Mechanism of Protein Access to Specfic DNA Sequences in …rpdata.caltech.edu/courses/PBoC ASTAR/files_2011/articles... · Sequences in Chromatin: A Dynamic Equilibrium Model for

J. Mol. Biol. (1995) 254, 130–149

Mechanism of Protein Access to Specific DNASequences in Chromatin: A Dynamic EquilibriumModel for Gene Regulation

K. J. Polach 1,2 and J. Widom 1,2*

We present evidence for a mechanism by which regulatory proteins may1Department of Biochemistrygain access to their target DNA sequences in chromatin. In this model,Molecular Biology, and Cellnucleosomes are dynamic structures, transiently exposing stretches of theirBiology, NorthwesternDNA. Regulatory proteins gain access to DNA target sites in the exposedUniversity, 2153 Sheridanstate, and bind with an apparent dissociation constant equal to theirRoad, Evanstondissociation constant for naked DNA divided by a position-dependentIL 60208–3500, USAequilibrium constant for site exposure within the nucleosome. A sensitive2Department of Chemistry assay, based on the kinetics of restriction digestion of sites within

Northwestern University nucleosomes, reveals this dynamic behaviour and quantifies theEvanston, IL 60208, USA equilibrium constants for site exposure. Our results have implications for

many aspects of chromatin function. They offer new mechanisms forcooperativity (synergy) in regulatory protein binding and for activeinvasion of nucleosomes.

7 1995 Academic Press Limited

Keywords: nucleosome, cooperativity; binding; nucleosome positioning;active invasion*Corresponding author

Introduction

DNA sequences that are organized in nu-cleosomes are largely inaccessible to other proteins.This inaccessibility is due to steric exclusion, asimple and necessary consequence of the proximityof DNA to an impenetrable surface. It applies toDNA that is held on a flat surface such as mica(Rhodes & Klug, 1980), as well as to DNA held onthe curved surface of the histone octamer (Lutteret al., 1979; Lutter, 1981; Richmond et al., 1984;Arents et al., 1991; Arents & Moudrianakis, 1993).The recognition of DNA sequences on a nucleosomeis further hindered by steric exclusion from adjacentgyres of the DNA on the same nucleosome andfrom the organization of the nucleosome filamentinto higher order chromatin structures.

Most DNA in vivo is packaged in nucleosomes,but many DNA sequences are critical for biologicalregulation, and these must be accessible toregulatory proteins at appropriate or specific times.What, then, is the principle that guarantees thatregulatory proteins may have access to their DNAtarget sequences when necessary?

The answer to this important question is notknown. Current thinking focuses chiefly on threeideas (for reviews, see Felsenfeld, 1992; Kornberg &Lorch, 1992; Wolffe, 1992; Lewin, 1994). (1) Theremay exist a window of opportunity for regulatoryprotein binding, coupled to DNA replication.Perhaps regulatory proteins are given an opportu-nity to bind to DNA prior to chromatin assembly.(2) Chromosomes may be organized much morecarefully than has previously been appreciated.Perhaps DNA regions that are critical for regulationare simply never packaged in nucleosomes insuch a way as to be inaccessible. (3) Perhapsregulatory proteins may instead have some capa-bility of active invasion, so that steric exclusion doesnot apply. These three models each have somelimitations.

Model (1) has certain well-established counter-examples; most notably, phosphate induction of theyeast PHO5 gene and glucocorticoid induction ofMMTV-LTR transcription (for a discussion of thispoint, see Schmid et al. (1992)). The essentialobservations are that cells that are prevented fromundergoing DNA replication can still switchreversibly between transcriptional states, withcorresponding chromatin-structural states, in re-sponse to changes in their environment. Thus,model (1) may apply in some instances, but it is nota general solution to the problem of regulatoryprotein access.

Abbreviations used: GR, glucocorticoid receptorprotein; HSF, heat shock transcription factor; PCR,polymerase chain reaction; PMSF, phenylmethylsulfonylfluoride; BZA, benzamidine; BSA, bovine serumalbumin; TBP, TATA-binding protein.

0022–2836/95/470130–20 $12.00/0 7 1995 Academic Press Limited

Nucleosome-Dynamics Mechanism for Gene Regulation 131

Model (2) may be questioned on physicalgrounds. The known free energies that contribute tospecifying the positioning of nucleosomes along theDNA (Yao et al., 1993) are far too small to guaranteethat a particular DNA sequence will be similarlyorganized in the chromatin of every cell in a largemulticellular organism. This point has beenappreciated previously by Kornberg & Lorch (1992),who note that the >106-fold sequence selectivitytypical for sequence-specific DNA binding proteinsmay be an appropriate benchmark. The known freeenergies of nucleosome positioning fall far short ofthat required to achieve 106-fold selectivity. Theprior binding of a sequence-specific regulatoryprotein might provide the necessary free energy, butthis simply replicates the fundamental problem onelevel up in a regulatory hierarchy. Importantly,observations of precise nucleosome positioningin vivo (e.g. Pina et al., 1990; Bresnick et al., 1991;Shimizu et al., 1991) do not address the feasibility ofthis model. The key issue is the time-averaged andcell-averaged statistical precision of this positioning.Nucleosome positioning may appear to be preciseto the level of a single base-pair, but the modest freeenergies of positioning mean that the samechromosomal location in differing cells willfrequently have nucleosomes at differing positions,with probabilities >10−6. We do not intend thisanalysis to imply that nucleosome positioning andthe corresponding free energies are withoutimportance; indeed, in the context of the model thatwe propose below, these free energies and theresulting statistical positioning take on substantialregulatory significance.

Model (3) has not yet been developed to the pointof having a definite, testable, proposed mechanism.Nevertheless, it has arisen from studies in vitrowhich show that some regulatory proteins areapparently able to bind to nucleosomal targetsequences even though these target sequences areexpected to be sterically inaccessible (e.g. Archeret al., 1991; Taylor et al., 1991; Perlmann, 1992); insome cases, binding may be ATP-dependent (e.g.Cote et al., 1994; Imbalzano et al., 1994; Kwon et al.,1994; Pazin et al., 1994; Tsukiyama et al., 1994). Amajor unresolved question with this mechanism ishow proteins that are capable of active invasion ofnucleosomes know which nucleosomes to invade.An important aspect of our model is that it providesa conceptual framework for the analysis of activeinvasion.

In this paper, we propose a new mechanism thatmay contribute to providing access for regulatoryproteins to their target DNA sequences. Ourhypothesis is that perhaps nucleosomes are dy-namic structures, transiently exposing stretches oftheir DNA, and that regulatory proteins gain accessto target sites in the exposed state. Such nucleosomeconformational changes have previously beenproposed, but only for the very ends of the coreparticle DNA (McGhee & Felsenfeld, 1980; Shindoet al., 1980); the remainder of the nucleosomal DNAhas previously been considered inert. Here we

report the results obtained using a sensitive assay,based on the kinetics of restriction digestion, whichreveal this dynamic behavior for sites throughoutnucleosomes and quantify the equilibrium con-stants for site exposure. These results have severalramifications. They explain numerous observationsin the literature, they suggest mechanisms fortranscription and replication through nucleosomesand for nucleosome sliding, and most importantly,they offer a new mechanism for cooperativity(synergy) in regulatory protein binding, andprovide a framework for the analysis of activeinvasion.

Model, Assay, and Theory

Model

Our model is illustrated in Figure 1(a). Ourhypothesis is that nucleosomes (N) might bedynamic structures, transiently exposing theirDNA, such that in the exposed state (S), regulatoryproteins (R) may bind as though they were bindingto naked DNA. We make the simplifying assump-tion that sufficient nucleosomal DNA is exposedsuch that the rates and equilibria for binding to anexposed nucleosomal target sequence or to a nakedDNA target sequence are identical. We recognizethat, at some level, proximity to the histones (as wellas other effects) cannot be ignored (for example, thisintroduces coupling in the effects of rotational andtranslational positioning on protein binding; seeDiscussion). But, as will be seen, interpretation ofour new experiment with this simplifying assump-tion leads to results that are in broad agreementwith previously unexplained results in the literaturefrom very different kinds of experiments,suggesting that our simple model captures theessence of the system. With this assumption,

NFk12

k21S + RF

k23

k32RS (1a)

for binding to a nucleosomal target, and

S + RFk23

k32RS (1b)

for binding to a naked DNA target.Binding of a regulatory protein to a nucleosomal

target sequence will therefore occur with a net freeenergy change

DG0net = DG0

conf + DG0naked DNA, (2)

in which DG0naked DNA is the free energy change for

process (1b) and DG0conf is the free energy cost for site

exposure. At present, information is available onlyfor DG0

naked DNA, whereas the binding equilibrium isgoverned by DG0

net.Expressed in equilibrium constants, a regulatory

protein would bind to a nucleosomal targetsequence with an apparent dissociation constant

Kapparentd = Knaked DNA

d /Kconfeq , (3)

Nucleosome-Dynamics Mechanism for Gene Regulation132

where Knaked DNAd is the dissociation constant for

naked DNA which is measured in most studies, andKconf

eq the equilibrium constant for site exposure,

Kconfeq = e−DG0

conf/RT. (4)

In our model, Kconfeq may depend on the position of

the target sequence within the nucleosome.The general resistance of nucleosome core

particle DNA to nuclease digestion, and otherproperties of nucleosomes, suggest that Kconf

eq mightbe extremely small; we therefore devised a sensitive

assay to detect and quantify this equilibrium(Figure 1(b)). We replaced the regulatory proteinwith a restriction enzyme (E), and we constructednucleosomes having a site for E at a known positionin the particle. If this conformational equilibriumexists, the restriction enzyme can bind and catalyzecleavage of the substrate to yield products (P),which can be detected by gel electrophoresis andquantified using a phosphorimager. Thus,

NFk12

k21S + EF

k23

k32ES :

k34

E + P (5a)

Figure 1. Hypothesis and assay. (a) Hypothetical mechanism for binding of a regulatory protein (R) to a specific DNAtarget sequence (hatched) on a nucleosome (top) compared to binding to naked DNA (bottom). The Figure illustratesa single nucleosome viewed from above. We do not mean to imply specific structural details for the exposed state orthe resulting complex. Our hypothesis is that perhaps nucleosomes are dynamic structures, transiently exposing theirDNA through some non-dissociative process such that, in the exposed state, regulatory proteins can bind as thoughthey were binding to naked DNA. The relevant microscopic rate constants are indicated. (b) A sensitive assay to detectand quantify the hypothetical conformational equilibrium. We use a restriction enzyme (E) binding to its recognitionsequence (hatched) in place of a regulatory protein; the restriction enzyme can catalyze cleavage of the DNA to yielddetectable products. Rates of cleavage for nucleosomal DNA (top) are compared with cleavage of naked DNA (bottom)in identical solution conditions. The relevant microscopic rate constants are indicated.


and

S + EFk23

k32ES :

k34

E + P (5b)

for nucleosomes and naked DNA, respectively. Theassay is potentially very sensitive because one cancarry out the digestions for as long as necessary todetect the conformational equilibrium.

