Active fluctuations induce buckling of living surfaces

Abstract

Active tissues exhibit tension fluctuations that are correlated in space and time. We study a minimal overdamped surface model in which such fluctuations enter as a zero-mean, multiplicative modulation of the local surface tension. Although the deterministic elastic dynamics (tension plus bending) stabilizes the flat state for all nonzero wave numbers, we find that sufficiently persistent active fluctuations generate positive ensemble growth rates for a finite band of Fourier modes, leading to stochastic buckling with wavelength selection. A non-Markovian theory based on the Novikov--Furutsu theorem captures the instability threshold and unstable band observed in simulations.

Figures (3)

• Figure 1: Space--time kymographs of the height field $h(x,t)$ from simulations of Eq. \ref{['eq:phys_eom']} with colored tension noise ($\lambda=1$, $\tau=0.2$), shown for noise strength $\epsilon=5,8,10$ (left to right) on a common color scale. White dashed curves serve as a guide to the eye, highlighting the late-time spatial modulation at larger noise strength.
• Figure 2: (a) Equal-time height correlation $C(x)=\langle h(x)h(0)\rangle$ at $t=11.6$ from simulations of Eq. \ref{['eq:phys_eom']} with colored tension noise [Eq. \ref{['eq:noisecorrfourier']}] of correlation length $\lambda=1$ and persistence time $\tau=0.2$. Curves correspond to noise intensities $\epsilon=4,6,8,10,12$ (legend) and are averaged over $5\times10^{4}$ independent realizations. Inset: same data with expanded vertical scale (note $10^{-4}$), highlighting the weak-noise regime. (b) Structure factor $S(q)=\langle |h_q|^2 \rangle$ obtained from the Fourier transform of $C(x)$ in (a), averaged over the last 100 saved time points of the dynamics. Inset: dominant wave number $q^*$ as a function of noise intensity.
• Figure 3: Properties of unstable modes predicted by the non-Markovian mean-field theory. (a) Mode growth rate $\gamma(q)$ (shown as $\partial_t\langle h_q\rangle|_{t=0}$ for a unit seed) as a function of wave number $q$ for the indicated noise strengths $\epsilon$ at fixed ${\tau=0.2}$ and ${\lambda=1}$. The dashed line marks marginal stability, ${\gamma=0}$; a finite band with ${\gamma(q)>0}$ appears for ${\epsilon\gtrsim 8}$. Inset: dominant wave number as a function of noise strength $\epsilon$. (b) Marginal wave number $q^{\star}$ (color code) at onset (${\max_q\gamma(q)=0}$) as a function of $\tau$ and $\lambda$ for ${\epsilon=10}$. White dashed lines are contours of constant $q^{\star}$ (values displayed on dashed line).