The gift of gab: probing the limits of dynamic concentration-sensing across a network of communicating cells

TL;DR

This paper investigates how communication among cells affects their ability to estimate dynamic signals, revealing that network topology and noise regimes influence estimation accuracy and convergence speed.

Contribution

It introduces a general framework for signal estimation in cellular networks and analyzes the effects of Poissonian and super-Poissonian noise regimes on collective estimation.

Findings

Communication accelerates convergence to steady-state MSE.

Super-Poissonian noise reduces MSE with more neighbors.

Clustering coefficient does not improve individual MSE but reduces total population MSE.

Abstract

Many systems in biology and beyond employ collaborative, collective communication strategies for improved efficiency and adaptive benefit. One such paradigm of particular interest is the community estimation of a dynamic signal, when, for example, an epithelial tissue of cells must decide whether to react to a given dynamic external concentration of stress signaling molecules. At the level of dynamic cellular communication, however, it remains unknown what effect, if any, arises from communication beyond the mean field level. What are the limits and benefits to communication across a network of neighbor interactions? What is the role of Poissonian vs. super Poissonian dynamics in such a setting? How does the particular topology of connections impact the collective estimation and that of the individual participating cells? In this letter we construct a robust and general framework of signal estimation over continuous time Markov chains in order to address and answer these questions. Our results show that in the case of Possonian estimators, the communication solely enhances convergence speed of the Mean Squared Error (MSE) of the estimators to their steady-state values while leaving these values unchanged. However, in the super-Poissonian regime, MSE of estimators significantly decreases by increasing the number of neighbors. Surprisingly, in this case, the clustering coefficient of an estimator does not enhance its MSE while reducing total MSE of the population.