[Paper Review] Does nematic order allow groups of elongated cells to sense electric fields better?

Kurmanbek Kaiyrbekov, Brian A. Camley|arXiv (Cornell University)|Apr 6, 2024

Liquid Crystal Research Advancements4 citations

TL;DR

This study investigates whether nematic order—where elongated cells align their long axes with neighbors—enhances collective electric field sensing. Using a minimal 2D model of self-propelled cells with orientation-dependent sensing precision, it shows that when cells are more accurate at detecting fields when oriented perpendicular to the field, nematic alignment significantly improves group directionality. The key finding is that nematic order amplifies directional response only when sensing accuracy is strongly orientation-dependent.

ABSTRACT

Collective response to external directional cues like electric fields plays a pivotal role in processes such as tissue development, regeneration, and wound healing. In this study we focus on the impact of anisotropy in cell shape and local cell alignment on the collective response to electric fields. We model elongated cells that have a different accuracy sensing the field depending on their orientation with respect to the field. Elongated cells often line up with their long axes in the same direction - "nematic order" - does this help the group of cells sense the field more accurately? We use simulations of a simple model to show that if cells orient themselves perpendicular to their average velocity, alignment of a cell's long axis to its nearest neighbors' orientation can enhance the directional response to electric fields. However, for cells to benefit from aligning, their accuracy of sensing must be strongly dependent on cell orientation. We also show that cell-cell adhesion modulates the accuracy of cells in the group.

Motivation & Objective

• To investigate whether nematic order among elongated cells improves collective sensing of electric fields.
• To determine under what conditions cell alignment enhances directional accuracy in response to electric fields.
• To examine the role of cell-cell adhesion and velocity-orthogonal alignment in modulating collective galvanotaxis.
• To resolve conflicting experimental results on the necessity of cell-cell adhesions for collective field response.

Proposed method

• A 2D self-propelled particle model simulates elongated cells with defined long-axis orientation φ and polarity direction ζ.
• Cells estimate the electric field direction with orientation-dependent precision κ(φ), where perpendicular alignment (φ = 90°) maximizes accuracy.
• Cell-cell interactions are modeled via isotropic springs with fixed equilibrium length, and neighbor lists are updated dynamically based on distance thresholds.
• Cells align their long axis with neighbors (nematic interaction) and orient perpendicularly to their average velocity (velocity-orthogonal alignment).
• Numerical integration uses the Euler-Maruyama method to update orientation with rotational noise, and polarity is updated every τforget = 10 min.
• Simulations use 64 cells per run, with 40 independent runs per parameter set, initialized with random positions and orientations, and parameters are calibrated to match experimental observations.

Experimental results

Research questions

• RQ1 Does nematic order among elongated cells improve their collective ability to sense the direction of an applied electric field?
• RQ2 Under what conditions does orientation-dependent sensing precision enhance group directionality in galvanotaxis?
• RQ3 How do cell-cell adhesions and velocity-orthogonal alignment influence the accuracy of collective field sensing?
• RQ4 Why do experimental studies report conflicting results on the role of cell-cell adhesion in collective galvanotaxis?

Key findings

• When sensing precision is strongly dependent on orientation, with maximum accuracy at 90° to the field, nematic alignment significantly enhances the group’s directional response to electric fields.
• Cells aligned perpendicularly to their average velocity show improved field sensing accuracy, especially when combined with nematic order.
• Nematic interactions between cells increase cluster directionality only when sensing precision varies strongly with orientation.
• Strong cell-cell adhesion enhances the directional response to electric fields, and its disruption can explain conflicting experimental reports on adhesion necessity.
• The rotational diffusion coefficient D_r = 0.003 rad²/min was selected to match experimental orientation distributions, validating the model’s biological relevance.
• Simulations show that the final steady-state directionality stabilizes after ~5 hours, with mean values reported over the last 5 hours of each run.