Chemodiversity and molecular plasticity: recognition processes as

Review

Special FocuS: computational chemiStRy

Chemodiversity & its meaningChemodiversity begins with the simplest chemi-cal objects, namely atoms. Indeed, there is some electronic diversity in a given atom, since it has a number of electronic states available depending on ionization and occupation of atomic orbit-als. However, genuine geometric states emerge at the level of molecules, where conformational states, mainly, and tautomeric states, occasion-ally, dramatically expand the property space open to molecules compared with atoms [1,2]. As is well known, a given molecule can exist as a number of conformers. To use a metaphor, a molecule is a ballerina and not a statue. In plain terms, the 3D-geometry of a molecule fluctu-ates within its energy-allowed range [3,4], thus, defining a conformational space that comprises all the microstates energetically accessible to the molecule. These states are snapshots of the mol-ecule at a given moment in time and they are characterized by a definable form. The confor-mational space delineated by all conformers of a molecule can be seen as its basin of attraction [5,6] or an energy landscape [7], namely a hypersurface whose dimensions are the energy of the system, plus all its geometric variables.

Considering the described molecular variabil-ity, it comes as no surprise that a detailed ana-lysis of molecular flexibility for both ligand and receptor is now usually taken into account, with a view to enhancing the classical static drug-design methodologies. Modern docking programs rou-tinely account for ligand flexibility as well as receptor flexibility, which can be modelled con-sidering both conformational changes at a mac-romolecular level and small variations involving one or a few residues. The former is generally due to domain rearrangements and can be accounted for by multiple protein structures obtained exper-imentally or by in silico techniques, whereas the latter is due to side chain flexibility and can be simulated by exploiting rotamer libraries [8]. Similarly, pharmacophore mapping greatly ben-efits from an assessment of flexibility since the flexible superimposition of biologically active molecules is a crucial step in similarity ana lysis and, hence, in ligand-based drug design [9]. In addition, quantitative structure–activity relation-ship (QSAR) analyses have evolved towards mul-tidimensional approaches, which consider both the three-dimensional structures (3D-QSARs) and their flexibility (nD-QSARs) [10].

Chemodiversity and molecular plasticity: recognition processes as explored by property spaces

In the last few years, a need to account for molecular flexibility in drug-design methodologies has emerged, even if the dynamic behavior of molecular properties is seldom made explicit. For a flexible molecule, it is indeed possible to compute different values for a given conformation-dependent property and the ensemble of such values defines a property space that can be used to describe its molecular variability; a most representative case is the lipophilicity space. In this review, a number of applications of lipophilicity space and other property spaces are presented, showing that this concept can be fruitfully exploited: to investigate the constraints exerted by media of different levels of structural organization, to examine processes of molecular recognition and binding at an atomic level, to derive informative descriptors to be included in quantitative structure–activity relationships and to analyze protein simulations extracting the relevant information. Much molecular information is neglected in the descriptors used by medicinal chemists, while the concept of property space can fill this gap by accounting for the often-disregarded dynamic behavior of both small ligands and biomacromolecules. Property space also introduces some innovative concepts such as molecular sensitivity and plasticity, which appear best suited to explore the ability of a molecule to adapt itself to the environment variously modulating its property and conformational profiles. Globally, such concepts can enhance our understanding of biological phenomena providing fruitful descriptors in drug-design and pharmaceutical sciences.

Giulio Vistoli†1, Alessandro Pedretti1 & Bernard Testa2

1Dipartimento di Scienze Farmaceutiche ‘Pietro Pratesi’, Facoltà di Farmacia, Università degli Studi di Milano, Via Mangiagalli, 25, I-20133 Milano, Italy 2Department of Pharmacy, University Hospital Centre, Rue du Bugnon, CH-1011 Lausanne, Switzerland †Author for correspondence:Tel.: +39 025 031 9349 Fax: +39 025 031 9359 E-mail: [email protected]

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However, while the emergence of clearly distinct geometric states is well recognized [11], the marked dependence of several molecu-lar properties on conformational state is sel-dom made explicit. Thus, properties such as dipole moments, hydrophobic forces and polar interactions are dependent on conformational state [12–16]. Such properties are best visualized as molecular interaction fields. Among these fields, molecular hydrophobic potentials play a major role in drug design and protein modeling to evaluate the lipophilicity effects in molecu-lar recognition and folding processes [17–24]. In particular, two main approaches (namely hydro-phobic interaction [HINT] and molecular lipo-philicity potential [MLP]) were developed to calculate hydrophobic potentials [25,26], which are based on the assumption that the lipophilic atomic increments can be projected on molecu-lar surfaces (or, more generally, on the space around a given molecule), using a predefined distance function. The ensemble of such pro-jected values defines the molecular potential. The two methods differ mainly by the atomic constants used to compute the hydrophobic potentials (an adaptation of the CLOGP [27] method for HINT and the increments of Broto et al. for MLP [28]) and the selected distance function (a Boolean linear function for HINT and a Fermi-like distance for MLP). Both meth-ods can be used to compute conformer-depen-dent ‘virtual’ log P values and to derive hydro-phobic force fields to evaluate apolar interactions in ligand binding [29,30]. Notably, the possibility to determine conformer-dependent log P values has received experimental validation. Indeed, kinetic NMR studies have afforded a direct proof that conformers differ in their solvent/water partition coefficient [31]. In the property space applications here described, the lipophi-licity space, which is often taken as illustrative example of property space, is evaluated using the MLP approach as implemented in VEGA. This choice can be justified considering that VEGA [32,101], which is indeed a homemade suite of programs, proved the best performing method among the 3D conformer-dependent approaches as demonstrated by a recent bench-marking ana lysis of many log P prediction algorithms [33].

It should be noted that previous studies have already exploited molecular interaction fields to evaluate the dynamic behavior of such molecu-lar properties, especially in assessing the hydro-phobic/hydrophilic contribution of proteins and

peptides, but this was performed in an unsystem-atic way and never inserted in a solid framework, such as the property space concept on which this review is focused. As illustrated by FiguRe 1, the concept of property space is based on the finding that a flexible molecule (which, by definition, assumes numerous conformations) will exhibit different values for a given conformation-depen-dent physicochemical property [34]. The concept of conformational and property spaces can be used to describe the variability of small ligands, but it also applies to macromolecules, although simplified assumptions are often used in compu-tations [35]. Here, it is meaningful to distinguish between backbone flexibility and the flexibility of the side chains in the residues.

The concepts of molecular diversity and molecular property should not be confused with the concepts of chemical diversity and chemical spaces as applied to sets of com-pounds. Chemical diversity is indeed of great interest in medicinal chemistry when attempts are made to identify drug-like compounds within large chemical libraries [36]. A nice illustration of this approach and of the type of descriptors used to characterize chemical compounds is afforded by the work of Feher and Schmidt [37]. They used a set of 41 descrip-tors and applied them to a library of 670,536 combinatorial compounds, a library of 10,968 drugs and a library of 3287 natural products. Principal components were calculated, each of which was a dimension in a multidimensional space, in this case a chemical diversity space. The point to stress is that each compound is statically represented as a single point in this chemical space. This should be compared with the fact that only approximately 66% of the variance in the datasets was explained by the first three principal components, meaning that a marked proportion of the information in the datasets was not accounted for.

