Speaker
Description
Biochemical reaction networks often display robust responses to persistent perturbations despite high dimensionality, feedback, and uncertain kinetics. Classical robust perfect adaptation (RPA) captures one important mechanism: after sustained input changes, a designated output returns to a fixed steady state independent of perturbation magnitude. However, many cellular systems do not relax to a single adapted point. Instead, their steady states lie on lower-dimensional sets such as lines or planes, indicating regulation of relations between species rather than fixed absolute levels.
We introduce manifold robust perfect adaptation (manifold RPA), a framework in which persistent perturbations drive the system to an invariant manifold in steady-state concentration space. We show that manifold RPA can arise as a structural property of biochemical reaction networks and derive sufficient conditions for it without assuming specific kinetic forms. This yields a rigorous characterisation of adaptive behaviour that preserves ratios or linear relations among molecular species while allowing absolute concentrations to vary.
Our results extend the classical notion of adaptation and reveal structural constraints on steady-state reachability imposed by network architecture. This provides a principled explanation for non-pointwise steady-state responses in metabolism and signalling, and suggests a design principle for synthetic biological circuits requiring adaptive behaviour under relational, rather than fixed, targets.
