X-ray Crystallography-1 X-ray crystallography and diffraction of protein crystals provides an atomic...
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X-ray Crystallography-1 X-ray crystallography and diffraction of protein crystals provides an atomic resolution picture of proteins: 1) Grow crystal, 2)
X-ray Crystallography-1 X-ray crystallography and diffraction
of protein crystals provides an atomic resolution picture of
proteins: 1) Grow crystal, 2) collect diffraction pattern, 3)
construct and refine structural model to fit X- ray diffraction
pattern. Overview of crystal properties, space groups, Miller
planes Diffraction, Braggs law, von Laue condition X-ray
diffraction data collection Several slides adopted from Prof. W.
Todd Lowther, Dept. of Biochemistry, Wake Forest University
Additional slides adopted from Prof. Ernie Brown, formerly in the
Dept. of Chemistry, Wake Forest University Reading: van Holde,
Physical Biochemistry, Chapter 6; the two Watson & Crick papers
Additional optional reading: Gale Rhodes, Crystallography Made
Clear, sections of Chapters 1-4 Homework: (see next page), due
Monday, Feb. 24 Remember:Pizza & Movie, Sunday, Feb. 23, 4:00
pm PBS/Nova The secret of Photo 51; and The DNA story Both movies
on reserve at library; also, The secret of Photo 51 at:
http://www.youtube.com/watch?v=0tmNf6ec2kU Midterm 1: Wednesday,
Feb. 26
Slide 2
Homework 4.1 (Chapter 6, X-ray diffraction), due Monday, Feb.
24 If not stated otherwise, assume = 0.154 nm (CuK -radiation)
1.van Holde 6.1 2.NaCl crystals are crushed and the resulting
microcrystalline powder is placed in the X-ray beam. A flat sheet
of film is placed 6.0 cm from the sample and exposed. Ignoring the
possibility of forbidden reflections (which is in fact the case
with NaCl, because the lattice is centered), what would be the
diameters and indices of the first two (innermost) rings on the
photograph? NaCl is cubic with unit cell dimension a = 0.56nm.
3.van Holde 6.6 a-c (Fig. 6.18, dont need to do 6d) 4.You are
working with a linear crystal of atoms (assume to be planes), each
spaced 6.28 nm apart. You adjust your x-ray emitter so that it
emits 0.628 nm x-rays along the axis of the array. a.You place a 1
cm 2 spherical detector 1 cm from the sample, centered on the
x-axis, on the opposite side of the emitter. Draw the pattern you
expect to detect. Clearly mark the expected distances. b.If you
performed the experiment on a linear crystal with atoms spaced 0.1
nm apart, what pattern would you detect? Would you have the same
pattern if your detector were 1 m 2 ? What does this say about the
resolution of your experiment? Homework 4.2 (Chapter 6, X-ray
diffraction), due Wednesday, March 5 If not stated otherwise,
assume = 0.154 nm (CuK -radiation) 1.van Holde 6.2a (Hint: put one
atom at x, y, z, the other atom at x+1/2, -y, -z) 2.van Holde 6.3
3.van Holde 6.9 a-c (in c), real space means on film) 4.van Holde
6.9 d but: Sketch the fiber diffraction pattern expected for A-DNA
(not Z-DNA).
Slide 3
Visible light vs. X-rays Why dont we just use a special
microscope to look at proteins? Resolution is limited by
wavelength. Resolution ~ /2 Visible light: 400-700 nm X-rays: 0.1-
100 (0.01- 10 nm) But to get images need to focus light (radiation)
with lenses. It is very difficult to focus X-rays (Fresnel lenses,
doesnt really work for X-rays) there are no lenses for X-rays
cannot see atoms directly. Getting around the problem X-ray
Crystallography Defined X-ray beam, typically = 0.154 nm (created
by hitting Copper target with high energy electrons, Cu K 1
radiation) Regular structure of object (crystal) Result diffraction
pattern (not a focused image).
