Exceptions to the Meyer-Overton rule are commonly cited
as evidence against indirect, membrane-mediated mechanisms of general anesthesia. However, another interpretation is possible within the
context of an indirect mechanism in which solubilization of an
anesthetic in the membrane causes a redistribution of lateral pressures
in the membrane, which in turn shifts the conformational equilibrium of
membrane proteins such as ligand-gated ion channels. It is suggested
that compounds of different stiffness and interfacial activity have
different intrinsic potencies, i.e., they cause widely different
redistributions of the pressure profile (and thus different effects on
protein conformational equilibria) per unit concentration of the
compound in the membrane. Calculations incorporating the greater
stiffness of perfluoromethylenic chains and the large interfacial
attraction of hydroxyl groups predict the higher intrinsic potency of
short alkanols than alkanes, the cutoffs in potency of alkanes and
alkanols and the much shorter cutoffs for their perfluorinated
analogues. Both effects, increased stiffness and interfacial activity,
are present in unsaturated hydrocarbon solutes, and the intrinsic
potencies are predicted to depend on the magnitude of both effects and
on the number and locations of multiple bonds within the molecule. Most
importantly, the intrinsic potencies of polymeric alkanols with
regularly spaced hydroxyl groups are predicted to rise
with increasing chain length, without cutoff; such molecules should
serve to distinguish unambiguously between indirect mechanisms and
direct binding mechanisms of anesthesia.
 |
INTRODUCTION |
The potency of a general anesthetic is usually
described by its concentration in the phase in which it is administered
(gas or aqueous); the lower the concentration, the higher the potency. A century ago, Overton (1901
, translation 1990) and Meyer (1899, 1901)
independently discovered that for many compounds the anesthetic potency
(as measured by the inverse of its aqueous phase molar concentration
c*w) is nearly linearly
correlated with its oil/water partition coefficient
Ko/w = co/cw,
where co and
cw represent relative equilibrium concentrations of the anesthetic in the oil and water phases, respectively. There is a thermodynamically equivalent correlation between the oil/gas partition coefficient
Ko/g = co/cg
of the anesthetic and its potency measured by the inverse of its gas phase concentration c*g. The
correlation is remarkably good over a wide range of anesthetics, using
olive oil as the oil phase, as in the original work of Meyer and
Overton, and improves considerably in both the quality of the
correlation and the increased range of anesthetics if bulk octanol
(Franks and Lieb, 1978) or a fully hydrated fluid lipid bilayer (Janoff
et al., 1981; Taheri et al., 1991; Vaes et al., 1997; Meijer et al.,
1999) is used as the "oil" phase. To the extent that anesthetics
obey this Meyer-Overton correlation, the anesthetic concentration in
the oil phase, c*o = Ko/g
c*g = Ko/w
c*w, will be constant. If the oil is a
lipid bilayer, then c*o
represents the molar concentration of anesthetic in the
bilayer, which indicates that anesthetic potency is determined by the
bilayer concentration of anesthetic, independent of its molecular
identity. As was realized long ago, this correlation strongly suggests
an indirect mechanism of anesthesia in which the activity of the membrane protein(s) responsible for anesthesia is modulated by variations in some crucial property of the membrane, which is perturbed
by the incorporation of an anesthetic solute to a degree determined by
its concentration in the bilayer.
In the context of an indirect mechanism, it is natural to
define an intrinsic potency as inversely proportional to the membrane concentration of anesthetic, which would be expected to vary little among anesthetics that closely follow the Meyer-Overton rule. The
apparent potency for such compounds, inversely proportional to
c*g (or
c*w) may vary widely, but
Ko/g (or
Ko/w) varies in inverse proportion so
as to keep the intrinsic potency roughly constant. The concentrations in lipid bilayers of many such anesthetics can be determined from measured partial pressures or aqueous concentrations and bilayer/water or bilayer/gas partition coefficients (Janoff et al., 1981; Taheri et
al., 1991; Vaes et al., 1997; Meijer et al., 1999). For pure lipid
bilayers such as dimyristoylphosphatidylcholine (DMPC), the clinically
relevant mole fraction of anesthetics in the lipid bilayer is roughly
x* = 0.02 to 0.05 for anesthetics that obey the
Meyer-Overton rule (Janoff and Miller, 1982), although the value
decreases considerably if cholesterol is incorporated in the bilayer
(Miller, 1985; Franks and Lieb, 1986). Clearly, the "typical" value
of x* will depend on the choice of anesthetic endpoint, the
molecular composition of the bilayer, etc., so this range of values of
x* provides only a rough estimate.
It is not surprising that the exceptions to this rule have
received much attention. For example, short chain 1-alkanols have somewhat greater intrinsic potency than the rule would predict (Fang et
al., 1997). However, as their chain length n increases, the
intrinsic potency decreases (x* increases) up to
n 
12, beyond which the alkanols have no potency,
i.e., the homologous series exhibits a cutoff (Pringle et al., 1981;
Franks and Lieb, 1986). Within this series,
Ko/g (or
Ko/w) increases very rapidly with increasing chain length (by a multiplicative factor of approximately 3 per added methylene group.) Thus, the gradual decrease in intrinsic potency occurs simultaneously with an increase in apparent potency for
this series, resulting in a cutoff that is abrupt only for the apparent
potency. This behavior is observed for other homologous series. For
example, for 
,
-alkanediols, a decrease in intrinsic potency
occurs with increasing chain length, but less rapidly than for alkanols
(Moss et al., 1991). Alkanes, which are much less potent than the rule
would predict even when short, further lose intrinsic potency with
increasing chain length, with a cutoff at shorter length than for
alkanols (Liu et al., 1993, 1994b). Perfluorinated alkanes and
perfluoroalkyl methanols of the form Cn
1F2n1CH2OH
also exhibit a cutoff, but at even shorter chain lengths (Pringle et
al., 1981; Liu et al., 1994a; Eger et al., 1994, 1999a).
Deviations from the Meyer-Overton rule can be interpreted in
various ways. Most commonly, they are presented as evidence that the
fundamental premise of an indirect mechanism is incorrect, and that
anesthetics therefore are more likely to act by binding directly to
protein sites (Krasowski and Harrison, 1999; Franks and Lieb, 1994),
although the direct experimental evidence for the location of such
sites on ligand-gated ion channels is sparse (Eckenhoff and Johansson,
1997; Pratt et al., 2000; Mascia et al., 2000). However, there are
other interpretations. The most obvious one is that an anesthetic
mechanism may indeed be membrane-mediated, but those solutes that
disobey the rule have different intrinsic potencies. In other words,
the effect of solutes on that property of the bilayer that alters
protein conformational equilibria depends not only on membrane
concentration but also on the identity of the solute. What property of
the membrane is altered upon incorporation of anesthetics but not by
nonanesthetics, is mechanistically linked to protein conformational
equilibria, and causes significant shifts in protein equilibria at
clinically relevant anesthetic concentrations?
