J. Mol. Biol. (1992) 223, 781-789

Thermodynamics

of DNA Branching

Min Lu, Qiu Guo, Luis A. Marky, Nadrian and Neville R. Kallenbach

C. Seeman

Department of Chemistry, New York University New York, NY 10003, U.S.A. (Received 29 April

1991; accepted 23 September 1991)

Branched DNA molecules arise transiently as intermediates in genetic recombination or on extrusion of cruciforms from covalent circular DNA duplexes that contain palindromic sequences. The free energy of these structures relative to normal DNA duplexes is of interest both physically and biologically. Oligonucleotide complexes that can form stable branched structures, DNA junctions, have made it possible to model normally unstable branched states of DNA such as Holliday recombinational intermediates. We present here an evaluation of the free energy of creating four-arm branch points in duplex DNA, using a system of two complementary junctions and four DNA duplexes formed from different combinations of the same set of eight 16.mer strands. The thermodynamics of formation of each branched structure from the matching pair of intact duplexes have been estimated in two experiments. In the first, labeled strands are allowed to partition between duplexes and junctions in a competition assay on polyacrylamide gels. In the second, the heats of forming branched or linear molecules from the component strands have been determined by titration microcalorimetry at several temperatures. Taken together these measurements allow us to determine the standard thermodynamic parameters for the process of creating a branch in an otherwise normal DNA duplex. The free energy for reacting two 16-mer duplexes to yield a four-arm junction in which the branch site is incapable of migrating is + l.l( t-04) kcal mol-’ (at lS”C, 10 mM-Mg’+). Analysis of the distribution of duplex and tetramer products by electrophoresis confirms that the free energy difference between the four duplexes and two junctions is small at this temperature. The associated enthalpy change at 18°C is +27.1( + 1.3) kcal mollr, while the entropy is + 89( f 30) cal K-r mol-‘. The free energy for branching is temperature dependent, with a large unfavorable enthalpy change compensated by a favorable entropy term. Since forming one four-stranded complex from two duplexes should be an entropically unfavorable process, branch formation is likely to be accompanied by significant changes in hydration and ion binding. A significant apparent ACp is also observed for the formation of one mole of junction, + 0.97( f 005) kcal deg-‘mol-‘.

Keywords: recombination;

Holliday

1. Introduction

junctions;

thermodynamics

arms are stably base-paired, it has become possible to investigate the structure, substrate and binding properties of stable branched analogues of Holliday junctions (Seeman, 1982; Seeman & Kallenbach, 1983; Kallenbach et al., 1983; Seeman et al., 1985). The synthetic four-arm junction shown in the left of Figure 1, which we refer to as Jl, is a stoichiometric tetrameric complex formed from four 16-mer strands. The tetramer is stable in solution under appropriate conditions of concentration, temperature and salt concentration (Kallenbach et al., 1983; Seeman et al., 1985) and folds into a tight conformation in the presence of divalent cations such as Mg2+ (Seeman et al., 1985).

Branched DNA molecules arise naturally in vivo. Four-stranded recombination intermediates (Low, 1988; Craig, 1988; Holliday, 1964; Meselson & Radding, 1975), Holliday junctions (Holliday, 1964), tend to resolve spontaneously into duplexes by means of the branch migration reaction (Thompson et aZ., 1976; Robinson & Seeman, 1987). This is an isomerization whereby the branch relocates along one or another pair of arms if the sequences of these are identical, or nearly so. By deliberately designing molecules that lack sequence homology, and ensuring at the same time that the 781 0022-2836/92/030781~9

$03.00/O

0

1992

Academic

Press

Limited

(Chen et nl., 198%; Duck&t ef al., 29X8). Apart from the branch site, the TINA in the arms of J1 remains predominantly in the B form, based on c.d. (t: Seeman et al.! 1985; Marky et al., 1987) and ‘PI n.m.r. spechroscopy (Wemmer et al., 1985), while r,he base-pairs flanking the branch appear to remain paired at low temperatures in the presence of Mg2+ (Wemmer et al., 1985). We would like to know more about the molecular forces and interactions that stabilize these junction molecules, especially in t’he vicinity of the branch point. We have previously invest.igated the thermal stability of Jl relative to that of a set of four model octameric duplexes that provide models for the isolated arms of this junction (Marky et at., 1987). The results indicate that t,he stability of the junction (measured by tm; the temperat,ure at which the junction melts to form a,mixture of its four strands) is closer to that of an average of the four octameric arms t,han of intact~ IS-mers. The tra.nsit,ion enthalpy is roughly equal in magnitude to the melting of four octameric duplexes, suggesting that the branch disrupts the base-pair stacking between the two separate arms. We evaluate here the thermodynamics of forming the branched tetramer Jl from a pair of 16-mer duplexes representing its component helical domains (Fig. 1). The equilibrium constant for formation of each branched structure from its matching duplexes has been estimated directly using labeled strands in a competition assay on polyacrylamide gels. The equilibrium constant for branch formation can be evahmted from these data. The heats of format,ion of the branched and linear molecules from the component strands have been determined by titration microcalorimetry at several temperatures. The results provide for the first time a standard thermodynamic profile for the process of branch formation in DXA. Previously, the free energy of cruciform formation in covalently circular DNA duplexes has been estimated from the change in winding that, accompanies extrusion of the cruciform (Courey 87 Wang, 1983; Lilley $ Hallam, 1984; Greaves et ai., 1985; Kaylor et al., 1986). Extrusion requires branch