This review will discuss the fundamental con-cepts of property space analyzing relevant appli-cations in which they are exploited in molecular modeling, such as QSAR analyses and protein simulations. Special emphasis will be given to the interest of the property space concept to ana-lyze ligand–protein complexes and the under-lying adaptability processes which govern the molecular recognition. Globally, the property space concept can find fertile applications in drug design and molecular modeling providing tools and concepts to explore the dynamic nature of biological phenomena.

Key Terms

Chemodiversity: Term covering chemical variability, which can be subdivided into atomic diversity, molecular diversity, and chemical diversity. The first refers to the various electronic states an atom can occupy. The second encompasses the conformational and property spaces of a given molecule. The third pertains to the diversity exhibited by a library of different chemical entities.

Property space: Ensemble of all values a conformer-dependent property can assume for a given (flexible) molecule.

Molecular sensitivity: Ability of a molecule to modulate its properties by varying its conformational profile. This allows one to distinguish between sensitive molecules whose property values are markedly influenced by small conformational changes and insensitive molecules whose properties change little even during major geometric fluctuations.

Review | Vistoli, Pedretti & Testa

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Molecular properties & their adaptability: the concept of property spaceAs described in the Introduction and depicted by FiguRe 1, the concept of property space is based on the variability of conformer-dependent physico-chemical property. For flexible molecules, there will be a one-to-one relation between a given conformer and the resulting property value. In this dynamic vision, a molecular property can be described either by an average value or by descriptors defining its property space.

The average value of a property, and especially a weighted average, contains more information than a single conformer-specific value, even if this conformer is the most probable (low-energy) one or the bioactive one. However, this average value does not yield information on the prop-erty space itself. To this end, one should define descriptors specifying the variability of a given property in terms of range and distribution over the entire conformational space, and how its variation relates to other properties.

Specifically, a property space can be defined by two classes of descriptors. The first class includes descriptors that quantify the variability (spread) of values and is usually defined by the range, namely by a simple difference between maximum and minimum property values, even if in some cases normalized range values are also considered. As described in the section titled ‘Property space and molecular recognition: the case of carboxylesterase substrates’, normal-ized range values (and normalized range differ-ences) allow the dynamic behavior of different molecular properties to be directly compared (as seen in FiguRe 2). The second class of descriptors relates the dynamic behavior of a given prop-erty with other geometric or physicochemical properties. Such correlations can reveal whether and how two molecular properties vary in a coherent manner, leading to the concept of molecular sensitivity.

As may be easily understood, the ana lysis of property space cannot be separated by the evaluation of the structural variability which was assessed in the following property space applications using three methods: the number of rotatable bonds, the root-mean-square devia-tion (RMSD) average considering all nonre-dundant conformers and the dynamic profile of the radius of gyration values. The last approach underlines that the variations in geometrical descriptors can be seen as an indirect measure for the molecular flexibility. As discussed in the

section titled ‘Property space and molecular recognition: the case of carboxylesterase sub-strates’, the radius of gyration was chosen to estimate molecular flexibility since it is a well-known descriptor encoding molecular shape and size [38]. Exemplarily, the acetylcholine, on which the next section is focused, possesses two rotatable bonds, which pertains to the choline moiety, while the RMSD value and the varia-tion in radius of gyration, as derived by in vacuo simulations, are 2.82 and 0.38 Å, respectively. As discussed in the section titled ‘Property space and QSAR analyses’, it should be noted that the first one is a 2D descriptor, while RMSD and variation in radius of gyration require simula-tions and depend on the constraining effects exerted by the simulated medium. The different nature of such flexibility descriptors is confirmed by the fair correlations between them as com-puted considering a large dataset of compounds (rotors vs RMSD: r2 = 0.49; rotors vs radius variation: r2 = 0.59; RMSD vs radius variation: r2 = 0.44) [39].

� The fertile case of acetylcholineIn the first series of studies [40–43], we investi-gated the property space of the neurotransmitter

Figure 1. Schematic representation of the one-to-one relation between a given conformer (as seen for some representative geometries of acetylcholine) and the resulting property values (taking lipophilicity as an example). The figure also emphasizes possible correlations between physicochemical (P) and geometrical properties (t), which lead to the concept of molecular sensitivity. Notice that the acetylcholine conformations are depicted with folded geometries (g+g+, g-g-, g+t and g-t, which represent in vacuo approximately 80% of all monitored conformers) on the top of the conformational space and the extended ones (tg+, tg- and tt, which represent in vacuo approximately 8% plus approximately 12% constituted by anticlinal transition forms, ga, ta, ag, at, aa) at the bottom.

Conformational space Lipophilicity space

- 2.22

- 2.30

- 2.40

- 2.45

- 2.35

P = ƒ(τ )

ƒ : τ P

Chemodiversity & molecular plasticity | Review

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acetylcholine using molecular dynamics (MD) simulations. The molecule was placed in a vacuum, in various isotropic and anisotropic media, or it was bound to human muscarinic receptors (specifically, mAchR

1, mAchR

2 and

mAchR5 subtypes) as modeled by homology

techniques [44]. The results of these studies (as summarized by table 1 and FiguRe 3) have shed light on some key features of the property space, which can be summarized as follows, taking the lipophilicity space as an example:

�In all simulated media and within the limits of its property spaces, acetylcholine tends to preserve much of its conformational and property spaces and adapts its physicochemi-cal properties to those of the environment even if such adaptability can involve different mechanisms;

�Isotropic media (vacuum, water and CHCl3)

do not have a marked effect on the conforma-tional space of acetylcholine, which preserves all its conformational clusters in such media (compare the RMSD values). FiguRe 3 clearly shows that adaptability is obtained not by major conformational constraints, but because the medium selects in each conformational clusters those conformers whose polarity most resembles its own. This implies that confor-mational space and property spaces are par-tially unrelated and that each cluster of con-formers spans most of the property space of acetylcholine. Globally, isotropic media are seen to inf luence only modestly the conformationa l and property space of acetylcholine;

�In contrast, anisotropic media such as a mem-brane model vastly constrain the conforma-tional space of acetylcholine, as seen in the total disappearance of some conformational clusters in a membrane model (as seen in FiguRe 3). Conversely, the lipophilicity space is not reduced proportionally since it exhibits ranges very similar to those observed in iso-tropic solvents (as compiled in table 1). This would suggest that anisotropic media select conformational clusters, whereas isotropic solvents select individual conformers within each cluster. The conformational and lipophi-licity property spaces thus appear variously influenced by such environments. Also, the ability of a molecule to modulate differen-tially its conformational space and property spaces leads to the concept of molecular plas-ticity, which finds its genuine application when analyzing ligand–protein complexes;

�The binding to muscarinic receptors has con-straining effects, which appear even stronger than those of a membrane model. Remarkably, the property space of the ligand is more con-strained than its conformational space since the receptors recognize more than one confor-mation of acetylcholine [43], while its property range is significantly reduced (compared with that in a vacuum). The average virtual log P values are significantly lower than in vacuo and

Key Term

Molecular plasticity: Ability of a molecule to adapt itself to the environment by variously modulating molecular flexibility and property variability. This concept finds the most genuine application to describe ligand behavior when bound to a biological target and allows the intrinsic activity to be hypothesized.

