Biochimica et Biophysica Acta, 1087 (1990) 55-60


Elsevier BBAEXP92160


repressor-operator interaction: DNA length dependence

A n a s t a s i a M. K h o u r y *, H y u n J o o Lee, M a r c e l l a Lillis * * a n d P o n z y L u Department of Chemistry, University of Pennsylvania, Philadelphia, PA (U.S.A.)

(Received 8 March1990)

Key words: lac operon; Operon; Generegulation; DNA bindingprotein The interaction of the E. coli lac operon repressor with its operator D N A has been directly examined as a function of the length of operator-containing DNA. The apparent bimolecular association rate constants were calculated as k a ~- ( k d / K D ) , where the dissociation equilibrium constant, K D and the dissociation rate constant, kd, were measured by nitrocellulose filter adsorption assays. The values obtained for the overall association rate constants are compared with theoretical association rate curves for specific mechanisms. Association of the repressor with short operator containing D N A fragments ( < 70 base pairs) occurs at rates expected of three-dimensional diffusion. Our data also imply that at longer D N A lengths a combination of three-dimensional diffusion with one-dimensional sliding along with hopping a n d / o r intersegment transfer must be involved to facilitate the repressor operator association.


Gene regulatory proteins act by binding to specific DNA sequences which occur only once or twice in the genome. However, before specific binding occurs, these proteins must first locate these binding sites. The recognition process is actually a search when one considers the size of a recognition site for a DNA-binding protein in relation to the average size of a genome. In the prototypical E. coli lac operon, the lac operator is about 27 base pairs (bp) [1,2] in length, while the entire genome contains 4.7.10 6 bp of DNA [3]. Since lac repressor interacts with nonoperator DNA, a specific DNA binding site therefore competes with well over 106 potential non-specific sites for regulatory protein binding [4-7]. Under equilibrium conditions, this in vivo specificity is accounted for by an association constant of repressor tetramers for bulk nonoperator DNA of 103 [38] compared with 1012 M -1 and 109 M -1 association constants for repressor tetramers and inducer-repressor tetramer operator complex formation, respectively. The original in vitro measurement of lac repressor-lac operator association rate, ka, fitted to a simple bimolec-

* Present address: Department of Cellular and Developmental Biology,Harvard University,Cambridge,MA 02138, U.S.A. * * Present address: Sogetal,Hayward,CA 94545, U.S.A. Correspondence: P. Lu, Department of Chemistry, University of Pennsylvania,Philadelphia,PA 19104, U.S.A.

ular interaction model, obtained by Riggs and coworkers [7] was found to be 7.109 M -1. S -1. If the association of these two macromolecules were diffusion controlled with bimolecular kinetics governed by molecular weight only, the expected association rate would be between 107 to 188 M -1 • s -1 [8-11]. This estimate uses the molecular weight of tetrameric lac repressor as 154 kDa and the DNA as 30 MDa, since it was contained on a lambda phage. The apparent paradox inspired the proposal of several mechanisms that suggest that the protein seeks its target site by reducing either the dimensionality or the volume of the search [8,10]. These mechanisms involve: (1) one-dimensional sliding of the protein along the DNA while nonspecifically bound via ionic interaction [5,9-14]; and (2) intersegment transfer of the protein through a series of nonadjacent DNA near-encounters where the protein momentarily spans two segments of nonadjacent DNA sequences [5,9,11, 13]. Although the mechanism of lac repressor-DNA association has been examined extensively [6,7,13-16], previous studies explored the dependence of the association rate constant (ka) on salt concentration, solution viscosity, pH and temperature to infer a relation between k a and DNA length. The problem has been addressed theoretically but not directly by experimental methods, due to the historic difficulty in obtaining defined DNA fragments of varying lengths containing the operator sequence. This study investigates the length dependence of lac repressor-operator association kinetics directly, using DNA containing the approx. 27 bp lac operator located

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56 in the center of 36-3300 bp. lac repressor-DNA complex formation was monitored by the nitrocellulose adsorption assay [6,7,17]. This assay was originally used by Nirenberg and Leder [18] to detect anticodon stimulated tRNA binding to ribosomes and later by Jones and Berg [19] to study RNA polymerase binding. An apparent bimolecular association rate constant k a was derived from a combination of equilibrium binding (KD) and dissociation rate (kd) measurements for 363300 bp DNA fragments. These k a values are then compared to values predicted by models involving onedimensional diffusion or intersegment transfer mechanisms for lac repressor-operator association. Materials and Methods

Tetrameric lac repressor protein was isolated from E. coli CSH46 strain according to the method of Sommer et al. [20]. DNA samples of lengths varying from 36 to 3300 bp, each containing the approx. 27 bp lac operator sequence, were obtained from various plasmids. The 3300 and 203 bp DNA sequences were generated from the same plasmid, pOP203 [21], by applying restriction enzymes EcoRI for the 203 bp and SmaI and HindlII for the 3300 bp. DNA fragments obtained from the restriction digests contained one operator site at the midpoint of the fragment. The 36 bp fragment was isolated from pOP101 of Sadler et al. [22]. The isolated DNA fragments were dephosphorylated at the 5' end using calf intestinal alkaline phosphatase and subsequently rephosphorylated using T4 kinase and [732p]ATP. The dissociation rate constant (kd) and the dissociation equilibrium constant (KD) were measured for each DNA fragment with the repressor using the nitrocellulose filter adsorption assay employed by Riggs and Bourgeois [6,7] to study the interaction of lac repressor and operator DNA contained on a derivative of coliphage lambda. The overall association rate constants were obtained by measuring k d and K D and then calculating the apparent k a from k, = k d / / K D . Measuring ka directly proved erratic for the shorter operator DNA fragments, because of the high dilution, to 10-11 M, and high 32p specific activity necessary to bring the rate of complex formation to a manageable time scale and a detectable count rate. For the sake of consistency, all filter adsorption experiments were carried out in buffer B (10 mM Tris-HC1, pH 7.5, 10 mM KC1, 10 mM Mg(OAc)2 , 0.1 M EDTA, 0.2 /~M 2-mercaptoethanol, 50 mg/ml bovine serum albumin and 5% dimethyl sulfoxide) as described by Riggs and Bourgeois [6]. Nitrocellulose filter paper used was Millipore HAWP cut into 25 mm round discs (0.45 #m). Samples were allowed to equilibrate at room temperature (25 ° C) for 20-30 rain before filtration. Typically; 0.2-1.0 ml samples were applied to the filters depending on the activity

