Developments in fiber diffraction.

Improved specimen preparation methods, third generation synchrotron sources, new data processing algorithms and molecular dynamics refinement techniques are, together, allowing the high-resolution structure determination of larger and larger macromolecular complexes by fiber diffraction. New synchrotron sources are also making possible both time-resolved studies and studies of ordered fibers only a few microns in diameter.     

Muscle diffraction theory. Relationship between diffraction subpeaks and discrete sarcomere length distributions.

A theoretical discussion is presented that describes the diffraction on monochromatic light by a three-dimensional sarcomere array having the following properties. The basic repetitive diffracting unit is the sarcomere. The contiguous arrangement of physically attached serial sarcomeres in the myofibril is contained within the model so that relative position of sarcomeres depend upon the lengths of intervening ones. Sarcomere length is described by a distribution function. This function may be discrete or continuous and contain one or more subpopulations. Two arrangements of sarcomeres are considered: (a) when sarcomeres of different lengths are arranged randomly in myofibrils the amplitude and width of mth order (m greater than or equal to 1) peaks and associated secondary diffraction maxima decrease and increase monotonically, respectively, as the standard deviation of the length distribution increases. No subpeaks are present regardless of the number of subpopulations within the distribution function. This behavior is shown to follow from the dependence of sarcomere position on the length of intervening sarcomeres. (b) When sarcomeres belonging to the same length subpopulation are arranged in serial contiguous fashion to form domains and more than one length subpopulation is present, then mth order diffraction peaks split to form subpeaks. The theoretical basis for this behavior is developed for the first time and may explain the subpeaks evident in diffraction patterns from cardiac and skeletal muscle.     

Neutron diffraction study of carbonmonoxymyoglobin.

Neutron diffraction data from a crystal of carbonmonoxymyoglobin were refined by PROLSQ, a modern restrained least-squares procedure in reciprocal space, in conjunction with a solvent analysis technique, to a final R-factor of 11.3%. The ligand CO occupies two sites and its binding conformations are distorted from the linear conformation. The N epsilon atom of the distal histidine residue is deprotonated (not deuterated), and a water molecule is bound to the N delta atom of the distal histidine. The side-chain of Lys56 (D6) exists in two alternative charge-binding sites. His24 (B5) and His119 (GH1) share a hydrogen atom. His12 (A10) and His36 (C1) are deprotonated. The deprotonated imidazole ring of His12 (A10) may act as a hydrogen-bond acceptor. The heme group is planar within 0.09 A root-mean-square (r.m.s.) deviation from planarity. The solvent environments for the two propionic acid groups are different. The side-chain of Arg45 (CD3) forms hydrogen bonds with the side-chain of Asp60 (E3) and one of the two propionic acid groups. An average N-2H . . . O angle in helical regions is 147 (+/- 11) degrees. Eleven main-chain amide hydrogen atoms from hydrophobic residues do not exchange with deuterium. The overall atomic occupancy factors for the main-chain and side-chain atoms are quite uniform, at 0.97 (+/- 0.07) and 0.93 (+/- 0.10), respectively, as shown by an occupancy analysis made at the end of the refinement procedure.     

X-ray diffraction studies of lecithin bilayers.

Counting the individuals in a population before and after an annual period of environmental stress allows the proportion s of the initial population surviving the period to be computed. A series of such observations over n annual periods gives a sequence s₁, s₂, …, s_n. A statistical model is formulated from axioms describing the survival process, and it is concluded that these observed values may usefully be regarded as realizations of a random variable that arises from the normal generated distribution (n.g.d.). Equations for estimating the n.g.d. parameters ζ and τ² from observed survival proportions by the method of moments and maximum likelihood are given. The distributions of parameter estimates ζ and τ² are obtained and discussed in the context of testing hypotheses comparing survival among different populations. Finally, the dependence of the n.g.d. upon parameters ζ and τ² is examined in terms of altering survival, either by population self-regulation mechanisms or man-induced controls. The intent is to provide insight into the relationship between the n.g.d. and its supporting axioms and, more generally, basic knowledge of population processes.     

X-ray diffraction studies of the corneal stroma.

A low-angle diffraction pattern has been obtained from corneal stroma. This pattern arises both from the arrangement of the collagen fibrils and from the packing of the tropocollagen molecules along the axes of the fibrils. The spacing arising from the packing of the fibrils increases homogeneously on swelling although the tissue as a whole swells only radially referred to the intact eye. The necessary rearrangement of the fibrils for this type of swelling to occur might result in the formation of regions devoid of collagen fibrils and the water not in the lattice of collagen fibrils could be synonymous with the lakes postulated by Benedek (1971) to explain the loss of transparency on swelling.The spacings due to the packing of the tropocollagen molecules are unusual in that, although they index as the third and fifth orders of the well-known 66 nm repeat, the first order of this spacing is absent. Calculation of the Patterson function for corneal collagen leads to peaks in electron density separated by distances of 0.38 and 0.24 of the repeat distance.     

Frequency-dependent diffraction from enzymatic breathing modes.

The intensity of the time-dependent Fourier transform of any macro-molecule which contains a cleft of the sort that exists in the protein lysozyme is derived. It is shown that there is a region of this transform in which this intensity varies nearly sinusoidally with time with a frequency equal to that of the macromolecule's breathing mode of vibration, and where, therefore, the diffracted power will be primarily at this single frequency. Observation of this power will allow the experimental determination of the frequency of this mode, which is expected to be much lower than those observable by Raman spectroscopy.     

An X-ray diffraction study of poly-L-homoarginine hydrochloride.

