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Energetics of B-Z junction formation in a sixteen base-pair duplex DNA
J. Mol. Bid. (1990) 212, 3-6
Energetics of B-Z Junction Formation Sixteen Base-pair Duplex DNA Mitchel
J. Doktycz,
Albert
in a
S. Benight
Department of Chemistry, Box 4348 University of Illinois at Chicago Chicago, IL 60680, U.S.A.
and Richard
D. Sheardy?
Department Pennsylvania
Hazleton
Campus,
of Chemistry State University Haxleton, PA 18201, U.S.A.
{Received 23 June 1989; accepted 10 October 1989) We report analysis of the NaCl-induced B-Z transition in a 16 base-pair duplex DNA with sequence designed such that when NaCl is increased the left half of the molecule undergoes the B-Z transition while the right half remains in the B-form. An equilibrium thermodynamic model based on the body of available published experimental data and the recent theoretical work of Soumpasis, which indicate, in tbe salt range above - 69 M-NaCl, the transition free-energy of B-Z conversion in DNA is a linear function of the NaCl concentration, is employed. Analysis of the B-Z transition of the junction-containing molecule indicates the B-Z junction formed in this I6 base-pair DNA is composed of approximately three base-pairs and has a free energy of formation of - 4.7 kcal/mol junction. These values for the junction are in excellent agreement with published estimates of B-Z junction size and energy derived from much longer DNA pieces.
B-Z
junction formed in this 16 base-pair duplex DNA oligomer in high salt (4.5 M-NaCl) was reported (Sheardy, 1988; Sheardy & Winkle, 1989). Figure 1 shows the three molecules of this study. Molecules I to III contain the core duplex sequence 5’(C*G),3’ (C * is 5-methyl-cytosine) but differ in the type of DNA environment adjoining the common core duplex. Short alternating C*G sequences of similar length have been previously demonstrated B-Z transition (Pohl, to undergo a salt-inducible 1982; Quadrifoglio et al., 1984). Molecule I is the eight base-pair core duplex. Molecule II has the eight base single strand sequence 5’ACTGACTGS’ extending on the 3’ end of each strand of the core duplex region. Molecule III contains I6 base-pairs, the core duplex on the left half and the duplex sequence 5’ACTGACTGS’ on the right half. The B-Z transition in molecules I to 111. of Figure 1 was assayed by monitoring the o.d. slpectrum as a function of NaCl concentration at 25°C. C.D. spectra were recorded on either a Jasco 600 or AVIV spectropolarimeter. Plots of the spectrally determined values of fi (fraction of Z-form) versus NaCl concentration for molecules 1 to III are depicted in Figure 2. The transition curves of molecules I and II in Figure 2 are virtually identical between fz = 61 and O-9 over the entire range of NaCl concentration from 0.2 M to 1.9 M. This result apparently indicates that the eight base dangling single strand ends of molecule II do not significantly
It is a widely believed notion that left-handed Z-DNA actually exists in, vivo (Jaworski et al., 1987), and as such serves as an instrumental conformational element. This notion has been the primary motivation for a number of studies undertaken to elucidate the structural conversion of right-handed B-DNA to left-handed Z-DNA (Zacharias et al., 1988; Luthman & Behe, 1988; Sheardy, 1988; Soumpasis, 1988; Jovin & Soumpasis, 1987; Manzini et al., 1987; Chen et al., 1987; Singleton et al., 1983; Klysik, et al., 1983). Thermodynamic aspects of the interface or “junction” between contiguous B and Z forms on the same duplex DNA molecule have been investigated in supercoiled DNA (Zacharias et al., 1988; Ellison et al., 1985; Singleton et al., 1983) cloned restriction fragments (Klysik et al., 1983) and polymerized repeating sequences (Luthman & Behe, 1988). Here we report thermodynamic analysis of the NaCi-induced B-Z transition in a 16 base-pair duplex DNA with sequence designed such that the left half of the molecule undergoes the B-Z transition while the right half remains in the B-form. Recently, the design strategy and preliminary characterization by circular dichroism (c.d.$) and nuclear magnetic resonance (n.m.r.) analysis of the t Present address: Department of Chemistry, Hall University, South Orange, NJ 07079, U.S.A. $ Abbreviations used: c.d., circular dichroism; nuclear magnetic resonance; C*, 5-methyl-cytosine.
