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Living cells deploy many resources to sense their environments, includingreceptors, downstream signaling molecules, time and fuel. However, it is notknown which resources fundamentally limit the precision of sensing, like weaklinks in a chain, and which can compensate each other, leading to trade-offsbetween them. We show by modeling that in equilibrium systems the precision islimited by the number of receptors; the downstream network can never increaseprecision. This limit arises from a trade-off between the removal of extrinsicnoise in the receptor and intrinsic noise in the downstream network.Non-equilibrium systems can lift this trade-off by storing the receptor stateover time in chemical modification states of downstream molecules. As wequantify for a push-pull network, this requires i) time and receptors; ii)downstream molecules; iii) energy (fuel turnover) to drive modification. Thesethree resource classes cannot compensate each other, and it is the limitingclass which sets the fundamental sensing limit. Within each class, trade-offsare possible. Energy allows a power-speed trade-off, while time can be tradedagainst receptors.

How biochemical resources determine fundamental limits in cellular sensing