Effect of circumference size on pattern formation.

<p>(<b>A</b>) The growth rate has positive values for wavenumbers within the interval (0,<i>q</i><sub><i>m</i></sub>), implying that these modes are unstable. Since the wavenumber is a function of <i>L</i>, represented as <i>q</i> = 2<i>nπ</i>/<i>L</i>, the value <i>q</i><sub><i>m</i></sub> defines the minimum length, , at which the <i>n</i><sup>th</sup> Fourier mode becomes unstable. Using the parameter values in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012025#pcbi.1012025.t002" target="_blank">Table 2</a>, we have determined , and so on. As <i>L</i> increases (which means <i>q</i> decreases), the type of instability changes from oscillatory to stationary, as indicated by the kink in the growth curve. For all , however, the result of the simulations is an oscillating pattern. (<b>B</b>) A comparison of the measured perimeters of cells showing first-order oscillatory patterns (Osc m1), second-order oscillatory patterns (Osc m2), and first-order stationary patterns (Pol m1). The red lines denote the respective median values: <i>L</i>(Osc_m1) = 38 (36 to 41) μm, <i>n</i> = 31; <i>L</i>(Osc_m2) = 48 (42 to 51) μm, <i>n</i> = 15; <i>L</i>(Pol_m1) = 43 (40 to 45) μm, <i>n</i> = 9, (median, interquartile range); * means <i>P</i><0.01, while n.s. means not significant.</p> <p>(PDF)</p>