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DynaPro
Data Interpretation Guide
Understanding Results Obtained from the
DynaPro Light Scattering Instrument
Operated in Batch Mode
An overview of Size Distributions,
Autocorrelation Functions, and Molecular Weight Estimates
Quickly and Easily determine the ‘goodness’ of results
by comparing actual data to typical data.
December 15, 2002
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Table of Contents
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Part I: Introduction
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Part II: Size Distributions
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Introduction
Glossary of common terms
Interpreting a Dynamic Light Scattering Measurement
Size Distribution Results
Monomodal size distribution
Multimodal size distribution
Polydispersity
Size Distribution Interpretations
Hydrodynamic radius: the physical interpretation of ‘size’
The physical interpretations of size distributions
Part III: Goodness of Data
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Good or Bad: Judging the goodness of the data
Summary of Operation
The Autocorrelation Functions
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Summary of Goodness of Data
Part IV: Molecular Weight Estimates
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Sample vs. Solvent
Large particles, Large Fluctuations
Large particles, Multimodal Size Distribution
Weak Signals
Molecular Weight Estimates
Molecular Weight Interpolated from Radius
Interpreting the BSA Standard
The many size distributions of the BSA Standard
Part V: Beyond the Single Data Point – The Experiment
December 15, 2002
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Part I: Introduction
• Introduction
• Glossary of common terms
• Interpreting a Dynamic Light Scattering Measurement
December 15, 2002
Proterion Corporation. ©
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Introduction
• The purpose of the DynaPro Data Interpretation manual is
to provide a basic understanding of the results obtained
from your DynaPro Light Scattering instrument.
• The manual will define the common terms associated with
data interpretation, provide a framework for determining if
the data are ‘good’ or ‘bad’, and explain typical results.
• The manual will not cover the basic theories of light
scattering, however it will provide you with references
which do cover the theories in detail.
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Glossary: Common Terms
•
The DynaPro determines Size distributions of particles in solution. Size Distributions are defined by several terms.
– Size: refers to the radius or diameter of the particle modeled as a sphere that moves or diffuses in the solution
(in contrast to the Molecular Weight of the particle). Usually expressed as the mean value of the peak of the
size distribution.
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Size Distribution: the manner in which the sizes of the particles are dispersed or spread or allocated among
one or more peaks; presented in a graphical form known as a Histogram.
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Peak: A Peak in a Size Distribution represents a distinct and resolvable species or population of analytes or
particles. A Peak is comprised of several size particles, represented by bins or bars, and is defined by a mean
(average) value and polydispersity.
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Modality: refers to the number of ‘peaks’ in the size distribution. A size distribution with one peak is called
Monomodal. A size distribution with more than one peak is called Multimodal (Bimodal, Trimodal are
common terms for size distributions with 2 or 3 peaks).
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Mean value: the mean value of the peak is the weighted average of the various size particles (bins or bars) in
the distinct or resolvable population. The various sizes are weighted by their probability of being detected.
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Polydispersity: the standard deviation of the histogram which refers to the width of the peak. Sometimes
referred to as the percent polydispersity (polydispersity divided by the mean value), it is a measure of
heterogeneity or homogeneity of the species comprising the population.
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Bin: a discrete numerical particle size component of the Histogram or Size Distribution which is defined by an
x-axis value in nanometers (size), and a y-axis value in relative amount of light scattered by the bin to the
other bins. The number of bins, the value or particle size represented by the bin, and relative amount of
scattered light are determined by numerical algorithms associated with the analysis of the raw data from the
DynaPro. The bins do not reflect actual, physical particles.
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Interpreting a Measurement
What is a measurement?
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The DynaPro defines a measurement as a
collection of acquisitions for a particular
sample. An acquisition is a period of
time, typically 10 seconds, during which
the light scattered by the sample is
averaged and correlated. We recommend
a measurement last 100 seconds (10
acquisitions, 10 seconds each or 20
acquisitions, 5 seconds each).
The result of a measurement contains N
number of acquisitions, which are
averaged and presented in a number of
ways.
