Which type of amino acids tend to cluster in the interior of proteins in an aqueous solution?

Biophysical Properties of Inhaled Anesthetics: Partial Pressure, Hydrophobicity, and Partition Coefficients

Inhaled anesthetics are administered as a component of a gas mixture. Biophysical properties of inhaled anesthetics are summarized inTable 20.1.2-11Partial pressure is the portion of total pressure contributed by one component of a gas mixture, where each component contributes pressure in direct proportion to its molar fraction. For example, 1.5% isoflurane in air (21% O2 and 79% N2) at 1 standard atmosphere (atm) (760 mm Hg) is a mixture of O2 at 157.2 mm Hg, N2 at 591.4 mm Hg, and isoflurane at 11.4 mm Hg. The partial pressure of an anesthetic gas is a measure of its thermodynamic activity and determines its pharmacologic effect. The partial pressure of an anesthetic is usually reported as the percentage (or fraction) of the delivered gas mixture, where atmospheric pressure is near 1 atm (760 mm Hg). Correcting these values to absolute partial pressure is important under conditions when local atmospheric pressure differs significantly from standard, such as at high altitude, underwater, or in a hyperbaric chamber. The same inhaled concentration of an anesthetic gas results in a reduced pharmacologic effect at higher altitudes because the partial pressure of the anesthetic is lower. Because partial pressure is the thermodynamic force for gas transfer between compartments in a system, anesthetics move from regions of high partial pressure to low partial pressure, unaffected by the other components of the gas mixture, and equilibrium is achieved when the partial pressure of an anesthetic is equal in the different compartments.

The maximum partial pressure of a volatile compound is itsvapor pressure; this is the partial pressure of volatile anesthetic (VA) within the drug reservoir of a vaporizer. Vapor pressure is unique to each anesthetic and increases with increasing temperature. VAs are defined by a vapor pressure less than 1 atm at 20°C and a boiling point above 20°C (seeTable 20.1). Gaseous anesthetics are defined by a vapor pressure above 1 atm at 20°C and a boiling point below 20°C (seeTable 20.1). VAs typically compose a small fraction of the gas mixture delivered to patients. In contrast, gaseous anesthetics such as nitrous oxide (N2O) and xenon, because of their relatively low anesthetic potencies, typically compose a large fraction of an inhaled gas mixture, and thus produce additional effects (e.g., concentration effect, second gas effect, and airspace expansion) that are negligible with VAs.

Hydrophobicity is a molecular property of certain chemicals, including most general anesthetics that do notreadily form hydrogen bonds and therefore display low water solubility. Hydrophobic compounds are also usuallylipophilic, demonstrating high solubility in low polarity solvents such as oils. Common measures of hydrophobicity arepartition coefficients between water and olive oil (which is mostly oleic acid, an 18-carbon fatty acid) or between water and n-octanol. Usually represented by the Greek letter lambda (λ), a partition coefficient is the ratio of two solute concentrationsatequilibrium (i.e., at equal partial pressure) in two separate but adjacent solvents or compartments such that the solute moves freely between the compartments (Fig. 20.1). Another useful way to conceptualize a partition coefficient is that it represents therelative volume of two phases or compartments that contain an equal amount of the solute at equilibrium (seeFig. 20.1).

Database-Independent Predictions: The Hydrophobicity Profile

Hydrophobicity profiles have been used to predict the location of turns in proteins. A hydrophobicity profile is a plot of the residue number versus residue hydrophobicity, averaged over a running window. The only variables are the size of the window used for averaging and the choice of hydrophobicity scale (of which there are many). No empirical data from the database is required. Peaks in the profile correspond to local maxima in hydrophobicity, and valleys to local minima. Prediction is based on the idea that apolar sites along the chain (i.e., peaks in the profile) will be disposed preferentially to the molecular interior, forming a hydrophobic core, whereas polar sites (i.e., valleys in the profile) will be disposed to the exterior and correspond to chain turns.

