Models for decay of Escherichia coli lac messenger RNA and evidence for inactivating cleavages between its messages

J. Mol. Bio2. (1979) 135, 369-390

Models for Decay of Escherichia coli Zac Messenger RNA and Evidence for Inactivating Cleavages between its Messages LOUIS W. LIM AND DAVID KENNELL Department of Nicrohiology and Immunology Washington University School of Medicine St. Louis, MO. 63110, U.S.A. (Received 9 April

1979)

Tha size distributions of decaying polycistronic EschekAia co5i lac messenger RNA have been followed on polyacrylamide gels. At the same time, oquations have been derived that generate the theoretical size distributions of decaying macromolecules for different mechanisms of degradation. Using observed values of lac mRNA metabolism, it was possible to reproduce the in. vivo patterns with a model in which cleavage occurs at the start of each of the three message@ and is followed by a net 5’ to 3’ wave of mass loss. Other models of degradation could not generate the observed in vivo patterns. These alternative mechanisms include : ( 1) tile same number of primary cleavage sites (three) but at different positions on t,ho full-length molecule; (2) an exclusive 5’ to 3’ directional degradation from tile start of the Zac mRNA (no cleavages); or (3) the presence of many internal targets. Further support for primary cleavage at the start of messages came from the observed accumulation of the intact z mRNA released by cleavage at the z/w boundary and from the predictable effect,s of specific deletions on the resultant. size distributions. The significance of these cleavages has been assessed ; they could be necessary “processing” events or, conversely, inact,ivate t’he message for translation. Full-length molecules as well as cleavage fragments have been fractionated by successive sucrose gradient centrifugation and tested for their capacity to form translation initiation complexes irt, w&o. Full-length lac RNA could form such complexes at one or more of it.s three ribosome-loading sites, whereas the y or a message fragments were inactive. These results suggest that a cleavage at or near the start of a message inactivates it. 1. Introduction Escherichia coli messages decay exponentially (Kepes, 1963). Each one has a unique decay rate that is nob a function of its size or position on a polycistronic messenger RNA (Blundell et aE., 1972). The last message of the polycistronic Zac mRNA is inactivated and lost faster than is the first message (Kepes, 1967; Blundell et aE., 1972; Pastushok & Kennell, 1974), the converse is true for the first and last trp messages (Blundell et al., 1972; Forchhammer et al.. 1972), while the second of three messages in the gal mRNA decays more rapidly than does the first or last (Achord & Kennell, t Abbreviations used: message, mRNA coding for a single, functional polypeptide (a polycistronic mRNA carries several messages); j3Gase, j3-galactosidase (EC 3.2.1.23) coded by z gene; TA or transacetylaue. galactoside acetyltransferase (EC 2.3.1.18) from the Q gene ; fmet-tRNA, formylmethionyl.tRNA; IF, initiation factor(s). 360 0022 2836/79/340369 22 $02,00/O /ci 197!1 Academic Press Jnc. (London) Ltd.

370

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rAThI dim

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KENNELL

1974). These observations suggest that the initial events in the breakdown of a po]ycistronic mRNA molecule can occur internally rather than by an exclusive sequential decay in the 5’ to 3’ direction, as had been proposed by Morikawa & lmamoto (1969) and Morse et al. (1969). Direct evidence for endonucleolytic cleavage of polgcistronic mRNA came with analyses of the sizes of molecules released during decay of Zac or gal mRNAs (Blundell bi Kennell, 1974; Achorld Nr Kennell, 1974). However. 6hescl earlier analyses lacked the resolution to identify the number or the positions of thca int’ernel cleavage sites. Tn this paper we extend the mathematical analysis and present evidence that cleavage occurs only at) the start, of each of the three messages of the Zac mRNX. What could be the function of such a cleavage in a prokaryotic mRNA’! It could inactive the message or. conversely, it could be necessary for its activity as a template in protein synthesis. Eukargotic mRNAs are “processed” from larger precursors (Firtel & Lodish, 1973 : Pcltz, 1973 : Holmes & Bonner. 1973 : Perry, 1976: Ross. 1976 : Bastox & Aviv. 1977) as are prokaryotic transfer RNA (Altman, 1975) and ribosomal RNA (Dunn & Studier. 1973; Nikolaev et al.. 1974:
clea,vage

is associated

to form

translatjion--initiation

message

fragments

chomplexes

and

activity.

released Ity intrrshow

that

cleavage

wit,h decay.

2. Materials and Methods (a) Bacteria

and growth

conditions

E:. coli strain 1000, P-, thiamine (Blundell & Kennell, 1974; Lim & Kennell, Kenrlell & Riezman, 1977) was grown in inorganic salts plus caseirr l~ydrolysatn time. w/v) and glycerol (0.296, v/l-) at. 37°C’ with a 48 min doubling (b) Determination

of lac m&VA

1974; (0.20/;,.

sizes

Preparation of [3H]RNA for fractionat,iorr on gels has been described (Blundell & Kcnuell, 1974). The electrophoresis of RNA through 2.7% (w/v) polyacrylamide gels, measurement of a molecular weight scale from of 3H-labeled Zac RNA in each slier. and const,ruction 14C-laboled stable RNA markers were described by Achord Sr Kermell ( 1974). (c) Preparation

of componerhts

for

ir&&ion

reaction

E. coli strain MRE600 (RNase I-deficient) (provided by Dr Maxine Singer) was grown in the following medium (Zubay et UT., 1970): per liter, KH2P0,, 5.6 g; K2HP0,, 28.9 g; yeast extract, 10 g; glucose, 10 g. Bacteria were harvested hy chilling followed by centrifugation and the pellets stored at -80°C. Ribosomes and IF were prepared by modificatiotls of tllr: procedures of Hershey et al. (pH 7.5), 50 miw(1971), from alumina-ground bacteria extracted illto 20 mM-TriseHCl NH,Cl, 10 mM-M&l, and 7 m&l-mercaptoethanol. Ribosomos were pelleted at 150,000 g through a 10% glycerol cushion made in extraction buffer and the supernatant saved for charging enzyme. The ribosomal pellet was resuspended overnight in 50 InM-TriS-HCl 1 mx-EDTA arrd 1 mm-dithiothreitol and (pH 7*5), 0.5 M-NH,Cl (high salt), 40 rnsr-MgCl,, then pelleted again. The pellet was washed twice in the same solution and resuspended in 60 mu-NH&Cl, 1 mM-dithiothreitol, buffer I (10 m&I-Tris.HCl (pH 7.5), 10 mnz-MgCl,, containing 10% glycerol), dialyzed against buffer 1 and then stored in liquid nitrogen.

