Function of an internal bacteriophage T7 core during assembly of a T7 procapsid.

(1)

Function of

an Internal

Bacteriophage

T7

Core During

Assembly of

a

T7 Procapsid

PHILIPSERWER* AND ROBERT H. WATSON

DepartmentofBiochemistry, The UniversityofTexasHealth Science Center, San Antonio, Texas 78284

Received 28 October 1981/Accepted 13 January 1982

ADNA-free, proteinaceous procapsid of bacteriophage T7 (capsidI)hasbeen

shown in previousstudies toconsist of an

external,

spherical shell (envelope) and aninternal, cylindrical corewith fibrous projections that connect the core to the

envelope.Todeterminetherole of the core in assembly of the envelope of capsid

I, the kinetics of appearance of capsid I and possibleintermediates in capsid I

assembly (AG particles)weredetermined in the presence and absence of the core.

Forobtaining these data,agarose gel electrophoresis was used and appeared to be atechniquemoreaccurate and efficient than techniques used for obtaining similar

datainthe past. The results of these experiments were: (i)in thepresence of the core,AGparticles behavedkineticallyasintermediatesin theassembly of capsid

I;(ii)in the absence ofthecore, assembly of capsid I terminated prematurely and

AG particles accumulated. These and other data have been interpreted by

assuming that: AG particles are breakdown products of precursors of capsid I; theseprecursorshaveuncorrectederrorsin the assembly of their envelopes; anda

function

of thecoreistocorrect these

errors.

Ithas been shown that proteinaceous subunits in the envelopes of spherical, viral capsids are

arranged with icosahedral symmetry to

mini-mize thefreeenergyofthe envelope (3-5, 7, 9). Todetermine the mechanismsby whichsubunits

of envelopes of viral capsidsassemble,attempts are made to isolate incomplete capsids from

virus-infectedcells. Results withbacteriophages

that containdouble-stranded DNApackaged in

a capsid with a spherical envelope, including

bacteriophages

X, T3,

T7,

P2, P4, and P22,

indicate thataspherical, DNA-free capsid

(pro-capsid)

is assembled and undergoes structural

and compositional alterations before or (and) during

packaging

of DNA (reviewed in

refer-ences2, 6, 10, 11,22).

Asdescribed in the above-referenced

reviews,

theprocapsids of

bacteriophages X,

P22, T3,and

T7 have internal

proteins

that assist

assembly

of theirouter

envelope

and that insome cases are

ejected

from the

envelope

or

digested

before or

during

DNA

packaging (see

Fig.

2of reference

19 for modelsof thebacteriophageT7

procapsid

[capsid I] and the

capsid

to which

capsid

I converts

[capsid II]

during

packaging

of

DNA).

It has been

proposed

that these internal

pro-teins, sometimes referred to

collectively

as a

core, assist

assembly

of

protein

in the outer

envelope

by:

(i)

converting

the

envelope

protein

from a

nonassociating

to an

associating

form

(P22

[8]), (ii)

forcing

the

proteins

of the

envelope

to the orientation needed to

produce

an

enve-lope with the needed curvature

(T7

[15];

P22

[8]), (iii) forminganucleus forpolymerization of

other subunitsof the capsid (reviewed for

sever-al

bacteriophages

in reference 11), or (iv)

pre-venting host proteins from entering the capsid

(6). Hypotheses (i), (ii), and (iii) predictthat in

theabsence of the procapsidcore, assembly of

the procapsid eitherdoes not occur oris slower

than in thepresenceof thecore. Hypotheses(i)

and (iii) also predict thatin the absence of the

core, proteins of the capsid envelope

accumu-late in unpolymerized form. Therefore, the above hypotheses can be tested by measuring thekinetics ofassembly ofprocapsids and pre-cursors of procapsids in the presence and ab-senceofcores. Measurementof the kinetics of assembly ofprocapsids intheabsence ofacore

protein has apparently been

performed only

once (for P22 [1]), and in this

experiment

only

twotimesweresampled;theresultssuggest that

procapsidassembly is slowedin theabsenceofa

functional core.

Impediments

to

obtaining

the above dataaredifficultiesin

identifying

procap-sidprecursors and thelargeinvestment oftime

and resources needed if the

procedure

for

quan-titating

procapsids

is(asit

usually

is)

centrifuga-tion.

