(A) The shape of the velocity autocorrelation (VAC) functions for (i) subdiffusive/elastic/hindered, (ii) diffusive and (iii) superdiffusive/processive dynamics. Red line indicates a lag equal to the sampling time (the time over which the velocity was measured). In subdiffusive/hindered processes, movement is biased towards the direction the particle came from; in a diffusive process there is no directional bias, while in superdiffusive processes (e.g. directed movement), the particle is biased to keep moving in the same direction. This results in the VAC between frames (i.e. at a lag equal to the sampling time) being negative, zero and positive, respectively (indicated by the red line). The orange curves are generated using the normalised velocity autocorrelation /2 for any process with and taking (i) , (ii) and (iii) . The purple line in (iii) is a sketch of what the VAC might look like for oscillatory dynamics. (B–C) Mean position autocorrelation (PAC) and VAC of trajectories from cells with one plasmid (n=897). Shaded area indicates standard deviation. The autocorrelation time-scale , in B and C, was obtained by fitting the PAC to and the VAC to (red lines), where is the time over which the velocity is calculated (1 frame = 60 s) and c is a constant accounting for any old-pole/new-pole bias. These functions arise from a model of over-damped spring-like motion. See the methods for further details. (D) Mean PAC of trajectories from different populations with 1,2,3, or 4 plasmids (n=879, 5044, 3129, 961). (E) As in (D) but for the VAC. (F) MSD measured every 60 s (n=2558). (G) MSD measured every 1 s (n=75). The diffusion constant D=2.01 ± 0.14e–4 μm2/s (mean ± 95% CI) was obtained by fitting to the MSD-curve (red line).