Figure 2: Statistical analysis of correlated switching.

(a) Example on/off trajectory of the major crystal at −10 mV and 10 pA. White and black denote ethyl rotors pointing up (on; 1) and down (off; 0), respectively. Correlated switches are highlighted by green boxes. (b) Corresponding switching trajectory. Blue and red denote switching off (1→0) and switching on (0→1), respectively. Statistical analysis of 1,724 events reveals non-random switching and the predominance of several correlated switching events. The correlations plotted here are (c), the ratio of the conditional probability of an ethyl rotor at position j (j=i−5, …, i−1, i+1, …, i+5) switching off (1→0), given that the ethyl rotor at position i switches on (0→1), to the average probability of an ethyl rotor switching off (1→0) and (d) the ratio of the conditional probability of an ethyl rotor at position j switching on (0→1), given that the ethyl rotor at position i switches off (1→0), to the average probability of an ethyl rotor switching on (0→1). The relative position of j to i is defined so that i+1 is the NN of rotor i, while i−1 is the FN of rotor i. The red and blue bars are results from experiment and from simulation of random switches, respectively. (e) Histogram of experimentally observed populations of [00], [01]/[10] and [11] (left, red), compared to a binomial distribution calculated with an optimized off probability of 0.36275 (right, blue). (f) Free energies of the nine most populated [ab][cd] microstates. Error bars are the weighted s.d. Similar free energy diagram using three-pair microstates [ab][cd][ef] can be found in Supplementary Fig. 20.