Slide 4
The Electromagnetic Spectrum Wavelength of the radiation needs
to be smaller than object size. Diffraction limit (separation of
resolvable features): ~
Slide 5
X-ray crystallography in a nutshell Protein is crystallized
X-Rays are scattered by electrons in molecule Diffraction produces
a pattern of spots on a film that must be mathematically
deconstructed (Fourier transform) Result is electron density
(contour map) need to know protein sequence and match it to density
coordinates of protein atoms put in protein data bank (pdb)
download and view beautiful structures. Currently there are about
100,000 structures in the pdb (2014). Check out protein data bank:
(http://www.rcsb.org)http://www.rcsb.org
Slide 6
X-ray Crystallography in a nutshell Reflections: h k l I (I) 0
0 2 3523.1 91.3 0 0 3 -1.4 2.8 0 0 4 306.5 9.6 0 0 5 -0.1 4.7 0 0 6
10378.4 179.8. ? Phase Problem ? MIR MAD MR Electron density: (x y
z) = 1/V |F(h k l)| exp[2 i (hx + ky + lz) + i (h k l)] Braggs law
Fourier transform Protein crystal X-ray diffraction pattern
Electron density Fit molecules (protein) into electron density
Phase angle not known Need lots of very pure protein
Slide 7
End result! Fourier transform of diffraction spots electron
density fit amino acid sequence Protein DNA pieces (Dimer of
dimers) X-ray crystallography in a nutshell
Slide 8
Why determine the 3-D structure of your favorite protein or
protein-ligand complex? A picture is worth a thousand words.
Insight into structure-function relationships Recognition and
Specificity Might identify a pocket lined with negatively-charged
residues Or positively charged surface possibly for binding a
negatively charged nucleic acid Rossmann fold binds nucleotides
Zinc finger may bind DNA. Aids in the design of future experiments
Rational drug design Engineered proteins as therapeutics Chicken
Fibrinogen S-Nitroso-Nitrosyl Human hemoglobin A
Slide 9
Crystal formation Start with saturated solution of pure protein
Slowly eliminate water from the protein solution Add molecules that
compete with the protein for water (3 types: salts, organic
solvents, PEGs) Trial and error Most crystals ~50% solvent Crystals
may be very fragile Lysozyme crystals (Biophysics lab 2014)
Slide 10
Growing crystals Figure 6.7 Vapor diffusion methods of
crystallization. In the hanging drop method of vapor diffusion, a
sample in solution is suspended above a reservoir, R, that contains
a high concentration of precipitant. The lower vapor pressure of
the reservoir draws water from the sample solution, S, to reduce
the volume of the sample, V S, below its initial volume, V 0.
Consequently the concentration of molecules in the sample solution,
[S], increases to above the intrinsic solubility, S 0, of the
molecule, resulting in precipitation or crystallization. In the
sitting drop method, the sample solution sits in a well rather than
hanging suspended, but otherwise the two methods are the same.
Slide 11
What are crystals? Ordered 3D array of molecules held together
by non- covalent interactions Unit Cell Sometimes see electrostatic
or salt interactions Lattice network Defined planes of
atoms/molecules
Slide 12
Unit cell vectors
Slide 13
Solids that are exact repeats of a symmetric motif. Molecules
in a crystal are arranged in an orderly fashion (regular,
symmetric, repeating). Basic unit is unit cell. In a crystal, the
level at which there is no more symmetry is called asymmetric unit.
Apply rotational or screw operators to construct lattice motif.
Lattice motif is translated in three dimensions to form crystal
lattice. The lattice points are connected to form the boxes unit
cell. The edges define a set of unit vector axes unit cell
dimensions a, b, c. Angles between axes: ? What are crystals?
Slide 14
Cystal stack unit cells repeatedly without any spaces between
cells Unit cell has to be a parallelepiped with four edges to a
face, six faces to a unit cell. All unit cells within a crystal are
identical morphology of (macroscopic) crystal is defined by unit
cell There are only seven crystal systems (describing whole
(macroscopic) crystal morphology): Triclinic, Monoclinic,
Orthorhombic, Tetragonal, Trigonal, Hexagonal, Cubic (defined by
length of unit vectors and angles). There are only fourteen unique
crystal lattices fourteen Bravais lattices. P = primitive lattice
point at corners of unit cell, F= face centered lattice point at
all six faces, I = lattice point in center of unit cell, C =
centered, lattice point on two opposing faces. What are crystals ?