The reader may consider this assay surprising,since the failure to observe restriction digestion isroutinely used by others as an assay for nucleosomepositioning. In essence, our results establish thatthe protection against restriction digestion which isafforded by nucleosomal organization of theenzyme’s target sequence is quite finite; byquantifying this finite protection, we observe andquantify the non-zero equilibrium constants for siteexposure.

Theory

The kinetic analysis of mechanisms such asequations (5) is well established; we follow thederivation from the formally analogous study ofShore et al. (1981).

Experimentally, we monitor the loss of reactantnucleosomal DNA (D),

(D) = (N) + (S), (6)

which disappears according to a first order rate lawwith an observed rate constant kobs,

kobs = −1(D)

d(D)dt . (7)

Making the steady state approximation for (S) andfor (ES), one obtains (Shore et al., 1981)

kobs = k34(E)Km

k12

k12 + k21 + k34EKm

, (8a)

with

Km = k32 + k34

k23(8b)

There are two limiting cases for equation (8a) (Shoreet al., 1981).

Case I: slow conformational transition

0k34(E)Km

� k21; and k21 � k12 for small Kconfeq 1. (9)

In this limit, equation (8a) reduces to:

kobs = k12. (10)

Case II: rapid conformational pre-equilibrium

As will be seen below, the present kinetic studiesobey this opposite limit:

(k21 � k23(E)). (11)

In this limit, equation (8) reduces to

kobs = k34(E)Km

Kconfeq

1 + Kconfeq

. (12)

If Kconfeq is small (�1), as anticipated, and if the

experiment is set up such that (S) �Km, so that(E)1(E0), the total concentration of added restric-tion enzyme, then the observed first order rateconstant for loss of reactant nucleosomal DNA(equation (12)) becomes

knucleosomeobs = k34(E0)

KmKconf

eq . (13)

If, in separate experiments, naked DNA is digestedunder identical solution conditions (but possiblywith different (E0)), the reactant naked DNA willdisappear with an apparent first order rate constantgiven by:

knaked DNAobs = k34(E0)

Km. (14)

Combining equations (13) and (14) yields:

Kconfeq = knucleosome

obs /(Enucleosome0 )

knaked DNAobs /(Enaked DNA

0 ). (15)

Thus, in this rapid pre-equilibrium limit, we obtainan experimental measurement of Kconf

eq from the ratioof two observed rate constants scaled by theirrespective enzyme concentrations, one for nucleo-somal DNA targets and one for naked DNA.

The two limits are readily distinguished bythe dependence of kobs on (E0); for limit I, thedependence is zero-order, while for limit II,the dependence is first order. In the presentwork, limit II applies. We find experimentally thatkobs is rigorously first order in (E0). Moreover, limitII is anticipated on theoretical grounds. Theavailable concentrations of restriction enzyme areunlikely to exceed 100 nM. For a diffusion-con-trolled encounter between a target DNA sequenceand an enzyme active site, one expectsk23E108 M−1 s−1, hence, we expect k23 E0E10 s−1. Bycontrast, simple theoretical models for the siteexposure and recapture process, assuming either anactivated or a diffusive process for recapture lead tothe expectation that k21e105 s−1 (J. Widom, unpub-lished results), in which case k21 � k23 E0.

Experimental design

The DNA constructs used in the present studyutilize a known nucleosome-positioning DNAsequence from the sea urchin 5 S RNA gene,characterized by Simpson and colleagues (Simpson& Stafford, 1983), incorporating specific basechanges to generate restriction sites within thesequence. The majority of this DNA sequence isknown not to be essential for its positioning ability,and, with one exception, we have restricted thelocations of sequence changes to those regions ofthe sequence that are not essential for positioning(FitzGerald & Simpson, 1985). The DNA length


Figure 2. DNA constructs andrestriction enzyme sites for kineticassays. Constructs (a), (b), and (c)are illustrated as rectangles repre-senting the 150 bp long DNA mol-ecules. The histone octamersorganize the DNA from positions 5to 150 (bp), corresponding to theregions between the arrows markedL and R. In construct (c), the locationof the dyad is indicated. Sequencesfor each nested set of restriction sitesare shown below the schematics.The positions of key restriction sitesin each construct are illustrated. A,AluI; BH, BsaHI; BJ, BsaJI; BN,BstNI; Br, BsrI; BU, BstUI; Hc,HincII; M, MspI; S, SalI; T, TaqaI. Thenumbers above each construct at theleft and right ends of the hatchedregions indicate the precise locationsof those stretches of sequencewithin the overall 150 bp longsequence (nucleotide 1 is defined asthe left end of the DNA sequence).

used in all of these studies is 150 bp, just slightlylonger than the protected length in the core particle;consequently, multiple positions of the octamer onthe DNA are not anticipated. In addition, we carryout control studies to assess the homogeneity of theproduct particles and to map the actual location(s)of the histone octamers on the DNA.

The three constructs used in our experiments areillustrated in Figure 2. Together, they span the fullrange of locations within the core particle, rangingfrom near the core particle DNA end to theparticle’s dyad axis of symmetry. An importantaspect of these constructs is that, rather thanengineering single sites, we nest together sites formultiple enzymes within a short patch of roughlyone DNA helical turn. While any one site might beaccessible simply because it faces ‘‘out’’ (althoughthis is doubtful, on steric grounds), the other siteswithin that patch will necessarily be protected. Bycomparing apparent equilibrium constants for siteexposure for sites within one patch, we distinguishdynamic exposure of a stretch of DNA fromexposure of a single site that inadvertently faces out.

Another aspect of the design of these DNAconstructs lies in the choice of restriction enzymes.We chose to use restriction enzymes from ther-mophilic organisms, so that we could, if necessary,raise the temperature, with the goal of making the

nucleosomes artificially more ‘‘dynamic’’. Oursubsequent results showed this feature of theexperimental design to be unnecessary, and certainadditional studies were carried out at 37°C.

For the experiments themselves, two parallelreactions were set up in identical solution con-ditions, one for naked DNA, and one forreconstituted core particles. Optimal (E0)s thatallow the reactions to go to near completion on a 5to 60 minute timescale are found by trial and error.Typically, (E0) was 102 to 103-fold lower for thedigestions of naked DNA than for the digestions ofparticles.

Results

Characterization of reconstituted coreparticles

The reconstituted nucleosome core particles wereprepared by dialysis from 2.0 M NaCl and thenpurified by sucrose gradient centrifugation. Theprofile resulting from a typical sucrose gradient isillustrated in Figure 3(a). The reconstituted coreparticles are well-resolved from naked DNA andfrom aggregates, and on re-analysis in sucrosegradients, they appear homogeneous. In otherstudies, we confirmed that they comigrate in


(a) (b)

(c)

Figure 3. Isolation and characterization of reconstituted core particles. (a) Sucrose gradient purification andre-analysis. Core particles are reconstituted by gradual salt dialysis and isolated from naked DNA and othernon-nucleosomal contaminants on 5 to 30% (w/v) sucrose gradients. w, Preparative run of reconstituted core particles;r, naked DNA only; Q, re-analysis of gradient-purified particles. (b) Native gel analysis. W indicates the bottom ofthe loading wells. Lane 1, naked DNA; lanes 2 to 4, purified reconstitutes for constructs (a), (b), and (c), respectively.The isolated core particles show the appropriate mobility shift. For a comparison of the relative mobility of thereconstituted core particles compared to the mobility of naked DNA size standards, see Figure 7. Phosphorimageranalysis of the gel reveals contamination by free DNA and other non-nucleosomal aggregates to be < 1%. (c) Directmapping of nucleosome positioning for nucleosomes reconstituted with construct (a). The sample was digested with0.04 units ml−1 (Worthington) of micrococcal nuclease for 0, 1, 8, 16, or 32 minutes (lanes 1 to 5), then extracted andanalyzed by sequencing gel electrophoresis and autoradiography. Lanes 6, 7, 9 and 10, which are included ashigh-resolution size standards, show G, A, T, and C sequencing lanes, respectively, from sequencing reactions onpGEM3Z (Promega) template DNA using the sequencing primer 5'-gttttcccagtcacgac-3' which was end-labeled with 32Pprior to sequencing. Lanes 8 and 11 reproduce lanes 1 to 5, respectively. The results are consistent with a distributionof positioning of the entire sample of 0–1 bp. No products having positions differing by, e.g. 3 to 5 bp, can be detecteddespite the overexposure of the autoradiogram.


sucrose gradients with authentic chicken erythro-cyte nucleosome core particles (D. S. Scherl andJ. Widom, unpublished results). We used native gelelectrophoresis to examine further the quality of thepurified reconstitutes (Figure 3(b)). The gels revealthe purified particles to have negligible contami-nation by free DNA. The relatively sharp bands andthe absence of resolved multiple species areconsistent with the particles having a uniquepositioning of the histone octamer on the DNA thatis equivalent for all three constructs.

