Statistical analysis of protein evolution suggests a design for natural proteins in which sparse networks of coevolving amino acids (termed sectors) comprise the essence of three-dimensional structure and function. However, proteins are also subject to pressures deriving from the dynamics of the evolutionary process itself--the ability to tolerate mutation and to be adaptive to changing selection pressures. To understand the relationship of the sector architecture to these properties, we developed a high-throughput quantitative method for a comprehensive single-mutation study in which every position is substituted individually to every other amino acid. Using a PDZ domain (PSD95(pdz3)) model system, we show that sector positions are functionally sensitive to mutation, whereas non-sector positions are more tolerant to substitution. In addition, we find that adaptation to a new binding specificity initiates exclusively through variation within sector residues. A combination of just two sector mutations located near and away from the ligand-binding site suffices to switch the binding specificity of PSD95(pdz3) quantitatively towards a class-switching ligand. The localization of functional constraint and adaptive variation within the sector has important implications for understanding and engineering proteins.