Homochirality in the Vicsek model: Fluctuations and potential implications for cellular flocks

Chirality is a feature of many biological systems, and much research has been focused on understanding the origin and implications of this property. Famously, sugars and amino acids found in nature are homochiral, i.e., chiral symmetry is broken and only one of the two possible chiral states is ever observed. Certain types of cells show chiral behavior, too. Understanding the origin of cellular chirality and its effect on tissues and cellular dynamics is still an open problem and subject to much (recent) research, e.g., in the context of drosophila morphogenesis. Here, we develop a simple model to describe the possible origin of homochirality in cells. Combining the Vicsek model for collective behavior with the model of Jafarpour et al. [Phys. Rev. Lett. 115, 158101 (2015)0031-900710.1103/PhysRevLett.115.158101], developed to describe the emergence of molecular homochirality, we investigate how a homochiral state might have evolved in cells from an initially symmetric state without any mechanisms that explicitly break chiral symmetry. We investigate the transition to homochirality and show how the "openness" of the system as well as noise determine if and when a globally homochiral state is reached. While hypothetical and explorative in nature, our analysis may serve as a starting point for more realistic models of chirality in flocking multicellular systems.