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MOVEMENT OF AMOEBAE

MOVEMENT OF AMOEBAE. Mathematical Biology Summer Workshop. DICTYOSTELIUM DISCOIDEUM. Social Amoeba act like either a unicellular or multicellular organism depending on circumstances Pseudopodial Extension protrusion of part of the cell and streaming of cellular contents.

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MOVEMENT OF AMOEBAE

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  1. MOVEMENT OF AMOEBAE Mathematical Biology Summer Workshop

  2. DICTYOSTELIUM DISCOIDEUM • Social Amoeba • act like either a unicellular or multicellular organism depending on circumstances • Pseudopodial Extension • protrusion of part of the cell and streaming of cellular contents

  3. CHEMOTACTIC MOVEMENT • Purposeful movement of organisms in response to a chemical gradient

  4. AGGREGATION OF DICTYOSTELIUM DISCOIDEUM • cells begin to emit pulses of cAMP when starved • other cells are attracted to cAMP causing movement towards source • moving cells emit their own pulses, amplifying and propagating the signal • eventually cells meet to become multicellular unit called a slug

  5. ORIENTATION OF DICTYOSTELIUM DISCOIDEUM (RESPONSE TO THE cAMP SIGNAL) • rotates its body axis • elongates its surface along one side and contracts on the other sides • eventually leads to polarization of the cell along the chemical gradient

  6. Model #1: Rotational Movement • Amoeba orientation based on chemical gradient grid • Consider a finite 2D grid: • Assume chemical is more heavily concentrated at the top of the grid • Possible Governing Equations: Uxx = 0, BC: U(0) = A, U(L) = a High Low

  7. Normal Distribution Rotational Movement Cont…. Problem: No Rotational-like movement Solution: Chemical Gradient non-constant across grid

  8. Rotational Movement Cont…. • CELLULAR AUTOMATA • double grid • RULES OF MOVEMENT • conservation of area (2D model) • always attached • move in direction of higher concentration

  9. Model #2: Chemotaxis Movement • Receptors used as antenna • Travels in direction of receptor with highest concentration • Less Rotational, More of a morphing action • Concerned more with x-y movement

  10. Chemotaxis Movement Cont…. • CELLULAR AUTOMATA • double grid (chemical gradient) • RULES OF MOVEMENT • conservation of area (2D model) • always attached • move in direction of higher concentration • jenga movements

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