Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Chemical analysis
Reexamination Certificate
2002-07-24
2003-11-18
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Chemical analysis
C702S030000, C356S432000, C250S574000
Reexamination Certificate
active
06651009
ABSTRACT:
BACKGROUND
Molecules in solution are generally characterized by their weight averaged molar mass M
w
, their mean square radius
⟨
r
g
2
⟩
,
and the second virial coefficient A
2
. The latter is a measure of the interaction between the molecules and the solvent. For unfractionated solutions, these properties may be determined by measuring the manner by which they scatter light using the method described by Bruno Zimm in his seminal 1948 paper which appeared in the Journal of Chemical Physics, volume 16, pages 1093 through 1099. The light scattered from a small volume of the solution is measured over a range of angles and concentrations. The properties derived from the light scattering measurements are related through the formula developed by Zimm:
R
(&thgr;)=
K*M
w
,cP
(&thgr;)[1−2
A
2
M
w
,cP
(&thgr;)]+
O
(
c
3
), (1)
where R(&thgr;) is the measured excess Rayleigh ratio in the direction &thgr; per unit solid angle defined as R(&thgr;)=[I
s
(&thgr;)−I
solv
(&thgr;)]r
2
/I
0
V, I
s
(&thgr;) is the intensity of light scattered by the solution a function of angle, I
solv
(&thgr;) is the intensity of light scattered from the solvent as a function of angle, I
0
is the incident intensity, r is the distance from the scattering volume to the detector, V is the illuminated volume seen by the detectors, P(&thgr;) is the form factor of the scattering molecules defined as P(&thgr;)=lim
c→0
R(&thgr;)/R(0), K*=4&pgr;
2
(dn/dc)
2
n
0
2
/(N
a
&lgr;
0
4
), N
a
is Avogadro's number, dn/dc is the refractive index increment, n
0
is the solvent refractive index, and &lgr;
0
is the wavelength of the incident light in vacuum. The form factor is related to the mean square radius by
P
(
θ
)
=
1
-
16
π
2
n
0
2
3
λ
0
2
⟨
r
g
2
⟩
sin
2
(
θ
/
2
)
+
O
(
sin
4
(
θ
)
/
2
)
(
2
)
The collection of light scattering data over a range of scattering angles is referred to more commonly as multiangle light scattering, MALS. The data are then fit to Eq. (1) to extract M
w
,
⟨
r
z
2
⟩
,
and A
2
. For this purpose, the reciprocal of Eq. (1) is more commonly used which may be written as:
K*c/R
(&thgr;)=1
/[M
w
P
(&thgr;)]+2
A
2
c+O
(
c
2
). (3)
There are several methods by which the data may be fit to Eq. (3). The most popular, historically, is to mimic in software the graphical method presented by Zimm. This is often referred to as the Zimm Plot method. Alternatively one may use the global nonlinear least squares fit described below.
A powerful method of characterizing a molecular solution is to fractionate the sample first by chromatographic means, such as size exclusion chromatography, SEC, and then measure the scattered light and concentration as a function of elution volume &ngr;. If the fractionation is sufficiently resolved, each volume sample can be considered to be essentially monodisperse. If A
2
is known from prior experiment, or the concentrations are low enough that the effect of A
2
on the scattered light is negligible, one may fit the data to Eq. (1) or (3) to extract the distributions M(&ngr;) and r
g
2
(&ngr;). This is routinely performed by commercial software such as the ASTPA® program developed by Wyatt Technology Corporation of Santa Barbara, Calif.
One may define a figure of merit, FOM, which characterizes when the A
2
term may be neglected. Equation (1) shows that A
2
is the prefactor of the c
2
term. By comparing the magnitude of the bracketed terms in Eq. (1), the FOM may be defined as
FOM=2
A
2
M
w
c.
(4)
When the FOM<<1, as was assumed in the derivation of the Zimm equation, the second virial coefficient has only a small effect on the light scattering signals. When one wishes to measure the second virial coefficient by light scattering, the FOM must be large enough that the effect is measurable with good precision, but it must not be made so large that higher order concentration terms are required in Eq. (1). Since SEC columns dilute the sample by about an order of magnitude per column, it is usually the case that the concentrations resulting from chromatographic separations are small enough that A
2
can usually be neglected. Details of the chromatographic separation methods, the definitions and calculations of the mass and size moments, and an explanation of the terminology used to describe the associated distributions may be found in the 1993 review article by Wyatt in
Analytica Chimica Acta
, volume 272, pages 1 through 40.
In summary, there are two modes of light scattering measurements. In the batch mode, a series of light scattering measurements of a single sample are made at different concentrations. The concentration and angular dependence of the scattering signals allows M
w
,
⟨
r
g
2
⟩
,
and A
2
to be determined. In the chromatography mode, the sample composition changes as the sample elutes, so a priori knowledge of A
2
is required, but the distributions M(v) and r
g
2
(v) can be measured. From the distributions, the averages M
w
, and
⟨
r
g
2
⟩
may be calculated. It should be noted that the values calculated from the fractionated sample measurements should be identical to the values measured from batch samples. Discrepancies arise from the assumption of A
2
=0 and the distortions due to interdetector band broadening.
Although A
2
can be determined from batch measurements, the question remains; can the second virial coefficient be measured accurately when the sample concentration is changing continuously in time, as is the case for a chromatographic elution? In U.S. Pat. No. 5,129,723 by Howie, Jackson, and Wyatt, a method was described whereby an unfractionated sample was injected into a MALS detector following dilution and thorough mixing. This procedure produced a sample peak passing through the light scattering detector whose profile was assumed to be proportional to the concentration profile of the diluted, yet unfractionated, sample. Since the mass distribution at each slice was the same, it was assumed that each point of the profile was proportional, at that point, to the sample's concentration times the weight averaged molar mass by referring to Eq. (3) and setting A
2
=0. On this basis, a Zimm plot could be produced using a set of these points, and the associated weight average molar mass, mean square radius, and second virial coefficient were then derived. It was thought that a concentration detector was not needed, since knowledge of the total mass injected was sufficient to convert the sample peak curve into a concentration profile. However, the method was flawed because the assumption that A
2
was zero contradicted the derived result that it was not.
A second method is to use a chromatography configuration, in which both a light scattering and a concentration detector are used. If one injects a monodisperse sample, or develops the chromatography method to fractionate peaks that are monomeric, the weight average molar mass at each eluting fraction should be constant throughout each peak. From the MALS and concentration data, a Zimm plot analysis may be performed from values at several different slices or sets of slices of the elution profile. The weight average molar mass, mean square radius, and second virial coefficient then may be derived. However, for most proteins, the mean square radius is too small to be accurately measured.
While this method may work in principle, there are practical difficulties that prevent it from being generally applicable. The experimental setup described above requires two detectors. Since the fluid must pass through capillaries and unions as it travels between the detectors, mixing and diffusion
Trainoff Steven P.
Wyatt Philip J.
Barlow John
Vo Hien
Wyatt Philip J.
Wyatt Technology Corporation
LandOfFree
Method for determining average solution properties of... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Method for determining average solution properties of..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method for determining average solution properties of... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3181440