Zac mRNA

DECAY

371

These ribosomes constituted the 0.5 M-NH,Cl-washed ribosomes (without IF) used in most, of t,he experiments. A second preparation of ribosomes was not exposed to high salt (0.5 %I-NH,Cl); they were resuspended and washed twice in huffer I. (low salt) and used in t,he last experiment in Table 1 (ribosomes with IF). (NH4).&)+ was added to O-4 g/ml of the supernatant from tile centrifugation of the 0.5 finNH,Cl-washed ribosomes with the pH kept betwtlen 7 and 8 by addition of KOH. The precipitated protein containing the IF was dissolved in buffer II (buffer I with 2 rnyr inst,ead of 10 111~.M&l,) and dialyzed against buffer II. This crude 1F fraction was stortbd in liquid nitrogelk. Both ribosomes and IF remained active for more than 6 months. (‘rude enzyme fraction for charging t RNA was prepared from the S 150 (Zubay, lQ62). Aft,er concentmt~ion by dialysis against polyetllylelle glycol 6000 and then dialyzing against 20 mivr-potassium phosptlate buffer (pH 7.6), with 5 mivr-/3-rnercaptoethanol. thr prot,ein solut,ion was applied to a DEAE-cellulose (Whatman DE-52) column and elutrd wit,11 the same buffer containing 0.25 M-NaC’l. Fractions xvith Iligllest absorbance at, 280 nm were pooled as the charging enzyme fraction. [ 35S]fmet -tRNA was prepared under t,he following conditions: 0.1 >I-Tris HCl (pH 7.5). 6 rnBr-MgCl,, 6 m&l-ATP (pH 7.(l), 0.3 mg leucovorin/ml, 6 mg of E. coli B tRNA/ml 20 @v-methionine; 1 mCi [35S]methionine/ml (300 (Schxarz-Mann), charging enzymes: to 400 Ci/mmol. New England Nuclear) were reacted at, 37°C for 20 min with excess cllarpirlg enzyme fraction, previously calibrated wittl a small trial sample. The tRNA was purified by ext,ract,ion with phenol and precipitated with ethanol. Percentage [35S]fmet tRNA was est,imated by the ethyl acetat,e procedure of Leder & Bursztyn ( 1966). [35S]fmettRNA was discharged by incubating in 0.2 x-sodium acetate (pH 5.5) plus 10 mM-CuSO, at 37°C for 20 min (Schoffield & Zamecnik, 1968), and the copper removed by repeatetl precipit,ation with ethanol in the presence of 5 mw-EDTA. (d) In vitro

assay for message activity

The capacity of mRNA to form an initiation complex has been used to assay its act,ivity. ‘l’hr assay (Revel et al., 1969) included (in 50 ~1): ribosomes, washed in 0.5 M-NH,Cl (0.7 [35S]fmet-tRNA, 10 rg; NH,Cl, 100 mM; dithiothreitol, 1 mM; GTP, 0.5 myI: il 260 unit); Tris.HCl (pH 7.5), 50 InM; MgCl,, 5 mM; crude IF fraction, 20 pg; [3H]RNA. With thrb low salts-washed ribosomes, 160 pg of ribosomes were used. The reaction was performed at 37°C for 10 min, initiated by addition of ribosomes, and was t’erminated by bringing to 0°C. The content~s were layered onto a 5% to 20% (w / w ) sucrose gradient made in gradient buffer (10 mM-Tris.HCl (pH 7.5). 20 mM-NH,Cl, 5 mfir-MgCl,, 1 rnM-dit’hiothreitol) (5 ml in t,he Spinco SW 50.1 or 4 ml in the IEC SB405 rotor) and centrifuged for 60 min at 5 ‘C’ at 50.000 revs/min in the Spinco or 55,000 revs/min in the IEC rotor. Fractions wet-t’ collected directly onto 25 mm nitrocellulose filters (Millipore, HA) supported in a 30. chimney filter-holding box. The filters were washed twice with 5 ml of gradient buffer. dried and counted. The patterns given by E. coli RNA are showr~ in Fig. 1. First, it can be seen that a stable complex of [35S]fmet-tRNA with ribosomes is dependent both on added IF (Fig. l(b)) and on the presence of mRNA. E. coli RNA, almost completely depleted of mRNA, was prepared by liarvesting cells 10 min after rifampicin inhibition. It stimulated a very marginal level of 35S binding to ribosomes, consistent, with the expected level of residual mRNA in this preparation (Fig. l(c)). However, the association of E. coli [3H]mRNA with ribosomes is only partially IFdeperldent; the amount of [3H]RNA bound is increased about 3-fold by IF addit,iotl. This is similar to the IF stimulation of binding to the R17 A protein initiator region (Steitz, 1973a,6). The IF-independent binding does not require fmet-tRNA, since added [%]fmet-tRNA does not react (Fig. l(b)). Furthermore, the presence of 3H does not result from non -specific trapping of [3H]RNA, since 3H-labeled stable RNA is not bound (Fig. l(c)). Thus, we think that the low level IF-independent binding represents genuinch complexes and also measures the competence of mRNA to initiate. It has been proposed (St,eitz &, .Jakes, 1975) that a high degree of complementarity between the init,iation region of a message and the 3’ end of tho 16 S rRNA (Shine & Dalgarno, 1974,1975) can prodllccb an init,iation complex that is indeperLdutlt of tho usual factors and fmet-tRNA; the extent

372

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W. LIM

AND

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KENNELL

I

Fraction

(a)

number

(cl

(b)

FIG. 1. Formation of translation initiation complex. The assay for initiation was performed as described in Materials and Methods using 3H-labeled E. coli RNA (a) with or (b) without IF. After gradient separation of the 70 8 initiation complex, fractions were collected directly onto Millipore filters. The filters were washed, dried and t,he filter-bound radioactivny determined. Sedimentation is from right to Ieft in the Figure. (c) The result of an assay identical t,o (a), except that the [3H]uridine label was only in t,he stable HXA. This RNA was prepared from cells in which the label was added (to give 0.2 pCi/ml) 3 generations before harvest,, and rifampicin was added (to give 300 PgLglml) 10 min before harvest. The 3H cts/min reacted were 2.5 x lo6 in (a) and (b), 2.8 x lo6 in (c). [35S]fmet-tRNA (-ci?--0---), (---a-(>--); “H (-•-•-). of this complex formation would be a funct,ion of the degree of complemeritarity for a specific message. It is also shown in Fig. 1 that the assay for initiation complex that) relies exclusively on filter binding can be inaccurate. While most of the C3H]RNA that is not, in an initiation complex does pass through with washing, some does not. This non-specific binding becomes more significant as the fraction of [3H]RNA t’hat is active message becomes lower. An extreme case is the long-labeled RNA in Fig. l(c). Thus it. is necessary to measure only RNA associated with ribosomes. The analysis of Zac mRNA sizes in bacteria requires procedures that, eliminate degradation during RNA preparation. These have included the presence of diethylpyrocarbonate from the time of lysis to inhibit RNases irreversibly. Diethylpyrocarbonate-treated RNA was as competent to form complexes as non-treated (data not, shown) ; thus we could use it to inhibit nuclease activities. The concentrations of ribosomes and IF were chosen as the maximum that still gave the best resolution. With larger amounts the reaction became less IF-dependent’ and less specific for mRNA (not shown). (e) Other procedures Induction and labeling procedures, centrifugation in sucrose gradients and detection of lac RNA in fractions, hybrid formation in 50% formamide plus 3 x SSC (SSC is 0.15 MNaCl, 0.015 M-sodium citrate, pH 7), and radioactivity measurements of aqueous samples have been described by Blundell & Kennel1 (1974) and preparation of phage, DNA and DNA filters by Kennel1 (1970).

