Note: Intro -- Biological Small Angle Scattering -- Copyright -- Preface -- Contents -- Acknowledgments -- Part 1. Introduction -- 1. Introduction -- Part 2. Theory of Small Angle Scattering -- 2. Theoretical Background -- 2.1 Introduction -- 2.2 Scattering Basics -- 2.3 Multi-Scatterer Systems: The Debye Equation -- 2.4 The Pair Distance Distribution Function, P(r) -- 2.5 The Concept of Contrast in Solution Scattering -- 2.6 Resolution and Information Content -- 2.7 Summary -- 3. Quantities Directly Measurable by Scattering -- 3.1 Introduction -- 3.2 Invariants -- 3.2.1 Molecular Mass from Intensity at the Origin -- 3.2.2 Radius of Gyration Rg: Low Angular (Guinier) Region -- 3.2.3 The Guinier Approximation -- 3.2.4 The Porod Invariant, Q -- 3.2.5 Particle Volume, V or Vp -- 3.2.6 Maximum Particle Dimension, Dmax -- 3.2.7 Correlation Length -- 3.2.8 Remaining Invariants -- 3.3 Global Characteristics of the I(q) Curve -- 3.3.1 Intermediate Angular Region (or Shape Region) -- 3.3.2 The Porod Region -- Net scattering comes primarily from surfaces -- Asymptotic scattering varies as q-4 -- Particle surface area, S -- Volume of correlation, Vc -- 3.4 Comparison of Invariants -- 3.5 The Kratky Plot Distinguishes Globularity and Flexibility -- 3.6 Summary -- 4. Shape Reconstructions from Small Angle Scattering Data -- 4.1 Calculating Scattering Profiles from Three-Dimensional Models -- 4.1.1 Debye Equation -- 4.1.2 Gaining a Feel for the Spherical Harmonic Function -- 4.1.3 Spherical Harmonic Representation of Envelopes -- 4.1.4 Expansion of the Structure Factor Equation in Spherical Harmonics -- 4.1.5 Zernicke Polynomial Expansion -- 4.1.6 Solvent Considerations -- 4.2 Ab Initio Modeling -- 4.2.1 Modeling by Simple Shapes -- 4.2.2 Simple Model Examples -- 4.2.3 Envelope Fitting Using Analytical Functions. , 4.2.4 Envelope Fitting Using the Sum of Simple Volumes -- 4.3 Flexible Fitting -- 4.4 Rigid Body Modeling -- 4.5 Docking Algorithms -- 4.6 Mixtures -- 4.6.1 Principal Component Analysis and SVD -- 4.7 Ensembles -- 4.8 Hybrid Modeling -- 4.9 Summary -- Part 3. Practical Aspects of Small Angle Scattering -- 5. Before the Beamtime -- 5.1 Sample Production -- 5.2 Buffer Choice and Matching -- 5.3 Sample Optimization -- 5.4 Transport of the Sample -- 5.5 Practical Preparations before Data Collection -- 5.6 Quality Control Checks -- 5.7 Contrast Matching for X-Ray and Neutron Cases -- 5.8 Summary -- 6. Making the Best Use of Beamtime -- 6.1 Sample-to-Detector Distance -- 6.2 Instrument Calibration -- 6.3 Sample Concentration -- 6.4 Number of Exposures/Exposure Time -- 6.5 Image Integration -- 6.6 Buffer Collection and Subtraction -- 6.7 Initial Parameter Evaluation -- 6.8 The Guinier Plot -- 6.9 Estimating the Radius of Gyration, Rg -- 6.10 Calculating the Pair Distance Distribution Function, P(r) -- 6.11 Estimating Forward Scattering, I(0), and Maximum Dimension, Dmax -- 6.12 Assessing Flexibility -- 6.13 Estimating Volume and Molecular Weight -- 6.14 Evaluating Radiation Damage and Concentration Dependence -- 6.15 Assessing Accuracy of Buffer Subtraction -- 6.16 Summary -- 7. Examples of Data Collection and Processing -- 7.1 Sample -- 7.2 Data -- 7.3 Checking Buffer Blanks -- 7.4 Avoiding Radiation Damage -- 7.5 Qualitative Comparison of Concentrations -- 7.6 Using Guinier Plots To Detect Interparticle Interactions and Calculate Rg and I(0) -- 7.7 Calculating P(r) and Dmax -- 7.8 Assessing Flexibility -- 7.9 Checking for Accurate Buffer Subtraction -- 7.10 Zero Extrapolation -- 7.11 Extracting Structural Information -- 7.12 Summary -- 8. Instrumental and Experimental Considerations -- 8.1 Detector Considerations -- 8.2 Integration. , 8.3 Limitations on Minimum q Resolution -- 8.4 Desmearing -- 8.5 Signal-to-Noise Considerations -- 8.6 Zero Extrapolation -- 8.7 Summary -- 9. SAXS Instrumentation -- 9.1 Laboratory SAXS -- 9.1.1 Laboratory X-Ray Sources -- 9.1.2 Laboratory SAXS Instruments -- 9.2 Synchrotron SAXS -- 