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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