Xray Crystallography Workshop

1
X-ray Crystallography Workshop

• DAY 4
• Recap PHASER job with search_model_2.pdb
• Lecture electron density maps, model building
• Run one cycle Refmac refinement for rigid body
  refinement
• Open maps and models in COOT
• Learn basic COOT tools
• Manual adjustment of model
• Lecture on refinement
• Run refinement to 1.5 A with Refmac
• Look at maps again, find waters etc.

2
The goal of model building and refinementis to
fit the model (the set of atomic coordinates
from whatever source) to the real experimentally
measured diffraction data.

• BUT, with the caveat that this should not produce
  unreasonable protein structure.
• Sources of error in the model
• The model used for molecular replacement is not
  exactly homologous to your real protein, either
  because of sequence differences, or bound ligand,
  or point mutations.
• The model generated by heavy atom phasing is not
  correct or not complete, due to various reasons.
• Sources of error in the data
• Measurement error due to
• Detector other set-up problems
• Crystal decay or absorption
• Unknown

3
Here are some links for you with (I hope)helpful
information

• Protein structure basics
• A series of articles in Acta Cryst. on basic
  practice and recent developments
• Link to a refmac tutorial
• I will also download two tutorial documents on
  the blackboard, one on COOT, one on Refmac, by
  the people that wrote these programs, e.g.
• coot_tutorial.pdf

4
What does an electron density map look like?

• This is some near-perfect electron density from a
  refined model that I recently did for a UNC
  collaborator

5
What does an electron density map look like?

• This is some not-as well fit electron density
  from a step earlier in the process of the
  previous model.

6
What does an electron density map look like?

• This is what I would call un-interpretable.
  There are no recognizable features - and lots of
  disconnected density

7
What happens if you calculate an electrondensity
map from a bad molecular replacementsolution?

• See many breaks in this helical region - many
  atoms not in density and some unaccounted-for
  density

8
What happens if you calculate an electrondensity
map from a good molecular replacementsolution?

• This is from our data set and our PHASER
  molecular replacement solution

9
Before we go on, lets talk about several
typesof electron density map that are important

• a. Using phases from a model
• i. 2Fo-Fc or 3Fo-2Fc (think of as Fo (Fo-Fc))
  uses phases calculated from the model and
  amplitudes from the measured data minus the
  calculated data. Gives you the model electron
  density PLUS the differences between the OBSERVED
  data and the CALCULATED data
• ii. Fo Fc (difference map) uses phases
  calculated from the model and amplitudes from the
  OBSERVED minus the CALCULATED data. Tells you
  where you either need atoms (positive difference
  density) or where you need to get rid of atoms
  (negative density).
• b. Omit maps Like a, except leave out some
  atoms from the phase calculation that may be
  biasing your phases in a region of the maps where
  the density is poor then the good parts of the
  model should help bring back the density in the
  bad parts of the structure if there really is
  density there.
• c. Using experimental phases (from heavy atoms
  and solvent flattening and NCS averaging - we
  will talk more about this next week). Fobs maps.

10
Look at electron density mapsfrom the PHASER
output

• If I open ccp4i, and click on the view files from
  job, I can look at the output .mtz file from the
  PHASER molecular replacement (using
  search_model_2.pdb)

11
We can look at the contents of a binary mtz file
using the GUI like that it runs a program
called mtzdump - dumps the contents of the
mtz to the standard output

• The columns labeled FWT and PHWT are the
  amplitudes and phases for a 2Fo-Fc map the
  DELFWT and PHDELWT are for Fo-Fc. Fc is
  calculated structure factors, F_karen is our
  original measured data. See that phases are just
  like they should be - angles that describe the
  offset of the reflections wave from the reference
  wave. So they run from
• -180 to 180 or 360.

12
The electron density map is calculated from the
equation using the absolute value of the
F(thats our FWT or other) times the two
exponentials
So, we have everything we need in the file, the
f, h, k, l, x, y, z, Fhkl. All we need is a
fast computer to do all the sums
13
Before we look at our maps, we are goingto run a
rigid body refinement on our PHASER output
coordinates

• Open the ccp4i GUI, and go to your project for
  this lysozyme Molecular Replacement
• Start the Refmac program by clicking on the
  Refinement menu, and then Refmac
• Fill in the blanks that I tell you - we will talk
  more about refinement later

