Optimal resource allocation in cellular sensing systems

Living cells deploy many resources to sense their environments, including receptors, downstream signaling molecules, time, and fuel. However, it is not known which resources fundamentally limit the precision of sensing, like weak links in a chain, and which can compensate each other, leading to trade-offs between them. We present a theory for the optimal design of the large class of sensing systems in which a receptor drives a push-pull network. The theory identifies three classes of resources that are required for sensing: receptors and their integration time, readout molecules, and energy (fuel turnover). Each resource class sets a fundamental sensing limit, which means that the sensing precision is bounded by the limiting resource class and cannot be enhanced by increasing another class--the different classes cannot compensate each other. This result yields a previously unidentified design principle, namely that of optimal resource allocation in cellular sensing. It states that, in an optimally designed sensing system, each class of resources is equally limiting so that no resource is wasted. We apply our theory to what is arguably the best-characterized sensing system in biology, the chemotaxis network of Escherichia coli. Our analysis reveals that this system obeys the principle of optimal resource allocation, indicating a selective pressure for the efficient design of cellular sensing systems.