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Abstract

The efficacy and subsequent success of a pharmaceutical is strongly dependent on its shelf life and its stability under tar- geted solution conditions. A typical man- ifestation of formulation instability is an increase in particle size, due to aggrega- tion of the analyte or carrier. As the par- ticle size increases, efficacy is diminished, primarily due to the decrease in the active surface area. Because of the corre- lation between efficacy and size, particle sizing is quickly becoming a routine step in the development of more stable and effective formulations. Dynamic light scattering (DLS), also known as photon correlation spectroscopy (PCS) and quasi-elastic light scattering (QELS), provides many advantages as a particle size analysis method. DLS is a non- invasive technique that measures a large population of particles in a very short time period, with no manipulation of the sur- rounding medium. Modern DLS instru- ments, notably the Zetasizer Nano system (Malvern Instruments, Southborough,
The efficacy and subsequent success of a
pharmaceutical is strongly dependent on
its shelf life and its stability under tar-
geted solution conditions. A typical man-
ifestation of formulation instability is an
increase in particle size, due to aggrega-
tion of the analyte or carrier. As the par-
ticle size increases, efficacy is diminished,
primarily due to the decrease in the
active surface area. Because of the corre-
lation between efficacy and size, particle
sizing is quickly becoming a routine step
in the development of more stable and
effective formulations.
Dynamic light scattering (DLS), also
known as photon correlation spectroscopy
(PCS) and quasi-elastic light scattering
(QELS), provides many advantages as a
particle size analysis method. DLS is a non-
invasive technique that measures a large
population of particles in a very short time
period, with no manipulation of the sur-
rounding medium. Modern DLS instru-
ments, notably the Zetasizer Nano system
(
Malvern Instruments, Southborough,
MA), can measure particle sizes as small as
0.6 nm and as large as 6 µm across a wide
range of sample concentrations. Because of
the sensitivity to trace amounts of aggre-
gates and the ability to resolve multiple
particle sizes, DLS is ideally suited for
macromolecular applications necessitating
low sample concentration and volume,
such as the development of stable food,
drug, and surfactant formulations and in
the screening of protein samples for crys-
tallization trials.
Particles and macromolecules in solution
undergo Brownian motion. Brownian
motion arises from collisions between the
particles and the solvent molecules. As a
consequence of this particle motion, light
scattered from the particle ensemble will
fluctuate with time. In DLS, these fluctua-
tions are measured across very short time
intervals to produce a correlation curve,
from which the particle diffusion coeffi-
cient (and subsequently the particle size)
is extracted.
In contrast to separation techniques, where
particles are separated and then counted, in the
DLS technique, all of the size information for
the ensemble of particles is contained within a
single correlation curve. As such, particle size
resolution requires a deconvolution of the data
contained in the measured correlation curve.
While standard algorithms exist for transform-
ing the correlation curve to a particle size distri-
bution, an understanding of the precision and
accuracy of the distribution necessitates a solid
understanding of the underlying principles
behind the DLS technique itself. This article
presents a brief overview of the DLS tech-
nique, along with common algorithms used
to deconvolute the size distribution from
the measured correlation curve.
Dynamic light scattering
Light scattering is a consequence of the
interaction of light with the electric field
of a particle or small molecule. This in-
teraction induces a dipole in the particle
electric field that oscillates with the same
frequency as that of the incident light.
Inherent to the oscillating dipole is the
acceleration of charge, which leads to
the release of energy in the form of scat-
tered light.
For a collection of solution particles illu-
minated by a monochromatic light source
such as a laser, the scattering intensity
measured by a detector located at some
point in space will be dependent on the
relative positions of the particles within
the scattering volume. The scattering
volume is defined as the crossover section
of the light source and the detector
optics. The position dependence of the
scattering intensity arises from construc-
tive and destruction interference of the
scattered light waves. If the particles are
static, or frozen in space, then one would
expect to observe a scattering intensity
that is constant with time, as described in
Figure 1. In practice, however, the parti-
cles are diffusing according to Brownian
motion, and the scattering intensity fluc-
tuates about an average value equivalent
to the static intensity. As detailed in
Figure 1, these fluctuations are known as
the dynamic intensity.
