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5
CHAPTER
Complex Agonism
5
...
Basal, Spontaneous, and Constitutive
Activity
Many activities run through effector molecules in the
natural state of resting cells
...
Let us think of these
activities at rest as basal activity by the various effector
molecules
...
In a way, such a view is even more obvious in
enzymology and transport physiology, since substrates or transported molecules in many types of
experiments must be present in order to allow
measurement of function
...
1995; Milligan & Bond 1997), and explain the
behavior of inverse agonists (Bond et al
...
5
...
1
...
Understandably, during this period of transception,1
the discoveries and recognition of spontaneous receptor
activity briefly confused the definition of what agonists
and ant-agonists should be, how to designate them, and
furthermore, how to design experiments, including
which drugs to choose for ones own experiments
(Kenakin 1987; Jenkinson 1991; Hoyer & Boddeke
1993; Kenakin et al
...
In those years, new notions
and formulations were introduced, e
...
, concepts appeared such as ‘inverse agonism’, ‘negative efficacy’, and
‘negative intrinsic activity’ as well as ‘negative antagonism’ (Costa et al
...
1993;
Kenakin 1994; Milligan et al
...
1995;
Kenakin 1995a,b; Kenakin et al
...
Those lacunae in our understanding almost evaporated
again with the re-recognition of the cyclic two-state
model (cTSM) (Robertson et al
...
1996 a,b,c)
(Chapter 7)
...
1
...
Function and Binding Concepts
When we focus on receptor controlled protein function,
as mentioned, activity in the absence of agonists can
be either basal or spontaneous/constitutive activity
...
Thus, the acronym CAM, standing for
‘constitutively active mutants’, has emerged
...
For the modeler of
reaction schemes, activity observed in functional studies
can be either (1) basal/spontaneous/constitutive, or (2)
agonist-induced activity
...
# 2008 N Bindslev
...
0
Unported License (http://creativecommons
...
0/), permiting all non-commercial use, distribution, and reproduction in any medium, provided the original
work is properly cited
...
3402/bindslev
...
8
109
110
Part II: Two-State Models: Complex Agonism and Modulation
In binding studies, the term ‘activity’ is meaningless
...
Thus, spontaneous high-or-low-affinity-states in occupancy studies has a direct parallel to the spontaneous
activity in functional studies and is delineated here for
TSMs in Section 5
...
4
...
2
...
2
...
Inverse Agonists
Increasing numbers of compounds, considered agonists,
are observed to inhibit spontaneous or constitutive
activity instead of stimulating the activity
...
The thought-to-be agonists with a reducing effect on
spontaneous activity are now known as ‘inverse agonists’,
whereas compounds that ant-agonize the inhibitory
effect of inverse agonists, but without an effect on their
own in the absence of inverse agonists, are still signified
as ant-agonists or even better as neutral ant-agonists
(Milligan et al
...
Moreover, many competitive antagonists have been found to be inverse agonists (Chidiac
2002; Strange 2002; Kenakin 2004)
...
As we shall see,
the effects of inverse agonists are immanent in the cTSM
and its formulation
...
3) still live on in parallel
...
2
...
Multi-functional Agonists
New models are required as novel ligand-receptor
interactions are discovered
...
Acetylcholine at muscarinic
receptors is one example (Winding & Bindslev 1993)
...
2B and 4
...
To date, the
behavior of these types of drugs has not been well
described and therefore demands new modeling
...
5
...
3
...
Thus, binding of
ligands in the binding sites of a receptive unit is often
more than the simple view of a ‘key-in-the-lock’
...
Again, innovative modeling may be required for this
catalytic system (Roberts & Atkins 2007)
...
3
...
3
...
Two-state Receptor Models
As we start to examine dose-response relationships that
do not follow simple load theory, some of the problems
and challenges we face have already been presented in
preceding sections on partial agonism, on possible spare
receptors, on allostery, on spontaneous activity, and on
inverse agonism (Chapter 1)
...
Although A
...
Clark, the farther of
pharmacology, hinted at receptor reserve as an explanation for the linear drug concentration-response for
narcotics and had his doubts about the applicability of
a simple load theory in the mechanistic Langmuirian
sense (Clark 1937, p
...
215Á217), he tenaciously purported formulations along the lines of a
power equation, i
...
, response 0occupancy raised to a
power of n (Clark 1937)
...
Based on
earlier observations and with sharp insight, Wyman
imagined a concerted conformational change in hemoglobin subunits as oxygen would bind, affecting the
binding of the next oxygen to bind (Wyman & Allen
1951; Edsall 1980)
...
They drew reaction schemes involving intermediate states for activity of the enzyme
(Tonomura & Watanabe 1952; Watanabe et al
...
This
culminated in the late 1950s, when a cTSM for enzymes
was finally formulated
...
1
...
(A'B) DelCastillo and Katz (1957, p
...
380) reaction schemes 2 and 3
(dC&K)
...
In panel B a nearly irreversible step 0S'R? is added
...
e
...
(C) Katz and Thesleff (1957) reaction scheme 5 (K&T5)
...
(D) Botts and Drain (1958) reaction scheme 14 (B&D14)
...
explicit involvement of a conformational change for unliganded receptive units between a reactive and an active
state in a fully reversible reaction scheme (Fig
...
1D)
...
4
...
4
...
Stephenson’s Reaction Scheme
Recognition of a need to explicitly express the existence
of a conformational change for the un-liganded receptor ran in parallel with observations of partial agonism
and receptor reserve (Furchgott 1955; Nickerson 1956;
Stephenson 1956)
...
However,
to incorporate both partial agonism and receptor
reserve, Stephenson (1956) gave a simple approach for
the formulation of response as a function of a stimulus
...
5
...
17), i
...
not the property ‘efficacy’ as used in
relation to response (see also the following discussion
and sub-chapter 1
...
Furthermore, the actual response
or activity was now an unknown function of this stimulus
(see Eq
...
2)
...
5
...
Thus for various agonists, dialing on a nob-of-efficacy,
that is, varying the efficacy constant in Eq
...
2,
Stephenson could explain the observation of response
for partial agonism including a possible receptor
reserve (Fig
...
12A'B) (Stephenson 1956, Figs
...
Similar plots are generated later from the functional
form of the dC&K model (Fig
...
6)
...
4
...
Efficacy and Efficacy Constant
Starts to Merge
Although, the two terms ‘efficacy’ as a property and
‘efficacy’ as a constant were intended as separate
concepts, a slip of the mind due to wording later
brought the two together as equal
...
380), was unfortunately not clearly
differentiated from ‘efficacy’ as a constant used throughout most of the paper by Stephenson (cf
...
9 (1956), reproduced in
Fig
...
12B, and his Table V)
...
3
...
3
...
6
...
In the intervening years, Stephenson’s model for
efficacy has been refined by several authors in an attempt
to experimentally isolate and determine an entity such as
the efficacy (Furchgott 1966; MacKay 1966, 1977; Black &
Leff 1983; Clarke & Bond 1998; Clark et al
...
Why
the effort? Well, if one can obtain experimental data for
the activation process per se, i
...
, the efficacy in absolute
112
Part II: Two-State Models: Complex Agonism and Modulation
terms as an efficacy constant, that would give us an
opportunity to assay and understand the conformational
change that is elicited in a protein molecule when it
activates
...
In
addition, as pointed out by several authors, all efforts
to dis-entangle dose-response relations and isolate an
efficacy constant will be in vain (Kenakin 1994, 2002;
Colquhoun 1998)
...
6Á7)
...
2000, Chapter 5, p
...
5, (Christopoulos et al
...
This goes together with
other variations on the theme (Rusch et al
...
2005; Durroux 2005),
and is also combined with receptor ensemble hypotheses (Onaran & Costa 1997; Kenakin & Onaran 2002)
...
3)
...
5
...
Two main trends are presently being pursued, the
TCM and three-state models (IIISMs)
...
5
...
The Ternary Complex Model (TCM)
One trend is that of the TCM, detailed as the INTERVENTION model in Chapter 2
...
1980; Birnbaumer et al
...
1980),
and further detailed by Ehlert (1988)
...
Shortly after, the TCM expanded
to the extended ternary complex model (ETCM) (Iyengar et al
...
1993; Samama et al
...
1995; Weiss et al
...
1996a,b,c; Onaran & Costa
1997), and further to a dynamic variation on the CTCM
theme in the form of a cubic ternary-complex activation
model (CTCAM) (Shea et al
...
Both the ETCM and
the CTCM take into account the idea of two states for the
receptor in a fully reversible scheme, the cTSM
...
