Matched Static Feedback Permits Different Notch-Delta Patterning Dynamics

Abstract Notch--Delta lateral inhibition amplifies differences between neighbouring cells, but its steady-state response leaves several dynamical predictions unresolved. We compare explicit signalling circuits while successively matching their static response, mean downstream response time and local linear spectrum. Static loop gain fixes stationary onset. For a negative graph mode, sufficiently strong cis inactivation makes the mode block sign-similar to a Metzler matrix; static gain then gives a necessary and sufficient stability criterion. This condition holds at 775 of 4,000 reference parameter sets; all 12 disagreements between the static-gain test and the full K-mode spectrum lie outside this regime. At a reference patterning point, replacing finite ASC relaxation by its matched quasi-static response raises the K-mode growth rate from 0.103 to 1.597. Dividing the downstream response into four stages at the same mean time makes a uniform oscillation grow faster than the stationary K pattern. Finally, circuits with identical local linear spectra can select different ASC-high cells within the same competent patch. These comparisons connect graph-based gain criteria to explicit pathway kinetics and identify which predictions require information beyond the static response.