Before revision:  We derive general formula for the gradient sensing limit from the uncertainty in instantaneous receptor activity configurations and find that cooperativity by non-adaptive receptors could significantly lower the sensing limit at the biochemically-relevant regime of balanced free energy difference between active and inactive receptor states . Cooperativity by adaptive receptors are beneficial to gradient sensing under a broad range of background concentrations.
After revision:  We derive general formula for the gradient sensing limit from the uncertainty in instantaneous receptor activity configurations and find that cooperativity by non-adaptive receptors could significantly lower the sensing limit in a chemical concentration range determined by the biochemical properties of ligand-receptor binding and ligand-induced receptor activity . Cooperativity by adaptive receptors are beneficial to gradient sensing under a broad range of background concentrations.