Tuning nonequilibrium colloidal structure in external fields by density-dependent state switching

Biological cells have the ability to switch internal states depending on the density of other cells in their local environment, referred to as "quorum sensing." The latter can be utilized to control collective structuring, such as in biofilm formation. In this work, we study a simple quorum sensing model of ideal (noninteracting) colloids with a switchable internal degree of freedom in the presence of external potentials. The colloids have two possible discrete states, in which they are affected differently by the external field, and switch with rates dependent on the local density in their environment. We study this model with reactive Brownian dynamics simulations, as well as with an appropriate reaction-diffusion theory. We find remarkable structuring in the system controlled by the density-mediated interactions between the ideal colloids. We report results of different functional forms for the rate dependence and quantify the influence of their parameters, in particular, discuss the role of the spatiotemporal sensing range, i.e., how the resulting structures depend on how the environmental information is "measured" by the colloids. Especially in the case of a rate function with sigmoidal dependence on local density, i.e., requiring a threshold density for switching, we observe significant correlation effects in the density profiles which are tuneable by the sensing ranges but also sensitive to noise and fluctuations. Hence, our model gives some basic insights into the nonequilibrium structuring mediated by simple quorum sensing protocols.