J. Mol. Biol. (1992) 226, 59-68

How Lac Repressor Finds lac Operator in Vitro Reimund Fickert and Benno Miiller-Hill Institut ftir Genetik der Universittit zu K6ln Weyertal 121, D-5000 K&n 41, FRG (Received

16 September 1991; accepted 12 February


Filter-binding and gel mobility shift assays were used t’o analyse the kinetics of the interaction of Lac repressor with lac operator. A comparison of the two techniques reveals that filter-binding assays with tetrameric Lac repressor have often been misinterpreted. It has been assumed that all complexes of Lac repressor and lac operator DNA bind with equal affnity to nitrocellulose filters. This assumption is wrong. Sandwich or loop complexes where two lac operators bind to one tetrameric Lac repressor are not or are only badly retained on nitrocellulose filters under normal conditions. Taking this into account, dimeric and tetrameric Lac repressor do not show any DNA-length dependence of their association and dissociation rate constants when they bind to DNA fragments smaller than 2455 basepairs carrying a single symmetric ideal lac operator. A ninefold increased association rate to ideal Zac operator on 1 DNA is observed for tetrameric but not dimeric Lac repressor. Tt is presumably due to intersegment transfer involving lac operator-like sequences.

Keywords: Lac repressor;

lac operator;


Repressors and activators of gene transcription play an important role in all biological systems. Their interaction with DNA target sites has therefore been a major field of interest. Structures of complexes of DNA binding proteins with their specific DNA targets have been analysed in great detail (Steitz, 1990; Sauer et al., 1990), but little is known about how these proteins find their chromosomal target sequences in vivo. In 1968 Riggs et al. introduced a method that seemed suitable to characterize the kinetic parameters of protein-DNA interactions in vitro. The socalled filter-binding t,echnique makes use of the fact that proteins in solut’ion will be retained on nitrocellulose filters upon filtration, whereas DNA molecules will pass through. In a situation where complexes of proteins and radiolabelled DNA can form in solution, the radioactivity that is retained on the filter presumably corresponds to all proteinDNA complexes that are bound to the filter through the protein. Riggs rt al. (1970a,b) analysed extensively the kinetic properties of the interaction between Lac repressor of ILwherichia coli and its operator DNA, this filter-binding assay. Their results using indicated that Lac repressor finds its operator on Adlac DNA a,t least 100.fold faster than the upper $03.00/O



limit estimated for an ordinary diffusion-controlled process (von Smoluchowski, 1918) presumably would allow. Tn 1981, von Hippel and colleagues presented a comprehensive study of the kinetics of the interaction between Lac repressor and lac operator DNA again using the filter-binding assay (Berg et al., 1981; Winter & von Hippel. 1981; Winter et aZ., 1981). Increasing the length of unspecific sequences around the target operator and decreasing the salt concentration both seemed to increase the apparent association rate. From this they proposed two possible mechanisms for the observed facilitated target location: sliding, where initial non-specific binding is followed by onedimensional diffusion of the protein along the DNA, and direct intersegment transfer. This mechanism involves formation of a transient loop complex. where tetrameric Lac repressor binds simultaneously non-specifically to two DNA segments (for a review, see Berg & von Hippel. 1985; von Hippel & Rerg, 1989). Both mechanisms were t,hought to facilitate the association react’ion by reducing the free diffusional search process to one along and within a DNA molecule dimension? (Adam & Delbriick. 1968). They seemed also to explain the increased halflives of complexes with long Za.c operator DNA fragment’s (Whitson & Matthews, 1986). However, the operator DNAs used in most of these experiments were derived from the

