Lab: Crystals and Diffraction · for X-rays and two-dimensional patterns for three -dimensional crystals of atoms. In the second part of the lab, you will use the diffraction of laser

$Page 1: Lab: Crystals and Diffraction · for X-rays and two-dimensional patterns for three -dimensional crystals of atoms. In the second part of the lab, you will use the diffraction of laser$
Södertörns högskola Structural biochemistry X-raylab VT02

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Lab: Crystals and Diffraction Introduction

Clearly, no technique currently available rivals the potential precision of X-ray diffraction when applied to single crystals of molecules. However, determination of the three-dimensional structure of a molecule by diffraction techniques requires a regular periodic array of identical and identically-related molecules – in short, crystals. Some examples of protein crystals are shown (left). A crystal exhibits the highest degree of organization and under proper conditions, allows precise, atomic resolution structures to be determined. In the case of small molecules (few hundred Da), precisions of a few thousandths of an Å in coordinates and bond lengths and a few tenths of a degree in bond angles can be achieved although the precision in larger molecular system is somewhat less.

Due to the considerable theoretical and technical skills needed to collect the data and solve the structure, often sample preparation and crystal growth is overlooked. It is not uncommon that the expression, purification and crystallization of the molecule constitute half or more of the investment of the time, effort, and ingenuity of the entire structure determination project. The big problem is that crystal growing is as much an art as it is a science. In this lab, you will get some first-hand experience preparing protein crystals with the protein lysozyme.

While the procedure of macromolecular structure determination using X-ray diffraction techniques is in short rather complicated, the basic principles of diffraction are not and can be explored in the student laboratory. To minimize the potential hazards associated with using X-rays in a course lab, the basic principles of diffraction and structure determination can be illustrated by substituting visible light for X-rays and two-dimensional patterns for three -dimensional crystals of atoms. In the second part of the lab, you will use the diffraction of laser light to explore the relationship between real space and reciprocal space and use diffraction patterns to determine the dimensions of 2D unit cells.

X-ray Diffraction Laser Diffraction

Figure 2. Schematic diagrams comparing X-ray and laser diffraction

Figure 1. A selection of protein crystals from McPherson, 1989.


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Experiment 1. Crystallization of Hen Egg Lysozyme Introduction

Crystallization is a biochemical technique much older than X-ray diffraction itself and has been used as a way to isolate and purify proteins. The protein lysozyme from hen eggs is perhaps one of the most easily crystallizable proteins known. It is inexpensive and readily obtained in pure form (actually crystallization is a purification step!), which makes it ideal for our crystallization experiments. However for high-resolution X-ray diffraction, not just any

crystals will do. Since the intensity of the diffraction pattern is roughly proportional to the volume of the crystal and inversely proportional to the crystal unit cell volume (not smaller than one protein), X-ray diffraction analysis requires not only that the molecule crystallize, but also that the crystal be of substantial size for X-ray analysis. For example, proteins with a molecular weight of < 50 kDa, a crystal of 0.1 mm in all dimensions will allow the unit cell dimensions to be deduced, but a crystal of some 30-times the volume (0.3 mm per side) will be needed for collection of atomic resolution data.

The impetus for a molecule to crystallize is that under certain conditions, the crystal form is the thermodynamic state with lowest free energy, despite the entropic cost of ordering the molecules. The crystal state occurs when the number of attractive interactions (hydrogen bonds, salt bridges, hydrophobic interactions, etc.) are maximized and the repulsive interactions are minimized. Of course for biological molecules, another state is the soluble, aqueous hydrated state we are used to. In extremely concentrated solutions where there is insufficient water to maintain the hydration shell, the protein molecules have two options: aggregate as an amorphous (unordered) precipitate or crystallize. An amorphous precipitate corresponds to one local minimum in the protein’s phase diagram, populated when aggregation occurs too rapidly. If the local energy minimum is deep, the molecules may become kinetically trapped. However, sometimes the barrier is small and crystals may form from the amorphous precipitate. In general, the slow approach to inadequate solvation is best, allowing the molecules time to order themselves in a crystalline lattice. The strategy most often used in the crystallization of macromolecules is to bring them slowly to a state of minimum solubility and thus achieve a limited degree of supersaturation.

Protein solubility The crystallization of proteins is determined by both thermodynamic (solubility)

and kinetic (nucleation and growth) factors. The solubility behavior of macromolecules in solution is complex to say the least, with a number of possible minima as a function of many environmental variables (concentration, temperature, pH, …). As has long been recognized by biochemists, protein solubility (and activity) is strongly affected by other components of the solution. In very general terms all solutes can be classified by their effect on protein solubility and stability. Lyotropic solutes are those that stabilize the native form whereas chaotropic solutes destabilize it.