14
Ccp4 can calculate electron density maps(in a
program called FFT Fast Fourier Transform, but
COOT does it for us

• So lets DO IT
• Open COOT

15
Refinement Links

• A slide show on Refmac from the CCP4 people
• An online lecture from one of the CCP4 authors
  no theory
• Another online lecture from Randy Read - a really
  really smart crystallographer

16
Refinement is the automated partof adjusting
the model to fit the data

• What do we mean by the model ?
• Here is a line from a coordinate file in pdb
  format
• ATOM 1 N LYS A 1 -20.428 45.403
  9.798 1.00 15.98 A N
• There are four parameters (x,y,z, and B-factor
  15.98) about the atom that describe its position
  and average disorder B-factor includes thermal
  motion and crystalline disorder of unspecified
  nature

17
At lower resolution, (2.5 - 3 Å)

• The way that the ratio of observations to
  parameters is increased is to add observations
  as bond lengths, bond angles, van der Waals
  contacts, deviations from planarity or chirality,
  non-crystallographic symmetry - these are called
  restraints
• These are weighted with respect to the
  positional parameters such that they are not
  allowed to deviate as much (from their standard
  values in known, well-refined small molecule
  structures) when the resolution is lower this
  prevents us from overfitting density that does
  not have the detail we need to REALLY say where
  an atom is, for example
• You will see this graphically when you look at
  your higher resolution refinement maps.

18
So, the parameters are shifted and optimized in
some way,while some target function is
evaluatedthat measures the fit of model to data

• Examples of optimization methods
• Gradient descent methods calculate shifts for the
  parameters, and then, using differential
  equations, re-calculate shifts based on trying to
  make the gradient zero (to be at a minimum of the
  target function
• Search methods generate a random set of models
  (e.g.simulated annealing uses molecular dynamics
  to generate these models applies kinetic energy
  to atoms to move them) and then - require more
  computer power but have larger radius of
  convergence

19
Examples of target functions

• Empirical energy - something like using the model
  with the lowest conformational energy. Not very
  realistic because it doesnt lend itself to error
  analysis
• Least squares residual - sum of squares of the
  difference between the observed minus predicted
  parameter divided by the standard deviation -
  suffers from the bad assumption that errors in
  the observations have a normal distrubution
• Maximum likelihood - Allows for more arbitrary
  distributions of errors in observations - uses
  Bayesian statistical methods (beyond my current
  ability to understand well enough to try and
  explain) to create models of this error that
  supposedly make it a better target than least
  squares, which was used routinely before the
  1990s

20
Optimization methods and target functionsof
commonly used refinement programs

• Refmac - uses gradient descent method to minimize
  maximum likelihood OR least squares
• CNS - Uses simulated annealing search method to
  minimize maximum likelihood
• Others - see Tronrun paper Table at the end

21
Checking the success of refinement
cross-validation by R-free

• Equation for conventional R-factor residual
  agreement of model with data
• R S Fo - Fc / S Fo
• If refinement is done incorrectly - this number
  can be deceptively low, which we want, but the
  model can be extremely inaccurate (low
  resolution).
• What if we set aside a small percentage (e.g. 5)
  of the data to calculate an Rfactor for, but NOT
  to use in the refinement itself - a more unbiased
  R-factor (Brunger, 1993).

22
Rfree should drop along with Rworkingduting the
refinement, and stay within somethinglike 4
percentage points of each other
23
Refinement is finished when you decideyou
cant flatten the difference map any more, or
you get the lowest possible Rfree

• Ususally, you cant ever flatten the difference
  map, and you stop when you cant stand it any
  more, or, really, when you dont drop the Rfree
  by doing anything reasonable
• You will see papers where Rfree is as high as say
  29 - but these are usually hot structures at
  fairly low resolution, like membrane proteins or
  enormous complexes (ribosome e.g.) where
  publication often happens before refinement is
  really finished
• But, how do you know your structure is correct???

24
COOT has a nice set of tools for lookingat areas
of the structure that are unusualor bad

• If we go to the Validate menu in COOT and
  select Ramachandran plot, we will see residues
  that are in preferred areas of PHI/PSI backbone
  angles, (pink), in allowed but less preferred
  by energetics and known structures (yellow), and
  dis-allowed (for all by Gly)
• Can click on the residues and COOT takes you to
  it so you can take a look!

25
Also, Refmac prints out (in the pdb file) a set
of error measures that are usefuland required
for deposition

• The RMS deviations from ideal values are a bit
  misleading, since you use them to restrain the
  refinement
• Coordinate error is always lower at higher
  resolution, of course