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Chapter 6. VolSurf Descriptors
The interaction of molecules with biological membranes is mediated by surface properties such as shape, electrostatic, hydrogen-bonding and hydrophobicity. Therefore, the GRID [8-9] force-field was chosen to characterize potential polar and hydrophobic interaction sites by the OH2 and DRY probe, respectively, and to transform this information into a quantitative scale by calculating the volume or the surface of the interaction contours.
As outlined below, 40 descriptors from the OH2 probe, 28 descriptors from the DRY probe, 4 OH2-DRY mixed descriptors and 6 other descriptors (not depending on GRID maps) are generated. All these will be referred to as VolSurf descriptors. Moreover, when a third polar probe is used (like the carbonyl O), 16 additional variables are part of the molecular description, giving a total of 94 descriptors.
| OH2 | DRY | BOTH | polar | charged | |
|---|---|---|---|---|---|
| Molecular Volume (V) | yes | ||||
| Molecular Surface (S) | yes | ||||
| Hydrophilic regions (W1-W8) | yes | yes | yes | yes | |
| Hydrophobic regions (D1-D8) | yes | ||||
| Hydrophilic Best Volumes | yes | yes | yes | yes | |
| Hydrophobic Best Volumes | yes | yes | yes | yes | |
| Integy moment (Iw1-Iw8) | yes | ||||
| Hydrophobic Integy moment (ID1-ID8) | yes | ||||
| Capacity Factor (Cw1-Cw8) | yes | ||||
| Volume/surface Ratio (R) | yes | ||||
| Molecular Globularity (G) | yes | ||||
| Hydrophilic Local Interaction Energy Minima (Emin1-3) | yes | ||||
| Hydrophilic Local Interaction Energy Minima Distances (d12-d13-d23) | yes | ||||
| Hydrophobic Local Interaction Energy Minima (Emin1-3) | yes | ||||
| Hydrophobic Local Interaction Energy Minima Distances (d12-d13-d23) | yes | ||||
| Hydrophilic-Lipophilic balance (HL1-HL2) | yes * | ||||
| Amphiphilic moment (A) | yes * | ||||
| Critical Packing (CP) | yes * | ||||
| Hydrogen Bonding (HB1-HB8) | yes * | ||||
| Elongation (Elon-EEFR) | |||||
| Diffusivity | |||||
| LogP | |||||
| TOTAL (max. number of variables, for 8 levels) | 10+8x3 | 4+8x2 | 8 | 2x8 | 8 |
* variables computed only when there is present also a water probe.
The first 4 parameters describe the size and the shape of the molecule; descriptors 5-12 indicate polar interaction sites at 8 different energy levels.
The newly introduced "Best Volumes" descriptors are 13-18: descriptors 13-15 are referred to the local hydrophilic volumes at -1.0 kcal/mol produced with the water probe, whereas 16-18 are referred to the local hydrophilic volumes at -3.0 kcal/mol.
The "integy moment" (19-26) is defined in analogy to the dipole moment and describes the distance of the center of mass to the barycenter of polar interaction sites at a given energy level. The higher the integy moment, the clearer is the separation between polar and hydrophobic interaction sites; the lower the integy moment, the closer are the center of the molecule and the barycenter of polar moieties. This could be due either to polar moieties close to the center of mass or at opposite ends of the molecule.
Descriptors 27-34 calculate the concentration of polar interactions on the molecular surface (Capacity descriptors) at 8 energy levels.
The best three local minima of interaction energy between the water probe and the target molecule give rise to six descriptors, which represent their energy of interaction in kcal/mol (35-37) and the distances between them (38-40).
Descriptors 41-48 indicate interactions with the hydrophobic probe at 8 different energy levels, which have been adapted to the energy range of the DRY probe.
The newly introduced "Best Volumes" descriptors for the hydrophobic region are 49-54: descriptors 49-51 are referred to an interaction energy for the DRY probe of -0.6 kcal/mol, whereas 52-54 are referred to -1.0 kcal/mol.
