Expanding Coefficient: A Parameter to Assess the Stability of Induced-Fit Complexes

Article abstract of DOI:10.1021/acs.orglett.1c00165

Here we propose a new parameter, the Expanding Coefficient (EC), that can be correlated with the thermodynamic stability of supramolecular complexes governed by weak secondary interactions and obeying the induced-fit model. The EC values show a good linear relationship with the log Kapp of the respective pseudorotaxane complexes investigated. According to Cram's Principle of Preorganization, the EC can be considered an approximate mechanical measure of the host's reorganization energy cost upon adopting the final bound geometry.

Full text of DOI:10.1021/acs.orglett.1c00165

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Letter
Expanding Coefficient: A Parameter To Assess the Stability of
Induced-Fit Complexes
Carmen Talotta,* Gerardo Concilio, Margherita De Rosa, Annunziata Soriente, Carmine Gaeta,
Antonio Rescifina,* Pablo Ballester,* and Placido Neri*
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ABSTRACT: Here we propose a new parameter, the Expanding
Coefficient (EC), that can be correlated with the thermodynamic
stability of supramolecular complexes governed by weak secondary
interactions and obeying the induced-fit model. The EC values
show a good linear relationship with the log Kapp of the respective
pseudorotaxane complexes investigated. According to Cram’s
Principle of Preorganization, the EC can be considered an
approximate mechanical measure of the host’s reorganization
energy cost upon adopting the final bound geometry.
olecular recognition is a fundamental phenomenon at
infra), independently from their actual stability, thus vanishing
any comparison.
M
the ground of every biological function.1 Its funda-
mental relevance was recognized since the early days of
chemical and biological sciences,2 and afterward, many studies
have been devoted to comprehending its underlying principles
and explaining the origin of the amazing selectivity3 or affinity4
observed in some instances. Two main models are currently
adopted to describe a molecular recognition complexation: (i)
the lock-and-key model5 and (ii) the induced-fit complex-
ation.6 In the first one, the degree of geometrical (steric) fitting
between a rigid, undeformable receptor and substrate is
evaluated, while, in the second one, the best match of flexible
counterparts is considered after their mutual adaptation.
In the field of synthetic receptors, a single value parameter,
the Packing Coefficient (PC), defined as the ratio between the
van der Waals volume of the hosted guest and the volume of
the host cavity,7 was introduced by Rebek and Mecozzi to
simplify the assessment of the complex stability for rigid, lock-
and-key-like systems. It was found that the optimal PC value,
the fraction of occupied volume, is 0.55 0.09 (55%)7 in the
liquid state when weak intermolecular interactions (dispersion
forces, van der Waals interactions) are present. The PC can
increase (up to 70−84%) when stronger interactions (hydro-
gen bonds, solvation effects) come into play8a,b or can decrease
(down to 40%) when gaseous molecules are involved.8c,d This
simple rule has been validated in many synthetic host−guest
systems,9 has been used to explain reactivity results,10 and has
also been extended to biological receptors.11
It is evident that another useful and straightforward rule is
necessary to assess the stability of induced-fit complexes in
order to predict the ideal host−guest couple. We propose here
a new single-value parameter to address such point.
The induced-fit system chosen for this work is the
pseudorotaxane complex formed by hexamethoxy-p-tert-
butylcalix[6]arene13 1 and alkylbenzylammonium axles 2a−
k+ (Scheme 1). In previous studies,14 we have demonstrated
that this kind of dialkylammonium axles can thread the
calixarene cavity when coupled to the weakly interacting
BARF− (or TFPB−) “superweak anion” to give the 2+⊂1
pseudorotaxanes (Scheme 1). In addition, we have found that
the aromatic cavity mostly prefers to host the alkyl portion of
the axle with respect to the benzyl one (the so-called “endo-
alkyl rule”).14a−e
The aromatic walls of receptor 1 are freely rotating through
the macrocyclic annulus, and thus they adapt their relative
orientation to give the best interactional fitting with guest 2. As
a result, a less-symmetrical induced-fit complex is obtained in
which each aromatic ring is differently inclined toward the
+
cavity (vide infra). Since the PhCH2NH2 moiety is common
to all the 2a−k+ axles and since it is external to the aromatic
calix-cavity, we can assume that the stability constant of 2+⊂1
pseudorotaxanes could be directly linked to the best interac-
Received: January 20, 2021
Published: February 16, 2021
From the above definitions, it is evident that the PC
parameter cannot be applied to induced-fit systems because the
void receptor cavity volume tends to adapt to that of the guest
to give the best fitting with it.12 Therefore, it is expected that
the PC value of induced-fit complexes calculated for the final
adapted geometry will always overcome the 55% rule (vide
© 2021 The Authors. Published by
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https://dx.doi.org/10.1021/acs.orglett.1c00165
Org. Lett. 2021, 23, 1804−1808
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both free and complexed hosts (see Supporting Information
(SI)).15 In some instances, competition experiments with
known pseudo[2]rotaxanes were also used (see SI).