Seton n.m.r., 3
0022-2~3c;/SOjOZOOO3-o4 $03.00/O
0 1990 Academia Press Limited
M. J. Doktycx et al.
0
0
.
d 1:drK”G)4~Ac T G,,,
.
2+2=II C’C C’G C”G C”G A c T G A c Y 0 G T c A G T c * G c*o C’G C”G C’
.
q . q .
q
. c 0.0
Figure 1. DNA fragments of this study. DNA oligomers were synthesized by the trityl-on phosphoramidite method (Caruthers, 1982). Complete products were purified from untritylated failure sequences by reverse phase high-pressure liquid chromatography, deprotected by overnight incubation at 60°C in 3 vol. 100% ammonium hydroxide and detritylated by treatment with 80% (v/v) acetic acid. Samples were dried under vacuum, resuspended in sterile double-distilled water (ddH,O), and subjected to a 2nd pass over the preparative chromatography column. Purity of oligomers was > 99% as determined by electrophoresis on 20% (w/v) polyacrylamide gels. Strand annealing was achieved by heating the oligomers in ddH,O to 95°C for 5 min and slowly recooling. Molecules I to III were formed by annealing the appropriate oligomers as shown.
affect the transition behavior of the d[(C*G),] core duplex. The transitions in molecules I and II occur at lower NaCl concentrations and span a much narrower range than that of molecule III. Wolecules I and II have a transition midpoint at 1.04 M-NaCl; the transitions are complete at 2.1 M and 2.6 M-NaCl, respectively. The transition of molecule III has a midpoint at 3.55 M-NaCl and is complete by 4.5 M-NaCl. The presented transition data can be interpreted in terms of a two-state model where base-pairs can exist in only one of two possible states, the B or Z state. fi is the average fraction of base-pairs per molecule in the 2 conformation. We assume the salt induced B-Z transitions of duplex base-pairs in the (C*G), region are equilibrium processes at all salt concentrations and the equilibrium conformational transitions can be represented as, B + An[NaCl]
2 Z
(1) where R and Z represent a molecule with its potentially Z-forming core duplex in either the B or Z is the total equilibrium state, respectively. K,, constant and is a constant independent of [NaCl] that only depends on the temperature and pressure. K,, can be represented as: K,,
where brium
= KobsKp~,
is the equilibrium constant that includes all K di&ences in the polyelectrolyte characteristics of a particular molecule when it is in either the B versus Z conformation. From equations (1) and (3): = K,b,/[NaC1]A”,
I.0
1
1
1
1
2-o
3.0
4.0
5.0
[NaCl]
Figure 2. B-Z transition curves of molecules I to HI. Titrations of DNA with salt from 0 to 50 M-Pu’acl were performed by first dissolving freeze-dried portions of each DNA molecule to the same concentration in either buffer A (10 mM-phosphate, 1 mM-EDTA, pH 7.0) or buffer B (5.0 M-NaCl, 10 mM-phosphate, I mm-EDTA, pH 7.0) and combining portions of DNA in buffer A and buffer B solutions in the appropriate amounts to achieve the desired salt concentration. DNA concentrations determined from the absorbance at 260 nm were typically around 075 absorbance units/ml. After equilibration for 5 min, c.d. spectra of DNA solutions at every NaCl concentration remained constant for over 24 h. The low salt cd. spectra of molecules I and II were typically B-like, characterized by a trough at 255 nm and a peak at 286 nm (Sheardy, 1988; Sheardy & Winkle, 1989). In high salt the spectra were inverted and typically left-handed with a trough at 295 nm and a peak at 275 nm (Sheardy, 1988; Sheardy & Winkle, 1989). The low salt spectrum of molecule III was essentially B-like, with a trough at 253 nm and peak at 280 nm while the high salt spectrum had spectral features of both right-handed and lefthanded DNA, i.e. a shallow trough at 295 nm, a peak at 278nm and another trough at 253nm (Sheardy, 1988; Sheardy & Winkle, 1989). This observation suggests the high salt form of molecule III contains both right-handed B and left-handed 2 structures and must therefore contain a B-Z conformation junction. Recently reported n.m.r. and c.d. studies of molecule III in high salt verified the existence of a stable B-Z junction at high salt (Sheardy $ Winkle, 1989). Extent of the B-Z transition (fz) for molecules I to III, between the low (0 ivI-NaCl) and high salt (~OIVI-NaCl) forms that define the endpoints, was determined by monitoring the change in molar ellipticity at 295 nm (A+). de, is the difference between the molar ellipticity (~~-6~) at 0 salt and 50 M-Nacl. From the measured change in molar ellipticity at 295 nm as a function of NaCl concentration, As(NaCl), fz was determined according to: fi = [(A&r-As(NaCl))/A+]. fz, the spectroscopically determined fraction per molecule described in the text, is plotted NaCl concentration. The open squares and filled are the transitions of molecules I and IT. squares indicate the molecule III transition.
