REVIEW
Dynamic light scattering: a practical guide and applications
in biomedical sciences
Jörg Stetefeld
1,2
& Sean A. McKenna
1,2
& Trushar R. Patel
3,4
Received: 13 June 2016 /Accepted: 8 September 2016 /Published online: 6 October 2016
#
International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag Berlin Heidelberg 2016
Abstract Dynamic light scattering (DLS), also known as pho-
ton correlation spectroscopy (PCS), is a very powerful tool for
studying the diffusion behaviour of macromolecules in solu-
tion. The diffusion coef ficient, and he nce the hydrodyna mic
radii calculated from it, depends on the size and shape of mac-
romolecules. In this review, we provide evidence of the useful-
ness of DLS to study the homogeneity of proteins, nucleic
acids, and complexes of protein–protein or protein–nucleic acid
preparations, as well as to study protein–small molecule inter-
actions. Further, we provide examples of DLS’s application
both as a complementary method to analytical ultracentrifuga-
tion studies and as a screening tool to validate solution scatter -
ing models using determined hydrodynamic radii.
Keywords Analytical ultracentrifuge
.
Diffusion coefficient
.
Dynamic light scattering
.
Hydrodynamic radius
.
Light
scattering
.
Protein–ligand interactions
.
Protein–nucleic acid
complexes
.
Protein–protein complexes
Introduction
Detection of light scattering from matter is a useful technique
with applications in numerous scientific disciplines where, de-
pending on the light source and detector, specific properties of
molecules can be studied. In a typical light-scattering experi-
ment, sample is exposed to a monochromatic wave of light
and an appropriate detector detects the signal. One of the earliest
light-scattering experiments was described by John Tyndall,
which characterized light scattering from colloidal suspensions
(Tyndall effect), where particles are larger than the wavelength
of the incident light (Tyndall 1868). Soon after, Lord Rayleigh
described light scattering from part icles that are smaller tha n the
wavelength of light (Rayleigh scattering), which explained both
that the sky’s blue colour is a result of scattering of light due to
atmospheric particles and that the refractive index of the scatter-
ing medium plays a crucial role in light scattering (Strutt 1871a,
b). In contrast to Rayleigh theory, Gustav Mie (1908) described
a theory (Mie theory) to study the scattering of light from ab-
sorbing and non-absorbing particles that are large compared to
the wavelength of light by taking into account particle shape and
thedifferenceinrefractiveindexbetweenparticlesandtheme-
dium the particles are present in. Peter Debye suggested that
scattering for particles can be studied independently of assump-
tions on mass, size, or shape as a function of angle (Debye
1915), which is often referred as Rayleigh–Debye scattering.
The usefulness of light scattering as a method to character-
ize the diffusion behaviour of particles in solution resulted
from a series of seminal discoveries. Einstein and
This article is part of a Special Issue on ‘Analytical Quantitative Relations
in Biochemistry’ edited by Damien Hall and Stephen Harding.
* Jörg Stetefeld
jorg.stetefeld@ad.umanitoba.ca
* Trushar R. Patel
trushar.patel@uleth.ca
1
Department of Chemistry, University of Manitoba, 144 Dysart Road,
Winnipeg, Manitoba R3T 2N2, Canada
2
Department of Biochemistry and Medical Genetics, University of
Manitoba, 745 Bannatyne Avenue - Basic Medical Sciences
Building, Winnipeg, Manitoba R3E 0J9, Canada
3
School of Biosciences, University of Birmingham, Edgbaston,
Birmingham B15 2TT, UK
4
Alberta RNA Research and Training Institute, Department of
Chemistry & Biochemistry, University of Lethbridge, 4401
University Drive, Lethbridge, Alberta T1K 3M4, Canada
Biophys Rev (2016) 8:409–427
DOI 10.1007/s12551-016-0218-6
Smoluchowski proposed that liquid should be considered as a
continuous medium where thermal fluctuations create inho-
mogeneities, which result in density and concentration fluctu-
ations (Fluctuation theory of light scattering, Einstein (1910);
v. Smoluchowski 1908 ). Einst ein (1905) also established
Brownian motion theory (named after Robert Brown)
explaining molecular motion of particles. He established that
particles were subjected to random forces due to constant col-
lision with solvent molecules resulting in random walk of
particles, and that the mean squared displacement of
particles due to Brownian motion is p roportional to time.