0

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Figure 2. Monitored differences for lipophilicity ranges (shaded bars, encoding the property constraints) and flexibility ranges (white bars, encoding the conformational constraints). (A) The ionization states of temocapril and temocaprilat between vacuum and hCES1. (B) The ionization states of (R)-propranolol and its butyl ester between vacuum and hCES1 or hCES2. For a direct comparison of lipophilicity and flexibility ranges, the range differences are normalized in respect to the corresponding range average in vacuo and represented as percentages.



this trend suggests the involvement of more extended conformers, which are allegedly involved in receptor interaction (as shown by FiguRe 3). This suggests that the muscarinic receptors do not require a very narrow, highly specific bioactive conformation but rather an optimal value of some molecular property (here, lipophilicity). Such optimal value is not limited to a single conformer but can be assumed by distinct conformers in various conformational clusters;

�Remarkably, the ability of a given ligand to differently modulate its property space and conformational flexibility (namely molecular plasticity) appears useful to analyze the mutual ligand–receptor adaptability, while the ranges as descriptors of property spaces proved successful to account for the (often-disre-garded) entropic component in receptor recognition and binding.

Although conformational and property spaces seem only partly related, the MD simula-tions of acetylcholine in different environments revealed a remarkable correlation between its flexibility (as assessed by the RMSD averages computed for each MD simulation) and its lipophilicity ranges in various media (as com-piled in table 1). This finding means that the ratio between molecular flexibility and property range is seemingly constant for acetylcholine and independent of the medium being simu-lated. This also suggests that such a ratio is an intrinsic attribute of a given compound and can find fertile applications in quantitative descrip-tions of its dynamic behavior. This ratio leads to the concept of molecular sensitivity, which has been indirectly examined by considering the pair-wise correlations between physicochemical and geometric properties, and which can find a more exact mathematical definition as described in following sections.

� Property space & molecular recognition: the case of carnosineThe usefulness of the concept of property space to study the effects of molecular recognition, as seen with acetylcholine bound to human muscarinic receptors, was confirmed in a second study on the property space of carnosine [15]. This compound was chosen as it represents the archetype of a series of histidine-containing dipeptides whose physiological role has been extensively investi-gated in recent years [45]. The study involved a comparison of the dynamic profile of carnosine

as derived by MD simulations in isotropic sol-vents, with simulations of carnosine bound to serum carnosinase (CN1), a specific dipeptidase expressed in plasma and brain whose 3D struc-ture was generated by homology techniques [46]. As detailed by table 1, the study revealed that the conformational space of carnosine bound to CN1 (as parameterized by RMSD) is globally larger than that in isotropic media. This behavior can

Table 1. The lipophilicity space of acetylcholine and carnosine in different environments, as calculated by the molecular lipophilicity potential for all conformers generated by long-duration molecular dynamics simulations.

Medium Average log P Range log P Mean root-mean-square deviation (Å)

Acetylcholine

Vacuum -2.34 0.38 2.82Water -2.42 0.34 2.35Water plus Cl¯ -2.42 0.34 2.35CHCl3 -2.36 0.35 2.37Hydrated octanol -2.40 0.28 1.85Membrane model -2.39 0.28 1.05mAchR1 receptor -2.43 0.23 0.61mAchR2 receptor -2.40 0.29 0.70mAchR5 receptor -2.39 0.27 0.66

Carnosine

Water -4.28 0.59 1.61CHCl3 -4.20 0.66 1.52Carnosinase -4.17 0.55 1.99

-2.5

-2.45

-2.4

-2.35

-2.3

-2.25

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Chl

orof

orm

Mem

bran

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mA

chR

1

mA

chR

2

mA

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5

log P

FoldedExtendedGlobal

Figure 3. Effects on average log P values of major conformational clusters in the simulated media including isotropic and anisotropic environments as well as human muscarinic receptors.



be explained considering that the flexibility of carnosine is markedly constrained by the intra-molecular ionic bond, while the polar residues lining the enzymatic cavity can compete with this intramolecular salt bridge favoring more extended conformations. The structural rigidity of carnosine reflects on its property spaces which appear remarkably restricted. Nevertheless, the molecule preserves an ability to adjust its physi-cochemical properties to the simulated medium suggesting that property spaces can conserve a significant elasticity even in highly constrained molecules. These results appear to agree with those already obtained by acetylcholine, and confirm that property spaces could not be sig-nificantly constrained by unstructured media. Despite the greater flexibility, the property spaces of carnosine bound to CN1 appear comparable with those in isotropic media. This confirms what was already seen for acetylcholine, namely that a receptor allows a certain degree of confor-mational variability of the ligand while selecting well-defined property values best suited for the molecular recognition.

Taken globally, carnosine and acetylcho-line suggest that a flexible molecule may show a noteworthy adaptability, which strongly influences its biological activity. The biologi-cal implications of such an adaptability can be conveniently examined by comparing the conformational and property spaces in isotro-pic media (or more simply in vacuo) with those of the same molecule bound to a protein. Such considerations prompted us to reanalyze some MD studies recently published by us with the aim to reveal the effects of molecular recogni-tion on the flexibility and adaptability of the simulated compounds.

� Property space & molecular recognition: the case of carboxylesterase substratesThis ana lysis involved computational stud-ies performed with human carboxylesterases (namely hCES1 and hCES2) in which the con-trasting behavior of substrates and products was investigated by MD simulations [30,47,48]. Specifically, the attention was focused on the MD studies carried out on the different elec-tronic states of temocapril and temocaprilat bound to hCES1 with a view to analyzing the relation between ionization state and dynamic behavior [47]. Also, the MD simulations on (R)-propranolol and its butyl ester bound to hCES1 and hCES2 were here investigated in order to reveal how the monitored spaces can

be differently influenced by two isozymes [48], also considering that (R)-propranolol esters are preferentially hydrolyzed by hCES1 [49].

In the previous study [48], (R)-propranolol and its butyl ester were simulated when bound to hCES2 only, hence MD simulations of the two possible ionization states (neutral and pro-tonated) of (R)-propranolol and its butyl ester bound to hCES1 were performed here. The complexes of hCES1 with (R)-propranolol butyl ester were taken from a previous docking study [30], while the complexes of the enzyme with (R)-propranolol were generated by manu-ally transforming the previous ones. The four MD runs lasted 5 ns and were carried out using the same computational protocol as detailed else-where [30]. Briefly, the complexes obtained were inserted into a 50-Å-radius sphere of water mol-ecules, and the minimized systems underwent 5 ns of all-atoms MD simulations with the fol-lowing major characteristics: spherical boundary conditions were introduced to stabilize the simu-lation space, Newton’s equation was integrated using the multiple-time-step reversible reference system propagator (r-RESPA) method, the tem-perature was maintained 300 ± 10 K by means of Langevin’s algorithm, a frame was stored every 5 ps, yielding 1000 frames and no constraints were applied to the systems. The simulations were carried out in two phases: an initial period of heating from 0 to 300 K over 6000 iterations (6 ps, i.e., 1 K/20 iterations) and a monitored phase of simulation of 5 ns.