1. Introduction




0 1992 Academic Press Limited


R. P’icke,rt

wnd B. id!fiiller-Hill

wild-type 2ac operon and contained often two OI three lac operator-like sequences (Reznikoff et al., 1974: Gilbert et al., 1976). Therefore the measured DNA-length dependence of the association as well as dissociation rates, which are the experimental underpinning of the proposed sliding mechanism. are open to doubt. DNA-length dependencies of kinetic const’ants were also reported for other systems. Llsing the filter-binding assay, Kim et al. (1987) found that association of 1 cro repressor to its operator site is faster for long operator fragments than for short fragments. Here unspecific binding could not be clearly distinguished from specific binding, sinc*e 2 cro repressor has a high affinity to non-specific DT\;A (Hubbard et nl., 1990). The facilitated target locations deduced for EcoRI (Terry et al., 1985: Ehbrecht et al.. 1985) and RNA polymerase (Singer & Ru, 1987; Ricchetti et al., 1988) are explained 1)~ linear diffusion along the DNA. but ot’her possible search mechanisms seem not t’o be totally excluded. 1l?e tested the interpretations of t,he filter-binding data of the Lac repressor-operator interaction by a second technique, the gel mobility shift assay (Fried & Crothers. 1981; Garner & Revzin, 1981). In these experiments we have ensured that all operator DNAs were of a known sequence and cont,ained only one single symmet)ric ideal lac operator (Oid: Sadler et al.. 1983: Simons et al., 1984) and none of the two auxiliary operators of the lnc syst,ern (Oehler it ~1.. 1990). To investigate the role of the postulatjetl intersegment t)ransfer mechanism, we used t’hr mut,ant La,cT gene Pdi. This mutant has lost the first base-pair

of codon 330 and c&es

for a dimthrica I,aca

repressor that is active in operator binding, but unable to form tetramers (Lehming it ~1.. 1988; Alberti et al.. 1991). Dimeric Lac repressor cannot form looped complexes and should therefore have an impaired ability to find its operator, if the intersegment transfer mechanism is valid. We present evidence that t)he widely used filterbinding assay produces artifacts under certain conditions. Loop and sandwich complexes. where t)he two DNA binding s&es of a tetrameric 1,~ repressor are both occupied, are not retained on nitrocellulose filters under conventional conditions (Besse et al., 1986). When we take this into account’ we do not, observe any DNA length dependence of kinetic rate constant,s that would prove directI> sliding in citro. Furthermore. our results indicat,r that) Lac repressor finds its operator on high molecular weight (A) DNA via intersegment t,ransfer. We find no evidence for sliding although WP cannot’ exclude it.

2. Materials (a) Bacterial


and Methods plasmids

and phages

Strain KldAHIA trp has the genotype: SmRZacZ am Abio-zrvrB A&PEA2 (Liz’ am7-S am53 cl 857 AHI) and is a kind gift from Dr W. Fiers. Cniversit,v of Ghent (Remaut et a,l.. 1981). St,rain BMH 81171i”ll has the

genotype: (kc PTO)~ nalA thi supE F’lac IqmZ y pro’ The episomr t,hat carries a deletion reaching from tbts middle of the I gene into the middle of the % gene has been described by (iho &ZMiller (1974). All bavt,eria wvre grown under standard c.onditions according to .\lillrl (1972). Pla,smid p310, is a derivative, of pHE4 (~Xstnatin ct c/l.. 1987) with symmetric ideal Lnc operator (( Vd) inserted ilr the LVlr,sl site of pEE4. The nucleotide srquenc~ of O’d i:. AATT(:T(:A(,~(‘*(:(‘T(~~~(“~~.~TT. which is an invrrtecl repeat of 10 base-pairs of the left half of ttrv wiltl-type operator (Sadler fd *I.. 1983: Simons ~1rrl.. 19X4) The expression vrctor pl’L(~d8. a gift t’rorrr I)r \\’ IJirrs. IInivrrsity of (ihrnt, makes use of the Irftwartl promotor (I’,) of phage i It van be repressed by thr th~~rtrtolabilv reprrssor produc*t of’ thr ixlX57 genr RIICI activat,rd 1, heat-induction (Rrmaut rt al.. 1981). I’lasmitl p\1’H1000 was derived from p~~B100 by repairing t be framrshift mutation in codon 330 that leads to an active dimeric, I,ac, repressor (Lrhming pt 01.. 1988). The ,%Rl-Hglll f’rapmerits in p~~‘B1000 or pWBIO0 eodr for trtrameric. 01’ dimerir Lac repressor. respectively. These fragments wrre cloned into the /CcoRT KwuHT linrarizrtl rsl)ression vector pPLc2X. to c*reat,r t,hr plasmidn pTet ant] pI)ittl. (~ligonuc,lrotides were s?nthesizrd on an Apl)lied fsiosys terns 394 Dr\‘A Syntheslzrr. ,111I)KA tnanipulations w(‘rt’

performckdaccording to Maniatis et nl. (1989). Phagr i,EwtOOO is described b,v Orhlrr (31rsl. ( ~!M)o). Phage i.EstiW \vas c~onstruc*tetl II?; Strfan Orhlt.r, I,>, replacGq the wild-type lac operator 0, in i,Ewt 100 I)y t IIt> hyinnicltric, icltaal ltrc operatot, Oid usinp thta ~~ro~~~lurc~h described by Orhler rt al. (I 9!)0).