Therefore, to testtheabove

hypotheses,

it is advantageous to

develop:

(i)

efficient

(in

time

and cost)

techniques

for

identifying

and

accu-rately

quantitating

either

procapsid

precursors or at least breakdown

products

of precursors

(such precursors and theirbreakdown

products

will both be referred to as

procapsid assembly

595

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intermediates) and (ii) techniques more efficient thanthe techniques ofcentrifugationused inthe past for accurately quantitating procapsids. Agarose gel electrophoresis has been demon-strated to be an accuratetechnique for identify-ing T7capsid I, and it meets the above criteria for a technique to quantitate capsid I during

kinetic labeling experiments (16, 17). In addi-tion, agarose gelelectrophoresis is used in the accompanying communication (19) to identify particles (AG particles) whichareproduced dur-ingassembly of capsid I andarepossibly capsid Iassemblyintermediates (AG particlesare iden-tifiedby their failure to form asharpbandduring agarosegelelectrophoresisand theirpossession ofseveral characteristics ofcapsid II; most AG

particles are converted by trypsin to particles that migrate with capsid II during agarose gel

electrophoresis). Therefore,inthepresent

com-munication,the kinetics of appearance of capsid I and AG particles were determined in the presence and absence of the T7 core, using

agarosegelelectrophoresistoquantitate capsidI and AG particles. The results indicate that hypotheses (i) to (iii) do notaccuratelydescribe

the role of the T7 core and suggest another

hypothesis for the role ofthe T7 coreduringthe

assembly of capsidI.

MATERIALSAND METHODS

Bacteriophageand bacterial strains.Wild-type

bacte-riophageT7andT7ambermutants(20)werereceived

from F. W. Studier. The following amber mutants

were used: gene 5-28 and gene 8-11. The host for

bacteriophageT7and thenonpermissivehostfor am-bermutants wasEscherichiacoliBB/1;thepermissive

hostfor ambermutants wasE.coli 0-11'. Lysates of

the nonpermissive host infected with a T7 amber

mutantwill be referredtobythe number of themutant

T7 gene;particles isolated from such lysates will also

be referredtobythe number of themutantgene.

Buffers and media. Standard/G buffer is 0.15 M

NaCl,0.05 M Tris-chloride, pH 7.4, 0.005 M EDTA,

and 100 ,gof gelatin per ml. Electrophoresis buffer is

0.05 M sodium phosphate, pH 7.4, and 0.001 M

EDTA. Sample buffer is 0.005 M sodium phosphate,

pH 7.4, 0.001MEDTA, 100 ,ug of gelatin perml, 4%

sucrose, and 400 ,Lg of bromophenol blue per ml.

Cultures used for radiolabeling were grown in M9 medium (14).

Stocksofambermutants. Stocks of amber mutants

and wild-type phage T7 were grown and purified as

previously described (19).

Kinetic radiolabeling and artificial lysis of amber

mutant-infected E.

coil.

Log-phase cultures (1.25 ml) of

E.coli BB/1 were grown in M9 medium with aeration

at 30°C to 4 x 108/ml and were then infected at a

multiplicity of 15. At 14 min after infection,

14C-labeled algal hydrolysate (Schwarz/Mann;12 ,Ci/ml)

wasadded to the infected culture, and1min later 100

,lof the culture waschilled,as previouslydescribed

(13);simultaneously with chilling, 15

pl

of20%

Casa-mino Acids (freshly prepared) was diluted into the

culture,and aeration was continued at 30°C. Further

100-p,l samples were chilledat15.5, 16.3, 17, 18, 20,

22.5,and 27 minafter infection.

Allchilled samples were centrifuged in 1-ml

cellu-loseacetatebutyratecentrifuge tubes (Sorvall)at4°C

and 11,000 rpm for 10 min. Pelleted bacteria were

suspendedandlysed withlysozyme and the nonionic

detergent Brij 58 aspreviously described (13), except

that volumes used were one-half those previously

used.

Kinetic labeling, lysis, andprefractionation of

wild-typeT7-infected E. coHl. Wild-type Ti-infected E. coli

were subjected to kinetic labeling, lysed (with

lyso-zymeandBrij58), andfractionatedbysedimentation

in a biphasic gradient of sucrose and metrizamide

(sucrose-metrizamide gradient), as previously

de-scribed (16).