Later, Einstein also established a relationship between the
diffusion coefficient of particles to their translational friction
by including the discovery from Sir George Stokes (1845)that
suggested that the friction exerted by a moving particle is
proportional to its radius and to the viscosity of the solvent
surrounding particles (Einstein 1906). At the same time,
William Sutherland also presented a very similar derivation
of the Stokes–Einstein equation independently (Sutherland
1905). However, until this point the role of optical anisotropy
on angular dependence, intensity, and polarization of scattered
light had not been studied. Cabannes and Rocard (1929)and
Gans (1921; 1923) addressed the theory of optically aniso-
tropic scatters as well as their influence on polarisation of
scattered light. By this time the Rayleigh –Gans–Debye
(RGD) theory was established that included scattering from
large particles; however , Zimm’s(1945; 1948)modifications
to RGD equations led the foundation of modern light-
scattering approaches that are being utilized to determine size,
shape, and molecular weight of macromolecules in solution.
On the other hand, Leon Brillouin (1914; 1922) proposed
formation of two peaks in the frequency distribution of
scattered light caused by the scattering of light by phonons
(quasi-particles of sound), resulting in two peaks in the
Rayleigh (central) line in the frequency spectrum which was
later named as the Brillouin doublet. This phenomenon was
further evaluated by Gross (1930) and Landau and Placzek
(1934), which in conjunction with the development of laser
optics in the 1960s would revolutionize the light-scattering
studies of molecules in liquids. Pecora (1964) established that
the dif fusion of macromolecules in solution led to broadening
of the frequency profile of scattered light. Pike and co-workers
developed the first digital autocorrelator in 1969 and performed
experiments on haemocyanin to determine its diffusion coeffi-
cient (Foord et al. 1970). Thus, the relationship between light
scattering and diffusion behaviour of particles was established
and experimentally verified, which eventually allowed charac-
terization of m olecules in solution using light-scattering
methods. These events are briefly summarised in Table 1.
Over the years, Pecora, C ummins, Pike and others
(Bloomfield and Lim 1978; Cummins et al. 1964; Fujime
1972; Jake man and Pike 1969;Pecora1972; Pike 1972)had
developed various approaches to determine the diffusion
coefficient of molecules in solution, and ultimately their contri-
butions led to the development of the modern dynamic light-
scattering (DLS) instrument, with Malvern Instruments
(Malvern, UK) commercializing the first modern DLS instru-
ments followed by Brookhaven (Long Island, USA) and ALV
(Langen, Germany). Since its ince
ption, DLS has proven parti-
cularly popular in determining hydrodynamic behavior of pro-
teins, nucleic acids, and viruses due to its ability to provide infor-
mation on both size and aggregation. There are already a number
of excellent reviews detailing the theory and applications of DLS
(Bloomfield 1981;Fujime1972;HardingandJumel1998;
Harvey 1973;Jamiesonetal.1972;Lorberetal.2012;
Nieuwenhuysen and Clauwaert 1981;Nobbmannetal.2007;
Rimai et al. 1970; Schurr 1977; Serdyuk et al. 2007;Van
Holde 1970; Zakharov and Scheffold 2009). Here, our aim is to
provide a brief theoretical background, an update on applications
of DLS in studying proteins, nucleic acids, and their complexes,
and a discussion of the benefits that modern instruments offer .
Theoretical considerations
When a monochromatic beam of light encounters solution con-
taining macromolecules, light scatters in all directions as a func-
tion of the size and shape of the macromolecules. In static light
scattering, the intensity of scattered light is analysed as time-
averaged intensity, which provides useful information on mo-
lecular weight and radius of gyration of macromolecules. On
the other hand, if the intensity fluctuations (caused due to
Brownian motion of macromolecules in solution) of scattered
light is analysed, the diffusion coefficient (D
τ
) that is related to
hydrodynamic size o f macr omolecules can be obta ined.
Dynamic light scattering, also known as photon correlation
spectroscopy or quasi-elastic light scattering, is a tec hnique that
primarily measures the Brownian motion of macromolecules in
solution that arises due to bombardment from solvent mole-
cules, and relates this motion to the size (or D
τ
)ofparticles.
Such motion of macromolecules depends on their size, tempe-
rature, and solvent viscosity (Harding and Jumel 1998).
Therefore, knowledge of accurate temperature is essential for
DLS measurements, since the viscosity of solvent depends on
the temperature (Harding 1999). When the movement of parti-
cles over a time range is monitored, information on the size of
macromolecules can be obtained, as large particles diffuse
slowly, resulting in similar positions at different time points,
compared to small particles (such as solvent molecules) which
move faster and therefore do not adopt a specific position.