3. Results (a) Th~eoretiud size distributions A population mechanisms

of linear

polymer

: (1) an exclusive

of lac m.RNA

molecules

net directional

could

with d$erent decay

degradation

by any

modes qf decay one of three

basic

t’hat proceeds from one end

Znc mRNA

DECAY

373

of the molecule to the other; (2) cleavages at many internal sites ; or (3) a limited number of internal cleavages only at specific targets. In cases of internal cleavages the resulting fragments would have to be eliminated by secondary processes. Each of these mechanisms defines a unique distribution of sizes as a function of age of the molecules. Comparison of the generated patterns with the observed distributions provides insight into the basic mechanism of degradation. The lac mRNA of E. coli and its metabolism have been characterized in considerable detail (see the Appendix) and provide a good case for such an analysis. Some general assumptions will be present,ed here that could relate to any mRNA and have been used in generating the patterns based on the preceding mechanisms. Experimental support for them follow from earlier observations as well as results to be reported in this paper. (1) It is assumed that the initiation of any process in the decay occurs with random hit kinetics. Support for this assumption comes from the observation that in all cases of mRNA decay, whether it be loss of function, mass, or potential (Kennel1 & Talkad, 1976), the loss occurs with exponential kinetics (Kepes, 1963). (2) An internal cleavage is followed by a net 5’ + 3’ wave of degradation of the distal fragment. The initiation of this mass loss after cleavage also occurs statistically. Not#e that this would generate two-hit kinetics for the initiation of mass loss. (3) The net 5’ --f 3’ degradation proceeds to the end of the polycistronic mRNA. unless distal fragments have been released by cleavage, i.e. there are no stops at the end of a message. Such stops would generate patterns with very sharp peaks of discret’e message-sized fragments (Blundell & Kennell, 1974), which are not observed. Note that with this assumption an internal message can decay either by cleavage or from the wave of degradation proceeding from the preceding message. The sum of these two processes must generate the observed decay rate of that message. The introduction of two distinct, events for decay provides a major improvement over the earlier analysis presented by Blundell & Kennel1 (1974). It introduces added complexity to the equations, but allows some variability within the rather severe constraints of each model. Fortunately, with the aid of a computer it is possible to generate families of distributions resulting from the choices of rate constants for these events. The equations used to calculate the distributions of sizes of a t,ime-set of decaying molecules are presented in the Appendix and the following discussion refers to their application to Zac mRNA degradation. A “time-set” of Zuc mRNA includes molecules initiated from time zero (isopropyl-@-n-thiogalactoside addition) to time t (rifampicin addition). The most simple model is an exclusive 5’ + 3’ wave of degradation, and the equations lnesented by Blundell & Kennel1 (1974) apply. The most striking feature of this mechanism is that the relative mass distribution does not change with time of decay. The bulk of the mass is always contributed by the full-length species (Fig. 2(a)). The resolution in gels presented here is considerably better than it was in the sucrose gradients used by Blundell & Kemrell (1974). The opposite extreme would be degradation resulting from cleavages at many potential internal targets, e.g. any phosphodiester bond could be a target. This model would be biologically inefficient (Blundell & Kennell, 1974). We have not calculated the patterns resulting from cleavage at any of the thousands of such bonds in lac mRNA, but the expected patterns are approached by a model in which there are 15 equally spaced targets. Since a cleavage inside a message must surely inactivate it, the sum of all cleavage rates for a given message must give the observed inactivation

374

L.

W.

LIM

AND

D.

KENNELL

M, x 1o-6 M, x to-6 2.0 I.3 0.8 23s I

0.4 /

0.2 I

12

2.0 I.3 0.8 04 1, ,,, 23s 16s

0.2

M, x IO-+ 2.0 l-3 0.8

0.4

o-2

16s 1 ~f--jG--

61 I 6

:I :: ’ : :

Fraction number

(a)

(b)

(c)

FIG. 2. The expected size distributions of Zrcc mRPu‘A mass as a function of time of decay with different mechanisms of degradation. The molecular weight scale and overlap corrections are for 2.7% polyacrylamide gels. The total mass under each curve has been normalized to equal th(: relative Zac mRNA mass/ml at that time of decay (Schwartz ef (II., 1970). The calculations assume that rifampicin is added at 0.5 min after induction but that transcription initiation is first inhibited at 0.8 min and is then completely inhibited. The time constants for transcription and functional decay are from observed values. It is assumed that the wave of mass loss proceeds at, 1900 nucleotides/min, which is close to the observed rate of transcription (2100 nucleotides/min). (a.) The Znc mRNA molecules decay exclusively by a net 5’ to 3’ wave of degradat,ion. In t,his case the full-length molecule (about 28 S) accounts for the bulk of the mass at all times and t,hr relative amounts of any 2 sizes do not change with t,ime (Blundell & Kennell, 1974). (b) The expected size distributions of Ztcc mRNA mass as a functionoftime ofdecayif themolecules decay by cleavages at any of 15 equally spaced int,ernal targets, and 95% of the inactivation results from these cleavage* and only 5% from the wave of degradation proceeding from a preceding message. It is assumed that each target, in a specifir message has the same decay constant (k) but the total decay rate for that. message must equal the observed rates for z and for u and the same intermediate value for y as assumed in all cases, e.g. each k value for z mRNA is significantly lower t,han each of the: k values for n mRNA, since z mRNA decays t,wic( x as slowly and also there arc 4 times as many targets in z as in (1 mRN.4. (c) The same model as in (b), but 95% of the functional decay result,s from a wave of degradation entering a mrssagc from a preceding one and t,he remaining 5’%, from a direct cleavage in thv message. The eqltat.ions are derived in t.hP .4ppontlix and the timcx (in min) aftrr induct,ion arc’ shown.

rate for that mesxagre, e.g. the ten targets in t,he 2 message must ha,ve rate constants whose sum would generate an inactivation rate corresponding to t,he observed 90 second half-lift. We consider two extreme cases here. In the first, most of the decay (-95%) is initiated by endonucleolytic cleavage, while the remaining (-6o/;) results from the wave of degradation from the preceding target. Its pattern is shown in Figure 2(b). This model would result in a,n unacceptably slow mass decay of the total lac mRNA (3 min 17 s half-life here) compared to the observed 90 second half-life. This followsZ since the fragments resulting from cleavage would have t,o accumulate. The other extreme of this “many-endo” model is one that emphasizes the cumulative effects on a specific internal target of the attacks on all the preceding ones. A total of 95:/, of the hits results in a wave that proceeds into the next, target. In this case the

lno mRNA

M,

r

2.0 !

I.3 I 23s

x 10-s 0.4 I

0.8 1

375

DECAY

0.2 I

2,o

I-3

I

I

04

04 I

1

23s

16s

1

b

o-2 I

16s

I ::

2c

0 Fraction

number

Yrc. 3. (a) The expected size distributions in gels of Znc mRN4 mass as a function of time of docay if the molecules decay by cleavages at the start of each of the 3 messages followed by a net) 5’ to 3’ wave of degradation. The equations used to determine numbers of molecules are shown in the Appendix. Transcription and functional decay rates of the messages are the same as those given in Fig. 2. The shapes of the curves were affected by the 3 cleavage rates, which were chosen to generate patterns most similar to those observed (t ,L - 6 min for the z/y junction and - 3 ruin for the y/(x junction). (h) The same oonditions as in (a), except that the wave of degradation proceeding from a cleavage occurs at half the rate of transcription (1050 nuclrot~ides/min). The times (in min) after inrlr~ct ion are shown.

rate of mass loss is similar to the observed rate. The result,ant patterns are shown in Figure 2(c). The third class of models would be intermediate between the exchlsive direct)ional degradation and the many-endo models. They would specify a limited number of internal target’s at specific sites in t,he molecule. We have considered the case in which these t*arget)s are between the messages or at their start; because only this case for internal targets would maintain maximum biological efficiency and because the pre1iminar.v observations with both t,he Iac and gal mRNAs were consistent with such a model (Blundell & Kennell, 1974; Achord 6t KennelI. 1974). Cleavage at. the start of the /I-galactosidase message would be undetectable in a size analysis because it is too close to the 5’ rnd of the mRNA molecule (Maizels, 1973; Gilbert & Maxam, 1973). Cleavages at the other two sites would generate fragments of five-sixths, two-t,hirdn, one-third and one-sixth of the full-length size. These fragmenhs are themselves decaying to give a continuum of sizes from zero to full-length at any time; sharp discrete bands for each of the cleavage fragments, such as can be seen in the case of certain viral mRNAs that are more stable, will not be seen. One set of patterns is shown in Figure 3(a). However, it is possible to achieve a certain variability in the distributions

376

I,.