Figure 3. X-ray crystal structure of hen egg lysozyme


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Experimentally, the following lyotropic series (Hoffmeister series) has been determined and is generally applicable to most proteins:

Cations : Li+ > Na+ > K+ > NH4

+ > Mg2+ Anons : sulphate2- > phosphate2- > acetate >citrate3- > tartrate2- > bicarbonate- > chromate2- > chloride- > nitrate- >> chlorate- >

thiocyanate-

Organic solutes affect the dielectric of the medium and in general decrease the solubility of proteins. Ions can have different effects on proteins depending on concentration as can be seen from the graph above. At low concentrations they increase solubility (called salting in) whereas at high concentrations, they decrease solubility (salting out ). These effects are not completely understood, but can be thought of using the following picture. At low ionic strength, the protein is surrounded by an excess of ions of complementary (opposite) charge which increases the protein solubility. As salt concentration increases, the ions begin to compete with the protein for water until there is not sufficient water available to maintain the protein hydration and the protein becomes insoluble (i.e., aggregates or crystallizes). For a compact protein, solubility (S) is described by the equation:

)1(2ln

22

aDTRNeZ

Sκκ

+=

eq. 1 where Z is the charge of the protein, N is Avogradro’s number, D is the dielectric of the medium, R is the ideal gas constant, e is the elementary charge of an electron, a is the sum of the radii of the protein and the average of the supporting ions in solution. The constant κ is given by:

IDkT

Ne1000

8 2πκ = eq. 2

where I is the ionic strength of the solution given by:

Figure 4. The effect of ionic strength on protein solubility. Data are for the protein lysozyme taken from A.A. Green J. Biol. Chem. 95, 47-67, 1932.


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2

21

ii

i ZCI ∑= eq. 3

where C is the concentration of the ionic species whose charge is Z. Note that according to equation 1, solubility increases with the square root of ionic strength and that solubility is also at a minimum when the protein charge is zero (recall that the pH at which the charge is zero is called the isoelectric point).

At conditions of high ionic strength, protein solubility is observed to decrease almost linearly with salt concentration (Fig. 4), C, and can be described by the relation:

CKS s−= βlog eq. 4

where β and Ks are empirical constants specific to the protein and conditions in question. Temperature also effects protein solubility differently at high salt concentrations with most proteins less soluble at 25 °C than at 4 °C (might this have something to do with the hydrophobic effect?). Crystallization Techniques

The vapor diffusion technique is the most popular method for the crystallization of macromolecules. Approximately 90% of all crystallization experiments reported in the literature during 1996 and 1997 were performed using this technique. The principle of the vapor diffusion method is straightforward. A drop composed of a mixture of sample and reagent is placed in vapor equilibration with a liquid reservoir of reagent. Typically the drop contains a lower reagent concentration than the reservoir. To achieve equilibrium, water vapor leaves the drop and eventually ends up in the reservoir. Both the sample and solutes increase in concentration as water leaves the drop for the reservoir. Equilibration is reached when the reagent concentration in the drop is approximately the same as that in the reservoir. If the protein concentration is close to saturation to start with, increasing its concentration may exceed the thermodynamic solubility limit (saturation) and create the metastable condition referred to as supersaturation. If the process proceeds sufficiently slowly under the appropriate conditions, crystal formation will occur in order to restore the equilibrium.

Central to the problem of crystal growth is that there is no way to predict a priori what conditions are best for crystal growth for a given protein. The search for optimal crystallization conditions is a trial-and-error process with no single correct solution. Experience has shown that a given protein form a number of different crystal forms from very different solution conditions. In practice there are two basic strategies for identifying crystallization conditions: the grid search which involves a systematic variation of few conditions, and the shotgun approach in which one tries many, widely different conditions. Usually, the shotgun approach is used first to identify likely conditions followed by a grid search to refine and optimize crystal growth.

There are many techniques for setting up crystallization experiments (often called trials) and add to the number of experimental variables. These include sitting drop vapor diffusion, hanging drop vapor diffusion, free interface diffusion, dialysis, batch techniques. We will apply the methods of hanging drop and sitting drop vapor diffusion to the crystallization of hen egg white lysozyme.

