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X-Ray Crystallography

Crystallography using X-rays is a highly effective non-destructive method for determining how molecules form the crystal. The X-ray crystallography technique utilizes the...

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X-Ray Crystallography
X-Ray Crystallography

Crystallography using X-rays is a highly effective non-destructive method for determining how molecules form the crystal. The X-ray crystallography technique utilizes the principles of X-ray diffraction in order to examine the specimen, however it’s conducted in a variety of directions, so it is possible that the 3-D structures of the sample can be constructed. It is a method that has been used to determine three-dimensional crystal structures of numerous substances, particularly biological ones.

If you consider X-ray difffraction (XRD) the 2D pattern of diffraction will come to mind for the majority. The most basic patterns that are generated by the X-ray crystallography process are 2D patterns of diffraction, however the major distinction in the process is that the samples are scanned in several directions. The diffraction patterns are put together and refined several times to analyze and reveal how the molecules of the samples are structured. It is possible to analyze extremely large or complex molecules and proteins are one of the most important examples.

Introduction

In 1895, Wilhelm Rontgen discovered x- rays. The nature of x-rays and whether they were actually electromagnetic radiation or particles, was a subject of debate up to 1912. If the idea of a wave was true, scientists knew that the wavelength of the light had to be in the range of one Angstrom (A) (10-8 cm). The measurement and diffraction of such tiny wavelengths will require a gradient having a spacing of the same magnitude like the intensity of the light.

The year 1912 was the time Max von Laue, at the University of Munich in Germany proposed that the atoms of crystal lattices had an ordered, periodic structure with interatomic distances of the range one A. In the absence of any evidence to back his assertion regarding the periodic arrangement of atoms within a lattice and further speculated that the structure of crystals could be used to diffuse the x-rays in the same way that the gradient of an infrared spectrometer, which can diffract light from infrared. The theory he proposed was founded on the following assumption that the atomic structure of crystals is regular and x-rays are electromagnetic radiation and the interatomic distances of a crystal is of the same scale as the x-ray light. Laue’s theories were confirmed by two researchers: Friedrich and Knipping, were able to capture the diffraction pattern that is associated with the x-ray radiation in crystals of CuSO45H2O . The technology of x-ray crystallography was birthed.

The arrangement of atoms must be organized and periodic arrangement in order for them to scatter the beams of x-rays. A set of mathematical calculations is utilized to generate the diffraction pattern specific to the particular arrangement of the atoms within that crystal. Crystallography using X-rays remains in use to this day as the principal instrument employed by scientists for studying how the structures and bonds properties of organic compounds.

Principles and Workings of X-Ray Crystallography

In the device the sample is placed to a goniometer which is used to place the crystal in specific positions in order to be studied from different angles. If the sample is not pure and the crystal’s structure isn’t clear The crystal sample must be cleansed prior to analysis.

The X-rays originate by an X-ray tube and then removed to be Monochromatic i.e. with a single wavelength. The crystal’s atoms reflect X-rays, and the beams of X-rays are scattered to the detector. Since they are scattered elastically they are able to absorb the same energy as incident X-rays directed at the crystal. This results in an 2D Diffraction design of the crystal in one direction.

If the pattern of diffraction isn’t clear, the sample might not be clean and should be filtered at this moment. Other factors can also hinder a diffraction pattern getting created. These include a tiny samples (needs to be less than 0.1 millimeters in all dimensions) or a distorted crystal structure, or the presence of internal imperfections, like cracks or cracks within the crystal.

In the event that the sample is determined to be safe, the analysis and Xray bombardment toward the crystal continues. The sample is rotated on the goniometer, causing the series of 2D Diffraction patterns are created from different areas that the crystal. The intensity of the light is recorded at each angle as a result. The end product is a multitude of 2D patterns of diffraction which correspond to various parts in the 3-dimensional structure. From this point, a computer-based approach analyzes the different Diffraction phases, angles, and intensities to create an electron density map for the samples. This map of electrons is then used to build anatomic models of the samples. The model is continuously adjusted to ensure it is precise and, once the final model of atomic structure has been created, the information is stored in the central database, which acts as a reliable source.

