Mol MicroErhardt lab

Single-cell motility simulation

How does the number of flagella change how far a bacterium swims? This simulation compares three Salmonella strains with fewer or more flagella than the wild type, in liquid and in an agarose-like mesh of obstacles. All speeds and motile fractions come from single-cell measurements.

  1. PproAFewer flagella than the wild type2.1 flagellar hooks per cell on averageflhDC from the synthetic promoter PproA
  2. Wild typeReference strain2.7 flagellar hooks per cell on averagenative flhDC promoter
  3. PproBMore flagella than the wild type4.4 flagellar hooks per cell on averageflhDC from the synthetic promoter PproB

Schematic cells: number of flagella rounded from the measured mean.

Medium
Speed
0.0 s
PproA fewer flagella · 2.1 hooks per cell

Wild type reference strain · 2.7 hooks per cell

PproB more flagella · 4.4 hooks per cell

Coloured cells: motile cells, drawn 1.5 times larger than real. Light grey cells: non-motile cells. Black outline: cell stalled at an obstacle. Grey disks: obstacles of the agarose mesh. Each field is 148 × 96 µm; a run lasts 20 s.

Net displacement of the motile cells

Mean distance from the start position. The walls of the small field limit the displacement after a few seconds; for the quantitative comparison the preprint uses a field eight times larger in each direction.

What to look for

  • Liquid: cells with more flagella swim faster (PproA 19.9, wild type 27.6, PproB 32.0 µm/s), and more of them swim.
  • Agarose: all strains are slower and turn more often. Cells with fewer flagella stall more often at obstacles, so PproA stays close to its start position.
  • Press New run for a new random field: single runs vary, but the order of the strains usually stays the same.

From the preprint

The cost-benefit trade-off of flagellation

Flagella let Salmonella swim, but they cost the cell protein and energy. We expressed flhDC from promoters of different strength and measured growth, proteome allocation, swimming and spreading for each level of flagellation. The animation summarises the study (59 s).

How the model works

  • A fixed fraction of the cells is motile. Non-motile cells only diffuse.
  • Motile cells run with a constant speed. Their heading changes slowly by rotational diffusion, and at a constant rate they turn by a random angle.
  • In agarose, static disks (19 % of the area) act as obstacles. A cell that hits a disk slides along its surface or, with a strain-specific probability per contact, stalls for a short time.
  • The walls of the field reflect the cells.

The model leaves out chemotaxis, interactions between cells and hydrodynamics. It is an illustrative but data-based track generator. All parameters and their sources are listed in Supplementary Table X of the preprint.

Code

This page runs a JavaScript version of the corrected model of the preprint in your browser (time step 0.005 s).

Model concept: Marc Erhardt and María José Giralt-Zúñiga. Code review and restructuring: Michael Jahn (Max Planck Unit for the Science of Pathogens).