Similarity restraints

In addition to specific impulse, the vehicle requirements usually influence propellant selection in terms of storability, density, toxicity, and other hazards, and other application-sensitive factors, including exhaust plume properties and radar cross section and radiation emissions. Other factors being essentially equal, the higher the heat of reaction of a propellant (or combination). Hie more attractive die propellant. Sharp exceptions to this rule occur in some missiles because of volume limitations, the need for smokeless exhaust or similar restraints. 

Sensitivity is exercised by realizing that through family intimacy, members learn a lot about each other s vulnerabilities. Out of consideration for this understanding, all parties resolve not to act in ways that knowingly will cause each other hurt. Just as they, when frustrated in conflict, do not strike out in anger to deliberately hurt their child, so they expect the only child to exercise the similar restraint with them. 

The similarity restraint SADI restrains the distance between two (or more) pairs of atoms to be equal within a default standard uncertainty s of 0.02 A, no matter what that distance might be. The syntax is similar to DFIX / DANG, except that no target value for the distances is specified ... 

C(13) and C(15)) but rather two atoms before them (right before Ga(l) and Ga(2)). Also make sure that the atoms are all in the right order The similarity restraints SIMU and DELU (DELU is ignored by SHELXL if the named atoms are refined isotropically) make the atomic displacement parameters more reasonable. The critical portion of the new file, ga-03.ins, looks like this ... 

Give also some similarity restraints for the disorder. SIMU and DELU should be used for the whole stmcture. In addition, equivalent 1,2- and 1,3 distances should be restrained to the same value using SADI. Be very careful when dealing with symmetry equivalents (use the EQIV instruction). All these changes have been made in the file ti-04.ins. The EQIV/SADI instructions look like this ... 

Do not forget to change the site occupancy factors and to set the second free variable, as well as to give the similarity restraints (SAME) and SIMU, delu and FLAT for the disordered atoms as it has been done in the file tol-02.ins. Take also into account the symmetry equivalents (use EQIV). 

The file sin-08.res contains the final publishable model with adjusted and converged weighting scheme and htab commands for all hydrogen bonds. As you saw, the refinement of this stracture was not particularly difficult. The non-crystallographic symmetry merely increased the work and computing time but did not cause a specific problem, as global pseudo-symmetry can, and if we had a resolution problem, we could even have used similarity restraints to indirectly improve the data-to-parameter ratio. 

It was necessary to introduce some restraints there are nine chemically equivalent phenyl rings, so all chemically equivalent 1,2- and 1,3-distances in the nine rings are restrained to be the same. For every phenyl ring a planarity restraint is employed. For the anisotropic displacement parameters of the carbon atoms it was necessary to use the rigid bond and similarity restraints. There is also one disordered ethanol molecule in the cell distance and ADP restraints are employed to refine it. 

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

A similar problem arises with present cross-validated measures of fit [92], because they also are applied to the final clean list of restraints. Residual dipolar couplings offer an entirely different and, owing to their long-range nature, very powerful way of validating structures against experimental data [93]. Similar to cross-validation, a set of residual dipolar couplings can be excluded from the refinement, and the deviations from this set are evaluated in the refined structures. 

Figure 3 Model building by Modeller [31], First, spatial restraints in the form of atomic distances and dihedral angles are extracted from the template stmcture(s). The alignment is used to determine equivalent residues between the target and the template. The restraints are combined into an objective function. Finally, the model for the target is optimized until a model that best satisfies the spatial restraints is obtained. This procedure is technically similar to the one used in structure determination by NMR.

In the second step, the spatial restraints and the CHARMM22 force field tenns enforcing proper stereochemistry [80,81] are combined into an objective function. The general form of the objective function is similar to that in molecular dynamics programs such as CHARMM22 [80]. The objective function depends on the Cartesian coordinates of —10,000 atoms (3D points) that form a system (one or more molecules) ... 

Figure 4 Sample spatial restraint m Modeller. A restraint on a given C -C , distance, d, is expressed as a conditional probability density function that depends on two other equivalent distances (d = 17.0 and d" = 23.5) p(dld, d"). The restraint (continuous line) is obtained by least-squares fitting a sum of two Gaussian functions to the histogram, which in turn is derived from many triple alignments of protein structures. In practice, more complicated restraints are used that depend on additional information such as similarity between the proteins, solvent accessibility, and distance from a gap m the alignment.

To put the errors in comparative models into perspective, we list the differences among strucmres of the same protein that have been detennined experimentally (Fig. 9). The 1 A accuracy of main chain atom positions corresponds to X-ray structures defined at a low resolution of about 2.5 A and with an / -factor of about 25% [192], as well as to medium resolution NMR structures determined from 10 interproton distance restraints per residue [193]. Similarly, differences between the highly refined X-ray and NMR structures of the same protein also tend to be about 1 A [193]. Changes in the environment... 

Aitemativeiy, the beam end couid have compiete rotational restraint and no transverse displacement, i.e., clamped. However, a third boundary condition exists in Rgure D-3 just as in Figure D-2. That is, an axial condition on displacement or force must exist in addition to the conditions usually thought of as comprising a clamped-end condition. Note that the block-like device at the end of the beam prevents rotation and transverse deflection. A similar device will be used later for plates. Whether all of the three boundary conditions can actually be enforced depends on the order of the differential equation set when (necessarily approximate) force-strain and moment-curvature relations are substituted in Equations (D.2), (D.4), and (D.7). 

Despite the contribution of the above factors, it is clear that bending of the two alkyne moieties toward each other increases the energy of the system as illustrated by the three plots in Fig. 7.24 These plots illustrate the relation between the ring size and calculated cyclization parameters in more detail and dependence of the total energy of the system from the c-d distance. Interestingly, simple bending of alkyne moiety reproduced the effect of cyclic restraints reasonably well. A similar conclusion has been reached even earlier by Kraka and Cremer.40... 

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