of lifetimes of states, observable at almost any temporal resolution that methods

of lifetimes of states, observable at almost any temporal resolution that methods would allow. Early and representative studies comparing the fit of the data with hierarchical scaling functions versus a sum of a small number of Markovian exponentials included studies of a calcium activated potassium channel in human fibroblasts (Stockbridge and French, 1989) which yielded evidence to support both models, as did studies of membrane conductances in corneal epithelial cells by another group (Korn and Horn, 1988). In a systematic comparison of scaling and Markov exponential modes of the gating kinetics of GABA activated chloride channels, acetylcholine activated end plate potentials, calcium activated potassium channels and fast chloride channels (McManus et al, 1988), it was found that the latter fit the data best in most experiments. Similar results were reported in studies of the glutamate and delayed rectifier potassium channel with respect to distributions of open and closed times (Sansom et al, 1989). Space does not permit a systematic account of the continuing debate and conflicting studies about these representations and the implicit biophysics of discrete, finite versus continuous, hierarchical channel event heterogeneity. It is interesting that recent experiments making use of Hurst rescaled range analyses of time series of whole cell membrane voltage fluctuations (without the assumptions and current renormalizing procedures associated with patch clamping) have yielded additional evidence for multiply correlated, Hurst > 0.5, a < 2 power law behavior of what some might regard more generally as a protein relaxation time mediated hierarchical array of ion conductance behaviors (Liebovitch and Todorov, 1996). Following the discovery of (very) subsaturating (“far from equilibrium”) rat brain levels of the common cofactor for tyrosine and tryptophan hydroxylases, tetrahydrobiopterin (Bullard et al, 1978), studies of amino acid substrate saturation functions and time courses determined at these low, physiological co-reactant concentrations manifested patterns of hierarchical multiplicity and discontinuities suggestive of bifurcations and time-dependent fluctuations with fractional (hierarchical) time scaling exponents that were sensitive to psychotropic drugs 212 HOUSE_OVERSIGHT_013712