Hydrophobic polymers

Numerous synthetic polymers are used in medicine and some of these are biodegradable (or bioresorbable)in vivo.Fig. 16.7 shows examples of the chemical structures of biodegradable polymers that could be used in tissue engineering. Among these, the polyesters poly(glycolic acid) (PGA), poly(lactic acid) (PLA) and poly(ε-caprolactone) (PCL) and their copolymers such as poly(lactide-co-glycolide) (PLGA) have been widely used in tissue-engineering approaches.58 The mechanical strength and degradation rate of these polymers can be tuned over a wide range by changing the polymer properties (molecular weight, composition, molecular architecture, crystallinity, hydrophobicity).59 However, many biodegradable synthetic polymers are quite hydrophobic, unlike the ECM. Exposure of such surfacesin vivo can lead to nonspecific adsorption of proteins of mixed orientation and states of denaturation, potentially resulting in a foreign-body reaction (FBR) to the material.60

II Hydrophobicity and Hydrophobic Moment

Hydrophobicity, measured as a free energy change for the transfer of an amino acid from an apolar solvent such as n-octanol to water has been used, in general, to describe protein segments containing non-polar amino acid residues compatible for interaction with lipid bilayer (Kyte and Doolittle, 1982). Hydrophobicity is basically a measure of the degree of affinity between water and the side chain of an amino acid. Amino acids with non-polar side chains have higher hydrophobicities compared to amino acids with polar or charged side chains. To estimate the hydrophobicity of a protein segment, hydrophobicity of individual amino acids are averaged, assuming that the transfer of a chemical group from an apolar solvent is independent of the larger molecule to which the group is attached.

Prediction of membrane spanning segments of proteins works well with hydrophobicity calculations (Kyte and Doolittle, 1982) only for proteins having continuous stretches of peptide segments having significant hydrophobicity. Several protein segments although known to interact with membrane lipid bilayer have lower average hydrophobicities. It has been noticed that such protein segments have α-helical foldings which allow an asymmetric distribution of hydrophobic and hydrophilic amino acid residues resulting into an amphiphilic structure compatible for interaction with non-polar lipid bilayer. A quantitative estimation of the degree of amphiphilicity or the asymmetric distribution of the hydrophobicity is carried out by calculating the hydrophobic moment (Eisenberg et al., 1982; 1984; 1987). Hydrophobic moment is similar to the electric dipole moment. Electric dipole moment estimates asymmetry of electric charge whereas hydrophobic moment estimates asymmetric distribution of hydrophobicity.

When atomic coordinates of a protein segment are known, the hydrophobic moment (called the structural hydrophobic moment) can be calculated as follows (Eisenberg et al., 1987)

where, Hn is the hydrophobicity of the nth residue of the protein segment, and Sn is the unit vector pointing from the α-carbon atom to the center of the residue's side chain. Thus, hydrophobic moment is a measure of the sum of the directions of amino acid side chains, each weighted by its hydrophobicity. Hydrophobic moment can be estimated for a protein segment even if the atomic coordinates of amino acid residues in its sequence are not known. Such hydrophobic moment (called the sequence hydrophobic moment) can be estimated as follows (Eisenberg et al., 1982; 1984) assuming an α-helical or ß-sheet folding of the segment.

(2)μ={[∑nHnSin(ϕn)2]+[∑nHnCos(ϕn)2]}1/2

where, Hn is the hydrophobicity of the nth residue, ø is the angle (in radians) at which successive side chains emerge from the central axis of the structure, ø for α-helical structures is 100° whereas for ß-sheet structures, it is 160°. Both in structural and sequence hydrophobic moments, an amino acid residue with high hydrophobicity contributes strongly to the moment, whereas a hydrophilic residue having negative hydrophobicity contributes in the opposite direction. However, when hydrophobic residues protrude on one side of the structure and hydrophilic residues on the opposite side, this results into a large hydrophobic moment because both hydrophobic and hydrophilic residues contribute to the sum with the same sign. Thus, a highly amphiphilic peptide segment will have relatively large hydrophobic moment.

The membrane-spanning portions of transmembrane proteins are usually hydrophobic α helices

How can membrane-spanning proteins remain stably associated with the bilayer in a conformation that requires at least some portion of their amino-acid sequence to be in continuous contact with the membrane's hydrophobic central core? The answer to this question can be found in the special structures of those protein domains that actually span the membrane.

