Limitations to extracellular concentration sensing through signaling cascades

Signaling cascades refer to sequential biochemical reactions that occur in the cytoplasm of living cells in response to the binding of a ligand to a cell surface receptor, triggering a cellular response. Living cells need to sense extracellular concentrations with high precision. In this paper, we study the limitations of extracellular concentration measurement in linear signaling cascades. We find that as long as the cascade is linear and measurement times are much larger or much smaller than the timescales of the cytoplasmic reactions, the error in concentration measurement is independent of cascade length, the nature of the reactions and their rates. Our results can also be extended to generic non-linear signal cascades when the measurement time is much smaller than the timescales of cytoplasmic reactions. We illustrate this by considering the specific example of the accuracy of concentration detection in E. coli.