NaCl (salt) crystals are cubic (Image: M. Guthold) Cl, green; Na,
blue
Slide 15
What are crystals? Bravais Lattices and Space Groups 7 crystal
systems 14 Bravais lattice systems Space group = Lattice identifier
+ known symmetry relationships Molecules within the crystal will
most likely pack with symmetry
Slide 16
What symmetry operations (e.g. rotation axes, (2-, 3-, 4-, 6-
fold axis, mirrors, inversion axes , at corner, at face, (see Table
1.4) can be applied to the unit cell (inside crystal)? This defines
the 32 point groups of the unit cell. The combination of the 32
symmetry types (point groups) with the 14 Bravais lattice, yields
230 distinct space groups. In biological molecules, there are
really only 65 relevant space groups (no inversion axes or mirrors
allowed, because they turn L-amino acids into D- amino acids. The
space group specifies the lattice type (Bravais lattices, outside
crystal morphology) and the symmetry of the unit cell (inside).
What are crystals? Bravais Lattices and Space Groups
Slide 17
Examples of Symmetry Rotations 2-folds (dyad symbol) 3-folds
(triangle) 4-folds (square) 6-folds (hexagon) Rotations can be
combined Translations - moved along fractions of the unit cell -
see P2 1 example
Slide 18
What are crystals? Symmetry operators
Slide 19
Examples Two-fold axis protein Bovine Pancreatic Trypsin
Inhibitor P 2 1 2 1 2 1 (Primitive, orthorhombic unit cell with a
two-fold screw axes along each unit cell vector) (adapted from
Bernhard Rupp, University of California-LLNL)
http://www-structure.llnl.gov/Xray/tutorial/Crystal_sym.htm
Slide 20
Slide 21
Cell edges: a, b, c Cell angles: , , (100), (010), (001) planes
define the unit cell; (bc-plane, ac-plane, and ab-plane) What are
crystals? Cell Edges, Angles, and Planes
Slide 22
Diagonals through the unit cell denoted by how they
cross-section an axis e.g. 1/2 = 2, 1/3 = 3, 1/4 = 4, etc. e. g.:
(230) plane has intercepts at 1/2x and 1/3y (-230) plane has
intercepts at -1/2x and 1/3 y (slanted in other direction) What are
crystals? Examples of 2-D Diagonal Planes, Miller planes, Miller
indices
Slide 23
a b (100) planes a/2 b/3 (230) planes
Slide 24
Planes extend throughout crystal with different relationships
to the origin: e.g. (234) Negative indices tilt the plane the
opposite direction: NOTE that (210)=(-2-10)(-210). - sign usually
put as a bar above the number What are crystals? Planes in 3-D and
Negative Indices
Slide 25
Theory of X-ray diffraction Treat X-Rays as waves (CuK ~ 0.154
nm). Scattering: ability of an object to change the direction of a
wave. If two objects (A and B) are hit by a wave they act as a
point source of a new wave with same wavelength and velocity
(Huygens principle) Diffraction: Those two waves interfere with
each other. destructive and constructive interference. observe
where maxima and minima are on screen. get position of A and B
Constructive interference: Destructive interference: PD = n, n = 1,
2, 3, PD = n , n = 1, 3, 5, PD
Slide 26
Braggs law (simple model of crystal, but it works!) Crystal is
made up of crystal planes (the Miller planes we just discussed).
Assume a one-dimensional crystal: Reciprocal relationship between
the Bragg angle and the spacing, d, between the lattice planes. By
measuring , we can use Braggs law to determine dimension of unit
cell! d Fig. 6.10 Geometric construction in class What is the
relationship between diffraction angle 2 and unit cell dimensions?