The side chains of the eight amino acids listed in the upper portion ofTable 2-1 are hydrophobic. These aromatic or uncharged aliphatic groups are almost as difficult to solvate in water as are the fatty-acid side chains of the membrane phospholipids themselves. Not surprisingly, therefore, these hydrophobic side chains are quite comfortable in the hydrophobic environment of the bilayer core. Mostmembrane-spanning segments—that is, the short stretches of amino acids that pass through the membrane once—are composed mainly of these nonpolar amino acids, in concert with polar, uncharged amino acids.

The hydrophobic, membrane-spanning segments of trans­membrane proteins are specially adapted to the hydrophobic milieu in which they reside. The phospholipid molecules of the membrane bilayer actually protect these portions of transmembrane proteins from energetically unfavorable interactions with the aqueous environment. Transmembrane proteins tend to be extremely insoluble in water. If we separate the membrane-spanning segments of these proteins from the amphipathic phospholipids that surround them, these hydrophobic sequences tend to interact tightly with one another rather than with water. The resulting large protein aggregates are generally insoluble and precipitate out of solution. If, however, we disrupt the phospholipid membrane by adding detergent, the amphipathic detergent molecules can substitute for the phospholipids. The hydrophobic membrane-spanning sequences remain insulated from interactions with the aqueous solvent, and the proteins remain soluble as components ofdetergent micelles. This ability of detergents to remove transmembrane proteins from the lipid bilayer—while maintaining the solubility and native architectures of these proteins—has proved important for purifying individual membrane proteins.

Transmembrane proteins can have a single membrane-spanning segment (seeFig. 2-5B) or several (seeFig. 2-5C). Those with a single transmembrane segment can be oriented with either their amino (N) or their carboxyl (C) terminus facing the extracellular space. Multispanning membrane proteins weave through the membrane like a thread through cloth. Again, the N and C termini can be exposed to either the cytoplasmic or extracellular compartments. The pattern with which the transmembrane protein weaves across the lipid bilayer defines its membranetopology.

The amino-acid sequences of membrane-spanning segments tend to form α helices, with ~3.6 amino acids per turn of the helix (seeFig. 2-5B). In this conformation, the polar atoms of the peptide backbone are maximally hydrogen bonded to one another—from one turn of the helix to the next—so they do not require the solvent to contribute hydrogen-bond partners. Hence, this structure ensures the solubility of the membrane-spanning sequence in the hydrophobic environment of the membrane. Whereas most transmembrane proteins appear to traverse the membrane with α-helical spans, it is clear that an intriguing subset of membrane polypeptides makes use of a very different structure. For example, the porin protein (seep. 109), which serves as a channel in bacterial membranes, has membrane-spanning portions arranged as a β barrel.

Hydrophobicity

Hydrophobicity of the packing material describes the major interaction governing the retention process in reversed-phase chromatography. The alkyl chains attached to the surface of chromatographic particles are hydrophobic (nonpolar, nonionic). Therefore, they interact with the nonpolar, nonionic part of a solute owing to dispersion forces. Hydrophobicity or hydrophobic strength (also referred to as hydrophobic retentivity) of a stationary phase relates to the overall strength of dispersion forces between a nonpolar, nonionic solute and the stationary phase. In empirical tests, hydrophobicity is measured as the retention factor of a nonpolar nonionic compound. The retention factor can be related to the equilibrium constant of solute distribution between the stationary and mobile phases (and through that to the free energy of solute transfer) and to the volume phase ratio of the column. Accordingly, the absolute value of hydrophobicity is condition-dependent and also influenced by the extra-column volume of the LC unit and the selection of the unretained marker.

5.3.4 Hydrophobicity profiles

Hydrophobicity analysis has remained at the central focus for understanding protein folding and stability and, especially, secondary structures of proteins, interior and exterior regions, antigenic sites, periodicities in residue distributions, and membrane associated regions. Rose (1978) computed the first hydrophobicity profile for a set of proteins to predict the turn regions in them. Hydrophobicity profile is a graph showing the local hydrophobicity of the amino acid sequence as a function of position. To display a hydrophobicity plot, one has to choose a hydrophobicity scale and an averaging procedure. It is also possible to get the profile without any average for single residue hydrophobicity plot. As an example, hydrophobicity profile of T4 lysozyme using surrounding hydrophobicity scale (Ponnuswamy and Gromiha, 1993) is shown in Figure 2.14b.