Again, the conformational profile of all consid-ered ligands was evaluated in vacuo by a clustered MonteCarlo ana lysis, which generated 1000 con-formers by randomly rotating the rotors. All geometries so obtained were optimized to avoid high-energy rotamers. The 1000 conformers were clustered according to their similarity to discard redundant ones; in this ana lysis two geometries were considered as nonredundant when they dif-fered by more than 60 degrees in at least one torsion angle.

Here, also, the lipophilicity space was taken as a case in point while the structural properties were monitored by the radius of gyration. Hence, the variability of the radius of gyration can be seen as a useful flexibility descriptor and replaces the RMSD value, which here would be biased by ligand mobility within the catalytic cavities. Moreover, virtual log P and radius of gyration have very similar ranges (0.55–1.41 and 0.61–1.57, respectively) and can thus easily be compared, bearing in mind that they have different units.



table 2 reports the parameters (i.e., average values, standard deviations and ranges) of the lipophilicity and conformational spaces for the different ionization states of temocapril and its metabolite temocaprilat as calculated in vacuo or bound to hCES1. The results confirm what was observed in previous analyses, namely that an interaction with biomacromolecules should constrain the property spaces more than the conformational space. For a direct compari-son, FiguRe 2a shows differences between the range values in vacuo and when enzyme-bound for the computed descriptors (namely, radius of gyration and virtual log P). Such range dif-ferences are normalized in respect to the value in vacuo and can be seen as descriptors of the physical constraints experienced by a ligand during molecular recognition since they cor-respond to the range decrease (expressed as percentage) induced by binding compared with a vacuum. Specifically, the differences in ranges of the radius of gyration can be seen as a descriptor of the conformational constraints experienced (white bars), while the differences in lipophilicity ranges illustrate the constraints on property spaces (shaded bars).

table 2 and FiguRe 2a show that the dif-ferences in the lipophilic ranges are generally greater than those computed for the radius of

gyration, thus confirming that molecular rec-ognition may restrain primarily the property space so that the bound ligand assumes the properties most suitable to optimize intermo-lecular interactions. A more in-depth ana lysis of the property ranges unveils that the differences are on average greater for temocaprilat (0.35 for virtual log P and 0.32 Å for radius of gyra-tion) than for temocapril (0.33 for virtual log P and 0.14 Å for radius of gyration), a trend that is particularly evident for the conforma-tional constraints, which are exactly twice for temocaprilat.

This may confirm that a catalytically pro-ductive interaction with an enzyme allows a certain degree of conformational flexibility in the ligand, the latter dynamically adapting itself to the enzyme plasticity. Conversely, flexibility during egress appears dramatically restricted by the pressure caused by the catalytic chan-nel. This would suggest that exit from the enzyme can be an unfavorable process in which the product tends to minimize both steric hin-drances and intermolecular interactions to reach the cavity rim.

Nevertheless, in almost all considered cases the average value of radius of gyration is greater for the ligands bound to the enzyme than in vacuo. This suggests that the various

Table 2. Analysis of the lipophilicity space and structural variability (as encoded by the radius of gyration) of temocapril and its metabolite temocaprilat in vacuo and bound to hCES1.

Property Bound to hCES1 In vacuo (e = 1)

Log P MLP Radius of gyration (Å)

Log P MLP Radius of gyration (Å)

Temocapril

Anion state 4.56 ± 0.18†

0.88‡

4.16 ± 0.160.90

4.74 ± 0.211.21

4.42 ± 0.191.03

Cation state 3.21 ± 0.240.87

4.33 ± 0.140.63

3.45 ± 0.311.53

4.26 ± 0.240.89

Zwitterion 2.96 ± 0.301.41

4.51 ± 0.140.80

3.30 ± 0.241.47

4.41 ± 0.210.84

Temocaprilat

Dianion state 3.20 ± 0.130.76

4.58 ± 0.120.71

3.01 ± 0.131.30

4.29 ± 0.211.21

Anion state 0.91 ± 0.130.73

4.30 ± 0.140.80

1.48 ± 0.351.33

4.24 ± 0.201.32

Zwitterion 2.01 ± 0.191.05

4.35 ± 0.140.92

1.81 ± 0.231.14

4.33 ± 0.271.08

Cation state 2.34 ± 0.260.95

4.18 ± 0.150.87

2.56 ± 0.311.24

4.14 ± 0.291.16

†Top line reports the average value and the standard deviation‡Bottom line shows the property range.MLP: Molecular lipophilicity potential.



interactions a ligand can undergo within an enzymatic channel (irrespective of their cata-lytic role) favor more extended geometries, and this clearly exacerbates the structural restrains that a compound experiences during its egress.

Moreover, while property and conformational constraints are very similar for temocaprilat (0.35 vs 0.32), property constraints are significantly greater than conformational ones for temocapril (0.33 vs 0.14). This suggests that the property constraints of temocaprilat are due to the con-formational pressure experienced during egress, while the property constraints of temocapril are due to its dynamic adaptability to the enzyme, which selects the most catalytically productive properties of the substrate.

While the average values of the radius of gyra-tion are usually greater for the ligands bound to hCES1 compared with a vacuum (as discussed later), the virtual log P averages show contrast-ing behaviors. Indeed, temocapril is, on average, more hydrophilic when bound to the enzyme probably because it exposes its polar functional groups for catalytic interactions. In contrast, the product temocaprilat is more lipophilic when bound to the enzyme probably because it tends to minimize polar interactions with hCES1 to promote its egress.

When comparing the different ionization forms, one can note that the computed ranges decreased, on average, with the number of ion-ized groups. For the simulations in vacuo, this can be clearly interpreted in terms of reinforced intramolecular interactions. For protein–ligand complexes this can be similarly seen as the result of both intramolecular and intermolecular inter-actions, which synergically concur to freeze the ligand in few preferred conformations.

The lipophilicity and conformational spaces of (R)-propranolol and its butyl ester (as reported in table 3 and FiguRe 2b) show a behavior in encouraging agreement with those previously described. Indeed, the results allow the following considerations to be drawn:�As a trend, with some interesting exceptions

(see later), the lipophilicity space appears more restrained than the conformational space (as encoded by the radius of gyration). This confirms that molecular recognition requires well-defined ligand properties to optimize intermolecular interactions, although the ligand retains a significant part of its structural variability;

�The constraints exhibited by the enzymatic product (i.e., (R)-propranolol) are on average greater than those of the substrate (i.e., the butyl esters) and appear mainly due to the pressure exerted by the enzymatic cavity dur-ing exit, since the lipophilicity and conformational ranges decrease in parallel;

�The property constraints experienced by neu-tral (R)-propranolol butyl ester when bound to hCES1 appear more evident than when bound to hCES2. Although this can also be due to a different plasticity of the two isozymes, it seemingly reflects the greater efficiency of hCES1 towards this substrate, a hypothesis supported by the similar constraints that enzy-matic products show in the two hCES sub-types. This may suggest that the ratio between property constraints and conformational con-straints is not only an index able to discrimi-nate between substrates and products, but, more importantly, it is also approximately correlated with enzymatic efficiency;

Table 3. Analysis of the lipophilicity space and structural variability (as encoded by the radius of gyration) of (R)-propranolol and its butyl ester in vacuo and bound to hCES1 and hCES2.