Generally speaking we want to see the
‘size distribution’ of the sample: analyte
in solution. Information of the
distribution of the sizes of the analyte is
applied to protein crystallization, protein
based drug development, drug delivery
nanoparticle development, nanoparticle
characterization and many other areas of
advanced materials characterization.
The ‘tree’ lists the
measurements and
Their acquisitions.
December 15, 2002
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The size distribution
is data of interest.
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Part II: Size Distributions
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Size Distribution Results
Monomodal size distribution
Multimodal size distribution
Polydispersity
Size Distribution Interpretations
Hydrodynamic radius: the physical interpretation of ‘size’
The physical interpretations of size distributions
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Size Distribution Results
Results are shown in
graphical as well as
tabular form. The table
located below the size
distribution histogram
describes the number of
peaks and their mean
value (Radius),
polydispersity (Pd), %
polydispersity (%Pd),
molecular weight
estimated from the
measured radius (MWR), relative amount of
light scattered by each
population (%Int), and
estimated relative
amount of mass
(concentration) of each
peak or species (%Mass).
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Monomodal Size Distribution Histogram
This histogram has one peak so we
call it a monomodal size distribution.
The peak is defined by the mean value
and polydispersity.
Y-axis
Relative amount of
light scattered by
each bin, %
Intensity (% of
Total Light
Scattered).
Represents the
probability of
existence of the
species.
The ‘width’ of the peak is the standard
deviation of the weighted bin values, also
known as the Polydispersity.
The mean value of the peak is defined
by a weighted average of the number of
bins comprising the histogram, in this
case three. The bins by themselves do
not represent real, distinct, physical
particles however their mean and
standard deviation do.
December 15, 2002
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X-axis
Discrete particle sizes,
in nanometers
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Multimodal Size Distribution
What causes Modality?
The presence of different and resolvable
species in the sample cause modes in the
size distribution. To be resolved as a
separate peak, a species must have a size
(radius) larger than another species by a
factor of two or more, and be detectable
(produce sufficient scattered light for
detection by the DynaPro). Roughly
speaking a factor of two in radius is
equivalent to a factor of eight (octamer) in
MW. When the sizes of the species are
below this factor, a separate peak will not
be resolved for each species.
This histogram has more than one
peak so we call it a multimodal
size distribution. Specifically this
histogram is trimodal. The
DynaPro determined three distinct
populations exist in this sample.
By definition, a multimodal size distribution is heterogeneous: the
sample contains distinct populations of particles that are not the same
size. The DynaPro can resolve up to four or five modes in a size
distribution. For each mode, the DynaPro estimates the relative amount
of light scattered and the relative amount of mass based upon one of
several possible particle scattering properties. Often times the relative
amount of mass of a peak is quite small e.g. less than .1 % and is
considered to be negligible.
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Polydispersity
Each peak has a unique mean value
and width or Polydispersity. It is
useful to normalize Polydispersity to
the mean size of the peak, also
known as percent polydispersity.
Polydispersity refers to the level of
homogeneity of the sizes of the particles.
When the level of homogeneity is high, the
particles can be considered to be virtually
identical in their size, or monodisperse.
The level of homogeneity is considered
high when the percent polydispersity is
less than 15%. When the level of
homogeneity is low (percent polydispersity
greater than 30%), the particle population
can be considered to contain significantly
different sizes, or ‘polydisperse’.
What causes Polydispersity? Heterogeneity is caused by the presence of
different species that can not be resolved by the technique of dynamic
light scattering (species with sizes less than a factor of two relative to
other species exist in solution can not be resolved). A peak containing
100% monomer will have a smaller polydispersity than peak containing a
mixture of monomer:octamer. The peaks shown here all have %
Polydispersity greater than 30%.
Note: refer to appendix for an alternate cause of polydispersity.