5
...
2
...
e
...
In these theories, two different active states
are postulated for the receptor and each binds to a
different G protein allowing for the experimentally
observed bifurcation of signals for GPCRs
...
1997; Scaramellini & Leff 1998, 2002; Strange
1998; Surya et al
...
Thus, two-state
modelers engaged in GPCR transduction mechanisms
are bending towards the context of a TCM, a model
including a complexation step with a third component, the G protein, for both the receptor as such and
the ligand-receptor complex before the receptor performs its action (Scaramellini & Leff 2002)
...
The IIISM keeps the stick-shift of efficacy within
the receptive unit, so to speak, contrary to other
models that leave the efficacy transmission to a step
beyond the receptor as in classic receptor theory, for
instance in the TCM, where the efficacy coupling is
down-stream of the receptor in the chain of events for
signal transduction
...
(2001) and the models by Tucek et al
...
These latter models for promiscuity are all one-state
models
...
5
...
5
...
3 for a survey
and segregation of these models
...
5
...
A Decisive Jump from Steps to States
Before moving on to these types of exciting new models,
we need an insight into their base, which are the cTSM
and its modulatory versions in the form of the ATSM
and HOTSM
...
Simple two-step
A
and
C
CS
OS
C
CS
OS D
B
5
...
Two-steps Intermediate Complexes in
Non-active States
5
...
1
...
Katz
together with del Castillo suggested a hypothesis in
which they envisioned that binding of a ligand to a
receptor formed an intermediate complex, RS, which
could switch to a secondary active state, R*S, Fig
...
1A
...
369)
...
5
...
380), as
described earlier by several researchers (Fatt 1950;
Thesleff 1955)
...
The
complete del Castillo & Katz reaction scheme, which
explicitly included a transition from a liganded reactive
state Á non-active intermediate state Á to a liganded and
active state, was described as:
R ' S v RS v R1S;
in which R*S is an active conformation of the
receptive entity including a possible desensitized state
...
However, it is not a TSM
...
5
...
For enzymatic activity, two-step models with their
intermediate state or conformation were already proposed in the early 1940s (Glasstone et al
...
two-state models
C
dC&K
C
cTSM (K&T)
C
O
CS
OS
D
C
O
MWC
C
O
D
113
O
CS
OS
Figure 5
...
Simple reaction schemes including transcribed
originals from Fig
...
1
...
Models in BÁD are genuine two-state models (TSMs)
...
(A) Transcription of the two dC&K
schemes from Fig
...
1A'B
...
(C) Transcription of the K&T5
scheme from Fig
...
1C
...
Note that this scheme is not fully
reversible as for instance the K&T5 and B&D14 reaction
schemes in Fig
...
1
...
Impetus for this came from the development of techniques to measure fast reaction kinetics
by Eigen in Germany, Tonomura in Japan, Chance in
the USA, and Roughton in England
...
1941) as was Wyman’s reflections on
the response in hemoglobin upon oxygen-binding
(Wyman & Allen 1951)
...
Inspired
by the Perutz (1942) studies on hemoglobin, now
receptive units were described as existing in ‘aramagnetic’ to a ‘diamagnetic’ configuration (Wyman 1948;
Allen et al
...
1953; Shaw 1954; Blum 1955; Glynn 1955; Botts
1958)
...
5
...
1965) (also see Section 5
...
9
and Chapter 15)
...
5
...
7), and another for enzyme catalytic activity (Fig
...
1D) (Botts & Drain 1958)
...
6
...
The Misconception Induced by
Stephenson’s Efficacy Scheme
At this point in our development of models, it would be
beneficial to compare the scheme by Stephenson,
described in Chapter 1 and Eqs
...
1 and 5
...
Let efficacy parameter for conformational change be
given by the symbol ‘e’ and occupancy by the symbol ‘y’
...
5
...
The difference between Stephenson and dC&K is a
product operator in Stephenson’s expression, ‘ ×’ (Eq
...
3) versus a separation or listing operator, ‘,’ (Eq
...
4),
for the del Castillo & Katz interpretation of receptor
states (Fig
...
3)
...
’ formulation is subtle,
but the influence on the outcome of the formulated
equations is more than dramatic
...
For the dC&K model, the derivation of formulas takes
in its origin including explicitly a ‘new’ conformation of
the receptive unit
...
5
...
That is, Eqs
...
1 and 5
...
4 are combined, thus omitting the ‘function of’
...
3
...
(A) Occupancy, stimulus, and relative response
efficacy as formulated by Stephenson
...
S is ligand concentration
...
As is an association constant for S, and L’ an isomerization
constant, equal to Stephenson’s efficacy constant e
...
5
...
the lack of an explicit formulation for Stephenson’s
‘function of’
...
This
difference will be made even clearer by the end of subchapter 5
...
As mentioned, the temptation to ignore the ‘function
of’ operator in Eqs
...
2 and 5
...
3
...
Users of
the Stephenson scheme are misled by Eq
...
3, and as
mentioned in Chapter 1, Colquhoun (1998) has referred to the temptation to misinterpret Stephenson’s
scheme as ‘Stephenson’s error’
...
From conceptually being separable in the misconceived Stephenson scheme (Furchgott 1966; Venter
1997), the system entities y and e, insensibly, become
inseparable in the del Castillo & Katz scheme (shown
later in sub-chapter 5
...
10) (Fig
...
3B)
...
6
...
Formulations of the Two-step dC&K model
The expression in Eq
...
4 is open to many interpretations, one of which is the formulation of del CastilloKatz’s reaction scheme with an intermediate receptor
conformation, RS, and an additional conformation of
the bound receptor in an active form, R*S
...
Thus:
AS
L?
R'S X RS X R1S;
(Fig
...
3B)
...
Meanwhile, when equating this reaction
scheme, the system constants As and L? become microscopic constants, i
...
, they become inseparable (see
Sections 5
...
1Á5
...
3)
...
In terms of a distribution formulation in the Langmurian sense, we can write the fraction of receptors in
an active form for a dC&K response as:
response
R1S
0
;
total
R ' RS ' R1S
and this represents the actual functional level
...
5
...
In case the experiment on our lab-bench is a binding
assay, involving a receptive unit that is activated due to
the binding, then, assuming that the underlying receptor kinetics follow the two-step dC&K model at equilibrium, we have:
bound
total
0
RS ' R1S
R ' RS ' R1S
;
(5:6)
for the fraction of receptors in a bound form
...
5
...
and 5
...
We shall scrutinize the consequences of these two
equations, but before that, let me introduce the
distribution formulation for reaction scheme 5 by Katz
and Thesleff (K&T5), shown in Fig
...
1C, transcribed in
Fig
...
2C, and reconfigured to the cTSM in Fig
...
4
5
...
The Cyclic Two-state Model (cTSM)
5
...
1
...
5
...
2C, or Fig
...
4) (Katz & Thesleff 1957)
...
K&T5 is a milestone model in receptor theory
...
e
...
Furthermore,
a consequence of a reaction scheme with complete
reversibility is that one of the receptor conformations
must be an unbound active form, R*
...
5
...
Since the model by Katz and Thesleff involve desensitization, I shall refer to similar models describing
activation rather than the time-dependent desensitization as cyclic two-state models (cTSM) (Fig
...
4)
...
One was for activation and desensitization of ion
channels and the other was related to product formation
by enzymes
...
4
...
The reaction paths are indicated with rate constants,
association and dissociation constants, and isomerization
constants
...
6
...
Compare the cTSM in Fig
...
2C with a simplified
version of the Monod-Wyman-Changeux (MWC) model
in Fig
...
2D
...
The MWC model is described in detail in Chapters 14 and 15
...
7
...
Equating the cTSM
That an active state of the un-liganded receptors
certainly exists has, to put it mildly, burgeoned in recent
years in pharmacology (see literature cited in subchapters 5
...
2, 5
...
5)
...
5
...
8
for the two types of experiment, functional versus
occupancy
...
8
...
8
...
But, first, I must define some of the constants in the
reaction schemes in Figs
...
3B and 5
...
116
Part II: Two-State Models: Complex Agonism and Modulation
5
...
Constants, Formulations, and
Plots of dC&K and cTSM
5
...
1
...
5
...
In the following derivation of equations
for the dC&T and the cTSM, we will operate with both
dissociation and association constants as illustrated in
Figs
...
3 and 5
...
The reason for this redundancy is given
in the introduction to Part II, II
...
In the terminology of this text, the three system
constants of the cTSM are:
As an equilibrium association constant for ligand binding to non-active receptive unit
...
