Phyllotaxis and patterns on plants

Biochemical factorsReinhardt (2000) showed that hormone Auxin is instrumental ingrowth <strong>and</strong> uneven distribution of Auxin is the reason for theformation of phyllotaxisMeyerowitz, Traas, Reinhardt et al (2006): Auxin efflux proteinPIN1 on the cell wall can redistribute themselves so as to pumpAuxin form low concentration to high concentrationdA(i)dt= D ∑ k(A(k) − A(i)) + T ∑ k(A(k)P(k, i) − A(i)P(i, k)) + c − dA(i)P(i, j) = P ij = PA(j)κ + ∑ (k)A(k) jA(i): Auxin concentration in cell iP(i, k): PIN1 concentration on cell wall (i,j) pointing to cell jThe continuum limit PDE:g t = −Lg −H ▽ 2 g −▽ 4 g − ¯κ 1 ▽(g ▽g)− ¯κ 2 ▽(▽g ▽ 2 g)−δ ′ g 3g(r, α): auxin fluctuation around stationary uniform concentration∼ growth strainAlan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants