Flow field-flow fractionation: new method for separating, purifying, and characterizing the diffusivity of viruses.

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Flow

Field-Flow

Fractionation:

New

Method

for Separating,

Purifying, and Characterizing the Diffusivity

of Viruses

J. CALVIN GIDDINGS,* FRANK J. YANG, AND MARCUS N. MYERS

Department of Chemistry, University of Utah, Salt Lake City, Utah 84112

Received for publication 6July 1976

The nature and theory of flow field-flow fractionation is described, and its

potentialapplicabilityto virus-likeparticles isdiscussed. Different virus types

are shown to be retained at different levels. Retention can be controlled by

variation of the experimental parameters, in good agreement with theory.

However, amild adsorption effectisindicated and requires thedevelopmentof

alternate strategies for measuring diffusion coefficients. For Q(3, our value

agrees well within 10% of literature values; the values obtained for other

viruses, using Q/3as an internal standard, areuntested. Finally, it is

demon-strated thatflowfield-flowfractionation can cleanlyfractionatetwovirusesfrom

one another and from an albumin impurity, that samples as large as several

milligrams in size can be analyzed, and that the method has potential utilityin

the quantitativeand qualitative analysis of virussystems.

Field-flowfractionation (FFF) is a relatively

new tool, developed primarily for the

separa-tion and characterization of macromolecdles

andparticles (4, 5, 10).The technique has

dem-onstrated a capability of dealing with an

enor-mous massrange. Various subtechniques have

beenusedtohandle components varying from a

molecularweight of 600 up to particles of 1 ,um

in diameter. This represents a mass range of

approximately 109.

FFFtakesadvantage of the nature of viscous

flow in narrow channels. Under laminar flow

conditions,the velocity of flow approaches zero as oneapproaches the wall of the channel. Any

soluteor particle confinedinthe quiescent

re-gion nearthe wall will have itsmotionretarded relative to solutes distributed over the total flowcross section.

FFF employs an external field to partition

the desired solutes into the quiescent wall

re-gions of a narrow column. The field isapplied

alonganaxisperpendiculartothe flow axis. As thestrengthof the field isincreased,the solute

is driven further and further toward the wall

and its downstream motionisincreasingly

re-tarded. Differentsolutes will beretarded

differ-entiallybecausetheywillinteract to a different

degree with thefieldand/or theywillexhibita

differentlevelofdiffusivitythatwillselectively

oppose the induced drift toward the channel

wall.

The subtechniques ofFFFare characterized

accordingto the kindof field employed. Many

possibilities exist, but we have so far utilized

thermal gradients (givingusthermal FFF) (1,

6, 14, 19), electrical fields (7), sedimentation

fields (SFFF) (7, 8, 20), and flow gradients (9)

(Giddings, Yang, and Myers, Science,inpress).

A combination of these techniques has given

evidence ofbeing applicable to an

extraordi-nary rangeof solute mass and properties andof

solvent types.

The rate of migration of solutes in FFF

de-pends onthe magnitude and type offield, the

channel dimensions, the solute-field

interac-tion, and the solute-solvent diffusion

coeffi-cient. Inasmuch as the channel is designedto

have a simple and tractable geometry with

per-fectly understood flow characteristics, the

re-tentionof components canbe,intheideal case,

mathematically describedintermsofthese

pa-rameters. Therefore, measurements of

reten-tion canbe inverted to yield some combination

of parameters related to field-solute coupling

anddiffusivity.Ithas beenshown, for example,

that sedimentationFFFcanbe usedtoyield the

effective mass and, therefore, ultimately the

molecularweight of viruses (8).

Inflow FFF, the "field"orinfluenceselected

todrive solute towardachannel wall issimply

thesuperposition of lateral cross-flow fromone

side of the channel to the other. This lateralor

secondary flow is superimposed upon the

pri-maryaxial flow which carriessolute fromone

end of thecolumn tothe other (seeFig. 1). The

maintenance oflateral flowis assuredby

con-structingthe column such that it consistsof the

space between two flat, semipermeable

mem-branes. Thelateral flow proceedscontinuously

throughout the experiment, passing crosswise

131

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132 GIDDINGS, YANG, AND MYERS

C:ROSS I_(%k

VrECTlORS

11011[ZONIlALl

IFLO\N

lea,,velicity<v>)< *

VO)LUM.\E Rlt['C

IFLOW\sRATIE ;

VeOLUMAlETRIC F )\ RATIE,

I

Viru..B3

FIG. 1. Schematic edgeviewof flow FFF channel showsthe crossedflow vectors.

through the column, permeating first theupper

membraneand then the lower membrane. The membranes must be semipermeable such that theypreventthepassageof thedesired solutes.

Inasmuch as the imposed cross-flow acts identically onalldissolved materials, diffusion

becomestheonly selective variable in flow FFF thatcontrols the degree ofcompression of solute layers against the channel wall. Diffusion, therefore, controls retention. Because of this, differential retention (separation) is based on

differential diffusion alone. As a consequence,

themeasurementof retentionparameters can,

in theory, be employed to obtain the diffusion coefficients for the different fractionated

spe-cies. This conclusion, which has already been shownvalid forothersystems(9), will betested forviruses inthis paper.

Thediffusion andtransportofparticles in the virus size range are ordinarily very sluggish.

Therefore,alengthyamountof timeisrequired

for experiments based on considerable

dis-tancesoftransport. Thisproblem is largely cir-cumvented in FFF by virtue of the small di-mensions that can be employed for channel

width, i.e., of the order of0.35mm.This

advan-tage ismagnified by the fact that the solute is confined to a narrow layer on one side of the

channel, whose thickness may be 10 to 100

times smaller than the thickness or width of

the channel itself. The advantage of rapid

transport inthin (downto6 ,um) solute layers ofsedimentation FFF has been demonstrated

in the rapid measurement of the molecular weight of T2 virus (8). Itwasfound possibleto

complete a molecular weight measurement in

2.5 h. The same advantage should eventually

prove applicable in measuring diffusivities of individual viruses.

In this paper, we present some preliminary results demonstrating the applicability of flow FFF to theretention, fractionation, and charac-terization ofvirus systems. Despite the exist-enceofan apparentadsorption effect, valid

re-sults are obtained by using an internal

stan-dard method. Additional research is likely to

eliminate the adsorptive effect. This effect

ap-pears to be almost negligible for most ofthe macromolecularandparticle systemsstudiedin the laboratory (9).

The theory of flow FFF has been described (9). Here we review only those results

neces-sary for experimental interpretation and

de-velop a rationale and procedure for using an internal standardinthe measurementof

diffu-sioncoefficients.

Soluteparticlesareforcedby the interplay of

cross-flow and opposing diffusioninto an

expo-nentialsteady-statelayer nearthe lower

(accu-mulative) semipermeable membrane. The con-centration relative to that at the membrane

surface is therefore (5, 10) c/c0 = exp(-xIl)

(equation 1), wherexisthe distance above the

walland1 isthe characteristicthickness of the

layer. The parameter 1 is given by 1 = D/U

(equation 2), where D is the diffusion

coeffi-cient and U is sideways velocity imposed by

the cross-flow. Itishelpfulto express 1 inthe

dimensionless form, X = l/w, where w is the

channel width-the spacing between

mem-branes. We have X =DIUw (equation 3). If

lateral velocity, U, is replaced by volumetric

cross-flow,

Vi,

over the channel (membrane)

area (breadth a times length L), equation 3

becomesX =

DVOIV(,wI

(equation4),where VI

= awL is thecolumn void volume.

The retention ratio R is an experimental parametergiving the ratio of the elution

vol-ume ofa "void" peak (a peak eluted without

cross-flow), VO, to thatofthe retained compo-nentof interest, Vr. Accordingtothetheory of

FFF,R isrelatedto X by (5, 10) (VO/Vr) =R =

6X[coth(1/2X) - 2X] (equation 5).

From equation 5, it is possible to obtain X

values in terms of themeasuredretention pa-rameterR. (This is done mostsimplyby using aplotof R versus X.)WithX sodetermined, a

diffusivity value can be obtained from

equa-tion 3 or 4 asD= XUw = X

VIw2/VO

(equation 6).

We now describe a newprocedure for using an internal standard to eliminate systematic influences frommeasurements of D. If

system-atic departures occur from equation 4 due to

imperfect membrane surfaces, etc., an

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nal standard, i, canbe selected for which D is

known to have the value

Di.

Inthis case

equa-tion 4 (or 5) gives for the unknown D D =

Di (Vc/ V.i)x

(equation 7), where

(Vc/Vci)K

is

the ratio of cross-flow rates at some fixed

value. We use the ratio of

Vc's

at constant A

rather than the Xratiounder constant

experi-mental cross-flow,

Vc,

because surface

dis-turbances are expected tobe a function ofX

andtherefore comparable at a givenX value.

In practice, equation 6 iseasily used by

con-structingacurve ofXversus

VC

or

1IVC

for the

internal standard i, thereby making available

the

Vci

value at any X value assumed bythe

unknown.

MATERIALS AND METHODS

The flow FFF column and basic system have been previously described (9) (Giddings et al., Science, inpress). The channel dimensions usedin

this study were 44.0 by 1.1 by 0.038 cm, giving a volume of 1.84 ml, a volume verifiedbymeasuring the elution volume of a nonretained (void) peak.

Cellulose acetate membranes were used in this

study. Theywere cast on aporouspolypropylene frit by modifications of a standard method (12). The membranehadathicknessof 0.1 mm.

Thecarrier solution usedwas 0.02 Mphosphate bufferadjustedtopH7.12. This buffersolutionwas

fedintoboth the carrier and the cross-flow streams

by using two Cheminert metering pumps

(Labora-tory Data Control). The desired flow rate of the carrier stream was controlled by using a Nupro

needle valve after a UVdetector (Laboratory Data

Control).

Ferritin and bacteriophages Q8, MS2, f2, and

qX174werepurchasedfrom MilesLaboratories,Inc.

4OX174

asreceivedhad a concentration of 3 x 10'3to 4 x 10l3 particles/ml. The f2,MS2, andQ18viruses

each had aconcentration of 8 x 1014to 11 x 1014

particles/ml. Ferritin had a concentration of 72.4

mg/ml.

Samples of virus were injected into the carrier stream with aHamilton syringe. As little as 10 ,ug

couldbedetected, and samplesof as much asseveral milligramscould also beemployed.

Allexperiments werecarriedout at ambient

labo-ratory temperature, 24.6t0.5°C.The retention

vol-umeof the eluted virus samplewas measured by using a 10-ml buret. The fractogramwasrecorded

with an Omniscribe recorder (Houston Instru-ments).

RESULTS AND DISCUSSION

Foranynew class of solutematerials,such as

virusesinthe present study, the crucialtest of

the applicability of flow FFF is the positive

retention of solutecomponents beyond that of

theso-called "voidpeak." (The voidpeakis one

thatdoes not interact with thefieldorthat is

elutedinthe absence ofafield.)The retention

should increase smoothly asthe cross-flow

in-creases. Furthermore, the solutesmust not be

lost by adsorptionand should be elutedin

com-pactsymmetrical peaks.

These well-behaved retention requirements

have beenobserved forviruses. Figure 2shows

the consistent trend among a group of four

viruses inhavingadecreasingretentionratio,

R, with increases in the volumetric rate of

cross-flow,

V,.

InthatparameterRisthe ratio

of thevoid-peak elution volume(attime)tothe

elution volume (time) of the designated virus

peak; low R values indicate highretention.The

figure shows that R values downtoabout0.07

areobservedathigh cross-flows. This indicates

that the retention volumes up to about 1/0.07,

or approximately 14, times the channel void

volume can be systematically utilized. Sucha

high retention range is an advantage in

provid-ing elution "space" in which fractionation can

occur and in which characterization can be made selective and relatively accurate.

The adherence of experimental retention to

theory is an important consideration for

charac-terization workasopposedtosimple

fractiona-tion.Equation4suggeststhataplot ofXversus

0.4

H-0.3k

R

0.2

F-0 0.002 0.004 0.006 0.008 0.010 0.012 0.014

[image:3.505.255.442.334.600.2]

VC (ml/sec)

FIG. 2. Systematic decrease in retention ratio, R

(equivalenttoasystematicincrease in retention

vol-ume),withincreasingvolumetric cross-flowrate,Ve, for four viruses. These plots indicate a systematic

controllable retention.

