A Model for Regulation of ColE1-Like Plasmid Replication by Uncharged TRNAs In Amino Acid-Starved Escherichia Coli Cells

A Model for Regulation of ColE1-Like Plasmid Replication by Uncharged TRNAs In Amino Acid-Starved Escherichia Coli Cells
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  0147-619X/02 $35.00 ©2002 Elsevier Science (USA)All rights reserved. ThefirstobservationaboutthecopynumberincreaseofColE1-likeplasmidpBR322duringtherelaxedresponsewaspublishedbyHecker etal. (1983).About10yearslater,Herman et al. (1994b)reportedthatstarvationfordiffer-entaminoacidshasdifferenteffectsonrepli-cationofColE1-likerepliconsduringthere-laxedresponse.RecentstudiesconfirmedthoseresultsforotherColE1-likeplasmids(WróbelandWe  grzyn,1998).Although the replication mechanism of ColE1-like plasmids was extensively investi-gated in a quantitative manner (Bremer and Lin-Chao,1986; Ataai and Shuler,1986,1987;Keasling and Palsson,1989a,b; Brendel andPerelson,1993; Paulsson and Ehrenberg,1998),the kinetic models presented thus far do not ex-plain the difference in copy number of ColE1-like plasmids in the rel A bacteria starved for dif-ferent amino acids.ArolefortRNAintheregulationofreplica-tionofColE1-likeplasmidsinaminoacid-starvedcellswasfirstsuggestedbyYavachevandIvanov(1988).Therearethreeloopsinthe Plasmid 47, 69–78 (2002)doi:10.1006/plas.2001.1562,available online at on AModel for Regulation of ColE1-like Plasmid Replication by UnchargedtRNAs in Amino Acid-Starved Escherichia coli  Cells Zhijun Wang,* Guowei Le,* ,1 Yonghui Shi,* Grzegorz We  grzyn,† and Borys Wrobel‡ *AnimalScienceResearchInstitute,SouthernYangtzeUniversity,214036Wuxi,People’sRepublicofChina; †  DepartmentofMolecularBiology,UniversityofGdan´sk,Kladki24,80-822Gdan´sk,Poland;and  ‡  InstituteofOceanology,PolishAcademyofSciences,Sw.Wojciecha5,81-847Gdynia,Poland  Received August 6,2001; revised November 29,2001It has been previously observed that various ColE1-like plasmids replicate differentially in  Es-cherichia coli cells during the relaxed response to amino acid starvation. Here we develop a kineticmodel to explain these observations based on the possibility of interaction of the 3  CCA-OH se-quence with the UGG triplets in loops of RNA I and RNA II encoded by ColE1-like plasmids. Ac-cording to our model,when the interaction of uncharged CCA with RNA I is possible,the replicationof the ColE1-like plasmid is affected by differences in the concentration of various tRNAs in thestarved cell,but it is not affected by the tRNA concentration if the hypothetical pairing occurs betweenthe CCA-OH and RNA II. Using the previously determined parameters for the pBR322 plasmid,theconcentration of uncharged tRNAs in the amino acid starved relaxed strains and the assumed effi-ciency of binding of tRNA and RNA I,we show that our model explains the differences in pBR322copy number in the relaxed strain starved for several amino acids. ©2002 Elsevier Science (USA) Key Words: ColE1-like plasmids; tRNA in replication; pBR322; amino acid starvation; relaxed re-sponse. ColE1-like plasmids are probably the mostwidely used vectors in biotechnology. Althoughtheir replication in amino acid-starved bacteriahas been investigated in considerable detail (seeWe  grzyn,1999,for a recent review),it is stillpoorly understood. The alarmon of amino acidstarvation,ppGpp (guanosine-5  -diphosphate-3  -diphosphate),plays an inhibitory role in reg-ulation of ColE1-like plasmid replication (Her-man et al. ,1994a). The interaction of ppGppwith the RNA polymerase leads to the inhibitionof synthesis of stable RNA (rRNA and tRNA)(Cashel et al. ,1996). In the relaxed strain,dys-function of the rel A gene causes deficiency inthe function of ppGpp synthetase I duringamino acid starvation. Since the ppGpp syn-thetase II activity of the SpoT protein is absentduring amino acid starvation,but this protein isactive in ppGpp degradation,the ppGpp levelsdecrease in the relaxed amino acid-starvedstrains (Cashel et al. ,1996). 