ASTRA Summary Report Explanation Chart
The ASTRA Summary Report contains information about the calculated molecular
weights (MW) as well as collection and processing parameters that were
applied during data analysis.
The following chart is designed to guide you through the Summary Report
(adopted from ASTRA manual; Wyatt Technology). Please note that the
Result section presents data for ALL peaks selected for analysis.
Peak selection and boundaries are shown on the attached "Peak ID" graph.
COLLECTION INFORMATION
This part of the report contains information about data collection,
instrument used, type of flow cell in the LS detector and solvent
in the mobile phase.
The values of the calibration constants used during data processing
are shown along with the information regarding mass detector (refractive
index or UV) was used to estimate eluted mass:
AUX1: UV detector (which might be used as a mass detector when the
extinction coefficient is known)
AUX2: RI detector (might be used as a mass detector when the dn/dc
value is known)
Flow rate used during SEC run is also shown.
PROCESSING INFORMATION
This part of the report refers to the fitting method that was used
by ASTRA to carry out the molecular mass determination
Processing time:
date and time of processing
Fit method/model:
Calculation method:
provides information relating to how the eluted mass was estimated
(for each individual slice):
dn/dc value + AUX constant:
means that the known dn/dc was used along with the AUX detector reading.
Alternatively, the total injected mass can be used with the assumption
of 100% recovery of that mass within the analyzed peak value (dn/dc is
a refractive index increment of the solute, which usually means the increase
in refractive index with protein concentration).
Detectors used:
the subset of signals from LS detectors used in the analysis (there
is a total of 18 detectors in the DAWN instrument but for aqueous solutions
the signal from lower angle detectors, i.e. detectors #3-6 and #16-18,
is very noisy and for some samples these readings may be deleted during
data processing)
RESULTS
This section summarizes the molecular weight calculations for each peak
selected (please refer to attached "Peak ID" graph for peak identification).
Volume:
indicates the boundaries for the selected peak (in mL or elution time)
Slices:
refers to number of slices for which the MW is calculated (within the
peak of interest)
A2:
value of second virial coefficient used during the analysis. The value
of the second viral coefficient is negligible at the low concentrations
used during chromatographic applications.
Fit Degree:
degree of polynomial function used during the fitting protocol (1 means
linear function)
Injected Mass:
used for mass estimation if a total injected mass is used instead of
depending upon the "dn/dc value + AUX constant" method
Calc. Mass:
indicates the mass estimated by ASTRA within the boundaries of the
particular peak
dn/dc value:
dn/dc value used for mass calculation using the RI detector signal
(dn/dc is the refractive index increment of the solute).
Polydispersity (Mw/Mn):
indicates whether the peak is homogenous with respect to molar mass.
A homogeneous (i.e., monodisperse) sample is one that contains only one
type of molecule of defined MW (e.g. pure monomeric protein), thus the
average mass is independent of the averaging method and polydispersity
will equal 1. If the sample contains a mixture of species of different
molar masses (i.e., polydisperse sample; for example, a mixture of dimer
or tetramer and monomer) the average mass will depend on the averaging
method and the polydispersity will be different from 1.
Polydispersity (Mz/Mn):
Molar Mass Moments (g/mol)
Mn:
Number-average molar mass defined as:
Mn is the molar mass (or molecular weight, MW); this might for
instance be measured by osmometry.
Mw: Weight-average
molar mass is defined as:
Mw is the molar mass (or molecular weight, MW); this might for
instance be measured by light scattering method.
Mz: Z-average
molar mass is defined as:
Mz is the molecular weight (MW); this might for instance be
measured during sedimentation analysis.