While the native gels suggest that the particles areuniquely positioned, and the absence of additionalDNA makes alternative positions unlikely (Donget al., 1990; Pennings et al., 1991), we neverthelesscarried out studies to map the actual locations of thehistone octamers on the DNA in our reconstitutedparticles. We used micrococcal nuclease in twodifferent procedures to map the actual location ofthe histone octamers on the DNA in the purifiedparticles. In one procedure, particles which werelabeled at both 5' ends with 32P were simplydigested with the nuclease, and the productsanalyzed on sequencing gels. We found thatnuclease digestion reduced the size of the DNAfrom 150 bp to a new resistant length of 147 bp. Anexample of this experiment for construct (a) isshown in Figure 3(c). The fact that the DNA is stilldetected means that the nuclease cleavage occursonly on one end. This result demonstrates thatnucleosome core particle lengths of DNA areprotected in these particles, and it is consistent withthe expected wrapping of the DNA, which placesone end at the anticipated core-particle endposition. If alternative positions had been adopted,leaving a longer end hanging off the particle, shorterprotected lengths would have been detected, yetnone are visible, even on the overexposed auto-radiogram. A different procedure (D. S. Scherl andJ. Widom, unpublished results) used Tfl polymeraseprimer extension to map the sites of cleavage bymicrococcal nuclease; a pair of primers complemen-tary to the top and bottom strands near the middleof the DNA template were used. The observedlengths of the primer extension products (data notshown) confirm the expected positioning and theyrule out the possibility that significant fractions ofthe particles have alternative octamer positions.Finally, as will be discussed further below, many ofthe enzymes used in this study are expected towrap around their DNA target sites. For theseenzymes, no rotational orientation suffices to allowaccess without some sort of site exposure such asthat postulated in this study.

Kinetic assays

Parallel digestions of nucleosomal DNA andnaked DNA were set up in identical solutionconditions. Reactions are initiated by the addition ofenzyme. Aliquots were removed as a function oftime during the reaction and quenched, and theproducts were analyzed on denaturing acrylamide

gels and quantified by phosphorimager. Anexample of such an experiment is shown in Fig-ure 4, which probes a site very near the particle’saxis of dyad symmetry (construct (c)). It is clearfrom the gels themselves that even sites far withinthe nucleosome are accessible to the restrictionenzyme, as evidenced by the digestion productsthat are produced. Quantitative analysis of the gels(Figure 4(d) and data not shown) confirms that thereactions on the core particles can be followed tonear completion, even for these innermost sites:the results that we obtain evidently apply to themajority of the particles present. The results aredescribed by a first-order decay of the substrate, asexpected (equation (7)).

Similar data were obtained with this construct inexperiments at other temperatures and with theother restriction enzymes. And similarly, digestiondata obtained from constructs (a) and (b) revealedthat essentially all of these particles, too, wereaccessible to the restriction enzymes and partici-pated in the reactions.

Equilibrium constants

Equilibrium constants (Kconfeq ) were calculated

from the rates obtained for digestions of nakedDNA and reconstituted core particles (equation(15)) from data such as those in Figure 4(c) and (d).Experiments were carried out over a range oftemperatures, for each restriction enzyme and forthe three different constructs. The results are shownin Figure 5(a) to (c). No systematic temperaturedependence is evident; temperature dependencesare observed, but with both positive and negativeslopes, even for measurements of Kconf

eq made withinsingle patches of DNA. We conclude that the realtemperature dependences are small compared toour experimental error; we therefore calculateaverages of these data, shown in Figure 5(d).

Equilibrium constants for site exposure differsignificantly from zero for positions throughout thenucleosome core particle. Construct (a) probes sitesjust inside the end of the core particle. All threerestriction enzymes yielded comparable values forKconf

eq 11 × 10−2 to 4 × 10−2. These data are consistentwith exposure of a stretch of DNA, rather than anindividual outward facing site.

Construct (b) probes sites 030 to 40 bp in fromthe end. The values obtained for Kconf

eq at these sites,15 × 10−4 to 3 × 10−3, are substantially lower thanthose obtained for sites near the end. We concludethat equilibrium constants for site exposure onnucleosomes are position-dependent, decreasing asone moves inward toward the center of thenucleosome. As observed near the particle ends, thedifferent enzymes probing within this regionyielded similar values for Kconf

eq , again suggestingexposure of a stretch of DNA. Moreover, like otherenzymes which leave blunt ends after cleavage,BstUI is expected to wrap around roughly threequarters of the DNA circumference at its site(Winkler et al., 1993; Cheng et al., 1994); the


Figure 4. Example analysis of construct (c), probing site-exposure near the particle dyad. (a), (b) Denaturingpolyacrylamide gel analysis of the time-course of digestion for construct (c) using the enzyme TaqaI, which cleaves verynear to the axis of dyad symmetry in the reconstituted particles. (a) Naked DNA, digested with TaqaI at 40 units ml−1.(b) purified nucleosome core particles, digested with TaqaI at 10,000 units ml−1. Lanes 1 through 8 are obtained fromsamples removed at 0, 0.5, 1, 2, 4, 8, 12, and 16 minutes for the naked DNA, and at 0, 1, 2, 4, 6, 16, 32, and 64 minutesfor the core particles. In each case, the substrate (150 nt, S) is converted over time to two products (82 nt, P1, and 66 nt,P2; the sizes of S, P1, and P2 expected from the DNA sequence are confirmed on other gels, not shown, in which theirmobilities are compared to the mobilities of size standards. Size standards are not routinely run on the experimentalgels simply to increase the number of timepoints that may be quantified under identical conditions. Alternate lanesof the gel are left empty to optimize the accuracy of the quantification of individual bands.) (c), (d) Quantitative analysisof the time-course of digestion from the data in panels (a) and (b), respectively. The fraction uncut is plotted on a logscale versus time. The superimposed lines represent the results of unweighted least-squares fits to single exponentialdecays.

proximity of additional DNA segments on thenucleosome (Richmond et al., 1984; Arents et al.,1991; Arents & Moudrianakis, 1993) precludes suchbinding, whatever the rotational orientation of thesite, again suggesting that DNA must be exposedoff the surface of the nucleosome prior to bindingand cleavage by BstUI.

Construct (c) probes sites close to and over theparticle dyad axis of symmetry, over the full rangeof rotational positions. It is remarkable thatnon-zero equilibrium constants are readily detectedat these sites as well. In these regions, 10 to 20 folddifferences are detected in the averaged equilibriumconstants measured at closely spaced sites bydifferent enzymes. These may be real differences;alternatively, perhaps the apparent differencesbetween closely spaced sites reflect increasedexperimental error arising as a consequence of thesubstantially decreased Kconf

eq . In any case, theaverage accessibility of sites in these regions (110−5

to 10−4) continues the progressive decreasing trend

for Kconfeq with distance inward from the core particle

end.

Digestions at 37 °C

Kconfeq is, at most, only weakly dependent on

temperature, so we anticipate that similar confor-mational states will obtain at 37°C to those observedat 45°C and higher temperatures. Moreover, as willbe seen in the Discussion, Kconf

eq can also be extractedfrom equilibrium binding studies which have beencarried out by us and others at temperatures of 37°Cand lower, and the results for Kconf

eq obtained in thisway are in good agreement with the results ofFigure 5. Nevertheless, we have taken advantage ofrestriction sites for SalI, HincII, MspI, and AluI thatare present in our constructs to directly test thebehavior at 37°C. The results from two sets ofexperiments with these four enzymes are summar-ized in Table 1.


Figure 5. Summary of measured equilibrium constants for site exposure. (a) to (c) Equilibrium constants weremeasured at positions throughout the core particle, at two or more temperatures in the range 45 to 65°C. The resultsfor constructs (a) to (c) are shown in panels (a) to (c), respectively. R, BstUI; q, TaqaI; R, BsrI; Q, BsaHI; r, BsaJI;r, BstNI. (d) For each enzyme, for each construct, equilibrium constants obtained at varied temperatures (panels (a)to (c)) were averaged; the means and standard deviations are plotted. The approximate locations of each site in thevarious core particle constructs are represented beneath the plot. BU, BstUI; T, TaqaI; Br, BsrI; BJ, BsaJI; BN, BstNI; BH,BsaHI.

The results for SalI and HincII are in good agree-ment with the results at higher temperatures fromconstruct (a) which probe sites just inside from theend of the particle. Similarly, the results for AluI arein reasonable agreement with the results at highertemperatures for TaqaI on construct (b) and BsaJI onconstruct (c), whose sites bracket the locationprobed with AluI. Importantly, the results obtainedwith AluI provide clear evidence that sites well

inside a nucleosome (51 to 54 bp inside from theend of the core particle) have substantial dynamicaccessibility even at 37°C. Like BstUI (above), AluIalso leaves blunt ends after cleavage and hence isexpected to wrap around roughly three quarters ofthe DNA circumference at its site (Winkler et al.,1993; Cheng et al., 1994); again, we infer thatexposure of DNA off the surface of the nucleosomemust precede binding and cleavage by AluI.

Table 1. Equilibrium constants obtained from 37°C dataaCleavage site

(nt from nearest end cMean of cStd. deviationEnzyme of core particle) bKconf

eq log(Kconfeq ) of log(Kconf

eq )

SalI 7, 11 6.4 × 10−2 −1.33 0.52HincII 9, 9 2.6 × 10−2 −1.60 0.11MspI 43, 45 3.1 × 10−7 −6.52 0.07AluI 52 7.1 × 10−3 −2.19 0.26

a Positions of the cleavage sites on both strands, expressed in nucleotides from the nearest end ofthe DNA positioned on the core particle, which includes bp 5 to 150 of the construct DNA sequences.

b Equilibrium constants represent the mean value from two separate experiments.c The uncertainty in Kconf

eq , which is multiplicative in nature, is most naturally represented as the meanand standard deviation of the logarithm of Kconf

eq .


Figure 6. Order of the reaction in (E0). Core particlesreconstituted with construct (a) were digested withincreasing concentrations of TaqaI, and the observed rateconstant determined (see Figure 4 (b) and (d) andMaterials and Methods). The line represents a least-squares fit of the resulting data. The data are welldescribed by this line, which is straight and passesthrough the origin, indicating that the reaction isfirst-order in (E0).

pre-equilibrium limit (limit II), so ratios of cleavagerates yield the desired equilibrium constants Kconf

eq .

Stability of the particles during digestions

It is important that the nucleosomes do not simplydissociate when exposed to the digestion con-ditions. Previous studies revealed that exposure toelevated temperature (50°C) does not lead todetectable changes in nucleosome structure asprobed by hydroxyl radical footprinting (Bashkinet al., 1993); indeed, the positioning of histoneoctamers on the Xenopus 5 S phasing sequence ismaintained to at least 75°C (Bashkin et al., 1993), atemperature substantially greater than that probedin our studies.

Most importantly, our results themselves establishthat instability of the particles prior to or during thereactions does not contribute significantly to theobserved digestion. If dissociation of the particleswere substantial and rapid, then low enzymeconcentrations, comparable to those used for thenaked DNA digestions, should suffice for theparticle digestions. This is contrary to our obser-vations: we find that much greater enzymeconcentrations are required in order to achieve thedigestion of particles on a reasonable timescale.Alternatively, if dissociation were slow, the mechan-ism would approach limiting-case I (equation (9)),and the reactions would be zero-order in (E0)(equation (10)); but we find that the observed rateof the reaction is first-order in (E0), providing formalevidence against this hypothesis. A third possibility,that dissociation occurs on an intermediatetimescale, cannot apply to all of our results, sinceour measured kobs span four orders of magnitude.

We carried out additional control experiments totest the particle’s stability directly. Reconstituteswere carried through mock digestions (in digestionbuffer but without enzyme) for 15 minutes at 0, 37,or 65°C, then analyzed by native gel electrophoresis.The results are shown in Figure 7. Lane 3 shows theoriginal particles to be free from contaminatingnaked DNA, as expected. Lanes 4 to 6 reveal thepresence of a small amount of naked DNA (02% ofthe total), evidently caused by dilution of theparticles into the restriction enzyme digestionbuffer. There is no apparent effect of temperatureover this range (compare lanes 4 to 6). Importantly,this naked DNA will not significantly affect thekinetic analysis. Its absolute amount is negligible,given our likely experimental error. Also, as pointedout above, naked DNA is digested 0102 to 105 timesmore rapidly than is the DNA in particles; hadenzyme been added to these samples in amountsappropriate for digestion of the particles, thecontaminating naked DNA would have beendigested to completion within the mixing time, andwould not contribute to the measured first-orderdigestion of the bulk of the material.

Remarkably, for construct (a), in which only smallfragments of DNA are cleaved from the end, theparticles remain intact even after digestion essen-

MspI recognizes a site positioned 43 to 46 bp fromthe end of the core particle. The results with thisenzyme reveal accessibility at that site, also, at 37°C,but with a significantly lower Kconf

eq than is found forsites both closer to the particle dyad and further outtoward the ends at other temperatures. Thisobservation is discussed further below.

Order of the reactions in (E 0)

Our analysis hinges on the system obeyinglimiting case II of the kinetics. It was thereforeimportant to test the dependence of the observedrates of cleavage, kobs, on the concentration ofenzyme added, (E0). For each restriction enzyme forall three constructs, we observed qualitatively thatthe apparent rate of the reaction, kobs, dependedapproximately linearly on the total concentration ofenzyme added, (E0), suggesting that the reactionsmight be first-order in (E0). We examined thedependence in more detail for one of the sites.Figure 6 shows the results of quantitative measure-ment of kobs as a function of (E0) for digestions ofconstruct (a) reconstitutes with the restrictionenzyme TaqaI. The linearity of the plot, togetherwith the fact that the line passes through the origin,demonstrates that the digestions are first order in[TaqaI]. An alternative way of analyzing these datais to determine the value of the exponent that relateskobs and (E0). For any particular small range in (E0),we may write

kobs = a1(E0)a2. (16)

The value of a2 varies between the extreme valuesof 0 and 1, as the mechanism progresses fromlimiting case I to limiting case II, or, alternatively, asS is titrated with increasing (E0). We determined a2

by plotting ln(kobs) versus ln([E0]), and obtained theslope a2 = 1.07. These analyses provide firmevidence that the reactions take place in the rapid


Figure 7. Stability of reconstituted core particles duringrestriction digests. Core particles reconstituted withconstruct (a) were subjected to mock digestions or actualrestriction digestion and then analyzed by nativepolyacrylamide gel electrophoresis. Lanes 1 and 9: 100 bpladder used as size standards. Lane 2: naked DNA. Lane3: reconstitutes after initial purification, with noadditional treatment. Lanes 4 to 6: mock digestions;reconstitutes were incubated in TaqaI digestion buffer for15 minutes at 0°C, 37°C, or 65°C, then analyzed on the gel.Lanes 7 and 8: actual digestions; reconstitutes weredigested with TaqaI for 15 minutes at 65°C, and then eithercooled on ice and loaded directly on the gel (lane 7), orcooled on ice, quenched with 40 mM EDTA, and thenloaded on the gel (lane 8). Although small amounts (2%)of DNA are released upon exposure of the particles tobuffer (independent of the temperature over the range 0to 65°C), the great majority of core particles remain asintact core particles even after digestion with restrictionenzyme, which cleaves a short fragment from one end (theshort fragment runs off the bottom of the gel). When thereactions are quenched with concentrated EDTA (lane 8),some naked DNA is released from the particles; itsincreased mobility relative to that of the starting DNAshows it to have been cleaved, as expected. This tracenaked DNA, induced by quenching the digestions withEDTA, is of no consequence: in our kinetic analysis, all ofthe DNA in the particles is extracted prior to being runon denaturing gels.

those used in the determinations of Kconfeq , and the

restriction enzyme concentrations corresponded tothe high end of the concentration range used in thedeterminations of Kconf

eq . No traces of proteolysis,which would be expected to produce definite newbands at somewhat lower molecular mass (vanHolde, 1989; Wassarman & Kornberg, 1989), couldbe detected. We conclude that proteolytic actiondoes not contribute to the DNA site exposuredetected in this study.

Possible nucleosome sliding

It is possible that nucleosome sliding (Spadaforaet al., 1979; van Holde, 1989; Meersseman et al.,1992) might be responsible for the observed siteexposure. This is not a concern per se, since slidingmight be a means of guaranteeing that regulatoryproteins would have access to their DNA targetsequences. But in any case, sliding is unexpected inthe present studies because of the absence of anyunoccupied DNA for the octamer to slide onto. Andour results suggest that nucleosome sliding is notthe mechanism of site exposure in these studies.The data in Figure 4 show that even sites at theparticle dyad axis are readily exposed to restrictionenzymes; hence sliding, if it were responsible, mustbe of a very great magnitude (at least 70 to 80 bp).Particles in which the octamers had repositioned togreat but varying extents would be expected toreveal a range of mobilities on native acrylamidegels (Pennings et al., 1991), yet Figure 7 reveals nosuch behavior. We tentatively conclude that slidingdoes not account for the site exposure detected inthe present studies.

Possibility that added restriction enzymesdrive or catalyze the site-exposure process

One concern in these studies is raised by themechanism itself (equation (5a)): if (E0) is suffi-ciently high, binding of the enzyme will drive thesystem toward site exposure, directly altering theapparent equilibrium constants Kconf

eq . However, ourobservation of the exponent a2 = 1.07 (equation (16))provides formal proof that our experiments arecarried out in the low (E0) limit, so that thispotential concern does not apply to our results.That this is true is also demonstrated in anotherway: the equilibrium constants that we measure areexplicitly independent of (E0). By contrast, if wewere in the high (E0) limit, the exponent a2 wouldapproach the value 0, and the cleavage rate wouldapproach that for naked DNA, or, ultimately, itwould approach the rate constant for site exposure,k12. If we were in an intermediate (E0) range, theexponent would have a value intermediate between0 and 1, and the measured apparent equilibriumconstant would depend explicitly on (E0), allcontrary to our experimental observations. Weconclude that the restriction enzymes do not drivethe site exposure process at the concentrations usedin our studies.

tially to completion (lane 7). No naked DNA isdetected, and the majority of the label migrates asa band with slightly more rapid mobility than thatof the original particles. A trace amount of materialhaving lower than native mobility is also apparent.

We conclude from these studies that essentiallyall of the particles remain intact when exposed torestriction enzyme buffer conditions and elevatedtemperature, and that the site exposure detectedand quantified in our experiments occurs withoutcomplete dissociation of the DNA.

Tests for contaminating protease activity

The possibility also exists that the DNA siteexposure detected in this study could be facilitatedby proteases which may contaminate the restrictionenzymes or the histone octamer preparations. Toassess this possibility, reconstituted nucleosomecore particles were incubated with TaqaI, BstUI, orBsrI, at 65°C for 60 minutes (our most extensivedigestion conditions), and the products analyzed bySDS/gel electrophoresis and Coomassie staining.The core particle concentration was comparable to


We also tested the possibility that non-specificDNA binding by the restriction enzymes could beresponsible for the observed site exposure, eventhough the kinetic argument outlined aboveprovides formal proof that non-specific binding isnot a factor in our studies. We carried out twoparallel digestions on reconstitutes. To onesample we added an enzyme (TaqaI) which has asite in the particle; to the other sample, we addedboth TaqaI and a comparable concentration ofanother restriction enzyme (BsmAI) for whichthere were no cleavage sites within that construct.Both enzymes were used at concentrations nearthe upper end of those used for any of theexperiments in this study, and, in particular, nearthe upper end of the (E0)-dependence data ofFigure 6. We obtained identical rates of digestion,and hence identical apparent equilibrium con-stants, for the two samples. We conclude thatnon-specific binding by the restriction enzymes isnot involved in the mechanism of site exposure inour studies.