2:; C.6 II

T*A T*A A.T CZ*G G*C III

m JI

Figure 1. The sequences of the 2 synthetic DNA 4-arm junctions used in this study. Jl is composed of 4 hexadecadeoxynucleotides. The strand numbering is indicated by Arabic numerals and the arms are numbered by Roman numerals. Arrowheads are on the 3’ ends of the strands. Jl” is formed from the 4 strands complementary to those in Jl. The preferred solution structures of each junction are indicated, based on the results of previous experiments (Churchill et al., 1988; Seeman et al.; 1989; Guo et al., 1991).

Our current picture of the structure of Jl in solutions containing Mg 2 + is that two adjacent pairs

of duplexes stack as illustrated in Figure 1; such that

two

strands

retain

the

approximate

conforma-

tion they would have in a duplex, while t’wo others cross over between the duplexes. This model is based on the results of several experiments. Kydroxyl radical cleavage of the tetramer reveals a 2-fold symmetrical pattern of protection in two strands at the branch (Churchill et al., 1988). These two are assigned as the crossover strands; the remaining pair is assumed to have conformations and protection patterns closer to those in duplexes. Electrophoretic mobility measurements using pairs of extended DKA arms show t’hat the orientation of the arms is antiparallel rather than parallel (Cooper & Hagerman, 1987, 1989). Footprinting experiments on model junctions, in which the two duplex stacks have been tethered by means of short runs of thymine so as to lie antiparallel or parallel, suggest that the patterns of reactivity of the two helical stacks in Jl resemble the antiparallel rather than the parallel model (Lu et al., 1991). The free energy differential between the antiparallel and parallel models indicates that the former is more stable by a small amount (Lu et al., 1991). Other experiments on different junctions suggest that this preference for one stacking partner and the antiparallel isomer may be quite general (Chen et ai., 198%;Duckett et al., 1988; Murchie et al.: 1989). Comparison of junctions containing different base sequences flanking the branch indicates further that the choice of stacking partners and extent of the preference is dictated by the sequences of bases flanking the

creation

of loops

in addition

to branch

formation

and this makes it difficult to evaluate the contribution of branching per se. The basis for our analysis is the following. Since the sequenceof each strand in the junction t.etramer is unique, it is useful to consider a system involving two junctions, Jl and its complement, JI”; formed from the four st’rands that are complementary to those in Jl. We have synthesized two sets of four IS-mer DSA strands that associate to form the branched tetramers, Jl and J1” (see Fig. I). The sequences of these strands a,re given in Figure I. Next we consider two sequences of reactSions t Abbreviations used: c.d., circular dichroism; n.m.r.. nuclear magnetic resonance; PAG(E), polyacrylamide gel (electrophoresis); h.p.1.c.: high-pressure liquid chromatography; u.v., ultra violet.

Thermodynamics

of DNA

whereby a stoichiometric mixture of eight single strands (denoted Si) is allowed to form two tetramerit molecules (Jl and Jl”) or four duplexes (denoted D,, D,, D, and D4):

Branching

*-

783

L

.

3

I

+

t4

*-

I

3 +

IC

,4

. IC

t

s Jl $ Jl”

s,+s,+s,+s, s,c+s,c+s,,+s,, S,+S,,$D, Sz+Sz,~Dz S3+Sjc=D3 Sq+S4f=D4 The reaction in which two junctions is then

four

K K K K K K

= = = = = =

KJl KJI= KD, KD, G, G,,

duplexes

D,+D,+D,+D,Y=J~+J~”

(l(a)) (l(b)) P(a)) P(b))

3c -I 2

Heat

P(c)) P(d))

convert

K = KIM

Cool

for comparison with duplex formation:

pathway

(S,+SJ)+(S1C+S3C)-)D1+D3.

of

and

lncubote

Run notlve

PAGE

ot 18 “C for 60

h

(20%)

Figure 2. Outline of electrophoretic equilibrium assay used in this study. Each non-complementing pair of strands, e.g. strands S,+S, of Jl; at equimolar concenis tration, 1 labeled with 32P ? the other non-labeled, allowed to partition at equilibrium between a slight excess of non-labeled complementary strands, S,, and S,, in the example, and a larger? known excess of the remaining 2 strands required to form Jl. After allowing sufficient time for equilibra,tion. the ratio of counts in the duplex and junction bands following electrophoresis of the complexes on native PAGE, is determined by excising the bands and scintillation counting.