Cid et al. (1992) generated hydrophobicity profiles for several proteins using the surrounding hydrophobicity scale (Ponnuswamy et al. 1980) and derived general rules for identifying secondary structures. The hydrophobicity profiles for α-helices, buried and exposed β-strands and turns are shown in Figure 5.4. The following facts have been taken into account for drawing the profiles: (i) Turns occur at those sites in the polypeptide chain where the hydrophobicity is at a local minimum, (ii) helices are generally located nearer the surface of the protein and tend to have hydrophilic and hydrophobic surfaces at opposite sides. This fact originates alternating regions with low and high hydrophobicity with a periodicity of every 3 to 4 residues, corresponding to the α-helix periodicity of 3.6 amino acid residues, (iii) β-strands have a tendency to be buried in the interior of the protein, which shows up by a clustering of hydrophobic amino acid residues in the region of the sequence where a β-strand occurs, and (iv) few β-strands lying on the protein surface will show the presence of alternating hydrophobic and hydrophilic amino acid residues. The advantages of this method are as follows: (i) it is simple, (ii) it predicts β-turns and loops with great accuracy, (iii) when predicting β-strands, it can distinguish between exposed and buried -strands, and (iv) it provides an independent criterion to differentiate between helical and β-structures in regions where they present similar probabilities according to the Chou and Fasman (1974) method. The main disadvantages are that (i) it cannot differentiate between buried helical structures and buried β-strands, and (ii) the database does not include all types of proteins, like membrane proteins or glycoproteins, and hence its application is restricted.

Gromiha and Ponnuswamy (1995) followed the method of Cid et al. (1982) and constructed different hydrophobicity profiles of different window sizes for all-α, all-β and mixed class proteins. These profiles have been combined with the preference of amino acid residues at N − 1, N, C, and C + 1 positions of α-helices and β-strands to predict the secondary structures of globular proteins. These hydrophobicitybased methods can provide the physical basis of secondary structures, and the accuracy is modest.

3.9.3 Predicting drug-membrane interactions

Hydrophobicity is important in drug interactions with biological membranes, bioavailability distribution, and blood-brain barrier permeability. Often it is estimated in vitro by octanol-water partition coefficient or capacity factors by HPLC. However, CE offers some advantages such as the small sample size, low operating costs and speed [46,47]. Microemulsion electrokinetic chromatography, a technique similar to MECC [47] was used to estimate octanol-water capacity factors for some drugs and the values were very close to those in the literature. Using oppositely-charged surfactant vesicles as a buffer modifier to estimate hydrophobicity, there was a linear relationship between the log of capacity factor and the octanol-water partition coefficient for both neutral and basic species. Vesicular electrokinetic chromatography using surfactant vesicles as buffer modifiers was used for the estimation of hydrophobicity [48]. The chiral surfactant dodecoxycarbonylvaline has been used as a pseudo-stationary phase for the separation of many enantiomeric pharmaceutical compounds [49]. Its hydrophobicity was a good predictor for n-octanol-water partition coefficients for 15 beta amino alcohols [49]. A correlation was obtained for capacity factors determined by MECC, involving the use of phosphatidylcholine-bile acid mixed micelles in the separation buffer, by HPLC and log P of octanol-water [50]. The combination of MECC and HPLC data yielded a better predictive model for hydrophobicity [50]. The concentration of apolipoprotein H, a plasma glycoprotein, was performed by CE. Based on this determination, an interaction model of apoliporotein H and lipid monolayer was constructed [51].

Liposomes can be used as delivery vehicles for peptide and oligonucleotide drugs, influencing drug tissue distribution and protection. A simple method has been described for free and encapsulated oligonucleotide drugs in liposomes by CE in entangled Polyacrylamide solution [52].