Digestionwithtrypsin.Samples weredigested with

trypsinaspreviously described(19).Trypsin-induced

conversion of AG particles in unfractionatedor

pre-fractionatedlysatestoparticlescomigratingwith

cap-sid IIduring agarose gelelectrophoresis (19)wasnot

decreasedbydecreasingtheamountoftrypsinusedby

afactor of 10, indicating thatthis conversion wasat

completion for allexperimentsreported here.

Electrophoresis in agarose gels. Samples were

broughtto13p.l with standard buffer andwerediluted

with 17 ,ulof sample buffer. Of thismixture,20,ulwas

layered beneath4 to6mmofelectrophoresisbuffer in

sample wells ofa0.9%oME agarose(MarineColloids,

Rockland, Maine) slab gelin electrophoresisbuffer,

andelectrophoresis wasperformedas previously

de-scribed(19) for16h.Afterelectrophoresis,gelswere

dried undervacuumandsubjectedtoautoradiography.

Densitometry. Theamountof 14C in selectedregions

ofgels wasdetermined by densitometric scanning of

autoradiograms (anR and Ddensitometer of Helena

Laboratories, Inc., Beaumont, Tex., was used) and

convertingareas thusobtainedto countsperminute,

usinganempiricallydeterminedcalibration factor.

RESULTS

Infections with T7 amber mutants. Tomeasure the kinetics ofappearance ofcapsid I andAG

particles,the amount of radiolabel in these parti-cles is measured as a function of time during

kinetic labeling (pulse-chase) experiments.

Agarose gel electrophoresis of unfractionated lysates can be used to quantitate 14Cin capsid I and also in those AG particles which are con-verted by trypsin to particles migrating with capsid II (19) (all references to AG particles madebelowwillrefer only to those AG particles converted by trypsintoparticles migratingwith

capsid II during agarose gel electrophoresis).

Advantageousaspectsof agarose gel

electropho-resisoflysates without prefractionation by

cen-trifugation are: (i) avoidance of the possible

selective loss of particles during a procedure that includes prefractionation by centrifugation and (ii) requirement for 1/10 to 1/100 the time

and cost of aprocedure which includes

centrifu-gation. However, if 14C-labeled capsid II is

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present in lysates, theseparticles, becausethey comigrate with trypsinized AG particles, will decrease theaccuracywith whichthe amount of 14C in AGparticles can bemeasured; the

pres-ence of

14C-labeled

phage T7 and T7

capsid-DNA complexes would further decrease the accuracyof such measurements (17, 18).

Therefore,tomeasurethe kinetics of appear-anceof capsidIandAGparticlesinthepresence

of the

17 core, 5am 17 were used to

infect

a

nonpermissive host(no DNA synthesized [21])

because capsid I, but neither capsid IInorphage

T7 nor capsid-DNA complexes, is produced

during such aninfection (16, 19, 21; P. Serwer andR. H. Watson, unpublished data). To mea-surekinetics ofappearance of AG particles and capsidIin the absence ofafunctionalcore, an

8am mutant was used to infectthe nonpermis-sive hostbecausean8ammutantis the onlyone

of thecore-defective T7 mutantsthatmakes no

capsid

II,

capsid-DNA complexes,

or

bacterio-phage T7 during such an infection (12, 19;

Serwer and Watson, unpublisheddata). Howev-er, the 8am mutant makes some capsid I in a

nonpermissive host; the envelope of 8am capsid

Iisindistinguishable from the envelope of

wild-type capsid I by electron microscopy (12) and

agarose gelelectrophoresis (19).

Alog-phase culture ofE.coli BB/1was infect-ed with the5ammutant,andasecondportion of the same culture was infected with the 8am

mutant at 30°C. Kinetic labeling (with

14C-la-beled amino acids) of both cultures was

per-formedas described in theMaterials and Meth-ods; samples takenateight times after thestart

of

labeling

were

subjected

toagarose

gel

electro-phoresis aftertreatment withtrypsin and

with-outtreatment with

trypsin.

No band at the

position

of

capsid

II was

presentinanyof the

untrypsinized

5am

lysates,

as expected (Fig. la, channels

3-10).

In the

trypsinized

5am

lysates

(Fig. la,

channels

11-18), a band at the

position

of

capsid

II was

observed;

this band is formed

by

AG

particles

(19). In Fig. la,

14C appeared

in AG

particles

earlier than it

appeared

in

capsid

I;

the amount

of

14C

inAG

particles

became maximalat16.3to

17 min after infection and

subsequently

de-creased

(shown

quantitatively

in

Fig.