of Z-form V~~SZLS the diamonds The filled
(2)
observed equiliKobs is the experimentally constant for the B to Z structural transition: K obs = [ZI/[Bl. (3)
K,,
‘Z’
(4)
indicating
for this treatment
that:
K,, = [NaCllPA”. (5) An in equations (1) and (5) includes the collective difference between the sequence-independent electrostatic interactions of the charged phosphate backbone with bulk water and the diffuse ionic cloud of hydration surrounding the DNA in the B or Z conformations”
5
Communications
range above concentration salt In the - 09 iw-NaCl, the observed free energy of the B-Z transition, AGnhs, is a linear function of [NaCl] and form as: can thus be written in the empirical
,
-4 -3
-2
,: -I
/' , '0
/
where IC and equation (7):
I
I I
In [NaCI]
An in equations (1) and (5) should not be confused with the salt uptake of the transition as required by Manning’s counterion condensation model of poly1978). Recently, in fact electrolytes (Manning, Soumpasis (1988) has shown that the counterion condensation and Poisson-Boltzmann approaches are inadequate representations of the B-Z transition in DNA. Alternatively, the calculations of Soumpasis, employing a hypernetted chain model of DNA and the sequence-independent, but saltdependent interactions represented by the factor An[NaCl] in equation (l), fit the available experimental data over the entire salt concentration range because the salt above - 0.5 M-NaCl. Therefore, dependence of these differences may vary for different DNA molecules, i.e. those molecules where a B-Z conformational junction must form and those not requiring junction formation, An in equations (a) and (5) is thus regarded as a constant coefficient of [NaCl] for a particular transition and indicates the salt concentration required to induce B to Z conversion. Likewise, the brackets on [NaCl] in equation (1) are meant to indicate An[NaCl] represents all salt-dependent reactions, not merely site binding of NaCl to phosphate groups. The calculations of Soumpasis (1988) predict a linear dependence (above - @9 M-NaCl) of the B-Z transition free energy, in excellent agreement with the published experimental data and the salt dependence of the transition free energies evaluated for the molecules of this study. The observed equilibrium constant for the reaction in equation (a), Kobs, is given by:
Mobs= fz/(l -fd = K,,[NaCl]*“, where ,fz is the spectrally determined molar amount of the d(C*G)41 core of each molecule in the Z-form, as given Figure 2. Taking the natural log of both sides of equation (6) yields: = In (K,,) +-An In [NaCl].
+ C, constants.
AG,,, = - RT In (K,,,,J = - RT An In [NaCl] - RT In (K,,,).
Figure 3. Plots of In (Robs) versus In [N&I] for molecules I to III. The slopes and y intercept of each of the linear regions indicated were determined by linear least-squares fits to the region corresponding to (@35
In (Is&)
AGobs = - K[NaCl] C are empirical
(7)
(8) From
(9)
The connection between the thermodynamic parameters of equations (1) and the empirical quantities in equation (8) can be found by equating equ;ations (8) and (9), which indicates:
-RT
In (K,,) = C
RTAn In [NaCl]
= k-[NaCi].
