List of Figures

• The peptide Met-enkephalin is shown, with the bonds/hinges numbered. Clusters are the chemical units connected by the hinges, such as the phenyl ring in tyrosine 1. The hinges are numbered to allow for analysis of the dihedral angles.
• Energy fluctuations, , for NEIMO(N) and Cartesian(C) dynamics simulations of Met-enkephalin. Simulations were run for 1 ps using timesteps ranging from 1 to 20 fs. N* and C* are the scaled fluctuations, *, where is divided by the number of degrees of freedom: for NEIMO simulations and 3n-6 for Cartesian coordinates.
• Energy fluctuations, , for NEIMO(N) and Cartesian(C) dynamics simulations of (Ala). Simulations were run for 1 ps using timesteps ranging from 1 to 35 fs. N* and C* are the scaled energy fluctuations, *.
• for 100 timesteps of NEIMO dynamics on (Ala).
• Avian pancreatic polypeptide (aPP), with the sidechain atoms removed for clarity. From the crystal structure 1PPT [38]).
• Energy fluctuations, , for NEIMO(N) and Cartesian(C) dynamics simulations of avian pancreatic polypeptide (aPP). Simulations were run for 1 ps using timesteps ranging from 1 to 15 fs, but all those above 11 fs caused the energy to blow up. N* and C* are the scaled energy fluctuations, *.
• Scaled energy fluctuations, *, for 1 ps NEIMO simulations of aPP. ``Rigid H'' differs from ``Normal'' NEIMO in that hinges which rotate only hydrogen atoms are held fixed. The ``Counterions'' simulation used the standard NEIMO method for the protein, but concurrently solved the Cartesian equations of motion for counterions (5 Na and 3 Cl) added to neutralize unpaired charges.
• The average energy fluctuations, , during 5 ps simulations of avian pancreatic polypeptide. Fluctuations in NEIMO(N) and Cartesian(C) dynamics were determined at 0.1 ps intervals during the course of the simulation, after which velocities could be rescaled and the CMM nonbond farfield calculation was updated.
• vs. protein size for Cartesian dynamics at 1fs and NEIMO dynamics at various timesteps.
• During 5 ps molecular dynamics simulations of Met-enkephalin, the 22 dihedral angles were written out at 0.1 ps intervals. The fifty values for each dihedral are plotted here for Cartesian and NEIMO dynamics simulations using 1 fs timesteps.
• The average dihedrals from the distributions in are shown here with error bars indicating , the standard deviations.
• The average dihedrals from NEIMO simulations using timesteps ranging from 1 to 10 fs.
• The overlaps between 1 fs and 2-10 fs NEIMO simulations of Met-enkephalin.
• The overlaps between 1 fs and 2, 5, and 10 fs NEIMO simulations of Met-enkephalin shown at higher resolution than .
• The overlaps between dihedral distributions from Cartesian dynamics vs. those from NEIMO dynamics simulations with timesteps ranging from 1 fs.
• The tomato bushy stunt virus asymmetric unit, showing the A, B, and C conformations as well as the associated Ca ions. From the crystal structure by Olson et al.b3.2tbv.
• Detail of the aspartic acid/Ca interactions at the contact site between the S domains of two coat proteins.
• The TBSV protein coat, with each P and S domain represented by a sphere.
• A second view of the TBSV coat, with the outer P domains removed to emphasize the symmetry of the virus.
• CPU times for CMM calculations, NEIMO acceleration calculations, and overhead, including coordinate updating for NEIMO.
• * during 1.0 ps NEIMO simulations.
• The radius of gyration during energy minimization.
• The potential energy of the TBSV triad, including CMM nonbonded interactions with the full viral coat, during energy minimization.
• The TBSV radius during 2.0 ps Cartesian and NEIMO dynamics simulations.
• The radius of the PH7 and NOCA models of TBSV during 4.0 ps of Cartesian (NVT) and NEIMO dynamics.
• Potential energy during the 3.0 ps Cartesian canonical dynamics simulations.
• The backbone (, , and ) and sidechain () dihedrals of arginine. The two outermost sidechain dihedrals, and rotate hydrogens, only, so they are not varied in the Probability Grid Monte Carlo method.
• 30 grids for the three standard residue types.
• grids for standard (non-Proline, non-Glycine) residues at grid spacings of 10, 15, 30, and 60.