Property Bound to hCES1 Bound to hCES2 In vacuo (e = 1)

Log P MLP

Radius of gyration (Å)

Log P MLP


Log P MLP


(R)-propranololester neutral

5.05 ± 0.17†

0.83‡

4.02 ± 0.110.90

5.17 ± 0.150.95

3.94 ± 0.170.92

5.27 ± 0.171.14

4.06 ± 0.181.09

(R)-propranololester cation

1.79 ± 0.220.78

3.88 ± 0.240.69

1.74 ± 0.210.85

3.90 ± 0.240.72

2.03 ± 0.271.24

3.83 ± 0.201.13

(R)-propranololneutral

3.50 ± 0.070.57

4.02 ± 0.110.70

3.51 ± 0.080.60

4.05 ± 0.160.81

3.47 ± 0.090.77

3.80 ± 0.201.24

(R)-propranololcation

0.11 ± 0.070.55

3.75 ± 0.130.69

0.12 ± 0.080.59

3.87 ± 0.090.61

0.17 ± 0.240.79

3.51 ± 0.271.05

†Top line reports the average value and the standard deviation.‡Bottom line shows the property range.MLP: Molecular lipophilicity potential.



�The constraints shown by protonated forms are stronger than for unprotonated forms, a finding clearly explained in terms of rein-forced intra-and inter-molecular polar con-tacts that protonated ligands can stabilize. Moreover, the protonated (R)-propranolol butyl ester shows conformational constraints greater than lipophilicity constraints in both isozymes and this may confirm that human carboxylesterases preferentially hydrolyze neu-tral substrates, whereas protonated esters remain trapped within the catalytic cavity behaving as competitive inhibitors.

As summarized by FiguRe 4 and discussed later, the ratio between property and structural constraints experienced by a given ligand when bound to an enzyme can be seen as a measure of molecular plasticity, namely the ability to adapt itself, modulating diverse property and confor-mational constraints. This ratio may become an innovative, if time-demanding, parameter in the investigation of bioactivity profiles. In particular, the analyses reported herein suggest that property spaces that decrease more mark-edly than conformational flexibility point to a productive interaction with an enzyme, and that such a ligand should behave as a substrate or an agonist. Conversely, property spaces that decrease proportionally to conformational flex-ibility may indicate that the ligand cannot form a stable complex with the enzyme and progres-sively leaves the binding site. Finally, a confor-mational space more constrained than property spaces may be typical of competitive antago-nists, which physically engage the binding cav-ity without adapting themselves to the enzyme properties and, consequently, without triggering protein activation.

� Property space & QSAR analysesAs stated in the Introduction and evidenced by previous sections, two classes of descriptors can be used to parameterize the property space of a given molecule. The first class of descrip-tors accounts for the extent of the property vari-ability and can easily be quantified by property ranges; as for the second class, it describes the dynamic relations between a given property and other geometric or physicochemical properties and leads to the concept of molecular sensitivity, as discussed earlier.

From a mathematical point of view, the molecular sensitivity for a given conformation-dependent property can be obtained as the ratio between the property range and the RMSD

mean (as computed by comparing the atomic coordinates of all nonredundant conformers). In other words, molecular sensitivity can be conceived as the property range normalized by the RMSD value or, better, the property vari-ability that a molecule can exhibit per each Å of difference in atomic positions.

Considering also the well-known correlation between molecular flexibility and the number of rotatable bonds, this suggests that the latter descriptor can also be used to derive a somewhat different definition of molecular sensitivity, namely the ratio between a property range and the number of rotatable bonds. This new defini-tion yields sensitivity values modestly correlated with previous ones (r2 = 0.39), suggesting that their information content is different, mak-ing the latter perhaps advantageous compared with the former. Indeed, the new definition is more intuitive, being based on a parameter (the number of rotatable bonds) that is commonly used by medicinal chemists; it is also easier to compute, the number of rotors being derivable

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Figure 4. Graphical representation of the molecular plasticity expressed as the ratio between normalized property and conformational constraints derived by comparing simulations of a given ligand in vacuo and complexed with a protein (as seen in FiguRe 2). The figure highlights the possibility to exploit this ratio to evaluate the biological activity of the simulated ligands. Notice that the reported molecular plasticity is a dimensionless property since it is computed as a ratio between percentage values.



from 2D molecular formula. Moreover, there is no cross-correlation with the computed properties (sensitivity vs log P range: r2 = 0.23;

sensitivity vs number of rotors: r2 = 0.05; see table 2), whereas the former definition of sen-sitivity gave a fair correlation with the log P range (r2 = 0.58), suggesting overlapping infor-mation in the two descriptors. Conversely, the lack of cross-correlations for the new sensitivity descriptor implies that it indeed contains novel information not encoded by other descriptors and suggests that it could find fertile appli-cations in dynamic QSAR (or quantitative structure–property relationship) studies.

In the first application of the property space, range and molecular sensitivity were exploited to rationalize the pharmacological properties of a dataset of 36 ligands of the a

1a, a

1b and a

1d

adrenoceptors as published by Bremner et al. [50]. As expected, neither the range nor the sensitivity of any of the considered physicochemical proper-ties correlated with receptor affinities, which we hypothesize depended on the ability to assume well-defined property values irrespectively of the property variability. In contrast, range and sensi-tivity showed promising correlations with ligand selectivity ratios. In particular, DpK(a-b) (i.e., the a

1a /a

1b selectivity) afforded a remarkable

correlation for the complete dataset. The cor-relations were lower for DpK(a-d) (i.e., the a

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selectivity), whereas there was no correlation at all with DpK(b-d). These results are consis-tent with those derived from MD simulations of acetylcholine bound to mAChRs and sug-gest that the different ability to bind to receptor subtypes is mostly due to entropic differences, which can be suitably parameterized by property space descriptors.

The concept of molecular sensitivity and the discrimination between ‘sensitive’ and ‘insensitive’ (in fact, less sensitive) molecules was substantiated by considering the property space of a heterogeneous set of 125 biologically active compounds [39]. Despite what one would expect a priori, there is only a fair correlation between property ranges and molecular flexibil-ity (as defined by the number of rotors, r2 @ 0.5, FiguRe 5a) and this underlines that information encoded by property spaces cannot be reduced to mere structural variability. Thus, property spaces seem better suited to characterize the dynamic profile of a given molecule, while their parameters (namely, range and sensitivity) can give a richer information compared with simple flexibility descriptors. What is more, FiguRe 5b shows that the distribution of log P sensitiv-ity values for the 125 molecules as obtained from the ratio log P range/number of rotatable

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Figure 5. Lipophilicity space and molecular sensitivity as computed for the database of 125 heterogeneous compounds. (A) Correlation between logPMLP ranges and the number of rotors. The figure emphasizes the modest correlation between property variability and molecular flexibility and introduces the concept of molecular sensitivity since it allows to subdivide the compounds into sensitive ones (above the regression line) and insensitive ones (in fact less sensitive, below the regression line). The arrow points to ketokonazole, which is the most sensitive compound within the explored database. (B) Distribution of logPMLP sensitivity values, computed as the ratio of logPMLP range over the number of rotors. The statistics refer to the calculated monomodal distribution curve (black line) and to its deconvolution into two Gaussians (dashed line). Reproduced with permission from [39]. © Wiley-VCH.



bonds can be conveniently deconvoluted in two Gaussian-type peaks, which define two clear-cut clusters, the less sensitive molecules being the majority.