Operator fraytnt~nts \verv clrrivotl lroin lL~10, 1)X.\. which was purified OII a (‘~(‘1 gradirnt. 1Cil0, was rarlt \\,ith tc:coRI!Hi~~~dIII. ~cwRI/S~~I or BcoKI. rt+pevti\ely. to create operator USA fragments of 84 bpt. 406 bp and 245.5 bp length. Thv symmet,ric* 23 l)f) oligonuc.lttotidt. synthesized (5’.t:G.UTT(:Tconta,ining Oid was (:~~(:(“*G(‘T(‘~\(‘ABT’r(‘-3’). These fragmrnt,s wvre end lat~elltd with [s-32PJdATI’ or [a-“*P]d(‘TP by till-in reactions using Klenon fragment of’ IIS. polymrrasel and purified on polyacrylamide gels or’ W~JIY’precipitated with ethanol in the presence of 4 M-ammonium acetate (Maniatis rt ul.. 1989) depending on the size of the operator DXA. E.Ewt,OOOand IEstiOO were purified on (M’l gradients as described by Maniatis PI al. (1989) and end-labelled wit.h [a-32P]dCTP in the presence of dATP. dTTP and dGTP by Klenow fragment after incubation at 60CC for 15 min, to dissociate the vohesivr ends. D;2-A concent)rations were measured spectrophotometrically at 260 nm. All enzymes used were pur(*hased from Boehringrr-Mannheim. R,adionucleotides were purchased from Amersham (spew. art. SO00 (‘iimmtrl). Dimeric and Mrarnrric La (Riggs rf /I/.. 19700). Both Lac repressor preparations were RO”,, active in l*r operator binding. ---. ___t Abbreviations used: hp. base-pair(s): DMSO. dimethylsulphoxide: BSA. bovine serum albumin: IPTG. isopropylthiogalactosidr.

Lac Repressor-h All binding studies with Lac repressor and lac operator BB binding buffer DNA were performed in (10 mill-Tris HCl 0.1 mM-EDTA, 3 rnM(PH 7% magnesium acetate, 10 mivr-KCl, 5% DMSO. 50 pgBSA/ml and 61 mM-dithiothreitol; Riggs et ~2.. 1970a) at room temperature. In a typical binding reaction, lac operator DNA was added first to yield the desired concentration. Freshly diluted Lac repressor was added last. followed by gentle mixing. (r) Filter-binding


Filter-binding assays were performed essentially as described by Riggs et al. (1970a). To estimate the fraction of complexes within a reaction mixture, portions of 61 ml were withdrawn and applied to Sartorius nitrocellulosr fibers (25 mm; 645 pm). Filters had been boiled in water for 5 min. and equilibrated with FB (BB binding buffer without dithiothreitol and BSA) at least 30 min before use. The filtration was performed on a Hoefer Scientific Instruments manifold and took about 10 to 15 s. Filters were washed immediately with 94 ml FB, dried and 5 ml of Zinsser scintillator QS361 was added. Cerenkov radiation was counted in a Betaszint BF5000 scintillation caounter. A 01 ml portion from the reaction mixture was measured without filtering, to determine the input radioactivny. A background radioactivity of 3 to 5% was retained on the filter, when (1) no Lac repressor was present, (2) non-operator DNA was used, or (3) the binding reaction was performed in the presence of I mx-IPTG. Our results were reproducible with an estimated error of 4 to 67;. About 90% of the input radio activity could be retained on the filter when operator fragments were saturated with repressor. This value corresponds to RO,,,. The fraction of complexes within a solution was then calculated by f = ROIRO,,,, where RO represents the counts measured on the filter. (d) Jitrocellulose