I I I I I I

* Qf

o f2

o3 MS2

A

OX

174

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http://jvi.asm.org/

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l/Veshould be astraight line passing through

the origin. Such a plotis shown in Fig. 3 for the

four viruses reported in the previous figure.

The solid lines are least-squares plots of the

experimental data. Thedashedline is that

pre-dicted by theory for virus

Q,8.

This line is based

on D = 1.61 x 10-7, a value taken from the

literature andcorrected to the temperature of

ourexperiments (2).

Figure 4 shows that the experimental data

follow the expected general trend, but are

anomalous in that they uniformly intercept the

1/iV axis at about 75 s/ml. This shows that

retention becomesabnormally large at high V,

(low

1/V,)

values.

Several mechanisms can be postulated for

the nonzero intercept,but it mostlikely results

from some added component of retention for

those particles in thatimmediatevicinity ofthe

membrane. Reversible adsorption could give

this result, as well asa "trapping" process, in

whichparticles found in microscopic basins (or

evenlarge pores) are retarded because they are

removed from the normal flow streamlines that

impel them throughthe column.

Some insight into the anomaly is provided

byacomparisonof the retention of ferritin and 0.10

0.08

OQf 0.06 * f2

O MS2

A 0

PX174

Q,8

on the same column. The results are plotted

in Fig. 4according to equation 4:XversusDV°/

Vcw2.

This form of the retention plot should

yield a universal curve of zero inteceptand unit

slopeforallsolutes. To make thisplot,the D for ferritin, corrected to our temperature, was

takenas3.50 x 10-7cm2/s. This wascalculated

from sedimentation (16) and molecular weight

(11) data.

Figure 4shows that the least-squares line for

ferritin comes very close to intercepting the

origin. Thisimplies that the intercept anomaly

observed for virusesinFig.3isnotuniversal. It

suggests, but does not prove, a mild form of

reversible adsorption common to the viruses

employed.

Interestingly, the experimental slopes for

both ferritinandQ13inFig.4areabout 10% too

large. This suggests a systematic error inthe

measurementof some column parameter,

per-haps in VO or w2. Undoubtedly the membranes

change with use, affectingbothVO andw.

Fu-ture work should be directed atgaining accu-racy andstability inthese measurements, for

the inaccuracies willreflect themselves in

char-acterizationwork.However, calibration witha

singleknown component should beableto

elim-500

I/VC (sec/ml)

FIG. 3. Dataand least-squares plots ofXversus 1IiV, for fourviruses.

prediction for Q,3. The dashed line is a theoretical

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FRACTIONATION

inate this uncertainty because of the simple

linearity and predictability of the plots.

Measurementof diffusion coefficients. The

nonzero intercept of viruses does not hinder

fractionation (in fact, it increases the

selectiv-ity), but it does require the development of a

newstrategy forcharacterizing virus

diffusivi-ties.This is apparent from Fig. 5, a plot of the

diffusion coefficient forQ(3calculated from the

experimental data using equation 6. The D

val-uesappear to vary as adistinctfunction of cross

flow,

V,.

Consequently, there is an uncertainty

of up to 50% in D if the data are employed

directly, without further refinement.

One approach to improving the accuracy in D lies in recognizing that the greatest departure

from theory occurs at high

V,'s.

Therefore, an

extrapolation of the data to

V,

= 0 suggests

itself. The least-squares curve in Fig. 5

illus-trates this attempt. Unfortunately, this

ap-proach is hindered by the difficulty of gathering

meaningful data at low

V,

values; in this

ex-treme, retentiongraduallyvanishes and small

errors in retentionvolume are reflected in

in-creasing errors in D.The least-squares

extrapo-lation, shown by the curve, yields

Do

= 1.72 x

10-7 cm3/s. This is in fair agreement with the

correctedliterature value D = 1.61 x 10-7cm2/

s, noted earlier.

We should note that we have developed a

somewhatcomplicated model basedona

revers-ibleadsorptioneffect that isreasonably

consist-0.10 /

0.08

/// THEORY

Ferritin(*) / 0.06

0.04 /

0.02

a,0

(o

0.02 ~_ IO#

0 0.02 0.04 0.06 DV°

2V

w c

0.08 0.10

FIG. 4. Comparison of ferritin and Q13 ina

'uni-versal"plot of versus DV2Iw2Vc (see equation 4).