(5)

An independent procedure has been devised to determine the equilibrium constants and AG values for (3) directly by means of an electrophoretic assay. By definition:

KD+, = ~J~1~J~“1/~~~1~~~1~~31~~,1 = [J1l/P,IP,I x [J1”l/P,IP,I. Each non-complementing pair of strands, e.g. strands X1 +S, of Jl: at equimolar concentrat’ion, one labeled with 32P, the other non-labeled, is allowed t’o partition at equilibrium between a slight excess (enough to permit its concentration to be determined precisely) of their non-labeled complementary strands, X1, and Ssc in the example, in the presence of a larger known excess of the remaining two strands required to form Jl. The competing equilibria are (again suppressing the ionic and water components): S,+S,c+S3+S3c S,+S,+S,+S,

slowly,

(3)

(4)

the corresponding

very

3 min at 90 “C

to

the difference between reactions (1) and (2) at fixed concentration of strands. Note that the associated ion binding and solvation processes are not, indicated separately in writing these equations, but are present implicitly. The thermodynamics of reaction (3) ((3) =(l)-(2)) could be determined indirectly from a separate analysis of the heats and entropies of formation of duplexes, reaction (2), and tetramers, reaction (1) j using differential scanning calorimetric methods (Marky & Breslauer, 1987). However, this requires extrapolation of the thermodyna.mic parameters from the transition region to the range of interest. Instead we have used a titration microcalorimeter to measure the heats of mixing binary sets of non-associating strands, such as: (S,+S3)+(S2+S4)+J1

3c .

-I 2

= D,+D, = Jl.

After equilibration, the two mixtures, each corresponding to the labeled strand of S1 and S3, respectively, are run on polyacrylamide gels (PAG(E)) under native conditions, and the bands corre-

sponding to duplex and tetramer are excised and counted on a scintillation counter. An outline of the experimental plan is shown in Figure 2 for clarity. If a small quantity of labeled strand is introduced into a mix of non-complementary strands at equimolar concentration, so that an excess of S,, and S,, is present, with a still larger excess of strands S, and Sq, respectively, the ratio of concentrations of Jl* and D1* and D, * together with the known concentrations [S,,], [S,,], [S,] and [S,] fully determine the right side of the following expression effectively half of reaction (3):

KJI/&.&D~ =

~13

= ([J~*I/CDI*IP,*I) x ~~~,~l~~,~l/l~,l~~,l~~(6)

Repeating this for the non-complementing strands S,, and S,, of Jl” gives us a value other half of reaction (3): KJICIKD$D~

=

r24c

= ([J~“*l/Pz*lP4*l) x ~~~,~lr~4~l/r~,l~~,l~

pair of for the

(71

By symmetry, labeling each pair of non-complementing strands S2 and S4 of Jl; and S,. and SsC of Jl”, allows us to evaluate rz4 and rlaC in the same

M. Lu et al.

784

presented elsewhere (Wiseman et ai., 1989). DNA soiuiions for the calorimetric experiments were prepared in a 100 rnM-sodium cacodylate buffer containing 200m~-NaCl and IOrnM-i\IgC1,, adjusted to pH 76. A 100+1 syringe filled with solutions containing equimolar quantities of 2 strands was used t,o titrate the pair of complementary strands to yield either the formation of 2 duplexes or the tetrameric complex. Mixing was effected by stirring the syringe at 400 rev./min. The concentration of total strands in the syringe was generally lo-fold higher than the concentration of the solution of strands in the reaction cell. Typically 5 injections of 10 ~1 each into the 1.4 ml reaction cell were done in a single titration. Since the reference cell of the calorimeter serves only as a thermal reference to the sample cell, this cell was filled with water. The instrument was calibrated by means of a known standard electrical pulse. Association entha.lpies (AH, or AH,) were calculated by averaging the heats of the 1st 2 injections, normalized to the number of moles of the limiting reagent.

way. This is done

in order to estimat,e the error range of this measuring system. The values of r13 and rzdc or rz4 and r13C in equations (6) and (7) determine the interconversion shown in equation (3) in the solvent conditions of the experiment. The square root of the equilibrium constant for reaction (3) corresponds to format,ion of a single (average) junction from two unbranched 16-mer duplexes, the process in which we are interested.

2. Materials and Methods (a) Synthesis and pur@ation

of oligonucleotides

Oligonucleotides used in this study were synthesized on an ABI 380B automated synthesizer and deprotected by routine phosphoramidite procedures (Caruthers, 1982). Strands were purified by preparative h.p.1.c. on a Du Pont Zorbax Bio Series oligonucleotide column, following the manufacturer’s recommended elution protocol. Oligonucleotides were labeled at their 5’ termini using bacteriophage T4 polynucleotide kinase (Boehringer) and [y-3ZP]ATP and then the labeled strands were repurified by polyacrylamide gel electrophoresis. The concentration of strands in stock solutions was determined spectrophometrica.lly at 260 nm and 80°C using the molar extinction coefficients in Table 1. (b) E’lectrophoretic

analysis of junction foPmat&

---

(d) Equilibrium

distribution

experiments

For experiments starting with mixtures of the strands, a stoichiometric mixture of 8 single strands (S, to S,, and S,, t,o S,,) was annealed in 10~1 of 50 mM-TrisHC1 (pH 7.0): 10 mnr-MgCl,. An Eppendorf tube containing the solution was immersed in boiling water for 2 min, cooled to room temperature in 1 h, and finally to 18°C for 75 h before loading onto a native (20%) polyacrylamide gel. Gels were stained in 9 : I1 (v/v) formamide/water solution containing 0.01 o/o Stains-Ail dve. Each duplex (Dr t,o D4) orjunction (Jl and Jl”) was annealed in 2.54 or 5~1 of 50m;~-Tris.HCl (pH 76), 10 rnM-MgCl,: respectively. An Eppendorf tube containing the solution was immersed in boiling water for 2 min? cooled slowly to room temperature and finally to 18°C for 2 h. The 4 duplexes or 2 junctions were then mixed, respectively, and incubated at 18 “C for 75 h before loading into a native (20%) polyacrylamide gel. The gel was stained in 9 : 11 formamide/water, containing 0.01 “/;, Stains-All dye.

