dls help manual

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Table of Contents

Welcome

Whats New?

TECHNICAL QUESTIONSDynamic Light Scattering

What is a correlation curve?

How is the correlation curve measured?

Whats the relevance of the frictional coefficient?

What is the hydrodynamic radius (RH)?

Is it better to use longer acquisition times?

Whats the difference in the intensity, number, and mass distributions?

Static Light Scattering

What is the Rayleigh ratio?

How is the Rayleigh ratio measured?Whats the relevance of toluene in static light scattering?

Is the Rayleigh ratio of toluene wavelength dependent?

What are the units of the parameters in static light scattering?

When is multi-angle data necessary for MW determination?

Data Interpretation

What is the baseline?

What is the SOS?

What are number fluctuations?

Whats the difference between the old and the new Regularization?

Sample Preparation

Do samples need to be filtered?

Will filtering perturb the sample?

Why is the salt content relevant?

Calculations

What is the Regularization Method?

Can you get molecular weight information from DLS data?

How is the axial ratio calculated?

How is the mass distribution of radii calculated?

Are the %Mass calculations valid for all systems and conditions?

Sample Properties

Whats the significance of the refractive index () in DLS?

Is the refractive index increment (d/dC) wavelength dependent?

Is the solvent refractive index (o) wavelength dependent?

Are o and d/dC temperature dependent?


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Is it alright to estimate solvent viscosity values?

Software & Utilities

What is the _____ value of ______?

LABORATORY REPORTS

January 2000

Summary of Results

Lysozyme UV Analysis

Instrumental Error Effects in UV Analysis

Effects of Acquisition Time on DLS Results

Effects of Concentration on DLS Results

Defining a Quality Control Parameter

Maximum Acceptable CNF Value

Quality Control Specifications

May 2000

Summary of Results

Cell Comparison UV Measurements

Cell Comparison Beers Law Region for Lysozyme

Calculating Minimum Concentrations

Eppendorf UVettes - QC Analysis

Bovine Serum Albumin (BSA) UV Study

Effects of Laser Power on Scattering Intensity

DLS Study with Polystyrene Standards

Enhancing DynaPro Sensitivity

APPLICATION NOTES

Surfactants & Micelles

Characterization of Surfactant and Micellar Systems

Determination of Critical Micelle Concentration

Measurement of Mixed Micelle Size by DLS

Vesicle Size Distribution Analysis

Surfactants as Chaotropic Agents in Protein Systems

Representative Publications for Surfactant and Micelle Systems

Polymers & Polypeptides

Biological and Synthetic Polymer Characterization

TC Measurements of Recombinant Hydrophobic Polypeptides

Electrostatic Effects on Polyelectrolyte DLS Measurements

Polysaccharide Fractionation by Filtration

Characterization of Low Molecular Weight Peptides

Representative Publications for Polymeric Systems


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Protein Characterization

Protein Characterization

Conformation of Trimeric Form of Migration Inhibitory Factor

Insulin Quaternary Structure as a Function of pH

pH Dependent Monomer-Dimer Equilibrium Constants for GARTMonitoring Protein Thermal Stability - Glycosylated Hb Melting Points

Representative Publication in Protein Characterization

MANUALS & TUTORIALS

Utility ReadMe Files

PSI Archive Setup Instructions

PSI Books Setup Instructions

REFERENCESBackground References

Application References


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What is a correlation curve?

Photon Correlation Spectroscopy (PCS), also known as Dynamic Light Scattering (DLS), is

concerned with the investigation of correlation of photons. In a typical light scatteringexperiment single photons are detected with a single photon counting device. This detector

transforms the signal from a single photon into an electronic signal, basically a 1 or a 0,

depending on whether a photon was or was not detected in a certain time interval. The objective

of PCS is to find any peculiar properties of the scattered signal which can be used to

characterize and describe the seemingly random "noise" of the signal, and the correlation curve

is used to achieve this objective.

A typical way to describe a signal is by way of its autocorrelation. The autocorrelation

function of the signal from the scattered intensity is the convolution of the intensity signal as a

function of time with itself. In more abstract terms, if the detected intensity is described as a

function I(t), then the autocorrelation function of this signal is given by the followingexpression, where is the shift time.

The above function is also called the intensity correlation function, and it is used to describe the

correlation between the scattering intensities measured at t = 0 and some later time (tn = t0 + ).

Consider for example, the schematics shown below, where the frame represents the scattering

volume, the dark blue circle represents the particle, and the light blue region represents the

volume within which the particle must be contained. The scattering intensity at the detector is

dependent upon the position of the particle relative to the detector. If we consider very small

time increments (micro-seconds), then at t0 (t = 0) there is a finite volume of space within which

the particle can move during the first time increment. For reasons that will become evident

later, well call this finite volume of space the diffusional volume. At t = t1, the particle has

diffused a single step. Since the exact path is unknown, the diffusional volume or the volume of

space within which the particle must reside considering all paths has expanded. The change in

particle position is accompanied by a change in the measured scattering intensity at the detector.

However, this new scattering intensity is still strongly correlated with that measured at t0 due to

the finite diffusional volume and the correlation between the current and initial positions. As

the shift time increases, the diffusional volume also increases. The increased diffusional volume

is accompanied by a decrease in the correlation between the current and initial particle

positions. The correlation is still present however, as long as the diffusional volume is finite.

At longer times (frame 6), the diffusional volume becomes infinite, and the correlation between

the initial and current particle position and the respective scattering intensities is lost.


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The correlation in particle position at small shift times is contained within the measured

intensity correlation function, an example of which is shown below. In the absence of any

applied forces, the particle position is dictated by the degree of Brownian motion. As such, the

measured intensity correlation curve is an indirect measure of the particles diffusion coefficient.


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How is the correlation curve measured?

The intensity correlation function is defined as shown in the following expression.

The shift time () is often referred to as the delay time, since it represents the delay between the

original and the shifted signal. In reality, the continuous intensity correlation function can not

be measured. It can however, be approximated with discrete points obtained by a summation

over the duration of the experiment. This summation is performed by the correlator, a circuit

board composed of various logic chips and operational amplifiers which continuously multiplies

and adds measured intensity values.

A defining parameter for a correlator is its speed, i.e. its ability to add up numbers fast, or

inversely expressed, the smallest delay time that can be handled. This delay time () determines

the smallest accessible time of G(). Hence, G() is the first numerical point in the intensity

correlation curve that can be experimentally measured for a given correlator. Using a time

increment of , a grid of experimental data values can be obtained. At the start of the

experiment, t0 = 0. The first time then is at t1 = , the second is at t2 = 2, and so on. As an

array, the stream of numbers could be displayed in table format as shown below, with the

experiment ending at tn = n.

