PMC:6194691 / 208697-216069 JSONTXT

{"target":"http://pubannotation.org/docs/sourcedb/PMC/sourceid/6194691","sourcedb":"PMC","sourceid":"6194691","source_url":"https://www.ncbi.nlm.nih.gov/pmc/6194691","text":"Appendix C. Passive permeability of the blood–brain barrier: further consideration including the use of linear free energy relations\nThere are at least four reasons why the permeability-surface area product, PS, may not be predicted by comparison with the lipid solubility as assessed using n-octanol and molecular weight, i.e. with Kn-octanol/water MW−1/2: (1) a biological membrane is more ordered than a layer of n-octanol and thus partition into the membrane core may well differ from partition into the hydrophobic solvent particularly for larger solutes; (2) for large solutes the diffusion constant, even in a homogenous medium, is expected to vary with MW−1/3 rather than MW−1.2 [156, 157, 533]; (3) n-octanol, with the water it contains in a partition experiment [161], may differ from the membrane core in how it interacts with hydrogen bonding groups;24 (4) permeation may occur by pathways other than via the core of the membrane, e.g. transport for some of the substances considered may be via specific transporters (see Sect. 4.2), by transcytosis (see Sect. 4.3) or, particularly for small polar solutes, by a paracellular pathway (as mentioned in Sect. 4.1 an example may be mannitol); and (5) substances which are sufficiently lipid soluble to enter the endothelial cells may be effluxed or metabolised before they even reach the parenchyma (see Sect. 4.2.1).\nThe difference between partition into a membrane and partition into a liquid like n-octanol may be particularly marked for large solutes [162, 534]. The hydrophobic portions of membranes are composed of hydrophobic side chains of proteins and the chains of lipids both of which have positions constrained by the rest of the protein or the lipid headgroup. Attempts to insert large molecules into a membrane will inevitably require changes in membrane structure, e.g. lipid headgroups may be pushed apart, which will have an energy cost which must affect the permeability. However, it should be noted that the idea that larger molecules are excluded from the membranes was based on their failure to permeate which in many instances may have been because they were substrates for efflux transporters (see Sect. 4.2.1). It is somewhat puzzling that there have not been any attempts to correlate blood–brain barrier permeability with the partition of substances into easily obtained membranes, e.g. those of liposomes or red blood cells, rather than into simple solvents. Partition into red blood cell membranes was measured extensively in studies on the mechanism of general anaesthesia [535].\nThe predictions of the simple theory presented in Sect. 4.1 for passive, non-specific transport of neutral solutes across the blood–brain barrier describes important features of this transport, but leaves quite large discrepancies between the theoretical predictions and the experimental results (see Fig. 25). A more elaborate approach, based on the use of linear free energy relations has been described by Abraham and colleagues [165, 171, 536, 537]. In this approach each compound is represented by a set of quantitative descriptors that are properties of the substance considered in isolation. (Thus for instance Kn-octanol/water is not permitted). These have been chosen as far as possible to represent sufficient independent properties of the substances to allow characterization of their interactions with water, solvents, and sites of action (see below). To predict a property, e.g. the PS product, each descriptor is multiplied by a coefficient which depends on the property, but not on the substance. The sum of the products of coefficients and descriptors is the prediction of the logarithm of the property for that substance. Whenever the property concerned is an equilibrium constant, the logarithm of that property is, up to a constant, a free energy. Hence the name “linear free energy relation” as the prediction can be regarded as a linear sum of contributions to a free energy.\nFig. 25 Comparison of the predictions of the solubility-diffusion theory and of the linear free energy relation (LFER) for the PS product of the series of 18 compounds considered by Gratton et al. [166]. The solubility-diffusion theory, described in Sect. 4.1, predicts that log[PS] is proportional to Koctanol/water MW−1/2. MW is in turn approximately proportional to the McGowan characteristic volume used by Gratton et al. The straight, grey line with slope 1 indicates the predicted proportionality. It has one adjustable parameter that determines the vertical position of the line. The LFER prediction, described in this Appendix and shown as the line with multiple segments, has four adjustable parameters, three coefficients of descriptors of the compounds and the constant determining the vertical position of the whole curve. The improvement in fit is statistically significant (extra sum of squares test [640], F = 8.85 for 17 and 14 degrees of freedom, p \u003c 0.001)\nAbraham et al. [165] applied this approach to the prediction of partition coefficients from water into a number of solvents, including n-octanol for which25 logKn-octanol/water=0.088+0.562R2-1.054π2H-3.46∑β2H+3.81Vxwhere the descriptors are: excess molar refraction, R2; polarizability, π2H; solute hydrogen bond basicity, β2H, which is summed over the appropriate groups in the molecule; and molecular volume, Vx. See [165] and references therein for the rationale for choosing these descriptors and their definitions. The volume term makes the largest contribution to the differences between the 18 substances considered [166] with the larger substances being more soluble in n-octanol.\nGratton et al. [166] have applied this approach to the prediction of PS products using 18 substances to determine the values of the coefficients and test the accuracy of the predictions with the result:26 log[PS]=-1.21+0.77R2-1.87π2H-2.8∑β2H+3.31Vx.\nThis more elaborate theory does allow a statistically significant improvement in the fit of the calculated values of PS to those observed (see Fig. 25). Gratton et al. note that there is a strong dependence on molecular volume, with increases in volume being associated with increases in permeability.\nThe LFER approach does improve the ability to predict PS for a new substance. But it’s formulation has served to hide a major clue as to the mechanism of permeation. That clue can be revealed by calculating the prediction of the LFER approach for the ratio, PS/Kn-octanol/water:27 logPS/Kn-octanol/water=logPS-logKn-octanol/water=-1.12+0.21R2-0.82π2H+0.66∑β2H-0.5Vx.\nThus after allowing for the effect of the changes in n-octanol/water partition, there is much less variation to be explained and the remaining effect of an increase in molecular volume is predicted to be a decrease in permeability. (That this is the inverse square root relation predicted by the solubility-diffusion model is to some extent an “accident” of the choice of the preferred solvent for comparison, n-octanol. If olive oil had been chosen instead increases in volume would again be predicted to decrease permeability, but with a different more negative coefficient).\nFong [161] and Abraham [168, 171] provide discussions of which properties to use. Fong chooses desolvation from water, solvation in the membrane modelled by n-octanol, dipole moment and molecular volume. Molecular volume is negatively correlated.","divisions":[{"label":"title","span":{"begin":0,"end":132}},{"label":"p","span":{"begin":133,"end":1376}},{"label":"p","span":{"begin":1377,"end":2567}},{"label":"p","span":{"begin":2568,"end":4939}},{"label":"figure","span":{"begin":3965,"end":4939}},{"label":"label","span":{"begin":3965,"end":3972}},{"label":"caption","span":{"begin":3973,"end":4939}},{"label":"p","span":{"begin":3973,"end":4939}},{"label":"p","span":{"begin":4940,"end":5628}},{"label":"label","span":{"begin":5094,"end":5096}},{"label":"p","span":{"begin":5629,"end":5878}},{"label":"label","span":{"begin":5831,"end":5833}},{"label":"p","span":{"begin":5879,"end":6180}},{"label":"p","span":{"begin":6181,"end":6547}},{"label":"label","span":{"begin":6459,"end":6461}},{"label":"p","span":{"begin":6548,"end":7125}}],"tracks":[]}