Various bilayer properties have been considered as a possible
link between changes in bilayer composition and resulting modulations in the activity of key intrinsic membrane proteins. As discussed previously (Cantor, 1999a,c), membrane characteristics such as hydrophobic thickness, dipole potential, fluidity, curvature elastic properties, proximity to phase transitions, and the degree of lateral
microheterogeneity all vary with membrane composition and have thus
been suggested as having a potentially strong influence on membrane
protein function (Brown, 1997; deKruijff, 1997; Epand, 1996; Gruner,
1991; Hui, 1997; Lundbaek and Andersen, 1999; Morein et al., 1996;
Mouritsen and Jørgensen, 1997; Mouritsen and Bloom, 1993; Nielsen et
al., 1998; North and Cafiso, 1997; Qin et al., 1995). However, it has
been noted (Franks and Lieb, 1994) that the changes in most of these
properties (thickness, order parameter profiles, phase transition
temperatures) are very small at clinically relevant concentrations of
anesthetics and can be produced in the absence of anesthetic through
slight changes in other variables, such as temperature. [It is
important to note that the increase in gas-phase, but not
aqueous-phase, apparent potencies with decreasing temperature of most
inhalation anesthetics is accompanied by an increase in oil/gas
partition coefficients (Franks and Lieb, 1982) such that the clinically
relevant membrane concentration x* does not depend
sensitively on temperature. Thus, a plausible indirect mechanism would
require a bilayer property that is strongly affected by anesthetics but
only weakly by temperature changes.] Were there no bilayer properties
both sensitive to incorporation of solutes and capable of influencing
protein equilibria, it could be concluded that such indirect mechanisms
are likely to play at most a minor role in the modulation of
protein activity. However, it has been suggested (Gruner, 1991; Seddon
and Templer, 1995; Cantor, 1998, 1999a) that the distribution of
lateral stresses (i.e., the lateral pressure profile) in bilayers may
be such a property, because it is predicted (Cantor, 1998, 1999a) to be
strongly affected by incorporation of interfacially active
solutes as well as by altered lipid composition, but not by small
changes in temperature; more importantly, it is mechanistically
linked to altered protein conformational equilibria.
A stringent test of an indirect mechanism involving the
lateral pressure profile is, then, to determine whether it accurately predicts the known anomalies in the Meyer-Overton correlation. So, in
the present paper, statistical thermodynamic calculations are used to
predict the intrinsic potencies and thus the existence of cutoffs among
the series of alkanes, alkanols, ,-alkanediols, and their stiffer
perfluorinated counterparts, which can be compared to experimental
results, at least qualitatively. Predictions are also reported for
classes of molecules for which potencies have not yet been measured. In
particular, the intrinsic potency of oligomeric alkanols (i.e.,
alkanols with regularly spaced hydroxyl groups) is predicted to
increase roughly linearly with the number of repeat units in the
oligomer, and thus with chain length. Because it would appear difficult
for such increasingly large molecules to be accommodated in any binding
site (no matter how nonspecific), a measurement of the potencies of
such molecules would be expected to distinguish unambiguously between
indirect and direct binding mechanisms of anesthesia.
| |
THEORY |
An indirect mechanism: the lateral pressure profile
As discussed in detail elsewhere (Cantor, 1999a,b), a lipid
bilayer is characterized by very large lateral pressure densities p(z) distributed nonuniformly (i.e., varying with
depth z) in the hydrophobic interior, balanced largely by
tensions (negative pressures) at the aqueous interfaces (Israelachvili
et al., 1980; Seddon, 1990; Xiang and Anderson, 1994; Seddon and
Templer, 1995; Ben-Shaul, 1995; Harris and Ben-Shaul, 1997; Venturoli
and Smit, 1999; Lindahl and Edholm, 2000). Transmembrane domains of
proteins such as ligand-gated ion channels are necessarily subjected to these lateral pressures. A conformational transition of a membrane protein such as the opening of an ion channel results in a change in
shape that will, in general, be characterized by a lateral expansion or
contraction that varies with depth in the membrane, i.e., a nonuniform
change in protein cross-sectional area in the transmembrane domain
A(z). Because the bilayer exerts lateral pressures against which the protein expands or contracts laterally, this transition involves mechanical work, the amount determined by the
depth dependence of the lateral pressure profile and of the changes in
protein cross-sectional area. A change in membrane composition, such as
the incorporation of hydrophobic or amphiphilic solutes, is predicted
(Cantor, 1998, 1999a) to cause a significant depth-dependent
redistribution of these lateral pressures
p(z), resulting in a shift in the protein
conformational equilibrium and thus in altered sensitivity of the
protein to its normal agonist.
Unfortunately, there exists little direct experimental information on
the change in shape of the transmembrane domains of postsynaptic
ligand-gated ion channel proteins that accompanies the conformational
transition (channel opening) relevant to their function. Still, there
is considerable evidence (Popot and Engelman, 2000, and references
therein) suggesting that the transmembrane domains of many intrinsic
membrane proteins comprise bundles of predominantly -helical
secondary structural units that span the bilayer, and that for such
bundles, the protein may achieve its conformational change with a
relatively small expenditure of free energy through a cooperative
reorientation of the transmembrane segments of the bundle, as has been
reported for the nicotinic acetylcholine receptor (Unwin, 1993,
1995). In recent work (Cantor, 1999b), such collective
reorientations have been analyzed using simple geometric models of
collective tilts and rotations of bundles of both kinked and
cylindrical helices, and it is shown that such conformational changes
are particularly sensitive to redistributions of membrane lateral
pressures. More precisely, it is readily shown (Cantor, 1999b) that at
this level of approximation, the shifts in protein conformational
equilibria depend predominantly on changes in the first and second
integral moments of the pressure distribution. For symmetric bilayers,
the first moment can be expressed as
|
(1)
|
where z = 0 at the center of the bilayer and
z = 
h and h at the aqueous
interfaces. In essence, P1 is a
measure of a shift in the center of the lateral stress distribution in
each leaflet of the bilayer away from
(P1 > 0) or toward
(P1 < 0) the center of the
bilayer. (The interpretation of the second moment
P2 is more complex, but since the
trends for P2 and
P1 are predicted to be similar,
only the results for P1 are
discussed below.) Using these geometric models, the magnitude of
P1 required to generate a
significant change in protein conformational equilibrium can be
estimated (Cantor, 1999b). For example, it is shown that for a protein
of radius ~20 Å that undergoes a small tilt/rotation of order 5°
to 10°, a shift in conformational equilibrium by a factor of two
would be predicted for |P1| of
order 0.02 (in units of kBT
Å1), the direction of
the equilibrium shift determined by the sign of
P1. If the mole fraction of solute
in the bilayer is denoted x, then the intrinsic potency of
an anesthetic can be defined as S = P1/x. Taking
x* 0.02 to 0.05 as a rough estimate (Janoff and Miller,
1982) of the mole fraction of an anesthetic (one that follows the
Meyer-Overton correlation, as discussed earlier) in the bilayer at its
EC50 concentration (i.e., at
c*w), then S 0.5 kBT
Å1 provides an order of
magnitude estimate of the intrinsic potency of anesthetics that obey
the Meyer-Overton rule. Those molecules with anomalously low intrinsic
potencies will have smaller values of S. Molecules predicted
to have S 0 would be nonanesthetics in the sense
that they would not cause anesthesia at any membrane concentration, and
would be predicted to have no effect on the anesthetic potency of
standard anesthetics, as measured through additivity studies. Those
solutes predicted to have S < 0 would have negative
anesthetic potency, in the sense that they would be predicted to
decrease the potency (i.e., increase the EC50 or
MAC) of standard anesthetics in additivity studies, the magnitude of
the effect increasing with the magnitude of S.