Globally, the study of such a database of 125 compounds confirmed the fertility of the prop-erty space concept, which can find applications to improve the 3D prediction of lipophilicity by accounting for the dynamic profile of flexible molecules. Indeed, the introduction of prop-erty space descriptors in the correlation models allowed to enhance the predictions of both log P and log D

7.4. Specifically, the log D

7.4 predic-

tion was improved by considering (and com-paring) the different property spaces of neutral and ionized species. The relevance of improving the conformer-dependent log P predictions by exploiting property space parameters can find important applications in the log P calcula-tion of diastereoisomeric molecules and will be discussed below.

The property space descriptors found also interesting applications in predicting ADME parameters, since they were successfully exploited to predict both transdermal permeability and volume of distribution, both of which represent a measure of the relative partitioning of drugs between plasma and tissues [34,39]. In both cases, the remarkable enhancement of the predictive models exerted by the introduction of property space parameters emphasizes the relevance of accounting for molecular plasticity when mod-eling permeation processes, which depend on the adaptability a molecule can exhibit when inserted in media of different polarity.

Even if not fully devoted to the property space, two recent studies fruitfully exploited the property space concept showing that it can find intriguing applications to model molecular processes, where plasticity plays a key role. In the first study the lipophilicity of a set of poly-methylmetacrilate oligomers was rationalized in terms of the variability of their polar and apo-lar surfaces [51]. The second study involved the use of property space descriptors to develop an enhanced log P prediction equation especially targeted to steroidal derivatives, with the aim to explain the different chromatographic pro-files of a set of diastereoisomeric metabolites of methylprednisolone [52].

As mentioned previously, this second study deserves special attention because it represents one of the first examples in which property spaces allowed a better characterization of stereoiso-meric molecules. Indeed, the log P differences

between diastereoisomers cannot be calculated by 2D algorithms, which are generally more accurate (as recently reviewed by Mannhold and co-workers [33]) but do not account for con-figurational factors. Hence, it is necessary to use 3D approaches while enhancing their pre-dictive power so they may better predict log P differences between diastereoisomers. To this end, property space parameters can be exploited to derive targeted relationships (as seen in the reported study for steroids with r2 = 0.95) accu-rate enough to reliably predict the different log P of diastereoisomers. Therefore, one can imagine that property spaces can find general applica-tions to better analyze conformation-dependent physicochemical properties of diastereoisomers, accounting for the plasticity differences induced by configurational differences.

� Property space & biomacromoleculesThe concept of property spaces also applies to biomacromolecules and is of particular interest to evaluate the consequences of protein flexibil-ity. The relevance of the concept clearly emerges when considering the extreme difficulty to dis-criminate during extended protein dynamics (as derived, for example, from MD simulations) between relevant information (e.g., conforma-tional transitions, folding/unfolding mecha-nisms and aggregation processes) and computa-tional noise (insignificant local fluctuations or random conformational shifts). Moreover, it is meaningful to distinguish between backbone flexibility and the flexibility of the side chains in the residues.

With regard to local flexibility, MD simula-tions of the protein profilin Ib performed over 10 ns revealed large differences in the behavior of the side chains compared with the free amino acids, with their conformational space severely restricted and/or shifted to regions improbable in the free state [53,54]. The significant conse-quences of such constraints on side-chain recog-nition forces and interaction fields have not been sufficiently explored and deserve to be evaluated on a larger scale [55], also because such confor-mational constraints can contribute notably to protein recognition specificity towards other macromolecules and ligands as proposed by Loewenstein [56].

The need for fruitful approaches to describe backbone f lexibility is particularly evident when analyzing the mechanisms of protein folding/unfolding due to the remarkable dif-ficulty to extract critical information from long



MD trajectories. Such a problem is evident when analyzing multiple simulations for the unfold-ing process since simple structure-based com-parisons (mainly based on RMSD calculations) are not suitable to gain adequate information, whereas an ana lysis of time variation for selected physicochemical properties (namely a property space ana lysis) appears markedly more produc-tive. Kazmirski and co-workers applied such a method to analyze multiple unfolding simula-tions for three simple proteins whose unfolding pathways are quite similar, since they proceed via expansion of the core to yield the major transition state [57]. After the transition state, the trajectories for a given protein diverge as the protein loses further secondary and tertiary structure by a variety of mechanisms. Although the pathways differ in conformational space, the properties of the conformations are often similar, highlighting that there may be many different conformational trajectories of unfold-ing that fit within a common property space. These results are in excellent agreement with our previous consideration, namely that con-formational space and property space are quite unrelated and that biological processes require well-defined property spaces while allowing for marked conformational variability.

Considering the fruitfulness of such a pioneer-ing study, it comes as no surprise that property spaces have found several applications to ana-lyze protein simulations. For example, property space ana lysis was exploited to compare 46 MD runs in which refolding of the engrailed home-odomain protein was simulated, clearly cor-relating with the single simulation in which the protein successfully refolded [58]. Property space ana lysis was also exploited by Toofanny and co-workers to filter out the data from tra-jectories for 188 globular proteins [59]. In detail, the space of 15 physicochemical properties was explored by principal component ana lysis to define the unfolding reaction coordinates. The property space ana lysis allowed to easily distin-guish among unfolded, near-native transition state and folded structures, thus indicating that property space ana lysis represents an important approach to compare protein dynamics as well as to characterize the unfolding pathway of individual proteins.

Zhao and co-workers recently analyzed unfolding simulations of L and G proteins by comparing the spaces of twelve physicochemical properties [60]. Such an ana lysis allowed one to recognize the preferred unfolding mechanisms,

which are quite similar for the two simulated proteins. The results confirmed that property space ana lysis affords rich information that can-not be easily derived by simple conformational analyses. Property space can also find relevant applications to identify the potentially amyloido-genic conformations as derived by MD simula-tions for transthyretin and a mutant (L55P-TTR) with high tendency for amyloid formation [61]. Specifically, property space ana lysis allowed the conformations generated for both proteins to be suitably clustered and revealed those compatible with aggregation.

Finally, Kundu and Roy analyzed the MD run of a type III antifreeze protein by plotting the ratio between its physicochemical properties and RMSD values [62]. This procedure identi-fied the unfolding mechanism indicating that it occurs without detectable intermediates and suggesting a two-state unfolding kinetics. It is here interesting to note that this ratio between physicochemical properties and RMSD is com-parable to the molecular sensitivity concept and confirms that the ratio between physicochemi-cal and structural descriptors can be particularly informative to monitor molecular plasticity. The representative examples reported in this section clearly emphasize the potential of such an approach to explore the plasticity of large biomacromolecules also considering that it is really difficult to extract significant information from simulations of complex systems using only geometrical descriptors.