9.2.1 Synchrotron X-Ray Sources -- 9.2.2 Synchrotron Beamlines -- 9.3 Free Electron Laser X-Ray Sources -- 9.4 Sample Handling -- 9.4.1 Capillary Sample Holders -- 9.4.2 Automated Sample Handling -- 9.4.3 Specialized Sample Cells -- 9.4.4 Microfluidics -- 9.5 Detectors -- 9.5.1 Film and Image Plates -- 9.5.2 CCD Detectors -- 9.5.3 Mixed Mode Pixel Area Detectors -- 9.5.4 The Beamstop -- 9.6 Data Acquisition and Analysis Software -- 9.7 Instrumentation for Time-Resolved Studies -- 9.7.1 Stopped-Flow Mixers -- 9.7.2 Continuous-Flow Mixers -- 9.7.3 Microfluidic Implementations -- 9.7.4 Combining Microfluidics and X-Ray Microbeams -- 9.8 Summary -- 10. Distinct Instrumental Approaches to SAXS -- 10.1 SEC-SAXS -- 10.1.1 Application to Soluble Proteins -- Ion-exchange chromatography SAXS -- 10.1.2 Application to Membrane Protein Systems -- 10.2 Time-Resolved SAXS -- 10.3 High-Throughput SAXS -- 10.3.1 Sample Handling -- 10.3.2 Data Acquisition and Analysis -- 10.3.3 Applications of High-Throughput SAXS -- Crystallization -- Mapping of macromolecular conformation -- Rapid sample characterization -- 10.4 Summary -- 11. SANS -- 11.1 X-Rays and Neutrons -- 11.2 Neutron Sources -- 11.3 The Technique of Contrast Variation -- 11.4 Applications of Neutron Scattering -- 11.5 SANS Beamlines -- 11.6 Summary -- Part 4. Applications Past, Present, and Future -- 12. Examples of Biological Small Angle Scattering -- 12.1 The Use of Contrast Matching -- 12.1.1 The Neutron Case -- 12.1.2 The X-Ray Case -- 12.2 Time-Resolved Studies at Synchrotrons and XFELs. , 12.3 SAXS Providing Information Missing with Other Structural Techniques -- 12.4 Putting Complexes in Context -- 12.5 Functional Changes -- 12.6 Protein-Ligand Interactions -- 12.7 Dynamical Systems -- 12.8 Systems with Limited or No Structural Information -- 12.9 Intrinsically Disordered Proteins -- 12.10 Summary -- 13. Developments on the Horizon -- 13.1 The Impact of XFELs -- 13.1.1 Time-Resolved Applications -- 13.1.2 Snapshot SAXS -- 13.2 Working with Cryocooled Samples -- 13.3 Anomalous or Resonant Scattering in SAXS -- 13.4 Summary -- 14. Pushing the Envelope -- 14.1 Introduction -- 14.2 Retrieving Three-Dimensional Structure Factors from One-Dimensional Solution Scattering Data -- 14.3 Application to Real Data -- 14.4 Summary -- Epilogue -- Appendix -- A.1 The Structure Factor Equation -- A.2 Publication Guidelines -- A.3 Troubleshooting -- Acronyms (Excluding Sample Names, Facilities, and Beamlines) -- Glossary of Significant Terms -- Major Variables Defined -- References -- Index.

Note: Intro -- Contents -- Preface -- Chapter 1. Introduction -- 1.1 What Is X-ray Crystallography? -- 1.2 A Quick Look at Protein Crystals -- 1.3 Noncrystalline Specimens -- 1.4 Summary -- Further Reading -- Chapter 2. A Physical Understanding of Diffraction -- 2.1 What Is Diffraction? -- 2.2 Diffraction from One-Dimensional Crystals -- 2.3 Reconstructing Images from Diffraction Patterns -- 2.4 Summary -- Further Reading -- Chapter 3. Diffraction from Three-Dimensional Crystals -- 3.1 The Electron Density Function in Three Dimensions -- 3.2 Calculating the Diffraction Pattern from a Known Structure -- 3.3 Summary -- Further Reading -- Chapter 4. Phase Determination by Isomorphous Replacement -- 4.1 Measuring the Phases -- 4.2 MAD Phasing -- 4.3 Fitting Models to Experimental Electron Density Maps -- 4.4 Summary -- Further Reading -- Chapter 5. The Patterson Function -- 5.1 Definition of the Patterson Function -- 5.2 Using the Patterson Function to Locate Atoms -- 5.3 Summary -- Further Reading -- Chapter 6. Phasing with Partially Known Structures -- 6.1 Difference Fourier Maps -- 6.2 Molecular Replacement -- 6.3 Summary -- Further Reading -- Chapter 7. Crystallographic Refinement -- 7.1 Refinement Improves the Model -- 7.2 Least-Squares Refinement -- 7.3 Summary -- Further Reading -- Glossary -- A -- B -- C -- D -- E -- F -- H -- I -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Z.