What is Diffraction?

Diffraction is a process that happens when light strikes an obstruction. Light waves can bend around the obstacle or, when a slit is present may pass between the slits. The resulting pattern of diffraction will reveal the areas that are subject to constructive interference when two waves interact in a phase relationship, and destructive interference, in which two waves interact outside of the phase. The process of calculating the phase differs can be explained by looking at the figure below.

In the diagram below, two waves, BD and AH are creating a gradient at an angle . This incidental wave BD travels further than AH by an amount of CD before it reaches the gradient. A scattered wave (depicted beneath the gradient) HF, is farther than the scattering wave DE by an amount of HG. Thus, the total distance between the paths AHGF BCDE and path AHGF BCDE will be CD – HG. To be able to observe a wave of high intensity (one caused by constructive interference) and the differences CD – HG must be equal to an integer amount of wavelengths that can be observed at an angle of that is psi. CD-HG = nl , which represents the frequency of light. Utilizing the basic trigonometric properties The following two equations are able to be drawn on the lines:

Diffraction

What is Bragg’s Law?

The x-ray beam is diffraction. beam happens when light is in contact in the cloud of electrons around the atoms in the crystal solid. Because of the periodic crystalline structure of a solid you can think of it as a sequence of planes that have an interplaner distance equal to. If an x-ray’s light hits the crystal’s surface at an angle ? certain portions of the light will be diffracted at the same distance from the solid (Figure 2.). The remaining light will penetrate the crystal, and certain portions of it will be absorbed by two atoms in the same plane. A portion of the light will be diffracted in an angle that is theta, while the rest will travel further inside the crystal. The process repeats across the various planes of the crystal. The beams of x-rays travel in various lengths before striking the different crystal planes and, after diffraction beams will be constructively interacting only if their path lengths differ by equivalent to an integer amount of wavelengths (just like the normal difffraction scenario earlier). In the diagram below, the difference between lengths of beams striking one plane as well as that hitting the second plane are similar to BG plus. Thus the two diffracted beams are likely to constructively interfer (be at a synchronized angle) only when both beams are BG+GF=nl . The basics of trigonometry tell us that the two beams are equivalent to each other using the interplaner distance multiplied by that of the angle’s sine of . So we get:

Bragg's Law

The equation is referred to as Bragg’s Law. The name comes from in honor of W. H. Bragg and his son W. L. Bragg who first discovered this geometric relation in 1912. The law of Bragg’s connects to the space between planes of crystals, and also angles of reflection to wavelength of the x-ray. The x-rays diffracted by the crystal must be in phase to transmit a signal. Only angles that meet the following conditions will be registered:

Bragg's Law

Components of X-Ray Crystallography

The major components of an xray instrument are the same as the optical instrumentation for spectroscopy. This includes an instrument to source light and a device that can select and limit the wavelengths that are used to measure and a holder for your sample, an instrument and a signal conversion device and readout. In the case of x-ray difffraction it is just a matter of a source the holder for the sample, and a signal readout/converter are needed.

1. The Source

X-ray tubes are a method to produce x-ray radiation within many analytical instruments. An evacuated tube is home to an tungsten filament, which functions as a cathode, in contrast to a bigger anode that is water-cooled and composed of copper and an aluminum plate. The plate could be constructed of all of the elements including chromium, tungsten silver, copper, rhodium cobalt, iron, and. The high-voltage is applied to the filament, and high-energy electrons are created. The machine requires some method to regulate the frequency and intensity of the light resulting from it.

The intensity of light is managed by adjusting how much current flowing through the filament. It is serving as a temperature control. The wavelength of light can be determined by setting the correct acceleration voltage for electrons. The voltage that is applied across the system determines the energy of electrons moving toward the cathode. X-rays are generated when electrons strike the target metal. Because light’s energy is proportional to its wavelength ( E=hc=h(1/l ) which controls the energy, it controls the length of the beam.