of the radioactively labelled DNA and were washed with two equal aliquots of buffer. The K D for the repressor-operator complex was measured by titrating a constant amount of radioactively labelled operator, at a concentration less than the estimated KD, with repressor until 100% retention was achieved. A plot of the log of complex retained by the filter versus repressor concentration yielded a sigmoidal curve where the inflection point represents the K D of lac repressor with the particular DNA fragment. Each titration was also subjected to Scatchard analysis [23,24] and yielded equivalent results. The relative stoichiometries of each repressor-operator complex were confirmed by titrating a constant amount of 32p-labelled DNA (at a concentration 10-100-fold higher than KD) with repressor and locating the break in the curve for complex retained. To determine the dissociation rate c o n s t a n t ( k d) for the repressor-operator complex, sufficient repressor was complexed with 32p-labelled operator DNA (again at a concentration of 10-100-fold greater than KD) to give 60-70% saturation of the operator with repressor. The solution was equilibrated for 30 min at 25°C. At t 0, a 50-fold excess of unlabelled operator on the corresponding fragment was added and mixed. Aliquots of this solution were filtered at various times and the time-dependence of the disappearance of radioactive complex was measured. The slope from the plot of the logarithm of retained radioactivity versus time yielded the dissociation rate constant [6]. These assays determined the fraction of DNA which was bound, but not the fraction of repressor bound to the DNA because only the DNA was radioactively labelled. The estimate of the fraction of repressor molecules that actively bound the operator came from the fraction of radioactive DNA molecules retained on the filter at saturation as compared to the input radioactive DNA. Our repressor was found to be 50-80% active assuming one binding site per DNA Scatchard analysis also revealed a maximum ratio of proteins bound per DNA as being 2. Although minor deviations from unitary stoichiometry were reflected in K D measurements, the dissociation rate constant would not be affected by the stoichiometry deviations provided that the dissociation from each site is equal and independent. Results and Discussion

Dissociation equilibrium constants ( K n ) and dissociation rate constants (ka) measurements for lac repressor from four operator lengths are reported in Table I and Fig. 1 along with the calculated association rates (ka). This includes the k a for lac repressor association with ~-q580dlac DNA (= 50 000 bp) measured by Riggs and coworkers [7] at ionic conditions identical to condi-



Experimental equilibrium and rate constants

Literature values for association rate constants

D N A size









(MXl0 -s)

36 55 203 33~ 50000 a

1.3± 4.9 13.0±18 5.3± 1.9 0.9± 0.1 0.1

5.7±1.9 2.8±0.5 2.0±0.8 2.3±1.2 0.4

2.2±0.6 4.3±0.7 6.1±2.3 5.9±2.5 29

4.2± 2.1 2.1± 2.9 3.8± 3.1 25 ±14 70

a Measured by Riggs et al. [7]. The buffer conditions are identical to those used in our studies.

tions used in this study. F o r c o m p a r i s o n , T a b l e II a n d Fig. 2 are a c o m p i l a t i o n of k a values f r o m the literature, m e a s u r e d b y o t h e r investigators. I o n i c c o n c e n t r a tions in those studies are higher t h a n the ionic conc e n t r a t i o n s used here, therefore the a p p a r e n t rate of a s s o c i a t i o n for those p o i n t s c a n n o t b e d i r e c t l y c o m p a r e d with our e x p e r i m e n t a l d a t a since k d is very ionic strength d e p e n d e n t . D e s p i t e the difference in ionic conditions b e t w e e n the e x p e r i m e n t s p r e s e n t e d here a n d those r e p o r t e d in T a b l e II, the overall t r e n d of increasing ka increasing D N A l e n g t h is c o n s i s t e n t in b o t h cases with the c a l c u l a t e d curve for the t h r e e - d i m e n s i o n a l / o n e - d i m e n s i o n a l (Figs. 1 a n d 2). F r i e d a n d C r o t h e r s [37] showed that the a p p a r e n t k d is d e p e n d e n t on c o n c e n t r a t i o n a n d the r a t i o of lac o p e r a t o r D N A sequence to nonspecific sequence used in the c o m p e t i t i o n m e a s u r e m e n t d e s c r i b e d here. T h e i r e x p e r i m e n t s were d o n e over a c o n c e n t r a t i o n range of 10 -5 M to 3 • 1 0 - 4 M of c o m p e t i t i v e D N A b a s e pairs. T h e highest c o n c e n t r a t i o n of u n l a b e l l e d c o m p e t i t i v e

lo" // 10~° "7

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10' 10'

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DNA size (bp)

k. * ( M - k s I )

Lac repressor-operator interaction: DNA length dependence.

The interaction of the E. coli lac operon repressor with its operator DNA has been directly examined as a function of the length of operator-containin...
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