An X-ray study of the synthetic polypeptide poly(L -homoarginine hydrochloride) has been made to investigate whether, like the chemically related polypeptides poly(L -lysine hydrochloride), poly(L -arginine hydrochloride), and poly(L -ornithine hydrobromide), it can undergo conformational transitions merely from variations in its degree of hydration. X-ray photographs of powder and oriented specimens containing one to 15 molecules of water per L -homoarginine hydrochloride residue showed that this polymer forms only a β-pleated-sheet structure. The pleated sheets, formed by antiparallel polypeptide chains hydrogen-bonded to each other, are piled up along the b axis in an alternating sequence (“sandwich structure”). This structure did not appreciably change with variations of the degree of hydration, and the observed reflections at 56% relative humidity (1.8 molecules of water per residue) could be indexed satisfactorily in terms of a monoclinic unit cell, of space group P2₁, with a = 9.34 Å, b = 40.07 Å, c = 6.94 Å, and γ = 106°. These dimensions are shown by models to be compatible with the proposed structure, and the calculated density of 1.27 g/cm³ agrees well with the experimental value of 1.29 g/cm³. Removal of the last molecule of water results in a very diffuse pattern, while specimens containing 20 molecules of water per residue show only reflections due to water.     

Teaching electron diffraction and imaging of macromolecules.

Electron microscopic analysis can be used to determine the three-dimensional structures of macromolecules at resolutions ranging between 3 and 30 A. It differs from nuclear magnetic resonance spectroscopy or x-ray crystallography in that it allows an object's Coulomb potential functions to be determined directly from images and can be used to study relatively complex macromolecular assemblies in a crystalline or noncrystalline state. Electron imaging already has provided valuable structural information about various biological systems, including membrane proteins, protein-nucleic acid complexes, contractile and motile protein assemblies, viruses, and transport complexes for ions or macromolecules. This article, organized as a series of lectures, presents the biophysical principles of three-dimensional analysis of objects possessing different symmetries.     

High-angle electron diffraction of frozen hydrated collagen.

By using the techniques developed by Taylor et al. [(1975) J. Mol. Biol. 92, 165-167] (freezing of the hydrated specimen before its insertion into the electron microscope and keeping it frozen throughout the diffraction experiment), it was possible to obtain a high-angle electron-diffraction pattern from collagen fibrils. This pattern is in good agreement with that obtained by high-angle X-ray diffraction. Electron diffraction will be very useful to study collagen, because the diffraction pattern from a carefully selected area of one fibril is now feasible.     

Electron diffraction from single crystals of DNA.

Crystals of DNA have been grown in a form suitable for study by electron diffraction and electron microscopy. Preliminary electron diffraction patterns of any type that have been obtained from single crystals of highly polymerized DNA. The patterns, obtained from frozen, hydrated crystals with the beam approximately parallel to the DNA strand axis, show a hexagonal geometrical arrangement with a (1,0) Bragg spacing of 23.1 A.     

Patterson methods in fibre diffraction analysis.

The potential of the Patterson methods for X-ray diffraction studies of textures is examined in DNA fibres. Patterson analysis, which is rarely used in these situations, is shown to yield important information on the preliminary interpretation of diffraction patterns and to increase the reliability of the three-dimensional structural pattern obtained for polymeric molecules. We also show how the screw symmetry of helical molecules can be used to calculate their electron density by means of the three-dimensional Patterson function.     

X-ray diffraction of myelin membrane. I. Optimal conditions for obtaining unmodified small angle diffraction data from frog sciatic nerve

The X-ray diffraction pattern of myelin of frog sciatic nerve has been investigated, using a Kratky small angle slit camera to obtain the electron density distribution across the membrane. All major reflections observed were related to a fundamental repeat distance of 171 ± 2.8 A. There was no further increase in the number of reflections on varying the experimental conditions (varying pH, applying tension, immersion in various isotonic buffer solutions, etc.) or by varying the camera slit arrangement. The degree of disorder within the myelin sheath was examined by comparing the crystallite size to the half-width of the diffraction peak at half-height. The limiting of the diffraction spectra to five major reflections was determined not to be caused by disorder. It is concluded that the observed X-ray diffraction pattern is a consequence of the particular electron density distribution of the membrane. Therefore, the membrane cannot contain sharply distinct step-function regions of electron density, but approaches a modified cosine distribution.     

Electron diffraction of Valonia cellulose. A quantitative interpretation

The crystal structure of native cellulose (Valonia) has been analyzed by electron diffraction. Possible models for the structure were refined by rigid-body least squares methods, which incorporated parameters defining the preferred orientation of the fibrils around their long axes in the cell wall lamellae. The structure was found to consist of an array of chains having the same sense (i.e., parallel), with packing parameters similar to those recently determined by X-ray diffraction. The eight-chain unit cell could be approximated adequately by a two-chain monoclinic unit cell with dimensions a = 8.18 Å, b = 7.84 Å, c = 10.38 Å (fiber axis), and γ = 97.04°; the space group is P2₁.     

Aspects of X-ray diffraction on single spider fibers.

Diffraction patterns of silk from several spider species have been obtained by synchrotron radiation using a beam size > or = 10 microm. Single fiber diffraction patterns were obtained for fiber diameters down to a few microns. Diffraction patterns recorded with a 10 microm wide X-ray beam displayed fiber texture. The presence of two fractions of different crystallinity was confirmed for a single Nephila clavipes fiber. The orientation distribution of the polymer chains of the crystalline fraction along the fiber axis was found to be about 23 degrees full-width at half maximum (fwhm). The azimuthal spread of the short-range order fraction was about 86 degrees fwhm.