The correlator now finds out how related these intensity numbers are to each other. It does this

by comparing each number to its neighbor a defined time interval later. This comparison is

carried through the duration of the experiment. As a summation, the comparison can be

expressed as follows, where the upper summation limit is given by the appropriate indexbelonging to the largest available summation term for k.

The above expression is very general and holds true for both linear and arbitrary delay times. To

understand the meaning of this summation, lets assume we would like to find G(t1) = G() .


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According to the previous equation, G(t1) is defined as:

In the same fashion, G(t2) is defined as:

In table format, the correlation function values can then be written as given below.

The series of G(t) values is typically normalized, such that the value for very large time (as t

) is G() = 1. For standard light (with Gaussian statistics), this normalization imposes a

theoretically limit of G(t0) = 2 at t = 0. However, only carefully optimized optical systems can

ever achieve such a high intercept or amplitude.

For a random signal and a large measurement time, all G values would add up to roughly thesame number. The signal would then be described as uncorrelated, and the resultant intensity

correlation curve would look like random fluctuations about the baseline, similar to intensity

correlation curve for H2O shown in the following figure.


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For light scattered from diffusing molecules however, the intensity correlation curve exhibits an

exponential decay, indicating that the signal is correlated.

For typical diffusion processes the correlation function has the form of 1 plus an exponential

decay function. The decay constant, in the following expression, is representative of the

diffusional properties of the particle under examination. Hence, evaluation of leads to the

particle diffusion coefficient, which in turn is used to calculate the hydrodynamic radius via the

Stokes Einstein equation.

G(t) = 1 + exp(- t )


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What's the relevance of the frictional coefficient?

In the Stokes model for motion of a hard sphere through a viscous liquid, the resistance to

motion is related to the shearing force between adjacent solvent planes moving at differentvelocities. The shearing force per unit area (Fs/A) at each slippage plane is described with the

following differential equation, where m is the mass, A is the surface area, dv/dt is the

acceleration, is the viscosity of the medium, and dv/dy is the velocity gradient across the

shearing planes.

For stick boundary conditions, where the limiting assumption that the fluid layer adjacent to the

particle has the same velocity as the particle is made, solution of the above equation gives thetotal force of viscous resistance (Fvis) as shown below, where R is the particle radius and vs is

the limiting steady state velocity of the fluid when y becomes very large.

The proportionality factor in the above expression is defined as the frictional coefficient (f = 6

R), and it is the frictional coefficient that is used to calculate the radius of a particle from the

measured diffusion coefficient (D) in dynamic light scattering studies.


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What is the hydrodynamic radius (RH)?

In dynamic light scattering experiments, the radius (R) of the particle is calculated from the

diffusion coefficient (D) via the Stokes-Einstein equation, where k is the Boltzmann constant, Tis the temperature, is the solvent viscosity, and f = 6R is the frictional coefficient for acompact sphere in a viscous medium.

By definition then, the DLS measured radius is the radius of a hypothetical hard sphere thatdiffuses with the same speed as the particle under examination. This definition is somewhatproblematic with regard to visualization however, since hypothetical hard spheres are

non-existent. In practice, macromolecules in solution are non-spherical, dynamic (tumbling),and solvated. As such, the radius calculated from the diffusional properties of the particle isindicative of the apparent size of the dynamic hydrated/solvated particle. Hence theterminology, hydrodynamic radius.

The effects of asymmetry and hydration on the radius calculated from the Stokes-Einsteinequation can be examined using lysozyme. From the crystallographic structure, lysozyme canbe described as a 26 x 45 prolate ellipsoid with an axial ratio of 1.731, a MW of 14.7 kDa,and a partial specific volume of 0.73 mL/g. Considering only the mass and partial specificvolume (Vp), the equivalent radius for a sphere with the same mass as lysozyme (RMass) is 1.62nm, considerably smaller than the 2.25 nm rotational radius (RRot) determined by rotating the

protein about the geometric center.

The Perrin or shape factor (F) is defined as the ratio of the apparent frictional coefficient for anellipsoid to that of a sphere of identical volume, and can be used to account for the non-sphericalshape of lysozyme. For a prolate ellipsoid with an axial ratio of 1.731, the Perrin factor is1.022. As shown below, the non-spherical shape of lysozyme leads to an increase in theexpected radius of the particle, designated here as RVol.

The hydrodynamic radius (RH) includes effects arising from both shape and hydration. For


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lysozyme, the measured RH is 1.90 nm. The 2.4 increase in RH compared to RVol isconsistent with the thickness (2.8 ) of a single layer of water, suggesting that thehydrodynamic radius includes a single hydration layer.

The various size parameters discussed above are represented in the following figure. As seen

here, asymmetry and hydration lead to an increase in the measured size of lysozyme compared tothat calculated for a hypothetical hard sphere of the same mass. However, this measuredhydrodynamic radius is still 15 % smaller than the rotational radius.


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Is it better to use longer acquisition times?

The number of photons striking the detector during the course of the experiment is directly

correlated with the acquisition or sample time. The more photons collected, the less noise in theautocorrelation curve. Hence, longer acquisition times are synonymous with smoother

correlation curves and enhanced confidence in the experimental results. Because of the

correlation with photons collected, longer acquisition times are usually required at low sample

concentrations, where the signal to noise (analyte to solvent) intensity ratio is inherently small.

There is a down side to long acquisition times. At longer acquisition times the likelihood of a

dust event is significantly increased. If a dust particle enters the scattering volume during the

course of measurement, the correlation curve is shifted upward proportionally, and baseline

evaluation becomes problematic. As a rule of thumb then, you should keep your acquisition

time as short as possible; but keep an eye on the noise in the correlation curve and the baseline

values.

On the upside, noise in the correlation curve can also be reduced via statistical averaging, i.e. by

collecting multiple runs at short acquisition times. This approach to noise averaging is

particularly useful for samples that arent really as clean as they should be, even though

significant data outlier editing is typically required. The technical support staff at Protein

Solutions Inc is currently developing a DYNAMICS software utility that calculates the optimum

acquisition time and number of measurements for samples of a given molecular weight and

concentration. Check with your Protein Solutions sales representative for availability.


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What's the difference between the intensity, number, and mass distributions?

According to static light scattering theory, the scattering intensity of the ith particle (Ii) in a

distribution of particles is proportional to both the molecular weight (Mi) and the concentration

as given in the simplified form of the Rayleigh expression shown below, where Ci is the weight

or mass concentration, Ni is the number concentration, and K is a constant.

The size or radius (R) of the particle can be estimated from the molecular weight via the partial

specific volume (Vp) as shown in the following expression, where NA is Avogadros number

and x is a shape parameter equal to 3 for spheres and 2 for coils.