Three to 4 nitrocellulose filters that had been boiled in water for 5 min. were sonicated for 20 min in 3 ml FB buffer. This mixture was vortexed and the soluble fraction poured into 1.5 ml reaction tubes. After centrifugation, the pellet,ed nitrocellulose particles were redissolved in 100 ~1 FB buffer. 7 ~1 of the nitrocellulose suspension were added to react,ion mixtures, that either contained single or sandwich complexes with tetrameric Lac repressor and Zac operator DrU’A in a volume of 10 ~1. After incubation for 15 s at room temperature this mixture was centrifuged for 20 s. The supernatant was then mixed with loading buffer (BB with 15”/0 Ficoll, 606% bromphenol blue and 606% xylene cyanol) and loaded onto a non-denaturing polyacrylamide gel. (P) Determination



qf kinetic



The reaction mixtures used to observe complex formation at equilibrium. had a volume of 0.25 ml BB and were incubated for 30 min at room temperature. The concentrations of active Lac repressor and lac operator DNA were in the range of 3x IO-“M to 1 x lo-“M. Lac repressor concentrations do always refer to the molarity of artivr tiimrrs. Kinetics of association Rates of association were determined by adding Lac repressor to solutions of Zac operator DNA in binding (ii)




buffer. Immediately after the addition of Lac repressor (zero time) the solution was mixed. The reaction was then terminated by filtration (01 ml during 10 s), timed at the point of sample application. Kinetics of association were performed in a volume of 1 ml BB. Data from 3 independent experiments were taken to calculate the rate constant k,, using the equation: 1 R-O


‘tR- R”) = k,t, R(O-RO)

where R and 0 correspond to the initial concentrations of Lac repressor and lac operator DNA. and HO to complexes at time t (Riggs et al., 19700). (iii) Kinetics of dissociation Lac repressor and Zac operator DNA were equilibrated in 1 ml BB to measure dissociation kinetics. At zero time a 150.fold excess of unlabelled lae operat,or DKA was added, as indicated, to trap dissociated Latr repressor. In order to follow the process of dissociation, portions of 6 1 ml were withdrawn from the solution and filt’ered after the desired inrubation period. Each experiment was repeated at least three times. The rate constant was ralculated with the following equation (Riggs et al.. 1970b): In E = -k dt. ROo where RO, represents the concentration of complexes at zero time. Measured dissociation rates were independent of the concentration of the chase DKA in a range between 50 and 200-fold. (f) Gel mobility



Gel electrophoresis was performed essentially as described by Kramer et al. (1987). A reaction volume of 15$ BB was used to observe binding at equilibrium, whereas dissociation kinetics were performed in a volume of 0.2 ml. The dissociation rate was determined according to the procedure described above. with the following modifications. Instead of filtering the samples after the desired inrubation period, portions of 15 ~1 were withdrawn, mixed with 3 ~1 of loading buffer (BB with 15 “/b Ficoll, 0.06% bromphenol blue and 0.06 y0 xylene cyanol) and loaded onto a running polyacrylamide gel.

3. Results (a) Comparison

of filter-binding and gel mobility shift measurements

The membrane filter-binding assay is a widely used tool for studying protein-DXA interactions. It is superior to other techniques because it is very sensitive. It can easily detect protein-DNA complexes in highly dilute solutions (Riggs et al., 1970b; Revzin, 1990). The refinement of the gel mobility shift assay introduced by Fried & Crothers (1981) and Garner & Revzin (1981), has now led to another powerful tool to investigate protein-DNA interactions. It has been shown that tetrameric Lac repressor can form sandwich complexes with two lac operator fragments bound to two units of dimeric Lac repressor (Kramer et al., 1987). Figure 1 (a) shows a gel mobility shift where a constant’ amount of Lac

