Friday, July 18, 2008

Paper-Project 2: PL fluctuations of chemical concentrations

Max system:
  • Basic dynamics: d/dt y = + x y - x y^2 - c y
  • Fluctuations: x --> x + dx(t), multiplicative exp-correlated noise (tau_cor)
  • Inverted PL for P(x) in the limit of small tau_cor
  • Idea: P(x) corresponds to the stationary, long-time case. Then x(t) is effectively white. Small tau_cor means just small effective variance of the white x(t).
  • Check if Fokker-Plack-Eq. is solvable analytically or numerically.

A similar system and result is discussed for gen expression in Nacher06:
  • Basic dynamics: d/dt y = + p - x y.
  • Fluctuations: p --> p + dp(t), additive white noise. Seems to be not so important.
  • x --> x + dx(t), multiplicative white noise
  • Stationary limit of Fokker-Plack-Eq. is solvable for large conc. x and gives a PL.
  • PL is of normal decaying type

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