After substitution, the simplified Rayleigh expression can be re-written in the following form,

which relates the scattering intensity to the mass and number concentrations of the ith particle.

The mass and number distributions are then calculated from the intensity distribution as shown

below.

As seen in the following figure, the mean values for the %Mass and %Number distributions are

shifted towards lower values as a consequence of the Ri dependence in the above equations.


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What is the Rayleigh ratio?

The Rayleigh ratio is defined as the ratio of the scattered (Is) to the incident (Io) light intensity,

with the scattered intensity being summed over all space. Because of geometric limitationsimposed by the restriction of measuring the intensity at a given angle () and distance (r) fromthe scattering volume, the working expression for the Rayleigh ratio is that shown below, where

is is the scattering intensity measured at fixed r and .

The scattering intensity is dependent upon a number of solvent and particle parameters, principle

of which are the polarizability () of the particle and the permittivity (o) of the solvent. Hence,

the Rayleigh ratio can also be written as shown below, where is the particle density, NA is

Avogadros number, M is the particle molecular weight, and o is vacuum wavelength of theincident radiation.

Using the Clausius-Mosetti equation to relate the polarizability to the permittivity of a molecule,

the Rayleigh equation can be reduced to the commonly used form shown below, where C is the

weight concentration, M is the weight average molecular weight, A2 is the 2nd virial coefficient,

indicative of solute-solvent interactions, and K is the optical constant.

The vacuum wavelength, solvent refractive index (o), and analyte specific refractive index

increment (d/dC) are incorporated into the optical constant as shown below.

The above two equations are those typically used for molecular weight determinations of small


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particles in static light scattering experiments. All of the variables in the optical constant (K)

are either known or can be easily measured. As such, a plot of KC/Rvs. C in the absence ofparticle interactions should be linear, with an intercept equivalent to 1/M and a slope

proportional to the 2nd virial coefficient (A2).


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How is the Rayleigh ratio measured?

The Rayleigh ratio (R) is defined as the relative scattering intensity measured at an angle and

a distance r from the scattering center. As shown in the following equation, where is is the r anddependent scattering intensity and Io is the incident intensity, one has simply to measure is, Io,

r and to determine the Rayleigh ratio for a solution of particles. However, this simplicity is

strongly attenuated in practical application, where the measurement of Io, r, and cannot be

accomplished with the precision necessary for accurate determination of the Rayleigh ratio.

An alternate approach is to compare the scattering intensity of the sample analyte to that of a

well characterized standard, such as toluene, with a known Rayleigh ratio. The expression for R

can be rearranged to the form shown below.

If the scattering intensities of the sample and toluene are measured under the same experimental

conditions, the Rayleigh ratio of the analyte can then be determined from the ratio of intensities

as shown below, where the A and T subscripts represent the analyte and toluene respectively and

the terms are included to account for differences in the refractive indexes of the toluene and

sample solutions.

Since it is the photon count rate (CR) rather than the scattering intensity that is measured at the

detector in typical light scattering instrumentation, the expression for RA is converted to the

working expression shown below.


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What's the relevance of toluene in static light scattering?

In static light scattering experiments, the concentration dependent scattering intensity of the

sample solution can be used to determine the absolute molecular weight (M) and 2nd virialcoefficient (A2) of the analyte under examination.

In the above expression, K is an optical constant, incorporating wavelength and refractive index

effects, P() is the shape factor, accounting for angle dependent multiple scattering from large

particles, and Ris the Rayleigh ratio of the scattered intensity to the incident intensity. For

particles with diameters more than 10 times smaller than the wavelength of the incident

radiation, the shape factor goes to 1. The Rayleigh ratio is calculated using the followingexpression, where is is the residual scattering intensity (sample - solvent), Io is the incident

intensity, is the scattering angle, and r is the distance from the scattering volume to the

detector.

The above expression can be rewritten in the form shown below, where the sample dependent

parameters are grouped on the left hand side of the equality sign and the instrument dependent

parameters are grouped on the right.

The instrument dependent parameters (Io, , and r) are difficult to measure with the precision

required for acceptable molecular weight and 2nd virial coefficient calculations. Rather than

attempting to measure these parameters directly, the typical approach in static light scattering

experiments is to calibrate the instrument parameters using a standard with a well defined

Rayleigh ratio value. Toluene is one of the generally accepted standards for instrument

calibration in static light scattering experiments. If the scattering intensities of the sample and

toluene are measured under identical experimental conditions, the Rayleigh ratio of the analyte

can then be determined from the ratio of intensities as shown below, where the A and T

subscripts represent the analyte and toluene respectively.


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The terms are included in the above expression to account for differences in the refractive

indexes of the toluene and sample solutions. There is some debate as to whether or not therefractive index terms should be included. For low concentration aqueous protein solutions, the

inclusion of the terms functions to scale the toluene Rayleigh ratio by a factor of 0.8.


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Is the Rayleigh ratio of toluene wavelength dependent?

The wavelength dependence of the Rayleigh ratio (R) is embodied in the definition shown

below, where is the particle density, NA is Avogadros number, M is the particle molecularweight, o is the wavelength of the incident radiation, is the polarizability of the particle, and o is the permittivity of the solvent.

As evident in the above expression, the Rayleigh ratio should vary linearly with -4. Thistheoretical linear dependence is consistent will experimental results, exemplified in the

following figure, which shows the measured Rayleigh ratio of toluene at 25 oC and a 90o

scatting angle as a function of -4.

For the DynaPro line of molecular sizing instruments, the laser wavelength is around 830 nm.

The Rayleigh ratio for toluene at 830 nm and 25 oC is 4.23 x 10-6 cm-1. For other wavelengths,

the toluene R90 value can be predicted using the following expression, where the units for the

Rayleigh ratio and the wavelength are cm-1 and nm respectively.


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What are the units in static light scattering?

The key to simplifying the units in static light scattering experiments is to recognize that the

units must be the same on both sides of the equality sign. When the Rayleigh equation is writtenin the standard form shown below, it is easily seen that the collection of units on the left hand

side of the equation must ultimately reduce to units of inverse molecular weight, i.e. mol/g.

The reduction to mol/g can be accomplished using the units listed in the following table.

The dimensional analysis is shown below. As seen in the final expression, incorporation of the

units from the above table reduces the units in the Rayleigh equation to those of inverse

molecular weight on both sides of the equality sign.


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When is multi-angle data necessary for MW determination?

