SCULPTING PROTEINS INTERACTIVELY - CONTINUAL ENERGY MINIMIZATION EMBEDDED IN A GRAPHICAL MODELING SYSTEM

We describe a new paradigm for modeling proteins in interactive comput er graphics systems - continual maintenance of a physically valid repr esentation, combined with direct user control and visualization. This is achieved by a fast algorithm for energy minimization, capable of re al-time performance on all atoms of a small protein, plus graphically specified user tugs. The modeling system, called Sculpt, rigidly const rains bond lengths, bond angles, and planar groups (similar to existin g interactive modeling programs), while it applies elastic restraints to minimize the potential energy due to torsions, hydrogen bonds, and van der Waals and electrostatic(4) interactions (similar to existing b atch minimization programs), and user-specified springs. The graphical interface can show bad and/or favorable contacts, and individual ener gy terms can be turned on or off to determine their effects and intera ctions. Sculpt finds a local minimum of the total energy that satisfie s all the constraints using an augmented Lagrange-multiplier method; c alculation time increases only linearly with the number of atoms becau se the matrix of constraint gradients is sparse and banded. On a 100-M Hz MIPS R4000 processor (Silicon Graphics Indigo), Sculpt achieves 11 updates per second on a 20-residue fragment and 2 updates per second o n an 80-residue protein, using all atoms except non-H-bonding hydrogen s, and without electrostatic interactions. Applications of Sculpt are described: to reverse the direction of bundle packing in a designed 4- helix bundle protein, to fold up a 2-stranded beta-ribbon into an appr oximate beta-barrel, and to design the sequence and conformation of a 30-residue peptide that mimics one partner of a protein subunit intera ction. Computer models that are both interactive and physically realis tic (within the limitations of a given force field) have 2 significant advantages: (1) they make feasible the modeling of very large changes (such as needed for de novo design), and (2) they help the user under stand how different energy terms interact to stabilize a given conform ation. The Sculpt paradigm combines many of the best features of inter active graphical modeling, energy minimization, and actual physical mo dels, and we propose it as an especially productive way to use current and future increases in computer speed.