II. Fruiting Body Formation in Myxobacteria

? Under starvation conditions, Myxobacteria aggregate into huge fruiting bodies.

? Within the fruiting bodies, the cells differentiate into myxospores that can survive for years in tough conditions.

Stages of Fruiting Body Formation

Rippling, Aggregation, Fruiting Body Formation, Sporulation

Rippling in Myxobacteria

Before aggregating into fruiting bodies, there may be periodic high density waves seen traveling through the population. These ripples may last for hours.

The exact mechanism for rippling is unknown and enigmatic. Ripples waves are unusual because

1. they propagate with no net transport of cells, and,

2. there is no interference, either constructive or destructive, where waves overlap.

Facts about Rippling

Isolated cells oscillate with a mean period of about 5-8 minutes.

Cells in a rippling swarm oscillate more quickly and travel about one wavelength between reversals.

Cell motion is approximately 1-D. The majority of cells move in lines parallel to one another, with or against the axis of wave propagation.

Hypothesis of Precise Reflection

Sager, B. and Kaiser, D. [1994] Intercellular C-signaling and the traveling waves of Myxococcus Xanthus

Head-on collisions between cells cause cell direction reversals. Thus, when two wave fronts collide, the cells reflect one another pair by pair in a precise way that preserves the wave structure in mirror image.

LGCA Model For Rippling

Cells are modeled as 3xl rectangles. Each cell occupies a single velocity channel with its center of mass. Cells may be right-directed or left-directed.

Cells interact with oppositely directed cells when a collision occurs between C-signal interaction nodes, which are located only at the cell poles.

C-signal collisions speed up an internal biochemical clock which regulates reversals. More collisions shorten the period of time between reversals. After reversing, cells are insensitive to further collisions for a period of time called the refractory period.

Ripple Model Results

1. Our model based on the hypothesis of precise reflections quantitatively reproduces the dynamics, density and wavelength of experimental ripples.

2. The refractory period is an essential feature of the model and comparison of our model results with experimental data indicates that the refractory period is 2-3 minutes.

3. When two ripples meet, it appears that they inter-penetrate.

4. In fact, each ripple reverses by precise reflection. Depending on when the cells reverse and their cell length, there may be a small phase shift between the two waves.

Aggregation in Myxobacteria

1. Aggregates form from a large area of swarming cells. These swarming cells align from a random distribution and form long chains that stream into aggregation centers.

2. The aggregates are at first flat, then round up into a mound.

3. In both flat and rounded aggregates, cells tend to be arranged tangent to a hollow inner region and move in a circular or vortex-like fashion around the hollow center.

4. Little is known about how cells organize during aggregation, but C-signaling plays a pivotal role.

LGCA Model Of Aggregation

1 Our Hypothesis: Cells align by C-signaling. In particular, cells will preferentially turn by a Monte Carlo process so that C-signal nodes overlap.

1 We model 3x21 cells on a triangular lattice. Each cell occupies only one velocity channel with its center of mass.

Results of LGCA Model For Aggregation

Cells immediately align into chains. Then, they begin condensing and

patches form. Circular orbits develop from these

patches. There is a hollow region within each circular orbit and cells are arranged tangentially to the hollow center. Many of these orbits are not stable.

Eventually stable orbits form which may be hollow, very dense, or span the lattice.

Cell center directions of common

LGCA stationary aggregate.

Cell center geometries of stationary aggregates listed in order of increasing density..

Area verses density for 400 randomly chosen aggregateswith different icons corresponding to different types:

I plusesII empty squaresIII filled squaresIV empty circlesV filled circles

A stream connects two stationaryaggregates. The bottom aggregategrows as the top aggregate dissolves.

Standard deviation of cell densityfor control 1 (dashed), control 2 (dotted)and lattice boltzman (solid).

Percent of cells in streams (squares)and stationary aggregates (circles)for control 1 (dashed), control 2(dotted)and lattice boltzmann (solid).

Positions of aggregates in area verses density space for agrgegatesin two LGCA simulations: (a) streams, (b) stationary aggregatesand c streams and stationary aggregates together.

Positions of aggregates in area verses density space for agrgegatesin lattice boltzmann simulations: (a) streams, (b) stationary aggregatesand c streams and stationary aggregates together.

Cell center directions of a typical orbit and a typical streamin the lattice boltzmann model.

Cell density for lattice boltzmann simulation after100, 500, 2200 and 3400 timesteps.

Cell density for an LGCA simulation after25, 200, 900 and 25000 timesteps.