Imaging of Biological Molecules in Solution by Small Angle Xray Scattering'

1
Imaging of Biological Molecules in Solution by
Small Angle X-ray Scattering.

• Mark J. van der Woerd1, Donald Estep2, Simon
  Tavener2, F. Jay Breidt3, Stefan Sillau3, James
  Bieman4, Michelle Strout4, Christopher Wilcox4
  Sanjay Rajopadhye4 and Karolin Luger1.
  1Department of Biochemistry Molecular Biology,
  2Department of Mathematics, 3Department of
  Statistics, 4Department of Computer Science,
  Colorado State University, Fort Collins, CO 80523.

2
The size of the problem
Approx 240 x 200 x 60 m 7 x 2.5 x
2.5 mm 10 x 10 x 3.5 nm
Factor 5 1013 Factor 1017
We are visualizing objects on the order of 10-9
m, guiding wavelength and technique
3
What motivates us?

• We are interested in understanding the function
  of the machinery that enables life
• Function is closely linked to structure
• The machinery consists of DNA and proteins, among
  other things
• We need to know the structure of individual
  biological molecules (protein, DNA, RNA) alone,
  and of their complexes in order to begin to
  understand function

4
An efficient package, yet accessible
5
How do we determine structure?

• Traditionally there are three methods
• Protein Crystallography
• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Modeling
• We are now pursuing Small Angle X-ray Scattering
  on biological systems in solution (SAXS).

6
How does SAXS work?
Radially symmetric scattering pattern
Incident X-rays
q
Sample in solution, typically 10 ml, inside a
quartz container. All particles in solution will
scatter X-rays, since electrons (present in all
atoms) are interacting with the X-rays.
How?
Structural information
7
Advantages of the technique

• Dont need to make (protein) crystals this is a
  very time consuming and complicated process this
  is a solution method
• Experimentally very simple, experiments can be
  done in a few minutes
• Can determine the global shape of large complexes
  of molecules, which is difficult to do with other
  techniques suitable for structure determination,
  while it is biologically very interesting.

8
Data processing consists of

• Signal correction (subtracting background,
  correcting for incident beam, time- and
  concentration-dependent corrections)
• Either ab initio model building from raw data
• Or using existing models as puzzle pieces
• Or a combination of these methods
• Generally build a model by some method,
  generate a calculated scattering pattern from
  the model and compare with experimental outcome.
  Iterate to minimize the differences.

9
Example Nucleosome Assembly Protein - 1

• It helps in compacting DNA into nucleosomes, the
  first step in the process of folding DNA into
  chromosomes
• It helps DNA to slide so the correct piece
  can be exposed and used at the right time
• How does it work?
• It interacts with what?

10
Nucleosome
11
Test the method with NAP-1 alone
Spheres approach
Build a model of spheres that has the appropriate
size and shape so that the predicted solution
scattering pattern closely matches the
experimental data. This is an ab initio approach
because there is no prior information put into
generating the model.
12
Test the method with NAP-1 alone
Puzzle piece approach
Acquire a model from another investigation and
use it as a puzzle piece, try to see if one or
more pieces combined can explain the experimental
data. This method is particularly useful when we
study large complexes of known structures. In
this case the model was obtained by means of
X-ray crystallography (spheres are
representations of atoms).
13
New Method Development

• We need reliable, scientifically transparent
  methods to interpret scattering data.
• New method development involves Biochemistry,
  Physics, Mathematics, Statistics, Computer
  Science.
• Next couple of slides are an outline of plans for
  ongoing and future research

14
Biophysics

• Is it possible to develop a method which can be
  used to include or exclude models that are deemed
  good or bad?
• Example protein molecules must be internally
  sound, they do not contain voids. This is
  similar to asking how does a protein fold?

15
Mathematics

• It is implicitly assumed in our model that all
  molecules tumble rapidly and all molecular
  orientations are equally likely in our sample.
• This may not be correct and we would like to test
  systems that do not incorporate completely
  randomly oriented molecules.
• How does this affect the scattering pattern (if
  at all)? Need alternative description?

16
Statistics

• Suppose you had two models that both seem
  reasonable, could you assign a quality descriptor
  to the models and tell which is best, i.e.
  which fits the experimental data the best?
• Possible approach use of maximum likelihood
  methods.

17
Computer Science

• The generation of possible models that fit the
  experimental data is very time consuming what
  are efficient methods to speed up the programs?
• The proposed process of image reconstruction from
  scattering data is complex what is a good way to
  write a program suite that works well and can be
  easily maintained?

18
Application

• We have our preliminary results can we extend
  into the unknown?
• How can we best assure that the results are
  scientifically sound?
• To which parts of the nucleosome does NAP-1 bind
  and how does this affect the formation of new or
  change of existing nucleosomes?

19
Application
?
20
Acknowledgments

• Funding
• HHMI
• NIH
• Center for Interdisciplinary Mathematic
  Statistics by extension Offices of the Dean and
  Vice President for Research

• Lot of help and patience
• Drs. Michal Hammel and Greg Hura (LBNL)
• ALS (LBNL) for beam time

21
Test the method with NAP-1 alone
Combined approach
Blue model from crystallography other
colors extension of the original model so the
experimental data are better explained. Each
color represents a different possible model that
fits the experimental data.
22
Application to a problemCombine and compare
methods
Combined approach
Data here.
Chicken wire particle envelope determined
without prior information Blue NAP1 model Red
and gray other proteins Orange flexible
additions not present in any model used.