DiscussionThe different applications of the concept of property space reported in this review empha-size that the dynamic nature of molecules is too often a missing dimension when encoding chem-ical information. Indeed, in several studies the molecules are considered statically whereas each compound spans specific property spaces whose variability is only partly controlled by molecular flexibility. What is more, the molecular plasticity parameter proposed herein, namely the capacity of a given molecule to modulate independently its conformational and property spaces, can find important applications when investigating its biological profile.

Taken globally, this review also enlightens the pivotal role of the ratio between property and conformational spaces. First, the dynamic rela-tions between a given property and structural variability leads to the concept of molecular sen-sitivity, which is defined as the ratio between



the property range and an index of flexibility such as the RMSD mean, or better the num-ber of rotatable bonds. The successful applica-tions reported may confirm that compounds can indeed be subdivided into sensitive and less sensitive ones (as seen in FiguRe 5b) and point to a potentially fruitful avenue of research for molecular sensitivity.

Moreover, by comparing the simulations of a given ligand in a vacuum and when protein-bound, it is possible to define a new ratio between the normalized constraints induced on property spaces and those affecting conformational flex-ibility. Such a ratio encodes the ligand’s plas-ticity, namely the capacity of a ligand to adapt itself during molecular recognition and binding, modulating in a different manner property vari-ability and molecular flexibility. As previously described and graphically represented in FiguRe 4, one may hypothesize that such a ratio can assume three classes of values depending on the intrinsic activity of the ligand. These three possible cases can be summarized as follows:�Property constraints greater than conforma-

tional constraints (i.e., ratio > 1) may be indic-ative of a ligand that actively interacts with a biological target, be it as an agonist (as seen for muscarine) or a substrate (as seen for carnosine, temocapril and propranolol esters). Such a ratio means that molecular recognition is based on a mutual adaptability by which the target selects the most suitable properties of the ligand while allowing a certain degree of con-formational variability. This observation does not support the traditional concept of a bioac-tive conformation, but points to the signifi-cance of an optimal value in some biorelevant molecular properties, at least when agonists or substrates are concerned. This ratio also sug-gests that the selection of an optimal property value does not necessarily translate into strong conformational constraints, an intriguing con-cept in drug design since it implies that an optimal property value can be reached through various bioactive conformations without an entropic penalty;

�Property constraints comparable to conforma-tional constraints (i.e., ratio ≈ 1) may indicate that the molecule is unable to form stable com-plexes with the receptor and, thus, tends to progressively exit from the catalytic cavity. This is the case for enzymatic products (as seen for temocaprilat and propranolol) or, more gener-ally, for compounds lacking significant affinity

for the simulated protein. The monitored con-straints are mainly due to the random pressure experienced by the ligand during its egress, in which case conformational constraints approximately parallel property constraints;

�Conformational constraints greater than property constraints (i.e., ratio < 1) may be indicative of an antagonist or inhibitor mol-ecule (as seen for the protonated forms of CES1/CES2 ligands), which stably engages the binding site without activating the pro-tein. This suggests that such an inhibitory mechanism involves an ability of the ligand to fit into the binding site without adapting its properties to the conditions needed for enzymatic activation, thereby leaving the pro-tein trapped in an unproductive conforma-tion. This would indicate that the concept of bioactive conformations can still prove useful in the design of inhibitors or antagonists for which the ability to induce an unproductive conformation of the protein seems to play a crucial role.

Even if time demanding, the ana lysis of con-formational and property constraints induced by binding to a protein may provide valuable information, unveiling the intrinsic activity of a given compound and evidencing the main factors governing its capacity for molecular recognition. Interestingly, our simulations of protein complexes and the studies here reported on protein unfolding suggests that a property space ana lysis can be fruitfully exploited to extract meaningful information from protein simulations of long duration while the simple structural comparison of trajectories does not afford such information. To this end, our suite of VEGA programs includes features purposely developed to support conformational and prop-erty space analyses. Specifically, a rich set of geo-metrical and physicochemical properties can be computed by VEGA for each frame in a given trajectory and the results can be further analyzed by statistical and mathematical tools (e.g., clus-tering ana lysis, frequency spectrum ana lysis and fast Fourier transform noise filtering).

Future perspectiveThe increasing computational power avail-able to researchers allows one to simulate ever more complex systems over ever longer dura-tions. This trend will produce very large tra-jectories the ana lysis of which requires sophis-ticated approaches in order to extract relevant



information. The studies reviewed here suggest that the concept of property space may support the ana lysis of such complex simulations, espe-cially if they will be supported by newer, more informative conformation-dependent physico-chemical and geometrical descriptors, which may lead to a better understanding of molecular flexibility. Although the concept of molecular flexibility is widely used in a qualitative sense to discuss chemical and biological effects of a given compound, very few descriptors are hith-erto known to quantitatively account for molec-ular flexibility. Not to mention the absence of conformation-dependent flexibility descriptors, excluding RMSD, which, however, is not of general applicability since it can be somewhat biased by rototranslational differences [63]. It is conceivable that the availability of in-depth and specific flexibility descriptors will allow the relations between conformational and property spaces to be better unveiled.

Apart from the studies on protein folding, the applications of property space we reported were focused on ligand plasticity and allowed to better rationalize complex stabilities and, consequently, ligand affinities, intrinsic activities, and interac-tion forces driving recognition and binding. It is

conceivable that, when analyzing protein plastic-ity, the concept of property space will enlighten protein conformational transitions involved in ligand recognition and so reveal mechanisms of protein activation.

The described results clearly emphasize that property space and its related concepts (namely molecular plasticity and sensitivity) could find fertile applications in drug design to model all biological phenomena, which are driven by molecular recognition processes, including both protein binding and membrane permeation. In other words, property space is particularly useful to analyze how a given mol-ecule dynamically adapts itself to the simulated medium. Notably, property space could find applications in ligand-based methods provid-ing novel dynamic descriptors to be included in QSAR equations as well as in structure-based approaches to quantitatively describe the mutual adaptability between a molecule and its environment.

A second field in which a property space ana lysis can find innovative applications is in assessing the role of stereochemical factors. Several studies reported significant differences in measurable physicochemical properties

Executive summary � The concept of property space is based on the assumption that a flexible molecule (which, by definition, assumes numerous

conformations) will exhibit different values for a given conformation-dependent physicochemical property. In such cases, there will be a one-to-one relationship between a given conformer and the resulting property value. The ensemble of all values a given property can take thus defines its property space

� By simulating the dynamic behavior of small molecules inserted on media of different levels of structural organization, the ana lysis of their property spaces showed that each molecule, irrespective of its flexibility, tends to preserve much of its conformational and property spaces and adapts its physicochemical properties to those of the environment even if such an adaptability can involve different mechanisms.

� The applications of property space concepts for the ana lysis of molecular recognition processes unveiled the key role for the ratio between property constraints and conformational constraints as induced by protein interaction. In particular, the reported analyses suggest that property spaces that decrease more markedly than conformational flexibility point to a productive interaction with an enzyme, and that such a ligand should behave as a substrate or an agonist. Conversely, property spaces that decrease proportionally to conformational flexibility may indicate that the ligand cannot form a stable complex with the enzyme. Finally, a conformational space more constrained than property spaces may be typical of competitive antagonists, which physically engage the binding cavity without triggering protein activation.