Forferritin,V=5.3 -6.3ml/h; forQ,B,V=3.3-9

ml/h. Thesolid line is theoretical; the dashedlines

areleast-squaresplots from the data.

1.8

1.6

1.4

u

1-.

E

r-0 x

a 1.2

1.0

0.8

0.6

0.4

0.2

0 1 2 3 4 5 6

c x103 (ml/sec)

FIG. 5. CalculatedDvaluesas afunction of

volu-metriccross-flow rate,Vt. The horizontal line

repre-sentsaliterature value(15). The arbitrarycurveD =

Do+aV,+ bVc+ bV'2,fit by leastsquares,permits

theextrapolation of the datatoV, =0. ThisgivesDo

=1.72 x10-7cm2/s(a =3.04 x102 andb = -1.86

x10-2). Channel flow,V,variedfrom3.3to9mlIh.

entwith the data and leadsto D = 1.55 x 10-7

forQf3.

The other approach to handling the

depar-ture from theory has already been outlined: a

reference such as

Q,8

is used. The parallel

be-havior of the four viruses shown in Fig. 3

en-courages such an approach. The application of thisconceptrequirestheconstructionofan

em-pirical curve of versus Vi, as noted in the

theory section.Thiscanbe doneusingthedata

already presented. With this and the

applica-tion of equation 7, the results of Fig. 6 are

produced forthe threeremainingviruses. The

valuesarefairlyself-consistent and drift

down-ward onlyslightly with large increases in

V,.

Theextrapolationback toV, = 0yieldsD

val-ues of 1.60, 1.49, and 1.39 x 10-7 for f2, MS2,

and 4X174, respectively, at our experimental

temperatureof24.6°C.

Comparisonswith literature dataareshown

inTable 1. The data have been reducedtoour

operating temperature, 24.6°C.ThetwoD's for

theprimarystandardQj3 obtainedin thisstudy

aresomewhatinconsistent,butfall in thesame

I I - 1 J I

0 0 LITERATURE

--VAL-UE-LEAST

_ ~~~~~SQUARE _

PARABOLIC REGRESSION

I

135 21, 1977

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1.8 1.6 1.4

1.2

E

IC

x

1.01 0.81 0.6 0.4

0.2

0 1 2 3 4 5 6 7 8

X103 (ml/sec)

FIG. 6. Least-squares linesforthediffusiondataacquired by applyingtheinternal standard methodof equation 7.The internal standardis Q/3.

TABLE 1. Comparison of diffusion coefficientsfrom

the literature andfromthisstudy

Phage _XMol_10-6wt_g D24.6._cm_2/sX 107 Reference

Q13

4.55 ±0.16 1.61 2

4.2 1.75 15

1.72 This worka 1.55 Thisworkb

MS2 3.6 1.85 15

3.6 1.99 18c

5.3 ±0.6 1.31 13

1.49 Thisworkd

f2 1.60 Thisworkd

OX174 6.2 1.79 17C

1.39 Thisworkd

a Byextrapolation to

V,

= 0.

bBy using the model for reversible adsorption

notedinthe text.

cCalculated by using the sedimentation

con-stant.

dInternal standard method;Q,B =reference.

range as the literature values. However, we

have,asnoted,used the value from reference 2,

1.61 x 10-7 cm2/s, as the primary standard

value inderiving the subsequentD's.

Theremainingdiffusion coefficients obtained

inthis work tend toward the low sidein

com-parison with the limited data. However, the

paucity ofthe data and its scatter disallow a

rigorousevaluationatthis point. Improvement

inthe flowFFFmethodshould leadnotonlyto

gainsinreliability but alsotoreliabilitychecks

fromtheself-consistency ofthedata itself.

Figure 7illustrates the separationof

Q3

and P22virusesfromeach other and from albumin. It is obvious that any salts or contaminants

withmolecularweightsaslow as orlower than

Voidpeak

P22 Virus

0 10 20 30 40 50

ELUTIONVOLUME (ml)

FIG. 7. Theseparation of albumin, Q/3, and P22 byflowFFF. V =8mlIh; V, =22.1 ml/h.

that of albumin would be removed from the

virusesduring fractionation.