Components of X-Ray Crystallography

2. X-ray Filter

Filters and monochromators are used to create monochromatic x-ray light. This wavelength range is vital for calculations involving diffraction. For example zirconium filters can be utilized to eliminate unwanted wavelengths in a molybdenum metal target (see Figure 4.). The molybdenum metal target produces the x-rays at two wavelengths. A filter made of zirconium is a good choice to block the unwanted emission at wavelength Kb and allow the desired wavelength Ka to go through.

X-ray Filter

3. Needle Sample Holder

The sample holder of an x-ray diffractometer is just an instrument that holds the crystal while the x-ray diffractometer reads it.

4. Signal Converter

In x-ray diffraction the detector functions as an instrument that measures the number of photons which cross it. This counter provides an informational readout of the quantity of photons per unit of time. Below is an illustration of a typical x-ray difffraction unit, with all components labeled.

What is Fourier Transform?

In math in mathematics, the term “fourier transform” is used to describe Fourier transform refers to an action that transforms one real function to another. In the instance of FTIR it is the Fourier transform applies to a function within the time domain in order to transform it to the frequency domain. One method of thinking about this is drawing the illustration of music by recording it on a piece of paper. Each note is placed in the”sheet” domain “sheet” area. Notes of the same kind can be played. The act of playing notes is considered as the process of converting notes of their “sheet” domain to”sound” “sound” area. Each note played represents what’s on the paper but in a different manner. This is exactly that is what the Fourier transform process does to the recorded data of an Diffraction of x-rays. This is done to determine the electron density of crystal atoms in real space. These equations are able to be utilized in determining electron’s location:

Fourier Transform

In this case, p(xyz) represents the electron density formula where p(xyz) is the electron density function, and F(hkl) corresponds to the electron density value in the real world. Equation 1 describes what is known as the Fourier extension of the electron density functions. To find the formula F(hkl) the equation 1 has to be evaluated across all possible values of h, K, and l leading to equation 2. The resultant formula F(hkl) is typically expressed as a complex figure (as shown at equation 3.) with the F(q)| which is the size of the function, and ph being the component of the function.

What is Crystallization?

To run an experiment using x-rays it is necessary to first create crystals. In organometallic chemical chemistry, a reaction could be successful, but if there is no formation of crystals it’s impossible to identify the components. Crystals form by cooling slowly a supersaturated solution. This solution is created by heating a solution in order to reduce how much solvent is present, and to enhance the solubility of the compound of choice within the solvent. After it is prepared, the solution needs to be slowly cooled. 

A rapid temperature drop will result in the compound crashing into the solution capturing impurities and solvent within the newly created matrix. The process continues to cool until the formation of a seed crystal. The crystal is in which the solute will be released out of the solution to the solid phase. Solutions are usually placed in freezers (-78 oC) to ensure that all the substance has crystallized. One method to ensure the gradual cooling process in a -78 freezing is to put the container in which the compound is stored in a beaker of alcohol. 

The ethanol serves as an insulator of temperature, which will ensure an even diminution in the temperature difference between the flask as well as the freezer. After the crystals have formed it is crucial that they remain cool, because any energy addition could cause a disruption in the crystal’s lattice. This could result in poor diffraction data. The results of crystallization of an organometallic chromium compound can be seen in the following figure.

How to Mount the Crystal?

Due to the air-sensitivity in the majority of organometallic compounds, crystals are transported using the form of a highly viscous organic substance known as paratone oil (Figure 7 ). Crystals are removed from their Schlenks by squirting the tip of a spatula using paratone oil before gluing the crystal on the oil. While there is a possibility of exposure of the substances to water and air crystals are able to withstand greater exposure than solutions (of preserved protein) before being destroyed. Apart from helping to protect the crystalfrom damage, the paratone oil serves as a glue that binds it to needle.

What is Rotating Crystal Method?