• grids of different structural types for standard (non-Proline, non-Glycine) residues in the SS58 dataset.
• grids for sidechains with one PGMC dihedral.
• grids for sidechains with two significant dihedrals.
• Results from several Monte Carlo simulations of Met-enkephalin. The simulations were identical except for the temperature used. The starting structure of each simulation was the 15 peak conformation and 15 and grids were used for conformational sampling. At 100 step intervals, the energy of the current conformation and the best overall conformation were recorded. The two graphs plot the current(a) and best energy(b) vs. Monte Carlo step.
• The best energy from 40 simulations of Met-enkephalin using 15 grid spacing at 1000 K. 20 simulations began with conformations generated at random (R) and 20 began with the peak 15 conformation, 15, (I).
• PGMC simulations were run at temperatures of 0 K, 300 K, 600 K, 1000 K and 5000 K, for each grid spacing (5, 10, 15, 30, and 60). For each spacing/temperature pair, ten simulations of 10,000 steps each were run. Here, the overall acceptance rate for the ten runs is shown for each spacing/temperature combination.
• For each of 25 temperature/grid spacing combinations, ten 10,000-step simulations were run and the minimum energy from each run was recorded. The plots show both the overall lowest energy for the ten runs (a) and the average minimum energy (b) for the ten runs.
• 20 simulations of 50,000 steps each were run at 300 K using grid spacings of 5 and 10. The best conformation from each run was energy minimized and the energy before and after minimization was recorded. The top two lines plot the unminimized energies while the bottom two, labeled ``(min)'', show the minimized energies.
• The peptide Met-enkephalin, with the dihedrals numbered as in .
• The dihedral angles from each of the 20 minima produced by 50,000-step simulations at 300 K. Only the dihedrals unsampled by the PGMC method, (dihedral 4) and the 's (6, 9, 12, and 17) are the same in every conformation. Even these degeneracies are broken during minimization.
• The top plot shows the distribution of dihedral angles for the eight conformations with energies within 1 kcal/mol of LS, the conformation with the lowest known energy . The bottom plot shows the same distribution minus the one conformation which differs significantly from the others at dihedrals 16, 18, and 19. The other seven conformations have virtually identical conformations for residues Phe 4 and Met 5.
• Three views of crambin: the C's (46 atoms), the peptide backbone (185 atoms), and the all-atom structure (402 atoms). From the crystal structure by Hendrickson and Teeter[77].
• Definition of virtual angle, , and dihedral, , for residue .
• The average rms deviation from the crystal structure for models of the crambin backbone built using various temperatures and pulse sizes.
• The average rms deviation in backbone atoms (RMSB) and C coordinates (RMSC) for crambin backbone models built using different C constraint force constants.
• Average backbone rms vs. the number of Monte Carlo steps. Also shown is the average time to build each backbone conformation.
• Average all-atom rms deviations for sidechain Monte Carlo simulations of crambin at different temperatures.
• Backbone rms per residue for crambin model.
• The deviation in for each residue of the crambin model.
• The peptide backbone of the model and crystal structures of crambin. The rms deviation is 0.538 Å.
• A comparison of helix 2 (residues 23 to 30) in the model and crystal structures. The rms deviation is 1.026 Å for all atoms and 0.394 Å for the backbone atoms.
• Helix 1 (residues 7 to 19) in the model and crystal structures. The rms deviation is 1.658 Å for all atoms and 0.209 Å for the backbone atoms.
• The Hierarchical Protein Folding Strategy, which converts lattice C coordinates into all-atom protein conformations.
• The probability distribution (0.01 Å resolution) for C-C bonds. The actual distribution is compared to that derived from the bond-stretch term of the CFF.
• 2000 virtual angle, dihedral () values.
• The probability grids for the entire H64 dataset, using 15 bins.
• The probability grids for HELIX and SHEET residues in the H64 dataset.
• A schematic diagram of an IgG molecule.
• The six hypervariable loops of the immunoglobulins HyHEL-5[114] and McPC603[115], shown as C coordinates only.
• C traces of the predicted and actual loop conformations of HyHEL-5.
• C traces of the predicted and actual loop conformations of McPC603.
• Backbone conformations of the predicted (yellow) and actual (red) loop conformations in HyHEL-5.
• Backbone conformations of the predicted (yellow) and actual (red) loop conformations in McPC603.