L an isomerization constant representing the ratio
between the activated unbound state of the receptive
unit, R*, and the non-active and unbound state of
the receptive unit; L 0R*/R
...
3
a an intrinsic efficacy constant at equilibrium as a ratio of
bound conformations times the ratio of unbound
conformations, {R*S/RS}×{R/R*} or an intrinsic association constant as a ratio of activated conformations times
the ratio of reactive conformations of the receptive unit
at equilibrium, {R*S/R*}×{R/RS} (see Fig
...
4)
...
Ks is an ‘equilibrium backward’
constant for a bi-mono-molecular process
...
A? is an equilis
brium ‘forward’ constant for a bi-molecular process
when receptive units are in an activated state
...
The K? is an
s
s
s
equilibrium ‘backward’ constant for a bi-monomolecular process
...
15
...
Both can be seen as identical,
although in MWC’s terminology, L is a reverse isomerization constant
of the L used here
...
1965)
...
L? an isomerization constant representing the ratio
between the activated bound state and the reactive,
not yet active, but bound state of the receptive unit,
L?0R* S/RS
...
The L? is an equilibrium ‘forward constant’ for a mono-molecular
process
...
5
...
5
...
4
Consequently, the parameter a is also the ratio between
the two dissociation constants, Ks//K? ; between the two
s
isomerization constants, L?/L, and the ratio between the
two association constants A? /As (Fig
...
4)
...
8
...
A Thermodynamic Constraint Due to
Complete Reversibility
It follows that due to thermodynamic equilibrium in the
cTSM, there is a constraint on the parameters
...
e
...
A more detailed description of this
constraint is given by Fersth (1999, pp
...
In the cTSM, apparent affinity constants are altered by
a conformational change at binding, as the apparent
activation constants are modulated by the binding
process
...
e
...
For convenience we will now switch from equilibrium
dissociation constants to mainly using forward association equilibrium constants, such that all system constants
become forward parameters
...
Subscript ‘ss’ indicates that the
constant is for the binding at an s-site by an agonist S
(Box 2
...
Unless needed otherwise, we will just use As for
the agonist affinity constant at the primary binding site
...
8
...
Formulation of the dC&K Reaction
Scheme and Plots
To start, we reformulate the two equations for the
dC&K reaction scheme, one for binding (Eq
...
6), and
another for function (Eq
...
5), by taking the agonist
4
See Sections 1
...
4Á 1
...
8
...
Section 6
...
2)
...
2002)
...
Further,
we arrange the equations such that the apparent
dissociation constant 0appKs, or EC50, can easily be
extracted for both binding experiments and for functional experiments
...
5
...
The maximal fraction of
liganded receptors, Bmax, is equal to unity, as the total
number of receptors becomes liganded at high [S]
...
5
...
5
...
6 are presentations of Eqs
...
9 and 5
...
Both graphs show examples of varying
constants As and L?
...
5
...
5
...
In binding for
dC&K’s model, increasing L? displaces the concentrationoccupancy curve to the left (Fig
...
5), while in functional
types for dC&K, increasing L? increases the relative
maximal response from zero to 1 (Fig
...
6)
...
5
...
9 shown in Fig
...
11B
...
1
...
5
...
4
...
5
...
Next, by equating the reaction
scheme started in Eqs
...
7 and 5
...
5
...
001
100
80
80
fractional binding (%)
100
fractional binding (%)
0
0
Here EC50 for fractional response in functional studies is
the last term in the denominator of the right hand side
fraction, equal to 1/(As ×(1'L?)) or Ks/(1'L?), while
the maximal response Rmax is equal to 1/(1'1/L?)
...
5
...
The association constant As for binding of ligand S to
the receptive unit is 100 in panel A and 0
...
The isomerization parameter L’ varies in five steps from 10Á2 (_____) to
102 (__
...
Circles indicate the EC50
...
001
B
100
80
80
fractional response (%)
fractional response (%)
100
60
40
20
0
–5 –4 –3 –2 –1
0
1
2
3
4
5
60
40
20
0
–5 –4 –3 –2 –1
0
1
2
3
4
5
log [agonist] (arbit)
log [agonist] (arbit)
Figure 5
...
Examples of plots for function in the dC&K reaction scheme
...
001 in panel B
...
__) by a factor 10 between steps
...
Compare this figure with Stephenson’s Fig
...
1
...
Also, compare with panel A in Fig
...
8
...
5
...
8
...
5
...
5
...
Transcribing reaction schemes to programs for computer software
is described in sub-chapter 9
...
Fourth is plotting of the concentration-response
curves for cTSM, as shown in Figs 5
...
8
...
1
...
1
...
5
...
Formulating the last term product in the denominator in the right hand side of Eq
...
11 with equilibrium
dissociation constant Ks instead gives the appKs 0(1'
S/Ks)/((1'S//K? ) ×L)
...
5
...
It turns out to be the same as
for the binding equation: appKs 0(1'L)/(As ×(1'
a×L)), derived in Box 5
...
After transcription of the fractional response equation
for function in cTSM (Eq
...
12) into Katz & Thesleff’s
nomenclature, it becomes identical with the K&Tequation derived for their 5th reaction scheme for
desensitization (Katz & Thesleff 1957)
...
This box is for readers with an extended interest in
details about the functional cTSM
...
In the following, we shall see how an
expression may be derived for the apparent dissociation constant, appKs, and the related EC50 of
the functional cTSM
...
1
...
Relevance
of ant-agonism in cTSM is briefly touched upon in
Box 5
...
6, and bifurcation of signaling through an
extended cTSM is mentioned in Box 5
...
7, in the
form of a cyclic three-state model (Scaramellini &
Leff 2002)
...
Chapter 5: Complex Agonism
A
B
a = 0
...
7
...
The association constant As for binding of ligand S to the receptive
unit is 1 in panels A and B, while parameter a (see Fig
...
4), is 0
...
The isomerization
parameter L varies in five steps from 10Á2 (_____) to 102 (__
...
Circles indicate the EC50
...
In Fig
...
7 of the cTSM for binding, parameter As is
kept constant at 1
...
For parameter a B1, increasing L displaces the c-o curves
to the right (Fig
...
7A), while for a 1, increasing L
pushes the c-o relations to the left (Fig
...
7B)
...
5
...
In
Fig
...
8A, L is 1/1000 and the dose-effect curve starts at
near zero
...
001 As = 1
A
maximal response (Fig
...
8B)
...
5
...
As before, As moves the dose-effect curve in a
proportional fashion along the concentration axis
(Fig
...
8B)
...
5
...
The appKss described in Box 5
...
A detail discussion of the implications of changing
cTSM parameters is presented in Section 5
...
4
...
01
B
100
80
80
fractional response (%)
fractional response (%)
100
60
40
20
0
60
40
20
0
–5 –4 –3 –2 –1
0
1
2
log [agonist] (arbit)
3
4
5
–5 –4 –3 –2 –1
0
1
2
3
4
5
log [agonist] (arbit)
Figure 5
...
Examples of plots for function in the cTSM
...
001 in panel A and 1 in panel B
...
01 in panel B as indicated by color code
...
__) by a factor 10 between steps
...
Compare
panel A with Fig
...
6
...
1
...
5
...
8 and 5
...
5
...
7 and 5
...
$appKs is the agonist concentration yielding a response midway between the level of basal activity and the maximal response
...
Expression for the appKs in the functional cTSM is derived in Section
5
...
2, and dose-response points for [S]0appKs appears in figures where it is relevant (Figs
...
8 and 5
...
A note on the terminology: in this text we have As, L, and a×As, while in the paper by Leff (1995) the same parameters are 1/KA, 1/L, and 1/KA*
...
g
...
(2002) and Buck et al
...
5
...
6
...
8
...
A Comparison Between cTSM and
HI-OSM
For novices who have the time, I highly advice going
through the details of the four-step exercise for the
cTSM as stipulated in Sections 5
...
4 and 5
...
5
...
2
...
The
FP-OSM may be expanded with an additional dimension, viz
...
The result of such an expansion
is a four-pane two-state model (FP-TSM) (Fig
...
9)
...
2
...
5
...
The FP-TSM
in Fig
...
9 also covers the so-called ATSM and the
HOTSM (Fig
...
10), both detailed further in Chapter 7
...
2
...
4
...
To obtain a good understanding of what agonism is in
the realm of TSMs, the listed exercise is paramount
...
I strongly
recommend it to all beginners
...
5
...
7
...
1
Parts of the results and conclusions in Table 5
...