To explain the periodic, three-dimensional nature of crystals The Laue equations are used:

a(cosθo–cosθ)=hλ——(10)

b(cosθo–cosθ)=kλ——-(11)

c(cosθo–cosθ)=lλ——–(12)

where a, b, and c represent the three main axes in the unit cell. however, o,?o represent the angle of radiation that is incident and ?,? represent the angles of diffracted radiation. Diffraction signals (constructive interference) occurs from the fact that h and l are integers. This method of rotating uses these equations. The X-ray radiation is projected onto the crystal as it spins around one cell’s axis. The beam hits on the surface of the crystal with a 90-degree angle. By using equation 1 we can see that if the angle is 90 degrees and costho is 0 degrees, then costho=0 . In order for the equation to be as true, we must set h=0assuming it is 90o . The three equations above are satisfied at different locations as the crystal rotates. This creates the diffractive design (shown in the picture below as multiple different h values). The cylindrical film is removed from the wrapper and then created. The following equation could be utilized to identify the length-axis on which the crystal rotated

Rotating Crystal Method

In this case, a defines the length and length of the axis it is the distance from zero to the h of concern where an estimate of the size and radius the company has and? represents the frequency of radiation used to generate x-rays. The first wavelength is easily determined However, the two other lengths require more effort and include changing the mounting of the crystal to ensure that it is rotated around the specific direction.

Rotating Crystal Method

X-ray Crystallography of Proteins

These crystals are thawed in liquid nitrogen before being transferred to the synchrotron, which is a high-powered variable sources of x-rays. They are positioned on a goniometer before being bombarded with beams of radiation. The data is collected when the crystal rotates an array of angles. The angle is determined by the crystal’s symmetry.

X-ray Crystallography of Proteins
This is a picture of a protein crystal mounted on a loop with respect to the UC Davis Structural Biology Lab;

Proteins are one of the numerous biological molecules that are utilized in an x-ray Crystallography research. They are involved in numerous ways in biology, typically catalysts of reactions, increasing the rate at which reactions occur. The majority of scientists employ x-ray crystallography to unravel the structures of proteins as well as to identify the what the functions of proteins, interactions with substrates and relationships with the other proteins and nucleic acid. Proteins may be co crystallized in these substrates or they could be absorbed in the crystal following the process of crystallization.

Protein Crystallization

Proteins can become crystals under certain conditions. These conditions are typically composed of buffers, salts, as well as precipitating agents. This is usually the most difficult part of the process of x-ray crystallography. A multitude of conditions, including pH, salts, buffer and other precipitating substances are incorporated with the protein to make the protein crystallize in the proper conditions. This is achieved with 96 well plates, each one containing a distinct condition and crystalsthat are formed over days weeks, days, or months. The images below show crystals of the APS Kinase D63N from Penicillium chrysogenum . They were taken in the Chemistry building at UC Davis after crystals formed over the course of about a week.

Applications of X-Ray Crystallography

In terms of application X-ray crystallography is employed in numerous fields of science. When it first became known as a method of study it was used primarily in basic science applications for measuring the dimensions of atoms, the lengths and various kinds of chemical bonds, the arrangement of atoms in materials, the differences between the materials on an atomic level as well as to determine the integrity of crystals and grain orientation, as well as the thickness of films, grain size and the roughness of interfaces between minerals and alloys.

Science has made significant progress since the beginning of time and, while these areas remain important in the study of new materials, it is commonly used to analyze the structure of many biological materials, vitamins drug molecules, thin-film substances as well as multi-layered substances. It is now one of the main methods to analyze a material when the structure is not known in the environmental, geological and chemical, material science and pharmaceutical industries (plus numerous others) because of its non-destructive properties and excellent accuracy and precision.

In the present, it is utilized to investigate specific ways to determine how the structure of the material, drug or chemical will behave with specific conditions. This has been especially useful in the pharmaceutical and proteomics sectors. A few of the areas that are now examined using X-ray crystallography are measuring thickness and size of film, finding specific crystal phase and orientations that aid in determining the catalytic capacity of materials as well as measuring the purity of a sample and determining how a substance may interact with particular proteins and how it could be improved, and analysing the way that the proteins interact with one another, studying microstructures and analysing the amino acids found in proteins that helps determine how catalytically active the enzyme is. These are only one of many examples that show the application of X-ray crystallography is widely used.

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