Sensitive particle shape dependence of growth-induced mesoscale nematic structure

TL;DR

This work investigates how growth, division, and particle geometry drive mesoscale nematic structure in colonies of sterically interacting rods. Using an in-silico agent-based model with a tunable tip-shape parameter $\mathcal{P}$ and division aspect ratio $a_d$, paired with a master equation framework for microdomain size distributions, it shows that subtle shape changes induce a transition from exponential to power-law tails in cluster sizes. The analysis derives how breakup rates $\beta(s)$ must depend on size to sustain exponential distributions, or remain constant to yield power-law distributions, and reveals domain-size dependent cut-offs that preserve spatially uniform bulk statistics. The results link microscopic shape and breakup physics to emergent mesoscale organization, offering principles for controlling self-organization in biological and artificial active materials by tuning particle geometry and boundary conditions.

Abstract

Directed growth, anisotropic cell shapes, and confinement drive self-organization in multicellular systems. We investigate the influence of particle shape on the distribution and dynamics of nematic microdomains in a minimal in-silico model of proliferating, sterically interacting particles, akin to colonies of rod-shaped bacteria. By introducing continuously tuneable tip variations around a common rod shape with spherical caps, we find that subtle changes significantly impact the emergent dynamics, leading to distinct patterns of microdomain formation and stability. Our analysis reveals separate effects of particle shape and aspect ratio, as well as a transition from exponential to scale-free size distributions, which we recapitulate using an effective master equation model. This allows us to relate differences in microdomain size distributions to different physical mechanisms of microdomain breakup. Our results thereby contribute to the characterization of the effective dynamics in growing aggregates at large and intermediate length scales and the microscopic properties that control it. This could be relevant both for biological self-organization and design strategies for future artificial systems.

Figures (6)

• Figure 1: (A) Illustrations of normal repulsion force between two touching agents and (B) an agent dividing with inherited width, orientation and half the original length. (C) Control parameter pointiness to define modified tip-shape. (D) Snapshots at different times of the early stages of a simulation with coloring to emphasize (nematic) orientations as defined in the color wheel.
• Figure 2: (A) Example snapshots for varied agent shapes. The pointiness $\mathcal{P}$ has values $(1,1/2,3/2,1,1/2)$ in i-v and the aspect ratios $a_\text{d}$ are 2 in i & ii and 5 in iii-v. The full time evolution of these examples is animated in the supplementary movies 1-5. (B) A growing and breaking microdomain is tracked over time with $\Delta t=0.5$ between snapshots. (C) Cluster size distributions $p(s)$ for rods with aspect ratio $a_\text{d} =3,\, 4,$ and $5$. (D) Average cluster size $s$ for varied pointiness $\mathcal{P}$ and aspect ratio $a_\text{d}$.
• Figure 3: Size distribution properties of rodcells. (A) Cluster size distribution $p(s)$ as a function of radial position for division aspect $a_\text{d}=5$. (B) Cluster size distribution over time with $a_\text{d}=5$. (C) Average cluster size for varied division aspect ratio $a_\text{d}$ and domain size. (D) Size distributions $p(s)$ for varied domain size at $a_\text{d}=6$, multiplied by $s^2$ to highlight tails. Regular distributions are shown in the inset.
• Figure 4: (A) Size distributions $p(s)$ for rods with varied division aspect ratio $a_{\text{d}}$. (B) Distributions multiplied by $s^2$ and normalized to give 1 at the left-most data point to emphasize the distribution tails. (C) Fit parameters of Eq. \ref{['eq:distributionfit']} to the data shown in \ref{['pan:rodlengthdistr']}.
• Figure 5: Cluster size distributions $p(s)$ for varied pointiness $\mathcal{P}$. (A) Distributions multiplied for pointiness $\mathcal{P} \in [0.5, 1,1.5]$ split into separate panels. Coloring indicates division aspect ratio $a_{\text{d}}$. (B) Distribution tail weight represented as the size $s$ at which the probability density crosses $p(s)=10^{-4}.$