K. Fickert

and B. Miiller-Hill

repressor was incubated with increasing amounts of lac operator DNA (up to lo-fold). The band with highly decreased electrophoretic mobility corresponds to such a sandwich complex. This sandwich complex starts to form at a twofold excess of lac operator DNA over Lac repressor. Surprisingly there are still single complexes present at a tenfold excess (see Discussion). A crude estimation of the equilibrium constants (O’Gorman et al., 1980) gives a K, of 1 x lo-l2 M for the single complex and a K, of 5 x IO-“M for the binding of the 84 bp lac operator fragment to the second binding site of tetrameric Lac repressor. As expected, the sum of the concentrations of the two shifted complexes remains constant under excess DNA conditions. The same reaction mixtures in a larger volume, but with comparable molar concentrations, were then applied to nitrocellulose filters. The results from the filterbinding assay are presented in Figure 1(b). They show that the specific radioactivity retained on the filter decreases with increasing amounts of excess lac operator Dh’A when tetrameric Lac repressor is used (Fig. l(b)). With dimeric Lac repressor. which cannot form sandwich complexes. we obtained a normal saturation curve (Fig. 1 (b)), shaded bars). Tt is suggestive to assume that, the filled columns in Figure l(b) correspond to t’he single complexes in Figure l(a), whereas sandwich complexes are not ret,ained on a nitrocellulose filter. The experiment shown in Figure 2 presents evidence for this assumpt,ion. Binding reactions between tetrameric I,ac repressor and an end-labelled Zac operator DNA fragment that either yield single or sandwich complexes were treated with a nitrocellulose suspension (Materials and Methods), centrifuged and the supernatant loaded onto a polyacrylamide gel. While free DNA is not affected (Fig. 2, lanes 1 and 2), most of the single complexes get trapped by the nitrocellulose particles (lanes 3 and 4). If a reaction mixture containing sandwich complexes is treated the same way, then only a small percentage of these complexes is retained by nitrocellulose (lanes 5 and 6). These observations will have consequences for t’he interpretation of kinetic parameters obtained from filter-binding assays. (b) Dissociation repressor-operator

of Lac complexes

In order to monitor the dissociation of Lac repressor from Zac operator DNA, an excess of unlabelled lac operator DNA was added at zero time to an equilibrated mixture of Lac repressor and lac operator to trap dissociated free Lac repressor. The t’ime-courses of the dissociation processes of tetramerit and dimeric Lac repressor from a 406 bp fragment carrying ideal lac operator in a gel mobility shift assay are presented in Figure 3. after the addition of excess lac Immediately operator DKA a sandwich complex is formed (Fig. 3, arrowheads). Depending on the size of the chase DNA (here 24 bp and 2455 bp containing one ideal lac operator) we obtain differently moving

Let repressor DNA/R



.-E 2 ij

500 I

I 0







DNA/R ( b) Figure 1. Titration of Lac: repressor with increasing amounts of an end-labelled 80 bp fragment carrying ideal Zac operator. (a) (:el mobility shift assay with tetramrrics Lac repressor (2 x IO-” 11) equilibrated with 0. 1. 3. 1. 8. 12 and 20 x IO-” wlccc operator I)PiA of a length of X4 bp in a vol. of 20~1 RR. The molarity is always the dimrr molar?@. Symbols on the left indirat’e the conformation of the complexes and free UXA (b) Filter-binding assa? with dimeric ( q ) and tetrameric (a) T,ac repressor (8 x 10-l ’ M) equilibrated each with 0. (1.4. 0%. 1%. 3.2. 4.8 and 8 x lO-‘o M-h operator DNA of a length of 84 bp in a vol. of 250 ~1 BH. Ctqmin indicates the counts/min on thrk filter after background subtraction. Each point is the average of 3 independent measurement#s.

sandwich caomplexes as indicated be- the symbols. Dimeric I,ac rt~prwsor cannot form sandwic&h complexes. Thr irrt3ensity of thr shif%ecl bands decreases only slowly over the incubation periotl. which proves a high stability of thr complesrs.

Lac Repressor-lac




repressor-operator complexes. Since the reaction mixtures with tetrameric Lac repressor form sandwich complexes immediately after the addition of chase lac 0 DNA, it is impossible to determine the dissociation constant for the single complex. The dissociation rate constants reported with filterbinding assays have to be corrected according to these results. Whitson & Matthews (1986) observed an apparent DXA-length dependence of the dissociation rate with tetrameric Lac repressor. We reproduced these filter-binding experiments with DNA fragments carrying a single ideal lac operator (Fig. 4, open symbols). In order to interpret these findings one has to consider that (1) sandwich complexes are formed, (2) sandwich complexes are not retained on nitrocellulose filters and (3) the halflife of a dimeric Lac repressor-operator complex is 60 minutes, independent of the DNA-length (Fig. 4, filled symbols). We assume that’ the threefold higher dissociation rate measured with the gel mobility shift assay is due to technical manipulation of the solution of the complex (i.e mixing with loading buffer, gel electrophoresis) and t’hat the halflife of a dimeric Lac repressor-operator complex measured with the filter-binding technique is more accurate. Taking all this into account, we propose a rate constant k, of 2 x 10m4 s-l (kd = 0.693 x tT,i where t 1,z = 3600 s, i.e. 60 min) for a complex of a dimeric Lac repressor unit with one lac operator fragment.