Scheme 1. Threading of Calix[6]arene 1 with
Alkylbenzylammonium Axles 2a−k+
At this point, to test the initial hypothesis, the log Kapp data
reported in Table 1 were correlated with the PC of the calix-
cavity in pseudo[2]rotaxanes 2a−k+⊂1 obtained using the
DFT-optimized structures at the B3LYP-D3/6-31G(d,p) level
of theory (D3 stands for Grimme’s dispersion correction
energy term16 and has been already used for DFT calculations
in calixarene-based pseudorotaxane structures17). As expected,
close inspection of the data reported in Table 1 revealed that
the PC of the calix-cavity in pseudo[2]rotaxane 2a−k+⊂1
structures overcomes the above-mentioned 55% rule (PC
range = 72−100%) and the correlation coefficient of the linear
fitting is low (R2 = 0.38, Figure S46), indicating that there is a
low correlation between the two parameters.
In Figure 1a−c, the superimposed calix[6]arene-wheels of
the optimized structures 2+⊂1 are reported (see also Figure
tional fitting of the alkyl moiety of 2 inside the aromatic cavity
of 1.
Figure 1. DFT-optimized structures, at B3LYP-D3/6-31G(d,p) level
of theory, of the following: (a) superimposed calix[6]arene-wheels of
2+⊂1 pseudorotaxanes (global minimum); (b) only 2a+⊂1, 2b+⊂1,
and 2j+⊂1; (c) only 2d+⊂1 and 2k+⊂1.
Based on these considerations, the question arises as to
whether the shape and dimension of the hosted alkyl moiety
can influence the effectiveness of complexation: is there any
cavity-filling effect? Is there a maximum or an optimal filling? Is
there any quantitative parameter in suitable agreement with the
experimental results?
S47). Inspection of Figure 1a reveals that the calix[6]arene-
wheels adopt two main conformations upon complexation: the
cone-1,3,5-out (2a−c+⊂1 and 2e−j+⊂1; see Figure 1b) and
the cone-1,4-out (2d+⊂1 and 2k+⊂1; see Figure 1c).
Moreover, it is evident that, during the induced-fit recognition
process, the calix-cavity deforms, allowing the change of the
void volume of the receptor.
Close inspection of Figure 1b,c reveals a remarkable change
of inclination of all the aromatic rings (−21° from yellow to
coral, and +23° from yellow to purple, on average,
respectively) of 1, in pseudo[2]rotaxanes 2a+⊂1, 2b+⊂1, and
2k+⊂1. Thus, the conformational freedom of 1 ensures the
The threading abilities of alkylbenzylammonium cations
2a−k+ toward calix[6]arene 1 (Scheme 1) were studied by 1H
NMR titration experiments (CDCl3, 298 K) by mixing
equimolar quantities of 1 and 2 in CDCl3 (3.8 mM solution)
(Figures S24−S45).14a With all the axles 2a−k+, the
pseudo[2]rotaxane stereoisomer with endo-alkyl stereochemis-
try was preferentially formed (see the Supporting Information
for further details), following the endo-alkyl rule14e previously
reported. The apparent association constants (Table 1) for the
formation of pseudo[2]rotaxanes 2a−k+⊂1 were determined
1
by integration of the slowly exchanging H NMR signals for
Table 1. Apparent Association Constants of 2+⊂1 Pseudorotaxanes and Their PC, CC, and EC Parameters
a
Axle
Kapp (M−1
)
log Kapp
PC (%)
CC (%)
EC
ΔGReorg (kcal/mol)
2a+⊂1
2b+⊂1
2c+⊂1
2d+⊂1
2e+⊂1
2f+⊂1
2g+⊂1
2h+⊂1
2i+⊂1
2j+⊂1
2k+⊂1
(1.1 0.2) × 106
(4.8 0.8) × 103
(6.5 0.9) × 104
(2.4 0.6) × 103
(4.2 0.6) × 104
(3.6 0.5) × 102
(5.1 0.6) × 103
(1.7 0.6) × 103
(6.9 0.8) × 103
(2.9 0.5) × 103
(2.7 0.4) × 102
6.04
3.68
4.81
3.38
4.62
2.56
3.71
3.23
3.84
3.46
2.43
72
100
88
94
74
82
88
86
89
87
97
70
72
74
71
71
77
74
75
75
76
80
5.5
7.2
8.0
10.1
7.2
9.5
9.5
10.8
8.4
10.5
11.6
19.2
28.0
28.8
32.0
25.5
36.9
37.6
31.9
31.6
35.3
41.1
a
The apparent association constant values were determined by mixing equimolar quantities of host and guest in CDCl3 (3.8 mM solution each, 298
K) by using the following methods: (i) H NMR competition experiment (2a+, 2b+, 2c+, and 2e+); (ii) quantitative H NMR experiment using
1
1
1,1,2,2-tetrachloroethane as the internal standard (2k+); (iii) integration of free and complexed H NMR signals of host or guest (2d+, 2f+, 2g+,
1
2h+, 2i+, and 2j+).
