Figure 1.
The evolution of a P. mirabilis colony.
Time after inoculation: (A) 8.5 hours, (B) 9 hours, and (C) 11 hours. (A) initially homogeneous bacterial lawn breaks into radial spokes in the central region of the colony, then bacteria and bacterial aggregates stream inwards following the radial spokes. (B) the radial streams gradually transform into CCW spirals, and the inner ends of each arm join together to form a solid toroidal mass. (C) a second rotating ring forms with spirals that arise further from the center, and a moving train of high cell density forms at some distance from the ring. In (A) and (B), the colony front is highlighted in blue, and a few arms of the streams are highlighted in red. In (C) the colony has covered the entire plate. (D) A different experiment that shows only stream formation without the structure of ring elements.
Table 1.
Chemotaxis analysis of swimmer cells using the amino acid drop assay.
Figure 2.
(A) The colony front and the patterning zone. (B) A vertical cross-section of the system.
The lower layer is hard agar that contains nutrients, and the top layer is slime generated during colony expansion. Swimmers move in the layer of slime, absorb nutrients that diffuse upward, and secrete attractant. Bacterial flagella are not shown.
Figure 3.
The cell density profile is in unit of . Parameters used:
,
,
,
,
,
,
, and the secretion rate of the attractant is
per cell.
Figure 4.
Simulated spiral streams in a disk using a swimming bias of .
The initial attractant gradient is , centered as before, and all other parameters are as used for the results in Figure 3.
Figure 5.
Individual cell tracks and average velocity profile during spiral stream formation in Figure 4.
(A)The positions of 10 randomly chosen cells, each position recorded every 30 sec by a blue dot. (B) schematics of cell movement with a swimming bias of individual cells.
Figure 6.
,
, Other parameters used are the same as in Figure 3.
Figure 7.
A comparison of predicted and observed spatial patterns.
Parameters used are the same as in Figure 3.
Figure 8.
A comparison of the cell-based and the macroscopic predictions of the diffusion matrix , chemotactic velocity
, and the angle between
and
.
Here and
are the diffusion rate perpendicular and in parallel to the signal gradient (along the
-axis), and
the cross diffusion rate. The horizontal axis (
) measures the signal gradient interpreted by a cell, with units
. The top row is obtained with no swimming bias as in Figure 3, and the bottom row is obtained with
as in Figures 4 and 6. Other parameters used are the same as in the Figures 3, 4, and 6. The blue, green, and cyan curves are obtained from stochastic simulations of the cell-based model, and the red curves are the predictions from the macroscopic chemotactic equation in [32].
Figure 9.
The numerical algorithm for the model.
(A) a schematic figure of the domains. The reaction-diffusion equations are solved on the grid, while the cells can move around the whole domain. (B) the area fractions used in defining the interpolators (5, 6).