The lateral pressure profile in membranes: a physical mechanism of general anesthesia

The lateral pressure profile in membranes: a physical mechanism of general anesthesia

Toxicology Letters 100 – 101 (1998) 451 – 458 The lateral pressure profile in membranes: a physical mechanism of general anesthesia Robert S. Cantor ...

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Toxicology Letters 100 – 101 (1998) 451 – 458

The lateral pressure profile in membranes: a physical mechanism of general anesthesia Robert S. Cantor * Department of Chemistry, Dartmouth College, Hano6er, NH 03755, USA Accepted 7 May 1998

Abstract l. A lipid-mediated mechanism of general anesthesia is suggested and investigated using lattice statistical thermodynamics. 2. Anesthetics are predicted to shift the distribution of lateral pressure within a lipid bilayer, and thus alter the mechanical work required to open ion channel proteins, if channel opening is accompanied by a non-uniform change in cross-sectional area of the protein. 3. Calculations based on this mechanical thermodynamic hypothesis yield qualitative agreement with anesthetic potency at clinical anesthetic membrane concentrations, and predict the alkanol cutoff and anomalously low potencies of strongly hydrophobic molecules with little attraction for the aqueous interface, such as perfluorocarbons. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Lipid-mediated mechanism; Lateral pressure; Alkanol cutoff; Perfluorocarbons

1. Introduction Although there is extensive evidence that the site of action of general anesthetics involves postsynaptic ligand-gated ion channels, a mechanistic understanding of general anesthesia does not yet exist (Miller, 1985; Forman and Miller, 1989; Franks and Lieb, 1994; Forman et al., 1995). On the one hand, the well-studied correlation between anesthetic potency and membrane concentration * Corresponding author. Tel.: + 1 603 6462504; fax: +1 603 6463946; e-mail: [email protected]

would imply an indirect mode of action of general anesthetics on membrane proteins, effected through some perturbation of the lipid bilayer. Explanations of this type have been offered, involving phase separation or changes in bilayer thickness, order parameters, or curvature elasticity, and have been extensively reviewed (Janoff and Miller, 1982; Miller, 1985). These approaches generally suffer from three weaknesses. Membrane perturbations are relatively small at clinical anesthetic levels, often duplicated with a small variation of a different property (e.g. a temperature increase of 1°C) that does not induce anes-

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thesia (Franks and Lieb, 1994). Also, exceptions such as the cutoff in potency for long n-alkanols and the anomolously low potency of perfluorinated hydrocarbons and the lighter inert gases remain unexplained (Franks and Lieb, 1985; Miller et al., 1989; Koblin et al., 1994). (The additional requirement of some degree of aqueous interfacial activity in addition to membrane solubility (Yoshino et al., 1994; Chipot et al., 1997; Pohorille et al., 1997) eliminates some of these anomalies, consistent with, and providing strong support for the results presented here). Most importantly, they usually do not provide a causal (mechanistic) relationship between anesthetic potency and the perturbed structural or thermodynamic property. One important exception is the seminal work of Gruner (Gruner and Shyamsunder, 1991; Keller et al., 1993; Gruner, 1994) who considered the spontaneous curvature of corresponding monolayers, intimately related to the pressure profile, and largely consistent with our proposed mechanism. Other evidence suggests a mechanism in which general anesthetics inhibit or activate an ion channel protein by direct binding (Franks and Lieb, 1987, 1994). The correlation between anesthetic potency and inhibition of the water-soluble protein luciferase favors such a mechanism, particularly because it exhibits a cutoff in inhibition for long n-alkanols. A direct binding mechanism is also supported by the observation of a mild difference in potency among stereoisomers of some anesthetics, although this result does not rule out a bilayer-mediated mechanism, given the existence of chiral molecules in the membrane. We present results of lattice statistical thermodynamic calculations that strongly support a novel nonspecific mechanism of general anesthesia. This mechanism avoids the shortcomings typical of bilayer-mediated mechanisms proposed previously. Rather, it provides a truly mechanistic and thermodynamic understanding of general anesthesia that correlates well with anesthetic potency at clinical anesthetic concentrations, including the alkanol cutoff and perfluorocarbon anomalies, and is largely consistent with observed structural effects such as membrane order parameter and thickness changes.