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best fit around the alkyl portion of guest 2a+, 2b+, or 2k+ to
establish an extended area of contact between them. In other
words, the aromatic walls of calixarene host 1 move to wrap
the guest and maximize the secondary interactions with it.
From the above data, it is evident that another useful and
straightforward rule is necessary to assess the stability of these
induced-fit complexes in order to predict the ideal cavity-filling
effect. Initially, we reasoned that the maximization of weak
secondary interactions should be parallel to the maximization
of the contact surface between host and guest; therefore, we
studied a new surface-based single-value parameter to address
such point. With this aim, we considered the Contacting
Coefficient (CC, eq 1) defined as the ratio between the
molecular surface of the guest in close contact with the cavity
surface (SContact) of the host, and the total surface of the guest
(SGuest).
Figure 2. Linear regression analysis of ECs vs log Kapp values for 2+⊂1
alkylbenzylammonium-based pseudorotaxane complexes.
evident that the EC parameter is now less affected than CC by
the structural differences of the variously branched alkyl chains
of 2a−k+.
SContact
SGuest
CC(%) =
× 100
(1)
The good correlation performance of the geometrical EC
parameter induced us to consider its possible physical
meaning. In fact, this EC can be considered an approximate
geometrical measure of the energy cost paid by the host when
it reorganizes itself from the initial lowest-energy conformation
to the final geometry adopted in the complex. A higher EC
value implies a higher deformation of the host, which in turn
implies a higher energetical cost. From another point of view,
the EC can be considered an approximate indirect inverse
measurement of the preorganization of the host for the
complexation of the given guest. The importance of this
reorganization cost was first recognized by Cram,3c who stated
that “preorganization is a central determinant of binding
power” leading to the formalization of the Principle of
Preorganization, which states that “the more highly hosts and
guests are organized for binding, and the lower the solvation
before their complexation, the more stable will be their
complexes”.
To verify the correctness of this “reorganization” point of
view, we decided to calculate the energy of the host 1 in its
bound conformation by performing a single-point calculation
on each 2+⊂1 complex after taking away the 2+ guest. The
difference between this single-point bound conformation
energy and the lowest energy of 1 gives a ΔGReorg value,
which can be considered the theoretically computed
energetical cost for the above-mentioned reorganization of
the host, from the initial lowest-energy conformation to the
final geometry adopted in the complex. The ΔGReorg values
computed for all the 2a−k+⊂1 complexes are reported in
Table 1. Interestingly, these data seem to be in accord with the
“reorganization” point of view, and indeed a good linear
correlation (R2 = 0.79) was found by regression analysis
between ΔEReorg vs log Kapp values (Figure S50). In summary,
this analysis indicates that, under the above assumption of
weak intermolecular interactions (dispersion forces, van der
Waals interactions), the primary determinant to the stability of
induced-fit complexes will be the degree of deformation with
respect to the ground conformation.
This new parameter does not consider the host cavity volume
and could be applied to host−guest processes that follow the
induced-fitting mechanism. In addition, the CC parameter
should be more directly related to the thermodynamic stability
of the complex because it considers the host−guest contacting
surface, which should be related to the extension of van der
Waals and C−H···π interactions between them.
