Calcium-Binding Protein Protocols Calcium-Binding Protein Protocols

Solution Scattering 143
For a complex of two components with different mean neutron-scattering densities,
the total scattering can be written as
I(Q,∆ρ A, ∆ρ B) = ∆ρ A 2 (Q) + ∆ρA∆ρ BI A(Q) + ∆ρ B 2 IB(Q) (2)
The subscripts A and B refer to each component and ∆ρ x = ρ x – ρ s where ρ x is
the mean-scattering density for the individual components, i.e., X = A or B.
Equation 2 assumes the difference between the mean-scattering densities for
the individual components is much greater than any internal density fluctuations
within each component. The three I(Q) functions in equation 2 correspond to
the three basic scattering functions. I A(Q) and I B(Q) represent the scattering of
components A and B, respectively, from which one can derive the structural
parameters for each component within the complex. I AB(Q) is the cross term
that yields information on the relative dispositions of the two components. A
set of neutron scattering measurements with different D 2O:H 2O ratios in the
solvent gives a set of equations in the form of Eq. 2 which can be solved using
multiple linear regression to give the three basic scattering functions.
In any contrast variation experiment, it is crucial to know the precise level of
deuteration in your sample. Without this information, you cannot calculate the
contrast factors in Eq. 2 that are required to solve for the basic scattering equations.
For a complex of a deuterated and a nondeuterated protein, a plot of the
square root of the forward scattering (I 0), normalized to molar protein concentration,
as a function of the solvent scattering density (i.e., D 2O content) will
be linear and will cross zero at the scattering-density value corresponding to
the solvent match point for the complex. From this value, and using the known
chemical composition and partial specific volumes of the proteins in the complex,
as well as knowledge of the number of exchangeable hydrogens, one can
calculate the deuteration level. Alternative methods for estimating deuteration
levels are to use NMR or mass spectrometry. To obtain good structural data on
both components within the complex from a contrast series, it is best to measure
scattering data on both sides of the solvent match point for the complex.
As a result, it is important to choose the deuteration level so that the match
point of the complex is around 50% D 2O.
3.2. Scattering Data Acquisition and Reduction
In a scattering experiment, the protein solutions are placed in the sample cell
and positioned in the X-ray or neutron beam to be irradiated while the intensity
of the scattered radiation is measured as a function of angle at the detector. The
X-ray or neutron beam must be smaller than the sample so that the entire beam
passes through the sample. The detector must be calibrated for flatness of
response and for precise Q determination at each point on the detector. The
detector response can be determined using an isotropic scatterer placed in the