2. Theory Fluid interfacial regions, such as found in selfassembled lipid bilayers, are of molecular thickness. The concentration of the large interfacial excess free energy over this microscopically narrow region leads to enormous local transverse stresses (lateral pressures) corresponding to bulk pressure densities of many hundreds of atmospheres (Gaines, 1966). The local lateral pressure depends strongly on depth within the interfacial region, i.e. the lateral pressure profile is nonuniform (Safran, 1994; Ben-Shaul, 1995). As described below, upon incorporation of interfacially active solutes (i.e. at least part of which is attracted to the aqueous interface) except long nalkanols, a large stress increase is predicted to occur near the aqueous interface, with compensating decrease distributed over the interior of the bilayer. Although the perturbation of the local pressures at clinical anesthetic concentrations is typically relatively small, it is large in absolute magnitude since the pressures themselves are enormous. By what mechanism might this shift in pressure profile modulate the opening of the ion channel of a postsynaptic receptor (Miller, 1985; Forman and Miller, 1989; Franks and Lieb, 1994)? The protein conformational change will likely be accompanied by a change in the cross-sectional area of the protein that depends, in general, on depth within the membrane. Simple thermodynamic arguments indicate that if the area change is greater near the interfaces, then the increase in lateral pressure at the interface would require more mechanical work to open the channel, shifting the equilibrium to favor the closed state. Conversely, if the area change is larger in the center of the bilayer, then less work is required, and the equilibrium will shift to favor the open conformation. This approach can thus rationalize either inhibition of excitatory synaptic transmission or potentiation of inhibitory synaptic transmission. Either way, anesthetic potency is determined by the amount of anesthetic required to alter the lateral pressure profile sufficiently to shift the conformational equilibrium of the protein significantly.

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Fig. 1. (a) A representative example of the pressure profile in a bilayer. The lipids on the right side of the embedded protein are sketched for simplicity as single-chain amphiphiles. On the left, the length and direction of the arrows indicate the magnitude and sign of the local lateral pressures of the membrane acting on the protein: strong tensions at the interfaces balanced by positive pressures through the interior, largest near the interfaces. (b) A plot of the corresponding p(z); the dashed line locates p =0. Note that the area under the curve is zero.

We first present a thermodynamic analysis to relate the lateral pressure profile to conformational equilibria of intrinsic membrane proteins. We then discuss predictions from statistical thermodynamic calculations of the shift in the pressure profile upon incorporation of a range of anesthetic molecules in the membrane. Finally, we provide an order-ofmagnitude estimate that clearly indicates that at clinical concentrations of anesthetics, the redistribution of the local lateral pressures is sufficiently large to result in a significant shift in protein conformational equilibria.

2.1. Thermodynamic analysis It is useful to imagine slicing the bilayer into thin layers, each of thickness dz and characterized by a local lateral pressure p(z), where z indicates the depth within the membrane. Then p(z) =p(z)/dz represents the lateral pressure density, with dimensions of bulk pressure. An example of the distribution of lateral pressure that might be expected in a lipid bilayer is presented in Fig. 1. A large negative pressure is localized at each of the two aqueous interfaces, similar to the tension found at bulk oil/water interfaces. At equilibrium, since the fluid membrane is self-assembled, it is free to expand or contract laterally to minimize the free energy, i.e. to ensure that there is no (or very little) overall lateral pressure p= Szp(z) : 0 ( = the area under the curve in Fig. 1b). Thus, the large inter-