Across a long time interval, the dynamic
signal appears to be representative of ran-
dom fluctuations about a mean value.
When viewed on a much smaller time
scale, however (
Figure 2), it is evident that
the intensity trace is in fact not random,
but rather comprising a series of continu-
ous data points. This absence of disconti-
nuity is a consequence of the physical
confinement of the particles in a position
very near to the position occupied a very
short time earlier. In other words, on short
time scales, the particles have had insufficient
time to move very far from their initial posi-
tions, and as such, the intensity signals are very
similar. The net result is an intensity trace that
is smooth, rather than discontinuous.
00 / DECEMBER 2003 • AMERICAN BIOTECHNOLOGY LABORATORY
APPLICATION NOTE
A Primer on Particle Sizing Using
Dynamic Light Scattering
by Kevin Mattison, Ana Morfesis, and Michael Kaszuba
Figure 1 Schematic detailing the scattering volume and subsequent static and
dynamic light scattering intensities.
Figure 2 Intensity time trace showing the lack of discontinuity expected for a
random signal when viewed across a short time interval.
Correlation is a second-order sta-
tistical technique for measuring
the degree of nonrandomness in
an apparently random data set.
When applied to a time-depend-
ent intensity trace, as measured
with DLS instrumentation, the
correlation coefficients,
G(τ), are
calculated as shown in Eq. (1),
where
t is the initial (start) time
and
τ is the delay time.
G(τ) =
0
I(t)I(t + τ)dt (1)
As a summation, the correlation equa-
tion can be expressed as shown in Eq.
(2), or expressed in a tabular format as
shown in
Table 1.
G
k
(τ
k
) =
i=0
I(t
i
)I(t
i
+ τ
k
) (2)
Typically, the correlation coefficients
are normalized, such that
G() = 1.
For monochromatic laser light, this
normalization imposes an upper corre-
lation curve limit of 2 for
G(t
o
) and a
lower baseline limit of 1 for
G(). In
practice, however, the upper limit can
only be achieved for carefully opti-
mized optical systems. Typical experi-
mental upper limits are approx.
1.8–1.9.
In DLS instrumentation, the correla-
tion summations are performed using
an integrated digital correlator,
which is a logic board comprising
operational amplifiers that continu-
ally add and multiply short time scale
fluctuations in the measured scatter-
ing intensity to generate the correla-
tion curve for the sample. Examples
of correlation curves measured for
two submicron particles are given in
Figure 3. For the smaller and hence
faster diffusing protein, the measured
correlation curve has decayed to
baseline within 100 µsec, while the
larger and slower diffusing silicon
dioxide particle requires nearly 1000
µsec before correlation in the signal is
completely lost.
Hydrodynamic size
All of the information regarding the
motion or diffusion of the particles in the
solution is embodied within the measured
correlation curve. For monodisperse samples,
consisting of a single particle size group, the
correlation curve can be fit to a single expo-
nential form as given in Eq. (3), where
B is
the baseline,
A is the amplitude, and D is the
diffusion coefficient. The scattering vector
(
q) is defined by Eq. (4), where ñ is the sol-
vent refractive index,
λ
o
is the vacuum
wavelength of the laser, and
θ is the scatter-
ing angle.
G(τ) =
0
I(t)I(t + τ)dt =
B
+ A e
–2q
2
D
τ
(3)
q = sin

(4)
The hydrodynamic radius is
defined as the radius of a hard
sphere that diffuses at the same
rate as the particle under exami-
nation. The hydrodynamic radius
is calculated using the particle
diffusion coefficient and the
Stokes-Einstein equation given in
Eq. (5), where
k is the Boltzmann
constant,
T is the temperature, and η
is the solvent viscosity.
