Crystal structure analysis interpretative problems

The problem of transference from the hydrogen bonds in the crystal to those in a biological process is not different, in principle, from the transference of molecular structural information determined by crystal structure analysis to the interpretation of the mechanism of a chemical reaction. In Chapter 4, we discuss the differences between the geometry of hydrogen bonds in crystals and in the free molecule models that are necessarily used by the theoretical methods. 

The early speculations about transition moment directions in the lower aromatics needed to be tested experimentally. The traditional vapour phase measurements of band lineshapes were not accessible with the spectroscopic resolving power we then had, but came later (sec 4.2). Most absorption systems of aromatics in the UV were in any case diffuse and structureless. The method that could be used was to get the polarization of the light absorbed by the crystal composed of the target molecules. The positions and orientations of the molecules in the laboratory frame were known from X-ray crystal structure analysis. The interpretation of results raised non-trivial theoretical problems of its own. The experiments will be described first. 

The complexity and volume of. available diffraction data requires that other than manual tediniques be used to match unknown to known spectra. Available computer programs have indeed simplified the problem of identifying an unknown substance (Refs 9,15,16,21 22). The work of Abel and Kemmey (Ref 16) in this area is worthy of note. Data taken from this report is presented as Table 4. The authors use values of 26 (<90°) to identify phase location instead of values of d in A. Major computer programs of this type endeavor to identify the crystal structure of an. unknown and cite a general factor of certainty to support the credibility of the analysis interpretation... 

The structural interpretation of dielectric relaxation is a difficult problem in statistical thermodynamics. It can for many materials be approached by considering dipoles of molecular size whose orientation or magnitude fluctuates spontaneously, in thermal motion. The dielectric constant of the material as a whole is arrived at by way of these fluctuations but the theory is very difficult because of the electrostatic interaction between dipoles. In some ionic crystals the analysis in terms of dipoles is less fruitful than an analysis in terms of thermal vibrations. This also is a theoretically difficult task forming part of lattice dynamics. In still other materials relaxation is due to electrical conduction over paths of limited length. Here dielectric relaxation borders on semiconductor physics. 

The direct experimental result of a crystallographic analysis is an electron-density map, and not the atomic model everybody looks at If errors occur in crystal structures, they most often occur at the level of the (subjective) interpretation of the electron-density maps by the crystallographer. A severe problem, especially at low resolution (lower than 3.0 A), is the so-called model bias. To calculate an electron-density map, one needs amplitudes and phases. The amplitudes are determined experimentally, but the phases cannot be measured directly. In later stages of refinement, they are calculated from the model, which means that if the model contains errors, the phases will contain the same errors. Since phases make up at least 50% of the information which is used to calculate the electron-density maps, wrong features may still have reasonable electron density because of these phase errors. 

Kakudo and Kasai have summarized the central problem well ( ) "There are generally less than 100 independently observable diffractions for all layer lines in the x-ray diagram of a fibrous polymer. This clearly imposes limitations on the precision which can be achieved in polymer structure analysis, especially in comparison with the 2000 or more diffractions observable for ordinary single crystals. However, the molecular chains of the high polymer usually possess some symmetry of their own, and it is often possible to devise a structural model of the molecular chain to interpret the fiber period in terms of the chemical composition by comparison with similar or homologous substances of known structure. Structural information from methods other than x-ray diffraction (e.g., infrared and NMR spectroscopy) are also sometimes helpful in devising a structural model of the molecular chain. The majority of the structural analyses which have so far been performed are based on models derived in this way. This is, of course, a trial and error method". Similar perspectives have been presented by Arnott ( ), Atkins ( ), and Tadokoro... 

A and B should form a complete range of solid solutions. This means that they should have the same crystal structure as well as similar molar volumes. The phenomenological transport problem here is concerned with the solution of Fick s laws for the given experimental conditions in this inhomogeneous system. The atomistic problem is concerned with the interpretation of the chemical diffusion coefficient which, for example, might have been determined by a Boltzmann-Matano analysis. It was shown in section 5.5.3 that, for the case of binary diffusion via vacancies, the chemical diffusion coefficient may be written as ... 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Finally, we have attempted to evaluate the possible impact of an intermediate liquid crystalline phase and the possibility of transfer of helical hand information from the melt to the crystal throughout this process. Assuming that the melt is structured, the melt of chiral but racemic polyolefins would be made of stretches of helical stems that are equally partitioned between left- and right-handed helices. Formation of antichiral structures (such as in a iPP) could be interpreted as indicating a possible transfer of information (but the problem of the sequence of helical hands would still remain). This analysis is, however, ruined by the observation that many of these polymers also form chiral structures (frustrated p phase of iPP, Form III of iPBul). For the achiral poly(5-methyl-pentene-l), the chiral, frustrated phase is actually the more stable one, and can be obtained by melting and recrystallization of a less stable antichiral phase. 

FT-IR spectroscopy is particularly useful for probing the structure of membrane proteins. Until recently, a lack of adequate experimental techniques has been the reason for the poor understanchng of the secondary structure of most membrane proteins. X-ray diffraction requires high quality crystals and these are not available for many membrane proteins. Circular dichroism (CD) has been widely used for studying the conformation of water-soluble proteins, but problems arise in its use for membrane proteins. The light scattering effect may distort CD spectra and lead to substantial errors in their interpretation. In addition, the reference spectra used for the analysis of CD spectra are based on globular proteins in aqueous solution and may not be applicable to membrane proteins in the hydrophobic environment of lipid bilayers. 

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