Sitting and Hanging drop vapor diffusion are perhaps the most popular crystallization methods because they are easy to perform, require a small amount of sample, and allow


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only a large amount of flexibility during screening and optimization. In short, one places a small (2 to 40 µl) droplet of the sample mixed with precipitant on a glass cover slip in vapor equilibration with the precipitant. The initial precipitant concentration in the droplet is less than that in the reservoir. Over time the reservoir will pull water from the droplet such that an equilibrium will exist between the drop and the reservoir. During this equilibration process the sample is also concentrated. If the starting conditions are close enough to saturation, vapor diffusion will slowly produce supersaturation. The difference between sitting and hanging drop techniques is the orientation of the drop with respect to the precipitant.

The advantages of the hanging drop technique include the ability to view the drop through glass without the optical interference from plastic, flexibility, reduced chance of crystals sticking to the setup, and easy access to the drop. The disadvantage is that a little ext ra time is required for set-up. The advantages of the sitting drop technique are speed and simplicity. The disadvantages are that crystals can sometimes adhere to the sitting drop surface making removal difficult. This disadvantage can turn into an advantage where occasionally the surface of the sitting drop can assist in nucleation.

The sandwich drop. For sandwich drop the sample solution mixed with the precipitant is placed in the middle of a lower siliconized glass cover slip and covered by larger glass cover slip which allows for a small amount of space between the glass panels but is close enough such that the drop is sandwiched between the glass plates. This provides an excellent optical pathway for microscopic examination and an alternate equilibration method.

Free Interface Diffusion crystallization is less frequently used than sitting or hanging drop vapor diffusion but it is one of the methods used by NASA in microgravity crystallization experiments in space. Using this method one actually places the sample in liquid contact with the precipitant. Over time the sample and precipitant diffuse into one another and crystallization may occur at the interface, or on the side of high sample/low precipitant or low sample/high precipitant. The technique allows one to screen a gradient of sample precipitant concentration combinations. The technique can readily be performed in small capillaries.

Batch crystallization is a method where the sample is mixed with the precipitant and appropriate additives creating a homogeneous crystallization medium requiring no equilibration with a reservoir. The technique is popular with small molecule crystallographers. The advantages to the technique are speed and simplicity but the disadvantage is that only a narrow space of precipitant/sample concentration can be sampled in a single experiment. One must be very close to the conditions which promote crystal growth in order for this technique to be successful.

Dialysis crystallization involves placing the sample in a small cell which is sealed with a dialysis membrane which will allow water and some precipitants to exchange while retaining the sample in the cell. The dialysis cell is placed in suitable container holding the precipitant or crystallization media. For example one might dialyze a sample requiring a high ionic strength for solubility against a solution of low ionic strength. The technique allows for salting in and salting out, as well as pH crystallization techniques.

What technique to choose? Use hanging or sitting drop vapor diffusion for screening and initial optimization of crystallization conditions. Try as many different methods as needed since the method can play a significant role in the quality, size, and number of the crystals.


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Set-up of Crystallization trials For large-scale crystallization trials special “Q-plates” (see box below) may be

used, but we will use Petri dishes for “hanging-drop” crystallization experiments. Each student will set up three Petri dishes with different crystallization conditions. In each of these three different protein concentrations will be tried. Stock solutions of the following will be provided. Ideally students should work in groups of 2 to share reagents and save time.

Crystallization Reagent Stock 1. 1.3 M NaCl + 0,1 M Na-acetate pH 4.6 2. 1.6 M NaCl + 0.1 M Na-acetate pH 4.6 3. 1.3 M NaCl + 0.1 M Na-acetate pH 5.2 4. 1.6 M NaCl + 0.1 M Na-acetate pH 5.2 5. 1.3 M NaCl + 0.1 M Na-acetate pH 7.0 6. 1.6 M NaCl + 0.1 M Na-acetate pH 7.0

Set up your crystallization trials with final lysozyme concentrations of 10, 20 and 40 mg/ml in water. You will be supplied with stock solutions of 5M NaCl and 1M acetate buffer, pH 4.6, 5.2 and 7.0 from which you will have to prepare the appropriate crystallization reagents. Your stock crystallization reagents can be made and stored in 15 ml tubes. Weigh out and dissolve the lysozyme in an eppendorf tube (100mg/ml). Centrifuge the lysozyme stock solution >10000 rpm for at least 10 min before use to remove insoluble material and transfer the supernatant (carefully) to a new tube.


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Experiment 1.

Crystallization by Hanging Drop Vapor Diffusion Method Procedure 1. Pipette ca 2 ml of crystallization reagent in a small Petri dish.

