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

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

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

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

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: U xx = 0, BC: U(0) = A, U(L) = a High Low

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

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

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

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