In a dynamic light-scattering instrument, when laser light
encounters macromolecules the incident light scatters in all
directions and scattering intensity is recorded by a detector.
The monochromatic incident light will undergo a phenome-
non called Doppler broadening as the macromolecules are in
continuous motion in solution (Harding and Jumel 1998). The
410 Biophys Rev (2016) 8:409–427
scattered light will either result in mutually destructive phases
and cancel each other out, or in mutually constructive phases
to produce a detectable signal. The digital autocorrelator then
correlates intensity fluctuations of scattered light with re-
spect to time (ns-μs) to determine how rapidly the intensity
fluctuates, which is related to the diffusion behaviour of
macromolecules. In a dynamic light-scattering experiment,
we measure the G
2
(τ), an intensity correlation function (or
second-order correlation function) that describes the motion
of macromolecules under investigation and can be
expressed as an integral over the product of intensities at
time t and delayed time (t + τ)(BerneandPecora1976):
G
2
τðÞ¼ ItðÞItþ τðÞhi ð1Þ
where, τ is the lag time between the two time-points.
The G
2
(τ) can be normalised as:
g
2
τðÞ¼
ItðÞItþ τðÞ
hi
ItðÞ
hi
2
ð2Þ
The braces in both equations represent averaging of prop-
erties over the duration of the experiment (time t).
In a typical light-scattering experiment, it is not possible to
precisely know how each particle moves in solution; however,
the motion of particles relative to each other is correlated by
means of an electric field correlation function, G
1
(τ), also
known as the first-order correlation function, which illustrates
correlated particle movement and can be defined as:
G
1
τðÞ¼ EtðÞEtþ τðÞ
hi
ð3Þ
where, E(t)andE(t+τ) represent the scattered electric fields at
times (t)and(t + τ)
Similarly to equation 2, an equation 3 can be normalized as:
g
1
τðÞ¼
EtðÞEtþ τðÞ
hi
EtðÞEtðÞ
hi
ð4Þ
The g
1
(τ)andg
2
(τ) can be coupled to each other by
the Siegert relation (1949) based on an approximation that
the scattering is homod yne (photodetector detects only
Tabl e 1 Timeline of major
events
Historical developments References
Friction experienced by moving particles is related to its radius
and solvent viscosity
Stokes (1845)
Tyndall effect: light scattering from colloidal suspensions Tyndall (1868)
Rayleigh scattering: blue colour of sky due to the scattering
of light by atmospheric particles, importance of refractive
index in light scattering
Strut t (1871a; 1871b)
Mie scattering: scattering of light from particles larger than
the wavelength of light
Mie (1908)
Brownian motion theory: collision with solvent molecules
results in random motion of particles
Einstein (1905)
Stokes–Einstein relationship: combines light scattering and
diffusion behaviour of particles
Einstein (1906), Sutherland (1905)
Fluctuation theory of light scattering: thermal fluctuations
result into local inhomogeneities and intensity of scattered
light can be determined by the mean-square fluctuations
in density and/or concentration
Einstein (1910), v. Smoluchowski (1908)
Rayleigh–Debye scattering: particles can be studied without
assumptions on mass, size or shape as a function of angle
Debye (1915)
Theory of optically anisotropic scatters Cabannes and Rocard (1929), Gans
(1921; 1923)
Brillouin doublet: theory and verification Brillouin (1914; 1922), Gross (1930),
Landau and Placzek (1934)
Siegert relation: relationship between the electric field
correlation and intensity correlation function
Siegert (1949)
Beginning of the modern light scattering approaches Pecora (1964)
Digital autocorrelator development and diffusion
coefficient measurement of haemocyanin
Foord et al. (1970)
Cumulant analysis method for monomodal systems Koppel (1972)
Exponential sampling method Ostrowsky et al. (1981)
Constrained regularization method for inverting data Provencher (1982a; 1982b)
Non-negative least squares analysis method Morrison et al. (1985)
Maximum-entropy method Livesey et al. (1986) Nyeo and Chu (1989)
Singular value and reconstruction method Finsy et al. (19
92; 1989)
Biophys Rev (2016) 8:409–427 411
scattered light) and that the photon counting is a random
Gaussian process,
g
2
τðÞ¼B þ β g
1
τðÞ
jj
2
ð5Þ
where, B is the baseline (∼1) and β is the coherence
factor that depends on detector area, optical alignment,
andscatteringpropertiesofmacromolecules.