R
H
=
(5)
A single exponential or Cumulant fit
of the correlation curve is the fitting
procedure recommended by the
International Standards Organization
(ISO). The hydrodynamic size ex-
tracted using this method is an aver-
age value, weighted by the particle
scattering intensity. Because of the
intensity weighting, the Cumulant
size is defined as the Z average or
intensity average.
While the Cumulant algorithm and the
Z average are useful for describing gen-
eral solution characteristics, for multi-
modal solutions, consisting of multiple
particle size groups, the Z average can be
misleading. For multimodal solutions, it
is more appropriate to fit the correlation
curve to a multiple exponential form,
using common algorithms such as CON-
TIN or Non Negative Least Squares
(NNLS). Consider, for example, the cor-
relation curve shown in
Figure 4. This
correlation curve, measured for a 10-
mg/mL lysozyme sample in 100 m
M
NaCl at 69 °C, clearly exhibits two ex-
ponential decays, one for the fast-mov-
ing monomer at 3.5 nm and one for the
slow-moving aggregate at 388 nm. The
size distribution shown in Figure 4 was
derived using the CONTIN algorithm.
When the single exponential Cumulant
algorithm is used, a Z average of 12.4 nm
is indicated, which is clearly inconsis-
tent with the distribution results.
System scope
The Zetasizer Nano system (Figure 5) includes
the hardware and software for combined dy-
namic, static, and electrophoretic light scatter-
ing measurements, giving the researcher a wide
range of sample properties, including the size,
molecular weight, and zeta potential. The sys-
tem was designed specifically to meet the low
concentration and sample volume requirements
typically associated with pharmaceutical and
biomolecular applications, along with the high
concentration requirements for colloidal appli-
cations. Satisfying this unique mix of require-
kT
6πηD
θ
2
4
π
~
n
λ
0
APPLICATION NOTE
00 / DECEMBER 2003 AMERICAN BIOTECHNOLOGY LABORATORY
Table 1 Correlation coefficient equations for selected k index values
k Intensity Correlation coefficient
0 I(t
0
)
1
I(t
1
) G
1
(t
1
) = I(t
0
)I(t
1
) + I(t
1
)I(t
2
) + I(t
2
)I(t
3
) + + I(t
k–1
)I(t
k
)
2
I(t
2
) G
2
(t
2
) = I(t
0
)I(t
2
) + I(t
1
)I(t
3
) + I(t
2
)I(t
4
) + + I(t
k–2
)I(t
k
)
3
I(t
3
) G
3
(t
3
) = I(t
0
)I(t
3
) + I(t
1
)I(t
4
) + I(t
2
)I(t
5
) + + I(t
k–3
)I(t
k
)
nI(t
n
) G
n
(t
n
) = I(t
0
)I(t
n
)
Figure 3 Intensity correlation curves for ovalbumin and silicon dioxide, measured with a
Zetasizer Nano ZS static, dynamic, and electrophoretic light scattering instrument.
Figure 4 Correlation curve and CONTIN distribution for 10-mg/mL lysozyme in 100 mM
NaCl at 69 °C, measured with a Zetasizer Nano ZS static, dynamic, and electrophoretic light scat-
tering system. The Z average of 12.4 nm is indicated by the solid line in the distribution results.
Figure 5 The Zetasizer Nano, a combined static,
dynamic, and electrophoretic light scattering system.
ments was accomplished via the integration of a
backscatter optical system and the design of a
novel cell chamber. As a consequence of these
features, the system specifications for sample
size and concentration are noteworthy, with a
size range of 0.6 nm to 6 µm and a concentra-
tion range of 0.1 mg/mL lysozyme to 40%
wt/vol. Also, the Zetasizer hardware is self opti-
mizing, and the software includes a “one click”
measure, analyze, and report feature designed to
minimize the new user learning curve.
Additional reading
Benight AS, Wilson DH, Budzynski DM, Goldstein RF.
Dynamic light scattering investigations of RecA self-
assembly and interactions with single strand DNA.
Biochimie 1991; 73(2–3):143–55.