69 1 To whom correspondence should be addressed. Fax:86510 5865545.  70 WANG ET AL. structureofRNAII,theRNAusedasaprimerinthereplicationoftheColE1plasmid,whichinteractwithloopsinRNAI,anantisensetran-scripttoRNAIIencodedbytheplasmid.YavachevandIvanov(1988)analyzedthese-quencesimilarityofdifferenttRNAsandbothRNAIandRNAIIoftheColE1plasmid.TheirresultsshowedthattRNAscanbeclassifiedintothreegroups:(a)tRNAssimilarinse-quencetoRNAI,(b)tRNAssimilartoRNAII,and(c)tRNAssimilartoboth.Ahighdegreeof sequencesimilarityoftRNAsandRNAIorRNAIIcouldallowforinterferenceoftRNAintheRNAI–RNAIIinteractioninthecondi-tionsofaccumulationoftRNAsinthecellsduringtherelaxedresponse.YavachevandIvanov(1988)proposedthatsuchinterferencemightexplainthevariationsinplasmidcopynumberinbacteriastarvedforvariousaminoacids.Itwassubsequentlyshownexperimen-tally(WróbelandWe  grzyn,1998)thattheeffi-ciencyofreplicationofColE1-likeplasmidsduringaminoacidstarvationcanbecorrelatedwiththehypotheticalpossibilitiesofinterac-tionbetweentheloopsofRNAIorRNAIIof theseplasmidsandtheanticodonloopsof tRNAmoleculescorrespondingtothekindof aminoacidthatisabsent.Althoughthehypothesesproposedthusfar(YavachevandYvanov,1988;WróbelandWe  grzyn,1998)stipulatethattheinteractionof tRNAandRNAsencodedbytheColE1-likeplasmidswillbemoreeffectiveifthetRNAisuncharged,thebasisofsuchassumptionswasnotobvious.Herewepresentamodelbasedonanotherpossibilityofinteraction:thatofthe3  terminalCCA-OHgroupoftRNAswithRNAIandRNAIIloops.Theassumptionthatsuchin-teractionsareprimarilyresponsibleforinter-ferenceoftRNAsintheformationoftheRNAI–RNAIIcomplexallowsustoanalyzethereplicationofaColE1-likeplasmid,pBR322,intherelaxedstrain,inaquantitativemannerandtoanalyzetheeffectsofgrowthrateonColE1-likeplasmidreplicationduringstarva-tionfordifferentaminoacids.Suchanassump-tionmightalsoexplainwhytheinteractionshouldbemoreeffectiveiftRNAsareun-charged. MATERIALS AND METHODS  Experimental Procedures Wehaveusedthe  Escherichiacoli K-12strainCP79( rel A leuargthrhisthi (  w )(Wróbel et al. ,1998).Bacteriaweregrowninaminimalmediumdescribedpreviously(We  grzyn etal. ,1991)withtheadditionoffouraminoacids(L-leucine,L-threonine,L-arginine,andL-histi-dine)at50  g/mleach.Starvationwasachievedbycentrifugationofthebacterialculture,wash-ingwith0.9%NaCl(twice),andresuspensionwiththemediumlackingagivenaminoacidandcontainingthreeothersorcontainingallfourwiththeadditionof1mg/mlofL-valine(toin-ducestarvationforisoleucine).PlasmidDNAwasisolatedbyalkalinelysisfromsamplesof bacterialculturewithdrawnatindicatedtimesandlinearizedbyrestrictionenzymes.Follow-ingagarosegelelectrophoresis,theamountof plasmidDNAwasestimatedbydensitometryasdescribedpreviously(WróbelandWe  grzyn,1998).Tocalculatetheamplificationfactor,theamountofplasmidDNAisolatedfromstarvedbacteriawascomparedtotheamountinsamplestakenfrombacteriagrownincompletemedium,takingintoaccountthenumberofcellsinbothsamplesdeterminedbyplatecounting.The growth rate of cells was determinedusing the CP79 strain carrying the pBR322 plas-mid by measuring colony-forming units as afunction of time (viable plate counting) at 10-min intervals near the indicated time points.Similar growth rates were observed for cellsstarved for five different amino acids and the re-sults were averaged.  