2).

These kineticssuggest that theAG

particles

are

capsid

Iassembly intermediates.

Initially, cells infected with the 8am mutant

(core

negative)

incorporated

14C into

capsid

I and AGparticlesat

roughly

thesamerateasthe cells infected with the 5am mutant

(core

posi-tive). However, in contrast toresults obtained with the5ammutant,withthe 8ammutant

entry

of

14C

into

capsid

I ceased

by

1.3 min after

termination of

labeling

with14C

(Fig.

lb and

2).

The prematurecessation oftheentryof 14C into

capsid I during infection with the 8am mutant was accompanied by an accumulation of14C in

AG particles, an accumulation not seenduring infection with the Sam mutant.

Thepremature cessation of the entry of 14C-labeled protein into capsid I during infection with the8am mutant could be caused byeither (i)adecrease inthecapabilityof theinfectedcell

forassembling capsid I withincreasing time or

(ii) thepresenceof twopathways forassembling capsid I, one in which capsid I is assembled

morerapidly than in theother, and the

require-mentforafunctional core in only the pathwayin which capsid I is assembled more slowly. If possibility (ii) iscorrect,itmustalso beassumed

that no

14C-labeled

protein can enter the

path-way of more rapid capsid I assembly laterthan 1.3 minaftercompletion of labeling.

To test the possibility of a time-dependent

cessation inthe capability of8am-infected cells forassembling capsid I, the experiment of Fig.1 was performed with labeling starting at 19 in-stead of14 min after infection. The amount of

14C thatentered8amcapsidIwas1.5times the

amountthat enteredintheexperimentof Fig. 1,

andaprematuretermination ofthe synthesisof capsidIoccurredat 1.3min afterthecompletion

oflabeling. Thus,it isconcludedthatthe

prema-turecessation ofthe assembly of capsid I does notresultfromadecreaseinthe capability of the

infected cell forassembling capsid I. It is likely,

therefore, that possibility(ii) above is correct.

Infectionwith wild-type 17. Although, as de-scribed above, kinetic labeling ofwild-type T7-infectedE. colidoes not yield data as accurate as data obtained with the above mutants, a

kinetic labeling experimentwas alsoperformed with wild-type 17-infected cells. To remove

interference

ofphage T7 and capsid-DNA

com-plexes, determination of the amount of

14C

in AG particles was performed with lysates

pre-fractionated by sedimentation in sucrose-metri-zamidegradients, asdescribed in Materials and Methods. The amount of 14C in AG particles

wasdetermined bysubjecting 14C-labeled

parti-cles

cosedimenting

with

capsid

II toagarosegel

electrophoresis with and without

prior

treatment

withtrypsin, and

subtracting

the amountof14C

migrating

as

capsid

IIin the

untrypsinized

sam-ple from theamountof 14C

migrating

as

capsid

II

in the trypsinized sample.

Figure 3 showsthe results of kinetic

labeling

ofwild-type 17-infectedE. coli. As found with

5am17-infectedE.coli in

Fig. 2,

the kinetics of

appearanceofAG

particles

suggested

thatmost

of the AG

particles

wereintermediates in

capsid

I

assembly.

However,

atthe later times in

Fig.

3,

14C

left AG

particles

less

rapidly

than it left

capsid

I.

Although

the reason for this effect is

not

known,

itcould result from the

production

of

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598 SERWER AND WATSON

0. Capsid I

*4.

4) W81;W d W

* .. 1 Xq. ... ..~~~~~AL

;.irie...t:: .:

IS%

I15~

10

15

20 -

Capsid

E

it

b.

--

Capsid

I

-4

I 10

5

10

15

20

FIG. 1. Kineticlabeling of5am-and8am-infectednonpermissive host. Akinetic labeling experiment was

performed, and infected bacteriawerelysedasdescribed in the text,usingastheinfecting bacteriophage: (a)

5amT7and (b)8am T7.Thesameculture ofE.coliBB/1wasused for both mutants. Aportion of eachlysatewas

digestedwithtrypsin,asdescribed in thetext.Trypsinized and equaluntrypsinized portions of the lysateswere

subjectedtoelectrophoresis,as werecapsidIandcapsidIIisolated bysedimentation (16), as described in the

text. Thechannels have,respectively: (1) capsid II; (2) capsidI;(3-10) untrypsinized samples taken at 15, 15.5,

16.3, 17, 18, 20, 22.5,and27min after infection; (11-18) the same samples as in channels 3 through 10, but with

trypsinization; (19) trypsinized capsid II; (20) trypsinized capsidI.

