112409 1 X-ray Crystallography NMR An Introduction to X-Ray by hmb46803

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Advantages and Disadvantages of Using NMR/X-ray Crystallography to
               Determine Macromolecular Structures

X-ray Crystallography                       NMR
Advantages:                                  Disadvantages:
• No size limit.                             • Effective size limit of 35 kDa.
• Structures can be very precise             • Structures are typically less precise
• Can be faster.                                  than those of very high resolution
                                                  crystal structures
Disadvantages:                               Advantages:
• You have to grow crystals (~50% don’t) • You don’t have to grow crystals.
• Electron density is the average for all    • You can use NMR to look at dynamic
     molecules in the crystals over the time      processes.
     of the data collection                  • You are determining the structure of
• Structure may be influenced by the              the protein in solution.
     crystal lattice.                        • Easily Detects multiple conformations.




              An Introduction to X-Ray Crystallography




   X-ray crystallography allows one to visualize the
   3-Dimensional structure of a macromolecule.

   Why would anyone want to do this?

   Understand the biochemical properties and
   the biological function

   i.e. a reaction mechanism (if an enzyme)
        or how a protein interacts in a complex.




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 A brief history....
Crystallography is analogous to fiber
diffraction (1953)
Crick & Watson published the double helical model for DNA
based upon knowledge of chemical structure and geometry,
possible chemical interactions, and fiber diffraction patterns
obtained by Rosalind Franklin.
                                  The structure immediately
                                  suggested the basis for
                                  replication and spurred,
                                  efforts to decipher the
                                  genetic code and the
                                  mechanism of protein
                                  synthesis.


                                   This reflects a common
                                   theme in structural
                                   biology. Function is most
                                   easily inferred when
                                   looking at the structure of
                                   a relevant complex.




Hemoglobin and myoglobin (~1960)
The first protein crystal structures were determined when
Max Perutz developed the method of isomorphous
replacement. Max Perutz and John Kendrew used this
method to determine the structures of hemoglobin and
myoglobin.
Subsequently determined high resolution structures of oxy
and deoxy-hemoglobin explained the basis for allostery.

This example illustrates that
functionally important motion can be
understood from a series of “snapshots”




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 Virtual Lab Tour
 Overview of the process and hardware.
                         Preparing the Protein Samples
Crystallographic studies usually start with at least 10mg of highly pure protein. This is a
huge amount compared to most other sorts of biochemical studies. Proteins are usually
expressed recombinantly in E.coli.




   Setting up crystallization trials
                                                   Looking at crystallization trials


                                                     96 conditions/screen x
                                                         10 screens x
                                                              2 temperatures x
                                                                3 protein concentrations

                                                     = a lot of time at the microscope
                                                     looking for crystals!!!!


    Many conditions are screened




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          Crystallization
                                                                  Reservoir
                                                      Protein     (precipitant)
                                                      solution.   solution.
• Protein is concentrated to about 10mg/mL.
• Protein and precipitant solutions are pipetted
into drop and reservoir solutions in individual
chambers of tissue culture (crystallization) trays.
Drop and reservoir solutions equilibriate by vapor
diffusion.
• Crystals grow as the solution changes to make
the protein less soluble. Often this is net loss of
water.
• Typical precipitant solutions include salts such
as ammonium sulfate or sodium chloride, alcohols
such as isopropanol or MPD, or polymers such as
PEG.
• Other important factors include pH and ligands.


Like making rock candy!!! (but slower, more
difficult and way more expensive....)




                               Cryo Data Collection
Crystals are mounted for data collection in small loops made of rayon. The
loop diameter is usually in the range of 0.1 to 1.0 mm. The crystals are
then rapidly cryocooled by plunging into liquid nitrogen.




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        Collecting x-ray diffraction data from a crystal
x-ray                             X-rays made here
beam
                                        Mirrors focus x-rays

                                                Cryostream -- cools crystal


99% of the x-ray beam passes
straight through crystal and is
stopped by the beam trap. 1%
of x-rays are diffracted.




