C7270 Biological X-Ray Crystallography and Cryo-Electron Microscopy

Přírodovědecká fakulta
podzim 2020
3/0/0. 3 kr. (plus ukončení). Ukončení: zk.
Vyučováno online.
doc. Mgr. Pavel Plevka, Ph.D. (přednášející)
doc. Mgr. Pavel Plevka, Ph.D.
Ústav biochemie - Chemická sekce - Přírodovědecká fakulta
Dodavatelské pracoviště: Výzkumná skupina Pavla Plevky - Centrum strukturní biologie - Středoevropský technologický institut
St 14:00–16:50 Pouze distančně
This course is aimed at students of general biology, molecular biology and genetics, specialised biology, biochemistry interested in macromolecular structure determination. This lecture series is complemented by practical series “Structural Biology Methods Practical“. The two courses are supposed to be read during the same semester.
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
Cíle předmětu
This course aims to provide understanding of theoretical background and practical aspects of X-ray crystallography (5 lectures) and cryo-electron microscopy (cryo-EM) (7 lectures). Both X-ray crystallography and cryo-EM use the concepts of reciprocal space and Fourier transform to allow calculation of electron density maps that show shapes of macromolecules. Cryo-EM part of the course will benefit from the mathematical concepts introduced in preceding X-ray crystallography lectures. Students will learn methodological approaches allowing determination of macromolecular structures with atomic details.
Výstupy z učení
By the end of this course, students should be able to do the following:
• Understanding of principles allowing the use of X-ray crystallography, cryo-EM.
• Undestanding of theory behind:
o Interaction of waves with objects
o Approaches to resolve phase problem in crystallography
o Use of electrons to display objects with high magnification and fine detail
o Calculation of three-dimensional reconstruction from two-dimensional projections of an object
• Use of structural biology approaches to study molecular processes necessary for the existence of life.
• Students will be able to describe how structural methods allowed fundamental discoveries in biology such as:

Students will learn skills that will allow them to apply for jobs with local high-tech companies such as Tescan and FEI. Knowledge gained in the course can be used in both basic and applied research to study structures of macromolecules, their complexes, viruses, and cells.
  • Course Outline
  • Week 1: Introduction, crystals, symmetry, and the Theory of X-Ray Diffraction
  • o Introduction to the course
  • o Crystallizing a Protein
  • o Crystals and symmetry I.
  • o Asymmetric Unit; Point Groups; Crystal Systems; Characterization of the Crystals; Matthew’s coefficient
  • o Waves and Their Addition; Argand diagram; Exponential Terms
  • • Read chapters 1, 2, 3, 4 and 16 from “Principles of Protein X-Ray Crystallography“.
  • The Theory of X-Ray Diffraction by a Crystal
  • o A System of Two Electrons; Scattering by an Atom; Scattering by a Unit Cell; Scattering by a Crystal; Diffraction Conditions; Reciprocal Lattice and Ewald Construction
  • o o The Temperature Factor; Calculation of the Electron Density ρ(x y z); Comparison of F(hkl) and F(h ̄k ̄l ̄); Symmetry in the Diffraction Pattern; Integral Reflection Conditions for Centered Lattices; Intensity Diffracted by a Crystal; The Polarization Factor; Scattering by a Plane of Atoms; Choice of Wavelength, Size of Unit Cell, and Correction of the Diffracted Intensity
  • • Read chapter 4 from “Principles of Protein X-Ray Crystallography“.
  • Week 3: Isomorphous Replacement Method and Phase Improvement
  • o The Patterson Function; Convolution; The Isomorphous Replacement Method; Effect of Heavy Atoms on X-ray Intensities; Determination of the Heavy Atom Parameters from Centrosymmetric Projections; Parameters of Heavy Atoms Derived from Acentric Reflections; The Difference Fourier Summation
  • o Anomalous Scattering; The Anomalous Patterson Summation; Refinement of the Heavy Atom Parameters Using Preliminary Protein Phase Angles; Protein Phase Angles; The Remaining Error in the Best Fourier Map; The Single Isomorphous Replacement Method;
  • o The OMIT Map With and Without Sim Weighting; Solvent Flattening; Non-crystallographic Symmetry and Molecular Averaging; Histogram Matching; wARP: Weighted Averaging of Multiple-Refined Dummy Atomic Models; Further Considerations Concerning Density Modification
  • • Read chapter 5, 6, 7, and 8 from “Principles of Protein X-Ray Crystallography“.
  • Week 4: Anomalous Scattering in the Determination of the Protein Phase Angles and the Absolute Configuration and Molecular Replacement I.
  • o Protein Phase Angle Determination with Anomalous Scattering; Improvement of Protein Phase Angles with Anomalous Scattering; The Determination of the Absolute Configuration; Multiple- and Single-Wavelength Anomalous Diffraction (MAD and SAD);
  • o The Rotation Function;
  • • Read chapters 9 and 10 from “Principles of Protein X-Ray Crystallography“.
  • Week 5: Molecular Replacement II., Laue Diffraction, Refinement of the Model Structure, The Combination of Phase Information, Checking for Gross Errors and Estimating the Accuracy of the Structural Model.
  • o The Translation Function; AMORE; Rigid-Body Refinement;
  • o The Accessible Region of Reciprocal Space; The Multiple Problem; Unscrambling of Multiple Intensities; The Spatial Overlap Problem; Wavelength Normalization;
  • o The Mathematics of Refinement; The Principle of the Fast Fourier Transform Method; Specific Refinement Methods;
  • o Phase Information from Isomorphous Replacement; Phase Information from Anomalous Scattering; Phase Information from Partial Structure Data, Solvent Flattening, and Molecular Averaging; Phase Information from SAD
  • o R-Factors; The Ramachandran Plot; Stereochemistry Check; The 3D–1D Profile Method; Quantitative Estimation of the Coordinate Error in the Final Model;
  • • Read chapters 10, 12, 13, 14 and 15 from “Principles of Protein X-Ray Crystallography“.
  • Week 6: Electron Microscopy of Macromolecular Assemblies I.
  • o The Contrast Transfer Theory; Determination of the Contrast Transfer Function;
  • • Read chapter 2 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
  • Week 7: Electron Microscopy of Macromolecular Assemblies II.
  • o The Contrast Transfer Theory; Determination of the Contrast Transfer Function;
  • • Read chapter 2 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
  • Week 8: Electron Microscopy of Macromolecular Assemblies III.
  • o Computational Correction of the Contrast Transfer Function;
  • • Read chapter 2 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
  • Week 9: Multivariate Data Analysis and Classification of Images I.
  • o Alignment Methods; Averaging and Global Variance Analysis; Resolution; Validation of the Average Image;
  • o Theory of Correspondence Analysis; Classification
  • • Read chapters 3 and 4 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
  • Week 10: Multivariate Data Analysis and Classification of Images II.
  • o Theory of Correspondence Analysis; Classification; Principal Component Analysis
  • • Read chapters 3 and 4 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
  • Week 11: Three-Dimensional Reconstruction
  • o General Mathematical Principles; The Rationales of Data Collection: Reconstruction Schemes; Overview of Existing Reconstruction Techniques; Reference-Based Methods and Refinement; Contrast Transfer Function and Fourier Amplitude Correction; Resolution Assessment
  • • Read chapter 5 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
  • Week 12: Symmetry and a-symmetry of macromolecular objects
  • o Symmetry, Rotation Matrices, Employing Symmetry in Reconstruction Process, Masking
  • • Read chapter 7 from “Three-Dimensional Electron Microscopy of Macromolecular Assemblies”.
    povinná literatura
  • o Joachim Frank. (2010) “Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State”, 3rd edition; ISBN-13: 9780195182187; Oxford Scholarship Online
  • Jan Drenth. (2007) “Principles of Protein X-Ray Crystallography”, 3rd edition; ISBN: 978-0-387-33334-2; JSpringer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA
  • Trache A, Meininger GA. Atomic force microscopy (AFM); Curr Protoc Microbiol. 2008; Chapter 2.
Výukové metody
Course Format
In this course, you will be acquiring knowledge in two main ways: in the lectures and by home study (which means by reading the assigned materials and working on assignments and homeworks). Reading the material will give you a base of factual knowledge. It will also introduce you to the main theoretical points. The lectures then will reinforce your understanding of the material. The lectures will also introduce you to concepts and theories that are not covered by the readings. Class sessions will also be a space for discussions.

Learning suggestions
o Read the readings before the day for which they are assigned. This will help you to acquire knowledge gradually in small chunks.
o When reading summarize for yourself the main points from each paragraph. You can write these little summaries in the margins.
o Last but not least, you are very welcome to come to my office hours or to contact me if you have any questions.
Metody hodnocení
Grade will be based on the final exam. The exam will be a mixture of multiple choice and essay questions.
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Předmět je vyučován jednou za dva roky.
Předmět je zařazen také v obdobích podzim 2014, podzim 2015, podzim 2017.
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