A Kinetic Model for pBR322 Replicationduring the Relaxed Response We describe the dynamic concentration of theColE1-like plasmid DNA as a function of con-centration of plasmid-encoded RNA I and RNAII. The dynamic concentration of Rom proteinwas not considered in this study. The Rom pro-tein is present at sufficiently high concentrationsto justify ignoring the chance of its depletion bythe interaction with free RNA I–RNA II com-plexes (Brenner and Tomizawa,1991; Atlung et al. ,1999).  MODEL FOR REGULATION OF ColE1-LIKE PLASMID REPLICATION 71The dynamic concentration balance of theColE1-like plasmid can be expressed as(1)where [ P ] is the concentration of plasmid, m isthe growth rate,[  RNAII  ] is the concentration of RNA II, K   is the rate constant of RNA II hy-bridization with DNA template to reach the ori-gin (formation of preprimer),and  is the frac-tion of RNA II molecules which are used asprimers in DNA replication. After RNA II syn-thesis reaches the replication srcin,the actionsof RNase H and DNA polymerase are rapid(Brendel and Perelson,1993). We have there-fore assumed that RNase H action and DNApolymerization are instantaneous,so the rateconstants of RNase H and DNA polymerase ac-tion are not included in our model. The proba-bility of the release of RNA II resulting in theinitiation of plasmid replication was determinedto be 0.5 (Ataai and Shuler,1986).Equation(1)describesthechangeofconcen-trationofpBR322DNA.Theinitiationofplas-midDNAreplicationutilizingRNAIIasaprimeroccursattherate a  K   .Theintroduc-tionofgrowthrateinthetermsin m [ P ]inEq.(1),andin m [  RNAI  ]and m [  RNAII  ]intheequa-tionsbelow,accountsforthedecreaseintheconcentrationofcellularcomponentsduetothegrowthofcell.The concentration of RNA II can be expressedas(2)Equation (2) describes the change in RNA IIconcentration,in which K   is the rate of formationof preprimer, â  II  is the degradation rate constant of RNA II, K   II  is the rate of RNA II synthesis,and K  b is the binding rate of RNA I and RNA II.After the RNA II transcripts escape the inter-action with RNA I,hybridize with DNA tem-plate at the origin of replication,and areprocessed by RNase H to form primers,theprimers are excised and released. Thus excisedand released RNA II was assumed to play nofurther role in replication control,so Eq. (2) in-cludes the term K   [  RNAII  ]. d RNAII dt K P K RNAI RNAII K RNAII   II b II  [ ][ ] [ ][ ]( )[ ]. =−−′+ + ε  m d Pdt K RNAII P [ ][ ] [ ], = ⋅′⋅ − ⋅ α  m Similarly,the dynamic mass balance of RNAI can be expressed as(3)where K   I  is the rate constant for initial RNA Isynthesis,[ tRNA un ] is the concentration of un-charged tRNA,and K  t  is the binding rate constantof uncharged tRNA and RNA I. We have as-sumed that the binding of uncharged tRNA withRNA I will completely prevent such RNA Imolecules from interacting with RNA II,rather than affect K  b and thus the term0.5 K  t  [ tRNA un ][  RNAI  ] in Eq. (3). Our model stip-ulates that the binding of tRNA to RNA II doesnot affect its ability to form a primer; hence thereis no such term in Eq. (2). Since in our model twouncharged tRNA molecules interact with oneRNA I molecule,we multiply K  t  [ tRNA un ][  RNAI  ]by 0.5.  