🧪Biophysical Chemistry Unit 10 – Crystallography & Microscopy Techniques

Fundamentals of Crystallography

• Crystallography studies the arrangement of atoms in solid materials, particularly in crystalline solids
• Crystals are solid materials with a highly ordered microscopic structure, where atoms, molecules, or ions are arranged in a repeating pattern
• The smallest repeating unit of a crystal structure is called the unit cell, which contains all the structural information necessary to build the entire crystal
• Crystals can be classified into seven crystal systems based on their symmetry: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic
• The study of crystallography involves understanding the internal structure of crystals, their symmetry, and how this relates to their physical properties (optical, electrical, and mechanical)
• Crystallography plays a crucial role in various fields, including materials science, chemistry, physics, and biology, as it helps in understanding the structure-property relationships of materials
• The main techniques used in crystallography include X-ray diffraction, neutron diffraction, and electron diffraction, which provide information about the atomic arrangement within crystals

Crystal Structure and Symmetry

• Crystal structure refers to the unique arrangement of atoms in a crystal, which is determined by the unit cell parameters and the positions of atoms within the unit cell
• Symmetry is a fundamental concept in crystallography, describing the periodic repetition of structural features in a crystal
• There are four types of symmetry elements in crystals: rotation axes, mirror planes, inversion centers, and translation vectors
• The combination of symmetry elements present in a crystal defines its space group, of which there are 230 possible unique arrangements
• Bravais lattices are the 14 distinct three-dimensional arrangements of points that can fill space without gaps or overlaps, and they form the basis for describing crystal structures
• Miller indices (hkl) are used to describe the orientation of planes and directions within a crystal, providing a convenient way to identify and analyze specific structural features
• The symmetry of a crystal often dictates its physical properties, such as cleavage planes, optical properties (birefringence), and electrical properties (piezoelectricity)
• Understanding crystal symmetry is essential for interpreting diffraction patterns and determining the atomic structure of materials

X-ray Diffraction Principles

• X-ray diffraction (XRD) is a powerful technique for determining the atomic structure of crystalline materials
• It relies on the interaction between X-rays and the electrons in a crystal, resulting in a diffraction pattern that contains information about the crystal structure
• Bragg's law ($n\lambda = 2d\sin\theta$) describes the conditions necessary for constructive interference of X-rays scattered by a crystal, where $n$ is an integer, $\lambda$ is the wavelength of the X-rays, $d$ is the spacing between crystal planes, and $\theta$ is the angle of incidence
• The intensity of the diffracted X-rays depends on the type and arrangement of atoms in the crystal, as well as the structure factor, which takes into account the scattering power of individual atoms and their positions within the unit cell
• Single-crystal XRD is used to determine the complete three-dimensional structure of a crystal, while powder XRD is used for phase identification and quantitative analysis of polycrystalline materials
• The Ewald sphere is a geometric construction used to visualize the conditions necessary for diffraction, relating the wave vectors of the incident and diffracted X-rays to the reciprocal lattice of the crystal
• Fourier transforms are used to convert the diffraction pattern from reciprocal space to real space, enabling the determination of the electron density distribution and, ultimately, the atomic positions within the crystal

Protein Crystallization Methods

• Protein crystallization is the process of obtaining well-ordered protein crystals suitable for X-ray diffraction studies, which is crucial for determining the three-dimensional structure of proteins
• The main challenge in protein crystallization is finding the right conditions that promote the formation of large, single crystals while maintaining the native structure and function of the protein
• Vapor diffusion is the most common method for protein crystallization, where a droplet containing the protein solution is equilibrated against a reservoir containing a higher concentration of precipitant
  • Hanging drop and sitting drop are two variations of the vapor diffusion method, differing in the orientation of the protein droplet relative to the reservoir
• Batch crystallization involves directly mixing the protein solution with the precipitant solution, allowing crystals to form over time
• Dialysis is another method where the protein solution is separated from the precipitant solution by a semi-permeable membrane, allowing gradual changes in the protein environment
• Seeding techniques, such as microseeding and macroseeding, involve introducing small crystals or crystal fragments into a new protein solution to promote crystal growth
• The choice of precipitant, buffer, and additives (salts, organic molecules) is critical for successful protein crystallization, and screening a wide range of conditions is often necessary to identify the optimal crystallization conditions
• Once protein crystals are obtained, they are harvested, cryoprotected, and flash-frozen in liquid nitrogen for data collection using X-ray diffraction

Data Collection and Processing

• Data collection in crystallography involves exposing a crystal to an X-ray beam and recording the resulting diffraction pattern using a detector
• Modern X-ray sources for crystallography include rotating anode generators and synchrotron facilities, which provide high-intensity, monochromatic X-rays
• Goniometers are used to precisely control the orientation of the crystal relative to the X-ray beam, allowing the collection of a complete dataset that covers all unique reflections
• Cryogenic data collection, where crystals are maintained at liquid nitrogen temperatures, helps to minimize radiation damage and improve data quality
• Data processing involves several steps, including indexing (determining the unit cell parameters and crystal orientation), integration (measuring the intensities of individual reflections), and scaling (merging and normalizing the data from multiple measurements)
• Data quality is assessed using various metrics, such as resolution, completeness, redundancy, and signal-to-noise ratio ($I/\sigma(I)$)
• The processed data, consisting of a list of reflections and their associated intensities, is used for structure determination and refinement