For monodisperse particles, the electric field correlation
factor, g
1
(τ) decays exponentially and is dependent on a decay
constant, Γ, for macromolecules undergoing a Brownian mo-
tion.
g
1
τðÞ¼e
−Γτ
ð6Þ
Therefore, equation 5 can be rewritten as:
g
2
τðÞ¼1 þ β e
−2Γτ
ð7Þ
However, for a polydisperse system, g
1
(τ)cannotberepre-
sented as a single exponential decay but as an intensity-
weighed integral over a distribution of decay rates G(Γ)rep-
resented as:
g
1
τðÞ¼
Z
0
∞
G ΓðÞe
−Γ
τ
dΓ
ð8Þ
The decay constant, Γ in equation 6 is directly related to the
diffusion behaviour of macromolecules (D
τ,
) as expressed in
the following equation.
Γ ¼ −D
τ
q
2
ð9Þ
In Equation 9, the Bragg wave vector q is proportional to
solvent refractive index n (Harding 1999).
q ¼
4πη
λ
sin θ=2ðÞ ð10Þ
Where, λ is the wavelength of incident light and, θ is angle
at which the detector is placed.
Therefore, equation 7 can be rewritten as:
g
2
τðÞ¼1 þ β e
−2D
τ
q
2
τ
ð11Þ
Thus, equation 11 connects the particle motion with the
measured fluctuations (Burchard 1983).
DLS instruments employ either a detector at 90 ° (e.g.,
DynaPro
®
NanoStar
®
from Wyatt Technology or Zetasizer
Nano S90
®
from Malvern Instruments) or a backscatter
detection system at 173 ° (e.g., Zetasizer Nano S
®
from
Malvern Instruments) and at 158 ° (DynaPro Plate
Reader
®
from Malvern Instruments) close to the incident
light of 180 °. Compared to the detection at 90 °, at a high
scattering angle, the contributions of rotational diffusion
effects in the observed autoc orrel atio n profiles ca n be
neglected and the D
τ
can be obtained (Harding 1999;
Pusey 1972). As light does not travel through the entire
sample in the cuvette, the backscattering detection system
also allows for measurement of the D
τ
of highly concen-
trated samples since multiple scattering phenomenon (scat-
tering of a photon by more than one particles in contrast to
scattering of a photon by only one particle) of scattered
light can be avoided. Furthermore, large dust particles and
contaminants scatter more light in the forward direction as
their scattering becomes wavelength-independent compared
to smaller size particles (Rayleigh scattering) that have
nearly equal scattering in both directions, scattering contri-
bution of large particles could be avoided in a backscatter
detecting system.
As the translational diffusion coefficient, D
τ
, is concentra-
tion-dependent, it should be measured at multiple concentra-
tions and extrapolated to infinite dilution (D
0
τ
) as a standard
practice. Furthermore, the D
0
τ
can be converted to the stan-
dard solvent conditions (viscosity and temperature of water at
20 °C) to obtain D
0
τ,20,w
(Harding and Jumel 1998; Raltson
1993). The D
τ
is extremely useful in the determination of
other important hydrodynamic parameters. For example, the
hydrodynamic radius (R
h
), which can be defined as the radius
of a hypothetical sphere that diffuses at the same rate as par-
ticle under investigation, can be obtained using the Stokes–
Einstein equation (Pusey 1972).
D
τ
¼
k
B
T
6πηR
h
ð12Þ
Where k
B
is Boltzmann coefficient (1.380 × 10
−23
kg.m
2
.s
−2
.K
−1
), T is an absolute temperature, and η is the
viscosity of medium.
Additionally, the translational frictional coefficient, f (F/v,
ratio of frictional force F experienced by moving particles due
to Brownian motion and the velocity v of the particle) that
provides information on the shape of macromolecules can also
be calculated using D
τ
by the following equation.
f ¼
RT
N
A
D
t
ð13Þ
Where R is a gas constant (8.314 × 10
−7
erg/mol.K), T is an
absolute temperature, and N
A
is Avogadro’snumber
(6.022137 × 10
23
mol).
The frictional coefficient can also be calculated using R
h
and equation (12)(Tanford1961).
f ¼ 6πηR
h
ð14Þ
The translational frictional coefficient can be further used
along with the D
τ
to calculate frictional ratio (f/f
0
, ratio of
Stokes r adius to that of a sphere with the volume of an
unsolvated macromolecule) of macromolecules that can pro-
vide information with regard to the solution conformation of
412 Biophys Rev (2016) 8:409–427
macromolecules. For a compact sphere, the frictional ratio is
unity and as the shape of macromolecules deviate from com-
pact sphere, f/f
0
increases.