5
Gero (1983) focusing on the desensitization mechanism missed the
spontaneous activity inherent in K&T5 by only equating the complex
R*S (RD) as active, not the R* (R)
...
9
...
9
...
Parameter-dependent Characterization of
Concentration-occupancy in dC&K
The maximum occupancy for the dC&K model in binding studies always reaches 100% at high ligand concentration, independent of system parameters As and L?
...
5
...
The isomerization constant, L?, only
moves the concentration-occupancy relations to the left
as it increases (Fig
...
5)
...
1)
...
Clearly as L? increases, the value of appKs decreases
identical with an increase in apparent affinity
...
5
...
Chapter 5: Complex Agonism
MR*M
MRM
MR
MR*
R*
RS
R
SR*
SR*M
SR
SRM
R*S
MRS
R*M
RM
MR*S
SRS
SR*S
FP-TSM
Figure 5
...
Reaction scheme for the four-pane two-state
model (FP-TSM)
...
The four-pane scheme in front is a one-state model (FPOSM), similar to the FP-OSM in Fig
...
4 in which the modulator
symbol ‘M’ is replaced with the interventor symbol ‘I’
...
9
...
Parameter-dependent Characterization of
Dose-response in dC&K
In the functional scheme of dC&K, the maximum
response is only dependent on parameter L?, while the
apparent affinity constant appKs is dependent on both
system constants L? and As (Table 5
...
As for the
binding studies, affinity constant As shifts the concentration-activity relations in a proportional fashion (Fig
...
6) and again as L? increases the appKs decreases,
thus left-shifting the dose-response curves and increasing the apparent affinity (Fig
...
6A'B, compare
Section 5
...
1)
...
The level of maximum response is given by 1/
(1'(1/L?)), obtained as the concentration of agonists
reaches high values
...
5
...
Since both the apparent affinity and the fractional
maximum increase with increasing values of L?, there
is a spree of apparent affinities from a value equal to
B1 to constantly
As at near-zero activity for L B
increasing values of the apparent affinity at 50% of
maximum activity as L? increases (see left-most curves
in Fig
...
6A'B)
...
For As fixed at unity,
it is easy to see that increasing L? from zero to unity
lifts the apparent affinity from As by a factor of 2,
while the apparent affinity increases unlimited as L?
increases above unity (Fig
...
6A'B)
...
10
...
5
...
The partial models are: the ternary-complex model (TCM), the four-pane one-state
model (FP-OSM), the cyclic two-state model (cTSM), the allosteric two-state model (ATSM), and the homotropic two-state model
(HOTSM)
...
122
Part II: Two-State Models: Complex Agonism and Modulation
Furthermore, notice the similarities between the
dependence on L? of dose-responses for this dC&K
model (Figs
...
3B and 5
...
3
...
5
...
11B)
...
5
...
Compare also the effects here of varying L? on the
apparent affinity with the effect of varying L? ( 0a×L)
on the apparent affinity in the cTSM in Section 5
...
4
(Fig
...
8)
...
This is discussed further in Section 5
...
5
...
9
...
Parameter-dependent Characterization of
Dose-response in cTSM
5
...
3
...
9
...
1, the maximum occupancy in the
cTSM at high ligand concentration always reaches 100%,
independent of values for the three system constants, As,
L and a (Fig
...
7)
...
1)
...
5
...
11 for changes in
parameters a and L
...
This is not observed when
As is kept at 1 in Figs
...
7 and 5
...
Now all three constants are intrinsic or microscopic
constants
...
11), they are ‘microscopic’ constants
...
5
...
For a1, increasing
L results in a left-shift of the c-o curves with appKs
moving from 1/As towards 1/(a ×As) (Fig
...
7B)
...
5
...
Therefore, when L is fixed, the
apparent affinity increases with increasing values of a;
confer with the expression for binding appKs in 5
...
Dose-response curves for the cTSM in its functional
version have two varying levels of activity
...
Thus, response at the first level is given by 1/(1'(1/L))
(Table 5
...
5
...
12)
...
For an isomerization constant equal to unity,
L 01, the spontaneous activity is equal to 50% of the
potentially possible 100% activity (Figs
...
8B and 5
...
The second level of activity (SL) at high concentration
of a ligand is the maximal response level for that
particular ligand and given by 1/(1'(1/(a ×L))) (Table
5
...
5
...
Note, L and a are both dependent on
the receptor and the ligand
...
1
L = 10
100
80
80
fractional binding (%)
fractional binding (%)
100
60
40
20
60
40
20
0
0
–5 –4 –3 –2 –1
0
1
2
log [agonist] (arbit)
3
4
5
–5 –4 –3 –2 –1
0
1
2
3
4
5
log [agonist] (arbit)
Figure 5
...
Binding aspects of cTSM
...
__) by a factor 10
between steps
...
1 in panel A and 10 in panel B
...
Compare
with Figs
...
5 and 5
...
Chapter 5: Complex Agonism
As = 1 with a = 0
...
01 and with a = 10 or = 0
B
100
80
80
fractional response (%)
100
fractional response (%)
123
60
40
20
0
60
40
20
0
–5 –4 –3 –2 –1
0
1
2
3
4
5
log [agonist] (arbit)
–5 –4 –3 –2 –1
0
1
2
3
4
5
log [agonist] (arbit)
Figure 5
...
Functional aspect of the cTSM
...
__) by a factor 10 between steps
...
1
...
Parameters As is either 100 or 0
...
01 or zero as indicated by color code
...
5
...
Circles indicate the EC50
...
5
...
8
...
5
...
SL is not dependent on the intrinsic affinity
constant As
...
5
...
Similar to L and a, As is also dependent on
both the receptor and the ligand
...
1) demonstrates that the difference between the two levels is
determined by parameters a and L (Fig
...
12)
...
5
...
However, this
also means that the second ‘maximum’ response level
(SL) due to a high ligand concentration is above, at, or
below the initial ‘spontaneous’ response level (FL)
exclusively determined by a, as this parameter varies
from above to below unity (Figs
...
8 and 5
...
Therefore, for a 1, the second level is above the initial level,
for a01: SL 0FL, and for a B1 the ‘maximum’ level SL
is below the spontaneous level FL (Figs
...
8 and 5
...
This functional behavior of the cTSM due to variations in system constant a is exactly related to the
behavior of agonists, ant-agonists, and inverse agonists
...
If after the addition of a
ligand, the two levels are identical with no change
in response, a01, but the compound changes
the response induced by agonists, then it is an antagonist (neutral ant-agonist by definition)
...
5
...
5
...
1) and by inspecting their reaction
schemes (Figs
...
3B and 5
...
6
...
The
major difference between the two models is the initial
level of response
...
Therefore, functional dose-response relations for
the two models may resemble each other when parameter L in the cTSM has a low value, thus suppressing
the first level of response for the cTSM towards zero
...
5
...
8A)
...
1)
...
Parameter a for the cTSM has taken over
the effects of the L? constant on appKs of the dC&K
reaction scheme (compare Figs
...
6 and 5
...
The
differences between the two schemes enter when L is
124
Part II: Two-State Models: Complex Agonism and Modulation
not significantly less than unity
...
Thus, although the two maximum levels are
comparable, that is 1/(1'(1/L?)) is comparable to 1/
(1'(1/(a×L))), by keeping a×L nearly equal to L?, the
initial levels are now different, zero for the dC&K versus
1/(1'(1/L)) for the cTSM (Figs
...
6 and 5
...
For
LB
B1, i
...
, R* near zero, then the cTSM actually
becomes a dC&K model (confer with reaction schemes
in Figs
...
3B and 5
...
Therefore, for L B
B1 the cTSM
also describes the Stephenson model in Section 1
...
5
(compare Figs
...
8A and 1
...
5
...
6
...
Therefore, with
L and a obtained, the system is left with one independent variable to be assessed, parameter As
...
Thus, all three parameters may be assessed in such systems when analyzing
experimental data
...
What is more, these studies
may also require tests for spare receptors to be excluded
by alkylating agents before an analysis for As and a can
be undertaken
...
If
values of the isomerization constant L are 1, it will be
difficult to separate the microscopic constants
...
This process has L values well above 30,
preventing the separation of As and L (Leff 1995;
Colquhoun 1998)
...
9
...
Extraction of Parameter Values from the
Functional dC&K
It will be possible to extract relative parameter values for
As and L? based on dose-response profiles of full and
partial agonists from the functional form of the dC&K
model, where there is no spontaneous activity level, but
for which a maximum level Rmax can be established as an
absolute value
...
9
...
What is a Pure Binding Effect and a Pure
Efficacy in Terms of Mechanisms?