(10) (11)
Following the analysis of others (Luthman & Behe, 1988; Pohl, 1982; Pohl & Jovin, 1972) and plotting In (Kobs) versus In [NaCl] for molecules I to III as shown in Figure 3, provides a graphical means by which to evaluate An (from the slope) and The linear regions fit In (K,,) from the y intercept. to each transition curve and employed in paralmeter evaluations are shown in Figure 3. Values of the resulting graphically evaluated tra’nsiltion parameters are given in the legend to Figure 3. Figure 3 reveals the plots of In (Kobs) ?)erSuS In [NaCl] for molecules I, II and III clearly display two transition regions. The first transition is rather broad and occurs up to fi = 0.3 while the second transition has a greater slope and takes plabce above fi = @3. Interpretation of the early transitions of molecules I and II is somewhat uneertain d-ue to deviations from linearity of the transition free energy, in conflict with our empirical model, that can be significant at the low salt eoncentra,tions of molecules I and IT over which the first transitions occur. The relatively higher salt concentration over which the first transition of molecule IT1 occurs allows a more meaningful interpretation. The distinctly biphasic transition of molecule III suggests that until the fraction of Z-form reaches 0.3, that is 0.3 x 8 = 2.4 base-pairs (on average) have flipped to the Z-form, B-Z conversion proceeds much less co-operatively. This being so: the lower limit on the critical size of the co-operative unit for the B-Z transition of molecule III must be of the order of 2.4 base-pairs. The shapes of the fi versus NaCli curve6 shown in Figure 2 for molecules I or II and III are quite similar near the transition midpoint (fz =: 0.5) except that the transition of molecule IIT is shifted upward in salt concentration by N 2~5 M-?iaCl. A qualitative interpretation consistent with these observations is: the first transition in molecule III corresponds to the formation of a stable conformational junction between the Z-forming (C*G:), block and the flanking heterogeneous eight base--pair B-form duplex region. Evidence supporting this conjecture obtained from n.m.r. measurements of molecule III at high salt (4.5 M-N&I) indicated the presence of a B-Z junction containing approxi-
M. J. Doktycz et al.
6
mately three base-pairs (Sheardy & Winkle, 1989). The present arguments suggesting formation of a stable B-Z conformational junction composed of between two and three base-pairs are entirely consistent with measurements previously reported (Luthman & Behe, 1988; Klysik et al., 1983; Ellison et al., 1985; Sheardy & Winkle, 1989; Dai et al., 1989). Quantitative verification of the interpretations given above can be obtained from our empirical model by considering the total free energies of molecules I or II, AG::, and molecule III AGF;. Since - RT In (K,,) = AG,,, equations (8) and (10) indicate: AG:li
= rc[NaCl] + AGf;;:
AC:: = Ic[NaCl] + AG::,. IC is a constant that can be evaluated at either [NaCl]: or [NaCl]:” using the graphically evaluated An values obtained from the plots in Figure 3 for each of the molecules. In general, IC is found by equating the derivatives of the expressions on either side of the equals sign in equation (11):
An dln [NaCl] d[NaCl] which
should
rca[NaCl] WCII,
AGj = 1875(355-
1.04) = 47 kcal/mol.
(16)
This value is in excellent agreement with published values of B-Z junction free energy (4 < AGj < 5 kcal/mol junction) evaluated from analysis of B-Z transitions in supercoiled (Singleton et al., 1983) and linear DNA polymers (Luthman & Behe, 1988; Klysik et aZ., 1983). The thermodynamic equivalence of the junction free energy in the 16 base-pair DNA of this study with that of junctions formed in DNA polymers, indicates B-Z junctions have similar structural independent characteristics of the molecular environments in which they reside. Therefore, it immediately appears that the 16 base-pair junctioncontaining molecule of this study is an ideal candidate with which to perform n.m.r. and X-ray erystallographic investigations of the solution structure and at,omic dimensions of a B-Z conformational junction. Such investigations are currently in progress. This work was supported by grants GM-39471 from the National Institutes of Health (ASB), and DMB-8616358 from the National Science Foundation (RDS).
