Keywords:
Ultrastructure (Biology).
;
Molecular structure.
;
Fourier transformations.
;
Imaging systems in biology.
;
Cytology -- Experiments.
;
Molecular biology -- Experiments.
;
Biology -- Experiments.
;
Electronic books.
Description / Table of Contents:
Imaging of Biological Materials presents the four most important approaches to the imaging of biological structures: crystallography, non-crystallographic diffraction, optical microscopy, and electron microscopy.
Type of Medium:
Online Resource
Pages:
1 online resource (397 pages)
Edition:
1st ed.
ISBN:
9780199930722
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=916055
DDC:
571.6/33
Language:
English
Note:
Cover -- Contents -- Preface -- Notes for the Reader -- PART ONE: Fundamentals -- 1. On the Scattering of Electromagnetic Radiation by Atoms andMolecules -- 1.1 What is electromagnetic radiation? -- 1.2 Atoms are electrically polarized by electromagnetic radiation -- 1.3 Oscillating dipoles emit electromagnetic radiation -- 1.4 The electrons in atoms and molecules scatter X-rays as though they were unbound -- 1.5 The scattering of X-rays by molecules depends on atomic positions -- 1.6 Radiation detectors measure energy, not field strength -- 1.7 If the radiation being scattered is unpolarized, the polarization correction depends only on scattering angle -- 1.8 The coherence length of the radiation used in scattered experiments affects the accuracy with which I[sub(d)] can be measured -- 1.9 Measurement accuracy also depends on transverse coherence length -- Problems -- Appendix 1.1 Exponential notation, complex numbers, and Argand diagrams -- Appendix 1.2 The polarization correction for unpolarized radiation -- 2. Molecular Scattering and Fourier Transforms -- 2.1 F(S) is a function of three angular variables -- 2.2 Fourier series are a useful way to represent structures -- 2.3 In the limit of d = & -- #8734 -- , the Fourier series becomes the Fourier transformation -- 2.4 The Great Experiment -- 2.5 The shift theorem leads to a simple expression for the scattering of molecules -- 2.6 The scaling theorem: Big things in real space are small things in reciprocal space -- 2.7 The square wave and the Dirac delta function -- 2.8 Multiplication in real and reciprocal space: The convolution theorem -- 2.9 Instrument transfer functions and convolutions -- 2.10 The autocorrelation theorem -- 2.11 Rayleigh's theorem -- Problems -- 3. Scattering by Condensed Phases -- 3.1 The forward scatter from macroscopic samples is 90& -- #176.
,
out of phase with respect to the radiation that induces it -- 3.2 Scattering alters the phase of all the radiation that passes through a transparent sample -- 3.3 Phase changes are indistinguishable from velocity changes -- 3.4 Polarizabilities do not have to be real numbers -- 3.5 Atomic polarization effects are small -- 3.6 The frequency dependence of polarizabilities can be addressed classically -- 3.7 When the imaginary part of & -- #945 -- is large, energy is absorbed -- 3.8 The refractive index of substances for X-rays is less than 1.0 -- 3.9 The wavelength dependences of the processes that control light and X-ray polarizabilities are different -- 3.10 On the frequency dependence of atomic scattering factors for X-rays -- 3.11 Real X-ray absorption and dispersion spectra do not look the way classical theory predicts -- 3.12 The imaginary component of f can be determined by measuring mass absorption coefficients -- 3.13 Scattering can be described using scattering lengths and cross sections -- 3.14 Neutron scattering can be used to study molecular structure -- 3.15 Electrons are strongly scattered by atoms and molecules -- 3.16 Electrons are scattered inelastically by atoms -- Problems -- Appendix 3.1 Forward scatter from a thin slab -- Appendix 3.2 A classical model for the motion of electrons in the presence of electromagnetic radiation -- Appendix 3.3 Energy absorption and the imaginary part of & -- #945 -- -- PART TWO: Crystallography -- 4. On the Diffraction of X-rays by Crystals -- 4.1 The Fourier transform of a row of delta functions is a row of delta functions -- 4.2 Sampling in reciprocal space corresponds to replication in real space (and vice versa) -- 4.3 Crystals can be described as convolutions of molecules with lattices -- 4.4 Lattices "amplify" Fourier transforms.