Descriptors 55-62 "hydrophobic integy moment" describe the distance of the molecular center of mass and the barycenter of hydrophobic interaction regions.
The best three local minima of interaction energy between the DRY probe and the target molecule give rise to other six descriptors, which represent their energy of interaction in kcal/mol (63-65) and the distances between them (66-68).
Further descriptors, such as HL1 (69) and HL2 (70), the amphiphilic moment A (71), and the critical Packing CP (72) measure the balance between hydrophilic and lipophilic moieties.
In the version 3 of VolSurf Polarizability and Molecular Weight completed the list of descriptors. From version 4, four new variables have been added: two of these describe the molecular elongation, whereas the last two are physico-chemical properties (diffusivity and LogP) directly calculated according to internal equations.
Summing up, the 3D molecular structure is translated into physico-chemically meaningful descriptors without the need for alignment. Thus, size, shape, hydrogen-bonding and hydrophobicity can be quantitatively differentiated within a series of molecules. The resulting collinearity of descriptors is properly taken into account by suitable multivariate statistics.
All the VolSurf descriptors are reported and explained in detail below.
6.1. Meaning of VolSurf descriptors
- Molecular Volume (V)
is defined when a water probe is interacting with a target solute molecule. It represents the water solvent excluded volume (in Å3), i.e. the volume contained within the water accessible surface computed at 0.20 kcal/mol.
- Molecular Surface (S)
is defined when a water probe is interacting with a target solute molecule. It represents the accessible surface (in Å2) traced out by a water probe interacting at 0.20 kcal/mol when rolling over the target molecule.
- Ratio Volume/Surface (R)
is a measure of molecular wrinkled surface (rugosity). The smaller the ratio, the larger is the rugosity.
- Molecular Globularity (G)
is defined as S/Sequivalent, in which Sequivalent is the surface area of a sphere of volume V. Globularity is 1.0 for perfect spherical molecules. It assumes values greater than 1.0 for real spheroidal molecules. Globularity is also related to molecular flexibility.
- Hydrophilic regions (W1 - W8)
are calculated at eight different energy levels (-0.2 -0.5 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 kcal/mol) and may be defined as the molecular envelope accessible by solvent water molecules. The volume of this envelope varies with the level of interaction energies between water and the solute molecule. In general, W 1-4 account for polarizability and dispersion forces, while W 5-8 account for polar and hydrogen bond donor-acceptor regions.
- Best Volumes (BV11 BV21 BV31 BV12 BV22 BV32)
are six new descriptors which represent the best three hydrophilic generated by a water molecule when interacting with the target. The best volumes are measured at -1 and -3 kcal/mol. To understand the concept of best volumes, we refer to the definition of common group used by VolSurf. When an atom is responsible the existence of two or more contiguous interaction enery points of the grid cage, these two points could be considered as belonging to the same group.
In the 3D grid map around the molecules, some groupsmay be identified and for specific energy values their volume can be calculated. BV descriptors refer to the first, second and third largest volumes among such groups.
The contribution to the field produced by each atom of the molecule can be appreciated by using the specific options in 3D-plots.
- Integy Moments (Iw1 - Iw8)
are calculated at eight different energy levels (-0.2 -0.5 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 kcal/mol) and measure the unbalance between the center of mass of a molecule and the position of the hydrophilic regions around it. Integy moments are vectors pointing from the center of mass to the center of W1-W8 respectively. If the integy moment is high, the hydrated regions are clearly concentrated in only one part of the molecular surface. If the integy moment is small, the polar moieties are either close to the center of mass or at opposite ends of the molecule; thereby, the resulting barycenter is close to the center of the molecule. Integy moments are visualized in the real 3D molecular space as red vectors.
- Capacity factors (Cw1 - Cw8)
are calculated at eight different energy levels (-0.2 -0.5 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 kcal/mol) and represent the ratio between the hydrophilic regions and the molecular surface, i.e. the amount of hydrophilic regions per surface unit.