Another formal possibility was that interaction ofrestriction enzyme with DNA on the surface of thenucleosome may influence or facilitate the sub-sequent dissociation of that DNA off the histonesurface. This possibility is excluded by our findingthat the equilibrium constants that we measure areexplicitly independent of (E0).

Other assumptions in the kinetic analysis

The results presented above demonstrate that thekinetics are first-order in both (D) and (E0) and thatthe reaction obeys the low (E0) limit of limiting-caseII. Two additional assumptions simplify ouranalysis. One assumption is that (S) � Km. Thiscondition is satisfied by construction, for both thenaked DNA and the particles. Typical Kms forrestriction enzymes are 01 to 10 nM. Our nakedDNA digestions are set up with (S) � 1 nM. For theparticle digestions, the total concentration of sites,including sites statistically present in the particlesthat contain carrier DNA, may approach several nM;but these sites are exposed with probabilities of 10−2

or less (Figure 5), so that again (S) � Km. Forparticles, the condition (S) � Km is required forlimit II to apply, and our demonstration that limit IIdoes apply establishes the validity of the assump-tion. Another assumption is that Kconf

eq � 1; thisassumption simplifies the analysis but is notessential (except as required to keep (S) � Km evenfor the measurements with particles). This result issubstantiated by the measured values for Kconf

eq thatwe obtain (Figure 5). The final important assump-tions in our analysis are that both S and ES(equations (5a), (5b)) are in steady state. The rapidpre-equilibrium, which is demonstrated by theobservation that the reactions are first-order in both(D) and (E0), together with the experimentallydetermined Kconf

eq � 1, are sufficient conditions forthe reaction to obey steady state behavior in S. Wehave not explicitly tested for steady state behavior

of ES, but we note that this is a general property ofenzyme-catalyzed reactions.

Discussion

The most important conclusion from this study isthat the site exposure which we postulated doesoccur, with substantial values for Kconf

eq . Thisdynamic property intrinsic to nucleosomes pro-vides a general mechanism guaranteeing thatregulatory proteins may have access to their DNAtarget sequences. Our data are consistent with, butdo not prove, the hypothesis that the mechanism ofsite exposure is that illustrated in Figure 1.

The binding of individual regulatory proteinsmade possible by site exposure is expected to occurin accord with equation (3). The occupancy of a site,the fraction of equivalent sites in a population ofcells occupied at any instant, or the fraction of timeduring which any one particular site is occupied,will depend on the location of the site within thenucleosome, the intrinsic affinity of the regulatoryprotein for naked DNA, and the free concentrationof the regulatory protein. No matter where a site iswithin a nucleosome, and even if the correspondingbinding protein has limited affinity or is present invery low free concentrations, the sites will beoccupied with a probability greater than zero and,averaged over time, any particular cell will have thatsite occupied a non-zero fraction of the time.

In some or many cases, a greater level ofoccupancy at a particular site may be required thancan be provided by the binding of a single proteinin accord with equation (3). The site exposuremechanism provides two additional routes throughwhich the occupancy may be increased. (1) Bindingof proteins to multiple sites within the samenucleosome can occur synergistically (coopera-tively), even if the proteins do not ordinarilyinteract, substantially increasing the occupancy byeach protein. (2) A regulatory protein that binds bythe site exposure mechanism may recruit additionalproteins, which may subsequently act to displacethe histone octamer. These ideas are discussed inmore detail, below.

Mechanism of site exposure

The simplest physical picture for the mechanismof site exposure is one in which DNA ‘‘unpeels’’ ina stepwise fashion starting from the end of the coreparticle. In this model, all sites may be reached byunpeeling half or less of the core particle DNA,allowing the site exposure process to be non-disso-ciative. A DNA molecule lying on a surfacenaturally makes contacts with surface residuesevery helical turn, when the backbone is oriented sothat the minor groove faces in toward the surface.If all such contact sites in the nucleosomerepresented equivalent protein–DNA binding sites,the free energy of site exposure would increase insteps with every additional 010 bp of DNAunpeeled, and there would be a corresponding


stepwise decrease in Kconfeq . This is consistent with the

majority of our data, which show that Kconfeq does

appear to decrease systematically (although notmonotonically) with increasing distance from theend in toward the center.

We emphasize, however, that other, quitedifferent, mechanisms for site exposure are notexcluded by our data. This is an important area forfurther analysis because, as will be discussedbelow, it bears directly on a new mechanism forsynergy (cooperativity) in the binding of multipleregulatory proteins to sites within the samenucleosome.

In the context of the unpeeling mechanism, theprimary determinant of Kconf

eq is the translationallocation of a target site within the core particle,since, in this model, exposure of the whole DNAregion precedes binding. Rotational positioning alsoplays a role, however, because the length of DNAthat must be unpeeled to allow unhindered accessof a protein to a nucleosomal target site will dependon the rotational setting of the site, the size andshape of the protein, and possible DNA bending.

Relation to chromatin structure in vivo

Chromatin in vivo differs in significant ways fromthe model system investigated in this study. One keydifference concerns histone H1, which is astoichiometric component of most nucleosomesin vivo. Histone H1 is sometimes thought to seal twoturns of DNA on the core particle, which wouldprevent our site exposure mechanism. However,studies of chromatin in vitro reveal that histone H1is in free exchange in physiological conditions(Caron & Thomas, 1981). Consequently, the pres-ence of histone H1 in vivo is likely to affect thequantitative values of Kconf

eq , but is not expected toalter the qualitative nature of the site exposureprocess revealed in this study.

Another significant difference between ourmodel system and chromatin in vivo arises from thefact that chromatin in vivo exists in very long chainsthat are organized into higher order structures. Ifsuch higher order structures were inert, theproposed site exposure mechanism could not occur.But physical studies of chromatin fragments in vitrosuggest that higher order chromatin structures areonly marginally stable in physiological conditions(Widom, 1986), and that the compact state is indynamic equilibrium with an extended nucleosomefilament state (Widom, 1989). Thus, it seems likelythat higher order chromatin structure, like thepresence of histone H1, may alter quantitative butnot qualitative aspects of our conclusions.

The present studies are carried out in non-physio-logical solution conditions, including 10 mM Mg2+

and 50 or 100 mM NaCl. These conditions arerequirements of our assay. Chromatin is consideredto be relatively insensitive to specific ion effects(van Holde, 1989; Widom, 1989), but the polyelec-trolyte properties of DNA cause the affinities ofprotein–nucleic acid interactions, and hence the

measured values of Kconfeq , to vary somewhat with the

solution conditions.The absence of a clear temperature dependence in

our results suggests that the elevated temperaturesused in many of the measurements in this study donot greatly affect the measured values of Kconf

eq ,consistent with previous hydroxyl radical footprint-ing studies which showed the basic nucleosomalorganization and positioning to be stable to at least75°C (Bashkin et al., 1993). Importantly, our nativegel analysis revealed that the particles remain intacteven after prolonged incubation at the highesttemperature studied, and our data for Kconf

eq obtainedat 37°C are in reasonable agreement with the dataobtained at higher temperatures.

We conclude that non-physiological aspects of ourmodel studies will cause our measured values ofKconf

eq to differ quantitatively from those that obtainin vivo, but these differences are not expected tochange the qualitative nature of the site exposuremechanism or its consequences.

Relation to earlier studies

Earlier studies which are consistent with our newresults were carried out by Linxweiler & Horz(1984). In that study, only small extents of digestionwere obtained and a possible requirement for siteexposure was not discussed, hence equilibriumconstants for site exposure were not provided. Theauthors estimated that the rate of cleavage at thedyad was greater than 1000× slower than for nakedDNA, which is in accord with our observation ofKconf

eq 110−4–10−5. For another site located a shortdistance in from the end of a nucleosome coreparticle, those investigators detected cleavage at arate 150× slower than for naked DNA, in goodagreement with our measured Kconf

eq 11 × 10−2 to4 × 10−2.

Relation to equilibrium binding studies

The site exposure mechanism revealed in thisstudy provides a simple and definite mechanismwith which previous studies in the literature maybe analyzed. Several previous studies have exam-ined the ability of a variety of regulatory proteinsto bind to nucleosomal target sequences. However,in the absence of a model for the binding process,the meaning of the results is unclear. The presentwork provides a natural explanation for this earlierwork. We suggest that the observed binding occursby the site exposure mechanism (Figure 1(a) andequation (1a)). In this case, we predict that the netfree energy of binding will be the sum of the freeenergy of binding to naked DNA and the freeenergy of the required nucleosome conformationaltransition; similarly, we predict that the effective, orapparent, dissociation constant for binding will begiven by the dissociation constant for binding tonaked DNA divided by the equilibrium constant forsite exposure measured in the present study(equation (3)).


