To the Editor:—

The critique by Eger et al.  1on the article by Eckenhoff and Johansson 2concerns combining the dose–response curves of several ion channels to make them steeper. The slopes of the in vivo  studies are steep, whereas those of the in vitro  studies are gradual. Both groups anticipate that when several binding sites among ion channels are combined, the dose–response curves may become steeper. The computation procedures were different. However, all dose–response curves become steep when plotted as quantal responses (hit or no-hit). In anesthesia, the animal responses are typically plotted as anesthetized or nonanesthetized (quantal response).

The Hill equation starts with the following form, where n molecules of an anesthetic A bind to the receptor R:


The binding number n is designated as the Hill number, nH. Hence, the Hill number should be an integer value. However, integer values are seldom found. The disagreement between nHand the real binding number was recognized when Archibald Hill measured the oxygen binding to hemoglobin in 1913. 3Hemoglobin has four oxygen binding sites, but the Hill number never reached three. This is because the first oxygen binding changes the binding affinity of the succeeding oxygen molecules.

The Hill equation does not count partially anesthetized intermediates:


Therefore, nHdoes not represent the binding numbers. Large Hill numbers indicate that unspecified multiple binding sites are acting with high cooperativity. Therefore, it is termed “cooperativity parameter.”

Large Hill numbers are not limited to quantal responses. My colleagues and I 4found large Hill numbers in brine shrimp, Artemia salina . These aquatic creatures swim at random with changing directions when placed in the artificial sea water. Their movement slows when anesthetics are introduced into the system. We digitized the swimming distances every 0.5 s for 30 s using a video camera and a computer system. 4Despite the fact that the plot was produced by the averaged swimming distances in a unit of time, which is not quantal, we found large Hill numbers: enflurane, 11.9; halothane, 14.8; isoflurane, 13.5. The continuous response, identical to the channel studies, produced two-digit Hill numbers.

Regardless of quantal or nonquantal responses, the dose–response curves of living animals are extremely steep. So are the grouped dose–response curves of in vitro  studies. 5It indicates that anesthetics act at numerous sites with highly cooperative mode. The pressure reversal of anesthesia 6shows that all systems are equally affected, including enzymes, channels, proteins, lipid membranes, and others. Anesthesia is a symptom complex and cannot be defined. It may be futile to designate a limited number of ion channels as the anesthetic action sites. All channels and all receptors may participate in anesthesia.

Eger EI II, Fisher DM, Dilger JP, Sonner JM, Evers AS, Franks NP, Harris RA, Kendig JJ, Lieb WR, Yamakura T: Relevant concentrations of inhaled anesthetics for in vitro  studies of anesthetic mechanisms. A nesthesiology 2001; 94: 915–21
Eckenhoff RG, Johansson JS: On the relevance of “clinically relevant concentration” of inhaled anesthetics in in vitro  experiments. A nesthesiology 1999; 91: 856–60
Stryer L: The binding of oxygen to hemoglobin is cooperative, Biochemistry. New York, WH Freeman, 1981, pp 66–9
Takasaki M, Tatara T, Suezaki Y, Shirahama K, Kamaya H, Ueda I, Totoki T: Effect of inhalation anesthetics on swimming activity of Artemia salina . J Anesth 1991; 5: 287–93
Yamakura T, Bartaccini D, Trudell JR, Harris RA: Anesthetics and ion channels: Molecular models and sites of action. Annu Rev Pharmacol Toxicol 2001; 41: 23–51
Johnson FH, Flagler EA: Hydrostatic pressure reversal of narcosis in tadpoles. Science 1951; 112: 91–2