and duplex

The experiment outlined in Fig. 2 was carried out using concentrations of 2,u~-Sr and S,, S,LLM-E$, and S,, and @96mM-S, and S,. Junctions and duplexes were formed by annealing a mix of strands in 20 ~1 of 50 miv-Tris.HCl (pH 7.0), 10 InM-&$l,. An Eppendorf tube containing the solution was immersed in boiling water for 2 min, cooled to room temperature in 1 h and finally to 18°C. After allowing 60 h for equilibration at 18°C: samples were loaded onto a native (20%) polyacrylamide gel. The gels were exposed for 1 h without an intensifying screen. The ratio of counts in the duplex and junction were determined by cutting out the bands and counting on a scintillation counter. Gel slices were placed in vials with 12 ml of scintillat,or solution containing 4 g/l PPO and 905 g/l POPOP (Amersham) in toluene (Aldrich) and counted on a Beckman LS 7500 counter. Gel slices that did not’ contain radioactive material were counted as background.

(e) Gel electrophoresis Native (2OyA) polyacrylamide gels were run at 18% for 20 h at 100 V (approx. 8 V/em). The electrophoresis plates were jacketed and cooled with circulating water to provide a running temperature of 18( + 1) “C in the gel throughout etectrophoresis. The buffer system contained 40 mM-Tris, 20 rnx-acetic acid; 1 rnM-EDTA, 10 m&rMgCl,, at pH 8.1 (TAEMg). No tracking dyes were added to samples in these runs. For denaturing gels: the samples were taken up in formamide loading buffer; heated briefly

(c) Calorimetry All experiments were carried out using the Omega titration calorimeter from Microcal Inc. (Northampton, MA). A detailed description of this instrument has been

Table 1 The molar

extinctions

of DNA %6O”IIl

Sequence

d(CGCAATCCTGAGCACG) d(CGTGCTCACCGAATGC) d(GCATTCGGACTATGGC) d(GCCATAGTGGATTGCG)

@M-l

CK’)

157 152

159 163

strands

used in this stzcdy Sequence

d(CGTGCTCAGGATTGCG) d(GCATTCGGTGAGCACG) d(GCCATAGTCCGAATGC) d(CGCAATCCTGAGCACG)

%XlWIl (nwl cm-‘) 155 161 161 157

The above values were measured with melting curves by extrapolation to 80°C of the molar extinctions calculated using the nearest-neighbor values of Cantor el a.1.(1970).

Thermodynamics

of DNA

Branching

785

Table 2 Xummary

of the measured values of r13, rz4, rIje, rz4= at 18°C by electrophoretic assays with equilibrium constants and free energy

r13 (x-l)

r24 (M-l)

0.13 0.12 0.11 0’12(&0.01)

*v.

*v.

0.14 0.16 @13 @14(+0.02)

to 9O”C, cooled, then run on a denaturing acrylamide gel for 3 h at 2000 V (approx. 40°C. ru‘o dyes were added in these runs.

r13c (M-l) @18 0.19 0.18 Av. @18(fO,Ol)

(20%) poly50V/cm) at

(f) U.V. melting curves Absorbance CersuS temperature profiles (melting curves) for the duplexes and junctions, at various strand concentrations and in a lOOmw-sodium cacodylate buffer containing 200 mM-KaCl and 10 rnM-MgCl,, adjusted to pH 7.0, were measured at 260 nm with a thermoelectrically controlled Perkin-Elmer 552 spectrophotometer interfaced to a PC-XT computer for acquisition and analysis scanned curves

of at allow

experimental data. The temperature was a heating rate of l”C/min. These melting us to measure the transition temperatures,

tm, which are the midpoints of the order-disorder transition of these DPI’A molecules, as well as the relevant thermodynamic parameters. These parameters were calculated by using standard procedures reported by IIarky & Breslauer (1987) and correspond to a S-state approximation

to

the

helix-coil

transition

of

each

molecule. Use of this approximation has been discussed in the context of Jl by Marky et al. (1987).

3. Results (a) Equilibrium

constants from assay

the electrophoretic

Table 2 summarizes the experimental values of the ratios r13: rZ4, rlSc and r24c measured by the electrophoretic analysis outlined above (see eqns (6) and (‘i)), t’hat fully determines the equilibria for the series of 16-mers in this study at 18°C. Each experimental r value is an average of the results of allowing strands i, it-2 of Jl or Jl” to equilibrate with a large excess of the remaining two strands needed to form the junction. The binary mixtures yield r13 and r24E or ri3< and rZ4, and allow us to complete the determination of the equilibrium constant, K,,,. Each value reported is a mean of three determinations. The equilibrium constant K D+J for the formation of two moles of junction from four moles of duplex at 18°C is calculated as: K D+J = r13r24c

= r13cr24

= 2.6 x

lo-*.