R.M.S. Radius Moments (nm)
NOTE:
The method for data analysis, namely, Zimm/Debye/Berry/random coil
plot describes the algorithm
employed by ASTRA for processing data for EACH INDIVIDUAL
slice. Technically, the molar mass calculated for each slice from
either of the fits (Zimm/Debye/Berry/random
coil plot) is weight-averaged and the radius is z-averaged. These
masses/radii can be used together with the concentration ci
(measured with the concentration sensitive detector, UV or RI, for each
slice) to find the average mass for the entire peak. Molar
masses, Mn, Mw and Mz, and radius
moments, Rn, Rw and Rz, represent average values obtained using different
averaging formulas. The summations are performed over one peak.
Please note that light scattering can be used to estimate size/radius of
objects that are of the size that correspond to at least 1/20th of the
incident light. For DAWN-DSP
instrument the laser wavelength is 633 nm. Thus, radii smaller
then ~ 20 nm cannot be estimated reliably.
The errors represent ONLY the statistical consistency of the data and
DO NOT PROVIDE AN ABSOLUTE ERROR FOR THE ANALYSIS. The sources of
errors that are not accounted for are, for example, uncertainty in the
dn/dc value, calibration constants or normalization coefficients.
Calculation
of MW by ASTRA
In general, ASTRA is solving the following
equation that relates the excess scattered light to the concentration and
weight-average molar mass:
(1)
where:
R(Q) is the excess
intensity of scattered light at DAWN angle Q
c is the
sample concentration
Mw is the weight-average
molecular weight
A2
is a second virial coefficient
K* is an optical parameter
equal to 4p2n2 (dn/dc)2
/ (lo4NA)
n is the
solvent refractive index and dn/dc is the refractive index increment
NA is Avogadro’s
number
lo
is the
wavelength of the scattered light in vacuum.
The function P(Q) describes the angular dependence
of scattered light.
The expansion of 1/ P(Q) to first order gives:
1/ P(Q) = 1 + (16p2/3l2)
<rg2>. sin2(Q/2)
+ f4 sin4(Q/2) +...
There are several ways in which Eq.
(1) (that relates excess of scattered light to concentration and weight-average
molar mass) can be solved to get Mw and <rg2>.
The parameter "Fit method/model" refers to the actual
method applied.
Debye Fit Method:
constructs a plot of R(Q)/K*c vs. sin2(Q/2)
and fits a polynomial in sin2(Q/2)
to the data, thereby obtaining Mw and <rg2> from
the intercept and slope at zero angle (the order of polynomial used during
fitting is given in the RESULT section as "FIT
DEGREE").
It gives good results over a wider range of molecular weight as compared
to the Zimm formalism.
Zimm Fit Method:
constructs a plot of K*c/R(Q) vs. sin2(Q/2)
and fits a polynomial in sin2(Q/2)
to the data, thereby obtaining Mw and <rg2> from
the intercept and slope at zero angle (the order of polynomial used during
fitting is given in the RESULT section as "FIT
DEGREE").
This is the most popular method for analysis of light scattering data.
It works well for mid-sized molecules (rms radius up to ~20-50 nm).
Berry Fit Method:
constructs a plot of SQRT{K*c/R(Q)} vs.
sin2(Q/2) and fits a polynomial in
sin2(Q/2) to the data (the
order of polynomial used during fitting is given in RESULT section as "FIT
DEGREE").
Useful for large molecules.
Random Coil Method:
Eq. (1) is
solved after inserting the theoretical form factor P(Q)
for random coils given by:
where u = (4p/l)2<r2>sin2(Q/2).
P(Q) is a nonlinear function of <r2>,
an iterative nonlinear least square fit is used during fitting. This fitting
method might be advantageous for large random coil molecules (the
order of polynomial used during fitting is given in RESULT section as "FIT
DEGREE").
Please note that all the above methods will give nearly identical results
for small molecules (rms radius <10nm). Thus, any of the fitting formalisms
can be used interchangeably for proteins with MW <1x106 Da.
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Introduction
to Light Scattering
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Light
Scattering Theory
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Light
Scattering Data Set
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Results
for Standard Proteins
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Light
Scattering Service
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Light
Scattering
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