Chemotaxis and Cellular Slime Molds

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Chemotaxis and Cellular Slime Molds
Junping Shi
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Basic diffusion mechanism
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You may have noticed these without realizing what
are if you see a slimy surface on your shower
curtains or walls or a dewy layer on your
lawn.... More photos http//waynesword.palomar.e
du/slime1.htm Video http//dictybase.org/Multimed
ia/development/development.html
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Growth of slime mold

• In its native state a slime mold population
  consists of
• hundreds or thousands of unicellular amoeboid
  cells, and each one moves independently and feeds
  on bacteria.
• When food becomes scarce, the amoebae enter a
  phase of starvation. An initially uniform cell
  distribution develops a multicellular mass. Cells
  are attracted to these loci called aggregate and
  move towards them. Eventually they become a
  sluglike multicellular mass.
• The sluglike collection of cells undertakes a
  sequence of shapes including that of a dome. And
  at the end, the result is a slender, beautifully
  sculptured stalk bearing acapsule at its top.
  (It is called a sporangiophore.)

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Life cycle of slime molds
http//www.sfu.ca/epalsson/research.html
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• Question What cause cells to aggregate, and how
  do
• cells know where an aggregation center should
  form?
• The starved slime mold amoebae secrete a chemical
  that attracts other cells. It is called cyclic
  AMP (cAMP), whose
• role is that of an intracellular messenger. To
  model the
• aggregation of slime mold, the following
  assumptions are made (Keller-Segel, 1970)
• Individual cells undergo a combination of random
  and
• chemotactic motions towards cAMP.
• Cells neither die nor divide during aggregation.
• cAMP is produced in a constant rate by each cell.
• The rate of degradation of cAMP depends linearly
  on
• its concentration.
• cAMP diffuses passively over the aggregation
  field.

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Initially, a and c are both in a uniform state,
which is presumably the equilibrium state. IF the
constant equilibrium is not stable, then under a
small perturbation, the solution may go towards a
spatially non-constant equilibrium solution. That
implies an aggregation may occur, and u will
become a function which concentrates at one point
or several points. Mathematical question for
which parameter values, the equilibrium solution
is unstable, and what is the unstable mode?
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