If the data are converted to AG” = - RT In K, the free energy for reacting four 16.mer duplexes to give two four-arm junctions at 18°C is + 2.1 ( kO.4) kcal mol-l (1 cal = 4.184 J), indicating that forming a four-stranded complex from two duplexes is energetically only a slightly unfavorable process at this

K D-1,X lo2 (M-')

r24c (M-l)

AG",,, (kcal mol-‘)

2.6 2.6 Av. 26( fO.05)

0.18 022 0.23 Av. @21(+@04)

+2,1

(&@4)

temperature. In contrast to the rapid equilibration seen upon forming either duplexes or junctions alone, the competition reaction requires much longer times to reach equilibrium. To evaluate the requirement for equilibrium, we have repeated the electrophoresis assay at different times and find stable values after 48 hours at 18°C. Measurements at lower temperatures, below 10°C for example, appear to require times in excess of 100 hours for equilibration. As a further control, the concentrations of the (excess) strands 2 and 4 were varied from 120 to 600~~, and the ratio r13 determined to be constant (data not shown). This verifies that the process we are monitoring is an equilibrium and not an artifact of the preparation of strands used, for example. (b) Calorimetric

reaction

enthalpies

Two kinds of titrations were performed using sets of solutions containing equimolar pairs of 16-mer strands. A titrant solution containing one pair of non-complementing strands was added to a second pair of strands in the reaction cell, either the diagonally opposite strands to form a junction molecule, or the complementary strands to form two duplexes. Typical concentrations of solutes used in these experiments were such that a total exothermic heat of 30( + 1.5) peal was measured for the formation of a junction molecule and 330( -+ 15) peal for the formation of a pair of duplexes. The molar heats for the four sets of experiments needed to complete the reactions indicated in equation (3) above at three different temperatures are summarized in Table 3. The enthalpy for formation of two junction

Table 3 Calorimetric tetramers

enthalpies of formation of duplexes and in kcal mol-l at different temperatures Temperature

Complex

12°C

17°C

20°C

Jl Jl’ D,+D, DI +D,

-142 -119 - 143 -158

-143 -133 -166 -162

-156 -138 -171 -186

100 mM-sodium Buffer used was 200 mM-N&l and 10 mM-MgCl,, adjusted

cacodylate to pH 7.0.

containing

786

M. Lu et al.

I

I

20

30

Temperature

(“C)

Figure 3. Dependence of the enthalpy of reaction (3) on the temperature. These experiments were carried out as described in Materials and Methods, with 100 mM-sodium cacodylate buffer containing 200 mMlSaC1 and 10 mM-MgCl,, adjusted to pH 7.0. The point at 30°C was obt’ained by chelating Mg’+ with Ka, EDTA in the calorimeter. The cell contained buffer with excess Na,EDTA, while the syringe held a solution of the 2 junctions.

molecules from four duplexes is given in Table 4. values at three different A plot of the enthalpy temperatures is shown in Figure 3, together with an independent determination at 30°C of the enthalpy of disrupting two junction molecules to form four

2

J

3

4

Figure 4. Equilibrium distribution analysis of duplexes and junctions by native PAGE starting from (aj a mixture of the 8 smgle strands and (b) either duplexes or junctions. All reactions were carried out at 18°C and with 10 rnM-Mg ‘+ for 75 h. Photographs of stained native gels are shown in each case. The native polyacrylamide gels were stained as described in Materials and Methods. (a) The equimolar 8 single strands were mixed each at a concentration of 20 PM (lane 2), or 30 ,uM (lane 3). Lanes 1 and 4 show t’he positions of duplex and junction controls, respectively. (b) Lanes I and 6 show t’he duplex a,nd junction controls, respectively. Lanes 2 and 4 mixed the 4 equimolar duplexes of 2Ofi~ and 30 PM. respectively; while lanes 3 and 5 mixed the 2 equimolar junctions of 20 /*M and 30 ,uM. respectively.

dupiexes, OS

nesium ment.

obtained ions

with

A linear gives the equation:

by chelating

the bound magin a dilution experianalysis of these data

Na,EDTA regression

AH = + 19268f where t is the temperature a strong apparent heat + 1.94( kO.097) kcal deg-’

1.938 t(kca1 molF’) in degrees C; indicative capacity effect equal mol-’ for two moles

of to of

junctions.

Thermodyna’mic parameters for the formation of a tetrameric junction from two duplexes at 18 “C are given in Table 4. Tnspection of these numbers

Thermodynamic and

paramerers for tXe formation Jl’ from four duplexes at 18°C

AG” (km1

T4S"

AH” ma-‘)

+2.1(+@4)

(km1

m01-~)

+542(rt1.3)

of S1

(km1

ml-‘)

+52~1(+9.0)

(kcal

de~‘mol-‘) + 1.94(

2 0.05)

Thermodynamics

indicates that of a branched the resultant opposed by a dissected into (c) Direct

qf DNA

Branching

787

at 18°C the free energy of formation tetramer from two duplexes is small, of an unfavorable enthalpy change favorable ( - TAS) entropy term when its components.