One may question if it is possible to vary a single
parameter in the functional or binding regime of either
the dC&K model or the cTSM, that will only affect either
affinity, i
...
, potency, or efficacy (Colquhoun 1998)
...
All parameters
are thus involved in the ‘potency’ of binding, while the
‘efficacy’ of binding is independent of variations in
either parameter (Table 5
...
From Table 5
...
Thus, in the functional theory of
both models, As is a pure parameter for apparent affinity
variations, but not the only parameter affecting affinity
(Table 5
...
Variations in both L’ and L ×a also affect the
apparent affinity
...
Therefore,
pure binding effects may be seen by varying As solely,
while, due to parameter variations without affinity
effects, pure efficacy effects are impossible
...
9
...
Extraction of Parameter Values from
Binding Studies
...
These two states are T0 and R0 when Hb is un-liganded
...
2
...
In pure binding experiments, increased ‘efficacy’ is part
of an isomerization to a higher ‘affinity’ state
...
1955; Edelstein 1975) and represent apparent affinities or
efficacies (Colquhoun 1998)
...
The total change in apparent
binding affinity is thus 703, some 3
...
In
reality, it is merely 300-fold (Table 5
...
Table 5
...
Symbols for the un-liganded conformations of twostate models
Two-state terminology
‘to have identity,
is to be alienated’
Receptors
un-liganded
Hemoglobin
un-liganded enzymes
‘Reactive’
‘Active’
R (non-deformed)
R* (deformed)
T0 (tense)
R0 (relaxed)
Chapter 5: Complex Agonism
Table 5
...
The relative affinity constants for O2 binding to
hemoglobin
No
...
7
7
...
For the
other association constants, see Box 2
...
5
...
The General Embedded Load Model
...
5
...
1
...
Hence, symbols for the dC&K model are
listed here for the receptor conformations, the ligand,
and the system constants, while corresponding terminology for symbols and responses from the B&L model
appear in parenthesis when relevant
...
10
...
Symbols for the dC&K regime:
R
RS
free receptive unit (R), and S an agonist
receptive unit bound with an agonist in
a reactive state
R*S
receptive unit bound with an agonist in
an active state
Rtot
sum of all possible receptor conformations in the system
R1
sum of active receptors needed for
tot
maximal response
ar
actual response
TR
total or maximal response, Rmax
L?
isomerization constant for liganded
receptive unit
Coefficients defined in B&LÁnot in dC&K:
(A)
(AR)
see
below
(R0)6
(E)
(Em)
(t)
125
the value of RS (AR) that elicits half-maximal
effect
...
R 0 / defined as the ‘transducer ratio’ 0t
...
10
...
R*S is equal to Stephenson’s stimulus ‘St ’ and
since the fractional response ar/TR is a function of
this stimulus, we have that ar/TR 0f (R*S)
...
10
...
Formulations of del Castillo & Katz and
Black & Leff Models
For the dC&K reaction scheme we have already derived
its formulation (see Eq
...
10), repeated here in a slightly
different form:
response
ar
S × L?
0
0
;
total response TR S × (1 ' L?) ' Ks
(5:13)
while a lightly reformulated B&L expression based on
their Eq
...
Examples of the B&L model are
shown in Fig
...
13
...
5
...
The
B&L model is derived based on an argument of logical
deduction, namely that the fractional effect E/Em is
related to the agonist concentration [A] by a hyperbolic
relation as well as the fractional occupancy AR/R0, which
is also a rectangular hyperbolic function of the agonist
concentration
...
13
...
7 The
mathematical approach in B&L is exemplified moreover
by use in general of the describing term ‘operational’ for
their models, including a subsequent, hasty introduction
of Hill’s exponentiation
...
However, this is incorrect, as
¨
we have already seen in Section 5
...
2
...
Let us see why
...
9
...
7
See Paton and Rothschild (1965) on embedded loads resulting in a
single load relation
...
13
...
The embedded load formulation is indicated on
the graph
...
The occupied receptors, here designated ‘St ’, is a fraction of the total receptors R0 and formulated
as: St 0R0*S/(S'Kss) in which S is the ligand concentration
...
Dissociation constant Kss is varied in
5 steps from 10Á2 (_____) to 102 (__
...
__) by a factor 10 between steps
...
The embedded load function is
itself a load function (Paton & Rothschild 1965)
...
5
...
3
...
On face value, receptor
reserve seems axiomatic in the B&L formulation, where
by diminution of Rtot (R0) in the transducer ratio t (cf
...
10
...
5
...
Hence, manipulating the size of R0 appears as a direct
tuning of the receptor reserve
...
Thus, even with a receptor
reserve less than sufficient for regular maximal
response, according to the formulation, we can decrease
KE, keep the parameter t constant, and regain a former
maximal response
...
How should KE be conceived?
In this context and to answer that question, parameter
L? can be regarded as a product of an absolute
parameter R0 and a relative constant 1/KE, where KE is
a virtual factor while L? has a physical meaning
...
Efficacy coefficients e or L?
are not mixed up with numbers of receptors, Rtot or R0,
as in the transducer ratio R0/KE, which is also an efficacy
coefficient
...
However, the
tot
pool of receptors that can be activated and the efficacy
coefficient are kept separate in the expression for
efficacy
...
First, when
Rtot is reduced to equal R1 ; then there is no receptor
tot
reserve
...
The B&L transtot
ducer ratio t is equal to L? or Stephenson’s e and
determines the maximum fractional response by
E/Em 0ar/TR 01/(1'1/t)01/(1'1/L?) (Fig
...
13)
...
10
...
Furchgott’s Intrinsic Efficacy
Furchgott derived his formulation for spare receptors
based on embedded load equations as later copied in
the operational model by Black and Leff (Furchgott
1955, 1964; Black & Leff 1983)
...
Thus ‘intrinsic efficacy’ o is equal to e/
Rtot, to L?/Rtot, or if you will, to 1/KE
...
On experimental extraction of values for o see, for
instance, MacKay (1977)
...
Operational modeling may be elaborated further,
involving Furchgott’s ‘efficacy’, encompassing his intrinsic efficacy coefficient o, and B&L’s ‘operational
efficacy’ subsuming their transducer ratio coefficient t
(Trzechiakowski 1999a,b; Frigyesi & Hossjer 2005
Kenakin 2007)
...
e
...
tot
A
MRM
MR*M
MR
MR*
RM
R*
R*S
SR*
SR*M
In the writings of Furchgott (1966) and Black and Leff
(1983), it can be observed that there is no clean
differentiation, as there should be, between Stephenson’s ‘efficacy’ as a property and ‘efficacy’ as a coefficient,
e
...
Also, in the general operational model,
according to Black and Leff the transducer ratio links the
number of receptors to the ‘intrinsic efficacy’ of the
agonist
...
Sections 1
...
4 and 5
...
2)
...
5
...
6
...
10
...
Jargon or Misuse of ‘Efficacy’ for ‘Efficacy
Coefficient’
MR*S
MRS
R*M
127
SR*S
In my opinion, the solution to Stephenson’s search is
simply the dC&K model, and to make Stephenson’s
‘efficacy’ operative I suggest a clear differentiation
between the property ‘efficacy’ (Stephenson 1956,
p
...
5
...
Induction Versus Selection
SRM
SR
B
SRS
MR*M
MR*
bL
MRM
MR
MRS
cAss
Amm
R
dacA ss
R*M
cAmm
MR*S
dabL
bAmm
R*
b’Ams
L
RM
FP-TSM
dbcAmm
aAss
R*S
aL
d’bc’Ams
Ass
RS
SR*M
SR*
d’ac’Ass
SR*S
Ams
b’L
SRM
SR
c’Ass
c’Ams
SRS
d’ab’L
FP-TSM
Figure 5
...
The combined allosteric two-state and homotropic two-state model
...
Panel A without
system constants, and panel B with system constants
...
11
...
Who is Right?
The title to this sub-chapter, ‘induction versus
selection’, covers an age-old problem that has reappeared many times
...
1965) and Koshland-sequential
induction model (Koshland 1966; Harber & Koshland 1967) for protein activation
...
Changeux
has argued once again for the selection model by
observing that channels can switch between closed
and open states in the absence of a ligand, i
...
,
demonstrate spontaneous activity, ‘which is readily
explained in terms of a selection mechanism’
(Changeux 2004, p
...
Meanwhile, his argument
is irrelevant for the question of what happens when
128
Part II: Two-State Models: Complex Agonism and Modulation
a ligand is introduced
...
5
...
2
...