Table 2. Comparison of measured and predicted dissociation constantsApproximate Kd Location of site Approximate Kd Predicted Kd

Protein for naked DNA (bp from end) for core particle for core particle

GAL4-AH 3 × 10−9 (1) 21 2 × 10−8a (2) 3 × 10−7

3 × 10−9 (1) 32 1 × 10−6 (1) 3 × 10−6

3 × 10−9 (1) 43 3 × 10−7 (1) 3 × 10−6

1.2 × 10−9 (3) 160 2.4 × 10−7 (3) 1.2 × 10−5

3 × 10−9 (1) 73 3 × 10−5a (4) 3 × 10−5

TBP 1 × 10−9 (5) 73 >2 × 10−6 (5) 1 × 10−5

MerR 2.8 × 10−11 (6) 15 1.5 × 10−9 (6) 2.8 × 10−9

Max 5.3 × 10−10 (7) 173 2.5 × 10−6 (7) 5.3 × 10−6

Mycb 1.4 × 10−9 (7) 173 >2.1 × 10−6 (7) 1.4 × 10−5

Mycb/Max 1.5 × 10−9 (7) 173 >3 × 10−6 (7) 1.5 × 10−5

Mycb–GCN4 1 × 10−9 (7) 073 1.1 × 10−7 (7) 1 × 10−5

GR 3 × 10−10 (8) 43 7 × 10−10 (8) 3 × 10−7

Binding constants measured for several transcription factors to reconstituted mononucleosomes have been compiledfrom the literature and are presented here. Data taken from the following references: (1) Cote et al. (1994); (2)Vetesse-Dadey et al. (1994); (3) Taylor et al. (1991); (4) Kwon et al. (1994); (5) Imbalzano et al. (1994); (6), J.W. unpublishedresults; (7) Wechsler et al. (1994); (8) Perlmann (1992).

a Values which were calculated by us from data within each paper; all other values were reported by the authors.b Myc in this Table refers to a truncated form of the c-Myc protein. Myc/Max is a heterodimer of truncated c-Myc

and Max; Myc-GCN4 is a hybrid protein. Binding data for TBP taken from experiments which include TFIIA in thebinding reactions. For Gal4-AH (Taylor et al., 1991) and Max (Wechsler et al., 1994), the rotational positioning of sitesis found not to influence the apparent Kd.

We have collected quantitative or semi-quantitat-ive data available in the literature (together with oneunpublished result from our own laboratory) to testthese conclusions. This analysis is complicated byambiguities or uncertainties in the nucleosomallocations of the target sequences and in themeasured affinities. For each case, we compare theapproximate apparent dissociation constant forbinding to a nucleosomal target sequence, to anapparent dissociation constant that we predict usingequation (3). The predictions require a measureddissociation constant for binding to a naked DNAtarget site, which we take from the literature; andthey require an estimate of Kconf

eq which we take fromthe results of the present study, making the bestestimates that we can about the appropriatenucleosomal positions of the target sequences.Variations in the ionic conditions from one study toanother, and differences in the conditions betweenthose studies and the present study, will alsocontribute to discrepancies in this analysis.

The results of this analysis are summarized inTable 2. The deviations that do exist in thiscomparison must be considered relative to the 104 to105-fold differences in affinity that may obtainbetween a naked DNA site and a site positionednear the nucleosome dyad. Given this benchmark,we consider that, in general, there is goodagreement between the predicted and the measuredapparent dissociation constants. We conclude thatthe site exposure mechanism and equations (2) and(3) provide a framework for the analysis andinterpretation of these binding studies.

Apparent exceptions andunresolved questions

These binding studies also suggest certainapparent exceptions to our ideas, and one unre-

solved question. Of the apparent exceptions, webelieve that certain of them are not exceptions at all,while others may not be failures of the model per se,but rather may represent the consequences of effectsthat are not included in the limiting case model ofFigure 1.

One apparent inconsistency between publishedbinding studies and the predictions of the siteexposure model pertains to the glucocorticoidreceptor protein (GR; Perlmann, 1992; Li & Wrange,1993). GR evidently binds to a site near thenucleosome dyad with a much greater affinity thanwould be predicted if it were necessary for GR topay the corresponding free energy cost of siteexposure. In those studies, the GR sites wererotationally oriented on positioned nucleosomesin vitro, such that the sites face outward. The DNAbinding domains of GR dimers are small and chieflycontact one face of the DNA (Luisi et al., 1991). It isplausible that GR may bind to nucleosomal targetsites without a need for further site exposure, whenthese sites face out. In that case, the apparent Kd forGR binding to a nucleosomal site would approxi-mate that for naked DNA, as observed. It is criticalto appreciate, however, that finite free energies ofpositioning mean that, in vivo, some nucleosomesmay have alternate positions such that GR sites areburied (see Introduction). Our new results suggestthat GR would be able to bind even if its site wasburied, but binding in such cases would occur withsubstantially reduced affinity.

Another set of possible inconsistencies seem notto be inconsistencies at all. The heat shocktranscription factor (HSF) is reported as beingunable to bind to a nucleosomal target site (Tayloret al., 1991). However, only HSF concentrations upto 1102× (perhaps 103 × ) higher than Knaked DNA

d wereinvestigated. The HSF sites were placed near thenucleosome dyad, so we anticipate that Kapparent

d will


be 1104 to 105 times greater than Knaked DNAd . Higher

HSF concentrations must be investigated before onecan safely conclude that binding cannotoccur. Interpretation of studies with HSF is furthercomplicated by a trimert hexamer equilibriumthat is coupled to DNA binding. Similarly, whileMax homodimers are able to bind to nucleosomaltargets, c-Myc homodimers and c-Myc/Max het-erodimers are reported to be unable to do this(Wechsler et al., 1994). However, as for HSF, thoseexperiments do not extend to sufficiently highprotein concentrations, and the results obtained arein accord with expectation based on the Kd valuesfor naked DNA and our estimates for Kconf

eq . Indeed,for c-Myc/Max, trace binding is detected, in accordwith [c-Myc/Max] � Kapparent

d . Moreover, values forKnaked DNA

d are in general difficult to measureaccurately (and the same applies to our Kconf

eq ), hencethese studies may not be probing as close to Kapparent

d

as anticipated; and for systems approaching Kapparentd ,

the occupancy of a site at equilibrium is a strongfunction of the concentration.

The present analysis has emphasized transla-tional settings, but, for the case of TATA-bindingprotein (TBP) (Imbalzano et al., 1994), the ability tobind to a nucleosomal target site (in the presence ofTFIIA, SWI/SNF, and ATP) is found to depend onthe rotational orientation of the site. We emphasizetwo important points. First, the rotational orien-tation of a site is expected in general to be explicitlyimportant, simply because proteins occupy volume,and therefore (in the context of our unpeelingpicture) the length of DNA that must be exposed inorder to allow binding will depend on the rotationalsetting of a binding site and the physical size andshape of the protein that needs to bind there. Sitesthat face ‘‘inward’’, and proteins having larger sizesor particular shapes, may require that more DNA beunpeeled in order for binding to be allowed. Thisextra unpeeling comes at greater free energy costand leads to an increase in Kapparent

d . These effects arepresumably present in our own measurementsusing the restriction enzymes. Second, in the case ofTBP, the authors make the plausible suggestion that,for certain rotational settings, the TBP-inducedDNA distortion will be greatly hindered by theadjacent histone surface. This is not a failure of ourmodel: rather, it is a clear example of an additionaleffect that will be important in many cases; inparticular, whenever binding of a protein changesthe bend of DNA, which is a frequent occurrence.

For the case of Myc–GCN4 homodimers, thereappears to be a discrepancy (in the application ofour model) compared to the results for Maxhomodimers binding to the same site (Wechsleret al., 1994): organization of the site in a nucleosomenear the nucleosomal dyad suppresses the affinityof Max homodimers by 1104× in accord with ourexpectations (Table 2). But binding of Myc–GCN4fusion protein homodimers to the same site issuppressed by only 1102×. Why can Myc–GCN4bind with significantly higher affinity? Threepossible explanations (in the context of our

unpeeling picture) are as follows. (1) Perhaps(Myc–GCN4)2 is smaller or has a more favorableshape than does (Max)2, such that less DNA needsto be unpeeled. (2) Perhaps there are differences infactor-induced DNA bending, so that the bendingresulting from Myc–GCN4 is accommodated in theparticle with lower free energy cost. (3) Perhapsthe Myc–GCN4 has a favorable free energy ofoligomerization and multiple molecules are bindingto DNA, in which case the experiment needs to beanalyzed in the context of the multi-site cooperativebinding model discussed below. Some observationsdiscussed by the authors supports this latterinterpretation (Wechsler et al., 1994).

The results of the present study also raise aninteresting unresolved question concerning thestability of the nucleosome core particle. Theproblem arises from the mechanism that weenvision for site exposure, which is that internalsites are reached by unpeeling from one end. If sitesnear the nucleosome dyad are exposed withprobability (Kconf

eq ) equal to 10−4 to 10−5 by thismechanism, then, with the square of this prob-ability, both DNA ends might be expected tosimultaneously unpeel into the dyad, leading todissociation. While the timescale of this hypotheti-cal process is not known, its quite moderateprobability suggests a fundamental problem fornucleosome stability. Perhaps the unpeeling mech-anism of exposure is wrong or misleading; orperhaps the affinity of DNA segments for thehistone octamer depends on whether DNA at theother end of the core particle is bound or exposedat any moment. Some experimental and theoreticalstudies that bear on this important question havebeen carried out (Yager & van Holde, 1984; Yageret al., 1989; Marky & Manning, 1991; 1995), andfurther studies are needed.

Finally, among all 13 sites that we probed usingten different enzymes, one site (MspI, in construct(b)) had a substantially lower value of Kconf

eq than didall of the others, despite being flanked on either sideby sites having higher values of Kconf

eq . With theexception of this one site, there appears to be aprogressive decrease in site exposure from the endof the core particle in toward the center. It remainsto be seen whether this represents a real break inthe otherwise consistent trend in the translationaldependence to Kconf

eq . The explanations given abovefor differences in transcription factor binding applyequally to restriction enzymes, and one or more ofthem may be operative in this case.

