Macromolecular Structure Introductory Article .
Macromolecular StructureDetermination by X-rayCrystallographyJoachim Jaeger, Wadsworth Center, Albany, New York, USAIntroductory articleArticle Contents. Introduction. Single Crystal X-ray Diffraction. The Phase Problem. Instrumentation. Crystallization and Structure DeterminationX-ray diffraction is a well-established method to elucidate the atomic structure of singlecrystal macromolecules. An image of the macromolecule forming the crystal cannot bedirectly recorded as the X-ray phase information is lost during the diffraction experiment.Through systematic variation of the chemical content in the crystal and/or through smallchanges in the wavelength of the incident X-ray beam, however, a sharp image can bereconstituted computationally. Within the Protein Data Bank, the vast majority of threedimensional structures available have been determined using X-ray diffraction. Thesestructures are used to correlate macromolecular structure with function, to studymolecular mechanisms and serve as templates for structure-based drug design of noveltherapeutic agents for the treatment of many diseases.Introduction‘‘There is something about protein crystallography thatmakes it uniquely satisfying. You might work away at astructure, perhaps for years, without an inkling of its nature, until it emerges one day like Venus from the wavesand reveals an undreamt of, intricate new facet of nature.’’Max F. Perutz, March 2000The analysis of the atomic structure of proteins and nucleic acids is a complex problem and a fascinating area ofresearch in the life sciences. The experimental techniquesused for these studies involve single-crystal X-ray diffraction or X-ray fibre diffraction. This article outlines theprinciples and the key methods involved in macromolecular structure determination by X-ray crystallography.HistoryX-radiation was discovered and applied by Roentgen in1895. Von Laue and colleagues conducted the first X-raydiffraction experiments using rock salt (Figure 1a) and otheralkali halides as crystalline samples. Von Laue’s discoveryand his mathematical formulation of X-ray diffractionfrom crystals earned him the Nobel Prize for Physics in1914. Independently, W. L. and W. H. Bragg carried outsimilar studies. W. L. Bragg found that the diffractionphenomenon could be treated mathematically as reflectionby successive parallel planes passing through crystal latticepoints (see Figure 2b). The Braggs, father and son, wereboth awarded the Nobel Prize for Physics in 1915.During the 1920s and 1930s the focus of X-ray diffraction studies shifted to more complex systems such as macromolecular fibres and protein crystals. W. T. Astbury and. Milestonesdoi: 10.1038/npg.els.0002723coworkers pioneered structural studies on large fibrousproteins such as hair, wool and quills and on DNA fibres.After taking the first fibre diffraction images of DNA, hecorrectly predicted the overall dimensions of the moleculeand found that the nucleotide bases were stacked at intervals of 3.3 Å perpendicular to its long axis. However, it wasleft to Watson and Crick to elucidate the detailed atomicstructure of the DNA double helix. In the Cavendish Laboratories at Cambridge, J. D. Bernal and D. Crowfootwere investigating the diffraction properties of pepsincrystals and recognized that these crystals must be kept inan aqueous, more native-like environment (mother liquor)rather than as dry-mounted crystals. In 1937, Max Perutzperformed the first experiments in Cambridge to discoverwhether it might be possible to determine the structure ofhaemoglobin by X-ray diffraction. It would take Perutzuntil 1953 to achieve the most critical breakthrough in actually visualizing the complex molecular structure of haemoglobin. He succeeded in incorporating heavy atoms,namely those of mercury, into definite positions in thehaemoglobin crystals (see Perutz, 1992). By this means thediffraction pattern is altered significantly, and the changescan be utilized to determine a direct image of the molecularstructure of the haemoglobin. Using the same techniqueKendrew succeeded in incorporating heavy atoms (mercury and gold) into myoglobin crystals. This approachprovided a solution for an often-insurmountable problemin X-ray structure determination known as the phaseproblem. By 1958, the structures of myoglobin and haemoglobin had been determined after more than 20 years ofdedicated labour, and for these groundbreaking discoveries Perutz and Kendrew were awarded the Nobel Prize inChemistry in 1962. For their work on the structure of theNATURE ENCYCLOPEDIA OF LIFE SCIENCES / & 2004 Nature Publishing Group / www.els.net1
