X-ray scanning microscopies of microcalcifications in abdominal aortic and popliteal artery aneurysms.

Abdominal aortic and popliteal artery aneurysms are vascular diseases which show massive degeneration, weakening of the vascular wall and loss of the vascular tissue functionality. They are driven by inflammatory, hemodynamical factors and biological alterations that may lead, in the case of an abdominal aortic aneurysm, to sudden and dangerous ruptures of the arteries. Here, human aortic and popliteal aneurysm tissues were obtained during surgical repair, and studied by synchrotron radiation X-ray scanning microdiffraction and small-angle scattering, to investigate the microcalcifications present in the tissues. Data collected during the experiments were transformed into quantitative microscopy images through the combination of statistical approaches and crystallographic methods. As a result of this multi-step analysis, microcalcifications, which are markers of the pathology, were classified in terms of chemical and structural content. This analysis helped to identify the presence of nanocrystalline hy-droxy-apatite and microcrystalline cholesterol, embedded in myofilament, and elastin-containing tissue with low collagen content in predominantly nanocrystalline areas. The generality of the approach allows it to be transferred to other types of tissue and other pathologies affected by microcalcifications, such as thyroid carcinoma, breast cancer, testicular microli-thia-sis or glioblastoma.

Effects of processing on structural, mechanical and biological properties of collagen-based substrates for regenerative medicine.

The aim of this work was to investigate the structural features of type I collagen isoforms and collagen-based films at atomic and molecular scales, in order to evaluate whether and to what extent different protocols of slurry synthesis may change the protein structure and the final properties of the developed scaffolds. Wide Angle X-ray Scattering data on raw materials demonstrated the preferential orientation of collagen molecules in equine tendon-derived collagens, while randomly oriented molecules were found in bovine skin collagens, together with a lower crystalline degree, analyzed by the assessment of FWHM (Full Width at Half Maximum), and a certain degree of salt contamination. WAXS and FT-IR (Fourier Transform Infrared) analyses on bovine collagen-based films, showed that mechanical homogenization of slurry in acidic solution was the treatment ensuring a high content of super-organization of collagen into triple helices and a high crystalline domain into the material. In vitro tests on rat Schwannoma cells showed that Schwann cell differentiation into myelinating cells was dependent on the specific collagen film being used, and was found to be stimulated in case of homogenization-treated samples. Finally DHT/EDC crosslinking treatment was shown to affect mechanical stiffness of films depending on collagen source and processing conditions.

Interfibrillar packing of bovine cornea by table-top and synchrotron scanning SAXS microscopy.

Bovine cornea was studied with scanning small-angle X-ray scattering (SAXS) microscopy, by using both synchrotron radiation and a microfocus laboratory source. A combination of statistical (adaptive binning and canonical correlation analysis) and crystallographic (pair distribution function analysis) approaches allowed inspection of the collagen lateral packing of the supramolecular structure. Results reveal (i) a decrease of the interfibrillar distance and of the shell thickness around the fibrils from the periphery to the center of the cornea, (ii) a uniform fibril diameter across the explored area, and (iii) a distorted quasi-hexagonal arrangement of the collagen fibrils. The results are in agreement with existing literature. The overlap between laboratory and synchrotron-radiation data opens new perspectives for further studies on collagen-based/engineered tissues by the SAXS microscopy technique at laboratory-scale facilities.

An optimized table-top small-angle X-ray scattering set-up for the nanoscale structural analysis of soft matter.

The paper shows how a table top superbright microfocus laboratory X-ray source and an innovative restoring-data algorithm, used in combination, allow to analyze the super molecular structure of soft matter by means of Small Angle X-ray Scattering ex-situ experiments. The proposed theoretical approach is aimed to restore diffraction features from SAXS profiles collected from low scattering biomaterials or soft tissues, and therefore to deal with extremely noisy diffraction SAXS profiles/maps. As biological test cases we inspected: i) residues of exosomes' drops from healthy epithelial colon cell line and colorectal cancer cells; ii) collagen/human elastin artificial scaffolds developed for vascular tissue engineering applications; iii) apoferritin protein in solution. Our results show how this combination can provide morphological/structural nanoscale information to characterize new artificial biomaterials and/or to get insight into the transition between healthy and pathological tissues during the progression of a disease, or to morphologically characterize nanoscale proteins, based on SAXS data collected in a room-sized laboratory.

Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections.

Scanning small and wide angle X-ray scattering (scanning SWAXS) experiments were performed on healthy and pathologic human bone sections. Via crystallographic tools the data were transformed into quantitative images and as such compared with circularly polarized light (CPL) microscopy images. SWAXS and CPL images allowed extracting information of the mineral nanocrystalline phase embedded, with and without preferred orientation, in the collagen fibrils, mapping local changes at sub-osteon resolution. This favorable combination has been applied for the first time to biopsies of dwarfism syndrome and Paget's disease to shed light onto the cortical structure of natural bone in healthy and pathologic sections.

The method of joint probability distribution functions applied to MAD techniques. The two-wavelength case for acentric crystals.

MAD (multiple-wavelength anomalous dispersion) techniques are often considered as a special MIR (multiple isomorphous replacement) case. The rigorous method of the joint probability distribution functions is applied to solve the phase problem for acentric crystals, on the assumption that the anomalous scatterer's substructure is a priori known. The two-wavelength case is considered: errors in measurements and in the model substructure are handled. The probabilistic approach provides a very simple and efficient formula for estimating structure-factor phases.