Braggs law: n integer, wavelength of X-ray
Slide 27
von Laue condition for diffraction Now well move on to a
three-dimensional crystal. Lattice still consists of only planes,
but now we have a three-dimensional grid (still just dots, no
internal structure, yet) In three dimensions (pp 263-265): h, k, l,
are the Miller indices. Every discrete diffraction spot on a film
has a particular Miller index. These are the same indices that
describe the Miller planes. E. g. reflection (1,0,0) h=1, k=l=0;
comes from (100) Miller plane is the angle measured from the
incoming X- ray beam Each cone (h=1, -1, 2, -2 ) 22
Slide 28
von Laue Condition for Diffraction One-dimensional crystal
(horizontal planes) Three-dimensional crystal (horizontal and
vertical planes) (Horizontal and vertical diffraction cones, dots
at intersections) a b c h = 2 h = 1 h = 0 h = -1 h = -2 k = -2, -1,
0, 1, 2
Slide 29
Determining the dimensions of the unit cell from the
diffraction spots. Precession photograph of Tetragonal crystal of
T4 lysozyme (X-ray aligned with third axis). Note: The spacing
(angle ) is not affected by the number of molecules in a unit cell
(more in a little bit). l = 1, 2, 3, l = -1, -2, -3, k = 1, 2, 3 k
= -1, -2, -3
Slide 30
Example A NaCl crystal is crushed and the resulting
microcrystalline powder is placed in an 0.154 nm X-ray beam. A flat
sheet of film is placed 6.0 cm from the sample. What is the
diameter of the innermost ring on the photograph. NaCl is cubic
with unit cell dimension 0.56 nm. (A powder gives diffraction rings
instead of spots, because of the random orientation of the
microcrystals in the powder.) Diffraction image:
http://www.union.edu/PUBLIC/PHYDEPT/jonesc/images/Scientific/Powder%20diff%20Al.jpg
Slide 31
Example The precession photograph in Fig. 6.18 was recorded
with a crystal to film distance of 7.65 cm and the spacing between
reflections was measured to be 0.15 cm. The third dimension for
this crystal is 3.777 nm. 1.Calculate the unit cell dimensions of
this crystal. 2.Propose one possible space group for this crystal.
3.If the third axis has 4 1 symmetry, what systematic absences
would you expect to see (later)? Fig. 6.18. Precession photograph
of the tetragonal crystal of lysozyme. The photograph was recorded
along the four- fold symmetry axis. The photograph is indexed using
the vertical and horizontal primary axis shown. (The diagonal axis
are an alternative set of primary axes for indexing, ignore for
problem.)
Slide 32
Is Braggs law still valid for two or more atoms in a unit cell?
Jensen and Stout Two atoms in a unit cell (reflect) waves from
their respective planes. The waves combine and form a resultant
wave, that looks like it has been reflected from the original unit
cell lattice plane. Diffraction spot is in the same place, but has
different intensity (intensity of resultant wave). Conceptually: We
assumed the electron density is in planes. In reality it is spread
throughout the unit cell. Nevertheless, the derivation is still
valid, since it can be shown that waves scattered from electron
density not lying in a plane P, can be added to give a resultant as
if reflected from the plane.
Slide 33
So far By observing the spacing and pattern of reflections on
the diffraction pattern, we can determine the lengths, and angles
between each side of the unit cell, as well as the symmetry or
space group in the unit cell. Still, how do we find out whats
inside the unit cell? (i.e. the interesting stuff, like
proteins).
Slide 34
Determining the crystal symmetry from systematic absences
Simple, conceptual example: P2 1 space group: Has a 2-fold screw
axis along c-axis On 00l-axis only every other spot is observed.
Each space group specifies its unique set of special conditions for
observed and unobserved reflections along the principal and
diagonal axes. (Can be looked up in tables). Sometimes it is very
tricky to assign proper space group, especially for centered
cells.
Slide 35
Translational symmetry elements and their extinctions. (Table
5.2 Jensen & Stout) Sometimes there is ambiguity, i.e. two
space groups have same pattern