= RTd[NaCl] IINaCI,,’ (13)
yield:
IC = RT(An,,,/[NaCl]~)
gives:
References Car&hers,
= RT(An,,,,/[NaCl]~“). (14)
ICis calculated from the values of An,,,, and An,,, and the mid-point salt concentrations stated above and given in the legend to Figure 3. For molecules I and II, the value of IC at the transition midpoint is found to be 1880 compared to 1869 cal/mol [NaCl] for molecule III (1 cal = 4.184 J). Considering the errors associated with fitting the linear regions on the plots in Figure 3 ( *5%) to obtain An, these IC values evaluated at the midpoints of the transitions of molecules I to III are in exact agreement. Such agreement in conjunction with the actual transition data of Figure 2 provides quantitative proof that the second transition of molecule III indeed obeys the same salt dependence as the transitions of molecules I and II. An explanation consistent with this notion is: molecule III undergoes the same equilibrium conformational transition as molecules I and II shifted to higher salt by the unfavorable free energy cost of forming a B-Z junction. Thus, the junction free energy, AGj can be obtained from the difference of the free energies given in equations (13) and (14). At the respective transition midpoints, [NaCl] = [NaCl]y or [NaCl]:, AGkii = AGi’& = 0, AG:J = rc[NaCl]y and AGFi = rc[NaCl]E. Therefore: AGj = RTk-( [NaCl]$-
[NaCl]p).
M. H. (1982). In Chemical and Enzymatic of Gene Fragments (Gassen, H. 6. 8r. Lang, A., eds), Verlag Chemie, Weinheim. Chen, C., Ringquist, S. & Hanlon, S. (1987). Biochemistiry, 26, 8213-8221. Dai, Z., Thomas, G. A., Evertsz, E. & Petieolas, W. L. (1989). Biochemistry, 28, 6991-6996. Ellison, M. J., Kelleher, R. J. III, Wang, A. II-J., Habener, J. F. & Rich, A. (1985). Proc. Nat. Acad. Synthesis
(W
Substituting in equation (15) the average value of IC given above (- 1875) and the appropriate midpoint salt concentrations provided in the Eigure 3 caption
Sci., O.S.A. 82, 832068324. Jaworski, A., Hsieh, W.-T., Blaho, J. A., Larson, J. E. Ss Wells, R. D. (1987). Science, 238, 773-777. Jovin, T. M. & Soumpasis, D. M. (1987). Anna 41ev. Phys. Chem. 38, 521-560. Klysik, J., Stirdivant, S. M., Singleton, C. K., Zacharais, W. & Wells, R. D. (1983). J. Mol. Biol. 168, 51-71. Luthman, K. & Behe, M. J. (1988). J. Biol. Chem. 263, 15535-15539. Manning, G. S. (1978). Quart. Rev. Biophys. 11, 179-246. Manzini, G.; Xodo, L. E., Quadrifoglio, F., van Boom, J. II. & van der Marel, G. A. (1987). 1. Biomol. Wuct. Dynam. 4, 651-661. Pohl, F. M. (1982). Cold Spring Harbor Symp. Quad. Biol. 47, 113-117. Pohl, F~ M. $ Jovin, T. M. (1972). J. 1Mol. Biol. 67, 375-396. Quadrifoglio, C., Manzini, G. & Yathindra, N. (1984). d. Mol. Biol. 175, 419-423. Sheardy, R. D. (1988). Nucl. Acids Res. 15, 1153-t 167. Sheardy, R. D. & Winkle, S. A. (1989). Biochemistry, 28, 720-725. Singleton, C. K., Klysik, J. & Wells, R. D. (1983). Proc. Nat. Acad. Xci., U.S.A. 80, 2447-2451. Soumpasis, D. M. (1988). J. Xiomol. Struct. Uynam. Q. 5633574. Zacharias, W., O’Connor, T. R. X: Larson, J. E. (1988). Biochemistry, 27, 2970-2978.
Edited by P. van Hippel
Energetics of B-Z Junction Formation Sixteen Base-pair Duplex DNA Mitchel
J. Doktycz,
Albert
in a
S. Benight
Department of Chemistry, Box 4348 University of Illinois at Chicago Chicago, IL 60680, U.S.A.
and Richard
D. Sheardy?
Department Pennsylvania
Hazleton
Campus,
of Chemistry State University Haxleton, PA 18201, U.S.A.