The scheme
for conformational induction may be written as:
(1) R'S X R'S X R1S:
We have already met this scheme in the dC&K model
(sub-chapter 5
...
5
...
3
...
The active state has a higher affinity for the agonist
than the reactive state
...
e
...
This increases the activity of the receptive unit by
conformational selection
...
5
...
The two schemes tells us that we can go from R to R*S
via two pathways
...
They are interlocked conceptually as well
as in reality (sub-chapter 5
...
5
...
4
...
1965) and sequential action (Koshland et al
...
In Monod’s model, the choice is a conformational selection, whereas in Koshland’s model the choice
is for the conformational induction
...
When a number of ligands one by one each
induces a conformational change on binding to a
receptive system, it is a sequential model
...
This was also assumed in the dC&K
model from 1957
...
The spontaneous
activity in the absence of a ligand, as mentioned above
by Changeux, was never excluded from the modeling by
Koshland and coworkers (Harber & Koshland 1967),
although ‘induced fit’ became synonymous with ‘Koshland’ (Bennett & Steitz 1978)
...
3)
...
11
...
The Dilemma Between Selection and
Induction in Pharmacology
The induction-selection schism has been a conceptual
dilemma in pharmacology as well
...
Burgen (1981) revived the discussion about the mechanism of how agonists increase the number of active
receptors Á was it by induction or was it by selection? The
question arose again in the 1990s as it was realized that
receptors also had to be considered as spontaneously
active in an agonist-independent manner (Costa & Herz
1989)
...
Kenakin summarized the
issue by a review on the subject, concluding that both
conformational induction and conformational selection
are possible mechanisms (Kenakin 1995b)
...
Instead of a direct response to Bruns, Kenakin
introduced the multi-state receptor and concluded that
Chapter 5: Complex Agonism
there were no dichotomy Á rather induction and
selection ‘are extremes of the same mechanism’ (Kenakin 1996) or ‘of a continuum’ (Lutz & Kenakin 1999,
Chapter 3
...
64Á68) of receptor conformations
...
2000; Kenakin & Onaran 2002)
...
5
...
6
...
When the two
reaction schemes in Section 5
...
1 are combined, they
constitute the cTSM reaction scheme (Haber & Koshland 1967), but not the original MWC model (Fig
5
...
The cTSM reaction scheme is thermodynamically the simplest cyclic or fully reversible two-statemodel
...
Thus, the quest for a
choice between supremacy of either induction or selection at equilibrium is a futile endeavor
...
11
...
Solving the Induction Versus Selection
Problem for Enzymes with Rate Kinetics
When a system is perturbed away from equilibrium, one
might expect that the two mechanisms, induction and
selection, can be studied separately, thus yielding a
solution to the induction-versus-selection (i-vs-s) problem
...
Halford studied
the activation of the alkaline phosphatase enzyme for
which a substrate-enzyme complex is formed by a
conformational change and/or by selection of the active
conformational form of the enzyme
...
The schism
about induction before selection or vice versa is still
debated by enzymologists (Gutfreund 1995; Changeux &
Edelstein 2005; Wang et al
...
2000)
...
217Á219; Kumar et al
...
129
5
...
8
...
5
...
Further, according to
Burns, for allosteric enhancers in conformational selection, one could specifically predict an acceleration of
agonist association rate constant k1 in Fig
...
4, without
an effect on the dissociation rate constant
...
Let us look at Bruns’ argument
...
5
...
This shift in process rate may be obtained by
either an increase in k1 or a decrease in k(1 in the
reaction scheme, and for that matter by an increase in
the isomerization constants L? and L
...
It is nonsense, possibly
due to a mix-up of rates and equilibrium conditions
...
2003, Le et al
...
2004)
...
The belief
remains that dynamic studies will be able to differentiate
between the two concepts (Gether & Kobilka 1998;
Gether 2000; Kobilka & Gether 2002; Kobilka 2002;
Urban et al
...
2004, 2005; Giraldo 2004;
Feng et al
...
2005; Sosa-Peinado &
Gonzalez-Andrade 2005; Ellis et al
...
2006; Granier et al
...
2007), although it
is realized that the schism is difficult to get rid off (Peleg
et al
...
Some groups convincingly present substrate
binding as induced fit or secondary induced fit, but
based on static X-ray images (Wang et al
...
5
...
9
...
In
return, dynamic complementarities emerge, and the
complementarity problem, which is virtual, remains
...
The answer to the question about i-vs-s does not boil
down to resolving which process is the fastest, the preequilibration between the two states or the binding
process proper
...
This is also my understanding
...
5
...
10
...
In studying biomedical and industrial drugs
as well as pharmaceuticals during the drug discovery and
development process, what is of interest and useful for
in vivo application is the quantitation of on- and off-rates
in chiralty, of racemic shifts, and of ligand-receptor
interactions including observations in vitro from kinetic
and dose-response experiments and their analysis (Giraldo 2004; Baranczewski et al
...
In the theoretical field, the i-vs-s quandary has left our
modeling with a complexity we refer to as ‘microscopic’,
i
...
, non-separable system constants
...
11
...
Conclusion on Complementarity
In our cTSM, induction and selection are but two
aspects of the same phenomenon
...
Box 5
...
1
...
A forward constant
isomerization constant for unliganded receptors
...
It is the ligand concentration for which the response is
midway up between the maximum level and the spontaneous level of activity (Box 5
...
This middle level of response we may call pssE50
is a new constant
...
Convince yourself that this
maximum level is identical with the maximum level for functional cTSM listed in Table
5
...
Thus: pssE50 01/2 ×[(L/(L'1/a))'(L/(1'L))]
Chapter 5: Complex Agonism
131
Box 5
...
2
...
The half-way response pssE50 on the actual
d-r curve is shown in Box 5
...
Inserting appKs for S in the expression for fractional response of
the cTSM (Eq
...
12b) yields an equation for the midway response pssEC50 equal to L/(L'Q); in which
Q0(1'As ×appKs)/(1'a ×As ×appKs)
...
Box 5
...
1
...
1
figure
...
Box 5
...
3
...
Box 5
...
e
...
Values for
lim pssEC50 are listed in column 2 of Box 5
...
The limiting values for appKs may be obtained from
Eq
...
1-2
...
1 table for all values of L
...
1 table for general and specific cases
...
1 table for
a01 and shown in Box 5
...
From Box 5
...
Due to natural reciprocity, or thermodynamic equilibrium, in the equilibrated cTSM, a and L are bound
together in determining the efficacy level in the presence of an agonist, see columns 1 and 2 in Box 5
...
132
Part II: Two-State Models: Complex Agonism and Modulation
Box 5
...
4
...
In Nature, where receptor-guided regulatory
mechanisms have evolved, the most abundant type of tabulated cases is the one in Box 5
...
This case is illustrated in Fig
...
8
...
Further analysis will show that partial agonists operate in the range of 0
...
For partial
agonism to occur in a classical display, based on functional cTSM, L must be much smaller than 1, L B
B1,
while a must be larger than 1, a 1 (Fig
...
8)
...
01 in many natural systems
without spontaneous activity, we can conclude that a must be larger than 10 when partial agonism is observed
(Fig
...
8)
...
Typically, thus,
for the full agonist a is 100 and efficacy may be said to be dependent on the product of a ×L, see Rmax
for functional cTSM response in Table 5
...
As a ×L increases above 0
...
5
...
When a×L
10 complete agonism
is obtained
...
Stated in a different manner, for a series of homologous drugs to display partial agonism (Nickerson 1956)
in cTSMs, the requirements are that a through the series of less and less efficacious ligands decreases towards
a value such that a ×L become B0
...
See the sweep of theoretical curves for partial agonist as depicted in
Fig
...
8
...
Additionally, the activating conformational change is the
most likely event for the liganded conformation compared with the non-liganded form of the receptor
...
5
...
When we trust the cTSM to be the underlying reaction scheme for our experimental observations at
equilibrium, it is justified to claim that the agonist stabilizes the active conformation, as it is to state that the
binding of an agonist to the non-active receptor conformation is that, which induces the conformational
change to an active state of the liganded receptor (confer sub-chapter 5
...
Box 5
...
5
...
This ought to trigger your curiosity and pose the
question: is the cTSM really a relevant role-model for what goes on in the real world? Meanwhile, I would
ˆ
formulate the question in a different way
...
Receptor conformations and natural ligands that do not follow the 0
...
Likewise the condition, that L B
B1, is also fixed by evolution in most
natural systems Á in particular when we believe in the cTSM
...
In case there are spare receptors, the
appAs and the true As deviate
...