Macromolecular Structure Determination by X-ray Crystallographyss0srs02θ(a)s0sθθdnn(b)Figure 2 The interaction of X-ray photons with matter. Principally, theelectric field of the X-ray photons induces in-phase dipole oscillations in theelectrons of the two electrons in the sample, which in turn give rise tocoherently diffracted radiation. (a) The two electrons in the sample areseparated by the distance r, the vectors s0 and s are unit vectors describingthe direction of the incident primary beam and the scattered rays,respectively. The path difference gives rise to interference between thescattered beams. (b) Scattering from crystalline lattice. The incident beamapproaching the lattice plane at an angle y is reflected from that plane at anequal angle (Glanzwinkel).Figure 1 X-ray diffraction patterns. (a) The first diffraction pattern ofrocksalt (NACL) recorded in 1911 by Laue and co-workers. (b) A highresolution diffraction image of a lysozyme crystal recorded with a prototypeCCD detector at beamline A1 at MacCHESS, Cornell, USA.DNA double helix J. D. Watson, F. H. C. Crick and M. H.F. Wilkins received the Nobel Prize in Physiology andMedicine in the same year. Within the next five years thefirst structures of the enzymes lysozyme, carboxypeptidase, RNase S, chymotrypsin, subtilisin andpapain were determined at near atomic resolution.Diffraction methods are still the most commonly usedand successfully applied techniques for elucidating mac-2romolecular structure. The Protein Data Bank (PDB) currently lists more than 20 000 entries with approximately85% of the deposited structures determined by singlecrystal diffraction. Recent advances in cryogenic techniques at liquid nitrogen or liquid helium temperatureshave allowed high-resolution studies using both electronand X-ray crystallography. Major advances in multidimensional nuclear magnetic resonance (NMR) techniquesnow contribute significantly to our knowledge of thestructure and in particular the dynamic properties of macromolecules. Correlating structure (and dynamics) withfunction provides a more complete understanding of proteins or nucleic acids.NATURE ENCYCLOPEDIA OF LIFE SCIENCES / & 2004 Nature Publishing Group / www.els.net
Macromolecular Structure Determination by X-ray CrystallographySingle Crystal X-ray DiffractionDiffraction occurs when X-ray photons interact with electrons (in the biological macromolecule). The electric fieldof the X-ray photons induces in-phase dipole oscillations inthe electrons, which in turn give rise to coherently diffracted radiation. A very simple experiment in which a collimated beam of X-ray photons interacts with two electronsis illustrated in Figure 2a. The two electrons are separated bythe distance r, the vectors s0 and s are unit vectors describing the direction of the incident primary beam and thescattered rays, respectively. The angle between s0 and s istypically denoted 2y. The path difference is defined as ineqn [1], where S is the scattering vector.r·s r·s0– r·Sλ λ[1]The length of S is a function of the X-ray wavelength andthe total scattering angle (eqn [2]).In principle, this equation can also be applied to a threedimensional lattice of a single crystal where atoms (andelectrons) are ordered in lattice planes (Figure 2b). The incident beam approaching the lattice plane at an angle isreflected from that plane at an equal angle (Glanzwinkel).Laue discovered that the conditions for observing a maximum in diffracted intensities requires the path differencebetween reflected beams from adjacent lattice planes be anintegral number of wavelengths (h 5 Sa, k 5 Sb or l 5Sc). With the distance between lattice planes defined as d5 1/ S and S 5 2 sin y /l, it follows that nl 5 2d sin y.W. H. Bragg first derived this equation in 1912.Biological matter interacts only weakly with electromagnetic radiation, as the sample is not densely packedwith electrons. Proteins and nucleic acid typically consistof atoms of light elements such as hydrogen, carbon, nitrogen, oxygen, phosphorus and sulfur. To enhance thediffraction signal it is necessary to increase the intensity ofthe incident beam as well as the scattering volume in ordered arrays of macromolecules. This is achieved by shining collimated X-radiation (preferably highly intensesynchrotron radiation beams) onto single crystals – highly ordered, symmetrical, three-dimensional arrays. According to Laue and Bragg, scattered intensities arisingfrom crystals result in sharply ordered diffraction maxima(diffraction spots). Symmetry operations such as rotationaxes, mirror planes, glide planes, rotation-inversion axes orcombined rotation/translation elements are used to describe the geometric relationships between the differentmolecules forming the crystal lattice. However, certain re-cabFigure 3 This figure shows a primitive, a C-centred, a face-centred and abody-centred orthorhombic unit cell. The orthorhombic system ischaracterized by orthogonal unit cell vectors of different lengths (a 6¼ b 6¼ cand a 5 b 5 g 5 908).strictions apply in the case of proteins and nucleic acids.They contain chiral centres (L-amino acids, D-riboses, etc.),which in turn are incompatible with the formation of thosespace groups that contain inversion centres and glideplanes. These restrictions limit the number of possiblespace groups for chiral molecules to 65.The repeat unit or unit cell is defined by the vectors a, band c and by the angles between them (a,b,g). Only sevendifferent