{Received 23 June 1989; accepted 10 October 1989) We report analysis of the NaCl-induced B-Z transition in a 16 base-pair duplex DNA with sequence designed such that when NaCl is increased the left half of the molecule undergoes the B-Z transition while the right half remains in the B-form. An equilibrium thermodynamic model based on the body of available published experimental data and the recent theoretical work of Soumpasis, which indicate, in tbe salt range above - 69 M-NaCl, the transition free-energy of B-Z conversion in DNA is a linear function of the NaCl concentration, is employed. Analysis of the B-Z transition of the junction-containing molecule indicates the B-Z junction formed in this I6 base-pair DNA is composed of approximately three base-pairs and has a free energy of formation of - 4.7 kcal/mol junction. These values for the junction are in excellent agreement with published estimates of B-Z junction size and energy derived from much longer DNA pieces.
B-Z
junction formed in this 16 base-pair duplex DNA oligomer in high salt (4.5 M-NaCl) was reported (Sheardy, 1988; Sheardy & Winkle, 1989). Figure 1 shows the three molecules of this study. Molecules I to III contain the core duplex sequence 5’(C*G),3’ (C * is 5-methyl-cytosine) but differ in the type of DNA environment adjoining the common core duplex. Short alternating C*G sequences of similar length have been previously demonstrated B-Z transition (Pohl, to undergo a salt-inducible 1982; Quadrifoglio et al., 1984). Molecule I is the eight base-pair core duplex. Molecule II has the eight base single strand sequence 5’ACTGACTGS’ extending on the 3’ end of each strand of the core duplex region. Molecule III contains I6 base-pairs, the core duplex on the left half and the duplex sequence 5’ACTGACTGS’ on the right half. The B-Z transition in molecules I to 111. of Figure 1 was assayed by monitoring the o.d. slpectrum as a function of NaCl concentration at 25°C. C.D. spectra were recorded on either a Jasco 600 or AVIV spectropolarimeter. Plots of the spectrally determined values of fi (fraction of Z-form) versus NaCl concentration for molecules 1 to III are depicted in Figure 2. The transition curves of molecules I and II in Figure 2 are virtually identical between fz = 61 and O-9 over the entire range of NaCl concentration from 0.2 M to 1.9 M. This result apparently indicates that the eight base dangling single strand ends of molecule II do not significantly
It is a widely believed notion that left-handed Z-DNA actually exists in, vivo (Jaworski et al., 1987), and as such serves as an instrumental conformational element. This notion has been the primary motivation for a number of studies undertaken to elucidate the structural conversion of right-handed B-DNA to left-handed Z-DNA (Zacharias et al., 1988; Luthman & Behe, 1988; Sheardy, 1988; Soumpasis, 1988; Jovin & Soumpasis, 1987; Manzini et al., 1987; Chen et al., 1987; Singleton et al., 1983; Klysik, et al., 1983). Thermodynamic aspects of the interface or “junction” between contiguous B and Z forms on the same duplex DNA molecule have been investigated in supercoiled DNA (Zacharias et al., 1988; Ellison et al., 1985; Singleton et al., 1983) cloned restriction fragments (Klysik et al., 1983) and polymerized repeating sequences (Luthman & Behe, 1988). Here we report thermodynamic analysis of the NaCi-induced B-Z transition in a 16 base-pair duplex DNA with sequence designed such that the left half of the molecule undergoes the B-Z transition while the right half remains in the B-form. Recently, the design strategy and preliminary characterization by circular dichroism (c.d.$) and nuclear magnetic resonance (n.m.r.) analysis of the t Present address: Department of Chemistry, Hall University, South Orange, NJ 07079, U.S.A. $ Abbreviations used: c.d., circular dichroism; nuclear magnetic resonance; C*, 5-methyl-cytosine.
Seton n.m.r., 3
0022-2~3c;/SOjOZOOO3-o4 $03.00/O
0 1990 Academia Press Limited
M. J. Doktycx et al.
0
0
.
d 1:drK”G)4~Ac T G,,,
.
