A cellular solution to an information-processing problem

Signaling receptors on the cell surface are mobile and have evolved to efficiently sense and process mechanical or chemical information. We pose the problem of identifying the optimal strategy for placing a collection of distributed and mobile sensors to faithfully estimate a signal that varies in space and time. The optimal strategy has to balance two opposing objectives: the need to locally assemble sensors to reduce estimation noise and the need to spread them to reduce spatial error. This results in a phase transition in the space of strategies as a function of sensor density and efficiency. We show that these optimal strategies have been arrived at multiple times in diverse cell biology contexts, including the stationary lattice architecture of receptors on the bacterial cell surface and the active clustering of cell-surface signaling receptors in metazoan cells.The molecular characteristics of signaling receptors and their spatiotemporal organization have evolved to optimize different facets of information processing at the cell surface. A canonical information-processing problem involves designing strategies for a collection of distributed, noisy, mobile sensors to faithfully estimate a signal or function that varies in space and time (1). This problem appears naturally in many contexts, biological and nonbiological: (i) chemoattractant protein sensors on the bacteria cell surface (2, 3); (ii) galectin-glycoprotein assemblies designed for effective immune response on the surface of metazoan cells (4, 5); (iii) ligand-activated signaling protein receptors on the surface of eukaryotic cells (6–10); (iv) coclustering of integrin receptors to faithfully read and discriminate the rigidity and chemistry of a substrate (11); (v) clustering of e-cadherin receptors for effective adherence at cell–cell junctions (12); and even (vi) radio frequency (RF) sensor networks monitoring the environment or mobile targets (13). In the signal-processing community, this problem is known as data fusion or more generally information fusion (14, 15); however typical applications do not consider mobile sensors.In this paper we show how biology has, on multiple occasions, arrived at a solution to this optimization problem. The optimal solution needs to balance two opposing objectives, the need to locally assemble sensors to reduce estimation noise and the need to spread them out for broader spatial coverage. We show that in the space of strategies, this leads to a phase transition as a function of sensor density, sensor characteristics, and function properties. At very low sensor density, the optimal design corresponds to freely diffusing sensors. For sensor density above a threshold, there are two different optimal solutions as a function of a dimensionless parameter constructed from the sensor advection velocity and the correlation length and time of the incident signal. One optimal solution is that the sensors are static and located on a regular lattice grid. This is the strategy used in bacteria, such as Escherichia coli, to organize their chemoattractant receptors in a regular lattice array (3, 16), and in metazoan cells, where galectin-glycoproteins are organized in a lattice on the cell surface to effect an optimal immune response (4, 5). To realize this strategy, the cell needs to provide a rigid cortical scaffold that holds the receptors in place. Another optimal solution is to make the receptors mobile in such a way that a fraction of them form multiparticle nanoclusters, which then break up and reform randomly, the rest being uniformly distributed. Recent studies on the steady-state distribution of several cell-surface proteins reveal a stereotypical distribution of a fixed fraction of monomers and dynamic nanoclusters (6–9), and our information theoretic perspective could provide a general explanation for this. To realize this dynamic strategy, the cell surface needed to be relieved of the constraints imposed by the rigid scaffold and to be more regulatable. This strategy change needed the innovation of motor proteins and dynamic actin filaments, a regulated actomyosin machinery fueled by ATP, and a coupling of components of the cell surface to this cortical dynamic actin (17).