Brown RGW. Miniature laser light scattering instrumentation
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D’Arcy A. Crystallizing proteins—a rational approach. Acta
Cryst 1994; D50:467–71.
Fusett F, Dijkstra BW. Purification and light-scattering analy-
sis of penicillin-binding protein 4 from
Escherichia coli.
Microbiol Drug Res 1996; 2(1):73–6.
Hutchinson FJ, Francis SE, Lyle IG, Jones MN. The charac-
terization of liposomes with covalently attached proteins.
Biochim Biophys Acta 1989; 978(1):17–24.
Moradian-Oldak J, Leung W, Fincham AG. Temperature and
pH-dependent supramolecular self-assembly of amelogenin
molecules: a dynamic light-scattering analysis. J Struct Biol
1998; 122(3):320–7.
Phillies GD. Quasielastic light scattering. Anal Chem 1990;
62(20):1049A–57A.
Pecora R. Dynamic light scattering: applications of photon cor-
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of thermal excitations of F-actin solutions and of growth
kinetics of actin filaments. Biopolymers 1992; 32(11):
1471–89.
Sam T, Pley C, Mandel M. A hydrodymanic study with quasi-
elastic light scattering and sedimentation of bacterial elongation
factor EF-Tu.guanosine-5
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sociating conditions. Biopolymers 1990; 30(3–4):299–308.
Santos NC, Sousa AMA, Betbeder D, Prieto M, Castanho
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The authors are with
Malvern Instruments, 10 Southville Rd.,
Southborough, MA 01772, U.S.A.; tel.: 508-480-0200; fax:
508-460-9692; e-mail: info@malvernusa.com; home page:
www.malverninstruments.com.
APPLICATION NOTE
00 / DECEMBER 2003 AMERICAN BIOTECHNOLOGY LABORATORY
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In the first part of this work we report quasielastic light scattering (QELS) studies of the internal dynamics of transient actin networks over a time range of 10 ⁻⁶ –10 ⁻² s, scattering angles between ζ = 20° and 150°, and a concentration range of 0.015 (0.3) to 0.7 mg/mL (15 μ M ). We confirm our previous result that (1) the dynamic structure factor g ( q, t ) is determined by the thermally excited undulations of the actin filaments and (2) that the initial decay of g ( q, t ) scales as g ( q, t )∝ exp(q α t) while the long time decay scales as g ( q, t ) ∝ exp[‐(Aq α t) 2/3 ] with α = 2.75. The deviation of α from the theoretical value of α = 3 predicted for Rouse‐Zimm chains is similar to that found for high molecular weight macromolecular solutions by QELS. A refined analysis of the dynamic structure factor showed that it can be interpreted in terms of three relaxation processes (besides the contribution of the residual monomer diffusion): (1) the dominant Rouse‐Zimm dynamics, which comprises between 65 (at high concentrations) and 85% of the signal; (2) a fast relaxation process with a decay constant of Γ = 9 × 10 ³ s ⁻¹ , which contributes at all concentrations with the same amplitude; and (3) a nonexponential ultraslow contribution of the form g us ∝ exp[(– Γ us t )] 1/4 . The third contribution appears only at high concen‐trations and increases strongly with decreasing scattering angles. It is thus attributed to fluctuations of the mesh size of the transient actin network. In the second part we show that high sensitivity QELS may be applied to follow the actin polymerization process at low temperatures (10°C). The apparent diffusion coefficient and the static scattering intensity of the actin filaments were determined as functions of polymerization time t pol . We show that the process consists of the rapid growth of a few filaments that become very long (≈10 μm; even at actin concentrations of 0.04 μg/mL) near the critical growth concentration of 0.012 μg/mL, as is expected for a growth process determined by nucleation. Finally, we studied actin networks polymerized in the presence of complexes of gelsolin with actin. By application of the CONTIN program we could determine the length distribution of the filaments. The very broad length distribution is nearly exponential, quite analogous to the distribution predicted for polymers grown by the polycondensation process; that is the association of monomers and oligomers. © 1992 John Wiley & Sons, Inc.
