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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
for particle size analysis. Appl Opt 1990; 29(28):1.
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-
relation spectroscopy. Plenum Press, 1985.
Piekenbrock T, Sackmann E. Quasielastic light scattering study
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
′
-diphosphate complex under nonas-
sociating conditions. Biopolymers 1990; 30(3–4):299–308.
Santos NC, Sousa AMA, Betbeder D, Prieto M, Castanho
MARB. Structural characterization of organized systems
of polysaccharides and phospholipids by light scattering,
spectroscopy, and electron microscopy. Carbohyd Res
1997; 300(1):31–40.
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