As shown previously for NMDA receptors, all of the anesthetic-sensitive ligand-gated, voltage-gated and leak channels examined in this study exhibited cut-off effects for each class of organic compounds, and these cut-offs were associated with the calculated molar water solubility of the hydrocarbon. The cut-offs occurred in a predictable order, with Nav channels K2P channels, and GABAA receptors cut-offs all clustered within roughly one order magnitude of saturated drug concentrations. In contrast, the glycine receptor cut-off was associated with drug molar water solubility values over two orders of magnitude lower. If previously determined NMDA receptor results are included , cut-off responses proceed in order of decreasing hydrocarbon solubility as follows: Nav1.2 ≈ Nav1.4 ≳ NMDA ≳ TRESK ≈ TREK-1 > GABAA >> glycine (Fig. 2).
Hydrocarbon cut-off responses in the present study, defined by <10% effect, confirm data available in published literature. Horishita and Harris  found that the ability of primary alcohols to modulate Nav1.2 channels was lost between 1-octanol and 1-decanol, and is consistent with our finding of a cut-off between 1-nonanol and 1-decanol for this channel. Likewise, Peoples and Weight  observed GABAA receptor potentiation with primary alcohol chains up to 1-dodecanol and a cut-off effect at 1-tridecanol and beyond, exactly where this cut-off was observed in the present study. The confidence interval for the GABAA receptor molar water solubility cut-off from this study also encompasses the calculated solubility cut-off values for substituted benzene and phenolic compounds .
Discrete water solubility-associated cut-off effects may be a common feature of all inhaled anesthetic-sensitive ion channels. Conventional volatile and gas anesthetics immobilize individuals at high aqueous phase concentrations  suggesting that they engage in low-affinity binding with target receptors. We postulate that these conventional anesthetic-receptor interactions mirror experimental hydrocarbon-receptor interactions, and we propose a molar water solubility hypothesis to describe non-specific drug binding to low-affinity and amphipathic allosteric sites on proteins. Before a ligand can alter protein function, it must first bind at a site capable of inducing a change in protein function. In order to bind, water molecules must be removed from the hydration shell surrounding the drug, and water molecules within the amphipathic protein pocket must be displaced. The ease with which the water is displaced from the protein pocket is described by its dissociation constant (Kd). Water that is only weakly bound to amino acid side chains within the protein pocket would have a high Kd and require fewer hydrocarbon molecules to successfully compete for access to this allosteric site. Consequently, this protein would have a lower molar water solubility cut-off. In contrast, water that is tightly bound within the pocket would have a low Kd, and therefore a high hydrocarbon concentration would be necessary to compete for access to this site. Such a protein would exhibit a high drug molar water solubility cut-off. It is possible that ion channels may have more than one amphipathic allosteric site for low-affinity interactions with inhaled anesthetics or other hydrocarbons [16,17,18]; however the methods employed in the present study would have identified receptor cut-off effects based only on the amphipathic allosteric site with the highest water Kd in that receptor and which would therefore exhibit the lowest hydrocarbon molar water solubility cut-off effect among all modulatory sites. Other lower water Kd sites could be important for binding and modulation by more soluble hydrocarbons and inhaled anesthetics when present at sufficient aqueous concentrations.
A second explanation for hydrocarbon molar water solubility cut-offs is possible. Desolvation of water molecules around the ligand is necessary for protein binding to occur. However, if the difference in free energy between the solvated protein-drug complex and the separated solvated protein and solvated drug is too great, then drug binding will be energetically unfavorable and no modulation of protein function will occur . Larger hydrophobic drug ligands are surrounded by larger and more rigid water shells for which desolvation may be associated with greater enthalpy. The strength of water complexes around the ligand might increase to the point that drug receptor binding—and thus drug-receptor modulation can only occur if there remains sufficient entropy to overcome increased enthalpy of binding .
In either case, a molar water solubility hypothesis is not predicated on any particular molecular size, shape, polarity, functional groups, or atomic arrangement of the drug for low affinity interactions to take place. Indeed, the diversity of conventional anesthetics and other hydrocarbons capable of modulating a single anesthetic-sensitive ion channel, as well as the relatively minor effect differences produced by dug enantiomers , suggest that ligand structure itself is not crucial for binding. However, ligand structure does determine the magnitude and type of modulation for the protein it binds. Whether there is inhibition versus potentiation of K2P channel currents, for example, will depend on the functional group of the hydrocarbon ligand (Table 2). Modulation magnitude also differed between functional groups; inhibition of Nav1.4 channels was approximately four times greater for alcohols, alkenes, and ethers than for amines or cycloalkanes. The importance of structural elements within receptor binding pockets has also been demonstrated through mutation studies that confer resistance to conventional anesthetic or other hydrocarbon modulation [22,23,24], although it is unknown whether some of these changes may also have altered the water Kd or drug desolvation enthalpy that, in turn, could have affected the ability of the drug to bind the allosteric pocket.
