To help cells cope with protein misfolding and aggregation, Hsp70 molecular chaperones selectively bind a variety of sequences ("selective promiscuity"). Statistical analyses from substrate-derived peptide arrays reveal that DnaK, the E. coli Hsp70, binds to sequences containing three to five branched hydrophobic residues, although otherwise the specific amino acids can vary considerably. Several high-resolution structures of the substrate -binding domain (SBD) of DnaK bound to peptides reveal a highly conserved configuration of the bound substrate and further suggest that the substrate-binding cleft consists of five largely independent sites for interaction with five consecutive substrate residues. Importantly, both substrate backbone orientations (N- to C- and C- to N-) allow essentially the same backbone hydrogen-bonding and side-chain interactions with the chaperone. In order to rationalize these observations, we performed atomistic molecular dynamics simulations to sample the interactions of all 20 amino acid side chains in each of the five sites of the chaperone in the context of the conserved substrate backbone configurations. The resulting interaction energetics provide the basis set for deriving a predictive model that we call Paladin (Physics-based model of DnaK-Substrate Binding). Trained using available peptide array data, Paladin can distinguish binders and nonbinders of DnaK with accuracy comparable to existing predictors and further predicts the detailed configuration of the bound sequence. Tested using existing DnaK-peptide structures, Paladin correctly predicted the binding register in 10 out of 13 substrate sequences that bind in the N- to C- orientation, and the binding orientation in 16 out of 22 sequences. The physical basis of the Paladin model provides insight into the origins of how Hsp70s bind substrates with a balance of selectivity and promiscuity. The approach described here can be extended to other Hsp70s where extensive peptide array data is not available.