1
...
Ant-agonists and the cTSM
Box 5
...
7
...
His paper is certainly worth consulting
...
Leff and Scaramellini et al
...
1997; Scaramellini & Leff 1998, 2002)
...
See Giraldo (2004) for another
approach to three-state models
...
1
...
Limiting values of pssEC50 and appKs in the cyclic two-state model
Table 0
...
Special cases
For L B
B1
a00
a0 $
a01
lim pssE50
lim appKs
L/2
½
L
1/As
1/(As ×a ×L)
‘1/As’
$The natural situation
...
Special cases
For L 1
a00
a0
a01
lim pssE50
lim appKs
½
1
1
L/As
1/(As ×a)
‘1/As’
Table 3
...
1
...
Principal plot of the functional cTSM
...
The EC50 is given by a level mid-way between the basic and the maximum levels, pssE50 0½ ×[1/
(1'1/L)'1/(1'1/aL)]
...
The apparent dissociation constant appKs is
equal to (Ks) ×[(1'L)/(1'aL)]
...
2, As 00
...
(B) Parameter values are a 030, As 00
...
A
Q = (1 + As·appKs) / (1 + a·As·appKs)
100
relative response (%)
80
a·L / (1 + a·L)
60
a>1
L/(L + Q)
40
½ · [a·L / (1 + a·L) + (L / (1 + L)]
L / (1 + L)
20
a=1
a<1
0
–3
–2
–1
appKs = (1 + L) / [(As·(1 + a·L)]
0
1
2
3
log [agonist] (arbit)
Q = (1 + As·appKs) / (1 + a·As·appKs)
B
100
relative response (%)
80
L>1
60
L /(L + Q)
a·L / (1 + a·L)
L=1
40
½ · [a·L / (1 + a·L) + (L / (1 + L)]
20
0
–3
L<1
L / (1 + L)
–2
–1
appKs = (1 + L) / [(As·(1 + a·L)]
0
1
2
log [agonist] (arbit)
3
Chapter 5: Complex Agonism
REFERENCES
Abramowitz J, Iyengar R & Birnbaumer L
...
Evaluation of basic activity states after removal of endogenous
GDP and interpretation of nucleotide regulation and hormone
activation in terms of a two-state model
...
Allen DW, Guthe KF & Wyman J Jr
...
J Biol Chem 187: 393Á 410, 1950
...
Affinity and intrinsic activity in the theory of competitive
¨
inhibition
...
Problems and theory
...
Baranczewski P, Stanczak A, Sundberg K, Svensson R, Wallin A, Jansson
J, et al
...
Pharmacol Rep 58: 453Á 472, 2006
...
Glucose-induced conformational change in
yeast hexokinase
...
Bindslev N
...
BMC
Pharmacol 4: 11, 2004
...
Transient and steady state kinetics of the interaction of guanyl
nucleotides with the adenylyl cyclase system from rat liver plasma
membranes
...
J Biol Chem 255: 3542Á 3551, 1980
...
Operational models of pharmacological agonism
...
Blum JJ
...
Arch Biochem Biophys 55: 486Á 511, 1955
...
Quantitative analysis of the binding of
ligands to their receptors
...
Boeynaems JM & Dumont JE
...
Amsterdam:
Elsevier, 1980
...
Physiological effects of inverse agonists in transgenic mice
with myocardial overexpression of the beta 2-adrenoceptor
...
Botts J
...
Trans Faraday Soc 54: 593Á 604, 1958
...
Analytical description of the effects of modifiers
and of enzyme multivalency upon the steady state catalyzed
reaction rate
...
Botts J & Drain GF
...
The committee of muscle chemistry of
Japan
...
1958
...
Conformational induction versus conformational selection:
evidence from allosteric enhancers
...
Buck M, Xu W & Rosen MK
...
J Mol Biol 338: 271Á 285, 2004
...
Conformational changes and drug action
...
Chang Y & Weiss DS
...
Biophys J 77:
2542Á 2551, 1999
...
Desensitization
mechanism of GABA receptors revealed by single oocyte binding
and receptor function
...
Changeux J-P
...
Cambridge: Belkamp Press of Harvard University
Press, 2004
...
Allosteric proteins: from regulatory enzymes to receptors Á
personal recollections
...
Changeux JP & Edelstein SJ
...
Science 308: 1424Á 1428, 2005
...
Considerations in the evaluation of inverse agonism and
protean agonism at G protein-coupled receptors
...
Christopoulos A & Kenakin T
...
Pharmacol Rev 54: 323Á 374, 2002
...
Allosteric interactions
at muscarinic cholinoceptors
...
Clark AJ
...
4, 1st ed
...
Clark RB, Knoll BJ & Barber R
...
Trends Pharmacol Sci 20: 279Á 286, 1999
...
The elusive nature of intrinsic efficacy
...
Colquhoun D
...
New York: Alan R
...
, 1987
...
Binding, gating, affinity and efficacy: the interpretation
of structure-activity relationships for agonists and of the effects of
mutating receptors
...
Colquhoun D
...
Colquhoun D & Farrant M
...
The binding
issue
...
Costa T & Herz A
...
Proc Natl Acad
Sci USA 86: 7321Á 7325, 1989
...
Structure of the transition state
of gating in the acetylcholine receptor channel pore: a phi-value
analysis
...
De Haen C
...
J Theor Biol 58: 383Á 400, 1976
...
A ternary complex model
explains the agonist specific binding properties of the adenylate
cyclase coupled beta-adrenergic receptor
...
del Castillo J & Katz B
...
J Physiol 146: 369Á 381, 1957
...
‘Induced-fit’ mechanism for catecholamine binding to the beta2adrenergic receptor
...
Downing SS, Lee YT, Farb DH & Gibbs TT
...
Br J
Pharmacol 145: 894Á 906, 2005
...
Principles: a model for the allosteric interactions between
ligand binding sites within a dimeric GPCR
...
Edelstein SJ
...
Annu Rev
Biochem 44: 209Á 232, 1975
...
Kinetics of reaction control and information transfer in
enzymes and nucleic acids, In: Fast Reactions and Primary Processes
in Chemical Kinetics, edited by Claesson S
...
Stockholm: Almquist & Wiksell, 1967
...
Conformational
induction is the key process for activation of the AT1 receptor
...
Eyring H
...
J Chem Phys 3:
107Á 115, 1935
...
The electromotive action of acetylcholine at the motor endplate
...
) 111: 408Á 422, 1950
...
Single mutations at Asn295 and
Leu305 in the cytoplasmic half of transmembrane alpha-helix
domain 7 of the AT1 receptor induce promiscuous agonist
specificity for angiotensin II fragments: a pseudo-constitutive
activity
...
Fersht A
...
A Guide to Enzyme
Catalysis and Protein Folding
...
, 1999
...
Direct observation in solution of
a preexisting structural equilibrium for a mutant of the allosteric
aspartate transcarbamoylase
...
Fong TM
...
Cell Signal 8: 217Á 224, 1996
...
Kinetic aspects of regulation of metabolic processes
...
J Biol Chem 245: 5788Á 5799, 1970
...
The pharmacology of vascular smooth muscle
...
Furchgott RF
...
Adv Drug Res 3: 21Á 55, 1966
...
Desensitization, two-state receptors and pharmacological
parameters
...
Gether U
...
Endocr Rev 21: 90Á 113, 2000
...
G protein-coupled receptors
...
Mechanism
of agonist activation
...
Gibb AJ
...
In:
Textbook of Receptor Pharmacology, edited by Foreman JC &
Johansen T
...
Giraldo J
...
FEBS Lett 256: 13Á 18, 2004
...
The catalytic power of
enzymes: conformational selection or transition state stabilization? FEBS Lett 580: 2170Á 2177, 2006
...
Theory of Rate Processes, 1st ed
...
, 1941
...
The ionic permeability of the red cell membrane
...
Gonzalez-Lebrero RM, Kaufman SB, Montes MR, Norby JG, Garrahan
PJ & Rossi RC
...
I
...
J Biol Chem 277: 5910Á 5921, 2002
...
Structure and conformational changes in the C-terminal domain
of the beta2-adrenoceptor: insights from fluorescence resonance
energy transfer studies
...
Gutfreund H
...
Receptors, Transmitters and
Catalysts, 1st ed
...
Haber JE & Koshland DE Jr
...
Proc Natl Acad Sci USA 58: 2087Á 2093, 1967
...
Escherichia coli alkaline phosphatase
...
Biochem J 126: 727Á 738, 1972
...
