  The signaling apparatus mediating bacterial chemotaxis can adapt to a wide
range of persistent external stimuli. In many cases, the bacterial activity
returns to its pre-stimulus level exactly and this "perfect adaptability" is
robust against variations in various chemotaxis protein concentrations. We
model the bacterial chemotaxis signaling pathway, from ligand binding to CheY
phosphorylation. By solving the steady-state equations of the model
analytically, we derive a full set of conditions for the system to achieve
perfect adaptation. The conditions related to the phosphorylation part of the
pathway are discovered for the first time, while other conditions are
generalization of the ones found in previous works. Sensitivity of the perfect
adaptation is evaluated by perturbing these conditions. We find that, even in
the absence of some of the perfect adaptation conditions, adaptation can be
achieved with near perfect precision as a result of the separation of scales in
both chemotaxis protein concentrations and reaction rates, or specific
properties of the receptor distribution in different methylation states. Since
near perfect adaptation can be found in much larger regions of the parameter
space than that defined by the perfect adaptation conditions, their existence
is essential to understand robustness in bacterial chemotaxis.