facial tensions must be compensated by positive pressures in the bilayer interior, arising predominantly from the strong repulsions among the hydrocarbon chains, which lose conformational entropy as they become partially orientationally ordered. An order-of-magnitude estimate of the average pressure density in the membrane interior is readily obtained. If each interfacial tension is estimated to be − 50 dyne/cm, then the compensating positive tension is : 100 dyne/cm, distributed over the interior of the membrane (of ˚ ), corresponding to an average thickness : 30 A ˚ ): 300 pressure density of (100 dyne/cm)/(30 A atm. In fact, the pressures are predicted to be considerably larger near the interface, decreasing to smaller values toward the middle of the bilayer (Ben-Shaul, 1995). Consider the lipid bilayer as a fluid interfacial phase in which the protein acts as a solute that can exist in different conformational states. For simplicity, the protein (with or without bound agonists) is assumed to exist in only two such states, labeled by the ion permeability of the channel: cl (closed) and op (open). In each state, the cross-sectional area of the protein may vary with depth within the membrane. Let Acl(z) and Aop(z) represent these area functions (of the entire protein, not just the channel.) The conformational shift from cl to op will be accompanied by a depth-dependent change in the cross-sectional area, DA(z)=Aop(z)Acl(z), as depicted (greatly exaggerated for emphasis) in Fig. 2.

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Fig. 2. (a) A slice through a bilayer membrane containing an intrinsic protein viewed in two different conformational states. (b) The cross-sectional area profile A(z) of each of the two states, plotted as a function of depth z within the membrane of thickness h. The difference in shape is greatly exaggerated for emphasis.

At equilibrium, the chemical potentials of the two states must be equal: mcl =mop. We need to express the dependence of the chemical potential of state r on its concentration [r], its crosssectional area profile Ar (z), and on the pressure profile p(z). Define p0(z) as the pressure profile of the membrane in the absence of anesthetic, and [r]0 as the corresponding equilibrium concentrations of the protein in each of the two states (r= cl or op). Addition of an anesthetic alters the lateral pressure profile by an amount Dp(z), accompanied by a shift in the equilibrium concentrations of each of the protein conformations from [r]0 to [r]. To good approximation, the chemical potential of the protein in state r can then be written as (Cantor, 1997b) ln [r] + NAvSzAr (z)Dp(z), mr = m*+RT r

(1)

where NAv is Avogadro’s number, m *r represents the standard chemical potential of the protein in conformation r, i.e. at unit activity and pressure profile p0(z), and Ar (z) is assumed to be unaffected by Dp(z). In the absence of anesthetic, Dp(z)= 0, so the chemical potential is m °= m *r + r RT ln [r]0. At equilibrium, the chemical potentials of the two protein states must be equal, both with anesthetic present (mcl =mop) and absent (m °cl = m °op). Subtracting the second equality from the first, m *r is eliminated, and the fraction of protein in the open configuration is easily shown to be

F=

[op] 1 = 1 a [op]+ [cl] 1+ K − 0 e

(2)

where K0 = [op]0/[cl]0, and a=(kBT − 1 Sz DA(z) Dp(z). Since a varies linearly with Dp(z), and Dp(z) is proportional to the concentration of anesthetic in the membrane (at the low membrane concentrations relevant to anesthesia), F is predicted to depend very sensitively (: exponentially) on anesthetic concentration. Clearly, a determines both the direction and magnitude of the shift in protein conformational equilibrium. The calculations discussed below indicate that anesthetics cause a pressure increase near the interfaces, with compensating decrease distributed through the membrane interior. If, for a particular protein, DA (interfaces)\DA (bilayer interior), then a will be positive and the equilibrium will shift toward the closed state, resulting in inhibition. [Note that the sign of DA is irrelevant: inhibition is predicted even if DA B 0 for all z, as long as it contracts more in the interior than at the interfaces.] If DA (interface)B DA (bilayer interior), then aB 0, and the equilibrium will shift toward the open state (potentiation). If DA is independent of z, i.e. if the protein expands or contracts uniformly, then the conformational equilibrium will be unaffected by any redistribution of the lateral pressure profile, since in that case

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%z DA(z)Dp(z)=DAD[Sz p(z)] =0.

