The long-term objective of this work is to build interactive computer software that lets users directly modify a protein's three-dimensional structure while the software maintains valid physical properties such as van der Waals separations, peptide geometry, and hydrogen bonds. This builds on Sculpt, a prototype graphical modeling system that maintains many protein properties as one interactively moves atoms. Phase I adds the following interactive capabilities through mathematical analysis and algorithm development: 1. edit protein topology interactively allowing residue insertion, deletion, and substitution; 2. assemble multiple chains (e.g. from homology) with valid peptide geometry; 3. decompose a model into regions with restricted, limited, or unrestricted atom motions; 4. move secondary structure directly while modeling sidechain interactions with other atoms; 5. model electrostatic interactions. Phase II further develops these algorithms and concentrates on interface issues. This will directly produce commercial software for protein modeling and develop a foundation for later products in crystallography, de novo drug design, structure determination based on NMR, nucleotide modeling, and education.