentiate

operationally the properties of

affinity and efficacy in the actions of classic orthosteric

ligands, but with the inclusion of additional parameters (a

and b inFigure 4) to quantify the magnitude and direction

of the allosteric effect on orthosteric ligand affinity and

efficacy, respectively. Figure 4A illustrates an example of

how operational modeling has been used to rationalize and

quantify the behavior of a novel allosteric modulator,

Org27569, of the cannabinoid CB1 receptor. An interesting

property of this modulator is that it enhances the binding

affinity of the orthosteric agonist WIN00212 (a>1) while

diminishing its signaling capacity (0<b<1), which can lead

to a dissimilitude in compound classification depending on

[Org26019] (μM)

[LY2533298] (μM)

%Inhibition

155

60

05

20

5

[ %

30

S]GTPγS Binding

155

60

05

20

5

-15 -9 -8 -6 -1

Log [WIN55212] (M)

-15 -9 -8 -6 -1 -0

Log [ACh] (M)

5

5.1

5.3

1

3

5

5.1

5.3

(a) (b)

KB = 25 nM

α = 11

β = 5.558

τ

B = 0

KB = 2 μM

α×β = 01

τ

B = 3.3

Key:

Key:


Figure 4. Operational model-fitting of allosteric modulator interactions. (a) Effect of the

modulator (Org27569) on the agonist (WIN55212) at cannabinoid CB1

receptormediated inhibition of the isolated vas deferens in mice. The term a refers to

the effect of the allosteric modulator on agonist affinity whereas b refers to its effect on

agonist

efficacy. Data re-plotted from [36]. (b) Effect of the allosteric modulator, LY2033298, on

acetylcholine-mediated [35S]GTPgS binding at the human M4

muscarinic receptor

stably expressed in a CHO cell line.


193the nature of the assay used (e.g. binding vs. function[36.)]

Figure 4B shows the effects of an allosteric potentiator of

acetylcholine, LY2033298, at the M4

muscarinic receptor.

In addition to enhancing the binding and function of the

endogenous orthosteric agonist at this receptor,

LY2033298 activates the receptor in its own right [37],

which is operationally quantified by a t

B value >0. These

types of studies are beginning to provide vital information

that can assist structure–activity, structure–function, and

mechanism-of-action studies of novel allosteric ligands

[38–11.]

Given the high attrition rates in modern drug discovery,

methods for improving the translational potential of in

vitro bioassays and in vivo animal data are urgently required. In this regard, another area in

which the analytical

pharmacology approach championed by James Black has

been adopted is in the study of mechanism-based pharmacokinetic–pharmacodynamic

modeling, which aims to predict drug exposure–response relationships in humans [42.]

Numerous examples now exist of the utility of the operational model in predicting in vivo

estimates of affinity and

efficacy using this methodology [13]. Operational modeling

has also proven useful in facilitating understanding of

interspecies variability in drug action [44]. This has unraveled apparently complex modes

of orthosteric antagonism

[10] ,rationalized efficacy differences as a consequence of

the variability of receptor distribution in tissues [46], and

quantified changes in receptor functionality due to receptor desensitization [16.]

The principles espoused by James Black continue to find

new ways of influencing the ongoing work of those interested in drug discovery. For

instance, the changing nature

of the bioassay means that assay miniaturization and the

measurement of an ever-increasing array of intracellular

signaling pathways based on second messenger accumulation or real-time determination

of transient responses can

lead to observations that are difficult to reconcile with

predictions based on classic receptor theory. Analytical

pharmacology can play a vital part in guiding the design

and interpretation of experiments. One example is with the

widespread use of intracellular calcium mobilization

assays for drug screening. Although easy to carry out,

the transient nature of response generation in these types

of assays, coupled with slow equilibration times for many

antagonist ligands, often leads to non-classical patterns of

antagonism that can be mechanistically misconstrued if

viewed through the lens of the equilibrium model (which

remains the most common type applied to the analysis of

pharmacological data). In such instances, dynamic (kinetic) models are more appropriate

because they explicitly

accommodate the non-equilibrium nature of the assay.

Such models can be used to explain otherwise anomalous

1.55

5.60

5.05

5.20

5.55

-9 -8 -6 -1 -0 -1 -3 -2 6.0 8.5 8.0 9.5 9.0 15.5

Log10 [A]

E/E

max

Response=ARn / (ARn+KE

n)

k6

k5

k1

k2

k3

k4

B + ARD

pKB Estimate

pEC25%

pEC50

Frequency

85

15

15

25

5

BR + A B + R + A B + AR

Desens. rate


Figure 5. A dynamic model of a transient response system in which: A, B and R denote

agonist, antagonist and receptor, respectively; k1 and k5

denote agonist and

antagonist association rate constants, respectively; and k2 and k6

denote agonist and antagonist dissociation rate constants. Response is a logistic function

of AR, where KE

denotes the efficiency of response generation and n is a logistic slope factor. Response

fade is determined by k3, whereas re-sensitization is determined by the rate constant,

k

1 .The model was used to simulate the concentration–response curves shown in the

bottom-left panel, with curve locations corresponding to the EC50, shown as circles.

The dotted line represents the control curve 25% equally effective response level (EC25%

level). The bottom-right panel shows the frequency distributions of pKB values

determined via nonlinear regression analysis of the pEC50 values or equally effective

agonist concentrations corresponding to the 25% maximal response level of the

control agonist curve, based on 250 simulated datasets (with random error). The arrow

indicates the correct value of the pKB assigned to the antagonist in the simulations.

Re-plotted from [50.]


191behavior as well as suggesting analytical approaches to

quantify ligand properties under non-equilibrium conditions. For example, Figure 5

outlines a relatively simple

kinetic model that incorporates the transition of an agonist-bound receptor (AR) into a

non-signaling species

(ARD) as a function of agonist concentration, agonist effi-

cacy (KE) and time. One interesting prediction of this

model is the saturable depression of maximum agonist

responsiveness in the presence of increasing concentrations of a competitive (orthosteric)

antagonist which

results as a consequence of the interplay between a transient agonist response

determined after pre-equilibration

of a slowly dissociating antagonist. This has been observed

experimentally [48,49] and can be misinterpreted as evidence of a non-competitive mode

of interaction if simple

equilibrium is assumed. Another revelation from this model is that the traditional use of

agonist EC50 values to

determine antagonist potency will underestimate the value of the latter, but can be

rescued by appropriate selection

of equally effective agonist concentrations for the Schild

analysis [50,51.]

The preceding examples represent a small ‘snapshot’ of

the ongoing challenges facing modern drug discovery that

can only benefit from the type of analytical rigor introduced

by Sir James Black. Such rigor is required at all levels of

study of biological systems going from the cellular to the

intact animal and man.

Concluding remarks

Quantitative models of drug action have been a part of

pharmacology since the inception of this discipline. A

consistent and diligent application of those models by

pharmacologists has not. James Black engendered a culture within pharmacology of clearly

defining the rules of a

pharmacological model and then letting those rules guide

the experiments to a practical endpoint (a therapeutic

drug). Black frequently stated how this method was directly aimed at eliminating what he

referred to as ‘wishful

thinking’, the hope that our favorite hypothesis and/or

model would be supported by a given interpretation of cold

hard data. The application of analytical pharmacological

techniques teaches us that the modifications of those hypotheses through quantitative

analyses leads to a more

lasting endpoint than wishful thinking ever could.

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