Fractal dimensions in the occurrence of miniature end-plate potential in a vertebrate neuromuscular junction

1. Occurrence of miniature endplate potentials (MEPP) in the sartorius muscle of Rana catesbiana in high Mg2+ Ringer solution were observed in standard intracellular recording. Intervals and amplitudes of sequentially occurring MEPP were registered and analyzed. 2. Interval histograms of a time series of MEPP showed exponential-like pattern as reported in the classical study by Fatt and Katz (1952). The cumulative distribution of the intervals plotted in logarithmic axes showed two distinct phases. In shorter intervals (< 1s), curve along exponential decay was observed, and in longer intervals (> or = 1s) linear decay can be seen. The latter power-law relation gave dimensions of 4.111 +/- 0.812 (mean and S.D.). Self-similarity in longer range implies a time-scale invariant nature and may suggest fractal nature in restoration process of synaptic vesicles, while exponential decay in the short time interval range implies random release of transmitter packet from the readily releasable pool. 3. Fluctuation of amplitudes in sequentially occurred MEPP were analyzed according to Higuchi's cumulative route-length analysis. The estimates for sequential amplitude curve showed the power-law relation in a logarithmic plot whose inclination (= D) estimated with linear regression analysis was 1.996 +/- 0.007 (mean and S.D.). This results indicate that fluctuation in the amplitude of MEPP shows possible maximum complexity as a graphic curve in 2-D plane. Similar result was obtained for fluctuation of intervals of successively occurring MEPP.