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

1. Occurrence of miniature endplate potentials (MEPP) in the sartorius musc le of Rana catesbiana in high Mg2+ Ringer solution were observed in standar d intracellular recording. Intervals and amplitudes of sequentially occurri ng MEPP were registered and analyzed. 2. Interval histograms of a time series of MEPP showed exponential-like pat tern as reported in the classical study by Fatt and Katz (1952). The cumula tive distribution of the intervals plotted in logarithmic axes showed two d istinct phases. In shorter intervals (<1s), curve alone exponential decay w as observed, and in longer intervals (<1s) linear decay can be seen. The la tter power-law relation gave dimensions of 4.111+/-0.812 (mean and S.D.). S elf-similarity in longer range implies a time-scale invariant nature and ma y 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 ac cording to Higuchi's cumulative route-length analysis. The estimates for se quential amplitude curve showed the power-law relation in a logarithmic plo t whose inclination (=D) estimated with linear regression analysis was 1.99 6+/-0.007 (mean and S.D.). This results indicate that fluctuation in the am plitude of MEPP shows possible maximum complexity as a graphic curve in 2-D plane. Similar result was obtained for fluctuation of intervals of success ively occurring MEPP.