| |
CALCULATION METHODOLOGY |
Mean-field statistical thermodynamic theory is used to calculate
the equilibrium properties of the lipid bilayer system, using a
modified lattice model to describe the chain conformational contributions to the free energy. Except as discussed below, the approach is essentially identical to that used in recent work (Cantor,
1999a) to predict pressure profiles for bilayers for a wide range of
lipid and lipid/solute compositions. A summary of the method and
approximations is provided here; the interested reader should refer to
Cantor (1999a) and references therein for details. The power of
this kind of methodology for predicting structural and thermodynamic
properties has been shown for aggregates of surfactants in solution,
and for self-assembled or spread monolayer and bilayer films
(Ben-Shaul, 1995; Ben-Shaul and Gelbart, 1994; Leermakers and Lyklema,
1992; Wijmans et al., 1994; Leermakers and Scheutjens, 1988; Cantor,
1995, 1996). As with all models, it relies on assumptions and
approximations that serve to make the calculations tractable and result
in interpretable predictions. The bilayer is treated as two compact
monolayers, in each of which the segments of the acyl chains occupy
space at constant bulk density, i.e., no free volume is permitted. The
distribution of chain segments is described using a lattice model, in
which a chain configuration is defined as occupying a particular set of contiguous lattice sites. As in previous work, the boundary between the
hydrophilic (head group) region and hydrophobic interior of the bilayer
is approximated by a sharp planar interface. For the lipids, the
junction of each acyl chain with its head group is constrained to
reside on that plane, so that, for example, the complexity of the
glycerol/carbonyl linkage between the phosphocholine head group and the
acyl tails in phospholipids is completely ignored, as is the
considerable roughness present in the interfacial region (Merz and
Roux, 1996; Tielemann et al., 1997). Although interfacial roughness
could readily be incorporated into the model (Leermakers and
Scheutjens, 1988), it would require assumptions about additional interaction energies that are not well known, so it is unlikely that
any additional predictive value would result. For purposes of
describing hydrophobic solutes, the calculation of the conformational free energy has been modified and extended in the present work to allow
all possible locations of the solute in the bilayer. For simplicity of
calculation, neither lipid nor solute chains are allowed to cross the
bilayer midplane, i.e., there is no interdigitation between monolayers.
This restriction certainly causes an increase in the fraction of bonds
oriented horizontally near the midplane, affecting the orientational
ordering and the lateral pressure in that region. However, for most
biological membranes there is little interdigitation, so this
approximation is expected to be of minor importance.
The bilayer free energy contains both entropic and energetic
contributions. The configurational entropy of the lipid and solute chains is calculated in mean-field approximation, incorporating bond-correlated excluded volume of chain segments. Three contributions to the internal energy of the bilayer are incorporated: segmental energies (including bending stiffness and, as appropriate, a local attraction of selected segments for the aqueous interface), interfacial tension, and head group interactions. At discrete values of the lipid
surface density (at which the membrane thickness is an integer multiple
of the size of a lattice site), the free energy is minimized with
respect to the probability distribution of chain conformations, subject
to the constraints of constant bulk density (one chain segment per
lattice site) within the hydrophobic core of the bilayer, from which
the depth-dependent pressures (and the total lateral pressure) are
obtained. The calculated free energy values are fit to a polynomial in
the surface density, the minimum of which determines the equilibrium
surface density and the lateral pressure profile.
For both lipid and solute molecules, the lattice statistical mechanical
approach provides the equilibrium probability distribution P(q) of chain conformational states q,
from which conformational averages such as the spatial distribution of
chain segments can be determined. For a solute of chain length
n, a conformational state q is defined by the set
of sites occupied by its n segments, each of which is
defined by its depth z in the membrane (as well as the
spatial direction of its bonds to the adjacent segments on the chain.)
For a given solute conformation q, we let
q(z) represent the total number of
segments of the solute at depth z in the lattice
(irrespective of the directional orientations of the bonds to adjacent
segments on the chain.) On average, the number of solute segments at
depth z is given by (z) = 
q P(q) q(z). Since each solute chain has
n segments, the spatial probability distribution of solute
segments, i.e., the fraction of solute segments found in a layer of
lattice sites at depth z, is 
(z) = (z)/n.
Solute and lipid characteristics
Solute: chain stiffness
In unsubstituted, saturated alkanes, the hydrocarbon chain is
semiflexible, whereas for some substituted alkanes, and at sites of
unsaturation (alkenes and alkynes) the molecule can become considerably
more rigid. In particular, for perfluorinated alkanes, the energetic
cost for local bending of the chain is considerably greater than for
alkanes. Also, detailed calculations (Smith et al., 1994) indicate that
the distribution of conformational states of perfluorinated alkanes is
more complex than for alkanes. The effective gauche/trans energy
difference is roughly twice that of alkanes, with a large additional
energy cost for adjacent gauche conformers, resulting in a reduction in
the probability of a chain bend by roughly a factor of three
compared to alkanes. In the lattice model used in the calculations, we
thus estimate [(CF2)x] 0.15, with
[(CH2)x] = flex 0.45 as in prior work (Cantor, 1999a). For simplicity, these values are taken to be independent of the
substituents on the adjacent segments. Note that in chain molecules of
n segments, the stiffness is only defined for the n 2 interior segments, i.e., at segments
i = 2, 3, ... , n 1.
