Molecular refinement

Crystallographic refinement is a procedure which iteratively improves the agreement between structure factors derived from X-ray intensities and those derived from a model structure. For macro molecular refinement, the limited diffraction data have to be complemented by additional information in order to improve the parameter-to-observation ratio. This additional information consists of restraints on bond lengths, bond angles, aromatic planes, chiralities, and temperature factors. 

This limited definition has the following implications. NMR techniques themselves are not discussed, except to the extent that one must understand the nature of the data to model them. Similarly, the methods for generating initial structures are treated superficially to understand their limitations and possible errors that might be propagated through a molecular refinement. Finally, ex-... 

When the positions of the downfield components of 4H-13C TROSY HSCQ cross-peaks286,287 are compared under the isotropic and aligned conditions, both RDC and CSA effects contribute to the observed difference A S = AS + RDC/2. These values, referred to as pseudo-CSA, can be used directly in molecular refinements.288 The reason for using combined A<5 values, rather than A<5 and RDC separately, is that it is easier to measure accurately the positions of downfield TROSY components for larger molecules, because of the optimized line width of these components. 

This chapter is structured as follows In Sect. 6.2, a basic introduction to molecular refinement is presented, stressing particularly relevant aspects. Section 6.3 reviews the recent work by Falklof et al., describing how the 2 x 2 x 2 supercell for the lysozyme structure was obtained. Section 6.4 reviews some modern advances in DFT, focusing on dispersion-corrected DFT, while Sect. 6.5 describes the effects of DFT optimization of atomic coordinates on the agreement between observed and calculated X-ray structure factors. The aim is to determine an optimal electronic-structure computational procedure for quantum protein refinement, and we consider only the effects of minor local perturbations to the existing protein model rather than those that would be produced by allowing full protein refinement. 

Separation of families by merely increasing the resolution evidently can not be used when the two chemical families have the same molecular formula. This is particularly true for naphthenes and olefins of the formula, C H2 , which also happen to have very similar fragmentation patterns. Resolution of these two molecular types is one of the problems not yet solved by mass spectrometry, despite the efforts of numerous laboratories motivated by the refiner s major interest in being able to make the distinction. Olefins are in fact abundantly present in the products from conversion processes. 

Spectroscopy is the most important experimental source of infomiation on intemiolecular interactions. A wide range of spectroscopic teclmiques is being brought to bear on the problem of weakly bound or van der Waals complexes [94, 95]. Molecular beam microwave spectroscopy, pioneered by Klemperer and refined by Flygare, has been used to detemiine the microwave spectra of a large number of weakly bound complexes and obtain stmctiiral infomiation... 

Several instniments have been developed for measuring kinetics at temperatures below that of liquid nitrogen [81]. Liquid helium cooled drift tubes and ion traps have been employed, but this apparatus is of limited use since most gases freeze at temperatures below about 80 K. Molecules can be maintained in the gas phase at low temperatures in a free jet expansion. The CRESU apparatus (acronym for the French translation of reaction kinetics at supersonic conditions) uses a Laval nozzle expansion to obtain temperatures of 8-160 K. The merged ion beam and molecular beam apparatus are described above. These teclmiques have provided important infonnation on reactions pertinent to interstellar-cloud chemistry as well as the temperature dependence of reactions in a regime not otherwise accessible. In particular, infonnation on ion-molecule collision rates as a ftmction of temperature has proven valuable m refining theoretical calculations. 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

A molecular dynamics simulation nsnally starts with a molecular structure refined by geometry optimization, but wnthont atomic velocities. To completely describe the dynamics of a classical system con lain in g X atom s, yon m nsl define 6N variables. These correspond to ilX geometric coordinates (x, y, and /) and iSX variables for the velocities of each atom in the x, y, and /. directions. 

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

D, H W Hoeffken, D Crosse, J Stuerzebecher, P D Martin, B F P Edwards and W Bode 1992. Refined 2.3 Angstroms X-Ray Crystal Structure of Bovine Thrombin Complexes Formed witli he 3 Benzamidine and Arginine-Based Thrombin Inhibitors NAPAP, 4-TAPAP and MQPA A Starting Point for Improving Antithrombotics. Journal of Molecular Biology 226 1085-1099. 

Semiempirical molecular orbital calculations have gone through many stages of refinement and elaboration since Pople s 1965 papers on CNDO. Programs like PM3, which is widely used in contemporary research, are the cumulative achievement of numerous authors including Michael Dewar (1977), Walter Thiel (1998), James Stewart (1990), and their coworkers. 

Assisted model building with energy refinement (AMBER) is the name of both a force field and a molecular mechanics program. It was parameterized specifically for proteins and nucleic acids. AMBER uses only five bonding and nonbonding terms along with a sophisticated electrostatic treatment. No cross terms are included. Results are very good for proteins and nucleic acids, but can be somewhat erratic for other systems. 

Model optimization is a further refinement of the secondary and tertiary structure. At a minimum, a molecular mechanics energy minimization is done. Often, molecular dynamics or simulated annealing are used. These are frequently chosen to search the region of conformational space relatively close to the starting structure. For marginal cases, this step is very important and larger simulations should be run. 

AMBER (assisted model building with energy refinement) a molecular mechanics force field... 

Cracking (Section 2 16) A key step in petroleum refining in which high molecular weight hydrocarbons are converted to lower molecular weight ones by thermal or catalytic carbon-carbon bond cleavage... 

The greatest value of molecular dynamic simulations is that they complement and help to explain existing data for designing new experiments. The simulations are increasingly useful for structural refinement of models generated from NMR, distance geometry, and X-ray data. 

Use the HyperChem Model Builder to construct an approximate geometry. If you want to look at the relative energies of a set of molecules, you may want to carry out the calculations using fully optimized molecular geometries. These geometry optimization calculations can use either molecular mechanics or quantum mechanics to further refine the molecular geometry beyond that given by the Model Builder. 

A vast amount of research has been undertaken on adsorption phenomena and the nature of solid surfaces over the fifteen years since the first edition was published, but for the most part this work has resulted in the refinement of existing theoretical principles and experimental procedures rather than in the formulation of entirely new concepts. In spite of the acknowledged weakness of its theoretical foundations, the Brunauer-Emmett-Teller (BET) method still remains the most widely used procedure for the determination of surface area similarly, methods based on the Kelvin equation are still generally applied for the computation of mesopore size distribution from gas adsorption data. However, the more recent studies, especially those carried out on well defined surfaces, have led to a clearer understanding of the scope and limitations of these methods furthermore, the growing awareness of the importance of molecular sieve carbons and zeolites has generated considerable interest in the properties of microporous solids and the mechanism of micropore filling. 

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