Schematic figure of the local geometry of the protein chain. The solid beads represent one amino acid. Neighboring amino acid beads are represented in dashed lines.
Schematic figure of the hydrogen bond interaction. The light beads (H and O) are not explicitly modeled in the simulation; their positions are inferred from their bonded neighbors.
Map of the nearest-neighbor dipole-dipole interaction for all sets of dihedral angles and (top) and the decoupled Fourier series approximation (bottom). The central part of the upper plot was not reproduced in order to emphasize local difference in other regions of the plot (as can be seen in Fig. 4, this anyway is a sterically hindered region). Sterically favored regions of the plot are circumscribed by a thick line, in addition to labels of and regions. The two graphs were shifted and scaled for comparison.
Free energy plots of tripeptides Gly-Gly-Gly (top) and Gly-Ala-Gly (bottom) as a function of successive dihedrals and , calculated at our reference temperature . The coloring represents the free energy difference with the lowest conformation, in units of .
RMSD of the CG proteins 2A3D (full line) and 1P68 (dashed line) compared with experimentally resolved structures. Both simulations were run at .
Equilibrated structures of (a) 2A3D and (b) 1P68 sampled at . Superposition of simulated structure (opaque) with experimental data (transparent) is displayed. The STRIDE algorithm (Ref. 52) was used for secondary structure assignment (thick ribbons represent -helices on the figure).
Free energy profile as a function of a nativeness order parameter below , at, and above the folding temperature .
Conventional (i.e., not using parallel tempering) simulation of 2A3D at . The nativity parameter is plotted against time. The protein alternates between folded and unfolded conformations .
Kinetic studies of the 2A3D three-helix bundle CG protein. The average folding time is plotted against temperature. For temperatures ranging from to , about ten simulations were run and we measured the first passage time to the native state. The line represents the average between the minimum folding time and the time scale of the simulation. This can be used to estimate the glass transition temperature (see text).
Schematic figure of the two possible topologies in forming a three-helix bundle. (a) The native fold of protein 2A3D corresponds to a counterclockwise topology and (b) that of 1LQ7 is clockwise.
Specific heat of 15 GNNQQNY peptides in a cubic box of size of 41 Å. The peak around separates a low temperature phase, rich in high- content aggregates, from a high temperature phase where no aggregates form.
Snapshot of a typical cluster that forms by peptide aggregation in the low temperature phase of Fig. 11.
Bonded interaction parameters used in the model. The dihedrals denoted with an asterisk were determined during parameter tuning (see Sec. IV). All parameters are expressed in terms of the intrinsic units of the system. represents the interaction strength of Fourier mode (see main text), with equilibrium value . refers to the dihedral around the peptide bond for a proline residue. The sign of the improper dihedral angle is linked to the chirality of the isomer; the L form requires a negative sign. For each angular potential, only a single mode was used.
Normalized scale of amino acid hydrophobicities using the Lorentz–Berthelot mixing rule for the cross terms, as well as relative and absolute error, and , from the diagonal elements of the MJ matrix (see text for definition). Note that the side chain of glycine (marked with an asterisk in the table) is not modeled.
Nonbonded interactions. The length represents the diameter of a bead. Most parameters were determined after parameter tuning, except the ones denoted by an asterisk. See Sec. IV.
Table of free parameters in this CG model. The main test that was used to determine a given parameter is denoted in the second column.
Structure and amino acid sequence of all proteins studied in this paper.
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