For the triple bonds in alkynes, the increase in rod-like stiffness at
each of the (interior) carbons is very high. In alkenes, both
trans and cis isomers are more rigid, but the
backbone of the trans isomer is better modeled as
more extended than that of saturated alkanes
(rod < flex),
whereas cis isomers are stiffly bent
(bent 
1). If the local rigidity at
internal segments i is denoted
ri, with
ri = s (rod-like,
rod), f (semiflexible, flex), or b (bent,
bent) then the distribution of molecular rigidity along the solute chain can be expressed as
{r2,
r3, ... , rn1}. An unsaturated bond between
adjacent segments increases the stiffness at both segments, except if
the unsaturation involves terminal chain segments. Using six-segment
solutes as an example (for which calculated potencies are reported
below) unsaturated chains with localized stiffness distribution
{s, f, f, f}, would serve as a crude model of 1-hexyne or 1-hexene, whereas
{s, s, f, f} and
{f, s, s, f} would
serve as models for 2-hexyne (or trans-2-hexene) and
3-hexyne (or trans-3-hexene), respectively. The multiply
unsaturated hexanes 1,3-hexadiyne, 2,4-hexadiyne, 1,4-hexadiyne, and
1,5-hexadiyne (or more approximately, for the corresponding
trans-dienes) would be represented as {s,
s, s, f}, {s,
s, s, s}, {s,
f, s, s}, and {s,
f, f, s}, respectively, and
1,3,5-hexatriyne would be {s, s, s,
s}. Of course, the conformational flexibility f
at an internal methylene group in, for example, 1,4-hexadiene or
1,4-hexadiyne is not identical to a methylene group in hexane, but for
simplicity, only one value of the stiffness, flex = 0.45, is used to describe a saturated
carbon in the calculations, regardless of its neighbors. Unfortunately,
a precise specification of the value of rod is
difficult, so in the present work results are reported for calculations
using rod = 0.15 (threefold lower probability
of a chain bend compared to saturated alkane chains, as used for
perfluorination) as a likely representative value for both alkynes and
trans-alkenes.
Solute: interfacial activity of chain segments
Each segment of the solute can be characterized by an
interfacial exchange energy 
, i.e., the energy to exchange it from the membrane interior with a segment of the lipid "solvent" (a CH2 group) at the aqueous interface. Clearly, the
interfacial attraction of a hydroxyl group is very strong ( < 0, with || kBT),
arising largely from its ability to donate a hydrogen bond, whereas the
exchange energy of a solute CH2 group is zero by
definition. There are smaller differences among
CH2, CF2,
CH3, and CF3 groups as
well. Results of molecular dynamics simulations (Cui et al., 1998)
suggest a net interfacial attraction of CH3 groups, a much smaller attraction of CF3 groups,
but a positive interfacial exchange energy (effectively an interfacial
repulsion) for CF2. For simplicity, and because
getting accurate numerical estimates of the strength of these
interactions is difficult, these differences in interfacial
interactions are ignored in the present work, as are the differences in
exchange pairwise interaction energies among CH2,
CF2, CH3, and
CF3 groups. However, they may well underlie the
marked differences in membrane distribution (North and Cafiso, 1997)
and anesthetic potencies (Koblin et al., 1994) among cyclobutanes of
different degrees of fluorination.
In addition to causing increased stiffness, the presence of
unsaturation in hydrocarbon chains is likely to result in a greater attraction to the aqueous interface (as compared to saturated bonds
between adjacent methylene groups), characterized by an interfacial
attraction per unsaturated segment u < 0. This net attraction is presumably larger for segments involved in
triple bonds than in double bonds, and would be expected to increase in
magnitude for molecules with delocalized pi-orbitals, such as
conjugated polyenes. It is difficult to quantify this interfacial attraction, so calculations have been performed for a range of plausible values (kBT 
u < 0).
Lipid characteristics
The properties of the bilayer depend not only on the
characteristics of the solutes but of the lipid solvent as well.
Variation in head group repulsions, acyl chain unsaturation, and
incorporation of cholesterol are all predicted (Cantor, 1999a) to have
a significant effect on the pressure distribution and on the
perturbation of that distribution by solutes. For simplicity, in the
present work, only saturated 16-carbon (palmitoyl) acyl chains are
considered, described by a uniform chain stiffness
[(CH2)x] 0.45. However, effects of varying head group repulsion are considered. It has been shown (Stigter et al., 1992) that the electrostatic interactions among phosphatidylethanolamine (PE) head groups are small and relatively insensitive to changes in temperature, whereas the repulsions among phosphatidylcholine (PC) head groups are strong and
increase significantly with rising temperature. In the context of a
simple mean-field approach (Cantor, 1999a), head group interactions can
be modeled as a pairwise additive energy that varies inversely with
molecular area, with constant of proportionality
uhg that is a measure of the strength
of the average repulsion of adjacent head groups. For pure PC,
uhg(PC) is roughly 1 to 1.5 in units of kBT (the value depending on
temperature), and uhg(PE) 0. Note that for a mixture of head groups, the effective
uhg is the average of all pairwise
interactions; thus a 50/50 mix of PC and PE would have
uhg 1/4
uhg(PC). Although it is difficult to
estimate the value precisely, the lipid head group composition of a
representative synaptic membrane might be expected to have
uhg of order 0.3 to 0.5kBT; we present results of
calculations for uhg = 0, 0.4, and 0.8 kBT to span the range of likely values.
| |
RESULTS |
Intrinsic potencies
Alkanes and monohydric alkanols
Fig. 1 a displays
predictions of intrinsic potency S as a function of chain
length for semiflexible solutes ( = 0.45) with no interfacial
attraction of any segment (1 = 2 = ··· = n = 0), as a model of alkanes, and with a large interfacial attraction of the
first segment only (1 = 10kBT, characteristic of a
typical hydrogen bond strength, with 2 = 3 = ··· = n = 0),
as a model for strongly amphiphilic solutes such as 1-alkanols. These
results are obtained using a range of values of the lipid head group
pair repulsion energy uhg, as
discussed above. Clearly, for short chains, the attraction of one end
of the molecule to the aqueous interface results in a much greater
potency, i.e., a much greater net shift in the pressure profile away
from the center of the bilayer. However, with increasing chain length
of the amphiphilic solutes, a marked decrease in intrinsic potency is
predicted, eventually approaching zero (cutoff). The magnitude of the
average lipid head group repulsion is important; at intermediate
values, a cutoff is predicted at about 12 to 14 carbons. For solutes
without any interfacial attraction, the intrinsic potency is fairly low
for short chains, and in the presence of lipid head group repulsions,
decreases through zero, with a cutoff at smaller n than for
amphiphilic solutes.