Most FFF systems so far tested have

dis-played peak widths thataremuchbroader than

the theoretical values(9). This istrueinthese studies as well, with the departure ranging

f2 (0)

0~~~~~~~~0

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- MS 2 (o) 'X 174(0)

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from 50% to a factor of 4 or more. Efforts are

being made to eliminate this discrepancy; if

successful, the method promises to be much'

more versatile than now in separating virus

mixtures at high resolution.

We nextinvestigated the question of whether

sample size can be scaled up to a level that

might be useful in subsequentstudies with the

viruses. When characterization by means of

re-tentionparameters is the objective, it is best to

work at the smallest sample size consistent

with gooddetectability to assure linear

behav-iorof the particles in the channel. To meet this

objective, we ordinarily used samples of 3 to 5

pi

containing, in the case of

Q,8,

25to 41 ,ugof

virus (8.2 g of virus/liter). However, in this

study, sample size was studied over a much

broader range, from 8.2 ug to4mg,by varying

the sample volume. Figure8shows theeffectof

the amount of

Q,3

virus on theelution volume

of thepeak.The effect is,infact,veryslight, as

indicated by the least-squares line shown in the

plot: a minor tendency to speed elution with

increased sample size is the only trend

ob-served. This indicates thatfairly large samples

canberunwithout a seriousdisturbance of the

[image:7.505.249.441.237.382.2]

retention.

Figure 9shows how sample size affects peak

width. Bothplate height (a conventional

meas-ureof peak width inchromatographic-like

sys-tems [3]) and relative peak width are shown.

Both are based on width at peak half-height.

Also given is the theoretical value for plate height, indicating the improvement potentially

possible inflowFFFsystems. (Peakwidth

var-ies as thesquare root of plateheight.)

It is clear from Fig. 9 that the peak width

begins to increase noticeably with sample size

at about 0.5 mg and then increases rapidly

beyond 1 mg. At 4 mg of

Q,3,

peak width is

almost70%greaterinmagnitudethanatsmall

sample sizes. This eventual deterioration of

peak sharpness probably constitutes the

ulti-2

-3

12 300

2 2(X)

(.M) 0.1 t1

AM YNT|NrOFQQVIRUS (ng)

FIG. 8. Dataforelution volumeversusmilligrams

ofQ,8virus, alongwith least-squares line.

Parame-ters:V=5.8ml/h; V, =17.7ml/h; VO =1.85ml;R

= 0.2.

matelimitonuseful sample size.

Finally, to check the possible value of peak

area for use inquantitative analysis, Fig. 10 is

plotted to show relative area (adjusted for

re-corder attenuation)versus amount. Areaswere

measuredby cutting thepeaksoutof thestrip chart and weighing them.

Linearity would be indicated by a straight

line of unit slope. Such a line isplotted in the

figure. The agreement of the data is fair,

al-though moderately distorted and scattered.

This can probably beattributed to thedifficulty

of locating the base linepreciselyand the

non-linearity of the signalfrom the UVdetectorat

high sample loads.

It should benoted that the qualitative

analy-0.10 1

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AMOUNT OFQ#BVIRUS (mg)

FIG. 9. Effect of samplesize onplate heightand relative peak width. The low theoreticalvalue

indi-catesthepotential oftheflow FFFmethod.

Experi-mentalconditions are the sameasthosedescribed in the legend to Fig.8.

En

._ .3

.0

-:

(ml) m

AMOUNT OFQ,8VIRUS (mg)

FIG. 10. Peak area versus sample size. The

pro-portionalityneededforquantitativeanalysisis indi-catedby the solid lineofunitslope.

21, 1977

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sisoridentification(asopposedtoquantitative

analysis)of viruses is implicitinthe

reproduci-bleretentionshowninFig. 2. This role is

rein-forced by the association thatcanbemade with

virusdiffusivity.