Chromatographic Methods of Determination of Hydrophobicity

Hydrophobicity or lipophilicity is understood to be a measure of the relative tendency of an analyte ‘to prefer’ a nonaqueous over an aqueous environment. The partition coefficients of the substances may differ if determined in different organic–water solvent systems but their logarithms are often linearly related. Octanol–water is a reference system that provides the most commonly recognized hydrophobicity measure: the logarithm of the partition coefficient, log P. The standard ‘shake-flask’ method for determining partition coefficients in liquid–liquid systems has several disadvantages. Having appropriate QSRR, the chromatographic data can be used to predict log P. Many good correlations of reversed-phase liquid chromatographic (HPLC or TLC) parameters with log P have been reported for individual chemical families of analytes and chromatographic methods for assessing the hydrophobicity of drugs and environmentally important substances have officially been acknowledged and included in the OECD Guidelines for Testing Chemicals.

On the other hand, the partition chromatographic systems are not identical with the n-octanol–water partition system. Each chromatographic system produces an individual scale of hydrophobicity. Hence attempts to reproduce log P by means of liquid chromatography are only partially successful. Centrifugal countercurrent chromatography (CCCC) provides a better chance of mimicking log P but the inconvenience of this method and the need for special equipment hinder its wider application.

The versatility of chromatographic methods of hydrophobicity assessment can be attributed to the use of organic modifiers in aqueous eluents. Normally, the retention parameters determined at various organic modifier–water (buffer) compositions are extrapolated to zero organic modifier content. The extrapolated parameters (log kw from HPLC and RM0 from TLC) depend on the organic modifier used.

Alkyl silica stationary phases and methanol–water eluent are most often used in hydrophobicity studies. The problem with these phases is that the hydrophobicity of nonionized forms of organic bases cannot be determined because of the chemical instability of silica-based materials at higher pHs (above about pH 8). Also, specific interactions of analytes with the free silanols of alkyl silicas disturb partition processes.

The limitations of standard reversed-phase materials have been partially overcome by introducing modern specially deactivated hydrocarbon-bonded phases, immobilized on alumina or zirconia supports and on polymeric materials. Using the latter two types of stationary phase materials one can determine HPLC retention factors under acidic, neutral and alkaline conditions. That way a universal, continuous chromatographic hydrophobicity scale can be constructed, as is the standard log P scale.

Hydrophobic properties of xenobiotics are assumed to affect their passive diffusion though biological membranes and binding to pharmacological receptors. If the hydrophobicity measuring system is to model a given biological phenomenon, then similarity of the component entities is a prerequisite. Hence the partition system to model the transport through biological membranes should be composed of an aqueous phase and an organized phospholipid layer. The immobilized artificial membranes (IAM) introduced by Pidgeon as a packing material for HPLC (Figure 4) appear to be reliable and convenient models of natural membranes.

Correlations between log k data determined on IAM-type columns and log P values are generally not high nor are the correlations between log k from IAM columns and log kw determined by liquid chromatography employing standard stationary phase materials. This means that retention data determined on IAM columns contain information on the properties of analytes that is distinct from that provided by the n-octanol–water system and by the hydrocarbon–silica reversed-phase columns. There is evidence that the hydrophobicity characteristics provided by IAM columns are better suited for modelling the pharmacokinetics of drug processes.

2.4.1.1.2 Hydrophobic substituent constant (π)

Hydrophobicity[12,13] is the association of nonpolar groups or molecules in an aqueous environment, which arises from the tendency of water to exclude nonpolar molecules. The hydrophobicity of the compounds in the series can be represented on a relative scale with the hydrophobic substituent constant π. The value for the substituent X is defined as follows:

(2.3)πX=logPX−logPH

In Eq. (2.3), PX is the partition coefficient of the derivative and PH is the partition coefficient of the parent compound. The variable πX expresses the variation in lipophilicity, which results when the substituent X replaces H in RH. For example, the value of the chloro substituent πCl is the difference between the partition coefficient values of chlorobenzene and benzene. As another example, one may note that the log P values for benzene and benzamide are 2.13 and 0.64, respectively. Since benzene is the parent compound, the substituent constant for CONH2 is −1.49 (Figure 2.4).

A positive value of π indicates that the substituent is more hydrophobic than hydrogen, and a negative value indicates that the substituent is less hydrophobic. The π value is a characteristic for an individual substituent and can be used to calculate how the partition coefficient of a drug would be affected by adding that particular substituent.