                                                           Detector (records images)




  We need to use crystals to get a measurable signal.
X-rays are scattered by electrons. But the interaction is to too weak to
record scattering from a single molecule. Crystals are therefore used
because they present trillions of molecules in exactly the same
orientation. The scattering from each of the molecules adds to give a
measurable diffraction pattern.




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                           Resolution of a Reflection
The term resolution is used to describe the details of features that can be seen in an
image. It is determined by the angle through which x-rays are scattered with respect to
the incident beam. The higher the scattering angle the higher the resolution and the
more detail that can be visualized.

           High resolution reflection.
           (usually weaker)




                    Low resolution reflection.
                    (usually stronger)




                                        Detector




                      Resolution of a Data Set
 Resolution is usually described in units of Å,
 which relates to the ability to resolve features
 that are closer than a given distance.




Reflections within this distance from the direct
beam position form a data set that is at low
resolution.
Reflections within this distance from the direct
beam position form a data set that is at higher
resolution. Higher resolution data sets have
many more reflns than lower resolution data sets.

A good set of data has a resolution of <3.0 Å




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                       Oscillation photography
 Most contemporary x-ray data
 collection uses rotation                           Oscillation (rotation) photograph.
 geometry, in which the crystal
 makes a simple rotation of a
 degree or so while the image is
 being collected.




            X-rays

  Crystal rotates
  during exposure

  Typical oscillation is
  1°/image...




                                                                       Small part of a data
 Computer controlled data collection & processing                      set of 9239 reflections
                                                                       from 30-4A

                                                                       H   K    L       F      SIGMA
                                                                       0   0    6      37.7     14.3
                                                                       0   0   10     200.1     29.4
                                                                       0   0   12   63004.3   5765.8
                                                                       0   0   14     814.5     72.8
                                                                       0   0   16   43695.5   2833.7
                                                                       0   0   18   11506.4    763.5
                                                                       0   0   20   49142.1   2188.1
                                                                       0   0   22     109.7     70.6
                                                                       0   0   24   23636.5   1069.9
                                                                       0   0   26     585.2     90.3
                                                                       0   0   28   20601.8    672.8
                                                                       0   0   30    8346.8    354.6
                                                                       0   0   32   14520.5    605.1
                                                                       0   0   34      36.5    126.3
                                                                       0   0   36   17276.3    704.1
                                                                       0   0   38    3228.6    187.2
                                                                       0   0   40    8212.1    372.6
                                                                       0   0   42    1950.9    161.7
                                                                       1   0    4     865.9     27.8
                                                                       1   0    5     730.6     28.1
                                                                       1   0    6    1543.8     52.3
                                                                       1   0    7    2943.3     97.5
                                                                       1   0    8     279.2     14.5
                                                                       1   0    9    1482.6     52.4
A complete data set contains many thousands of diffracted rays,        1   0   10    4055.5    134.9
                                                                       1   0   11     219.3     18.3
each of which is described by its intensity (I) and position (h,k,l)   1   0   12    8674.0    287.7




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Theory of Diffraction
Diffraction is reasonably well explained by a simple wave theory. X-rays
are electromagnetic radiation, i.e. they are comprised of sinusoidally
oscillating magnetic and electric fields.



                                                                    Amplitude
                                                                      F
            Origin

Wavelength ( ) = distance between successive maxima in the wave


Phase ( or ) = distance between the origin and the following maximum in
the wave. Usually expressed as an angle = distance X 360° / wavelength.

Amplitude (|F|) = half full width of the oscillation (= of Intensity).




               More about the electron density equation

    (xyz)   = (1/V) |F(hkl)| exp[-2 i(hx+ky+lz)-                         (hkl)]
The electron density equation is a summation of all the reflections (structure factors --
amplitudes and phases) in a data set. All of the terms in the electron density equation
are trivial. Except for the structure factor amplitude |F|, which has to be measured, and
the phase ( ), which is highly non-trivial, since it is not possible to measure it
directly.




                                                                      Amplitude
                                                                        F
              Origin




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                                The Phase Problem
               A source of headaches for students and postdocs around the world!