monitoring

of the equilibrium

at 18°C

If the free energy for reacting two duplexes to yield a four-arm junction is small at 18°C according to the electrophoretic competition assay, it follows that the equilibrium between mixtures of the strands, four duplexes or two junctions, should be detectable provided kinetic barriers are not present. In order to test this prediction, we mixed and annealed the eight single strands, holding the mixture at 18°C for a long enough time. The result of this experiment is shown in Figure 4(a). Lanes 2 and 3 show the presence of both junction and duplex. The control lanes contain only one duplex and junction for mobility references. The equilibrium constant calculated from this exchange experiment is roughly 2 x 10e2, assuming equal extinction coefficients for the species in each band, and this is consistent with the results of the electrophoretie competition assay. Since in this experiment the two limiting strands in the previous measurement are now at 15-fold higher concentration (30 PM versus 2 PM), this experiment gives us additional confidence that the behavior we are observing is due to strand association, and not some other process. In order to verify that the above experiment actually reaches equilibrium, the four duplexes (Dr to D4) were mixed together in one solution, and the two junctions (Jl and Jl’) in another, and the mixtures incubated at 18°C for 75 hours, again assaying each mixture by means of native PAGE at 18°C to resolve junctions from duplexes. The result is presented in Figure 4(b). It is seen that the exchange reactions proceed from either direction to a similar ratio of junctions to duplexes, indicating that the system has reached equilibrium completely within 75 hours incubation at 18°C. We conclude that the equilibrium is such that both species are detectable at 18°C and that the free energy difference is in fact small at this temperature.

4. Discussion The free energy for cruciform formation in a pBR322 derivative containing a palindromic insertion was first reported by Courey & Wang (1983), who measured the change in superhelical density at 68”C, the tm of the A.T base-pairs in the duplex, in order to eliminate the contribution from looping out bases in the process of extrusion. The value, + 17 kcal mall ‘, is evidently greater than the number we obtain at 18°C (Table 4). Reaction (3) cannot actually take place at 68°C in our system since this is above the tm value of the junctions at reasonable strand concentrations. We can nevertheless estimate the free energy difference between junctions and duplexes at higher temperature using the

hE \2.85

2.751

I -13

-12

.

1 -I I

In CT (single

.

I -10

-9

strands)

Figure 5. Dependence of the transition temperature on strand concentration in 100 mM-sodium cacodylate buffer chtaining 200 mM-NaC1 and 10 m&f-MgC& at pH 7.0. 0, JI’; 0, Jl; n , D,; 0, D,; A, D,; 4, D,.

thermal transition data shown in Figure 5. Neglecting the role of intermediate states in the denaturing of duplexes and junctions, we can use the two-state approximation to calculate that the difference in free energy between two moles of duplex and one mole of junction at 60°C would be taking the differential heat + 12.5 kcal mol-‘, capacity into account (Marky & Breslauer, 1987). At 18°C this would correspond to a AG” of +0.2 kcal mol-‘, not far from the value determined directly at this temperature. Thus, our value at higher temperatures is not completely at variance with the estimate by Courey & Wang (1983) at 68”C, particularly since the free energy for forming two loops is included in the latter. Other estimates of the free energy of cruciform formation have not taken loop unpairing into account, although the differences numerically do not appear to be large (Lilley & Hallam, 1984; Greaves et al., 1985; Naylor et al., 1986). Published estimates of the free energy for cruciform extrusion range from + 13 to + 18 kcal mol-’ (Courey & Wang, 1983; Lilley & Hallam, 1984; Greaves et al., 1985; Naylor et al., 1986), including the contribution for forming two loops from the duplex as well. Even the elegant measurement by Courey and Wang does not parse the entropy of the process into contributions from branch formation per se and loop formation. At high temperature, our estimate for the difference in free energy between duplexes and junction is actually in reasonable agreement with estimates from cruciform extrusion. The measurements described here allow one to determine a standard thermodynamic profile for branch formation without the additional formation of loops as occurs in cruciform extrusion, and at temperatures closer to physiological values. The enthalpy for the process of creating a branch from two duplexes turns out to be unfavorable, with a large apparent ACp. Why! First, since the calorimetric experiments are not carried out in the same buffer system as the electrophoretic measurements (100 mM-cacodylate, 200 mM-NaCl versus 50 mM-

