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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!