Chase lac 0 DNA

Figure 2. Gel mobility shift assay with tetrameric Lac repressor. The reaction mixtures (10~1) contained an end-labelled 84 bp lac operator fragment (25 x lo-” M)? trtramrric, Lav repressor (1.0 x 10-l” M) and a 600-fold excess of an unlahelled 24 bp lac operator fragment which was added after equilibrium (20min) and further incubated for 2 min. as indicated. To duplicate samples 7 ~1 of a nitrocellulose suspension in FB buffer (Materials and Methods) was added. This mixture was incubated for 15 s and centrifuged briefly (20 s). The supernatants as well as the untreated binding reactions were then analysed on a SC!,, (w/v) polyacrylamide gel. Symbols on the left indic&ate the conformation of the complexes and free DNA. The sizes of t)hta /UC operator DNu’As are not drawn to scale.

(c) Kinetics of Lac repressor and operator association Quantification of the bands Dynamics Phosphor Imager revealed a halflife of 20 minutes

using a Molecular (data not shown) for the dimeric Lac



Lac repressor


Chase /acO DNA Time (min.)

The rate constants for association were obtained from filt’er-binding experiments exclusively, because no sandwich formation is expected under these



24bp 1


v 10 15 20 0

2455 1


bp 10 15 20

24 bp

y 0



10 15 20 25 4 Slot

Figure 3. Gel mobility shift assay showing the dissociation of the Lac repressor-operator complex. Dimeric or tetrameric Lac repressor (4 x 10-l’ M) was equilibrated with an end-labelled 406 bp fragment carrying ideal Zac operator (1 x 10-l’ M) in O-1 ml binding buffer. At zero time (indicated by arrowheads) a 150-fold molar excess of unlabelled ideal lac operator DXA (24 bp or 2455 bp in length) was added to a final concentration of 1.5 x lo-* M. Portions of 15 ~1 were loaded ont’o a running 4% (w/v) polyacrylamide gel at the times indicated. Symbols on the left and right indicate the conformation of the complexes and free DPU’A. The sizes of the Zac operator DNAs are not drawn to scale.


R. Fickert

and R. Miiller-Hill

Table 1 Association rate constants k, for dimeric an,d tetrameric Lac repressor to various ideal lac operator DNAs that differ in length 50 40 DNA-length


Tetrameric Lac repressor k, ( x IO9 M-’ s--l):

I)imeri~ Ltrc~ repressor k,[X1()9MM’h


30 24

84 406 4455 49,000$
















Figure 4. Filter-binding data indicating the dissociation of dimeric (d) and tetrameric (t) Lac repressor complexes with various Zac operator Dlu’As that differ in length (24 bp, 406 bp and 2455 bp). Molar concentrations of Lac repressor and labelled Zac operator fragments are the same as in Fig. 3. Dissociation was measured in a volume of 1 ml binding buffer. A ISO-fold molar excess of supercoiled plasmid ~310, carrying one copy of ideal lac operator was added to the pre-equilibrated solution at zero t,ime to trap free Lac repressor. Portions of 100~1 were withdrawn from the reaction mixture and filtered at t,he times indicated. Open symbols refer to complexes with tetrameric Lac repressor and filled symbols to

dimeric Lac repressor-operator

complexes. Each point is

the average d 4455 bp; +,

of 3 independent measurements. A. d 406 bp; H. d 24 bp: A. t d4.55 bp: 0. t 406 bp: 0. t 24 hp.

conditions. Table 1 gives the k, values for tetrameric and dimeric Lac repressor association to five lac operator fragments that differ in length. All results were consistent with second-order kinetics. We had chosen low salt condit’ions (10 mM-K(Il. 3 rnM-magnesium acetate) in order to enhance unspecific binding, which is presumably involved in a facilitated target location (von Hippel & Berg, 1989). No DNA-length dependence is observed for the association of dimeric or tet,rameric Lac repressor t’o linear DNA fragments carrying one ideal lac operator up to 2455 bp in length (Table 1). In this range tetrameric and dimeric Lac repressors have essentially the same rate constants. Since these constants are strongly dependent on the salt concentration (Winter et al., 1981), the k, values measured are only valid for tjhe conditions used here (see &Iaterials and Methods). The association rates of tetrameric and dimeric Lac repressor to 2 DNA carrying one symmetric ideal lac operator (iEstiO0) reveal a st’riking difference. Whereas dimeric Lac repressor has a rate constant equal to the one obtained with short lac operator fragments, tetrameric Lac repressor shows a ninefold increase of its association rate t,o linear 1” DNA (Table 1).