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LJNI

AXD

1).

KENSELL

in this three-target model. Au axsumpt,ion in all the models has been that the 5’~ 3’ wave of degradation, or i’scavt?llgw decay”. proceeds at a rate of 1900 nucleotides per mimk, w-hi& is similar t’o the rate of transcription (2100 nucleotidrs,‘min). Thcrt~ is no experimental evidence for this assumption. SC)IVV have generated t,hc patterns in this model if the rate wcrc half as fast, arid it, (:a11 h(b see11 that tzhe basic distributions are not charlged significantly (Wig. 3(h)). A slower wave of degradation would include non-proctwivc cnzpmatic mechanisms in which the nuclease would st,op or pause hcforv the end of the mRKX molecule. The resumption of degradation could tw from the samcr or from a different nuclease molecule. The net effect’ for bhc, mRNA population \+wlld he R slon-rr wave of degradation. of lac mRNA (t)) The ob.served siw di.striOufions The observed size distributions of a time-set of decaying Zac mRNA as A function of time are shown in Figure 4. As had hern dorw in t8hr preceding model patterns. M, x 10-6 l-5 I.8 1

0.9

I.2 I I

I

O-6 I

23s

16s

1

1

0.3 1

Time (min)

IO

20

Fraction

30

40

number

FIG. 4. The size distributions of a decaying populat,ion of Znc mRNA molecules. E’. co& K12 strain 1000 was induced with isoI)ropyl-~-1~.thiogalactositlo to 0.5 ml\1 (at time 0) with c,4MP (2 nmr) added at minus 2 min, [5-3H]uracil (to 40 /rCi/ml and 2 nmol/ml) at minus 10 s, and for more than 2 rifampicin (to 300 rg/ml) at 30 s. Cells had been labeled with [.2-1*C] (0.1 pCi/ml) Samples WOI‘R brought to 0°C with chloramphenicol generations to give t,he stable RNA markers. and azide at the times indicated after induction, and RNA purified for electrophoresis. Each gel slice has been hybridized to @OdZuc DNA and the total Zae 13H]RNA at each time was normalized to be proportional to t,he total Znc [3H]RNA per ml in the culture at that time. This latter value is determined by the percent.ago of [3H]Rh-.4 that is Zuc-specific t,imes the amount of [3H]RNA/ml. Migmtion is from left to right,. The inset plots t~he amount of full-1engt.h Zuc mRNA (-•-•-) rersus time compared to tho oh+orvcd tot,al mass of Zrrc mRNA (- --- ---).

Ztcc mRSA

lIE(:AY

377

total Zac [3H]mRNA in each pattern has been normalized to the total Zac ] 3H]mRNX per ml of culture at that time. Several feat’ures can be noted. First? the full-length species is seen as a leading peak of 28 S that corresponds t’o the expected 1.8 x lo6 ih’, size. It is lost extremely rapidly; a semilogarithmic plot gives a’ half-life of 0.7 minute (the same value is obtained from the patterns shown on sucrose gradients several years ago, Blundell & Kennell, 1974: as plotted by Schneider et al., 1978). This is twice as fast as either the functional decay of the z message or the mass loss of 1~ mRNA (both about 1.5 min) and demonstrates directly that the polycistronic mol+ cules arc cleaved, since they are lost faster t’han is their mass. It approximates a logarithmic decline at the times measured here: however, strictly speaking it’ is incorrect, to assign a half-life to the full-length molecule in the mode of decay t,hat, reproduces the observed patterns (set t’he Appendix). Second, concomitant with loss of the full-lengt’h species there is a relative accumulation of smaller molecules. This shift to smaller sizes is also inconsistent with an exelusive 5’+ 3’ mode of degradat’ion, as not,ed above and by Blundell & Kennel1 (1974). Comparing t’he observed patterns of Figure 4 to those generated in Figures 2 and 3 1)~ t’he different models of decay. it is seen that only with the model of Figure 3, in which cleavages occur exclusively between messages, can one generate distributions that are quite similar to the observed patterns in Figure 4. n’ote that all the observed time constantIs arc accomodated in the equations used to generabe those patt’erns and RISO the rcsuhant mass decay rates agree wit’11 t’hc observed values.

23s

16s

23s

16s

i

1

P

I

IO

20

30 Fraction number

(a)

(b)

5. The observed size distributions of a decaying population of Znc mRNA moleculea (a) and those expected in the model in which cleavages occur only between the messages (b). Bacteria were treated (for (a)) as described in Fig. 4, except that rifampicin was added at 1 min, and harvested at the times shown. Tho expected patterns for (b) were derived using t,he model given in Fig. 3(a). FIG.

378

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AND

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The most prominent size class observed, with respect to enrichment with time, is a species of -23 S. Ibs prominence at late times is very reproducible, as is shown in another experiment (Fig. 5(a)). We have also derived the distributions for the same times using the model of cleavages between messages (Fig. 5(b)); the agreement with the observed patterns is quite good. Note that the other classes of models in Figure 2 cannot reproduce the accumulation of this species. (c) .Distributiwa OJ z ,mRNA The species that accumulates at, -23 S is t)hc size of z message (M,. 1-106). This mRNA would be expected to accumulate relative to other species if the polycistronic molecules were cleaved at the x/u boundary and since the mass decay of the z mRNA is slower than is that of the distal segment, (Pa&&ok & Kennell. 1974). To identify the presence of z mRNA. slices from alternate gels were hybridized t,o denatured DNA from @OdZac and /\pluc5 phages: this latter DNA contains only z and a small part of y. After normalizing to equal hybridization efficiencies, the patterns could be compared (Fig. 6). It can be seen that, the 23 S molecules that accumulate with time are essentially pure z mRNA. Also. a large species t,hat migrates between t’he 23 S and 28 S sizes is about, 80”’,‘0 2 mRNA; this is consistent wit,h the composition of a molecule of ZY mRNA that would be released by cleavage at the j//u boundary. These species are decaying t’o smaller sizes. ‘!JIc abrupt decrease in the z mRNA of sizes <23 S in the placfi pattern is consistent with t,he presence of t’hestl decaying fragments (compare to Fig. 2(a)). In contrast. the #OdZac patbern shows a species at, about 16 S, which is the size predicted by R fragment of !/a mRNA that’ would bc I.5 0.9 I.8 I.2 0.6

0.3

r---r

-~

I

T E > E :

23s

16s

4s

800

600

E

T LY 8

400

200

I

IO

20

30

40

50

Fraction number FIG. 6. The sizes and specificities of an induced time-set of Zac mRNA molecules at the cornpletion of synthesis. E. coli strain 1000 was grown, induced and labeled as for Fig. 4. The bacteria were harvested at 4.5 min and their RNA purified and fractionated by electrophoresis through polyacrylamide gels and the amount of Zoc RNA in each slice measured by hybridization to the indicated Znc DNA. Migration is from left to right. The full-length molecule has a molecular weight @OZac DNA (carries entire zyw DNA of the Zoc operon); ---~~--~-P, of 1.8 x 106. ----e-e-, hpZnc5 DNA (carries only the z DNA of the opcron).

