self-organisation in slime molds - carleton...
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Self-organisation in Slime Molds
Michael Iles4 February 2002
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Introduction
• Many types of slime molds• We’ll look at cellular slime molddictyostelium discoideum
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Life Cycle
• Amoebae are in ‘growth phase’ when food is available
• When starved, they enter the ‘developmental phase’
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Cell Movement
Individuals begin to ‘clump’ at centres of circles and spirals
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Cell Movement
Cells ‘stream’ more efficiently into the centres
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Cell Movement
Well-developed streaming morphology
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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
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Other Examples
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Other Examples
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Other Examples
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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
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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?
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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
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Mechanisms of Self-Organisation
• Amoebae also move upstream in the cAMP gradient
• Periodic waves of cAMP cause periodic movement of amoebae
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Modeling Slime Molds
• Modeling in two phases:– just cAMP waves– cAMP waves in conjunction with movement of
amoebae
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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
−−=∂∂
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Results
• Period of about 10 minutes• System absorbs small perturbances,
reacts strongly to large perturbances
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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
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Results
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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
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StarLogo Simulation
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Slime Computers?
• Slime mold physarum polycephalumfound the shortest path through a 5-inch square maze in only a few hours!