� Two classes of descriptors can be used to parameterize the property space of a given molecule. The first class of descriptors accounts for the extent of the property variability and can easily be quantified by property ranges; as for the second class, it describes the dynamic relations between a given property and other geometric or physicochemical properties and leads to the concept of molecular sensitivity, which can be obtained as the ratio between the property range and number of rotatable bonds

� Such descriptors found fruitful applications to enhance the prediction of physicochemical properties, to rationalize the pharmacological properties of a dataset of 36 ligands of the a1a, a1b and a1d adrenoceptors accounting for the entropic factors, which govern the molecular recognition, and in ADME prediction to account for molecular plasticity when modeling permeation processes, which depend on the adaptability that a molecule can exhibit when inserted in media of different polarity.

� Molecular dynamics studies on protein unfolding suggest that a property space ana lysis can be fruitfully exploited to extract meaningful information from protein simulations of long duration while the simple structural comparison of trajectories does not afford such information.



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between diastereoisomers, especially when such differences are due to a different flexibility of the isomers.

Financial & competing interests disclosureThe authors have no relevant affiliations or financial involvement with any organization or entity with a finan-cial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert t estimony, grants or patents received or pending, or royalties.

No writing assistance was utilized in the production of this manuscript.



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39 Vistoli G, Pedretti A, Testa B. Partition coefficient and molecular flexibility: the concept of lipophilicity space. Chem. Biodivers. 6, 1152–1169 (2009).

40 Vistoli G, Pedretti A, Villa L, Testa B. The solute–solvent system: solvent constraints on the conformational dynamics of acetylcholine. J. Am. Chem. Soc. 124, 7472–7480 (2002).

41 Vistoli G, Pedretti A, Villa L, Testa B. Solvent constraints on the property space of acetylcholine. I. Isotropic solvents. J. Med. Chem. 48, 1759–1767 (2005).

42 Vistoli G, Pedretti A, Villa L, Testa B. Solvent constraints on the property space of acetylcholine. II. Ordered media. J. Med. Chem. 48, 6926–6935 (2005).

43 Vistoli G, Pedretti A, Testa B, Matucci R. The conformational and property space of acetylcholine bound to muscarinic receptors. Arch. Biochem. Biophys. 464, 112–121 (2007).

44 Pedretti A, Vistoli G, Marconi C, Testa B. Muscarinic receptors: a comparative ana lysis of structural features and binding modes through homology modeling and molecular docking. Chem. Biodivers. 3, 481–501 (2006).

45 Hipkiss AR. Carnosine and its possible roles in nutrition and health. Adv. Food Nutr. Res. 57, 87–154 (2009).

46 Vistoli G, Pedretti A, Cattaneo M, Aldini G, Testa B. Homology modeling of human serum carnosinase, a potential medicinal target, and MD simulations of its allosteric activation by citrate. J. Med. Chem. 49, 3269–3277 (2006).

47 Vistoli G, Pedretti A, Mazzolari A, Bolchi C, Testa B. Influence of ionization state on the activation of temocapril by hCES1: a molecular-dynamics study. Chem. Biodivers. 6, 2092–2100 (2009).

48 Vistoli G, Pedretti A, Mazzolari A, Testa B. Homology modeling and metabolism prediction of human carboxylesterase-2 using docking analyses by GriDock: a parallelized tool based on AutoDock 4.0. J. Comput. Aided Mol. Des. 24, 771–787 (2010).

49 Taketani M, Shii M, Ohura K, Ninomiya S, Imai T. Carboxylesterase in the liver and small intestine of experimental animals and human. Life Sci. 81, 924–932 (2007).

50 Bremner JB, Coban B, Griffith R, Groenewoud KM, Yates BF. Ligand design for a(1) adrenoceptor subtype selective antagonists. Bioorgan. Med. Chem. 8, 201–214 (2000).

51 Cilurzo F, Gennari CG, Selmin F, Vistoli G. Effects of metal ions on entero-soluble poly(methacrylic acid-methyl methacrylate) coating: a combined ana lysis by ATR-FTIR spectroscopy and computational approaches. Mol. Pharm. 7, 421–430 (2010).

52 Panusa A, Aldini G, Orioli M, Vistoli G, Rossoni G, Carini M. A sensitive and specific precursor ion scanning approach in liquid chromatography/electrospray ionization tandem mass spectrometry to detect methylprednisolone acetate and its metabolites in rat urine. Rapid Commun. Mass Spectrom. 24, 1583–1594 (2010).

53 Bojarski AJ, Nowak M, Testa B. Conformational constraints on side chains in protein residues increase their information content. Cell. Mol. Life Sci. 60, 2526–2531 (2003).

54 Bojarski AJ, Nowak M, Testa B. Conformational fluctuations versus constraints in amino acid side chains: the evolution of information content from free amino acids to proteins. Chem. Biodivers. 3, 245–273 (2006).

55 Testa B, Raynaud I, Kier LB. What differentiates free amino acids and amino acyl residues? An exploration of conformational and lipophilicity spaces. Helv. Chim. Acta 82, 657–665 (1999).

56 Loewenstein WR. The Touchstone of Life: Molecular Information, Cell Communication and the Foundation of Life. Penguin, London, UK (2000).

57 Kazmirski SL, Li A, Daggett V. Analysis methods for comparison of multiple molecular dynamics trajectories: applications to protein unfolding pathways and denatured ensembles. J. Mol. Biol. 290, 283–304 (1999).

58 McCully ME, Beck DA, Fersht AR, Daggett V. Refolding the engrailed homeodomain: structural basis for the accumulation of a folding intermediate. Biophys. J. 99, 1628–1636 (2010).

59 Toofanny RD, Jonsson AL, Daggett V. A comprehensive multidimensional-embedded, one-dimensional reaction coordinate for protein unfolding/folding. Biophys. J. 98, 2671–2681 (2010).

60 Zhao L, Wang J, Dou X, Cao Z. Studying the unfolding process of protein G and protein L under physical property space. BMC Bioinformatics 10, (Suppl. 1), S44 (2009).

61 Rodrigues JR, Simões CJ, Silva CG, Brito RM. Potentially amyloidogenic conformational intermediates populate the unfolding landscape of transthyretin: insights from molecular dynamics simulations. Protein Sci. 19, 202–219 (2010).

62 Kundu S, Roy D. Temperature-induced unfolding pathway of a type III antifreeze protein: insight from molecular dynamics simulation. J. Mol. Graph. Model. 27, 88–94 (2008).

63 Todeschini R, Consonni V. Molecular Descriptors for Chemoinformatics. Wiley-VCH, Weinheim, Germany (2009).

64 Tsai RS, Carrupt PA, Testa B, El Tayar N, Grunewald GL, Casy AF. Influence of stereochemical factors on the partition coefficient of diastereomers in a biphasic octan-1-ol/water system. J. Chem. Res. 1901–1920 (1993).

65 Hutt AJ. Chirality and pharmacokinetics: an area of neglected dimensionality? Drug Metabol. Drug Interact. 22, 79–112 (2007).

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