Fig. 4

Spatial correlation in ferromagnetic and anti-ferromagnetic colonies. Spatial autocorrelation function C(r) in colonies of rod-shaped (a) and spherical (b) E. coli cells carrying the ferromagnetic (F) and anti-ferromagnetic (AF) systems with reporter vector 1 (F1 and AF1) or 2 (F2 and AF2). Points and error bars correspond to the mean ± the standard deviation of around 40 colonies for each system, and lines correspond to the best fit of the exponential decay equation \(y=y_0*\exp (-x/b)+C\) to the data. Insets show the oscillating behavior of the sACF around zero of individual anti-ferromagnetic colonies, which is lost when the data is averaged. c Length constant and colony size of ferromagnetic and anti-ferromagnetic colonies of spherical E. coli cells grown in M9 solid medium supplemented with glucose (Glu) or glycerol (Gly), showing that cell division rate does not affect the spatial correlations. Statistical analysis was performed using an unpaired two-tailed Mann-Whitney test (\(\alpha = 5\%\)). ns (not significant): P > 0.05; \(****\): P \(\le\) 0.0001. d Probability distribution P(S) (\(\log _{10}-\log _{10}\) plots) of the cluster size S (in pixels) for ferromagnetic populations simulated with CPIM (left) and ferromagnetic colonies of rod-shaped (middle) and spherical (right) cells. e Probability distribution of the cluster size for ferromagnetic populations simulated with CPIM at different cell birth rates, from 0.0350 to 0.0150 (top), and ferromagnetic colonies of spherical cells grown in glycerol (blue) or glucose (red) (bottom). Plots in d and e were obtained using the algorithms r_plfit with the default low-frequency cut-off [69]. Solid lines correspond to the power-law \(P(s) = Cx^{-\gamma }\) found by the algorithm. Insets show the probability distribution of all the clusters found in the populations (without cut-off), with solid lines corresponding to the best fit of the data to equation \(P(s) = A*s^{-\gamma }\) found by the least squares method. Dotted lines correspond to a curve with \(\gamma =2.00\)