2. Pipette 3 µl of protein onto the lid. (Note : Recommended total drop volume for this system is 1 to 40 µl). Repeat this with one drop of each protein concentration on the same lid – mark the outside of the lid near the protein drops so you know which concentration you have in each drop.

3. Pipette 3 µl of reagent from the dish into each drop on the lid containing a protein sample. (Note: Some people prefer to mix the drop while others do not. Proponents of mixing leave the pipette tip in the drop while gently aspirating and dispensing the drop with the pipette. Mixing ensures a homogeneous drop and consistency drop to drop. Proponents of not mixing the drop simply pipette the reagent into the sample with no further mixing. The important thing is to record what you do so that you can repeat it if necessary)

4. Carefully yet without delay invert the lid so the drop is hanging from the cover slide.

5. Place the lid over the Petri dish and seal it with Parafilm.

6. Repeat steps 1 through 6 for the remaining 5 reservoirs.

Viewing the Crystals Crystals of lysozyme grow rather fast under these

conditions and may already be present in the trial plates after pipetting. However, it will be best to look at your crystals after a few days. The crystals will be very small and difficult (if not impossible) to see with the naked eye. Therefore all crystal viewing should be done with a suitable dissecting microscope. The microscope you will be using is equipped with a two polarizing filters between which you can place your Q plate.

Crystals are distinguishable from amorphous substances (protein precipitate, dust, lint, junk, etc.) by their flat faces and their anisotropy (some of their physical properties are directional). By examining the trial plates under the microscope between polarizing filters, the birefringent properties of the crystals can be brought out. The birefringence (rainbow color effect) is due to differences in refractive index as a result of the order in the crystal. By turning one of the polarizing filters, the crystal faces can be made to appear clear and then black.

Sometimes it is not easy to identify protein crystals from other “junk” in the drops. If the object you are looking at does not have sharp edges or appear clear, chances are it is not a crystal. The following tests can be applied: Use the beveled edge of a syringe needle to cleave the crystal. Biomolecules tend to crush whereas small

Leica MZ 8 stereo microscope


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molecules are more brittle. Small molecule crystals are much more stongly birefringent than macromolecular crystals. Biomolecule crystals have about the same density as the mother liquor whereas salt crystals are more dense. There are some dyes (e.g., methyl violet) which bind protein and thus help discriminate protein from salt crystals. Macromolecule crystals contain large amounts of water and disintegrate when dehydrated, whereas salt crystals do not. Lastly, determination of the unit cell dimensions via diffraction will definitely distinguish between salt and protein crystals.

Photographing the Crystals

With the help of a course assistant, digital images can be obtained of your crystallization trials to be included in the lab report. Experiment 2. Diffraction Introduction In this lab we will explore some basic properties of electromagnetic radiation. It is common knowledge that a polished steel surface will form a well defined (specular) reflection when an incident beam falls on it but a sheet of paper will not (diffuse reflection). The difference between specular and diffuse is a matter of surface roughness. A reflected beam will form only if the average depth of the surface irregularities is much less than the wavelength of the beam. The bottom of a cast iron skillet (kastrul) is a poor reflector of visible light (λ = 400-700nm), but makes a good reflector of microwaves (λ = 0.5 cm). A second requirement for reflection is that the transverse dimensions of the reflector must be substantially greater than the wavelength of the incident beam. A 50 öre coin is a good reflector of visible light, but if placed in the path of short radio waves (λ = 1 m), the radiation will be scattered in all directions and no uniform reflected beam will result. This phenomenon is called diffraction.

Diffraction effects in our everyday experience are generally small and one must look hard for them. Complicating the observation of this phenomenon are two factors. One is that most light comes from an extended surface (rather than from a single point) and diffraction of light from one point in the source overlaps with that from another. The other is that most light sources are polychromatic and result in overlapping diffraction making the effect less apparent. In the laboratory we can control these parameters and use diffraction to explore the spatial arrangements of matter. Max von Laue recognized at the beginning of the century that electromagnetic radiation with

Two crystal forms of hen egg lysozyme: Tetragonal (left) and Orthorhombic (right) as seen trough the microscope.


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wavelengths on the order of atomic distances could be scattered by the atoms in a crystalline solid. To describe this, we need to review a few properties of waves.

When electromagnetic radiation from several sources overlaps in space, the individual waves add and is referred to as interference. Constructive interference occurs when the two waves are in phase (phase difference of 0, 2π , … radians or 0°, 360°, …) and destructive interference occurs when the two waves are exactly out of phase (phase difference

of π radians or 180°). The limiting case where two waves are identical with respect to amplitude, wavelength, and frequency is shown in the figure at left.