2+2=II C’C C’G C”G C”G A c T G A c Y 0 G T c A G T c * G c*o C’G C”G C’
.
q . q .
q
. c 0.0
Figure 1. DNA fragments of this study. DNA oligomers were synthesized by the trityl-on phosphoramidite method (Caruthers, 1982). Complete products were purified from untritylated failure sequences by reverse phase high-pressure liquid chromatography, deprotected by overnight incubation at 60°C in 3 vol. 100% ammonium hydroxide and detritylated by treatment with 80% (v/v) acetic acid. Samples were dried under vacuum, resuspended in sterile double-distilled water (ddH,O), and subjected to a 2nd pass over the preparative chromatography column. Purity of oligomers was > 99% as determined by electrophoresis on 20% (w/v) polyacrylamide gels. Strand annealing was achieved by heating the oligomers in ddH,O to 95°C for 5 min and slowly recooling. Molecules I to III were formed by annealing the appropriate oligomers as shown.
affect the transition behavior of the d[(C*G),] core duplex. The transitions in molecules I and II occur at lower NaCl concentrations and span a much narrower range than that of molecule III. Wolecules I and II have a transition midpoint at 1.04 M-NaCl; the transitions are complete at 2.1 M and 2.6 M-NaCl, respectively. The transition of molecule III has a midpoint at 3.55 M-NaCl and is complete by 4.5 M-NaCl. The presented transition data can be interpreted in terms of a two-state model where base-pairs can exist in only one of two possible states, the B or Z state. fi is the average fraction of base-pairs per molecule in the 2 conformation. We assume the salt induced B-Z transitions of duplex base-pairs in the (C*G), region are equilibrium processes at all salt concentrations and the equilibrium conformational transitions can be represented as, B + An[NaCl]
2 Z
(1) where R and Z represent a molecule with its potentially Z-forming core duplex in either the B or Z is the total equilibrium state, respectively. K,, constant and is a constant independent of [NaCl] that only depends on the temperature and pressure. K,, can be represented as: K,,
where brium
= KobsKp~,
is the equilibrium constant that includes all K di&ences in the polyelectrolyte characteristics of a particular molecule when it is in either the B versus Z conformation. From equations (1) and (3): = K,b,/[NaC1]A”,
I.0
1
1
1
1
2-o
3.0
4.0
5.0
[NaCl]
Figure 2. B-Z transition curves of molecules I to HI. Titrations of DNA with salt from 0 to 50 M-Pu’acl were performed by first dissolving freeze-dried portions of each DNA molecule to the same concentration in either buffer A (10 mM-phosphate, 1 mM-EDTA, pH 7.0) or buffer B (5.0 M-NaCl, 10 mM-phosphate, I mm-EDTA, pH 7.0) and combining portions of DNA in buffer A and buffer B solutions in the appropriate amounts to achieve the desired salt concentration. DNA concentrations determined from the absorbance at 260 nm were typically around 075 absorbance units/ml. After equilibration for 5 min, c.d. spectra of DNA solutions at every NaCl concentration remained constant for over 24 h. The low salt cd. spectra of molecules I and II were typically B-like, characterized by a trough at 255 nm and a peak at 286 nm (Sheardy, 1988; Sheardy & Winkle, 1989). In high salt the spectra were inverted and typically left-handed with a trough at 295 nm and a peak at 275 nm (Sheardy, 1988; Sheardy & Winkle, 1989). The low salt spectrum of molecule III was essentially B-like, with a trough at 253 nm and peak at 280 nm while the high salt spectrum had spectral features of both right-handed and lefthanded DNA, i.e. a shallow trough at 295 nm, a peak at 278nm and another trough at 253nm (Sheardy, 1988; Sheardy & Winkle, 1989). This observation suggests the high salt form of molecule III contains both right-handed B and left-handed 2 structures and must therefore contain a B-Z conformation junction. Recently reported n.m.r. and c.d. studies of molecule III in high salt verified the existence of a stable B-Z junction at high salt (Sheardy $ Winkle, 1989). Extent of the B-Z transition (fz) for molecules I to III, between the low (0 ivI-NaCl) and high salt (~OIVI-NaCl) forms that define the endpoints, was determined by monitoring the change in molar ellipticity at 295 nm (A+). de, is the difference between the molar ellipticity (~~-6~) at 0 salt and 50 M-Nacl. From the measured change in molar ellipticity at 295 nm as a function of NaCl concentration, As(NaCl), fz was determined according to: fi = [(A&r-As(NaCl))/A+]. fz, the spectroscopically determined fraction per molecule described in the text, is plotted NaCl concentration. The open squares and filled are the transitions of molecules I and IT. squares indicate the molecule III transition.