On integrating direct methods and isomorphous-replacement techniques: triplet estimation and treatment of errors.

The method of joint probability distribution functions has been generalized in order to include and treat different sources of error. The probability distributions of the isomorphous pairs (E(p), E(d)) and of the two triples (E(ph), E(pk), E(ph+k), E(dh), E(dk), E(dh+k)) are obtained, on the assumption that the lack of isomorphism and the errors in measurements cumulate on the E(d) variables. The conditional distributions of the two-phase and the three-phase structure invariants are derived, showing how the reliability of the probabilistic estimates depends on the errors.

The method of joint probability distribution functions applied to MAD techniques. The centric case.

Traditional probabilistic approaches consider MAD (multiple-wavelength anomalous-dispersion) data as a special MIR (multiple isomorphous replacement) case. The rigorous method of the joint probability distribution functions has been applied to solve the phase problem, with the assumption that the anomalous scatterers' substructure is a priori known. The probabilistic approach is able to handle measurement errors: it has been applied to symmetry-restricted phases and provides simple and efficient formulas.

The method of joint probability distribution functions applied to the one-wavelength anomalous-scattering (OAS) case.

The method of the joint probability distribution function is applied to the case in which the positions of the anomalous scatterers are fully or partially known. The mathematical technique is able to handle errors both in the model structure of the located anomalous scatterers and in measurements. A criterion for ranking the more accurate phase estimates is given.

The joint probability distribution function of structure factors with rational indices. IV. The P1 case.

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

The joint probability distribution function of structure factors with rational indices. V. The estimates.

The probabilistic formulae [Giacovazzo, Siliqi & Fernández-Castaño (1999). Acta Cryst. A55, 512-524] relating standard and half-integral index reflections are modified for practical applications. The experimental tests prove the reliability of the probabilistic relationships. The approach is further developed to explore whether the moduli of the half-integral index reflections can be evaluated in the absence of phase information; i.e. by exploiting the moduli of the standard reflections only. The final formulae indicate that estimates can be obtained, even though the reliability factor is a constant.

The probability distribution of structure factors with non-integral indices. II. The P1; case.

The probability distribution of the structure factors with non-integral indices is derived in P1;. For integral values of at least one of the indices, the intensity distribution coincides with that provided by Wilson's statistics, but may strongly differ when the indices are (or are close to) half-integers. The deviations are stronger when the integral part of the indices is small, and increase with the size of the structure. In favourable circumstances, moduli and phases of the reflections may be accurately estimated.

The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1; case.

The joint probability distribution function method has been developed in P1; for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F(p1), F(p2)) are found to be useful for phasing purposes, where p1 and p2 are any pair of vectorial indices. A variety of conditional distributions like P(|F(p1)| | |F(p2)|), P(|F(p1)| |F(p2)), P(varphi(p1)| |F(p1)|, F(p2)) are derived, which are able to estimate the modulus and phase of F(p1) given the modulus and/or phase of F(p2). The method has been generalized to handle the joint probability distribution of any set of structure factors, i.e. the distributions P(F(1), F(2),ellipsis, F(n+1)), P(|F(1)| |F(2),ellipsis, F(n+1)) and P(varphi(1)| |F|(1), F(2),ellipsis, F(n+1)) have been obtained. Some practical tests prove the efficiency of the method.

The joint probability distribution function of structure factors with rational indices. VI. Cases with reduced dimensionality.

The probabilistic formulas relating standard and mixed type reflections (these last show integral and half-integral indices) are derived. It is shown that probabilistic estimates can be obtained by using particular sections of the three-dimensional reciprocal space. The concept of structure invariant is extended to define the wider class of structure quasi-invariant. Their statistical behaviour is briefly discussed with the help of some practical tests.

The ab initio crystal structure solution of proteins by direct methods. VI. Complete phasing up to derivative resolution.

The procedure described in the papers I-V of this series [Giacovazzo, Siliqi & Ralph (1994). Acta Cryst. A50, 503-505; Giacovazzo, Siliqi & Spagna (1994). Acta Cryst. A50, 609-621; Giacovazzo, Siliqi & Zanotti (1995). Acta Cryst. A51, 177-188; Giacovazzo & Gonzalez Platas (1995). Acta Cryst. A51, 398-404; Giacovazzo, Siliqi & Gonzalez Platas (1995). Acta Cryst. A51, 811-820], aiming at estimating protein phases via a single heavy-atom derivative, has been improved so as to extend phase determination to all the reflections up to derivative resolution. The quality of the resulting electron-density maps is checked for a number of test strutures. Some of the maps are immediately interpretable, and some can be interpreted after some cycles of solvent flattening and/or histogram matching. The correlation with classical SIR techniques is also discussed.

The ab initio crystal structure solution of proteins by direct methods. II. The procedure and its first applications.

A direct phasing method is described that is potentially able to solve ab initio protein structures. The method uses the information contained in diffraction data of the native structure and of one isomorphous derivative. The various steps of the procedure are analysed in order to estimate their robustness against experimental errors in measurements and lack of isomorphism. Experimental tests involve four typical protein structures and show that crystal structure solution is attained in a rather straightforward way.