788

M. Lu et al

Tris.HCI) we must consider this contribution. Cacodylate is the buffer of choice for calorimetry because of its low heat of ionization. To ascertain the effect of this difference, we ran parallel native PAGE experiments on samples equilibrated in the two buffers; no substantial difference can be detected at a fixed temperature (data not shown). Comparing the results at different temperatures affords us an opportunity to estimate qualitatively the apparent van% Hoff reaction enthalpy. While we did not attempt to analyze the results quantitat.ively, the van’t Hoff enthalpy of reaction (3) appears to be smaller than the value obtained calorimetrically. Contributions from base-stacking interactions, base-pairing, counter ion uptake or release, as well as differential hydration effects, need to be considered in trying to explain this effect. Use of cacodylate has only a minor effect on the equilibrium we consider, the major effect being due to Mg2+ (Seeman et al., 1985; Duckett et al., 1990). We might suppose at the outset that the unfavorable enthalpy simply represents the loss of approximately two to three base-pair stacking interactions at the branch relative to the situation in the corresponding duplexes. This is consistent with the earlier thermodynamic analysis in which the junction Jl was found to unfold similarly to the set of its individual arms (Marky et al., 1987). Gough et al. (1986) observed that in the presence of Mg2+ the bases flanking the branch are chemically unreactive; this observation does not address the issue of stacking across the branch directly however. n.m.r. experiments suggest for example that pairing of the bases flanking the branch is not fully disrupted (Wemmer et al., 1985; Chen et al., 1991), although they might nevertheless be partially open and thus unstacked. The model we and others have derived for the Mg2+ complex of a junction has two phosphate groups apposed at the branch, in an unusual electrostatic environment (Churchill et al., 1988; Seeman et al., 1989; Chen et al., 1988; Cooper & Hagerman, 1987, 1989; Duckett et al., 1988, 1990; Murchie et al., 1989). It has also been observed that the crossover strands are cut preferentially by Fe” at the branch (Lu et al., 1990) and not at corresponding sequences in duplexes, implying that there is preferential interaction of the metal with the crossover strands at the branch. Duckett et al. (1990) have reported that junction structure is sensitive to the nature of the divalent ions present. In the absence of metal ions, the structure is different (Cooper & Hagerman, 1987, 1989; Duckett et al., 1988, 1990; Murchie et al., 1989). Differential basestacking interactions across the branch thus provides one tenable explanation for the observed unfavorable enthalpy of branch formation from duplexes. A second consideration is that the process of branch formation from duplexes entails changes in metal or counter ion binding and differences in hydration between the two structures. The existence of significant changes in the latter processes allows one to rationalize several aspects of the

thermodynamics of reaction (3). A difference between the van’t Hoff and calorimetric enthalpies could arise from the fact that the latter heat, includes the total contributions of ions and solvation, whereas the former refers to an intermediate step in the overall reaction. Second, the direction of the entropy change on branching reported in Table 4 is not the direction anticipated for pairing two duplexes to form a tetramer. This unfavorable term must be exceeded by differential hydration and/or ion binding upon junction formation. The latter processes can account for the temperature dependence of the reaction enthalpy also. The large positive volume change that has been measured in the same reaction by densimetry (IL. A. M. & Iiupke, D., unpublished results) is consistent with these ideas. Taken together, these results are consistent with a model in which forming a branch between two initially intact duplexes involves an enthalpy/ entropy compensation process that presumably originates in the loss of favorable stacking and pairing interactions (enthalpic in nature) eompensated by a significant change in electrostatic interactions that affect ion binding and solvation. It is perhaps worth noting that. use of competing equilibria and labeled strands affords a general and useful approach to deriving the thermodynamics in formation of mismatches, bulges or other alternative states in DNA. Even if the equilibrium constants involved are large, use of excess (buffering) concentrations of strands in each partial reaction with radioactive labels that, are detectable in the piw concentration range should make it possible practically to determine equilibrium constants over a very wide range of values. The major source of errors in the procedure can be ascribed to two factors: (1) errors in measuring concentrations of strands in the reaction mixes and (2) the need to attain equilibrium. To reduce the level of errors in (l), we have adopted a procedure of weighing out solutions following volumetric addition of reagents. Since several additions of small volumes of reagents are necessary, this increases the precision, at the expense of tedium. The second factor is one that can be verified experimentally. The free energies we measure using the labeled strand equilibrium agree with the value determined by measuring the ratio of junction to duplexes as in Figure 4. A third source of uncertainty in this approach is the question of purity of the strands used to carry out the partition experiment. If the ratio of counts measured in the junction and duplex bands is extreme, there is a possibility that contamination of the synthetic material might interfere with accurate determination of the equilibrium constant. We have eliminated t,his possibility by measuring the distribution over a range of concentrations of the strands involved, as described above.

This research was supported by grants no. CA-24101, to N.R.K., (X-42223, to L.A.M. and GM-29554, to N.C.S., from the U.S. National Inst.itutes of Hea.lth.

Thermodynamics

References Cantor, C., Warshaw, M. W. & Shapiro, H. (1970). Oligonucleotide interactions. III. Circular dichroism studies of the conformation of deoxyoligonucleotides. Biopolymers, 9, 1059-1077. Caruthers, M. H. (1982). Oligodeoxynucleotides using the phosphite triester intermediates. In Chemical and Enzymatic Synthesis of Gene Fragments (Gassen, H. G. & Lang, A., eds.), pp. 71-79, Verlag Chemie, Weinheim. Chen, J.-H., Churchill, M. E. A., Tullius, T. D., Kallenbach, N. R. & Seeman, N. C. (1988). Construction and analysis of monomobile DNA junctions. Biochemistry, 27, 6032-6038. Chen, S.-M., Heffron, F., Leupin, W. & Chazin, W. J. (1991). Two-dimensional ‘H NMR studies of synthetic immobile Holliday junctions. Biochemistry, 30, 766771. Churchill, M. E. A., Tullius, T. D., Kallenbach, N. R. & Seeman, N. C. (1988). A Holliday recombination intermediate is twofold symmetric. Proc. Nat. Acad. Sei.,

U.S.A.

85, 46534656.

Cooper, J. P. & Hagerman, electrophoretic analysis of four-way junction. J. Mol. Cooper, J. P. & Hagerman, P. branched DNA structure Acad.

