The ability of a cell to respond to an inducing signal is called:
Competence is defined as time-limited physiological capacity of a tissue to perceive and correctly translate a specific inductive cue into altered fate. Molecular basis includes presence of appropriate receptors, intracellular signal transducers, transcription factor availability and accessible chromatin at target gene loci during critical window. Xenopus ectoderm competence to respond to neural inducers exists only during gastrula stages when FGF receptors and Smad machinery are expressed. After this period, BMP signaling consolidation and chromatin closure extinguish responsiveness. Loss of competence involves receptor downregulation, upregulation of inhibitors and epigenetic silencing, ensuring inductive events occur sequentially and preventing ectopic induction later.
Ref: Gilbert, Developmental Biology, 12th ed., Chapter 4: Competence Windows in Embryonic Induction.