View larger version (20K):
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|
FIGURE 1
Intrinsic potency, S, as a function of
solute chain length, n, for solutes of the form
Cn, i.e., with no interfacial attraction
(dotted lines) and for solutes of the form
ACn1, i.e., with strong interfacial attraction
for the first segment only (solid lines). Lines are
drawn only as a guide to the eye. (a) Semiflexible
chains ( = 0.45). (b) Chains with greater
(linear) stiffness ( = 0.15). Lipid head group repulsion:
uhg/kBT = 0.0 ( ), 0.4 ( ), 0.8 ( ). For ease of comparison, the two
panels are plotted using the same ordinate scale.
|
|
The effect of increasing solute stiffness uniformly along the entire
molecule (reducing from 0.45 to 0.15) is shown in Fig. 1
b. Unlike the results shown in Fig. 1 a, the
decrease in intrinsic potency is extremely rapid for the amphiphilic
solutes, regardless of lipid head group repulsion, with a much shorter
cutoff predicted at n ~ 4 or 5. For longer stiff
amphiphiles, the potency is calculated to be large in magnitude but of
opposite sign, i.e., a large negative anesthetic effect is predicted.
For chains without interfacial activity, the increase in stiffness has
a somewhat milder effect on the shape of the curve, but since
S is small even for short chains, the cutoff is predicted to
drop to only 3 or 4 segments.
If the predictions portrayed in Fig. 1, a and b,
are accurate, then only the long-chain, stiff amphiphilic molecules,
(large n for solid lines in Fig. 1 b) are
predicted to have large negative intrinsic potencies. These might
correspond best to long-chain perfluorinated alkanols; for the choice
of parameters used ( = 0.15, and no interfacial activity for
any but the first segment) the effect is not predicted to be of large
magnitude until n 8. The most closely related experimental
work is that of Eger et al. (1999a) on 1-alkanols that are
perfluorinated on all but the hydroxylated carbon (and thus somewhat
less stiff). They find a clear trend with increasing chain length
n from strong intrinsic potency at n = 2 to
nonanesthetic at n 7 or 8, qualitatively consistent
with the predictions, although the crossover occurs at somewhat higher
chain length than predicted, which may result from the fact that the
first carbon is hydrogenated. However, additivity studies were not
performed for longer chain lengths, which according to the predictions
of the present work would be required for negative intrinsic potency to
be observed. It has recently been shown (Ueno et al., 1999) that unlike
the shorter-chain analogues,
CF3(CF2)5CH2OH
decreases the potentiation of GABAA (
-aminobutyric acid) receptor response to isoflurane (and
pentobarbital) expressed in Xenopus oocytes.
Additivity studies have also been performed (Liu et al., 1994a) for
perfluoroalkanes. The predictions (dashed lines in Fig. 1 b)
indicate that stiff, interfacially inactive molecules show only a
mildly negative potency, and then only for n 
6 or
so. The studies of Liu et al. (1994a) are inconclusive in that
C4F10 and
C5F12 do show mild negative
potency, i.e., a 30% increase in MAC of halothane and isoflurane (but
not desflurane), whereas C6F14 shows no negative
potency in additivity studies with isoflurane or halothane. Liu et
al. (1994a) found that only CF4 had
anesthetic potency (using MAC as the anesthetic endpoint), whereas in
earlier studies (Miller et al., 1972) using abolition of the righting reflex in mice as the endpoint, it was found that
CF4,
C2F6, and C3F8 were anesthetics (the
C3F8 results were obtained
from additivity studies with N2O.)
The results on alkanols described above only consider the interfacially
active (hydroxyl) group on the terminal methyl segment, corresponding
to 1-alkanols. Calculations have also been performed to predict the
effect of varying the position, labeled j, of the single
interfacially active segment (i.e., the hydroxymethylene group) along
the alkanol chain. (For alkanols, for simplicity of notation, chain
segments with 0, corresponding to
-CH2- or -CH3 groups are
labeled C, and those with strong interfacial attraction,
such as -CHOH- or -CH2OH, are labeled
A. Thus, alkanes of length n are symbolized as
Cn, 1-alkanols as ACn1, 2-alkanols as
CACn2, ,-diols as
ACn2A, etc.). Fig.
2 shows results for alkanols of two
representative chain lengths, n = 9 and
n = 13, with the hydroxyl at position j = 1, 2, ... , (n + 1)/2, i.e., from the terminal methyl
group (ACn1) to the central methylene group
(C(n1)/2AC(n1)/2). For a given n, the intrinsic potency is predicted to
be lowest by far for the 1-alkanols, i.e., for j = 1;
moving the hydroxyl toward the middle of the chain is predicted to
result in a sharp increase in potency up to roughly the third segment,
beyond which the potency varies relatively little as the hydroxyl is
moved toward the center of the chain. This marked increase in potency is to be expected, since a flexible chain strongly attracted to the
aqueous interface at or near its center should behave similarly to two
1-alkanol molecules of roughly half the chain length. Because shorter
alkanols have greater intrinsic potency (Fig. 1), and because there are
effectively twice as many molecules, the increase in potency is large.
Although octanol/water and bilayer/water partition coefficients have
been reported for octanols with hydroxyl group at different positions
on the chain (Hansch and Dunn, 1972; Jain and Wray, 1978), no
experimental information is available on their anesthetic potencies, so
a comparison to predicted intrinsic potencies is not yet possible.
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FIGURE 2
Intrinsic potency, S, of semiflexible
solutes of the form
Cj1ACnj, i.e., with a
single segment with strong interfacial attraction A as a
function of the position j of that segment along the
chain. This serves as a model of monohydric alkanols of fixed length
but of varied position of the hydroxyl group along the chain. Results
are presented for two chain lengths: n = 9 ()
and n = 13 (). All calculations were performed
with head group repulsion
uhg/kBT = 0.4. Lines are drawn only as a guide to the eye.
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Polyhydric alkanols
Predictions have also been obtained for longer hydrocarbon chains
with multiple hydroxyl groups. One group of calculations involves
chains with interfacially active segments spaced at regular intervals
(every L segments) along the chain between the first and
last segments; using the notation described above, these alkanols can
be represented as
(AC2M)yA,
with 2M = L 1, and y = (n 1)/L = 1, 2, 3, ... .