Znc mKNA

379

DECAY

released by cleavage at the z/y boundary and a species of about 10 S that corresponds t,o the size of either y or a mRNA. The distribution of these smaller molecules is more difficult to reproduce, a result to be expected from the fact that the mass of the distal lac mRNA is lost faster than is that of the z mRNA (Pastushok & Kennell, 1974). Thus these results also support a model in which the internal cleavages occur onl! between the individual messages. (d) Distributions

of 1~ m RNA

in deletion

mutants

The preceding conclusion can be tested by observing the size disbributions of decaying lac mRNA from strains that have defined deletions in this operon. In each model t,he size distributions would be changed in a unique way. If the molecules wertb degraded by an exclusive 5’+ 3’ wave of degradation, the relative mass distribution would be invariant in all cases, with the full-length molecule now reflecting the total remaining length of the operon. The patterns expected from cleavage at, man) internal targets would also be a function only of the total length of the remaining operon. In cont’rast, cleavage restricted to message junctions would be affected most, by deletions t)hat removed such targets specifically. We have compared the pat,terns observed from two defined deletion strains. One mutant contains a, deletion tha.t includes the z/y ,junction. In the other. about half of the x DNA has been deleted but all of the regions containing the start of ea.ch gene are intact. Both of these deletions are approximately the same length. removing about one-third of the operon. If cleavages occurred only at the start of messages, deletion of the central Z/ZJboundary would produce a full-length molecule with only one internal cleavage site that, is quite &ar the 3’ end; the resultant pattern of decap should he more similar t,o the exclusive 5’+ 3’ degradative model than is that from the parent strain. lndeed. there was a fairly constant fraction of mass representing full-length molecules with little relative increase of smaller fragments with time (Fig. 7(a)), supporting the assumption in the models of a net A’ to 3’ wave of degradation of fragments released by cleavage. In contrast, the strain with a.11such sites still intact should show a relative decrease of full-length molecules with a large accumulation of relatively small fragments resulting from the internal cleavages: this pattern wa,s observed (Fig. 7(b)). Thus bot’h deletion strains gave size distributions expected for the model of cleavages between messages. (e) Cleavage

and decay

With cleavages between messages of the polycistronic lac mRNA the population should include molecules of five-sixths, two-thirds, one-third and one-sixth length corresponding to fragments containing zy. Z. ya, and y or a, respectively, as well as the full-length zya molecule. These molecules can be tested for their capacity to serve as templates for translation. The most critical size to assay is the one-sixth length. which includes t’he y or a message. If cleavage inactivated the message immediately distal to the clip, these molecules would have no activity. The ideal assay would measure the capacity of the RNA to direct synthesis of its enzyme in a cell-free translation system, but this assay was unsuccessful. The high level of non-specific transacetylase activity in these cell-free extracts gave a, very high background that could not’ be reduced sufficiently. Since the cleavage appears to Occur at or near t’he ribosome loading site, a reasonable I ::

380

L.

W.

LIM

AND

.I).

KENNELL

I.2 0.8 r I 235

05 I 16s

0.3 I

:

Fraction

(a)

number Ib)

FIG. 7. The size distributions of decaying Ztrc mRN4 in a host strain that has a complete deletion of t,he lac operon and carries an F’ episome with tho lac oporon containing a specific deletion. (a) E. cc& RV, F-, thi, Alnc (F’MS37) (f ram M. Malumy) which co&aim the Zoc operon with a deletion of about one-third its length in its central portion t,hat includes the z/y boundary. (b) E. coli RV, F-, thi, Alec (F’lncdrl), which contains tho kc operon with a tlelet,ion of about one-third its length located only within the z gene. The bacteria were grown, induced, labeled and harvested (as described in the legend to Fig. 4) at the indicated times. 411 other procedures for measuring the size distributions are described in thr legend to Fig. 4. The expected pat,tem of sizes for the exclusive 5’ -h 3’ cxonucleolytic degradation is drawn for comparison (. . .).

hypothesis is that inactivation is caused by loss of capacity t)o form a translation initiation complex. We have used this assay to measure functional activity. [“H]RNA from preparative volumes of induced cells was fractionated by size in two successive sucrose gradients and fractions corresponding to full-length, one-third or one-sixth length Zac mRNA were pooled (Fig. S(a)). Each of these RNA sizes was tested for capacity to form a stable initiation complex with 13H]fmet-tRNA and ribosomes (Materials and Methods), Each pooled fraction contained a mixture of cell mRNAs and was competent to form such complexes (Fig. S(b) to (d)). These were detected by sedimentation of monoribosome complexes (at, 70 S) or heavier complexes representing polycistronic mRNAs with more than one init,iation site occupied by a ribosome. The presence of luc RNA in these complexes was detected by hybrid formation either to @OdZac DNA (carries entire operon) or to @OpEac20 DNA (carries distal half of operon; see Fig. 1 of Lim & Kennell, 1974). In several such experiments the results showed that significant levels of full-length lac molecules formed initiation complexes of one or more ribosomes. In contrast, we could detect no significant binding by the one-sixth size class (Table 1). The one-third length molecules had weak, but measurable capacity to form initiation complexes. These results are consistent both with cleavage being at the start of a message and with it being an inactivating rather than a processing event.

Znc mRNA

DECAY

14

(b)

12

IO

8

6

4 5 w t

2

“0 3 9 lx T I!5

12 8 4

3

-f

5 2

! ;

j- 4

-‘

-5 I

-2

1

I I55 Fraction

5

IO

I5

20

25

number

Pm. 8. :Purification-of RNA of different sizes (a) and assay for their ability to form initiation complex ((b), (c) and (d)). After preliminary fractionation on a 35.1111 5% to 20% sucrose gradient. fractions corresponding to the complete, l/3 and l/6-sized Zac mRNA were pooled and centrifuged The sedimentation patterns are again through 3 separate 12.ml 5% to 2Oq/; sucrose gradients. and the fractions that were pooled for shown together in [a), complete (a), l/3 (~1). l/S (A), marker, 23 S rRNA was centrifuged initiation assays arc also indicated (I-1). A: \ an additional in a 4th gradient ( ----). Patterns of the initiation complex gradients with complete (b), l/3 (c) and l/6 (d) length were obtained by counting the radioactivity retained on a l/S sector from each Millipore filter on which a fraction w&s collected; the remaining sector was used to measure 35S (O), 3H (0). The parallel assays without IF the amount of Zac mRNA by hybrid formation. are shown for a% (a). Sedimentation is from right to left in all panels except the insets, in which absorbance profiles are from left to right. The heavy arrows point to the approximate position of the 70 R mtmoaome complex.

382

1,.