New roles for nucleosome positioning,posttranslational modifications of histones,and particular histone variants

The present study suggests an important newrole for the forces and principles that together affectthe statistical and time-averaged positioning ofnucleosomes along the genome (Yao et al., 1993). Theanalysis outlined in the Introduction leads one toconclude that static and perfect positioning, which


Figure 8. Model for cooperative (synergistic) binding ofmultiple regulatory proteins. The model depicts ahypothetical case in which the DNA of a particularnucleosome has sites for two sequence-specific DNA-binding proteins, X and Y; X and Y may be two differentmolecules of the same protein, or two entirely differentproteins. The binding of X and Y is linked in athermodynamic cycle; each facilitates the binding of theother, with no special requirement for additionalprotein–protein contacts or other specialized properties.

illustrated in Figure 8. The net free energy changeis given by

DG0net = DG0

conf + DG0X, naked DNA + DG0

Y, naked DNA, (17)

where DG0conf is the free energy of the conformational

change required to allow binding of both X and Y;DG0

X, naked DNA and DG0Y, naked DNA are the free energies for

binding of X and Y, respectively, to naked DNA. Inthis illustration, binding of protein X may take placewith no further conformational transition onceprotein Y has bound; hence, binding of Y increasesthe apparent affinity of X for its nucleosomal targetsite. Conversely, the ability of X to bind facilitatesthe binding of Y, since at least some of the final costin DG0

conf is already paid. (Note that the two bindingevents are linked in a thermodynamic cycle.) Theimportant conclusion is that X and Y may actcooperatively (synergistically) even if they do nottouch: the binding of one protein radically alters thebinding ability of the other. No special propertiesare required of X or Y: they need only bind DNAfor this cooperativity to be manifested. X and Y maybe two different proteins, or they may be twomolecules of the same protein. One example of thisphenomenon in the literature may be the synergisticeffects of multiple GAL4 binding sites within asingle nucleosome (Taylor et al., 1991). This ideaprovides a natural explanation for the clustering ofregulatory protein binding sites in eukaryoticgenomes.

This synergy (cooperativity) is a necessaryconsequence of the site exposure mechanism if, andonly if, site exposure occurs simultaneously atmultiple sites. If the site exposure process somehowoperates in such a way as to expose individual siteswhile even closely positioned flanking sites are keptoccluded, then cooperativity would not be ob-served.

Mechanisms for active invasion

Existing ideas on active invasion have twolimitations: there is a lack of definite mechanismswhich can be tested experimentally and thereremains the underlying question of how themolecules know which nucleosomes are to beactively invaded. Our site exposure mechanismprovides a framework for analysis of the proposedphenomenon of active invasion. We distinguishthree different classes of models in which someprotein factor ‘‘A’’, having a capacity of activeinvasion, may facilitate the binding or action of aregulatory protein. Several researchers have re-cently reported that certain proteins or proteincomplexes are able to facilitate the binding ofregulatory proteins to nucleosomal target se-quences in an ATP-dependent manner (Cote et al.,1994; Imbalzano et al., 1994; Kwon et al., 1994; Pazinet al., 1994; Tsukiyama et al., 1994). The requirementfor ATP is strongly suggestive of active invasion. Atthis time, however, there is not enough additionalinformation available to relate these observations tothe specific mechanisms outlined here.

is often implied, is unlikely to occur. Nevertheless,nucleosomes do occur with substantial statisticaloccupancies at particular locations (Simpson, 1991),and the present study reveals that such positioningcauses the effective dissociation constant for bindingby regulatory proteins to vary over several orders ofmagnitude. In this way, even very modest forces,such as particular DNA sequence preferencesinherent to histone octamers, which affect thestatistical positioning of nucleosomes but which arefar too small to confer perfectly precise positioning,nevertheless may have substantial regulatory conse-quence.

The site exposure mechanism also suggests anatural way that posttranslational modifications ofthe histones or the presence of particular histonevariants (van Holde, 1989; Wassarman & Kornberg,1989) could be coupled to gene regulation. It isplausible that certain posttranslational modifi-cations of the histone octamer or the presence ofcertain histone variants may alter the effective rateconstants or the dissociation constant for regulatoryprotein binding. These may be considered tobe mechanisms of active invasion (see below).Modifications to histone H1 (or the presence ofparticular H1 variants) that alter its binding affinityto the nucleosome core may have analogousconsequences.

Cooperative binding of regulatory proteinswithout protein–protein contacts

The site exposure mechanism leads to asurprising possible synergy or cooperativity inthe binding of multiple regulatory proteins tosites on a single nucleosome. Such a process is


Model I: nucleosome displacement

In this model, the site-exposure mechanism(equation (1a)) allows a sequence-specific regulat-ory protein R to bind at its recognition site in accordwith equation (3). Even though the occupancyobtained by R alone may be modest, R may recruita protein or protein complex A, which acts todisplace the histone octamer, leading to the bindingof additional proteins and assembly of a long-livedcomplex. This mechanism solves the problem ofhow A identifies which nucleosome to invade, andit allows for R having profound actions even if itsfree concentration is quite low compared to Kapparent

d

(equation (3)).

Model II: catalyzing site exposure

In this model, factor A acts by catalyzing thesite-exposure process, so that the overall process isdescribed by mechanisms such as equations (18a) or(18b):

N + AF NAFk12

k21S + A + RF

k23

k32SR (18a)

N + AF NAF N' + AFk12

k21S + RF

k23

k32SR (18b)

In these schemes, A effects active invasioncatalytically, increasing both rate constants k12 andk21 for interconversion of N and S, such that Kapparent

d

remains unchanged. For example, this is oneplausible consequence of posttranslational modifi-cation of the histones, yielding N' (equation (18b)).This form of active invasion will be significant onlyif k12 or k21 are rate limiting and if the complex SRis kinetically stable; whether this situation obtainsin vivo or in vitro remains to be explored.

Model III: driving site exposure

In model III, factor A acts to drive the siteexposure process for the binding of R. Rather thancatalyzing site exposure, as in model II, A maychange the two rate constants k12 and k21 unequally,such that Kapparent

d for subsequent binding of R isdecreased (i.e. the affinity for R is increased).

If A binds DNA and remains in the complex, thisform of active invasion is an example of thecooperative (synergistic) binding discussed above(equation (17) and Figure 8). This may be referredto as active invasion, but such terminology obscuresthe underlying mechanism. It is the dynamicactivity of the nucleosome itself that makes thismechanism possible; any protein that binds DNAhas the capacity of active invasion in this sense.

Alternatively, A could bind to the histones andremain in the complex,

N + AF NAFk12

k21AS + RF

k23

k32ASR. (19a)

In this scheme, A drives site exposure by changingKapparent

d , but by binding to the histones rather than toDNA, distinguishing this mechanism from thecooperative binding of equation (17) and Figure 8.

In another model of this class (19b), A could againbe an enzyme that catalyzes posttranslationalmodifications of the histones as in mechanism (18b),but in this case, with the result of changing the tworate constants k12 and k21 unequally, such that Kapparent

d

for binding of R is decreased. In another example,in vivo, conversion of N to N' could represent theenzymatic removal of histone H1.

N + AF NAF N' + AFk12

k21S + RF

k23

k32SR (19b)

In a rather different mechanism for driving siteexposure, A binds DNA, but with a mechanism forsubsequently removing it from the complex,perhaps by changing A’s state of posttranslationalmodification, yielding *A.

NFk12

k21S1 + AFAS2 + RFASRF

*ASRF SR + *A (19c)

S1, S2, and S represent differing states of thenucleosome, with only state S being suitable forbinding by R. This mechanism is significant only ifthe complex SR is kinetically stable. In one extremeexample of this model, the histone octamer may beentirely displaced from the DNA; note, though thatA has acted prior to the binding of R, in contrast tothe mechanism in model I.

Relation to other dynamic propertiesof chromatin

Finally, we note that our site exposure mechanismmay play a role in other dynamic processes ofchromatin. The site exposure process detected hereprovides a mechanism for elongation of RNA orDNA polymerase through chromatin: perhapspolymerases advance through a nucleosome’s DNAduring moments when DNA segments are releasedfrom the surface of the octamer (Kornberg & Lorch,1992). We further postulate that the site exposuremechanism may play a role in nucleosome mobility(Spadafora et al., 1979; van Holde, 1989; Meersse-man et al., 1992), perhaps representing a first kineticstep.

Conclusion

The present studies with restriction enzymesreveal the existence of a mechanism for siteexposure that is intrinsic to nucleosomes. Theresults imply that any protein that binds DNA hasthe ability to bind to a nucleosomal target sequence.In particular, there is no need to invoke mysteriousproperties that are unique to transcription factors,although the quantitative value of Kapparent

d maydepend on properties particular to each protein,such as its size and shape, and DNA bending, aswell as on the rotational and translational positionsof the binding sites. The idea of site exposurepostulated here and supported by the experimentalresults provides one answer to an importantquestion, namely, what principle guarantees that


regulatory proteins may have access to their targetsites in chromatin? Previously, there were nosatisfactory answers to this. The site exposuremechanism allows for cooperativity or synergism inthe binding of two or more proteins to sites withina nucleosome, even if these proteins do not toucheach other. Finally, the site exposure mechanismprovides a conceptual framework for an analysis ofactive invasion.