Estimation of the RNA I and RNA II BindingConstant  The rate constant of RNA I and RNA II bind-ing has been measured in vitro for the ColE1plasmid (Tomizawa,1990). We are not aware of any in vitro measurements for pBR322 or any invivo measurements of such constants. Kim andShuler (1990) compared the sequences of wild-type ColE1 and pBR322 (which carries the ori-gin derived from plasmid pMB1). There is onebase difference between pBR322 and ColE1,present in RNA I loop III. Although such achange might affect the binding,we havenonetheless assumed that such is not the caseand that the binding rate constant of RNA I andRNA II of pBR322 is similar to that of ColE1 invitro ,determined experimentally as 1.5  10 8 M  1 min  1 (Tomizawa,1990). For lack of otherdata we had to assume that the possible changesin the concentration of Rom protein are not sig-nificant and that the binding rate of RNA I andRNA II ( K  b ) remains constant during amino acidstarvation.  Estimation of the Concentration of Uncharged tRNA In order to determine the concentration of un-charged tRNA in the cell during the relaxed re- d RNAI dt K P K RNAI RNAII  RNAI K tRNA RNAI   I b I t un [ ][ ] [ ][( )[ ]. [ ][ ]. =−− +− ε  m 0 5  72 WANG ET AL. sponse,we need to first determine the concen-tration of total tRNA in the cell. Total nu-cleotides of tRNA in the cell can be determinedby subtracting nucleotides of ribosomal RNAfrom nucleotides of stable RNA,(4)where [ tRNA ] n ,[ sRNA ] n ,and [ rRNA ] n are theconcentrations of nucleotides of tRNA,sRNA,and rRNA,respectively. According to most in-vestigators (Rosset et al. ,1966; Dennis,1972),the ratio of nucleotides in rRNA to nucleotidesin stable RNA (sRNA) is nearly constant:(5)The RNA/DNA ratio is proportional to thegrowth rate (Dennis and Bremer,1974),(6)where[ gDNA ] n istheconcentrationofde-oxynucleotides(fromgenomicDNA).Pleasenotethattosimplifythediscussionwewillnottrytocarefullyputunitsintheequationsbeingderived.Assuming 84 for the average tRNA length,and the rough average of 1.33 chromosomes of 4.6 Mb in the amino acid-starved cell (Dennisand Bremer,1974),the molar concentration of tRNA in the cell can be estimated aswhere  N  is the Avogadro constant (6.023  10 23 )and V is the cell volume,assumed to be equal to7  10  16 L (Pramanik and Keasling,1997).Whenthe rel Astrainisstarvedforagivenaminoacid,thestableRNA,includingthetRNAforthisaminoacid,continuestobesynthesized.ItissafetoassumethatmosttRNAmoleculesforthisaminoacidremainuncharged.Basedonexperimentalresults,weassumethatthepropor-tionofdifferenttRNAspeciestototaltRNAre-mainsconstantduringdifferentgrowthcondi-tions(Ikemura,1981a,b).Aspreviouslydescribed(WróbelandWe  grzyn1998),wehy-pothesizethattherelativeabundanceofdifferenttRNAspeciesinthecellmeetstherequirements [ ]. . ., tRNA N V  =× × × × ×× × 1 33 2 4 6 10 252 0 1584 6 m  [ ][ ], sRNAgDNA nn = 252 m [ ][ ]. . rRNAsRNA nn = 0 85[ ] [ ] [ ] , tRNA sRNA rRNA n n n = − ofproteinsynthesismachineryandthuscanbeassumedtocorrespondtotherelativeabundanceofdifferentaminoacidsin  E.coli proteins.Sincetherelativeabundanceofvariousaminoacidsisnotgenerallyaffectedbythegrowthrate(Pra-manikandKeasling,1997),theconcentrationof unchargedtRNAduringtherelaxedresponsecanbeexpressed(afterenteringthevalueofpara-metersinEq.(7))as(8)where b istheproportionoftheaminoacidde-privedfromthemediumtototalaminoacidsinthecell.  Estimation of the Binding Constant of Uncharged tRNA and RNA I  The binding of uncharged tRNA and RNA Ican be expressed as:(9)In order to determine the binding constant of un-charged tRNA with RNA I,we assumed that theinteraction of two tRNA molecules with oneRNA I molecule is similar to the interaction of RNA I with RNA II when pairing happens onlyin loop I and loop II. Tomizawa (1990) deter-mined the binding constant of ColE1 RNA IIand a RSF1030 RNA I,which lacks similaritywith ColE1 RNA I in loop III,to be 1.8  10 5 M  1 min  1 . We have used this value as an esti-mate of the binding rate constant of two tRNAmolecules and one RNA I molecule. Other