Starting from the complexes’ DFT-optimized structures, the
molecular surfaces of the guest inside the cavity (SGuest) were
computed by YASARA software, which also permits the direct
measure of the contact surface between guest and host
(SContact). From the ratio of those surfaces, CC (%) values of
70, 74, and 80 were calculated, through eq 1, for 2a+⊂1,
2c+⊂1, and 2k+⊂1 pseudo[2]rotaxanes (Table 1), respectively.
The Scontact is represented in red in Figure S48, while the SGuest
indicates the total molecular surface of the guest. Close
inspection of Figure S48 reveals that, in addition to the Scontact
(in red), there are free portions of the guest’s molecular surface
not in contact with the calixarene cavity (in yellow).
Unfortunately, the CC of the whole set has only a discrete
correlation coefficient (R2 = 0.54, Figure S49).
At this point, we decided to evaluate another single-value
geometrical parameter, which could take more directly into
account the energy cost associated with the host reorganization
upon induced-fit complexation. Therefore, we considered the
Expanding Coefficient (EC, eq 2) defined as the ratio between
the final and the initial cavity volumes of the host, i.e., the
volume of the host cavity after the complexation
(Vcomplexed
_
at the global minimum) and that of the host
Host
cavity before the complexation (Vfree
_
at the global
Host
minimum).
V
complexed_Host
EC =
V
(2)
free_Host
The actual values of Vcomplexed_Host and Vfree_Host were measured
by using the DFT-optimized structures of the separated host
and guest for all the 2+⊂1 complexes (see the SI)18 with the
Caver software. From these values, the corresponding ECs
were then calculated (Table 1), and a linear regression analysis
was performed with the pertinent log Kapp data. As shown in
Figure 2, a good correlation coefficient (R2 = 0.74) was
obtained, demonstrating good linearity between the new EC
parameter and the complex’s thermodynamic stability. It is
In conclusion, we have defined the EC new parameter that
can be correlated with the thermodynamic stability of
supramolecular complexes governed by weak secondary
interactions that obey the induced-fit model. The EC values
show a good linear relationship with the log Kapp of the
respective pseudorotaxane complexes. This EC can be
considered an approximate mechanical measure of the
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ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.orglett.1c00165.
■
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Experimental details, characterization data, NMR
spectra, calculations details, and Cartesian coordinates
(PDF)
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AUTHOR INFORMATION
Corresponding Authors
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Carmen Talotta − Dipartimento di Chimica e Biologia “A.
Zambelli”, Università di Salerno, I-84084 Fisciano (Salerno),
Italy; orcid.org/0000-0002-2142-6305;
Email: ctalotta@unisa.it
Antonio Rescifina − Dipartimento di Scienze del Farmaco e
della Salute, Università di Catania, I-95125 Catania, Italy;
orcid.org/0000-0001-5039-2151; Email: arescifina@
unict.it
Pablo Ballester − Institute of Chemical Research of Catalonia
(ICIQ), The Barcelona Institute of Science and Technology
(BIST), 43007 Tarragona, Spain; orcid.org/0000-0001-
8377-6610; Email: pballester@iciq.es
Placido Neri − Dipartimento di Chimica e Biologia “A.
Zambelli”, Università di Salerno, I-84084 Fisciano (Salerno),
Italy; orcid.org/0000-0003-4319-1727; Email: neri@
unisa.it
Authors
Gerardo Concilio − Dipartimento di Chimica e Biologia “A.
Zambelli”, Università di Salerno, I-84084 Fisciano (Salerno),
Italy
Margherita De Rosa − Dipartimento di Chimica e Biologia
“A. Zambelli”, Università di Salerno, I-84084 Fisciano
(Salerno), Italy; orcid.org/0000-0001-7451-5523
Annunziata Soriente − Dipartimento di Chimica e Biologia
“A. Zambelli”, Università di Salerno, I-84084 Fisciano
(Salerno), Italy; orcid.org/0000-0001-6937-8405
Carmine Gaeta − Dipartimento di Chimica e Biologia “A.
Zambelli”, Università di Salerno, I-84084 Fisciano (Salerno),
Italy; orcid.org/0000-0002-2160-8977
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.orglett.1c00165
Notes
The authors declare no competing financial interest.
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Org. Lett. 2021, 23, 1804−1808