The expression used to describe the scattering of a dilute solution of particles is shown below,

where K is an optical constant, C is the particle concentration, Ris the Rayleigh ratio ofscattered to incident light intensity, M is the weight average molecular weight, A2 is the 2nd

virial coefficient, Rg is the radius of gyration, is the vacuum wavelength of the incident

radiation, and is the scattering angle.

The angular dependent portion of the second term arises from interference effects due to

multiple scattering from a single particle. For particles much smaller than the wavelength of the

incident radiation, this term goes to zero, and the angular dependence of the scattered light

vanishes. Under these conditions, the absolute molecular weight is determined from the

concentration dependence of the Rayleigh ratio, and angular dependent data is redundant. For

larger particles, it is still the concentration dependence that leads to the molecular weight, but

interference effects must be accounted for. It is at this point that multi-angle instruments

become necessary. In preface to the question of what is much smaller, the figure below, which

shows the dependence of the interference factor on the wavelength to particle size ratio at

different scattering angles is included here. As a rule of thumb, the size cutoff for angle

independent Rayleigh scattering is Rg 20*. Typical wavelengths for the DynaPro series of

instruments are on the order 800 nm, corresponding to an upper size limit for single angle

particle MW determination of circa 80 nm diameter.


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What is the baseline?

The baseline in the Cumulants Datalog is the measured value of the last coefficient in the

correlation curve. For ideal, noise free dynamic light scattering experiments the baseline shouldbe 1.000, indicating that there has been sufficient diffusion during the acquisition such that the

location of the particle is no longer correlated with its initial position. The DynaPro line of

molecular sizing instruments utilizes mono-modal fiber technology to minimize the introduction

of stray light or background noise. As such its not difficult to achieve baseline tolerances on

the order of 0.005.

Since the baseline value reported in the Cumulants Datalog is a measured, rather than a

calculated value, it is independent of the algorithm used to deconvolute the size and distribution

from the correlation curve. It is therefore a useful parameter for filtering out bad or outlying

correlation curves. One should remember however, that a good baseline value doesnt

necessarily mean the correlation curve is also good. Consider for example the following figure,which shows a 3 second acquisition time correlation curve for a dusty sample. The discontinuity

in the curve is indicative of number fluctuations caused by a dust particle passing through the

beam during the course of the acquisition. Even though this correlation curve is an obvious

outlier, the measured baseline is 1.000. Hence data filtering based solely on the measured

baseline value would leave this correlation curve unmarked, and lead to erroneous data

interpretation.


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What is the SOS?

The SOS is the sum of squares difference between the measured correlation curve and the best

fit curve calculated using the Cumulants method of analysis, where a dust and noise freemonomodal (single distribution) low polydispersity (narrow distribution) sample is assumed.

The SOS then is a quantitative value representative of the residual or the goodness of fit

between the measured and theoretical data (see figures below).


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In the DynaPro line of light scattering instruments, the SOS value for each correlation curve is

reported in the Datalog within the DYNAMICS software. Any deviation of the measured curve

from the theoretical will lead to increased SOS values. Sources of deviation could be noise,

dust, multi-modal samples, large polydispersity, etc. Hence, there is no absolute SOS value thatone should look for, particularly since the SOS value is also dependent upon the number of

correlation channels included in the calculations (see correlation channel cutoffs in the

DYNAMICS Data Filtering window).

The best way to use the SOS values in the Cumulants Datalog is to look for inconsistencies. As

an example: Because of background noise at low acquisition times, the SOS value for a dust

free sample might be on the order of 10 - 50. If dust passes through the beam during the

collection of a single correlation curve (during 1 acquisition time), the calculated SOS value will

jump by as much as 1 or 2 orders of magnitude. So the SOS value is a good indicator of

whether of not a dust free correlation curve has been collected. Depending upon how dirty, i.e.

dusty, the sample is, filtering the SOS values at around 500-1000 is typically sufficient to filterout bad correlation curves arising from the presence of dust during the acquisition. But these

numbers should not be taken as absolute or even as a rule of thumb. For longer acquisition

times, the cutoff could be much lower. In a like fashion, multi-modal samples could lead to

very large SOS values, as evident in the following figures.

The figures below show the Cumulants Datalog, the correlation curves for Measurements #1 and

#2, and the Regularization histograms for a PEGylated hemoglobin sample, before and after data

filtering based on inconsistencies in the SOS values. A discontinuity is evident in the

correlation curve for Measurement #2 (the same discontinuity is seen in Measurement #3),


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suggesting the presence of dust. The elevated SOS values in the Datalog for Measurements #2

and #3 are a consequence of the discontinuities in the correlation curves. Prior to data filtering,

the Regularization histogram indicates a bi-modal system. After Marking the dusty

measurements (#2 and #3), the Regularization histogram shows a mono-modal system with a

relatively low polydispersity.


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What are number fluctuations?

Number fluctuations are caused by a non-constant particle concentration in the scattering

volume. In light scattering experiments, the scattering intensity is proportional to both the MWand the concentration of the particles in the solution. As a consequence of Brownian motion,

the particles within the scattering volume are moving, and the recombined scattering light from

these moving particles leads to constructive and destructive interference effects or short time

scale total intensity fluctuations at the detector. In dynamic light scattering, these intensity

fluctuations are correlated and then transformed to give the diffusion coefficient and

subsequently the hydrodynamic radius. During the acquisition of the correlation curve however,

the particle concentration within the scattering volume must be constant. If the particle

concentration fluctuates, then the average total intensity will be skewed or weighted by the

variation in concentration, and the resultant correlation curve will be discontinuous (see figure

below).

Number fluctuations are particularly problematic with high sensitivity light scattering

instruments such as the DynaPro-MS800. In order to produce a high power density in the

scattering volume, the laser beam in the DynaPro-MS800 is focused down to a diameter of 16

m. While the increased power density increases the sensitivity of the instrument to sampleconcentration, the smaller scattering volume increases the likelihood of number fluctuations if

larger particles are present (see figures below). As a direct consequence of the smaller

scattering volume, the upper size limit for the DynaPro-MS800 is around 100 nm (diameter).

For the larger size range DynaPro instruments such as the MS/X and LSR, the laser beam

diameter is focused to 100 m. This larger beam diameter increases the scattering volume, and

while some sensitivity to concentration is lost, a much larger size range is allowed, with the


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MS/X and LSR instruments being able to accurately measure particle sizes up to 2 m diameter.


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What's the difference between the `old' and the `new' Regularization?

In DYNAMICS software versions 5.26.36 and greater, the Regularization algorithm has been

replaced with a new and improved Regularization algorithm. The fundamental difference in thetwo algorithms is that the regularization parameter in the new algorithm has been diminished

slightly to be consistent with the smoothing parameters in other correlation curve analysis

algorithms such as DynaLS and/or CONTIN.

