Soft structures in nature, such as protein assemblies, can organize reversibly into functional and often hierarchical architectures through noncovalent interactions. Molecularly encoding this dynamic capability in synthetic materials has remained an elusive goal. We report on hydrogels of peptide-DNA conjugates and peptides that organize into superstructures of intertwined filaments that disassemble upon the addition of molecules or changes in charge density. Experiments and simulations demonstrate that this response requires large-scale spatial redistribution of molecules directed by strong noncovalent interactions among them. Simulations also suggest that the chemically reversible structures can only occur within a limited range of supramolecular cohesive energies. Storage moduli of the hydrogels change reversibly as superstructures form and disappear, as does the phenotype of neural cells in contact with these materials.