D-

Ca

psid

I

,.

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4

x

C

E

-C,n

0

3

2

15.0 20.0 25

Time

(min)

FIG. 2. Kinetics of appearance of capsid I and AG particles after infection with 5am and 8am T7.

Amounts of 14C in capsid I were determined by

densitometry ofproffles ofuntrypsinized lysates in

Fig. 1; amounts of"Cin those AG particles converted

bytrypsin to particles comigrating during agarose gel

electrophoresis with capsid II were determined by

densitometry ofprofilesof trypsinizedlysates in Fig.

1.Anempirical calibration factor was used to convert

integrated optical densities to counts per minute.

Plot-ted as a function of time after infection are the

amountsof"Cin:(@)SamcapsidI; (0)8am capsidI;

(U)

5amAG particles;(0)8am AGparticles.

a

comparatively

small amount of AG particles

afterassembly of capsidI.

DISCUSSION

The datapresented here indicate that thereare twopathways for theassembly of

capsid

I:

(i)

a

core-independent pathway in which AG

parti-clesare not an

assembly

intermediate and

(ii)

a

core-dependent

pathway

in which

assembly

of

capsid

Iis slower than in the

core-independent

pathway

and in which AG

particles

are an

as-sembly intermediate. Furthermore, in the ab-senceofafunctionalcore,AG

particles

accumu-late,

apparently

as abortive end

products

of

assembly. If so, two

questions

concerning

as-sembly of

capsid

Icanbeasked: Howmuch has the structure of AG

particles

changed

during

cellular

lysis

and

subsequent

fractionation? What is thefunction ofthecorein the

pathway

of slower

capsid

I

assembly?

Postlysischangesin AG

particles.

It has been shown that 9am 17

lysates

and 10am T7

lysates

contain noAGparticlesorcapsids of any

recog-nizable kind (19). Thissuggeststhat P9 andP10,

the two proteins of the capsid I envelope (14), must bind to each other before either of these twoproteinscan assemblein a capsid-like

com-plex. The final product of assembly, capsid I,

also has P9 and P10, apparentlybound to each other. Unless P9 andP10disassociate andthen

reassociateduring assembly, an unlikely occur-rence,both ofthese proteins must be present in

all intermediates in capsid I assembly.

There-fore,it islikelythatAGparticles (capsidII-like

particles without P9), shown here to be interme-diates in capsid I assembly, are a breakdown product of a capsid I-like particle (AG* particle) thathas P9; these ideas are illustrated in Fig. 4. Possiblefunction of the T7 core during capsid I

assembly.

The presence of an apparently

unal-tered pathwayofmore rapid capsid Iassembly in a nonpermissive host infected with the 8am mutantindicates that the core does not affect the rate ofcapsid I assembly in this pathway. The data inFig. 2 also suggest that in the absenceof

the core the rate of AG* particle assembly is not

1.0 E

E

>C

0

c)

0

j..

u

v

0.5F

15.0 20.0 25.0

Time

(min)

FIG. 3. Kinetics of appearance ofcapsidIandAG

particles after infection with wild-type T7. Kinetic

labeling ofwild-type T7-infectedE. coli and

fraction-ation oflysatesby sedimentationwereperformed as

described in Materials and Methods. The amountof

"CincapsidIwasdeterminedbyagarosegel

electro-phoresis of unfractionatedlysatesanddensitometryof

the resultant profiles. The amount of 14C in AG

particleswasdeterminedbysubjectingsamplesfrom

thecapsidIIregionsofgradients(usedto

prefraction-ate thelysates) to agarose gelelectrophoresis, with

and withoutdigestionwithtrypsin,andthen

subtract-ing the amountof

"4C

migratingascapsidII without

trypsinization from the amount of "C migrating as

capsidII aftertrypsinization.The ratio of theamount

of14Ctothemaximalamountisplottedas afunction

of time. Symbols: (-)AGparticles,maximalamount

of

"IC

=51,101 cpm;(0) capsid I,maximalamountof

14C =122,305 cpm. Thesamplesused in this

experi-ment arethe sameasthesamplesusedin reference 16.