Parameters Atlung etal. (1999)haveanalyzedthepro-portionofRNAItoRNAIIduringdifferentgrowthconditionsandshownthatitisconstantwithgenerationtimesincreasingupto100min.Here,weassumednoeffectsofgrowthrateandconditionsofaminoacidstarvationonRNAIandRNAIIsynthesis.Accordingtotheprevi-ouslypublisheddata(AtaaiandShuler,1986;BrennerandTomizawa,1991)RNAIandRNAIIbothhavesimilarhalf-lives.Forourmodel,wehaveassumedthedegradationratesofRNAIandRNAIItobeconstantandequalatdiffer-entgrowthrates( â  I   â  II   â ).Thevaluesof otherparametersusedarepresentedinTable1. 2 2 [ ] [ ][( ) – ]. tRNA RNAI tRNA RNAI  unK un t  +  →   [ ] . , tRNA un = × 0 0131 mb (7)  MODEL FOR REGULATION OF ColE1-LIKE PLASMID REPLICATION 73  Determination of Plasmid Copy Number duringthe Relaxed Response Using the Model Plasmid DNA concentration in the aminoacid-starved bacteria during stable status can bedetermined by setting Eqs. (1)–(3) to zero:(10)(11)(12)Plasmid concentration during the relaxed re-sponse is therefore(13)Using the parameters from Table 1,we find that(14)(15)Since the growth rate in the conditions underconsideration is below 0.012 min  1 (Fig. 2),(16) ε ε ε α ε  K K K tRNA K K K K K tRNA K   II II un t  II un t  ′+ ⋅ ⋅ ⋅′>>+′−′+ 0 5 2 . [ ]( [ ] ) m K K K K K   I II  ′−′> +′ ε  . ε ε ε α ε  K K K tRNA K K K K K tRNA K   II II un t  II un t  ′+ ⋅ ⋅ ⋅′>+′−′+′ 0 5 2 . [ ][ ][ ]( . [ ][ ] )( ). PK K K K tRNAK K K K tRNA K K K K K K K   II II unt II un t bI II  =′ ′+ ⋅ ⋅ ⋅′− −′+′−′−′+ +′+ α ε ε ε α ε ε  0 5 22 m K m mmm m m m d RNAII dt  [ ]. = 0 d RNAI dt  [ ] = 0 d Pdt  [ ] = 0 (17)Thus the concentration of pBR322 plasmid dur-ing the relaxed response can be estimated as(18)or(19)The plasmid copy number can be derived fromEq. 19 as(20)We can use Eq. (20) to calculate the relativeincrease in copy number (the amplification fac-tor):the ratio of the copy number at certain timepoints after the onset of starvation to the copynumber of the plasmid in cells grown in com-plete medium. We assume that in the completemedium the concentration of uncharged aminoacids is negligible,and thus this factor can becalculated from Eq. (19) as(21)and using Eq. (8),(22)where m 1 is the growth rate of the strain duringamino acid starvation,and m 0 is the growth ratein the complete medium. RESULTS Wróbel and We  grzyn(1998) analyzed the an-ticodon arm of uncharged tRNA and found theplasmid content to be positively correlated withhomology between the nucleotide sequence of RNA I or RNA II and the anticodon loops of tRNA molecules corresponding to the kind of amino acid starved.Here,we analyze another possibility of a verystrong interaction of the 3  CCA sequence of uncharged tRNA with loop I and loop II of RNAI of ColE1-like plasmid pBR322. An interaction  Af K  t  =+ ⋅ ⋅ ⋅ ( . . ), εε 0 5 0 0131 1 01  bm mm  Af tRNA K  un t  =+ ⋅ ⋅ ( . [ ] ), εε 0 5 01 mm nK K tRNA K K K K V N   II un t bI II  =′+ ⋅ ⋅−⋅ ⋅α ε ( . [ ] )( ).0 5 m [ ]( . [ ] )( ). PK K tRNA K K K K   II un t bI II  =′+ ⋅ ⋅−α ε 0 5 m [ ]( .[ ] )( ) PK K K K tRNA K K K K K K K   II II un t b I II  =′ ′+ ⋅⋅ ⋅′′−′α ε 0 5 m K K K K K   I II  ′−′>> +′+ ( ) . ε  m m TABLE 1Parameters Used in Calculations of the Copy Number andthe Amplification Factors of the ColE1-like Plasmid duringthe Relaxed ResponseParameterValueReference  0.5 min  1 Ataai and Shuler (1986)  0.35 min  1 Ataai and Shuler (1986) K   5 min  1 Brendel and Perelson(1993) K   I  2 min  1 Lin-Chao and Bremer(1987) K   II  0.33 min  1 Lin-Chao and Bremer(1987) K  b 1.5  10 8 M  1 min  1 Tomizawa (1990) K  t  1.8  10 5 M  1 min  1 This work (estimated)
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