Restraint

In general, the only assumption made during a refinement is that the structure consists of atoms. It is, however, possible to include all kinds of additional information a chemist or physicist may have about a certain molecule (e.g. that aromatic systems tend to be fiat or that the three methyl groups in a tert-butyl moiety are equivalent). This is done with the help of restraints. Restraints are treated as additional experimental observations, hence indirectly increasing the number of data points to refine against. In the presence of restraints the minimization function (Equation 2.1) changes as follows  

In this equation a is the standard uncertainty (or elasticity) assigned to a restraint Rt is the target value and Ro the actual value of the restrained quantity. 

Restraints must be applied with great care and only if justified (George Sheldrick said with the right restraints, you can fit an elephant to any data ). When appropriate, however, they should be used without hesitation, and having more restraints than parameters in a refinement is nothing to be ashamed of. 

In SHELXL, restraints are applied by adding a command with appropriate keywords and/or atom names in the. ins file. Even though the SHELXL reference manual, which is included as a. pdf file on the CD-ROM that accompanies this book, exhaustively elaborates on all restraints, the following pages briefly describe the most common restraints as they are used by this program. 

Because the NOE is due to dipolar interactions, its intensity, a, depends on the inverse sixth power of the distance r between the protons. As any macromolecule will contain protons at fixed distances, one should be able to calculate an unknown distance by comparison of its corresponding NOE with the NOE measured between protons at some reference distance rref from the simple relation 

This treatment ignores the fact that the reference distance and unknown distance may not be subject to the same motions2 and assumes that only pairwise interactions contribute to the measured intensities.41 Now, given that one can estimate distances in a molecule, there are several ways this can be turned into a penalty function. 

It is also clear that by reversing signs in Eq. [9], one can enforce a minimum distance between two particles. This may well be useful if one has accurate distance restraints or if one wishes to treat the absence of an NOE as indicative 

Continuing in the same vein, other workers have even used a sixth-power term to enforce distance restraints.44 45 In principle, there is no reason why one should favor Eq. [9] or [10], but it must be remembered that unless the scaling constant for this term is minuscule, a quartic or sixth-power term will very quickly rise so as to dominate other terms in a force field. This may be a danger if such methods are used during the early stages of refinement with poor models (large violations) and possibly less accurate NMR data.46 47 

Rather than simply adjusting a power term, Scarsdale et al.47 noted that the pseudo-energy term was being based on a distance r, but what was measured was more directly related to r 6. With this reasoning, they used a term of the form 

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The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the... 

In our implementation of SMD, modified versions of VMD and Sigma communicate with each other using a customized, lightweight protocol. Sigma sends atomic positions resulting from each molecular dynamics time step to VMD for display. When the user specifies restraints on parts of the displayed model, VMD sends them to Sigma, where they are converted into potential-well restraints added to the force field [21]. 

You can include geometric restraints—for interatomic distances, bond angles, and torsion angles—in any molecular dynamics calculation or geometry optim i/.ation. Here are some applications of restrain ts ... 

Tor all restraints, HyperChem uses named selections that contain two, three, or four atoms each. You use Name Selection on the Selectmenn to assign nam es to groups of selected atom s. Th en you can apply named selections as restraints for a calculation in the Restraint Forces dialog box from Restraints on the Setup menu. 

High temperature searches of conformational space (see Quenched Dynamics" on page 78), can produce unwanted conformational changes, such as cis-tmnx peptide flips, ring inversions, and other changes that you cannot reverse easily by geometry optimization. You can use restraints to prevent these changes. 

Rest lain Is can facilitalc (Jo eking a snhslralc in oiccii Ic Lo a birulm g sue. Reslralnts can also facilitate the interaction of two molecules in solution. In both cases, it is nn likely that two dilTereii I n eutral niolccti Ics won Id come into van dcr Waals con tact with cacli other without the use of restraints. 

Note MM-i- is derived from the public domain code developed by Dr. Norm an Allinger, referred to as M.M2( 1977), and distributed by the Quantum Chemistry Program Exchange (QCPE). The code for MM-t is not derived from Dr. Allin ger s present version of code, which IS trademarked MM2 . Specifically. QCMPOlO was used as a starting point Ibr HyperChem MM-t code. The code was extensively modified and extended over several years to include molecular dynamics, switching functuins for cubic stretch terms, periodic boundary conditions, superimposed restraints, a default (additional) parameter scheme, and so on. 

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

You need to specify two parameters the et uilibrium value ofthe internal coordinate and the force constant for the harmonic poten tial, T h e equilibrium restraint value deperi ds on the reason you choosea restraint. If, for example, you would like a particular bond length to remain constant during a simulation, then the equ ilibritirn restrain t value would probably be Lh e initial len gth of the bond. If you wan t to force an internal coordinate to a new value, the equilibrium internal coordinate is the new value. 

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. 

Use Restraints in the Setup menu to bring up the Restraint Forces dialog box... 

These molecular dynamics restraints are stored with the IIIX file and are relained as long as ihe Named Seleclions are slill active (structural changes not made to molecular systemli or the restraints are still rec iiested via the Restraint Forces dialog box. 

I lie default restraints are appropriate for molcciilar dyriam ics calculations where larger force constants would create undesirable h igh frequency motion s hut much larger force con slants may be desired for restrained geometry oplim i/ation. ... 

Fig. 9.24 A restraining potential that does not penalise struetures in which the distance lies between the leaver and upper distances di and and uses harmonie functions outside this range (left). The harmonic potentials may also he replaeed by linear restraints further from this region (right).

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