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Dynamic light scattering (DLS) measurements were performed on self-assembled solutions of RecA as a function of assembly time under strand exchange ionic strength conditions (10 mM MgCl2, 65 mM NaCl, 10 mM Tris-HCl, pH = 7.5, 1 mM DTT, 3-4 microM RecA) in the absence of ATP. These measurements yield distributions of the translational diffusion coefficients of the changing populations of assembling protein species. Interpretations of results of DLS measurements are made in terms of model hydrodynamic calculations that indicate, under the solution conditions employed, the smallest fundamental quaternary subunit of RecA is a hexamer in a toroidal or lock-washer configuration. Interactions of M13mp19 circular single strand DNA (ssDNA) with RecA assembled to different stages were also investigated. Additions of ssDNA to self-assembled solutions of RecA acts to dissociate the associated structures into hexamer subunits. However, the effect of ssDNA on assembled RecA is highly dependent on the RecA self-assembly state. The longer the assembly time, the less reversible the self-assembled structures of RecA become. Binding isotherms of titrated mixtures of ssDNA with RecA self-assembled to various stages were also determined. Evaluated dissociation constants of RecA/ssDNA complexes were found to increase with increases of the associated state of RecA. These results strongly suggest that, under the solvent conditions employed, the active ssDNA binding form of RecA is a hexamer.
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The hydrodynamics of the bacterial elongation factor EF-Tu have been studied in the presence of its ligand guanosine-5'-diphosphate (GDP) by sedimentation in the ultracentrifuge and quasielastic light scattering. Sedimentation studies have made it possible to establish experimental conditions under which only negligible aggregation of the protein occurs (neutral pH, concentration less than 3 mg/mL). Analysis of the light intensity autocorrelation functions under these conditions revealed two independent scattering species with diffusion coefficients of 0.71 X 10(-6) and 0.04 X 10(-6) cm2 s-1. The material with the lower diffusion coefficient, i.e., the aggregates, represented less than 1% of the total number of EF-Tu particles. The other 99% diffused as monomeric molecules with a molar mass corresponding to the value calculated from the known primary structure of the protein. The hydrodynamic parameters derived from the experimental data suggest that EF-Tu.GDP in solution is close to a spherical particle.
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The problem of characterising liposomes with covalently attached proteins has been analysed theoretically in terms of a normal weight distribution of liposome diameters. The polydispersity of protein conjugation is considered in terms of the width (standard deviation) of the liposome size distribution. It is shown that the weight-average number of proteins per liposome is a convenient parameter to use to define the protein content of proteoliposomes. Two types of proteoliposome have been prepared (small unilamellar vesicles and reverse phase evaporation vesicles) in which wheat germ agglutinin is covalently coupled to the liposomal surface. The liposomes cover a range of weight average diameter from 65 to 240 nm and of polydispersity (weight to number average diameter (dw/dn) from 2.6 to 11.4. The liposomes have been characterised by chemical analysis and photon correlation spectroscopy and the results are discussed in terms of the theoretical consequences of an equivalent normal weight distribution of diameters.
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Penicillin binding protein 4 (PBP4) from Escherichia coli is a protein involved in the recycling and maturation of the bacterial cell wall and it is inhibited by beta-lactam antibiotics. PBP4 exhibits D-Ala-D-Ala-endopeptidase as well as D-Ala-D-Ala-carboxypeptidase activity. To provide a structural template for the design of new, more specific antibiotics we started X-ray crystallographic studies of penicillin binding protein 4 from Escherichia coli. PBP4 has been overexpressed in Escherichia coli as a His-tagged protein. A large-sclae purification scheme, yielding a very pure material, has been set up and crystallization experiments have been started. Dynamic light scattering experiments suggested that PBP4 exhibits aggregation behavior with a number of different precipitating agents and additives. Only by addition of EDTA, PEG 4000, and ammonium sulfate is the molecular mass about 110 kDa.