1%‘. T,TM

ANI) ‘I’ABI,E

Functional

activities

of lac mRNA

1).

KEXNELT,

1

aasuyed by initiation

622 l/3

2400

l/6

940

complex fornaatio7p

4.6

0

3.0 19.6 0 0.7 0 0

637 34 63 35 0

3.8 8.4 1.9 3.6 6.8 0

205 543 2 35 :i 3.5

2.0 5.3 0 1 .o 0.1 0.9

x4 0 0

4.1 0 0

406 “621 0 16

Expt

IS

II

0

7611

1 /3

1755

l/6

518

293

!

Expt

1*X

III

10,184

l/3 116

With Expt

TV

lowsalt-washed IS l/3 l/6

1 til ‘5X

5403

6

4058

16 3 I5

l.ti 2.5 0.1 0.3 0.1 0.4

ribosomca 2067 1559 1581

a The DNA used for detection of Zuc mRNA was @OdZuc in experiment III and ~80pZrr~dO in rxpcriments I, II and IV. The extent of Zrtc DNA carried is given by Lim t Kennel1 (1974). b The sizes refer to the Znc mRNA in fractions pooled from the sucrose gradients as illustrated in Fig. 8(a). ’ Assay* with t,he 0.5 wsalt,-washed ribosomes were performed wit,h or without ll?. No 1 F WIW added in assays involving t,he low-salt-washed ribosomes which still had IF bound. d mRNA containing functional messages would form one or more initiation complexes and would be trapped on Millipore filters. The amount of functional kc mRNA in t,he complexes wxs then bot,h as 3H cts/min and as prrcent,age of measured by hybridization. The results are expressed input ZUC L3H]mRNA (column 2). In all experiments. initiation assi~y blanks using 13HjRN14 smaller than t,he y and (I messages havr been subt,racted. They are about 50 ctx/min in t,hc 70 K position and 20 ct,s/min in t,hr > 70 S wgion for rxlwriments I, II and TIT and 17 ct,s/min for experiment IV. r Not, determinctl.

4. Discussion (a) Evidence for cleavage between messages Bacteria contain a range of sizes of luc mRNA in all stages of decay. 1Molecules of less than full-length size do not result from premature termination of transcription (Lim & Kennell, 1974). The most direct evidence for cleavage is the very rapid loss of the full-length species at a rate twice as fast as the mass is lost (Fig. 4; and Blundell & Kennell, 1974). In this paper we derive equations that describe the size distributions of populations decaying by different mechanisms. When t’he resultant) pat,terns are

k/c mRN.4

DECAS

383

compared t.o those observed in vivo, it can be concluded that the model with cleavages between the messages is the only acceptable mechanism for the following reasons. (1) Cleavages at many internal sites (15 here) generated mass patterns that were very different from those observed in the cell, even when all the known rate constants for bat mRNA metabolism were used in the equations. The relative accumulation of the two-thirds length z mRNA was especially inconsistent with this model, which demands fragmentation of this piece at many internal sites; increasing the number of potentia.1 targets up to the limit of every phosphodiester bond would further accentuate its untenability. (2) In cont.rast, with cleavages only at. t,he start, of each message, all known values for Zuc mRNA metabolism could be incorporat,ed and the observed in viva patterns reproduced. (3) The patt’erns are not a function only of target number: with t,he same number of targets (three) kiut at different locations, e.g. equally spaced, the observed patterns cannot be generated (not shown). (4) The decay of the z mRn’A itself is consistent with an exclusive net 5’ to 3’ degradation (no internal targets) of the z mRNA with time is ex(Kennel1 & Riezman. 1977). (5) Th e accumulation plicablc only from its release by cleavage between :: and .y coupled with its observed slow decay compared to decay of the distal ya fragment. (6) Two strains containing tclc deletions of approximately equal length, knit in different regions, show Zuc mRNA size distributions that are consistent only with targets between the messages. (7) Finally. message-sized fragment’s released by cleavages are inactive : thus the cleavages must, bc near the beginning of the messages. (k,) Eu~tiou.

of cZeuvu~c.s

111eukaryotic cells the primary transcription product is processed to the smaller message (for a review, see Perry, 1976). It is very unlikely that intercistronic cleavage of the polycistronic mRNA in bacteria has a comparable function. If cleavage was necessary for activity, it would be difficult to explain how any full-length molecules could ever be made ; the inability of rihosomes to load and translate during transcript.ion would generate polarity. Furthermore: it was shown here that the full-length luc mRNA can form initiation complexes at internal sites, while the distal fragments from cleavage were inactive. This is consistent’ with cleavage inactivating the distal message rather than being necessary for its activity. It is not clear why the one-third length was not, more active, since it contains an intact a loading site. Possibly, ribosomes must translate y to make the n site available for initiation a,nd, when not present in the in. vitro conditions, the a site becomes inaccessible. In t)his case the internal loading on the full-length molecule would he only at the y loading site, and the ohserved diribosome complexes would result from loading at both z a,nd y. Expression of RNA phage RNA provides a piecedent, for such a control. Translation of the preceding coat prot)ein message is necessary for initiation of the sgnthetase message (Lodish, 1975). However, the possibility of different, requirements for initiation complex formatiou wit’h (%versus z message should not be ignored. For example, Petersen et al. (1978) concluded that internal lac messages ma.v have a stringent, requirement for fmettRNA and IF factors, while the z message does not. In t,his case such requirements would actually strengthen the conclusion that cleavages are associated with inactivation, since the IF-dependence of the reaction indicates that the internal messages are active in the full-length molecule, while the messages released by cleavage are not (Ta,ble 1).

384

L.

W.

LIM

AN13

1). KENXELL

(c) Kihosow~ densities, cleavage and mBNA

decay

It follows from the preceding analyses that inactivation of a message results from either a cleavage within or near its initiation site or from a directional wave of decay originating from a cleavage at the start of a,n upstream message. The fast decay of the TA message (ta = 50 s) is very close to the rate of loss of full-length molecules (49 s). This suggests that decay of TA mRNA results from cumulative inacbivations of all three messages. Bn internal deletion t,hat removes the !/ loading site, a,nd thus a preceding cleavage target. does increase the half-life of the distal T,4 message (Blundell et aZ., 1972). What determines the cleavage rate’! Experiments with translation inhibitors suggested that an intercistronic cleavage site can be protected by ribosomes (Schneider et al., 1978). Ribosomes initiate onto the a message five times slower t,han ont,o the 2 message (Kennel1 $ Riezman. 1977). The frequency of attack would bc! given l)y the time between successive ribosomes minus the time that the initiation complex protects the site. A ribosome protects about 40 nucleotides of RNA. If the gap between messages is of such length or smaller, the terminating ribosome could also pruvidc protection; the smaller the gap, the greater protection (time). Finally. each target could have a unique “intrinsic” vulnerabi1it.v that is determined by its nucleotidc sequence. How could a distal rnessage deca.v slowc~ than a proximal one! The preceding argument suggests that the a message decay iate reflects the cumulat,ive decay of all the targebs. However. suppose the II message wax first) and tjhc z mrasagcx last. Since ribosomes load five times faster to the latt,t:r, and if ribosornes also protect against the progression of decay from a preceding message, then the decay would pause or stop temporarily. This could result in a slower decay of t,he hypothetical dist,al z messages. In the tvp operon the distal trp BA mRNA decays faster with internal deletions that move it closer t,o the promoter (Porchhammer et al.. 1972). whereas deletions of distal genes of the trp operon do not affect decay of the upstrea,m ones (Blundell rt al.: 1972). This shows that the decay of a distal message can be slower as a result, of the presence of preceding messages. This could result from pause sites at mRNA the the start, of fast-loading internal messages. Therefore, in a polycistronic relative translation initiation frequencies as well as intrinsic vulnrrabilities of the messages could determine the decay rate of each message.

