A GEOMETRIC SEQUENCE THAT ACCURATELY, DESCRIBES ALLOWED MULTIPLE CONDUCTANCE LEVELS OF ION CHANNELS - THE 3-HALVES (3 2)-RULE/

Ion channels can express multiple conductance levels that are not inte ger multiples of some unitary conductance, and that interconvert among one another. We report here that for 26 different types of multiple c onductance channels, all allowed conductance levels can be calculated accurately using the geometric sequence g(n) = g(o)(3/2)(n), where g(n ) is a conductance level and n is an integer greater than or equal to 0. We refer to this relationship as the ''3/2 Rule,'' because the valu e of any term in the sequence of conductances (g(n)) can be calculated as 3/2 times the value of the preceeding term (g(n-1)). The experimen tally determined average Value for ''3/2'' is 1.491 +/- 0.095 (sample size = 37, average +/- SD). We also verify the choice of a 3/2 ratio o n the basis of error analysis over the range of ratio values between 1 .1 and 2.0. In an independent analysis using Marquardt's aligorithm, w e further verified the 3/2 ratio and the assignment of specific conduc tances to specific terms in the geometric sequence. Thus, irrespective of the open time probability, the allowed conductance levels of these channels can be described accurately to within similar to 6%. We anti cipate that the ''3/2 Rule'' will simplify description of multiple con ductance channels in a wide variety of biological systems and provide an organizing principle for channel heterogeneity and differential eff ects of channel blockers.