In addition to improving the algorithm, Protein Solutions, Inc. has also added a resolution slider

to the Regularization histogram display in DYNAMICS. If the user has apriori information

concerning the number of distributions, the resolution slider can be used to diminish the

smoothing parameter even further and perhaps resolve multiple distributions from a single

peak. The figures below show the resultant Regularization histograms at various resolution

levels, using DLS data derived from a mixture of PEGylated and non-PEGylated chymotrypsin

in 0.1 M NaCl after incubation for 3 hours at pH 8.0. At the lowest resolution level, thecomponents are unresolved and the histogram shows a single, highly polydisperse peak

(ignoring the noise peak at 0.06 nm). The second figure shows the distribution at the resolution

level for the old Regularization algorithm, and indicates two populations, one with mean radius

of 3.58 nm and another with a mean radius of 25.5 nm. The former is consistent with the size of

the PEGylated protein measured in the absence of the non-PEGylated component. The third

figure shows the histogram distribution at the optimal resolution for the new Regularization

algorithm. For this system, the results are the same, regardless of which Regularization

algorithm is used. In the fourth figure, the resolution slider is set to the maximum level, and the

resultant histogram indicates three different populations. Subsequent chromatographic analysis

verified the presence of all three components, with the 1st peak being composed of

oligio-peptide by-products of chymotrypsin self-digestion, the 3rd peak being aggregates of thesame, and the middle peak being the non-digested PEGylated chymotrypsin.


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While the above example indicated no significant difference between the old and newRegularization algorithms, there are occasions when the two algorithms can yield what looks to

be different results. The figure below shows an example of this. The old Regularization


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algorithm indicates four populations. Because of the reduction in the smoothing parameter, the

new Regularization algorithm is able to resolve the third peak into two distinct populations,

yielding five peaks. However, if the resolution in the new algorithm is reduced by one

increment on the slider (Unresolved New in figure below), the results from the new algorithm

are consistent with those from the old.


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Do samples need to be filtered?

The scattering intensity of a sample is proportional to both the concentration and the molecular

weight of the particles in the solution. For high molecular weight particles, the contribution tothe total sample scattering intensity can be quite large. Hence, light scattering experiments are

extremely sensitive to dust. As a general rule of thumb then, samples should always be filtered.

The effects of dust on light scattering results are dependent upon a number of factors, primary of

which are the concentration and the molecular weight of the analyte. The figures below show

the DLS results and sample correlation curves for lysozyme solutions at 0.07 g/L (1st figure) and

0.7 g/L (2nd figure), both prepared from unfiltered 0.1 M NaCl. In the first figure, for the low

concentration sample, two measurements are marked as outliers (red). The correlation curves

for these two runs are shifted upward, indicative of a small number of very large particles, i.e.

dust, entering the scattering volume during the course of the measurement. In the second figure,

for the high concentration sample, no outliers are noted. While the dust particles are stillpresent, their contribution to the total scattering intensity is insignificant, compared to that of the

concentrated analyte.


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The figure below shows the DLS results for a high molecular weight 40 nm polystyrene

microsphere standard at low concentration in the same unfiltered 0.1 M NaCl. As with the

higher concentration lysozyme sample, the scattering contribution from the dust is insignificant

and no outliers are noted. In this sample however, it is the high molecular weight analyte that

diminishes the importance of removing dust via filtration.


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Will filtering perturb the sample?

Depending upon the size of the analyte and the size of the filter pore, filtering can indeed perturb

the sample. The figure below shows the DLS radius by Cumulants and DynaLS size distributionresults for an unfiltered poly(-cyclodextrin) sample. As evident in the DynaLS histogram, thesample is bi-modal (2 peaks) and polydisperse.

The concentration dependence of the measured hydrodynamic radius for the large particle isshown below. The solid and open symbols are used to indicate filtered (100 nm Anotop) and

unfiltered samples respectively. For concentrations 10.5 g/L, the measured radii are 61 and 75

nm respectively for the filtered and unfiltered samples. The elevated values at 20.95 g/L are

likely a result of interparticle interactions, which slow down the diffusion and lead to an

increase in the apparent hydrodynamic radius.


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The 20% difference in radii between the filtered and unfiltered samples is a consequence of the

removal of higher molecular weight particles during the filtering process. The figure belowshows the effects of filter pore size on the distribution of diameters for the poly(-cyclodextrin)sample. The dashed lines represent the pore cutoffs for the filters. As the filter pore size is

decreased, the larger polymers are clipped out of the solution. The result is a decrease in the

mean diameter of the larger particles and an increase in the contribution to the scattering

intensity attributed to the smaller particles at circa 6 nm. Hence the better resolution of the two

particle sizes with filtration.


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The size distributions shown previously are intensity distributions. If a flexible coil model,

where the molecular weight is proportional to R2, is assumed with regard to particle shape, the

intensity distributions can be converted to a %Mass distributions. The %Mass distribution for

the filtered 10.5 g/L poly(-cyclodextrin) sample (200 nm filter) is shown below.


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As evident in the above figure, only 7% of the total mass of the poly(-cyclodextrin) sample canbe attributed to the large particle. This system exemplifies the effects of large particle scattering

in dynamic light scattering studies. Even though there is only a small amount of the large

particle present, 97% of the total scattering intensity is attributed to that particle. In the absence

of filtering, information would have been lost, due to the inability to resolve the small, low

polydispersity particle from the larger and more polydisperse one.


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Why is the salt content relevant?

In dynamic light scattering experiments, it is the diffusion coefficient (D), rather than the

hydrodynamic radius, that is directly measured. The hydrodynamic radius is calculated fromthe diffusion coefficient via the Stokes-Einstein equation. Any factors influencing the

translational diffusion coefficient, whether or not they have any direct influence on the radius,

will have an apparent effect on the calculated radius. At high sample concentrations for

example, particle interactions can lead to a decrease in the diffusion coefficient and a subsequent

increase in the calculated radius. Electrostatic interactions between the particles can lead to

similar effects, even at low sample concentration. Electrostatic interactions can be shielded on

the other hand, by the addition of salt. Hence the relevance of salt content in dynamic light

scattering experiments.


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What is the Regularization Method?

Protein Solutions, Inc. would like to thank Dr. Maria Ivanova and Dr. Ulf Nobbmann for their

contribution of the following article.

In Photon Correlation Spectroscopy (PCS), single photons are detected and auto-correlated.

