Self-organisation in Slime Molds

Michael Iles4 February 2002

Introduction

• Many types of slime molds• We’ll look at cellular slime molddictyostelium discoideum

Life Cycle

• Amoebae are in ‘growth phase’ when food is available

• When starved, they enter the ‘developmental phase’

Cell Movement

Individuals begin to ‘clump’ at centres of circles and spirals

Cell Movement

Cells ‘stream’ more efficiently into the centres

Cell Movement

Well-developed streaming morphology

Slug and Fruiting Body

• ‘Slug’ comprises 10 000 to 100 000 cells

• Cells differentiate into base, stalk, fruiting body and spores

• Spores are released, completing the life cycle

Other Examples

Other Examples

Other Examples

Why are They Interesting?

• Biological motivation for swarm systems• Example of resistance to the idea of

decentralisation• Could shed light on the evolution of multi-

cellular organisms

Why They Do It

• Cellular aggregation increases the chances that their progeny will be carried to a place where there’s more food

• What’s in it for the cells that form the stalk?

Mechanisms of Self-Organisation

• Amoebae excrete cyclic adenosine 3’, 5’-monophosphate (cAMP)

• cAMP is secreted in two scenarios: oscillatory release, and relay

• Positive and negative feedback loops of cAMP production exist

Mechanisms of Self-Organisation

• Amoebae also move upstream in the cAMP gradient

• Periodic waves of cAMP cause periodic movement of amoebae

Modeling Slime Molds

• Modeling in two phases:– just cAMP waves– cAMP waves in conjunction with movement of

amoebae

Modeling cAMP Waves• ρ = total fraction of receptors in active form• β = nondimensional intracellular concentration of cAMP• γ = nondimensional extracellular concentration of cAMP

γβρe

t khk

t−=

∂∂

βγρβit kk

t−−Φ=

∂∂ ),(

• rate of change of extracellular cAMP= secretion by cells – degradation

• rate of change of intracellular cAMP = synthesis by cells – secretion - degradation

• rate of change of active form of receptor = resensitisation of receptor – desensitisation of receptor

ργργρ )()1)(( 12 fft

−−=∂∂

Results

• Period of about 10 minutes• System absorbs small perturbances,

reacts strongly to large perturbances

Adding Cell Movement

• Cells can now detect cAMP concentrations and direction

• Cells move in the opposite direction as the cAMP wave

γγθγρθγ 2])([),()( ∇++−Φ=∂∂ dknnt e

• rate of change of extracellular cAMP = secretion by cells – degradation + diffusion

Results

StarLogo Simulation

• Cells that sense a concentration above the relay threshold emit cAMP and enter the refractory state

• Cells in the refractory state are insensitive to cAMP, and break down cAMP in their locality

• Each time step, each grid point shares 50% of its cAMP with its eight neighbours

StarLogo Simulation

Slime Computers?

• Slime mold physarum polycephalumfound the shortest path through a 5-inch square maze in only a few hours!