Isochannels and blocking modes of voltage-dependent sodium channels

Our results support the existence of three different Na-channel subtypes or isochannels. These isochannels can be readily distinguished as the predominant Na-channel types in mammalian brain, skeletal muscle, and cardiac muscle. The sensitivity to mu-conotoxin GIIIA and tetrodotoxin is sufficient to classify these channels. The skeletal muscle channel is very sensitive to both tetrodotoxin and mu-conotoxin, the brain channel is sensitive to tetrodotoxin but insensitive to mu-conotoxin, and the heart and denervated muscle channels are insensitive to both toxins. In addition to block at the external receptor site for guanidinium toxins, several other blocking modes can be generalized for batrachotoxin-activated Na channels. One mode is peculiar to certain hydrophobic molecules so far represented by our studies of benzocaine and procaine. These molecules induce discrete blocking events with dwell times that apparently increase with anesthetic concentration and a blocking frequency that increases with negative voltage. This mode is quite distinct from the fast internal block by charged organic molecules that increases with positive voltage. These results imply that it is not possible to ascribe the diverse effects of local anesthetics to a single site in the interior channel mouth, as previously proposed by Hille. Our observations thus support the conclusions of other workers who used mixtures of two local anesthetics to show that the dose-response behavior does not fit single-site behavior, but requires at least two distinct sites. Two additional blocking modes can be distinguished for the interactions of cations at the internal and external mouths of the channel. Organic molecules can apparently enter the electric field from the internal but not the external side of the channel. This result suggests a wide internal entry way to the field and an external constriction that prevents the entry of molecules with a single methyl group but permits entry of divalent inorganic cations such as Ca2+ and Co2+.

Two-stage global search designs for linkage analysis using pairs of affected relatives

We investigate the two-stage procedure proposed by Elston [(1992) Proceedings of the XVIth International Biometric Conference, Hamilton, New Zealand, December 7-11, 1992, pp 39-51, and (1994) "Genetic Approaches to Mental Disorders." Washington, DC: American Psychiatric Press, pp 3-21] for performing a global search of the genome to locate disease genes by linkage analysis using affected relative pairs. The optimal design depends on the type of pairs studied, the effect of the disease locus, the relative costs of recruiting affected persons and typing markers, how informative the markers are, and the amount of genetic heterogeneity. It is specified by the initial number of markers to use, the number of affected relative pairs to study, the initial significance level alpha* to use at the first stage, and the number of flanking markers to use at the second stage around markers significant at the first stage. Asymptotically, the optimal design does not depend separately on either the desired final significance level or power, but rather on a function of the two. Both as the effect of the disease locus increases and as the relative cost of recruiting a subject increases, the optimal number of initial markers increases and the optimal number of pairs decreases. The expected cost of the study decreases as the effect of the disease locus increases, but increases as the relative cost of recruiting a subject increases. The optimal initial number of markers decreases but the number of pairs increases when there is genetic heterogeneity present; conversely, the optimal initial number of markers increases when markers are less than fully informative. Compared to a one-stage procedure, a two-stage procedure typically halves the cost of a study.