The autocorrelation function is the convolution of the intensity signal as a function of time with

itself. If the detected intensity is described as a function I(t), then the autocorrelation function of

this signal is given by

The above function is also called the intensity correlation function. The shift time is oftenreferred to as the delay time since it represents the delay between the original and the shifted

signal. In reality, the continuous intensity correlation function can not be measured. It can

however, be approximated with discrete points obtained by a summation over the duration of the

experiment, where the upper limit of the summation is given by the appropriate index belonging

to the largest available summation term for k.

The above general expression holds true for both linear and arbitrary delay times. Here, we arenot concerned with the specific technicality of obtaining the correlation function. That job is

left to the digital correlator, usually a plug-in card or an external USB device connected to a

personal computer. The correlator produces the normalized intensity correlation function and

makes the measured values available for further interpretation. The remainder of this article

then, focuses on the interpretation of the numerical values obtained from the correlator, namely

an array of intensity correlation function values Gk and the corresponding delay time values k.

If the intensity statistics of the measured signal are gaussian (which is true for all diffusion and

for most random processes) then the Siegert relation holds true. The Siegert relation states that

the normalized intensity autocorrelation function can be expressed as the sum of 1 and the

square of the field autocorrelation function g (scaled with a coherence factor expressing theefficiency of the photon collection system).

This equation can equivalently be written in the discrete form with the index k. For ideal

detection, the coherency factor () = 1. As a first approximation then, we can ignore the


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coherency factor, and develop a table of gk and k values.

Here the negative root value is only used for the unphysical case of G < 1 to approximate the

experimental noise of real data. This method imposes less bias than either restricting data to the

only the positive root or completely eliminating the outliers.

The ideal field correlation function of hypothetical identical diffusing spheres is given by a

single exponential decay function with decay rate determined by the diffusion coefficient and

the wave vector of the scattered light. The main objective of the data inversion consists offinding the appropriate distribution of exponential decay functions which best describe the

measured field correlation function. In mathematical circles this problem is known as a

Fredholm equation of the first kind with an exponential kernel. It is also known as an ill-posed

problem, since relatively small amounts of noise can significantly alter the solution of the

integral equation.

The fitting function for gk then consists of a summation of single exponential functions which is

constructed as a grid of exponentials with decay rate i .

The factor Ai is the area under the curve for each exponential contribution, and represents the

strength of that particular ith exponential function. The best fit is found by minimizing the

deviation of the fitting function from the measured data points, where a weighing factor k isincorporated to place more emphasis on the good, rather than the noisy, data points.

The weights are proportional to the intensity correlation function values, i.e. correlation functionvalues at small times have a higher weight than those at large times. Consider for example, the

following sets of figures. In the upper figure, the correlation curve baseline for measurement #1

is noisy. This noise is absent in the lower curve (measurement #12). In the absence of a

weighing factor, the noise could be interpreted as decays arising from the presence of very

large particles. As a direct consequence of the weighting factor however, the subtle variations in

the baseline for the upper correlation curve are correctly interpreted as noise by the

Regularization algorithm, and no significant differences are observed in the resultant size


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distributions for the two curves.


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The normal procedure to find the solution of Ais in the grid of fitted gk expressions is to

minimize the deviation 2 with respect to each Ai, and then find the solutions from the resultingsystem of equations. In other words, if we construct the solution out of N exponential functions

there will be N differentiations of the following form.

Each of the terms in the above differential contains a sum over k. The whole equation system

can therefore conveniently be re-expressed in matrix form as shown below, where the Y-vector

turns out to be a convolution of the experimental data with the kernel (= the grid matrix or the

exponential decays) and the matrix W consists of a convolution of the kernel with itself.

The standard procedure to solve this equation is to find the eigenfunctions and eigenvalues, and

construct the solution as a linear combination of the eigenfunctions. However, when the

eigenvalues are small, a small amount of noise can make the solution extremely big. Hence the

previous ill-posed problem classification. To overcome the problem, a stabilizer () is added tothe system of equations. This parameter is called a regularization parameter, and with the


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incorporation of this term we are performing a first order regularization.

The above expression is called a first order regularization because the first derivative (in Ai) isadded to the equation system. The regularization parameter determines how much emphasis

we put on this derivative or the degree of smoothness in the solution. If is small, it has little

influence and the solution can be quite choppy; whereas larger will force the solution to be

very smooth. It is this value or degree of smoothness that the user controls with theresolution slider in the new Regularization algorithm in the DYNAMICS version 6 software.

In addition to the smooth solution constraint, it is also required that the solution be physical; that

is, all Ai be non-negative and uniformly constrained. In short, these additional constraints

require that the summation of all Ai yields a finite number.

With the above constraints, Z is minimized by requiring that the first derivatives with respect to

Ai be zero. As indicated previously, this minimization corresponds to solving a system of linear

equations in Ai. The solution of Ai values is found using an iterative approach called the

gradient projection method.

A spherical particle with radius Ri will produce a correlation function with decay rate iaccording to the following expression, where D is the translational diffusion coefficient, q is the

scattering vector, kB is the Boltzmann constant, T is the absolute temperature, is the viscosity, is the solvent index of refraction, is the laser wavelength, and is the scattering angle.

The normalized display of Ai vs. Ri is the %Intensity distribution of the Regularization

histogram. The mean radius of a particular sub peak is the intensity weighted average, and is

obtained from the histogram using the following expression.

The polydispersity () (or standard deviation), indicative of the distribution in the sub peak, isalso obtained directly from the histogram.


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Can you get molecular weight information from DLS data?

The molecular weight of a particle can be estimated from dynamic light scattering data using

MW vs. RH calibration curves developed from standards of known molecular weight and size.However, because of the correlation between the specific volume (1/) of a particle and its

tertiary conformation, a universal calibration curve has yet to be developed, although numerous

calibration curves, each particular to a specific family or type of macromolecule are available.

Hence, in order to select an appropriate MW vs. RH calibration curve, some a prioriinformation

regarding the conformation of the particle must be assumed. The calibration curves included in

the latest development version of the Dynamics software package are shown below. For

reference purposes, it is noted that all of the proteins in the Protein family are globular;

Pullulans are linear polysaccharides; Ficolls are densely branched polysaccharides; and

Dendrimers are CO2 starburst type polymers, described as spherical, with a density that

increases with radial distance from the core.


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How is the axial ratio calculated?

The volume of a hypothetical sphere of homogeneous density can be calculated as shown below,

where Rsph is the spherical radius, MW is the molecular weight, V (bar) is the partial specific

volume (1/), and NA is Avogadros number.

The radius of the sphere can be written as follows.

Assuming stick boundary conditions, the frictional coefficient of this sphere (fo), can then be

expressed as

The above equation is also valid for non-spherical systems, with the exception that the measured

hydrodynamic radius (RH) is used, rather than the hypothetical spherical radius.