types of cells are required to describe a vast arrayof different packing arrangements and crystal systems: triclinic, monoclinic, orthorhombic, rhombohedral, tetragonal, hexagonal and cubic. These space groups can befurther subdivided into 14 distinct Bravais lattices, considering additional symmetry elements on the faces or theinner centre of the unit cells. The most common macromolecular crystal lattices belong to the monoclinic and orthorhombic space groups. The orthorhombic system, forexample, is characterized by strictly orthogonal unit cellvectors of different length (a 6¼ b 6¼ c and a 5 b 5 g 5 908;see Figure 3). In addition to measuring the unit cell dimensions it is important to determine the space group of thecrystal. This is accomplished by analysing the location ofthe diffraction spots as well as symmetric repeats in diffraction intensities and systematic absences (extinctions).The symmetry of the diffraction pattern accurately corresponds to the symmetry of a given sample space group.The Phase ProblemThe total observed diffraction Itot(S) is directly proportional to F2tot(S), the square of the sum of all atomic formfactors f(S) and positions x, y, z contained within theasymmetric unit (eqn [3]).Inserting the Laue conditions, S 5 h/a, S 5 k/b or S 5 l/c, eqn [4] follows.NATURE ENCYCLOPEDIA OF LIFE SCIENCES / & 2004 Nature Publishing Group / www.els.net3
Macromolecular Structure Determination by X-ray CrystallographyThe molecular transform Ftot(h, k, l) is a complex quantityconsisting of a real and an imaginary part. During a diffraction experiment, only the square of the amplitude F 2,i.e. the real part of an individual Fourier component, canbe directly recorded in the form of diffraction spots. However, diffraction intensities are modulated by interferencefringes arising from arrays of atoms within the crystal lattice. As seen in Figure 2a and Figure 2b, the modulation is aconsequence of phase shifts along the path differences inthe lattice. A complete extinction of diffracted intensitiesoccurs when the scattered beams differ by a phase angle ofexactly 1808. For example, a translation of the crystal relative to the incident beam or a shift of origin does not causean apparent change in diffraction intensities or phases. It isnot possible to record these phase shifts directly. Therefore, phase information contained in the imaginary part ofthe molecular transform is lost in the X-ray diffractionexperiment and the image (which is dominated by phaseinformation) cannot be reconstructed in a straightforwardmanner. This experimental dilemma is often referred to asthe ‘phase problem’. A useful graphical representation ofthis complex quantity F has been devised in the form ofArgand diagrams where individual components fhkl of thetotal molecular transform are plotted as vectors in thecomplex plane with unit vectors A along the real axis (theamplitude F ) and B along the imaginary axis (the phaseangle).In 1951, Max Perutz succeeded in overcoming this problem for the first time by introducing additional intensitymodulations in the diffraction pattern. These particulardifferences arose from heavy-atom scatterers such as mercury or gold compounds added to pre-grown haemoglobincrystals. The Argand diagrams in Figure 4a and Figure 4bindicate that the formation of two heavy atom derivativesis sufficient to determine unambiguously the phase (or partB) of each Fourier component. The phase problem can besolved only if the lattices of the native crystal and theheavy-atom derivative are isomorphous, i.e. if differencesin diffraction intensities are due only to the addition of theheavy-atom scatterers and not a consequence of global(mechanical) changes in the crystal lattice. Recent advances in computational approaches using Bayesian statisticsand maximum-likelihood methods have helped to overcome problems in phase refinement and facilitated the accuracy of phase determination (the program SHARP).Image reconstruction from an X-ray diffraction patterncan also be achieved by other experimental techniques suchas single isomorphous replacement in conjunction withanomalous scattering (SIRAS), multiple-wavelengthanomalous dispersion (MAD, pioneered by Wayne Hendrickson) or by direct ab initio phasing methods. SIRAS andthe MAD method, rapidly becoming the phasing methodof choice, are based on the effect of anomalous dispersion.The phenomenon of anomalous dispersion is wavelengthdependent and usually occurs in heavy atoms such as sulfur, bromine, iodine and, prominently, in main and transition group metals. The anomalous effect is caused by theinteraction of X-ray photons with outer shell electrons.Some photons may be absorbed and re-emitted at lowerenergy (fluorescence) but, more importantly, some photonsare absorbed in a wavelength-dependent manner and immediately re-emitted at the same energy. Such a scatteredphoton gains an additional imaginary component to itsphase, indicating that it is being retarded compared to anormally scattered photon. Accordingly, the atomic formfactors of heavy atoms should be separated into severalcomponents (eqn igure 4 Graphical evaluation of a phase angle. (a) Phase circle or Argand diagrams showing observed amplitudes from the native (FP) and a derivatizedform of a protein (FPH’) in the complex plane. The phase angle can assume two different values (A or B) and, thus, the phase ambiguity cannot be resolved bya single derivative. (b) With information from two isomorphous derivatives (FPH’ and FPH’’) it is possible to unambiguously assign a phase value by threeintersecting phase circles (B).4NATURE ENCYCLOPEDIA OF LIFE SCIENCES / & 2004 Nature Publishing Group / www.els.net
