Barkai-Leibler model

A conceptual chemotaxis adaptation model in which saturated CheR action supplies receptor methylation while CheB preferentially demethylates active receptors. If $\dot{M}=r-bA/(K+A)$, the steady state output is $A_{\ast }=Kr/(b-r)$, independent of ligand whenever a physically accessible stable steady state exists. Changing enzyme abundance can change this baseline without destroying adaptation to a subsequent ligand step.^[ref]

If the forward receptor-modification flux depends on remaining unmethylated substrate, it generally depends indirectly on ligand through the modified receptor pool. The steady output then need not be ligand independent. Near-perfect adaptation may remain in a saturation limit; finite modification capacity and completely inactive receptor populations also bound the ideal perfect-adaptation result.