Such molecules, which are regularly tethered to the interface, might be
expected to behave like 2y short 1-alkanol chains, each of
effective length n* = M + 1. As an example,
(AC4)3A,
which corresponds most closely to 1,6,11,16-hexadecanetetraol, has
values of 2y = 6 and n* = 3, and thus
might be expected to have potency
S[(AC4)3A] 6 S(AC2), where
AC2 corresponds most closely to 1-propanol.
Using similar reasoning, the results for alkanols with one hydroxyl
group at the center of the chain can be generalized to oligomers of the
form
(CMACM)y,
where y = n/L = 1, 2, 3, ... , again defining 2M = L 1. Such solutes might analogously be expected to behave similarly to
2y short 1-alkanol chains, each of effective length
n* = M + 1. As an example,
(C3AC3)2, which corresponds most closely to 4,11-tetradecanediol, has values of 2y = 4 and n* = 4, and thus
might be expected to exhibit an intrinsic potency
S[(C3AC3)2] 4 S(AC3), where
AC3 corresponds most closely to 1-butanol.
Results for a wide range of such polyhydric alkanols are presented in
Fig. 3 a, in which the
potencies S are plotted as a function of chain length
n. Clearly, the potencies are predicted to get very large
compared to even the largest values for short alkanols. Within a given
series of either type,
(CMACM)y or
(AC2M)yA,
the value of S increases nearly linearly with the oligomeric
repeat index y, consistent with the above discussion. For
given value of y, the intrinsic potency drops slowly with
increasing M, i.e., with increasing separation between interfacially active segments. All of these results, i.e., for (CMACM)y
and for (AC2M)yA with
y 1 and thus for 2y > 1, can be
compared by replotting them in terms of the intrinsic potency per
amphiphilic subgroup (equivalent short 1-alkanol) i.e., plotting
S* = S/(2y) as a function of
n*, as shown in Fig. 3 b. The similarity of these
reduced potencies is evident: all the predictions from Fig. 3
a fall roughly on a single curve in Fig. 3 b,
similar to (but offset somewhat from) that for simple 1-alkanols, which
is included for purposes of comparison. Unfortunately, there is little
experimental data on potency of polyhydric alkanols to which these
predictions can be compared. Moss et al. (1991) measured the potencies
of ,-alkanediols; they observed no cutoff, but studied only diols
of lengths up to n = 12. Extrapolation of the
calculated results for ,-alkanediols to S = 0 predicts a cutoff in potency at n > 20; it would be
interesting to see if this obtains experimentally. Unfortunately,
partition coefficients have not been reported for the diols for which
Moss et al. obtained aqueous EC50 values, so the
prediction of an approximate doubling of their intrinsic potency can
not presently be tested.
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FIGURE 3
(a) Intrinsic potency, S,
as a function of solute chain length, n, for alkanols of
the general form
[CMACM]y
( ) and of the form
[AC2M]yA ( ), where
A corresponds to a strongly interfacially active segment
(  kBT, as a model for
-CH2OH or -CHOH- groups) and C to an
interfacially inactive segment ( = 0, as a model for
-CH3 or -CH2- groups). The
lines are drawn to group together solutes of a particular type and
particular values of either M or y: solid
lines for fixed y and varying M, and
dashed lines for fixed M and varying
y. (b) All results from (a)
re-expressed ( ) as a reduced intrinsic potency S* = S/(2y), i.e., the intrinsic potency per
amphiphilic subgroup, as a function of the number of segments per
subgroup n* = M + 1. In both panels, results for solutes of
the form ACn1 (models of 1-alkanols)
are provided (, dotted line). Lipid head group repulsion
uhg/kBT = 0.4 in all cases.
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A nearly linear increase in intrinsic potency for oligomeric alkanols
with increasing number of repeat units is predicted for all the
oligomeric series for which calculations were performed. In principle,
one can imagine that the hydrophobic/hydrophilic balance can be
manipulated by varying the number of alkyl segments per hydroxyl group,
which will presumably allow for tuning of the oil/water partition
coefficient to an experimentally useful range. In a first
approximation, increasing polymer index in such a series of molecules
would be predicted to maintain an oil/water partition coefficient that
is approximately constant, while increasing intrinsic potency roughly
linearly, and thus increasing apparent potency approximately linearly,
with no limit with respect to chain length, i.e., no cutoff.
Localized stiffness: unsaturated alkanes
It is interesting to examine the effect of increasing chain
stiffness nonuniformly along the solute chain, as can be achieved by
localized chain unsaturation or atomic substitutions. Molecules that
differ with respect to local rigidity (and if rigid, whether rod-like
or bent) but with otherwise identical characteristics (distribution of
segmental interfacial activity) are predicted to have significantly
different effects on the pressure distribution, as shown in Fig.
4 for the example of five-segment chains
with no segmental interfacial activity. For an otherwise semiflexible (flex = 0.45) chain, an increase in linear
rigidity (rod = 0.15) at any one of the
segments is predicted to cause a reduction in intrinsic potency, the
effect increasing roughly additively with the number of sites of
increased linear stiffness. By contrast, a chain with a single rigid
bend (bent 1) is predicted to have significantly increased potency, although additional stiff bends in the
molecule yield smaller increments in potency.
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FIGURE 4
Intrinsic potency, S, of five-segment
solutes without interfacial attraction but with nonuniform internal
stiffness. The three internal segments are progressively replaced by
stiffer bonds; either rod-like (, = 0.15;  , = 0.0) or rigidly bent (, 1). Results for both one and two
rigid bonds represent, in each case, averages over the different
possible spatial arrangements of the rigid bonds. Results are presented
for two values of the head group repulsion:
uhg/kBT = 0.0 (solid lines) and
uhg/kBT = 0.4 (dashed lines). Lines are drawn only as a guide to
the eye.
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For hexynes or trans-alkenes, the local stiffness and
increased interfacial activity (as compared to saturated alkanes) would be expected to have opposing effects on intrinsic potency. In Fig.
5 a, predictions of intrinsic
potency for six-segment solutes of varying location and degree of
unsaturation are plotted as a function of u,
the interfacial attraction of segments participating in unsaturated
bonds. For purposes of comparison, the predicted potency for hexane
{f, f, f, f} is
included. In Fig. 5 b, the results of Fig. 5 a
are replotted as a function of mol = 2nuu, the
interfacial attraction per molecule. With regard to intrinsic potency,
an increase in segmental interfacial activity can clearly compensate
for increased linear stiffness, to a degree that, for given total
stiffness, depends largely on the total molecular interfacial activity.
However, regardless of the value of u, a
greater intrinsic potency is predicted for 1-hexyne, which is stiff
only at one internal segment, than for 2- or 3-hexyne, which have
approximately the same interfacial attraction as 1-hexyne, but two
sites of chain stiffness.
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FIGURE 5
Effect of interfacial activity of unsaturated segments
on the calculated intrinsic potency, S, of six-segment
solutes (as models of hexynes or trans-hexenes).
(a) S is plotted as a function of
u, the magnitude of the interfacial attractive energy
per unsaturated segment, in units of
kBT. (b) Same
data as in (a), but plotted as a function of the
magnitude of the interfacial attractive energy per molecule,
mol = 2nuu (in units of
kBT) where
nu is the number of unsaturated bonds (and
thus 2nu is the number of unsaturated
segments) in the molecule. nu = 1 (solid lines): 1-hexyne {s, f,
f, f}, ( ); 2-hexyne {s,
s, f, f}, (); 3-hexyne
{f, s, s, f}, (+).
nu = 2 (short dashed
lines): 1,3-hexadiyne {s, s,
s, f}, (×); 1,4-hexadiyne {s,
f, s, s}, (*); 1,5-hexadiyne
{s, f, f, s}, ();
2,4-hexadiyne {s, s, s,
s}, ( ); nu = 3 (long dashed line): 1,3,5-hexatriyne {s,
s, s, s}, ( ). Predictions for the
fully saturated hexane {f, f, f,
f}, (), are included for purposes of comparison. In the
above list, the flexibility of the four interior bonds are indicated by
s (stiff, = 0.15) or f
(semiflexible, = 0.45). For all calculations,
uhg/kBT = 0.0.
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Segment distributions
At present, there is no experimental method by which the lateral
pressure profile can be measured. So it would be valuable to find
other, more readily measurable properties, the changes in which are at
least qualitatively related to changes in the pressure distribution.
The depth-dependent probability distribution of solute segments
(z), i.e., the likelihood of finding a segment of the
solute at a given membrane depth, independent of the location of the
segment along the solute chain, might be expected to serve as such a
property since it can, in principle, be measured, and is obtained from
the statistical mechanical approach used to calculate the lateral
pressure profiles. For small, strongly interfacially active solutes,
such as short 1-alkanols, the predicted large increase in pressures
near the aqueous interface is certainly related to the fact that the
segments of the solute are localized in the region where the pressures
increase, and this is consistent with the difference in spatial
distributions of some anesthetics and nonimmobilizers (North and
Cafiso, 1997; Tang et al., 1997; Chipot et al., 1997). However, this
correlation does not hold in a comparison of molecules of similar
interfacial activity, but of different stiffness, as shown by
comparison of the results in Figs. 1 and
6. In Fig. 6 a, plots of
(z) are reported over a range of chain lengths, for
solutes Cn, i.e., with no interfacial
activity (i = 0, i = 1, ... , n) and of the same flexibility as the lipid acyl
chains ( = 0.45). For very short chain solutes, which are
predicted to have small positive intrinsic potencies, the segment
probability distribution is nearly uniform, but with increasing chain
length, the distribution becomes strongly skewed toward the center of
the bilayer, consistent with neutron diffraction experiments of White
et al. (1981) on hexane. Comparison of these results with the chain
length dependence of the intrinsic potency, one might conclude that
potency is lost when the segment distribution shifts strongly toward
the membrane interior. However, different conclusions are reached when
the stiffness of the solute is increased at fixed chain length. In Fig.
6 b, the spatial distribution is plotted as a function of
increasing chain stiffness, for n = 8 segment solutes.
The increase in stiffness is predicted to have a small effect on the
probability distribution, if any, causing a shift from the
interior toward the aqueous interface. However, the increased stiffness
is predicted to cause a loss in intrinsic potency, as seen in a
comparison of Fig. 1, a and b. Results for alkanes of other chain lengths are similar.
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FIGURE 6
Spatial probability distribution (z)
of segments of solutes with no interfacial activity
(i = 0, i = 1, ... , n) for varying chain length (n) and
stiffness (). Bilayer depth z(Å) indicates the
distance from the bilayer midplane (in either direction, since the
bilayer is symmetric). (a) Semiflexible chains ( = 0.45) of length n = 1 ( ), 2 (), 4 (+), 6 (×), 10 (), and 14 (). (b) Fixed alkane chain
length n = 8, for varying chain stiffness: = 0.45 (), 0.30 (), and 0.15 ().
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In Fig. 7 a, the segment
probability distribution (z) is plotted for a range of
chain lengths for 1-alkanols (ACn1), i.e., for semiflexible solutes ( = 0.45) with one end attracted to the interface (1 = 10,
i = 0, i = 2, ... ,
n). Increasing the chain length of semiflexible 1-alkanols
is predicted to cause a marked shift of the segment distribution toward
the bilayer interior, and is accompanied by a more gradual decrease in
intrinsic potency (Fig. 1 a). In Fig. 7 b, plots
of (z) are presented over a range of chain stiffnesses
for alkanols of length n = 8. The increase in stiffness
at fixed chain length is predicted to result in a less pronounced shift
in the segment distribution than seen in Fig. 7 a for an
increase in length at fixed stiffness, but is accompanied by a much
greater drop in potency (to very negative values). Unfortunately, from
the results presented in Figs. 6 and 7, it seems that there is no
simple predictive relation between the intrinsic potency of a solute
and the depth distribution of its segments.
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FIGURE 7
Spatial probability distribution (z)
of segments of 1-alkanols (1 = 10
kBT; i = 0, i = 2, ... , n) for varying
chain length (n) and stiffness (). Bilayer depth
z(Å) indicates the distance from the bilayer midplane.
(a) Alkanols (semiflexible chains, = 0.45) of
length n = 4 (+), 6 (×), 10 (), and 14 ().
(b) Fixed 1-alkanol chain length n = 8, for varying chain stiffness: = 0.45 (), 0.30 (), and
0.15 ().
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Apparent potencies
The approach described above predicts the chain length dependence
of the intrinsic potency for linear molecules of varying interfacial
activity and stiffness. Although the intrinsic potency is a more
fundamental measure of potency in the framework of an indirect
mechanism of anesthesia, apparent potencies are much more commonly used
to express experimental results, so it may be useful to re-express the
predictions in terms of apparent potencies to facilitate comparison
with experiment.
The Meyer-Overton correlation, extended to account for differences in
intrinsic potency, can be expressed as S
c*o = constant, where the oil (bilayer)
concentration is given by
and thus
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(2)
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for inhalation anesthetics, with a single constant of
proportionality (for given bilayer composition). From Eq. 2, the change in c*g, and thus the change in
the apparent potency, can be determined within a homologous series of
compounds that differ only in chain length. For solutes such as alkanes
and many alkane derivatives, Ko/g
varies roughly exponentially with chain length; since n 2 represents the number of interior segments, then
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(3)
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where K0 is the partition
coefficient for solutes with n 2 = 0 interior
segments, and 
o/g > 1 is the multiplicative
increase in Ko/g per added interior
segment. As a rough guide, o/g 3 for
CH2 segments, while for CF2
segments o/g 2 (Eger et al., 1999a).