(3)

It is crucial to note that it is the variation of DA with z that affects the equilibrium; the average area change is irrelevant. The magnitude of a (proportional to anesthetic concentration) needed for the anesthetic to have a significant effect on the protein conformational equilibrium can be estimated using Eq. (2). Consider inhibition (a \ 0), for example. If it turns out that, upon ligand binding, 90% of the protein is in the open conformation in the absence of anesthetic (K0 =9; F0 =F(a =0) =0.9), then we might expect 1B a B4 at clinical anesthetic concentrations. Because of the exponential dependence of F on a, the minimum magnitude of a needed to shift the conformational distribution significantly does not depend strongly on F0.

2.2. Calculations Lattice statistical thermodynamic methods were used to predict the effect of anesthetics on the lateral pressure profile, the details of which are presented elsewhere (Cantor, 1997a). First, existing theory for lipid monolayers (Cantor, 1993, 1996) was modified to consider a fixed total concentration of anesthetic. The effect of varying the interfacial activity of the anesthetic (modeled as an energetic preference for the aqueous interface over the methylenic interior) on the pressure profile was examined for this case (Cantor, 1997a). Calculations were performed without added anesthetic, and for a mixture of 98 mol% double-chained lipid and 2 mol % of solute (corresponding to : 30 mM anesthetic, a typical clinical membrane concentration), yielding predictions of Dp(z), an example of which is presented in Fig. 3. A strongly interfacially active anesthetic increases the competition for sites among the lipid chains in that layer, increasing significantly the lateral pressure in the first layer, with compensating pressure decrease distributed over the remaining layers. However, for a solute equivalent in hydrophobicity to the methylene groups which comprise most of the bilayer interior, Dp(z) is predicted to vary slightly and gradually with z, the details depending on chain length and internal

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stiffness. If (as hypothesized) the anesthetic mechanism requires the lateral pressure acting on the ion channel protein to increase selectively near the aqueous interface (with compensating decreased pressure in the interior), then anomolously low anesthetic potency is predicted for solute molecules which are too hydrophobic. Calculations of excess chemical potentials (Chipot et al., 1997) as well as NMR studies (Baber et al., 1995; North and Cafiso, 1997; Tang et al., 1997) of partially to completely fluorinated alkanes indicate that those that are non-anesthetic are generally not attracted to the aqueous interface. Although the anesthetic Xe is nonpolar, it is more polarizable by interfacial water than the CH2 groups it would replace at the interface and is thus interfacially active, while Ne, He, and H2 are not, consistent with their anomalously low anesthetic potency. Alkanes can also be considered from this perspective. If CH3 (but not CH2) groups have some interfacial activity in a bilayer in contact with water, short alkanes (with a suffi-

Fig. 3. Predicted lateral pressure changes for a lipid monolayer (nlipid =12) upon addition of 2 mol % anesthetic, assumed to occupy a single lattice site. The layer index (z) is numbered from the aqueous interface. Results are presented for two extremes of anesthetic interfacial activity: no energetic preference for the interface ( ×); strong energetic preference for the interface ( ).