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Size Distribution Interpretations
Monomodal
Monodisperse
Monomodal
‘Polydisperse’
Multimodal
Polydisperse
BLGA, 4 mg/ml, PBS, T = 25 C
Peaks:
1
Mean Radius: 2.8 nm
% Poly:
13.8 %
Majority monomer
BLGA, 4 mg/ml, PBS, T = 5 C
Peaks:
1
Mean Radius: 3.4 nm
% Poly:
22.1 %
Increasing amounts of Dimer
BSA, 2 mg/ml, PBS, T = 25 C
Peaks:
2
Peak 1:
• Mean Radius: 4.3 nm
• % Poly:
32.1 %
• Monomer, Dimer, Trimer
Peak 2:
• Mean Radius: 130.9
• % Poly:
34.5 %
• Various non-specific aggregates
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Hydrodynamic Radius: The Physical Interpretation of ‘Size’
The DynaPro measures the size
distribution of the particles in the
sample. The size, previously
defined as the radius or diameter of
the particle, is represented in this
figure as Rh. Rh, or
Hydrodynamic Radius, is a particle
radius that embodies a ‘hard
sphere’ particle which is in fact
aspherical and typically surrounded
or covered by solvent. Please refer
to PSI Books or the article for a
more thorough explanation of the
physical interpretation of particle
size as measured by the DynaPro.
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Physical Interpretations of Size Distributions
Monomodal
Monodisperse
Radius = R1
Monomodal
Polydisperse
Radius = 1.5*R1
The samples contains two
types of particles, monomer
and trimer. The radius of the
trimer is less than twice the
radius of monomer so only
one peak is resolved, the
distribution is monomodal.
However the population
consists of two species and
this increase in size
heterogeneity causes an
increase in measured
polydispersity compared to
the samples containing 100%
monomer and 100% trimer.
Also, the mean radius of the
peak will be larger than R1
but smaller than 1.5 R1.
Radius = 5*R1
December 15, 2002
Bimodal
Monodisperse
The sample contains two
types of particles, the
monomer and a large
aggregate. The large particle
is more than twice the radius
of the monomer and in
sufficient quantities to be
measured, so two peaks are
resolved by the DynaPro. The
mean radius of Peak 1 will be
R1 and Peak 2 will be equal to
5*R1. Both species are
homogeneous so measured
polydispersity is low.
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Bimodal
Monodisperse
Polydisperse
The sample contains three
types of particles monomer,
trimer, and larger aggregate.
In this case the DynaPro
resolves only two peaks. The
monomer and trimer are not
resolved from each other and
form only one peak, a
polydisperse peak. The
second peak is formed by the
larger particle, which is
resolvable from both
monomer and trimer. The
second peak is monodisperse.
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Part III: Goodness of Data
• Good or Bad: Judging the goodness of the data
• Summary of Operation
• The Autocorrelation Functions
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Sample vs. Solvent
Large particles, Large Fluctuations
Large particles, Multimodal Size Distribution
Weak Signals
• Summary of Goodness of Data
December 15, 2002
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Good or Bad: Judging the Goodness of the Data
•
At this point we have covered the basic interpretations of DynaPro results,
describing size distributions and understanding the meanings of mean size,
modality, polydispersity.
•
However, how do we determine if the results are acceptable or unacceptable, good
or bad?
•
The DynaPro software, Dynamics, does provide basic data analyses that indicate
if the data are in ‘acceptable’ ranges. The analyses are based upon simple
numerical data filters or qualifiers. Yet these data filters do not always capture or
allow for good and bad raw data.
•
We will explain what is good or bad by commenting on various examples of raw
data. The name applied to the raw data is an autocorrelation function. An
autocorrelation function is a collection of correlation coefficients – unitless values
indicating the level of similarity among sets of data. At this time we will not
concern ourselves with the underlying theory and physical meaning of the
autocorrelation function. We will examine only how to interpret these functions.
December 15, 2002
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Intensity
Summary of Operation
Particles moving in solution,
illuminated by a laser, create time
intensity fluctuations (on the order
of microseconds).
Time
The rate of time intensity
fluctuations are determined by
Autocorrelation, resulting in an
Autocorrelation Function
Numerical methods determine the
rates of decay in the
Autocorrelation Function, which
are related to the particle sizes.
The result of the analysis of the
Autocorrelation Function is a Size
Distribution.