- Hydrophobic regions (D1 - D8)
are defined when a DRY probe is interacting with a target molecule. Hydrophobic regions indicate interactions with the hydrophobic probe at eight different energy levels, which have been adapted to the energy range of the DRY probe (-0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6).
- Hydrophobic Integy moments (ID1 - ID8)
are similar to the Integy moments, but are calculated from DRY probe 3D interaction maps. They measure the unbalance between the center of mass of a molecule and the position of the hydrophobic regions around it.
- Local Interaction Energy minima (Emin1 - Emin3)
represent the energies of interaction in kcal/mol, for the OH2 and DRY probes, of the best three local minima of interaction energy between the probe and the target molecule.
- Local interaction Energy minima distances (d12 d13 d23)
represent the distances, for the OH2 and DRY probes, between the best three local minima of interaction energy when the probe interacts with a target molecule.
- Hydrophilic-Lipophilic balance (HL1 HL2)
is the ratio between the hydrophilic regions measured at -3 and -4 kcal/mol and the hydrophobic regions measured at -0.6 and -0.8 kcal/mol. The balance describes which effect dominates in the molecule, or if they are roughly equal balanced.
- Amphiphilic Moment (A)
is defined as a vector pointing from the center of the hydrophobic domain to the center of the hydrophilic domain. The vector length is proportional to the strength of the amphiphilic moment, and it may determine the ability of a compound to penetrate a membrane.
- Critical Packing parameter (CP)
describes a ratio between the hydrophobic and lipophilic parts of a molecule. Conversely to HL balance, CP refers just to the molecular shape. It is defined as:
Hydrophobic calculation is made at -0.6 kcal while hydrophilic calculation at -3.0 kcal. CP is a good parameter to predict the molecular packing, such as in micelle formation.
- Polarizability (POL)
is an estimation of the average molecular polarizability, calculated following the additive method reported by K.J. Miller [10]. This method uses the structure of the compounds (extracted from the GRID kout files) and not any molecular field to compute the values; therefore it is independent of the number and type of used probes.
- Hydrogen Bonding (HB1 - HB8)
represent details about the hydrogen bonding capabilities of the targets, which can be different depending upon the nature of the polar probe used. These variables are obtained as the differences between the hydrophilic negative volumes (W1 - W8) between the water (OH2) and any other polar probe included, for each negative energy level considered. In fact, the water probe (OH2) presents an optimal ability to establish hydrogen bonds with the target, either donating or accepting one or more hydrogens. If a different polar probe is used, the interaction can be not so favorable due to the inability of this probe to accept or donate hydrogens.
- Elongation (Elon - EEFR)
El represents the maximum extension a molecule could reach if properly stretched. In addition, within each molecule a fixed part is considered as the rigid core, and a "Fixed Elongation" value can be calculated. Thereby, an additional descriptor is the Ratio between the Elongation and the Fixed Elongation (EEFR), which represents the portion of the extension given by the rigid part of the molecule.
- Diffusivity (DIFF)
is computed by mean of a linear equation derived by fitting VolSurf descriptors to experimental diffusivity data.
- LogP (LogP)
is computed by mean of a linear equation derived by fitting VolSurf descriptor to experimental data on water/octanol partition coefficient.
6.1.1. Conclusions
The pharmacokinetic properties of a drug often depend on a variety of physicochemical parameters and, therefore, require a multivariate description. The VolSurf descriptors quantitatively characterize size, shape, polarity, hydrophobicity and the balance between them. VolSurf descriptors are fast to calculate and independent of alignment of molecules.
Since the VolSurf parameters only encode physico-chemical properties, they are not suitable if active transport or extensive biotransformation and metabolism are involved.
However, if the pharmacokinetic phenomena to be modeled are linked with physicochemical properties, the VolSurf descriptors are ideally suited for lead optimization to explore the physicochemical property space by experimental design and to interpret quantitative structure-property relationships in terms of molecular structure. A further application can be envisioned as virtual screen in library design to bias the synthesis of compounds towards a common pattern of physicochemical properties as observed for well-absorbed drugs.
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