The hydrocarbon molar water solubility cut-off value for each channel is expressed as confidence intervals, and certain error is inherent in their measurement. Butane, the smallest n-alkane studied here, is a gas at room temperature and pressure, and therefore cannot be studied at a saturated aqueous phase concentration under normobaric conditions unlike the other liquid and solid hydrocarbons. All receptors were nonetheless modulated by 90% atm of butane, but had current modulation not been observed, a true cut-off could have been inferred at this submaximal concentration. Furthermore, carbon additions to the ω-end of the hydrocarbon chain produce discrete, non-continuous changes in molar water solubility. For each series of functional groups, there is a range of solubility values that lie between the CN modulating hydrocarbon and the CN + 1 cut-off hydrocarbon where the receptor effect is unknown. Most important, however, is the reliance on calculated solubility values for hydrocarbons in pure water at 25 °C and pH = 7.0 rather than measured solubility values under study conditions with a 250 mOsm electrolyte solution at 22 °C and pH = 7.4. Both accurate measurement and accurate prediction of solubility values are challenging for extremely hydrophobic compounds or for large or complex molecules with multiple functional groups. To limit this problem, only simple aliphatic compounds with the functional group on the first carbon, or central and symmetrical in the case of the dialkyl ethers, were studied. Even so, increasing hydrocarbon chain length is frequently accompanied by greater divergence between calculated and measured water solubility values [25, 26].
Whole cell current cut-off responses were measured using hydrocarbons at saturated aqueous concentrations. This was done to ensure that each cut-off was independent of any particular endpoint (e.g., amnesia, unconsciousness, or immobility). Lack of receptor modulation at a saturated hydrocarbon concentration implies absent modulation at a lower pharmacologic concentration, including concentrations relevant to anesthetic endpoints. Anesthetic efficacy is in mammals is unknown for many, but not all, of the hydrocarbons tested. Primary alcohol anesthetic potency increases with increasing carbon chain length from methanol to dodecanol, after which further carbon additions do not produce anesthesia at all . This anesthetic cut-off corresponds to the alcohol molar water solubility cut-off for GABAA receptors (Table 2). However, a general anesthesia cut-off effect has been reported to occur with n-alkanes and dialkyl ethers having around 11-to-15 or more carbon atoms  and cycloalkanes having eight or more carbons atoms . These molecules are far longer and have molar water solubility values far lower than occur with the GABAA receptor cut-off. Although observed anesthetic effects might be due to glycine receptor modulation, high affinity effects on one or more other anesthetic-sensitive receptors, or even systemic toxicity, it seems very possible that anesthetic effects could be the result of potent alcohol metabolites produced by oxidation of alkanes, cycloalkanes, and ethers by cytochrome P450 enzymes [30, 31]. Since the hydroxyl group confers greater molar water solubility, primary alcohols have receptor cut-offs at longer chain lengths than either alkanes or cycloalkanes or dialkyl ethers. These long-chain alcohol metabolites are also much more potent general anesthetics than their parent compounds , so even tiny quantities can have narcotic effects. Identifying simple parallels between in vitro receptor cut-offs and in vivo anesthetic cut-offs thus may be complicated for certain classes of organic compounds.
Channel studies were conducted using a reductionist biological system. However, in vitro electrophysiologic responses conducted at room temperature for relevant anesthetic-sensitive ion channels in oocytes seem to correlate with anesthetic potency in animals [33,34,35]. Likewise, the hydrocarbons studied in Table 1 administered in vivo would be expected to similarly modulate ion channels; in the case of drugs below the solubility cut-off, no in vivo modulation would be expected at all.
Finally, the molar water solubility hypothesis could offer practical applications to the development of new and novel inhaled anesthetic agents. Conventional volatile anesthetics bind promiscuously to a variety of cell proteins, but not all of these receptor interactions are essential to their ability to produce general anesthesia. For example, NMDA receptors contribute to immobilizing actions of inhaled anesthetics able to inhibit their function, but experimental inhaled anesthetics can still be immobilizers without producing NMDA receptor inhibition . Since there is nearly a 10-fold separation in the hydrocarbon molar water solubility cut-off effects between NMDA versus GABAA receptors, a volatile anesthetic might be modified to target calculated aqueous solubility values within this range to confer selectivity against higher cut-off NMDA receptors while preserving activity at lower cut-off GABAA receptors. With sufficient GABAA receptor potentiation and contributions of lower cut-off receptors, such an agent might retain immobilizing potency but lose adverse effects associated with the modulation of higher cut-off receptors. Consequently, molar water solubility could be key to identifying volatile anesthetics with new molecular mechanisms of action and improved pharmacodynamic profiles.