aPPENDIX

Mathematical

Models for Decay of Linear Macromolecules

The following analysis derives the size distributions of a population of linear macromolecules with time of degradation for three general mechanisms of deca‘y. A population is defined by all molecules that have in common the same ends for synthesis and for termination. The three mechanisms are : (1) a net unidirectional wave of degradation from one end to the other; (2) random cleavages at any of a large number of internal targets; and (3) cleavages only at a limited number of specific internal targets. The fragments resulting from cleavages could be eliminated by any

Zrrc mKNA

DECAY

386

number of different mechanisms. Here we assume the distal fragments are degraded by a 5’ to 3’ net decay (see Results in the main text). The predecessor to this work also considered the preceding mechanisms for the case of bat mRNA in E. coli (Blundell & Kennell, 1974). The present analyses go further in several important respects. (1) The patterns of size are calculated as a function of time of decay rather than only at a single time. This increases enormously the constrain& on any model with respect to matching observed patterns. (2) The distributions for many int’ernal cleavage targets are calculated: in the earlier study this model was discount’ed for the case of an mRNA, since the resultant production of incomplet’r polgpept’ides would be biologically wasteful. (3) D ecag at internal targets is treated as a two-st)ep process. The first event, is an endonucleolytic cleavage. But instead of an immediate start of degradation on the newly liberated 5’ end, as considered 1)~ Rlundell CyrKennel1 (1974), the init)iation of mass loss is treated as a separate event governed by a different rate constant,. Both the cleavage and the start of degradation. however. are still treated as exponential events in the present derivation so that’ their character of randomness is preserved. Mathematically, this situation is simply that of an ordered reaction sequence. Since each event can be assigned a specific rate constant. t’his allows more flexibility in generating a greater variety of patterns for a given mechanism. There is no direct evidence for this assumption; however, the kinetics of decay of an mRNA at early times could be consistent with a two-hit, rather bhan a simple one-hit, process (Kennel1 & Talkad, 1976). (4) The present equations contaiii an important refinement that corrects for the loss of a target, by a direct cleava,gc or from readthrough degradation from a proximal target, i.e. the equations given 1)~ Blundell & Kennel1 (1974) did not correct for the loss from one decay process wheti calculating the rate of the other. (5) Finally, the size separations were performed and slso estimated in the models for the case of electrophoresis in polyacrylamide gels. which give hetter resolution than do sucrose gradients. ;1t the ?Lth internal target, the sequence of events can be represented a,s:

XII x-z X

\/

C,

Y

In this scheme X represents the intact target. It may be attacked by a wave of degradation that originated from a proximal target, at the rate given by the constant .cn, to produce the eliminated target Z. At the same time, the target is also susceptible to cleavage at the rate c,, and would yield the cleaved target Y. The resulting fragment would he attacked subsequently at the rate x to become another lost target Z. The relative ratio of x, and c, determines the fraction of X being attacked by each mechanism. At any time, the fraction of X remaining is given by:

where k, is the total decay rate at that target and t, is the bime when the 72th target, is made. h-, = x,, + c,. (2)

386

L.

W.

LTM

AN11

I).

KEKI’JELI.

The fraction that comprises Z represents targets that have been lost. #‘or internal targets, the term (t - t,) is necessary because internal targets are made after the 5’ end and thus have existed for a shorter period of time. X and Y change at rates given by:

and

Solution of eyuation (3) gives X = X, eekflt; which can be substituted (4). The latter can be rearranged in the form:

into equation

dY =: c,,?L-~,,~ dt ~ xYdt. This differential

equation

each t,erm by ezt, noting that

can be solved by multiplying d(Yest)

:==eStdY

i- xYestdt.

Integration of equation (5) gives Y. The fract,ion exist at any time with the cleaved target Y is Y/X,, I’,

zzz

&

(,--a-t

1 _

V, of the botal molecules so that:

t’-k,,+t,,)).

(5) that

(6)

Tn the calculation of theoretical patterns, the molecules are first divided into classes depending on which targets are cleaved and which are still intact. Decaying molecules are not included at this stage but will be treated later in the computation. As an example, full-length mRNA molecules are those with all the targets in the intact state. The fraction of molecules (G) remaining in this class at time t is given by the product of the fractions of each target that are active in the molecule.

where A, = e:-lc t is the fraction with intact 5’ end (see below) and F, represents the fraction of the nth target that has been cleaved at time t and is calculated from the relation :

Similarly, fragments generated, by the cleavages at the internal target can be calculated. For example, cleavage at the ith target would produce two fragments. For the proximal fragment

(9) and for the distal fragment

Inc mRNA

DECAY

387

The factor A,/(A, + F,) gives the fraction of target n that is still intact, and the factor F,/(a, + Fi) gives the fraction of target i that has been cleaved. This may seem confusing, because equation (1) introduces A, as the fraction of intact n targets. The difference lies in what is the definition of the total (1OOo/o) target population. In equation (1) it is the number of molecules synthesized; A, is the fraction of all of the nth target that has remained intact. In the present calculation, the total (100q{3) is the sum, for the particular target, of those that have been cleaved (P,) and those that. are still intact (a,). Only these would contribute to the various classes of fragments being considered at that time for t,hat family of molecules. The remainder represent molecules attacked by the wave of degradation emanat’ing from a proxima,l target a,nd contribute to the continuum of decaying molecules. These latter molecules are not being considered in this family, since they are represented in the families of molecules that include those generated by cleavages to the more proximal targets. -Any internal target may be attacked by the wave of degradation from a preceding target, and hence the factor A,/(A, + E’,) is used. The final step in calculating the theoretical size distribution pattern focuses on the decaying molecules. Any molecule decaying at time t must have belonged at some earlier time to one of the fragment classes just described. The length distribut’ion of decaying molecules is a direct reflection of how the number of molecules in each parCcular class changes with time. Equations for converting such a time distribuCon into a size distribution have been described and used by Blundell 8: Kennel1 (1974). The t’imc interval, t,, required for the fragment to decay from a complet,e molecule of lenpt’h L t)o t,he present size m. is given by t,=--

L D

m ’

(11)

where D is the rate at which degradation progresses along the molecule. This relation can then be incorporated into the equation for calculating G for each size class (see Blundell 8 Kennell, 1974). Again taking the full-length as an example, the fraction G in equation (7) can now be written as (:

=

,-kl+U-m,/D,

(12)

The exponential term replaces A, and represents the value of 8, at time t - t,. Thus equation (12) represents the fraction of molecules that were full-length at time t - t, but some of which have now, at time t, decayed to length m. Using this equation the fraction that are now between lengths ml and m2 can be calculated by finding the corresponding values of G and then taking the difference (Blundell & Kennell, 1974). For convenience in these computations, the value of m is limited to m > L - 6, where h is the length segment between the first and second target. The wave of degradation continues into the next target but this class of molecules is no\* indistinguishable from those originating from cleavage at the next target and is included in the equation describing that family of molecules (see below). The substitution of the exponent’ial term for A, in equation (12) ca,n also be done for the cleavage fragments that still had the original 5’ end at time t - t, (eqn (9)). However. the procedure for calculating decaying molecules missing the original 5 end is different. Those that are attacked by the wave of degradation, which have been ignored so far. and those derived from attack on the distal cleavage fragments (eqn

388

L.