Modeling the functional effects of allosteric modulators at
pharmacological receptors: an extension of the two-state model of
receptor activation
...
Hille B
...
Sunderland:
Sinauer Associates, 2001
...
A quantitative description of membrane
current and its application to conduction and excitation in nerve
...
) 117: 500Á 544, 1952
...
Partial agonists, full agonists, antagonists:
dilemmas of definition
...
Hull WE, Halford SE, Gutfreund H & Sykes BD
...
Biochemistry 15: 1547Á 1561, 1976
...
Agonist induction and
conformational selection during activation of a G-proteincoupled receptor
...
Iyengar R, Abramowitz J, Bordelon-Riser M & Birnbaumer L
...
Nucleotide effects and analysis in terms of a simple two-state model for the
basic receptor-affected enzyme
...
Jacobs S & Cuatrecasas P
...
Application to insulin
...
Jenkinson DH
...
Trends Pharmacol Sci 12: 53Á 54, 1991
...
Importance of sequence specificity for predicting protein
folding pathways: perturbed Gaussian chain model
...
Katz B & Thesleff S
...
J Physiol 138: 63Á 80, 1957
...
Agonists, partial agonists, inverse agonists and agonist/
antagonists? Trend Pharmacol Sci 8: 423Á 426, 1987
...
On the definition of efficacy
...
Kenakin T
...
Kenakin T
...
I: Mechanisms of efficacy and
receptor promiscuity
...
Kenakin T
...
Trend Pharmacol Sci 17: 190Á
191, 1996
...
Pharmacological Analysis of DrugÁreceptor Interaction, 3rd ed
...
Kenakin T
...
Annu Rev
Pharmacol Toxicol 42: 349Á 379, 2002
...
Efficacy as a vector: the relative prevalence and paucity of
inverse agonism
...
Kenakin T
...
Kenakin T & Onaran HO
...
Kenakin T, Morgan P & Lutz M
...
Biochem Pharmacol 50: 17Á 26, 1995
...
The evolution of drugÁ
receptor models: the cubic ternary complex model for G
protein-coupled receptors
...
The Pharmacology of Functional, Biochemical, and Recombinant Receptor
Systems, 1st ed
...
Kobilka BK
...
J Pept Res 317Á 321, 2002
...
Use of fluorescence spectroscopy to study
conformational changes in the beta 2-adrenoceptor
...
Koshland DE Jr
...
Proc Natl Acad Sci USA 44: 98Á 104, 1958
...
Crazy, but correct
...
Koshland DE Jr, Nemethy G & Filmer D
...
Biochemistry 5: 365Á 385, 1966
...
Modelling of promiscuous
receptor-Gi/Gs-protein coupling and effector response
...
Chapter 5: Complex Agonism
Kumar S, Ma B, Tsai C-J, Sinha N & Nussinov R
...
Protein Sci 9:
10Á 19, 2000
...
The chemical kinetics of enzyme action
...
Le MT, Vanderheyden PM, Szaszak M, Hunyady L, Kersemans V &
Vauquelin G
...
Biochem Pharmacol 65:
1329Á 1338, 2003
...
The two state model of receptor activation
...
Leff P & Scaramellini C
...
Trends Pharmacol Sci 19: 13, 1998
...
A three-state receptor
model of agonist action
...
Lefkowitz RJ, Cotecchia S, Samama P & Costa T
...
Trends Pharmacol Sci 14: 303Á 307, 1993
...
Mutations remote
from the human gonadotropin-releasing hormone (GnRH)
receptor-binding sites specifically increase binding affinity for
GnRH II but not GnRH I: evidence for ligand-selective, receptoractive conformations
...
Lutz M & Kenakin T
...
Chichester: Wiley & Sons, 1999
...
A critical survey of receptor theories of drug action
...
Berlin: SpringerVerlag, 1977
...
Inverse agonism and the regulation of receptor
number
...
Milligan G, Bond RA & Lee M
...
Monod J, Wyman J & Changeux J-P
...
J Mol Biol 12: 88Á 118, 1965
...
Receptor occupancy and tissue response
...
Onaran HO & Costa T
...
Ann N Y Acad Sci 812: 98Á 115, 1997
...
The effect of varying calcium
concentration on the kinetic constants of hyoscine and mepyramine antagonism
...
Peleg G, Ghanouni P, Kobilka BK & Zare RN
...
Proc Natl Acad
Sci USA 98: 8469Á 8474, 2001
...
X-ray analysis of haemoglobin
...
Rang HP
...
Br J
Pharmacol 147: S9Á S16, 2006
...
Energetics of heterotropic cooperativity
between alpha-naphthoflavone and testosterone binding to
CYP3A4
...
Robertson MJ, Dougall IG, Harper D, McKechnie KC & Leff P
...
Trends Pharmacol Sci 15: 364Á 369, 1994
...
The determination of the
individual equilibrium constants of the four intermediate reactions between oxygen and sheep haemoglobin
...
Rusch D & Forman SA
...
Anesthesiology 102: 783Á 792, 2005
...
Gating allosterism at a single class of
etomidate sites on alpha1beta2gamma2L GABA A receptors
accounts for both direct activation and agonist modulation
...
137
Samama P, Cotecchia S, Costa T & Lefkowitz RJ
...
Extending the
ternary complex model
...
Scaramellini C & Leff P
...
Ann N
Y Acad Sci 861: 97Á 103, 1998
...
Theoretical implications of receptor coupling
to multiple G proteins based on analysis of a three-state model
...
Schwartz TW & Holst B
...
J Recept Signal Transduct Res 26:
107Á 128, 2006
...
Enzyme kinetics
...
New York: Wiley & Sons (reissued
1993), 1975
...
Na-pump (cited in Glynn 1955 op
...
Dissertation, Cambridge,
Cambridge University, 1954
...
Timing is everything the role of
kinetics in G protein activation
...
Sosa-Peinado A & Gonzalez-Andrade M
...
Biochemistry 44: 15083Á 15092,
2005
...
A modification of receptor theory
...
Strange PG
...
Trends Pharmacol Sci 19:
85Á 86, 1998
...
Mechanisms of inverse agonism at G-protein-coupled
receptors
...
Surya A, Stadel JM & Knox BE
...
Trends Pharmacol Sci 19: 243Á 247, 1998
...
Sequential binding of agonists to the beta2 adrenoceptor
...
J Biol Chem 279:
686Á 691, 2004
...
Probing the beta2 adrenoceptor binding site with catechol reveals
differences in binding and activation by agonists and partial
agonists
...
Thesleff S
...
Acta Physiol
Scand 34: 386Á 392, 1955
...
Theories and predictions of models
describing sequential interactions between the receptor, the GTP
regulatory unit, and the catalytic unit of hormone dependent
adenylate cyclases
...
Tonomura Y & Watanabe S
...
Nature 169: 112Á 113,
1952
...
Modelling the consequences of
receptor-G-protein promiscuity
...
Urban JD, Clarke WP, von Zastrow M, Nichols DE, Kobilka B,
Weinstein H, Javitch JA, Roth BL, Christopoulos A, Sexton PM,
Miller KJ and Mailman RB
...
J Pharmacol Exp Ther 320:
1Á 13, 2007
...
Limitations of molecular pharmacology
...
Adv Drug Res 3: 189Á 234, 1966
...
Efficacy
...
Eur J
Pharmacol 320: 223Á 231, 1997
...
Structural basis for
ordered substrate binding and cooperativity in aspartate transcarbamoylase
...
Wang Y, McMahon AP & Allen BL
...
Curr Opin Cell Biol 19: 159Á 165, 2007
...
Mechanism of muscular
contraction
...
Kinetic studies on muscle ATP-ase
...
Weiss JN
...
FASEB J 11:
835Á 841, 1997
...
The Cubic Ternary
Complex Receptor-Occupancy Model I
...
J Theor Biol 178: 151Á 167, 1996
...
The Cubic Ternary
Complex Receptor-Occupancy Model II
...
J Theor Biol 178: 169Á 182, 1996
...
The Cubic Ternary
Complex Receptor-Occupancy Model III
...
J Theor Biol 181: 381Á 397, 1996
...
Differential
expression of the beta-adrenergic receptor modifies agonist
stimulation of adenylyl cyclase: a quantitative evaluation
...
Wyman J Jr
...
Adv Protein Chem 4: 430Á 438, 1948
...
The problem of the heme interactions in
hemoglobin and the basis of the Bohr effect
...
Yao X, Parnot C, Deupi X, Ratnala VR, Swaminath G, Farrens D and
Kobilka B
...
Nat Chem Biol 2: 417Á 422,
2006