  We present an analytical theory for heteropolymer deformation, as exemplified
experimentally by stretching of single protein molecules. Using a mean-field
replica theory, we determine phase diagrams for stress-induced unfolding of
typical random sequences. This transition is sharp in the limit of infinitely
long chain molecules. But for chain lengths relevant to biological
macromolecules, partially unfolded conformations prevail over an intermediate
range of stress. These necklace-like structures, comprised of alternating
compact and extended subunits, are stabilized by quenched variations in the
composition of finite chain segments. The most stable arrangements of these
subunits are largely determined by preferential extension of segments rich in
solvophilic monomers. This predicted significance of necklace structures
explains recent observations in protein stretching experiments. We examine the
statistical features of select sequences that give rise to mechanical strength
and may thus have guided the evolution of proteins that carry out mechanical
functions in living cells.