Macromolecular Structure Determination by X-ray CrystallographyThe differences in intensities (Bijvoet differences) and inphase shifts (retardation) can be utilized to overcome thephase problem. The differences in anomalous amplitudesare usually considerably smaller than those obtained fromMIR and therefore MAD experiments require a tunablesynchrotron radiation source to optimize the signal andimprove accuracy in measuring individual amplitudes bymore sensitive detectors. Ab initio phasing methods arebased upon the analysis of amplitude triplet and quadruplet inequalities, maximum entropy, or phase averagingrequiring prior knowledge about molecular shape andcrystal packing. For very large structures with more than10 000 atoms the phase problem remains a serious obstacleeven with novel computational approaches. Macromolecular structure solution from first principles cannot yet berun as a service as in small-molecule crystallography.However, structure determination is increasingly facilitated through molecular replacement, whereby experimentalX-ray amplitudes are phased with complementary dataderived from an ever growing number of homologousstructures, cryo-electronmicroscopic molecular envelopes,and, to a lesser extent, structures determined by NMR.InstrumentationIn structural biology laboratories, X-radiation is generatedunder high vacuum by bombarding a copper or molybdenum target with electrons (accelerated at 50 kV). The deceleration of electrons by the copper anode generates anelectromagnetic spectrum consisting of a Bremsstrahlungcontinuum as well as two sharp peaks, which are due totransitions in the discrete electronic energy levels of thecopper. Monochromatic radiation is obtained by passingthe Bremsstrahlung through a nickel filter and a system ofplatinum-coated mirrors.In recent years, synchrotrons have had a major impacton the analysis of macromolecular structure. Synchrotronrings (and other storage rings) are large devices in whichelectrically charged particles circulate at close to the speedof light. The charged particles generate electromagneticradiation when they are diverted from a straight path by amagnetic field generated by a bending magnet. Inserteddevices such as multipole wiggler magnets or undulatorsfurther modify the path of the electrons (or positrons) andallow modification of the X-ray wavelength. The wavelength can now be selected to reduce radiation damage ortuned to meet specific attributes of the biological sample orbound ligands. This has been particularly successful inutilizing anomalous diffraction characteristics (or X-rayfluorescence) of heavier chemical elements such as Se, Fe,Zn, Cu, etc.Although protein or nucleic acid crystals are usuallyonly fractions of a millimetre in size, they contain 1012 –1014crystallographically ordered molecules. The diffractionpattern arising from such tiny crystals is imaged by proportional counters, X-ray sensitive films or imaging platesor, more directly, by electronic readout devices (chargecoupled device, CCD). Installation of electronic data collection devices resulted in a dramatic increase in data acquisition and processing speeds by orders of magnitude,reducing the experimentation time from days to minutes.Crystallization and StructureDeterminationStructure determination is a complicated, involved processconsisting of several crucial steps with potential shortfallsthat must be overcome. The rate-limiting step in macromolecular crystallographic studies is the production ofsingle crystals. Crystallization is achieved by slowly bringing the sample from a state of supersaturation to the crystalline state, avoiding nonspecific aggregation. This isachieved by a variety of methods such as vapour diffusion,(micro-)batch crystallization, (micro-)dialysis or free interface diffusion. The crystallization process is affected bysample saturation, concentration of precipitants and ionicstrength, buffer concentration and pH, temperature, andthe use of detergents and other organic additives. It is crucial to approach the nucleation point slowly and reproducibly. In some cases, seeding with previously growncrystals
Determination by X-ray Crystallography Joachim Jaeger, Wadsworth Center, Albany, New York, USA X-ray diffraction is a well-established method to elucidate the atomic structure of single-crystal macromolecules. An image of the macromolecule forming the crystal cannot be
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