W.

LJM

ANT)

2). KENNELL

(10)) are in this category. They can be treated together at this stage they are decaying, it is no longer possible to distinguish how each has Together, they make up the molecules remaining from subtracting int,act and of cleaved targets. Taking for example fragments decaying irrespective of the way they have been attacked :

From this point on, the relation introduced stitution into equations (1) and (6) :

in equation

beca,use. when been attacked. the fraction of from target i.

(11) ca,n be used. After

suh-

These two expression can in turn be used in equation (13) to calculate the fractions (: for decaying molecules. Equation (10) can be used for cleaved fragments that have not yet started to decay. The final class is molecules released by cleavages at both ends, e.g. .q message from cleavages at the Z/V and .y/a junct’ions : (16) The equations described so far are all that are required to calculate a theoretical pattern. Two additional steps have been introduced to make the calculated pattern more realistic. The first corrects for the time spread of the mRNA population by subdividing the time interval of induction and then summing t,o give the pattern for the complete time-set of mRNA (Blundell & Kennell: 1974). The second correction deals with the overlap of mRNA of a specific size from om gel fraction to adjacent ones. The spread of hhe 23 8 and I6 S rRNA is used to standardize this correction, ss had been done earlier tvith sucrose gradient, analyses (Blundell & Kennell, 1974). ln t’he computations, the amount of mRlZ’A in each fraction is spread over five fractions after this correction. These equations and corrections were used t,o generate a computer program for calculating theoretical size distribution patterns for a time-set of decaying mRPu’A molecules as a function of time. Since an essemial feature of the model incorporates cleavages at internal targets with an uninterrupted continuation of decay from proximal targets into distal ones, the program could be used in all situations where the distal segments of the mRNA decay faster than t’he proximal ones. In ca.ses in which a distal message decays more slowly than does A more proximal one, e.g. gal mRNA and try, mRNA. the program would require that) the wave of degradat’ion would have to stop for some fixed or variable time in some or all of the molecules before reaching the slower decaying message t,arget, e.g. at an intercistronic boundary. This modification would have to be introduced into the equations. All the pertinent values for the length of the complete mRNA, the number and position of the targets, the half-life of each target as well as t’he rate of cleavage and t’ime constant for the start of the mass loss atI each target can be entered separately

Zrtc mRNA

DECAY

389

and varied independently to generate considerable variations in a resultant theoretical pattern. In the case of decaying Zuc mRNA, the full-length molecule was taken to be 4830 nucleot’ides, with 3150 of these in the /3-galactosidase message and 840 each in the permease and transacetylase messages. These values were slightly larger than those required to code for the enzymes, but allowed for the possible presence of intercistronic sequences. The rate of transcription was 2100 nucleotides per minute in all eases considered, and the rate at, which degradation progressed along the mRNA was .I900 nucleotides per minute unless otherwise indicated. The /Lgalactosidase message is lost with t, = 90 seconds, the TA message with t, = 50 seconds and an intermedint’e value oft, = 70 seconds was assumed for the permea,se message. Paul Alfirtci participated in these experiments during two summers. This work is part of tlie thesis hy one of the authors (L. u’. L.) t,o fulfil requirements for the Ph.D. degree at LVashingt,oii University. The investigation was supported by research grants GB-43902 from tlir: Nationa. Science Foundation and GM-19375 from the National Inst,itutes of Health and hy Research Career Development i2ward (l-KG-4-GM06688) (to D. K.) from tlic National Institutes of Health. RmEFERENCES Achord, D. & Kennell, D. (1974). J. dfo2. BioZ. 90, 581~ 599. Altrnan, S. (1975). Cell, 4, 21-29. Bastos, R. N. &, Aviv, H. (1977). Cell, 11, 64lL650. Blundell, M. & Kennell, D. (1974). J. Mol. Biol. 83, 143 161. Blundell, M., Craig, E. & Kennell, D. (1972) Xnture New Biol. 238, 46-49. Dunn. .I. .I. & Studier, F. W. (1973). 1’roc. Nat. Acad. Sci., I/. S.4. 70, 3296 3300. Dunn, .J. ,J. & Studier, F. W. (1975). .r. ~Wol. Biol. 99, 487~~499. Firtel, It. A. & Lodish, H. F. (1973). .J. ,Wol. Biol. 79, 295-314. For&hammer, J.. Jackson, E. N. & Yanofsky, C. (1972). J. Mol. Biol. 71, 687-69!J. (:ilbort, IV. & Maxam, A. (1973). Proc. Nat. Acad. Xci., U.S.A. 70, 3581-3584. Hershey, ,J. w’. B., Remold-O’Donnell, E., Kalokofsky, D., Dewey, K. F. & Thach, R. E. (1971). In Methods in Enzymology (Grossman, I,. & Moldave, K., eds), vol. 20, part C. pp. 235 247, Academic Press, New York. 12, 2330-2338. Holmes, D. S. & Bonner, J-. (1973). Biochemistry, .Johnson, 8. (‘., Watson, N. bz Apirion, D. (1976). i2101. G’en,. Genet. 147, 29- 37. Kpnnell. D. (1970). J. ViroZ. 6, 208 -217. Kennell, D. dz Riezman, H. (1977). J. Mol. Biol. 114, l--21. Krnircll, D. K: Talkad, V. (1976). J. Mol. Biol. 104, 285 298. Kepes, A. (1963). Riochim. Riophys. Acta, 76, 293-309. Kepex, A. (l!J67). Hiochim. Riophys. Acta, 138, 107-123. Ledrr. I’. & Rursztyn, H. (1966). Proc. Nat. Acad. Sci., U.S.A. 56, 1579.-1585. Lim. L. \1’. & Kennell, D. (1974). Mol. (ien.. Genet. 133, 367 371. Lodish. H. F. (1975). In RNA Phages (Zindrr, N. D., cd.), pp. 301 ~318, Cold Spring Harbor Lahorat,ory, New York. AMaizrls, N. M. (1973). Proc. Nat. Acad. Sci., (;.#.A. 70, 3585-3589. Morikawn. N. & Imamoto, F. (1969). &‘ature (London), 223, 37.-40. Morse, D. E.. Mosteller, R. D., Baker, R. F. & Yanofsky, C. (1969). ,\;ature (I,onrlon). 223, 40-33. Nikolarv. N.. SchlessinSer, D. bt Wellaiier. D. K. (1974). J. &ZoZ. Hiol. 86, 741 -747. Past~nshok. (‘. & Kennell, D. (1974). J. Bucteriol. 117, 631 640. Pdtz, R. (1973). Riochim. Biophys. Acta, 308. 1488153. Perry. R. P. (1976). Annu. Rev. Bioch,em. 45, 605-629. I’etersori, H . C., .Joseph, E., Ullmann, a. & Darrchin, A. (1978). ,I. Bacterial. 135, 453-459. Revel. M., Herzherg, H. & Greenshpan, H. (1969). Cold Spring Harbor Symp. &uan.t. Riol. 34, 261.-275.

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