Figure 4.

Minimum observation times for ergodicity. Cumulative distributions of the looping probability for (A) different periods of TPM observations (10, 30, 40, 60, 80 and 100 min) and (B) different periods of MT observations (2, 5, 10, 12, 15 and 18 min) are plotted along with the cumulative distribution for the entire set of observations (black curves). All records used in this analysis were for 0.25 pN tension and 1.5% supercoiling. Only when observations last at least 60 min (A) or 12 min (B) do the cumulative distributions of the looping probabilities for individual molecules resemble the distributions for the maximum length observations. With shorter observation periods, the looping probabilities measured for individual molecules vary widely. For example, in the TPM data in panel (A), looping probabilities measured for molecules observed for 10-min intervals (blue) displayed a significant fraction of high probabilities that did not appear for the molecules observed for 60 min or more, up to 5 h (black). In panel (B), looping probabilities spanning the entire range result for 2- or 5-min period of observation but narrow to the 40–80% range when observation times are 12 min or longer.