Structure Determination and Refinement

• Structure determination is the process of obtaining an atomic model of the molecule (protein) from the diffraction data
• The phase problem, which arises from the inability to directly measure the phases of the diffracted X-rays, must be solved to determine the structure
• Methods for solving the phase problem include molecular replacement (using a known similar structure as a starting model), isomorphous replacement (introducing heavy atoms into the crystal), and anomalous scattering (exploiting the wavelength-dependent scattering of certain atoms)
• Once initial phases are obtained, an electron density map can be calculated using Fourier synthesis, which reveals the shape of the molecule and allows the building of an atomic model
• Structure refinement involves iteratively adjusting the atomic model to improve its agreement with the observed diffraction data, while maintaining reasonable geometry and conforming to prior knowledge about the molecule
• Refinement typically involves minimizing a target function that includes terms for the difference between observed and calculated structure factors, as well as geometric restraints (bond lengths, angles, and torsions)
• The quality of the refined structure is assessed using various validation tools, such as the Ramachandran plot (for proteins), clash scores, and B-factors (atomic displacement parameters)
• The final refined structure provides valuable insights into the function, interactions, and mechanisms of the studied molecule, and can be used for further studies in drug design, enzyme engineering, and understanding biological processes

Microscopy Basics

• Microscopy is a technique used to observe objects that are too small to be seen with the naked eye, providing valuable insights into the structure and function of biological systems
• The two main types of microscopes used in biophysical research are light microscopes and electron microscopes
• Light microscopes use visible light and a system of lenses to magnify the image of a specimen
  • The resolution of a light microscope is limited by the wavelength of light (around 200 nm), which determines the smallest features that can be distinguished
• Electron microscopes use a beam of electrons instead of light, allowing for much higher resolution (down to a few angstroms) due to the shorter wavelength of electrons
  • Transmission electron microscopes (TEM) and scanning electron microscopes (SEM) are the two main types of electron microscopes
• Sample preparation is crucial for microscopy, and often involves fixation (preserving the structure), dehydration (removing water), and staining (enhancing contrast)
• Fluorescence microscopy is a powerful technique that uses fluorescent probes to label specific molecules or structures within a sample, enabling the visualization of dynamic processes and interactions in living cells
• Confocal microscopy is an advanced light microscopy technique that uses point illumination and a pinhole to eliminate out-of-focus light, resulting in high-resolution, three-dimensional images of thick specimens
• Super-resolution microscopy techniques, such as STED (stimulated emission depletion) and STORM (stochastic optical reconstruction microscopy), allow for imaging beyond the diffraction limit of light, achieving resolutions of tens of nanometers

Advanced Microscopy Techniques

• Cryo-electron microscopy (cryo-EM) is a groundbreaking technique that allows the visualization of biological macromolecules in their native state, without the need for crystallization
  • Samples are rapidly frozen in liquid ethane, preserving their structure in a thin layer of vitreous ice
• Single-particle analysis is a cryo-EM technique used to determine the three-dimensional structure of macromolecular complexes by averaging many individual particle images
• Cryo-electron tomography (cryo-ET) enables the three-dimensional imaging of cellular structures and organelles by collecting a series of tilted images and reconstructing a tomogram
• Atomic force microscopy (AFM) is a scanning probe microscopy technique that uses a sharp tip to map the surface topography of a sample with nanometer resolution
  • AFM can also be used to measure mechanical properties, such as elasticity and adhesion, and to manipulate individual molecules
• Scanning tunneling microscopy (STM) is another scanning probe technique that uses a conductive tip to map the electronic structure of a sample surface with atomic resolution
• Total internal reflection fluorescence (TIRF) microscopy is a technique that selectively illuminates a thin layer near the sample surface, reducing background fluorescence and enabling the study of surface-associated events
• Förster resonance energy transfer (FRET) microscopy is a technique that measures the distance-dependent energy transfer between two fluorescent molecules, providing information about molecular interactions and conformational changes

Applications in Biophysical Research

• Crystallography and microscopy techniques have revolutionized our understanding of biological systems, from the atomic structure of proteins to the organization of cells and tissues
• X-ray crystallography has been instrumental in determining the structure of countless proteins, nucleic acids, and macromolecular complexes, providing insights into their function and guiding drug design efforts
  • Examples include the structure of DNA, the ribosome, and G protein-coupled receptors (GPCRs)
• Cryo-EM has emerged as a powerful alternative to crystallography, enabling the structure determination of large, dynamic, and heterogeneous complexes, such as viruses, membrane proteins, and molecular machines
• Fluorescence microscopy has transformed our understanding of cellular processes, allowing the visualization of protein localization, trafficking, and interactions in living cells
  • Applications include studying the dynamics of the cytoskeleton, membrane receptors, and signaling pathways
• Super-resolution microscopy has revealed previously unseen details of cellular structures, such as the organization of the nuclear pore complex and the architecture of the synapse
• AFM has been used to study the mechanical properties of biomolecules and cells, such as the unfolding of proteins and the elasticity of cell membranes
• Combining multiple techniques, such as correlative light and electron microscopy (CLEM), provides a more comprehensive understanding of biological systems across different scales
• Advances in instrumentation, data analysis, and computational methods continue to push the boundaries of what can be studied using crystallography and microscopy, opening new avenues for discovery in biophysical research