Fig. 3: Numerical simulations of RD/chemoEH model.
From: The reaction-diffusion basis of animated patterns in eukaryotic flagella
a Spontaneous oscillations of (i) shear γ = Δ/a, (ii) motor populations n± anchored to +/- filament and (iii) forces on an isolated element (see Fig. 2b). b Diffusion of shear from an initially curved configuration \(\gamma (s)=[1-\cos (2\pi s/L)]/4\) according to γt = Dγss − Eγ in the absence of sliding-controlled feedback. c Predictions (solid lines) of growth rate α and frequency ω of oscillations of the RD model from linear stability theory compared with simulations (filled circles) as a function of the bifurcation parameter \(\epsilon=({\mu }_{a}^{{{{{{{{\rm{crit}}}}}}}}}-{\mu }_{a})/{\mu }_{a}^{{{{{{{{\rm{crit}}}}}}}}}\). Other parameter values (μ, η, ζ) = (100, 0.14, 0.3). d Simulations of the RD model for increasing activity ϵ, showing progression from (i) standing waves for small ϵ to (iii) base-to-tip progression for ϵ = O(1). Simulations of the chemoEH model (Sp = 1) at the same parameter values in both the head frame and lab frame. e Oscillations of the motor populations n± for the case d(iii). Time t1 shows a principal (P) bend and time t2 a reverse (R) bend.