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ciently high CH3/CH2 ratio by volume) might be expected to have anesthetic potency, but not the longer alkanes, as observed experimentally. Consistently, the anesthetic cyclopropane, while nonpolar, is calculated to be interfacially active (Pohorille et al., 1997). In a second set of calculations, the theory was modified considerably (Cantor, 1997a) to model bilayers, in which the anesthetic was presumed to be comprised of a flexible hydrophobic chain bonded to a compact hydrophilic head-group constrained to remain in contact with the aqueous interface, as a model of alkanols. The effect of varying chain length was explored, to investigate the cutoff in potency for alkanol anesthetics. Calculations were performed for lipids of chain lengths nlipid 518, for a wide range of anesthetic chain length. In general, addition of anesthetic is predicted to increase the molecular interfacial area slightly more than the membrane volume, i.e. slightly decreasing the membrane thickness, in agreement with experiment (Janoff and Miller, 1982) as is the predicted lipid molecular area of ˚ 2. As expected, the predicted lateral pres:63 A sures p(z) and corresponding lateral pressure den˚ , the sities p(z)= p(z)/dz (using dz = 1.27 A vertical distance along the director of an all-trans alkane) are greatest nearest the aqueous interface (typically in excess of 600 atm) where the lipid chains are the most conformationally constrained, gradually decreasing toward the center of the bilayer. The pressure profile resembles the predicted orientational order profile, consistent with typical experimental results. In Fig. 4 are plotted the predicted changes in the lateral pressures in representative layers for nlipid =16 as a function of nalkanol, the length of the (alkanol) anesthetic. Only close to the aqueous interface is an increase in lateral pressure predicted over a wide range of nalkanol. Changes in the pressure densities near the aqueous interface are well in excess of 1 atm. The intrinsic alkanol potency is thus predicted to pass through a maximum at intermediate nalkanol, dropping to zero as nalkanol approaches nlipid. [For equal chain length, lipid and alkanol become identical at this level of approximation, so zero anesthetic effect is predicted, as has already been suggested (Miller et

Fig. 4. Predicted changes in lateral pressures in a bilayer upon addition of 2 mol % alkanol as a function of alkanol chain length nalkanol. Results are presented for nlipid =16, over the range 1 5 nalkanol 518. The left ordinate gives the change in lateral pressure Dp; the right ordinate gives the corresponding change in lateral pressure density Dp. Values are plotted for representative layers, as indicated.

al., 1987, 1989)]. The cutoff of potency with increasing nalkanol is clearly predicted. For nalkanol \ nlipid, a negative pressure change is predicted near the interface, i.e. such alkanols would tend to reverse anesthesia. Although these results are not quantitatively precise, the general trends and the prediction of the alkanol cutoff are significant. That local lateral pressures are enormous means that pressure changes are still large in magnitude, serving to amplify the effect of solubilization of anesthetic. Arguments that the effects on the bilayer of anesthetics at clinical concentration are small (Franks and Lieb, 1987, 1994) may be valid for structural properties and even some thermodynamic properties, but not for the lateral pressure profile. As discussed above, pressure changes at clinical anesthetic concentrations will be large enough to shift the protein conformational equilibrium significantly if a is of order 1. At clinical anesthetic concentrations of an anesthetic such as a mediumlength alcohol, we estimate Dp (near interfaces) : 0.4 dyne/cm (summing over the layers adjacent to

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the two aqueous interfaces, and considering (Cantor, 1997a) effects of added cholesterol), with Dp : −0.4 dyne/cm spread over the membrane interior. This represents an order-of-magnitude estimate, at best. It is much more difficult to estimate DA(z), since almost no experimental information is currently available for relevant ion channel proteins, except for recent crystallographic work (Unwin, 1993, 1995) on frozen semi-crystalline arrays of the nicotinic acetylcholine receptor (nACh). (Note that DA(z) refers to the entire protein, not just the ion channel. In general, the depth-dependence of the area change of the channel will not be related in any simple way to DA(z)) The radius of the protein in the membrane-spanning portion is typi˚ , as for nACh (Unwin, cally of order 30–35 A 1993). Suppose, for example, that the radius were ˚ in the interior, but increase to decrease by : 3 A ˚ near the aqueous interfaces. Then DA by :3 A (interfaces)\DA (bilayer interior), resulting in inhibition, and we can estimate a : (DAinterfaceDpinterfaces −DAinteriorDpinterior)/kBT : of order 1. Considering the lack of information about DA(z) for ion-channel proteins and the approximations of the lattice model from which the Dp(z) are predicted, the agreement is extremely encouraging: the redistribution of lateral pressure upon solubilization of anesthetics in the membrane is predicted to be of the right order of magnitude to shift the conformational equilibrium of proteins significantly.

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