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The Autocorrelation Function
The DynaPro determines the size of particles in
solution by exploiting the physical process of
Brownian Motion: the particles are moving in
solution as a function of time, and their rate of
motion is related to their size. The rate of motion
is measured by illuminating the particles with
laser light and determining the rate at which light
scattered or reflected by the particles changes with
time.
The technique of autocorrelation determines the
rate of these time intensity fluctuations, expressed
as an autocorrelation function (shown here).
An autocorrelation function is an exponential
function comprised of correlation coefficients (yaxis) dependent upon the ‘delay time’ (x-axis), the
time-value separating the sets of data. The
function can be mathematically described by one
or more decays. The rate of decay is related to
particle size. A faster decay indicates a smaller
particle, a slower decay a larger particle.
Autocorrelation functions are determined during
each acquisition comprising a measurement, as
described earlier.
December 15, 2002
Numerical algorithms are applied to determine the rates of
decay or size distributions of the exponential autocorrelation
functions. The DynaPro utilizes a proprietary ‘non-negative
least squares’ algorithm, a method that finds the size distribution
producing the smoothest distribution with the least amount of
error. The error is the difference between the measured
autocorrelation function and the fitted autocorrelation function.
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Autocorrelation functions: Sample vs. Solvent
Not all samples can be measured, nor are all samples
properly suited for measurement by the DynaPro, and
therefore not all samples produce valid autocorrelation
functions. Without a valid autocorrelation function, it is
not possible to determine a valid size distribution.
A valid autocorrelation function is generally smooth and
continuous, exponentially decaying from a maximum
value of 2 to a value of 1.
To the right is shown a valid autocorrelation function. By
eye we observe one decay in the function.
The function contains random values centered around 1,
asymptotically reaching 1. Randomness represents the
result from measuring pure solvent: solution containing
zero analyte or analyte below the limits of detection. The
size distribution analysis will attempt to find a result for
these functions. These must be marked and removed
from the analysis. It is generally a good idea to measure
the solvent to confirm its purity. If one unexpectedly sees
a function characteristic of solvent increase laser power,
measure the sample unfiltered (to avoid potential binding
to the membrane) or unspun, and/or increase the
concentration of the analyte.
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Autocorrelation Functions: Large particles, Large fluctuations
If during the measurement of an autocorrelation function
the total intensity scattered by the population of particles
changes rapidly or spikes, the detector and/or correlator
can saturate, resulting in a discontinuity as shown here.
These functions must be marked and removed from the
size distribution analysis.
The situation can be remedied by removing bubbles,
spinning or filtering the sample, or changing solvent
conditions to remove large aggregates or particles.
Alternatively, the particles may be larger than the size
range of the instrument (several microns in radius).
The decay of this function has not been fully captured, it
is prematurely terminated. This is caused by have an
acquisition time too short relative to the long decay of the
autocorrelation function. Generally a larger particle size
requires a longer acquisition time. The size distribution
analysis can be performed however there will be greater
error in the results. The additional autocorrelation
coefficients can be captured by extending the acquisition
time of the measurement. Note: increasing the number of
acquisitions will not capture additional coefficients in the
longer time delays.
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Autocorrelation Functions: Large Particles, Multimodal populations
The autocorrelation function shown here contains two
visually observable decays. One is faster, representing a
smaller particle and the other is slower, representing a
larger particle. These functions are valid and can be
analyzed.
The autocorrelation function associated with larger
particles has a longer decay, as shown here. Note the yvalue of the function has asymptotically reached a value
of 1 yet the function has some variation at the larger time
delays. The variation is referred to as ripple or noise.
The noise is due to insufficient numbers of correlation
coefficients being collected and calculated. The noise
can be reduced by collecting additional numbers of
acquisitions. With less noise, the size distribution
analysis will be of higher quality.
December 15, 2002
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Autocorrelation Functions: Weak signal
Ripple or a lack of smoothness of the function in the
short time delay area indicates a weaker signal from the
particles. These functions can be fitted however the
polydispersity may be greater due to this ‘noise’.
The remedy for this situation is to either extend the
acquisition time, collect more acquisitions, increase laser
power, and/or increase analyte concentration.
Refer to PSI Books for a discussion of the advantages and
disadvantages of increasing acquisition time and the
number of acquisitions.