Data analysis
Modern instruments are supplied with packages that per-
form data analysis, using various approaches to primarily
evaluate size and homogeneity of macromolecules. In this
section, we provide the background in brief on data anal-
ysis strategies. The correlation function (equation 11)con-
tains information on diffusion behaviour of macromole-
cules under investigation, which in turn has information
on R
h
(equation 12). In order to gain reliable information
on diffusion coefficient, primarily two approaches are used
to fit the correlation function – monomodal distribution
and nonmonomodal distribution methods.
Monomodal distribution — cumulant analysis
The cumulant analysis method, also known as the meth-
od that does not require a priori information, provides
mean values of the diffusion coefficient but not the
distribution of diffusion coefficients. Therefore, this
method is only suitable for Gaussian-like distributions
around the mean values. As explained in equation 6,
the electric fiel d correlation factor, g
1
(τ) decays expo-
nentially and is dependent on a decay constant,
Γ(Γ = − D
τ
q
2
). For a monodisperse system, the g
1
(τ)
can be treated as a single exponential decay function
to calculate the decay constant and hence the diffusion
coefficient. However, often the experimental system is
polydisperse, which requires the g
1
(τ) to be treated as
the sum of several exponential decay functions that de-
cays at different rates.
The cumulant ana lysis method was introduced by
Koppel (1972) w hich became widel y popular due t o
its ease and reliability, and was considered as the meth-
od of choice by the International Standards Organisation
(ISO) in 1996 and again in 2008 (ISO 2008). Other
methods including singular value and reconstruction
methods were also developed, however, they are not
as popular for the data analysis (Finsy et al. 1989,
1992). Koppel (1972) derived the cumulative-
generating function K(−τ, Γ) that is related to the loga-
rithm of g
1
(τ)andthem
th
cumulant of distribution func-
tion k
m
(Γ):
k
m
ΓðÞ¼
d
m
K −τ; ΓðÞ
m
d −τðÞ
−τ ¼ 0where; K −τ; ΓðÞ
¼ lng
1
τðÞ ð15Þ
The k
m
(Γ) can be rewritten to derive moments about the
mean (μ
m
):
μ
m
¼
Z
0
∞
G ΓðÞΓ −
ΓðÞ
m
dΓ
ð16Þ
as
k
1
τðÞ¼
Z
0
∞
G ΓðÞΓ dΓ ¼
Γ
; k
2
τðÞ¼μ
2
; k
3
τðÞ
¼ μ
3
; k
4
τðÞ¼μ
4
−3μ
2
2
… ð17Þ
where,
Γ is the mean of Γ values. Here, based on the
Taylor expansion of K(−τ, Γ) about (τ) = 0, the lng
1
(τ)
(see, equation 15) can be rewrit ten as:
K − τ ; ΓðÞ¼lng
1
τðÞ¼−
Γτ þ
k
2
2!
τ
2
−
k
3
3!
τ
3
þ
k
4
4!
τ
4
… ð18Þ
If we now recall equation 5, [Siegert relation (1949)]
and convert it to a logarithmic mode, we can obtain,
ln g
2
τðÞ−BðÞ¼lnβ þ 2lng
1
τðÞ ð19Þ
Finally, by combining equations 18 and 19, we can
obtain:
ln g
2
τðÞ−BðÞ¼lnβ
þ 2 −
Γτ þ
k
2
2!
τ
2
−
k
3
3!
τ
3
þ
k
4
4!
τ
4
…
ð20Þ
Equation 20 has some useful properties. First of all, the exper-
imentally measured and normalized g
2
(τ) could be plotted
against (τ) to fit the parameters on the right-hand side of the
equation. The
Γ (k
1
), k
2
, k
3
and k
4
represents average, vari-
ance, skewness and kurtosis of measured distributions respec-
tively for the decay rates of the Gaussian distribution. More
importantly, the polydispersity index (PDI) could be derived
by using k
2
/
Γ
2
relationship. Ideally, parameters above k
3
are not used to prevent over fitting of the data. It should
be noted that often data truncation is required (typically
when the autocorrelation function decays ∼ 10 % of the
maximum value) because as the signal decays into the
baseline, the higher noise could drive signal to negative
values which are not useful as the data processing requires
mathematical treatment of data such as square root and
logarithm. Also, random errors lead to huge variations
fitting of cumulants. For example, with the highly sophis-
ticated instruments, random errors in
Γ could be as low as
1%butfork
2
it could be as high as 20 %. Therefore, the
high-order cumulants are not recommended to be used
(Koppel 1972).
Biophys Rev (2016) 8:409–427 413