I.1 1.2 I4 9.0

I .:I 12 03 l.(,

t All operat,or DNAs used carry a single ideal /a~ opfmtor anti are derived from ~310,. 1 ka values were c:alculeted from tiltrr binding datii (brat Materials and Methods). Dimeric or trtrameric lJa(. repres~~ (5 x 1()-‘2 M dimer molarity) was added to a 3 x IO ‘* M solution of labelled DNA carrying a single ideal Inc operator al. WI’O tin)?. At intervals of 30 to 60 s 100 @I portions were withdrawf1 from the reaction mixture (1 ml binding buffer) and filtjered through nitrocellulose filters. 0 The .NJ,MH)bp linear operator DNA CYII.PILS~O~~:, to i.EstiMl. which carries a single ideal Inc operator

It has been claimed that Lac repressor tetramrhrs dissocia.te into dimers with a dissociation constant K, of 1.3 x 1OP8 ~1 at’ 21 ‘Y’ under high pressure (Royer et al., 1990) and also under normal pressure (Brenowitz et al.. 1991). We therefor? drtrrmined the fraction of Lacb repressor tetramers at concentrations ranging from 6 x 10 I331 to 3 x 10 * ‘31 by determining t,htl amount of sandnich c.omplexrs in the presence of excess lac operator 1)NA xincee onl? tetramers (2~11 fi)rm sandwich (~omplrxes. ;\ti~r equilibration of wild-type tetrameric lmr ref)rcbssor with an equimolar amount of an end-labelled 24 bp lac operator fragment, a 30-fold ex(~ss of the Sam? unlabelled fragmtxnt was added. Thtb c.onc,e,rltratiorl~ of sandwich complexes formetl wertb then rstimat Cal from filt,er-binding assays (Fig. 5). (Kc)-- h’O,)!KO (*orresponds to the fracdtion of dimeric I,ac. repressor. where IW is the concentration of initial complexe,: in equilibrium. KO, is t)he ooncnentration of sandwicah complexes and RO - KC), the caoncent ration of singIt complexes after t hv addition of P.YWSS /UC ~JfP?IYitOr dimc~r D?iA. Tn contrast to “loop-lnrcliat,etl” tetramer association (Brenowit,z d (11.. 1991). it ih unlikely that two separat’ed lnc operator l)N.-ls will improve the association of Lac repressor dimrrs. M’c, found that 30 to 50% of wild-type Lac repressor is present as t,etramer in the concent,rat,ion range of 3 x 10-12~ to 5 x lo- "M (Fig. 5). where the assoc.iation studies are performed. At a c~oncentration ot 3 x lo-“M, SOo,b of wild-type LAC rrpressor is present as tetramer, showing t,hat the trt)ramrr is at least two orders of magnitude more sta,blr t.han previously estimat,ed (Royer et al.. 1990). A det,ailrtl study of the dimer-tetramer cbquilibrium of 1,~. repressor will appear elsewhere. Tn order t 0 filrtlier investigat tt f he illc.rfha.scti association



AEstiOO. we analysetl association process.


the The




role of’ i. 1)X,\ in thr eEec,t of’ possible Iu(,

Lac Repressor-lac




Table 2


Effect of various non-operator DNAs on the association rate k, of dimeric or tetrameric Lac repressor to a 2455 bp operator fragment

90 80

'0 c


g co





No competitor 1EwtOOO (intact) mwtooo (HpuII)$ 280 hp non-op DNA5

Dimeric Lac repressor

Tetrameric Lac repressor

Competitor I)NA k,






I.0 < 02


How Lac repressor finds lac operator in vitro.

Filter-binding and gel mobility shift assays were used to analyse the kinetics of the interaction of Lac repressor with lac operator. A comparison of ...
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