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Summary of Goodness of Data
Proceed
December 15, 2002
Caution
Stop
Increase acquisition time
Spin or filter sample
Increase acquisition time
Increase acquisitions
Increase laser power
Increase concentration
If not pure solvent…
Increase acquisition time
Increase acquisitions
Increase laser power
Increase concentration
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23
Part IV: Molecular Weight Estimates
•
•
•
•
Molecular Weight Estimates
Molecular Weight Interpolated from Radius
Interpreting the BSA Standard
The many size distributions of the BSA Standard
December 15, 2002
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Molecular Weight Estimates
•
The Molecular Weight of a biological molecule can be estimated from the measurement of
the size or hydrodynamic radius. The estimate is based upon on an empirical curve of
known proteins and measured hydrodynamic radius.
•
The error of the estimated Molecular Weight from Hydrodynamic Radius ranges from
several percent to over 100%. The wide range of error is due to the nature of the estimate.
Not all proteins fall on the curve. The estimated value must be used with caution.
•
When applying the Molecular Weight estimate, make sure the intensity weighted size
distribution analysis is selected. The empirical curves are based upon the use of the
intensity weighted calculation of the mean of the peak.
•
Also, if the peak is determined to be polydisperse by the DynaPro size distribution
analysis, then the mean radius is a weighted average of more than one species. The
estimated molecular weight will be a weighted estimate based upon the weighted average
size.
•
The molecular weight estimate can be qualified by examining the shape factor, the
relationship between the measured hydrodynamic radius and the ‘hard sphere radius’
calculated from the known molecular weight and density of the protein. Please refer to
PSI books for a review of the concepts of the shape factor or axial ratio.
December 15, 2002
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Molecular Weight Interpolated from Radius
MW = 14
Rh = 1.9
MW-R is the Molecular Weight Interpolated from the Measured Hydrodynamic
Radius. Ideally the size distribution is monodisperse, otherwise the measured radius
is a weighted average of more than one species, and the estimated MW – even for a
protein or other particles that falls on the empirical curve – will be in error.
Select the model that best fits the a priori knowledge of the sample. Or, match the
model that best matches the known molecular weight or oligomer to obtain an
estimate on the shape or conformation of the sample.
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Interpreting the BSA Standard
MW ~ 130 kDa
MW = 66kDa
Rh = 3.5 nm
Rh ~ 4.5 nm
The DynaPro is provided with an ampoule containing 2 mg/ml of BSA prepared in a PBS solution.
Often the sample is measured and the molecular weight results are higher than the expected value
for monomeric BSA (Rh = 3. nm and MW = 66 kDa), sometimes as much as a factor of two larger.
The reason for the difference is that the BSA ampoule contains monomer, dimer, trimer, and large
non-specific aggregates. The majority peak of the size distribution typically comprises the specific
aggregates, and the minority peak (low % mass peak) typically comprises large non-specific
aggregates. Depending upon the relative amounts of the specific aggregates, the mean value of the
majority peak can range Rh = 3.6 nm (virtually 100%) monomer to 4.5 nm or more (dimer and
trimer), with the large amounts of polydispersity.
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The many size distributions of the BSA standard
Monomodal
Monodisperse
Monomer
Bimodal
Peak 1: Monodisperse Monomer
Peak 2: Monodisperse Aggregate
December 15, 2002
Monomodal
Polydisperse
Monomer,
Dimer, Trimer
Bimodal
Peak 1: Polydisperse M:D:T
Peak 2: Polydisperse Aggregate
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Multimodal
Peak 1: Polydisperse M:D:T
Peak 2: Polydisperse Aggregate
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Part V: Beyond the Single Data Point
Design, Perform, and Interpret an Experiment
The power of the DynaPro.
BLGA as a function of Temperature.
By determining the size distribution over a range of experimental conditions the DynaPro
determines that the mean size, total intensity, and polydispersity of BLGA increase with
decreasing temperature due to the formation of specific aggregates. Refer to all of our
application notes to learn how to capitalize on the DynaPro. www.protein-solutions.com
December 15, 2002
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