,
4.5 The Nyquist theoremtells you how often to sample functions when computing Fourier transforms -- 4.6 Lattices divide space into unit cells -- 4.7 The minimal element of structure in any unit cell is its asymmetric unit -- 4.8 The transform of a three-dimensional lattice is nonzero only at points in reciprocal space that obey the von Laue equations -- 4.9 The Fourier transforms of crystals are usually written using unit cell vectors as the coordinate system -- 4.10 Bragg's law provides a second way to describe crystalline diffraction patterns -- 4.11 Von Laue's integers are Miller indices -- 4.12 Ewald's construction provides a simple tool for understanding crystal diffraction -- Problems -- Appendix 4.1 The Bravais lattices -- Appendix 4.2 On the relationship between unit cells in real space and unit cells in reciprocal space -- 5. On the Appearance of Crystalline Diffraction Patterns -- 5.1 Diffraction data are collected from macromolecular crystals using the oscillation method -- 5.2 Measured intensities must be corrected for systematic error -- 5.3 Radiation damage kills crystals -- 5.4 Diffraction patterns tend to be centrosymmetric -- 5.5 Anomalous diffraction can provide useful information about the chemical identities of atoms in electron density maps -- 5.6 Anomalous diffraction effects can be used to determine the absolute hand of chiral molecules -- 5.7 Crystal symmetry results in reciprocal space symmetry -- 5.8 Real crystals are not perfectly ordered -- 5.9 Disorder weakens Bragg reflections -- 5.10 Disorder makes crystals scatter in directions that are not allowed by von Laue's equations -- 5.11 Thermal diffuse scatter need not be isotropic -- 5.12 Average B-factors can be determined directly from diffraction data -- 5.13 Most crystals are mosaic.
,
5.14 A single crystal structure can reveal the alternative conformations of a macromolecule that is polymorphic -- Problems -- Appendix 5.1 Debye-Waller factors and diffuse scattering -- Appendix 5.2 Correlated motions and diffuse scatter in one dimension -- Appendix 5.3 Random walks in two dimensions -- 6. Solving the Phase Problem -- 6.1 The phases of reflections are measured by comparing them to a standard -- 6.2 Macromolecular diffraction patterns can be phased by adding heavy atoms to crystals -- 6.3 The number of high-Z atoms per unit cell needed for phasing is small -- 6.4 The heavy atom isomorphous replacement strategy for phasing requires the comparison of intensities measured from different crystals -- 6.5 Anomalous data can also provide phase information -- 6.6 Patterson functions display the interatomic distances and directions of a crystal -- 6.7 Macromolecular crystal structures cannot be solved using Patterson functions alone -- 6.8 Heavy atom sites in derivatized crystals can be located using difference Pattersons -- 6.9 Atomic coordinates can be deduced from the Harker sections of the Patterson functions -- 6.10 Multiple-wavelength anomalous diffraction combines anomalous and heavy atom phase determination in a single experiment -- 6.11 Experimental error complicates the experimental determination of phases -- 6.12 Experimental phase data specify phase probability distributions -- 6.13 The impact of phase errors on electron density maps can be controlled -- 6.14 The likelihood that the experiments done to phase a diffraction pattern have produced reliable data can be assessed statistically -- 6.15 Diffraction patterns can be phased by molecular replacement -- 6.16 Molecular replacement searches can be divided into a rotational part and a translational part -- Problems.
,
Appendix 6.1 Heavy atom difference Pattersons and anomalous difference Pattersons -- 7. Electron Density Maps and Molecular Structures -- 7.1 Experimental electron densitymaps display the variation in electron density within the unit cell with respect to the average -- 7.2 Electron density maps are contoured in units of sigma -- 7.3 The point-to-point resolution of an electron density map is roughly 1/|S|[sub(max)] -- 7.4 How high is high enough? -- 7.5 Macromolecular electron density maps having resolutions worse than ~3.5 & -- #197 -- are difficult to interpret chemically -- 7.6 Solvent may be visible in macromolecular electron density maps -- 7.7 Initial models must be refined -- 7.8 R-factors are used to measure the consistency of molecular models with measured diffraction data -- 7.9 Free-R is useful tool for validating refinements -- 7.10 Phases rule -- 7.11 Regionswhere models do not correspond to electron densitymaps can be identified using difference electron density maps -- 7.12 Experimental electron density maps can be improved by phase modification and extension -- 7.13 Solvent flattening and the Nyquist theorem -- 7.14 Let the buyer beware -- Problems -- Appendix 7.1 The inverse Fourier transform of the spherical aperture function -- Appendix 7.2 Estimating the R-factor of crystal structures that are perfect nonsense -- Appendix 7.3 The difference Fourier -- PART THREE: Noncrystallographic Diffraction -- 8. Diffraction from Noncrystalline Samples -- 8.1 X-ray microscopy can be done without lenses -- 8.2 The Fourier transform of a projection is a central section -- 8.3 Continuous transforms can be inverted by solvent flattening -- 8.4 Can the structures of macromolecules be solved at atomic resolution by X-ray imaging? -- 8.5 Solution-scattering patterns provide rotationally averaged scattering data.
,
8.6 Solution-scattering experiments determine length distributions and vice versa.
Permalink