The Perrin or shape factor (F) then is defined as the ratio of the measured frictional coefficient

to the frictional coefficient for a hypothetical sphere of the same radius.

The above equation is that used in the Dynamics axial ratio calculator, where RH, Mw, and V

(bar) are input values and F is an output value.


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Once the frictional ratio is determined, the axial ratios for oblate and prolate ellipsoids of

revolution are interpolated from the data given in the following figure (see Cantor and

Schimmel reference).


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How is the mass distribution of radii calculated?

The mass distribution is calculated directly from the intensity distribution of radii via a

simplified form of the Rayleigh equation developed from static light scattering theory.According to static theory, the scattering intensity of the ith particle is proportional to both the

molecular weight (Mi) and the weight concentration (Ci) of the particle.

The molecular weight of the ith particle can be estimated from the expression shown below,

where vp is the partial specific volume and x is a shape parameter equal to 3 for spherical

particles and 2 for coils.

After substitution, the Rayleigh expression can be rewritten in the following form.

The %Mass of the ith particle is then defined as:

As evident in the above equations, the calculated %Mass is strongly dependent on the radius of

the particle. This dependence is exemplified it the following figures, which show the

Regularization distribution of radii displayed by %Intensity and %Mass for an 8000 molecular

weight poly(ethylene glycol) sample in 0.1 M NaCl. Comparison of the figures reveals a 10%

difference in the mean radius values for the two profiles, indicative of the 1/R2 dependence in

the %Mass calculations for coils.


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Are the %Mass calculations valid for all systems and conditions?

The complete expression describing the scattering intensity of a dilute solution of particles is

shown below, where Io is the intensity of the incident radiation with a vacuum wavelength of o, o is the solvent refractive index, d/dC is the particle refractive index increment, A2 is the

2nd virial coefficient, P() is a shape factor that ranges from 0 to 1, is the scattering angle, and

r is the distance from the scattering center to the detector.

In the %Mass calculations within the DYNAMICS software package, this equation is simplified

to the following form, where it is assumed that d/dCi is independent of particle size, A2Ci


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What's the significance of the refractive index () in DLS?

In typical dynamic light scattering studies, it is the autocorrelation function, an example of

which is shown below, that is measured during the course of an experiment. The correlationfunction can be fit to an exponential form, or more correctly, a summation of exponentials, with

the decay constants (i) containing the information needed to calculate the diffusion coefficients

(Di) of the system of particles under examination.

The diffusion coefficient is calculated using the expression shown below, where o is thesolvent refractive index, is the vacuum wavelength of the incident radiation, (= 1/) is the

inverse of the exponential decay time, and is the scattering angle. As seen here, the solvent

refractive index is introduced into the dynamic light scattering calculations through the

scattering vector (K).

A common misconception is that the subscript in o indicates that the refractive index to be

used is that for the pure/base solvent. Such is not the case. The scattering vector is dependentupon the dielectric properties of the medium, with o entering the expression via the

Clausius-Mosetti equation, which relates the polarizability to the permittivity of a molecule.

Hence, the refractive index that should be used is that for the medium within which the particle

is diffusing, i.e. the base solvent + any additives.

The CRC Handbook of Chemistry and Physicscontains a significant collection of temperature

and wavelength dependent refractive index values for aqueous mixtures of various


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Is the refractive index increment (d/dC) wavelength dependent?

In Chapter 6 ofLight Scattering From Polymer Solutions(Ed. M.B. Huglin; Academic Press:

New York, 1972), Huglin includes an extensive list of d/dC values (100 pages). According toHugglins empirical observations, the specific refractive index increment varies directly with -2. In order to verify this prediction, ten proteins were randomly selected from Huglins table

and checked. The figure below exemplifies the d/dC dependence on -2 for all of the proteins,with the BSA and Lactoglobulin data being the outer limits of the entire set of ten. As evident

below, the slope [(d/dC)/-2] is independent of protein type.

The effects of ionic strength on d/dC for BSA and -lactoglobulin at pH 7 are indicated in the

figure shown below. As seen here, (d/dC)/-2 is also independent of the ionic strength,although the addition of salt does lead to a decrease in the absolute d/dC value. Similar trends

were observed for all of the proteins in the original set of ten. (It is noted, that all of the proteins

are reported to be stable with regard to conformational changes under the cited conditions.)


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The independence of (d/dC)/-2 on protein type and solution salt content is likely a result of

the globular nature of the proteins examined. The refractive index is correlated with the densityof the media. For globular proteins, the specific volume (1/) is relatively independent of

protein type (vsp = 0.73 cm3/g). Hence the similarity between the d/dC and (d/dC)/-2values for the globular proteins examined here. As shown in the figure below however,

significant changes in both d/dC and (d/dC)/-2 are observed when the macromoleculesare coiled, rather than globular.


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Ideally, d/dC should be measured under the appropriate solution conditions and at the specified

wavelength, prior to beginning any static light scattering experiment. In the absence of theideal, one could estimate the protein d/dC value using the equation shown in the following

figure, where the symbols are the same as those used in previous figures. The equation is that of

the best fit line (black) for all ten of the protein data sets.


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The dashed lines are included in the above figure for estimating error. If solution conditions and

protein type are ignored, i.e. if the equation is used, the error in d/dC is 3%. If thewavelength dependence is ignored, i.e. via the use of a single d/dC value for all proteins underall solution conditions and wavelengths, the error in d/dC can jump to upwards of 10-15%.

With those observations in mind, it is instructional to consider the relative error in molecular

weight arising from d/dC error in static light scattering measurements. The Rayleigh equation

for static light scattering can be written as shown below, where is the solvent refractive index,

Ris the Rayleigh ratio of scattering intensities, is the wavelength of the incident radiation,NA is Avogadros number, A2 is the 2nd virial coefficient, and C is the analyte weight

concentration.

The derivative with respect to d/dC of the above expression can be written as follows.


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After rearrangement, the relative error in the molecular weight can then be expressed in the form

shown below. As evident in this equation, the relative d/dC error is amplified by a factor

proportional to the 2nd virial coefficient, the concentration, and the molecular weight, when

calculating the molecular weight from total intensity light scattering data.

Static light scattering measurements using ovalbumin, with M 43 kDa and A2 0.0005, havebeen conducted at Protein Solutions, Inc. The highest concentration was 0.02 g/L. Using these

parameters, the propagation factor (1 + 2A2CM) in the relative error equation is 1.0009 1.Under these conditions then, the relative error in calculated molecular weight is equivalent to the

relative error in the refractive index increment, implying that the 3% difference in d/dC for

globular proteins, due to different solvent conditions, is negligible. The 10 - 15% error in

d/dC arising from wavelength effects however, could be problematic, depending upon the

exact solution conditions employed and the properties (M and A2) of the particle under

examination.