In conclusion, the potential use of flow FFF in separating, purifying, identifying, quanti-tating, and characterizing diffusivity in virus systemshas been established. The method is in

an early stage ofdevelopment and, therefore,

still beset with anomalies. Still, even in this

initial applicationtoviruses, areasonable

util-ity is apparent. Withfurther refinements of the

method,anexpanded applicabilitycanbe

antic-ipated. The presentworkshouldserve to

intro-duce themethod and its approachestoworkers

concerned withthisimportant areaof research.

ACKNOWLEDGMENTS

We would like to thankSherwood Casjens of the Depart-ment of Microbiology, University of Utah, for valuable advice, data,and thesupplyofP22virussamples.

This research was supported by Public Health Service grantGM 10851-19 from the National Institute of General Medical Sciences.

LITERATURE CITED

1. Caldwell, K. D., L. K. Kesner, M. N. Meyers, and J. C. Giddings. 1972. Electrical field-flow fractionation of proteins. Science1976:296-298.

2. Camerini-Otero, R. D., P. N. Pusy, D. E. Koppel, D. W. Schaefer, and R. M. Franklin. 1974. Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses: R17, Qf8, BSV, PM2, and T7. II. Diffusion coefficients, molecular weights, solvation, and particle dimensions. Biochemistry 13:960-970.

3. Giddings, J. C. 1965. Dynamics of chromatography, part 1. Principles and theory. Marcel Dekker, New York.

4. Giddings,J. C. 1966. A new separation concept based on acoupling of concentration and flow nonuniformities. Sep.Sci. 1:123-126.

5. Giddings,J. C. 1973. The conceptual basis of field-flow fractionation. J. Chem. Educ. 50:667-669.

6. Giddings, J. C., L. K. Smith, and M. N. Myers. 1975.

Thermal field-flow fractionation: extension to lower molecular weight separations by increasing the liq-uid temperature range using apressurized system. Anal. Chem. 47:2389-2394.

7. Giddings,J.C., F. J. F.Yang,and M. N.Myers.1974. Sedimentationfield-flow fractionation. Anal. Chem. 46:1917-1924.

8. Giddings, J. C., F.J. Yang, and M. N. Myers. 1975. Application of sedimentationfield-flowfractionation tobiological particles: molecularweights and separa-tion. Sep. Sci. 10:133-149.

9. Giddings,J. C., F. J. Yang, and M. N. Myers.1976. Theoretical and experimental characterization of flow field-flow fractionation. Anal. Chem. 48:1126-1132.

10. Grushka, E., K. D.Caldwell, M. N. Myers, and J. C. Giddings. 1974. Field-flow fractionation, p. 127-151. In E.S. Perry, C. J.VanOss, andE.Grushka(ed.), Separation and purification methods. Marcel Dekker, New York.

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coeffi-cientsand molecularweightsof ribonucleic acidsand viruses. Proc. Natl.Acad. Sci. U.S.A. 51:501-508. 14. Myers, M. N., K. D.Caldwell, and J. C.Giddings. 1974.

Astudy of retentioninthermalfield-flow fractiona-tion. Sep. Sci. 9:47-70.

15. Overby, L. R., G. H. Barlow, R. H.Doi, M. Jacob, and S.Spiegelman.1966.Comparisonof twoserologically distinctribonucleicacidbacteriophages.I.Properties of the viralparticles.J.Bacteriol.91:442-448. 16. Rothen, A. 1944. Ferritinand apoferritininthe

ultra-centrifugestudies on therelationshipof ferritinand apoferritin: precision measurementsof the ratesof sedimentation of apoferritin. J. Biol. Chem. 1952:679-693.

17. Sinsheimer, R. L. 1959. Purification andpropertiesof bacteriophageOX174.J.Mol. Biol. 1:37-42. 18. Strauss, J.H., Jr., and R. L. Sinsheimer. 1963.

Purifi-cationandpropertiesofbacteriophageMS2andof its ribonucleicacid. J. Mol. Biol. 7:43-54.

19. Thompson, G. H., M. N. Myers, and J. C. Giddings. 1969.Thermal field-flow fractionation ofpolystyrene samples.Anal. Chem. 41:1219-1222.

20. Yang,F.J.F., M. N. Myers, and J. C.Giddings.1974.

Programmed sedimentation field-flow fractionation. Anal.Chem. 46:1924-1930.

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