Materials and Methods

Preparation of DNA constructs

DNA constructs were prepared by polymerase chainreaction (PCR) using the Simpson phasing sequence (fromthe 5 S RNA gene of sea urchin; Simpson & Stafford,1983). PCR primers complementary to the two ends of thedesired region of the phasing sequence (nucleotides 14 to163; Simpson & Stafford, 1983) were used; they includedspecific base changes to produce the desired restrictionsites. Six oligonucleotides were purchased to generatefour constructs (nucleotide changes capitalized): LE28,aacttccagggatttataagccgatgac; LE36, aacttGAagggatttataa-gccgatCacgtcataac; RE36, accgCGTCGACCAGtgcttgacttc-ggtgatcgga; RE64, aaccgagctctatgctgcttgacttcACGCGGT-GACCTCGACcTggtatattcagcatggtatg; RE88, aaccgagcccta-tgctgcgcgactCcAgtgatcggacgagaaccggtGCattcaCcCtggtat-agtcgACgTctcttgcttgatgTTa and RE19, aaccgagccctatgct-gcg. For constructs (a) and (b), the template for PCRamplification was the 256 bp EcoRI restriction fragmentoriginally described (Simpson & Stafford, 1983), purifiedby ion-exchange HPLC (D. S. Scherl & J. Widom,unpublished results). Construct (a) was produced usingthe primer pair (LE28, RE36); construct (b) was producedusing the primer pair (LE28, RE64). Construct (c) wasproduced in two steps. First, an intermediate PCRreaction using the same template and the primer pair(LE28, RE88) was carried out, and the product purified byHPLC (see below); this product was then used as atemplate with the primer pair (LE36, RE19) to produceconstruct (c). Oligonucleotides were purchased trityl-onand purified on a C–18 reverse phase HPLC column(Vydac 218TP54) using standard methods. After de-trity-lation, these primers were used in PCR reactionsconsisting of: template DNA (150 ng ml−1), Tfl poly-merase buffer (50 mM Tris-HCl (pH 9.0), 20 mMammonium sulfate, 1.5 mM MgCl2), primer oligonucleo-tides (1 mM each), dNTPs (200 mM each), and Tfl DNApolymerase (1 ml enzyme (Epicentre Technologies) per100 ml reaction). The annealing temperatures and numberof cycles were optimized for each reaction. The desiredproducts were HPLC purified on a Mono-Q HR5/5anion-exchange column using a linear gradient of0.65 M NaCl in TE (pH 8.0; room temperature) to0.8 M NaCl in TE, for 90 minutes, at a flow rate of0.25 ml/min. The purified material was then concentratedon Centricon 30 filters (Amicon) and resuspended in0.1 × TE. Typical yields from 5 ml PCR syntheses (50100 ml reactions) were 100 mg of DNA after HPLCpurification.

Reconstitution and isolation of core particles

Construct DNA was radioactively labeled with[g-32P]ATP prior to reconstitution onto the histoneoctamer. Each labeling reaction was divided in half for usein naked DNA digestions and reconstitutions. Reconstitu-

tion reactions (300 ml) contained 100 ng labeled constructDNA, 19.2 mg chicken erythrocyte core particle DNA,15.5 mg purified chicken erythrocyte histone octamer(Feng et al., 1993), 2.0 M NaCl, in 1 mM Tris (pH 8.0),0.1 mM EDTA (0.1 × TE), supplemented with proteaseinhibitors: 0.5 mM phenylmethylsulfonyl fluoride (PMSF)and 1 mM benzamidine (BZA). The reactions weredialyzed successively (minimum of two hours per step)into 2.0, 1.5, 1.0, and 0.5 M NaCl, followed by anovernight dialysis into 0.15 M NaCl. All buffers contained0.1 × TE, 0.5 mM PMSF, 1 mM BZA.

Reconstituted core particles were isolated from freeDNA and aggregates on 5% to 30% (w/v) sucrosegradients (in 0.5 × TE, 0.5 mM PMSF, 1 mM BZA) whichwere spun at 41,000 rpm in a Beckman SW41 rotor for 24hours at 4°C. Each gradient was fractionated into 00.5 mlfractions and quantified by Cerenkov counting. Fractionscontaining the reconstituted material were pooled andconcentrated on Centricon 30 microconcentrators andresuspended in 300 ml of 0.1 × TE for storage at 4°C. Theyield of reconstituted particles after purification wasapproximately 50% (of input DNA), measured byCerenkov counting.

Mapping of reconstituted core particles

The translational phasing of the reconstituted coreparticles was determined by nuclease digestion with orwithout primer extension, for constructs (a) and (c).Reconstitutes (1 mg of total DNA) were digested with0.002 Worthington units of micrococcal nuclease in a 50 mlreaction (240 mM Tris-HCl (pH 7.5), 8 mM CaCl) at 37°C.For each timepoint, 5 ml samples were removed, quenchedin 100 ml 0.1 × TE, extracted once each with 100 mlphenol:CIPA (1:1, by vol.); CIPA was chloro-form:isoamylalcohol (24:1, by vol.) CIPA, and ether, thendried in a Speedvac. The DNA was resuspended in0.1 × TE and either analyzed directly on sequencing gels,or used as a template in the primer extension reactions.

Primers specific to central portions of the core particlesequence were used to map the regions protected frommicrococcal nuclease digestion (D. S. Scherl & J. Widom,unpublished results). The A primer (atcaagcaagagcc-tacgacc) anneals to the bottom strand and maps cleavagesites at the right end of the construct; the B primer(ggtcgtaggctcttgcttgat) anneals to the top strand andmaps cleavage sites at the left end of the construct (seeFigure 2). Primer extension reactions were carried out onthe isolated template in 20 ml reactions containing 50 mMTris-HCl (pH 9.0), 20 mM NH4SO4, 1.5 mM MgCl2, 1 mM32P-labeled primer, 200 mM dNTps, and two units of Tflpolymerase. Extension products were analyzed on 6%(w/v) denaturing acrylamide gels using sequencing lanesas exact size standards.

Restriction digests

Reconstituted core particles and naked DNA weredigested with restriction enzymes as follows: construct(a): TaqaI, BsrI, and BstUI at 45°C, 50°C, 55°C, 60°C, and65°C; construct (b): TaqaI and BstUI at 45°C and 65°C;construct (c): TaqaI, BsaHI, BsaJI, and BstUI at 45°C and65°C. In later studies, construct (a) was analyzed at 37°Cwith AluI, HincII, and SalI, and construct (b) wasanalyzed at 37°C with MspI. All enzymes were obtainedfrom New England Biolabs, and all restriction digestswere carried out using buffers provided by NEB. Glycerolwas added to the naked DNA digestions and MgCl2 was


added to the reconstitute digestions to achieve identicalfinal concentrations in the parallel reactions. The con-centration of glycerol in the reactions never exceeded 5%(v/v); reactions carried out at 5% glycerol continued thefirst-order dependence on enzyme concentration observedfor digestions carried out at lower glycerol (and enzyme)concentrations (see the text).

The specific buffers used for each enzyme are: TaqaI:10 mM Tris-HCl (pH 8.4, 25°C), 100 mM NaCl, 10 mMMgCl2, 100 mg ml−1 bovine serum albumin (BSA); BsrI:10 mM Tris-HCl (pH 7.8, 25°C), 150 mM KCl, 10 mMMgCl2, 100 mg ml−1 BSA; BstUI, MspI, BsaJI, BstNI: 10 mMTris-HCl (pH 7.9, 25°C), 50 mM NaCl, 10 mM MgCl2,1 mM DTT; HincII; 50 mM Tris-HCl (pH 7.9, 25°C),100 mM NaCl, 10 mM MgCl2, 1 mM DTT, 100 mg ml−1

BSA; SalI: 10 mM Tris-HCl (pH 7.9, 25°C), 150 mM NaCl,10 mM MgCl2, 1 mM DTT, 100 mg ml−1 BSA; AluI: 10 mMbis Tris-propane-HCl (pH 7.0, 25°C), 10 mM MgCl2, 1 mMDTT; BsaHI: 20 mM Tris-OAc (pH 7.9, 25°C), 50 mMKOAc, 10 mM MgOAc, 1 mM DTT, 100 mg ml−1 BSA.

At various times during the digestion, 10 ml sampleswere removed and quenched with 40 mM EDTA. Sampleswere analyzed on denaturing acrylamide gels, andquantified using the phosphorimager. Background valueswere obtained from appropriate regions between bandson each gel track and were subtracted from the integralsmeasured for each band.

Data analysis

The fraction of uncut DNA was calculated asfollows. For construct (c), the substrate DNA (labeled S inFigure 4) and the two products (labeled P1 and P2 inFigure 4) are simultaneously resolved. We calculate thefraction uncut as (counts in S)/(counts in S + P1 + P2),after background subtraction. This definition is insensi-tive to variations in gel loading. For constructs (a) and (b),adequate resolution of all three species on a single gel wasdifficult to obtain. Instead, the gels were run such that theshorter labeled product strand (analogous to P2) waswell-resolved from the other two (analogous to S and P1).We calculate the fraction uncut as ((counts inS + P1) − (counts in P2))/(counts in S + P1 + P2) afterbackground subtraction. This definition, too, is insensitiveto variations in gel loading. Control studies with nakedDNA revealed two problems. The two ends of theconstruct DNA are not labeled with identical specificactivity. This does not affect the analysis of construct (c),for which all three species are well resolved, but it leadsto an artificial non-zero (positive or negative) baseline forconstructs (a) and (b). This problem was overcome byobtaining an experimental measure of the baseline, fromnaked DNA digested to completion. Experimentalbaselines were obtained for each different enzyme. Datafor constructs (a) and (b) were fit by least-squares toexponentials that decayed to the corresponding separatelydetermined baseline, whereas data for construct (c) werefit to exponentials that decayed to zero. A second problemwas that the enzymes BsaHI, BsaJI, and BstUI, which arerecommended for use at 60°C, were found to lose activityduring the course of digestions at 65°C. This problem wasovercome by restricting the analysis of the 65°C datasetsto early times only, during which the reaction continuesits first-order decay.

The rate constant obtained from each exponential decaydefined kobs. Equilibrium constants for site exposure werecalculated from pairs of observed rate constants accordingto equation (15).

AcknowledgementsWe are grateful to Valerie Tokars for her contributions

at an earlier stage of this work; to Lisa Utschig and TomO’Halloran for the generous gift of MerR protein; and toTed Jardetzky, Michael Kline, Daniel Linzer, PeggyLowary, Alfonso Mondragon, Tom O’Halloran, and MikeReigle for valuable comments on the manuscript. J.W.acknowledges research support from the NSF and theNIH, and the generous donation of equipment byBeckman Instruments, Perkin Elmer-Cetus, and HewlettPackard; K.P. acknowledges support from an NIHMolecular Biophysics Predoctoral Training Grant.

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Edited by K. Yamamoto

(Received 26 March 1995; accepted 22 August 1995)

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