Editors Note (10/13/00)

Please note that earlier versions of this document contained a unit error in the calculations of the relative error inovalbumin molecular weight and in the empirical equation for the wavelength dependence of d/dC. Wed like to

thank our friends at Wyatt Technology for bringing these mistakes to our attention (Thanks Ron - as always your

reviews and comments are greatly appreciated). The mistakes has been corrected, and the conclusions modified to

be consistent with the corrected value of the propagation factor in the relative error calculations. We apologize for

any inconvenience this oversight may have caused.


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Is the solvent refractive index (o) wavelength dependent?

The refractive index () of a medium is defined as the ratio of the speed of light in a vacuum to

that in the medium. As the light passes through an interface into a medium of higher density,say for example from a vacuum into a solvent, the decreased velocity of the radiation in the

solvent causes the light to be refracted or bent. According to Snells law, the magnitude of the

refraction, and hence the velocity of the radiation in the solvent, is dependent upon the

wavelength of the incident beam. Ergo, since the velocity of light in the solvent is wavelength

dependent, the measured solvent refractive index will be dependent upon the same.

On a molecular level, the decrease in the velocity of the radiation in the solvent arises from the

electromagnetic interactions of the light wave with the solvent molecules. If the solvent

molecules are more densely packed, the magnitude of the decrease in light velocity is

proportionate. Hence, the refractive index of the solvent is strongly correlated with the solvent

density. The dependence of the refractive index on density is described by the Lorentz-Lorenzformula shown below, where R is the molar refraction, M is the molecular weight, and is thedensity.

The figure below shows a compilation of refractive index values, extracted from the 77th edition

of the CRC Handbook for Chemistry and Physics, for pure water at different wavelengths and

temperatures. The linearity of the data at constant temperature is consistent with the Cauchy

expression, which predicts that the refractive index will be proportional to -2.


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As evident in the above figure, the solvent refractive index is also dependent on temperature.

This dependence arises from the temperature dependence of the solvent density. As the

temperature of the solvent is increased, the density decreases, leading to a subsequent increase in

the velocity of the radiation and a decrease in the measured refractive index. The equation

shown below, where T is the temperature in Celsius and is the wavelength in nm, is an

empirical expression developed from the above pure water refractive index data. While notgrounded in theory, it does simplify calculations of H2O for DLS experiments under normal

temperature and wavelength conditions.

Because of the wide use of toluene as a Rayleigh ratio standard in static light scattering

experiments, assorted temperature and wavelength dependent toluene refractive index values are

also included here. As evident in the figure below, Tol is proportional to -2, consistent with

the predictions of the Cauchy equation.


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Are o and d/dC temperature dependent?

Both the refractive index () and specific refractive index increment (d/dC) are closely

correlated with the density, and are hence sensitive to temperature. The correlation of therefractive index properties with density is evident in the figure below, which shows the

temperature dependence (0-25 oC) of d/dC for selected globular proteins. The similarity in the

(d/dC)/T tends is a direct consequence of the similarity in the partial specific volumes (1/)of the proteins.

The solvent refractive index is also temperature dependent, as evident in the following figures,

which show the reported (CRC Handbook of Chemistry and Physics) refractive index values for

pure water and toluene respectively, plotted against the square of the temperature (T2) in Celsius

at various wavelengths (). In the 1st figure, the slopes of the vs. T2 lines are independent ofwavelength, facilitating development of the empirical expression for H2O shown at the bottom

of the figure. The dependence of the refractive index on -2 is discussed elsewhere. As shownin the legend of the 2nd figure, the slopes of the vs. T2 lines are wavelength dependent for

toluene. Hence, development of an empirical expression relating the toluene refractive index to

both the temperature and the wavelength is more problematic.


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Is it alright to estimate solvent viscosity values?

The fundamental parameter extracted from the measured autocorrelation curve in dynamic light

scattering studies is the diffusion coefficient (D). The solvent viscosity () enters the picture via

the Stokes-Einstein equation for calculating the hydrodynamic radius (RH) of freely diffusing

spheres, assuming non-slip boundary conditions.

The standard error propagation expression for RH is shown below. Temperatures can be

measured quite precisely. Hence, T/T is negligible. If the questionable assumption that the

relative error in D (D/D) is negligible is also made, the best that can be expected is that the

%error in the radius is equivalent to the %error in the estimated viscosity value.

If the propagation of error ended here, small errors in the estimated viscosity would probably be

acceptable. Typically however, our clients also desire the particle molecular weight, which

cannot be directly calculated from the Stokes-Einstein equation and the measured diffusion

coefficient. As such, the molecular weight can only be estimated, using MW vs. RH calibration

curves developed from standards of know mass, size, and molecular conformation. Since these

calibration curves are empirical, error in the solvent viscosity is propagated even further, if

particle molecular weight is the desired parameter

With regard to the question then of whether or not it is OK to estimate solvent viscosity, the

answer depends upon how much error one is willing to accept in the target parameter and what

other a prioriinformation is available. If one it interested only in the radius of a system of

particles of singular size, then small errors in the viscosity might be acceptable. If however, the

solution is more complex or the target parameter is the estimated molecular weight, error in the

solvent viscosity becomes problematic. For example, the measured hydrodynamic radii for

dimeric and tetrameric insulin are 1.4 and 1.7 nm respectively. With only a 21% difference in

the size of the two inactive forms of insulin, a 10% error in the solvent viscosity can be fatal, if

one is attempting to determine the predominant form under a given set of solution or preparatory

conditions.

The CRC Handbook of Chemistry and Physicscontains an enormous collection of temperature

dependent viscosity values for solvents of various composition. The figure below shows a

compilation of 20 vs. W% (in water) data for some typical additives, extracted from the 77th

edition of the CRC. The empirical form of the 20 dependence on W% for all of the additives

presented here is a 2nd order polynomial, the coefficients of which are given in the figure legend.


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What is the _____ value of ______?

A number of solvent parameters, such as the viscosity and the refractive index, are incorporated

into the calculations in dynamic and static light scattering studies. Depending upon theconditions, error in the values for the solvent parameters can lead to significant error in the

results. Hence, questions of the form presented above are common. It would be impossible to

address all the permutations; but we can certainly try. The figure below shows a screen shot of

the new Archive utility developed at Protein Solutions, Inc. While it isnt as complete as the

CRC Handbook of Chemistry and Physics, it is always available and you can edit and/or add

your own information. This utility is currently available for download at the Protein Solutions,

Inc. web page, and will be included in the Dynamics 6.0 package.

ArchiveSetup Readme.txt

dls help manual

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