Dihedral space

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

The conformational distance does not have to be defined in Cartesian coordinates. Eor comparing polypeptide chains it is likely that similarity in dihedral angle space is more important than similarity in Cartesian space. Two conformations of a linear molecule separated by a single low barrier dihedral torsion in the middle of the molecule would still be considered similar on the basis of dihedral space distance but will probably be considered very different on the basis of their distance in Cartesian space. The RMS distance is dihedral angle space differs from Eq. (12) because it has to take into account the 2n periodicity of the torsion angle. 

Figure 3 The collapse of the peptide Ace-Nle30-Nme under deeply quenched poor solvent conditions monitored by both radius of gyration (Panel A) and energy relaxation (Panel B). MC simulations were performed in dihedral space 81% of moves attempted to change angles, 9% sampled the w angles, and 10% the side chains. For the randomized case (solid line), all angles were uniformly sampled from the interval —180° to 180° each time. For the stepwise case (dashed line), dihedral angles were perturbed uniformly by a maximum of 10° for 4>/ / moves, 2° for w moves, and 30° for side-chain moves. In the mixed case (dash-dotted line), the stepwise protocol was modified to include nonlocal moves with fractions of 20% for 4>/ J/ moves, 10% for to moves, and 30% for side-chain moves. For each of the three cases, data from 20 independent runs were combined to yield the traces shown. CPU times are approximate, since stochastic variations in runtime were observed for the independent runs. Each run comprised of 3 x 107 steps. Error estimates are not shown in the interest of clarity, but indicated the results to be robust.

There are two broad classes of dihedral space models for studying and building flexible chain molecules. The first, known as Rotational Isomeric State Theory (RIS) [25], was developed to study industrial polymers. The second, known as Chain Buildup (CB) [26], was... 

A t) ical Anneal-Flex run on a molecule such as the vitamin D3 ketone 1 consists of 20 runs of 1000 steps per temperature at 30 temperatures. Since the acceptance rate is usually around 30%, there are about 180,000 accepted steps or 9,000 lines of data for each 20-run file. In classical statistical mechanics, one Anneal-Flex run can be considered as one member of an ensemble [30]. The collection of twenty runs is the ensemble. In this type of formulation, the numerical value of the quantity of interest is obtained by calculating averages over this ensemble. While the quantities that we are interested in are too complicated to be represented by a single number, the same statistical mechanical principles can be used to create the distribution functions which accurately represent dihedral space. 

Note Restraints apply to distances, angles and dihedrals between bonded ornon bonded atoms. Yon can also restrain atoms to points in space. 

Note You can superimpose harmonic restraining forces to interatomic distances, angles, or dihedrals that you have set up as named selections. Yon can also restrain atoms to points in space. See Using Geometric Restraints" on page SI and "Restraints" on page 105. 

B. Normal Mode Analysis in Dihedral Angle Space... 

Compound Ref. Crystal Space Z Dihedral angle Selected intermolecular... 

Compound Ref. Crystal Phase Space group Z Dihedral angle between the phenyl ringsV° Selected intermolecular distances [A]... 

Hartung and Rapthel [64] described the crystal structure of the mesogenic 2-methylthio-5-(4 -n-butyloxyphenyl)-pyrimidine which forms a monotropic smectic A phase. The chemical structure of this compound is presented in Fig. 5. The compound crystallises in the triclinic space group PI with two molecules per unit cell. The molecules adopt a fully stretched and nearly planar form. The pyrimidine ring is nearly planar. The dihedral angle between the phenyl and the pyrimidine rings is 22.7°. The molecules are arranged parallel to each other. 

Compound Ref. Ri R2 Space group Z Dihedral angle between 2-phenyl and pyrimidine rings/° Dihedral angle between 5-phenyl and pyrimidine rings/°... 

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