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errors

DNA

-P9.9

pi-g

AGParticle CapsidI Capsid Phoge

-P9{Lysis

AGParticle

FIG. 4. Pathway ofslowercapsidIassembly. The

pathway of slower capsid Iassembly, asdeduced in

thetext,is illustrated. The models ofcapsidsI andII

werededuced from observationsin references14and

15(seealso reference19).

decreased; the onlyprocessincapsidIassembly whose rate appears to be decreased by the absence of the core is the conversion of AG* particles (capsid I-like particles) to capsid I. Therefore, hypotheses (i), (ii), and (iii)

men-tionedatthebeginning allappeartobeincorrect for the assembly of T7 capsid I. (The data presented herearenotatestofhypothesis [iv].) Knowledge of the difference in structure

be-tweencapsid I andAG*particlesshouldprovide

cluestothe function of the T7coreduring capsid

Iassembly. Because theAG*particleshave not yetbeenisolated, deductionof this difference in

structure must be made from the properties of

their breakdown products, AG particles. The

only property of AG particles that appears to

provide aclue is the sensitivity to trypsin ofa smallpercentage ofP10 moleculesinAG parti-cles and the lack of thistrypsin-sensitive P10in capsid 11(19). This suggests that the

trypsin-digestible molecules of P10 are incorrectly

as-sembled in AG and presumably AG* particles. Therefore, it is proposed here that: (i) the func-tion of the T7coreduring capsid I assembly isto

correct errors in the assembly of the capsid I

envelope and (ii) AG* particlesareparticles that

haveuncorrectederrorsinthe assembly of their

envelopes (error correction hypothesis) (see Fig. 4). The error correction hypothesis explains

particles of capsid I assembled in the pathway of

more rapid assembly as particles which, by chance, didnotmakeerrorsduring assembly of theirenvelopes and, therefore, did notneed the

coreforassembly. This hypothesis explains the

conversion of AG* particles to capsid I in the

pathway of slower assembly as a process of

errorcorrection, possibly performedby

proteol-ysis of incorrectly assembled P10and (or) P9. Thedatathatnowexistsuggestsomeaspects

of howaprocessoferrorcorrection mightwork. Theinternalcoreof capsid I has beenshownto

consist of:(i)acylinder connectedatits baseto

the capsid I envelope and (ii) fibers connecting

the cylinderto thecapsid Ienvelope (14, 15;see Fig. 4). The fibers may be designed to fit the envelope in complementary fashion (the binding of the fibers to the envelope would be analogous tothe fitting together of two separately

assem-bled halves of ajigsaw puzzle). If the correct binding of envelope and fibers does not occur afterassemblyof the capsid Ienvelope,anerror correction process is activated.

Some core-deficient particlesofcapsidI pack-age DNA and the particles of bacteriophage

formed are noninfectious (12). Therefore, a

core-promotedcorrection of errors in the

assem-bly of the capsid I envelope may increase the

efficiency of productionof infectiveparticles by reducing the probability of the packaging of DNA by core-deficient particles. This would occurbecause a particle with a defective core

wouldnotbe ableto correct errorsin the assem-bly of its envelope, and the resultant particles

with uncorrectedassembly errorsin their

enve-lopeswould beincompetenttopackageDNA.

Other capsid I assembly intermediates. Inter-mediates in capsid I

assembly

less assembled than AG*particlesmustexist, but havenotbeen analyzed in the present

study.

In a

slowly

than capsids (i.e., with sedimentation coeffi-cients less than 20) or more

rapidly;

the more

rapidly sedimenting

capsid proteins

areboundto

particles that haveproperties of membranes of

E. coli. Further studies of

capsid

I

assembly

intermediates less completely assembled than

AGparticles areinprogress.

ACKNOWLEDGMENTS

Fortechnical assistance we thank Elena S. T. Moreno. For secretarialassistance we thank Brenda Moylan.

Support was received from the National Institutes of Health (PublicHealthService grantAl16117).

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Rev.Biochem. 44:555-611.

3. Caspar, D. L. D. 1980. Movement and self control in protein assemblies: quasiequivalence revisited. Biophys.

J.32:103-138.

4. Caspar, D. L. D., and A.Klug.1962.Physical principles in the construction of regular viruses. Cold Spring Harbor Symp. Quant. Biol. 27:1-24.

5. Crowther, R. A., and A. Klug. 1975. Structural analysis of macromolecularassemblies by imagereconstruction from electronmicrographs. Annu. Rev. Biochem. 44:161-182.

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