The condition for constructive interference depends on the geometry of the reflecting surface. In all cases, the angle of incidence is equal to the angle of reflection (elastic scattering) and the phase of the ray is not altered by the reflection. If two parallel rays are reflected by neighboring centers, the distance each travels to the target will depend on distance between the centers. If the distance traveled is an integer of the wavelength of the incident ray, constructive interference results at the

target (See figure at above). A distinction is made between two limiting cases based on geometry (Bragg diffraction and Fraunhofer diffraction) as shown in the figure

Experiment 2a. Wavelength Calibration of the Laser Introduction Diode lasers are now quite inexpensive. However due to microscopic differences in laser diode crystals, the exact wavelength of light emitted cannot be controlled during assembly. Red lasers are within 660-680nm and green lasers are within 525-545nm. Therefore the exact wavelength must be determined by the user. Diffraction gratings (a surface containing precisely spaced parallel lines) work nicely for this purpose. The diffraction grating we will use has a line separation of 1.33 µM.

WARNING! This laboratory exercise uses lasers that emit intense visible light. NEVER look directly into the source of the laser beam and never point the laser carelessly so that the beam might be directed into the eyes of others. The intense light may cause damage to the retina.


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Procedure Arrange the laser, grating and target as illustrated on page 1 of this lab. Use a distance (L) that will allow for convenient and accurate measurements. Measure the distance (L) from the grating to the target. Turn on the laser and measure the diffracted lines on the target. From the geometry of the setup, determine the diffraction angle and calculate the wavelength of the laser. Record an estimate of the error of your measurements and calculate the resulting error in your wavelength determination. Determine the wavelength for both the red and green laser.

Experiment 2b. The Fraunhofer Equation Introduction While, diffraction of X-rays by crystals is an example of Bragg diffraction, the optical diffraction experiment is an example of Fraunhofer diffraction. Mathematically, the equations for Bragg and Fraunhofer diffraction have a similar functional dependence on d, λ, and the scattering angle φ.

Use the supplied 35 mm slides to perform the following experiments. Discovery Slide (Green), Unit-Cell Slide (Black). In the orientation shown, the pattern labeled "A" in Appendix I is in the upper left Exercises

1. Begin with the Discovery Slide. Parallel lines yield a line of diffraction spots oriented perpendicular to the original lines. As you move from D to C to A to B, the orientation and spacing will change. Make sketches of the patterns to compare to the diffracting pattern in Appendix I.

2. Explore the 2-dimensional arrays in F, H, G, and E with identical spacings as in

part 1. Make sketches of the diffraction patterns as in 1.

Experiment 2c. Symmetry Introduction If the unit cell is symmetric, then the reciprocal lattice is symmetric and certain sets of reflections are equivalent. The symmetry of the diffraction pattern is the same as the symmetry of the lattice causing the diffraction. This exercise will require the Unit Cell Slide (Appendix II). Exercises

1. Symmetry. Verify the following. Square patterns Unit-Cell Slide A-D have square symmetry. Rectangular patterns Unit-Cell Slide E and G have a rectangular symmetry. Hexagonal patterns Unit-Cell Slide H have a hexagonal symmetry.

2. Systematic Absences. Compare the patterns in Unit-Cell Slide A and B. These

patterns have the same repeat distance and differ in that A has an additional

“red” laser “green” laser


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spot in the center of the unit cell. Notice that the diffraction pattern from A is like the one in B, but with every second spot missing. These "systematic absences" occur because the added scattering centers cause destructive interference by scattering out of phase by 1/2 a wavelength with some of the waves produced by the corners.

3. Intensities. Unit-Cell Slide (Appendix II) C has the same repeat as D, but has a

larger dot in the center. Scattering centers of different sizes scatter light differently. Notice that the same square diffraction pattern is observed for each, but that the intensities of the diffracted spots are different. This illustrates another fundamental aspect of the diffraction experiment: the positions of the diffracted spots depend on the unit cell dimensions (repeat spacing) while the intensities of the reflections depend on the identity and content (locations of the atoms in the unit cell).


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Appendix I Discovery Slide

Appendix II Unit-Cell Slide

B D F H

A C E G

A C E G

B D F H

Documents

Lab: Crystals and Diffraction · for X-rays and two-dimensional patterns for three -dimensional crystals of atoms. In the second part of the lab, you will use the diffraction of laser