       The diffraction pattern gives us the location and intensity of
       each reflection. However it does not give us one very important
       variable we need to solve the electron density equation....
       the phase of the reflected X-ray.

       How do we solve this problem?           3 methods.....

1.    Multiple isomorphous replacement (MIR)- Soak the crystal in a
      solution containing a ‘heavy’ atom (i.e. lots of electrons, W, Pb, Hg, Au)
      If the protein molecule contains a suitable pocket for the atom
      to bind, it can change the intensity of the reflected X-rays. This
      change is measured and used to estimate the phase of the
      reflected X-ray, which then allows one to deduce the location of
      the heavy atom in 3-D space.
      (A lot of mathematics- don’t worry about it now)

              Very tedious, difficult and time consuming,
              but you get beautiful phase data!!!




                      The Phase Problem (continued)
               A source of headaches for students and postdocs around the world!



     Method 2: Multiwavelength Anomalous Dispersion (MAD)
          This method uses the same principle as MIR, using a
          heavy atom to change the behavior of the reflected
          X-ray. However, that change is observed more
          readily by changing the wavelength of the X-ray
          source. The heavy atom ‘interacts’ with the X-ray
          at a certain wavelength and changes the diffracted
          X-ray accordingly. This is also called anomalous
          scattering.
 Requires travel (of student and crystal!) to a synchrotron
 X-ray source. Reservation months in advance. Can use
 seleno-methionine derivatives as selenium interacts very
 strongly with X-rays of a ~1Å wavelength

 (most in-house X-rays are 1.54Å and cannot be changed!)




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                     The Phase Problem (continued)
              A source of headaches for students and postdocs around the world!


    Method 3: Molecular replacement
         This method involves guessing the phases of the
         reflected X-rays using phases from a similar
         structure solved previously.




          Fastest, cheapest and easiest way to go....
          but, you need a similar structure...and
          structural differences lead to messier data.


          Once the phases are approximated, the electron
          density equation can be solved and a map is made.




                   Introduction to Electron Density
Atoms in a protein molecule are surrounded by a ‘cloud’ of electrons.
The more electrons a particular atom contains, the larger the cloud.

An electron density map can be thought of as a map showing the distribution of
electrons in a protein crystal. In a crystallography experiment we determine
the density of electrons in the unit cell and we use this density to locate the
actual atoms in the protein.

The pine tree example:




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                                         Electron density = green mesh

                                         Protein model = ball & stick




 Use software to ‘build’ amino acids
 into the empty density. The result is
 the protein model.




Approximate models are built into initial maps
  and improved by a process of refinement




  Good initial maps show a clear
  distinction between protein and         Final map and model
            bulk solvent




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Low resolution maps can show overall
features such as the shape of the
molecule and the location of secondary
structural elements. The figure shows
a 7Å map of tropomyosin.

2.6 Å resolution. Main
chain trace is usually
fairly clear and many side
chains have obvious if
imprecisely defined
density. An unwritten
requirement for funding
is crystals that diffract to
at least 3.0Å resolution.




              1.2 Å resolution.




    Structure Validation...is the model we built into
    the electron density what the protein really looks like?

• The structure is essentially the same when the same
protein is crystallized from very different conditions.

• The structure is the same when determined by
NMR.

• Crystallized enzymes are active.

• When crystallized with ligands (e.g. substrate
analogs), proteins are seen to make interactions that
explain the known chemistry and genetics

• Do the residues in the structure
fit a Ramachandran plot?




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  The R-factor: How well does our model fit the data?


                            |Fobs| - |Fcalc|
                      R=
                                 |Fobs|

            An estimate of how well the model fits into
                the experimental electron density.

   It compares the intensities of the reflections to ‘theoretical’
        intensities back-calculated from the current model.

R = 0 perfect comparison, the model fits perfectly into the density
           R= .20 (or 20%) very good, easily publishable
     R= .6 the worst (implies random fit), if .4-.5, keep trying.
    Arguably the most important parameter for assessing the
                       quality of the model




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