Sci.,

U.S.A

P. J. (1987). Gel the geometry of a DNA Biol. 198, 711-719. J. (1989). Geometry of a in solution. Proc. Nat.

86, 733t%7340.

Courey, A. J. & Wang, C. J. (1983). Cruciform formation in a negatively supercoiled DNA may be kinetically forbidden under physiological conditions. Cell, 33, 817-829. Craig, N. L. (1988). The mechanism of conservative sitespecific recombination. Annu. Rev. Genet. 22, 77-105. Duckett, D. R., Murchie, A. I. H., Diekmann, S., von Kitzing, E., Kemper, B. & Lilley, D. M. J. (1988). The structure of the Holliday junction and its resolution. Cell, 55, 79-89. Duckett, D. R., Murchie, A. I. H. & Lilley, D. M. J. (1990). The role of metal ions in the conformation of the four-way junction. EMBO J. 9, 583-590. Gough, G. W., Sullivan, K. W. & Lilley, D. M. J. (1986). The structure of cruciforms in supercoiled DNA: probing the single-stranded character of nucleotide bases with bisulphite. EMBO J. 5, 191-196. Greaves, D. R., Patient, R. K. & Lilley, D. M. J. (1985). Facile cruciform formation by an (A-T)34 sequence from a Xenopus globin gene. J. Mol. Biol. 185, 461478. Guo, Q., Lu; M. & Kallenbach, N. R. (1991). Conformational preference and ligand binding properties of DNA junctions are determined by sequence at the branch. Biopolymers, 31, 359372. Holliday, R. (1964). A mechanism for gene conversion in fungi. Genet. Res. 5, 282-304. Kallenbach, N. R., Ma, R.-I. & Seeman, N. C. (1983). An immobile nucleic acid junction constructed from oligonucleotides. Nature (London), 305, 829-831. Lilley, D. M. J. C Hallam, L. R. (1984). Thermodynamics of the ColEl cruciform: comparisons between probing

qf DNA

Branching

789

and topological experiments using single topoisomers. J. Mol. Biol. 180, 179-200. Low, K. B. (1988). The Recombination of Genetic Material, Academic Press, Orlando, FL. Lu, M., Guo, Q., Wink, D. J. & Kallenbach, N. R. (1990). Charge dependence of Fe(II)-catalyzed DNA cleavage. Nuel. Acids Res. 18, 3333-3337. Lu, M., Guo, Q., Seeman, N. C. & Kallenbach, N. R. (1991). Parallel and antiparallel Holliday junctions differ in structure and stability. J. Mol. Biol. 221, 1419-1432. Marky, L. A. & Breslauer, K. J. (1987). Calculating thermodynamics data for transitions of any molecularity from equilibrium melting curves. Biopolymers, 26, 1601-1620. Marky, L. A., Kallenbach, N. R., McDonough, K. A., Seeman, N. C. & Breslauer, K. J. (1987). The melting behavior of a DNA junction structure: a calorimetric and spectroscopic study. Biopolymers, 26, 1621-1634. Meselson, M. 6. & Radding, C. M. (1975). A general model for genetic recombination. Proe. Nat. Acad. Sci., U.S.A. 72, 358-361. Murchie, A. I. H., Clegg, R. M., von Kitzing, E., Duckett, D. R., Diekmann, S. & Lilley, D. M. J. (1989). Fluorescence energy transfer shows that the four-way DNA junction is a right-handed cross of antiparallel molecules. Nature (London), 341, 763-766. Naylor, L. H., Lilley, D. M. J. & van desande, J. H. (1986). Stress-induced cruciform formation in a cloned d(CATG),, sequence. EMBO J. 5, 2407-2413. Robinson, B. H. & Seeman, N. C. (1987). Simulation of double-stranded branch point migration. Biophys. J. 51, 611-626. Seeman, N. C. (1982). Nucleic acid junctions and lattices. J.

Theor.

Biol.

99, 237-247.

Seeman, N. C. C Kallenbach, N. R. (1983). Design of immobile nucleic acid junctions. Biophys. J. 44, 201-209. Seeman, N. C., Maestre, M. F., Ma, R.-I. & Kallenbach, N. R. (1985). Physical characterization of a nucleic acid junction. In The Molecular Basis of Cancer (Rein, R. ed.), pp. 99-108, Alan Liss, NY. Seeman, N. C., Chen, J. H. & Kallenbach, N. R. (1989). Gel electrophoretic analysis of DNA branched junctions. Electrophoresis, 10, 345-354. Sigal, N. t Alberts, B. (1972). Genetic recombination: the nature of crossed strand-exchange between two homologous DNA molecules. J. Mol. Biol. 71, 795-798. Thompson, B. J., Camien, M. N. & Warner, R. C. (1976). Kinetic branch migration in double-stranded DNA. Proe. Nat. Acad. Sci., U.S.A. 73, 2299-2303. Wemmer, D. E., Wand, A. J., Seeman, N. C. & Kallenbach, N. R. (1985). NMR analysis of DNA junctions: imino proton NMR studies of individual arms and intact junction. Biochemistry, 24, 5745-5749. Wiseman, T., Williston, S., Brandts, J. F. & Lin, L. N. (1989). Rapid measurement of binding constants and heats of binding using a new titration calorimeter. Anal. Biochem. 179, 131-137.

Edited by P. van Hippel