Within a homologous series, the gas-phase concentration of an
anesthetic with n 2 interior segments,
c*g, relative to that of a
solute with no interior segments,
c*g(0), is obtained from Eqs.
2 and 3:
![<UP>log</UP><SUB>10</SUB>[c<SUP>*</SUP><SUB><UP>g</UP></SUB>/c<SUP>*</SUP><SUB><UP>g</UP></SUB>(0)]≈<UP>−</UP>(n−2)<UP>log</UP><SUB>10</SUB>&lgr;<SUB><UP>o/g</UP></SUB>−<UP>log</UP><SUB>10</SUB>(S/S<SUB>0</SUB>)](/content/vol80/issue5/fulltext/2284/img005.gif)
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(4)
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The analysis leading to Eq. 4 can also be expressed in terms of
aqueous potencies as
![<UP>log</UP><SUB>10</SUB>[c<SUP>*</SUP><SUB><UP>w</UP></SUB>/c<SUP>*</SUP><SUB><UP>w</UP></SUB>(0)]≈<UP>−</UP>(n−2)<UP>log</UP><SUB>10</SUB>&lgr;<SUB><UP>o/w</UP></SUB>−<UP>log</UP><SUB>10</SUB>(S/S<SUB>0</SUB>)](/content/vol80/issue5/fulltext/2284/img006.gif)
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(5)
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although for CH2 groups, o/w
is somewhat larger than o/g; of order 3.5 to
4.0. Predictions using Eq. 4 for the dependence of apparent potency on
chain length are plotted in Fig. 8 for the same solutes for which calculations of intrinsic potencies are
presented in Fig. 1. Clearly, for alkanes, alkanols, and perfluorinated alkanols, an increase in apparent potency accompanies a decrease in
intrinsic potency with increasing chain length. These predicted trends
are qualitatively similar to the results summarized recently by Eger et
al. (1999a,b).
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FIGURE 8
Predicted gas-phase apparent potency
c*g of solutes of length
n (with n 2 interior segments)
relative to the predicted apparent potency
c*g(0) of a solute of the same type
but of length n = 2 (i.e., with no interior
segments) as a function of (n 2), the number of
interior segments. The data are calculated using the approximate
relation of Eq. 4, i.e., as
log[c*g/c*g(0)],
using intrinsic potencies calculated for
uhg/kBT = 0.4. Results are presented for models of 1-alkanols [ = 0.45; 1 = 10kBT;
i = 0, i = 2, ... , n; o/g = 3.0, ()],
perfluorinated alkanols [ = 0.15; 1 = 10kBT;
i = 0, i = 2, ... , n; o/g = 2.0, ( )], alkanes
[ = 0.45; i = 0, i = 1, ... , n; o/g = 3.0, ()],
and perfluorinated alkanes [ = 0.15; i = 0, i = 1, ... , n;
o/g = 2.0, ()].
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DISCUSSION |
The results presented here, based on statistical thermodynamic
calculations using a mean-field lattice model to describe the conformational statistics of acyl chain packing, demonstrate that the
influence of hydrophobic or amphiphilic solutes on the bilayer pressure
profile depends sensitively on chain length and particularly on the
distribution of interfacial activity and stiffness over the length of
the solute chain. The large differences in intrinsic potencies among
alkanes, alkanols, and their fluorinated counterparts, including the
well-known cutoffs in anesthetic potency with increasing chain length,
correlate remarkably well with the predictions of intrinsic potency
based on the influence of the resulting changes in the pressure
distribution on protein conformational equilibria. In particular, the
differences in cutoffs for different types of solute chains are
qualitatively correctly predicted.
Intrinsic potencies are predicted for a range of monohydric and
polyhydric alkanols for which potencies have not yet been measured, but
which would serve as an excellent test of the pressure profile
mechanism. Predicted intrinsic potencies for monohydric alkanols in
which the hydroxyl group is placed on an interior chain segment are
predicted to be much greater than for 1-alkanols of the same length.
Alkanols of length n with a single hydroxyl group near the
middle of the chain are predicted have roughly twice the potency of
1-alkanols of chain length n/2; consequently, the
cutoff for such alkanols is predicted to occur at a length n > 20. In general, chains that are regularly tethered
to the aqueous interface, such as polyhydric alkanols with hydroxyl
groups regularly spaced along the chain, are predicted to act similarly to a collection of shorter 1-alkanol chains of length roughly equal to
half the spacing between hydroxyl groups on the chain. The intrinsic
potency of such polyhydric alkanols should thus increase with the
number of repeat units, without limit; certainly no cutoff would be
expected. A measurement of the potencies of such molecules would thus
distinguish between indirect and direct binding mechanisms of
anesthesia, since no binding site could possibly accommodate a molecule
without limit in size, the potency of which only increases with size.
Although this argument is made in the context of polyhydric alkanols,
it would be expected to hold for other oligomers with regularly spaced
interfacially active segments, such as polyethers and polyacids, or if
the hydroxyl group is attached to the alkane backbone through a short
alkyl spacer.
The predicted sensitivity of pressure redistribution to increased
solute stiffness implies that rod-like, interfacially inactive molecules should be nonimmobilizers, whether or not the stiffness is
due to perfluorination. However, other molecular manipulations that
cause increased chain linear rigidity, such as the incorporation of
chain unsaturation, will likely be accompanied by increased interfacial
activity, which has the opposite effect on the pressure distribution.
Unfortunately, an approximate measure of the strength of the
interfacial activity (such as approximate Lennard-Jones parameters for
united-atom carbons involved in multiple bonds) is not presently
available, so a simple comparison of the intrinsic potencies of alkanes
and alkynes, for example, will not yet serve as a test of this
mechanism. Still, molecules having the same total unsaturation (and
thus the same interfacial attraction) but with different degrees of
internal stiffness are clearly predicted to have different potency. For
example, chain molecules with unsaturation located at the terminal
methyl groups are more flexible, and thus should have higher intrinsic
potency, than those with the same degree of unsaturation located at
interior bonds. Thus, 1-hexyne is predicted to have higher intrinsic
potency than 2- or 3-hexyne.
On the plausibility of indirect (bilayer-mediated) mechanisms of
anesthesia
TOP
ABSTRACT
INTRODUCTION
