Figure 5

Cells’ reorientation during ‘wrapping-pause-push’ transformations. Reorientations in terms of turn angle and longitude are determined by combinations of pause initiation time \(\mathscr {P}_\mathrm{I}^k=(0.15+0.0017k)\) s, \(k=0, \ldots ,20\), and pause duration \(\mathscr {P}_\mathrm{D}^j=(0.025+0.005j)\) s, \(j=0, \,.\,.\,, 12\), where 0.017 s corresponds to the period of one cycle of flagellar rotation measured during the wrapping mode. Therefore, the potential pause initiation time is uniformly distributed over the time interval corresponding to two cycles of flagellar rotation. (a) Displays 11 individual trajectories (left) of the cell center, where a pause is initiated with \(\mathscr {P}_\mathrm{I}^k\), \(k=0, \ldots ,10\), and the longitudes \(\phi\) with \(\mathscr {P}_\mathrm{I}^k\), \(k=0, \ldots ,20\) (right), while the pause duration is fixed as \(\mathscr {P}^7_\mathrm{D}=0.06\) s. Cells move downward drawing helical curves (solid black) and tumble at different pause initiation times (dotted red) and then push forward (solid blue). Notice that the longitude makes approximately two turns in clockwise direction against pause timing corresponding to two cycles of flagellar rotation, see the right panel in (a) where each turn is distinguished by colors. The turn angles (b) and longitudes (c) of 273 events with all the combinations of \(\mathscr {P}_\mathrm{I}^k\) and \(\mathscr {P}_\mathrm{D}^j\) are drawn together with the collective histograms in the right panels. When the pause duration is less than 0.025 s, the cell displays the overwhirling motion rather than the push mode. For a fixed pause duration, the turn angles do not depend on pause initiation time but the longitude does. When the pause initiation time is fixed, the turn angle and the longitude converge to certain values as the pause duration increases. Whereas the turn angles form a unimodal distribution with a peak at \(70^\circ\)–\(75^\circ\) with the mean ± standard deviation being equal to \(78.7^\circ \pm 11.31^\circ\), longitudes spread out ranging from \(0^\circ\) to \(360^\circ\) and show no trend.