of Z-form V~~SZLS the diamonds The filled
(2)
observed equiliKobs is the experimentally constant for the B to Z structural transition: K obs = [ZI/[Bl. (3)
K,,
‘Z’
(4)
indicating
for this treatment
that:
K,, = [NaCllPA”. (5) An in equations (1) and (5) includes the collective difference between the sequence-independent electrostatic interactions of the charged phosphate backbone with bulk water and the diffuse ionic cloud of hydration surrounding the DNA in the B or Z conformations”
5
Communications
range above concentration salt In the - 09 iw-NaCl, the observed free energy of the B-Z transition, AGnhs, is a linear function of [NaCl] and form as: can thus be written in the empirical
,
-4 -3
-2
,: -I
/' , '0
/
where IC and equation (7):
I
I I
In [NaCI]
An in equations (1) and (5) should not be confused with the salt uptake of the transition as required by Manning’s counterion condensation model of poly1978). Recently, in fact electrolytes (Manning, Soumpasis (1988) has shown that the counterion condensation and Poisson-Boltzmann approaches are inadequate representations of the B-Z transition in DNA. Alternatively, the calculations of Soumpasis, employing a hypernetted chain model of DNA and the sequence-independent, but saltdependent interactions represented by the factor An[NaCl] in equation (l), fit the available experimental data over the entire salt concentration range because the salt above - 0.5 M-NaCl. Therefore, dependence of these differences may vary for different DNA molecules, i.e. those molecules where a B-Z conformational junction must form and those not requiring junction formation, An in equations (a) and (5) is thus regarded as a constant coefficient of [NaCl] for a particular transition and indicates the salt concentration required to induce B to Z conversion. Likewise, the brackets on [NaCl] in equation (1) are meant to indicate An[NaCl] represents all salt-dependent reactions, not merely site binding of NaCl to phosphate groups. The calculations of Soumpasis (1988) predict a linear dependence (above - @9 M-NaCl) of the B-Z transition free energy, in excellent agreement with the published experimental data and the salt dependence of the transition free energies evaluated for the molecules of this study. The observed equilibrium constant for the reaction in equation (a), Kobs, is given by:
Mobs= fz/(l -fd = K,,[NaCl]*“, where ,fz is the spectrally determined molar amount of the d(C*G)41 core of each molecule in the Z-form, as given Figure 2. Taking the natural log of both sides of equation (6) yields: = In (K,,) +-An In [NaCl].
+ C, constants.
AG,,, = - RT In (K,,,,J = - RT An In [NaCl] - RT In (K,,,).
Figure 3. Plots of In (Robs) versus In [N&I] for molecules I to III. The slopes and y intercept of each of the linear regions indicated were determined by linear least-squares fits to the region corresponding to (@35
In (Is&)
AGobs = - K[NaCl] C are empirical
(7)
(8) From
(9)
The connection between the thermodynamic parameters of equations (1) and the empirical quantities in equation (8) can be found by equating equ;ations (8) and (9), which indicates:
-RT
In (K,,) = C
RTAn In [NaCl]
= k-[NaCi].
(10) (11)
Following the analysis of others (Luthman & Behe, 1988; Pohl, 1982; Pohl & Jovin, 1972) and plotting In (Kobs) versus In [NaCl] for molecules I to III as shown in Figure 3, provides a graphical means by which to evaluate An (from the slope) and The linear regions fit In (K,,) from the y intercept. to each transition curve and employed in paralmeter evaluations are shown in Figure 3. Values of the resulting graphically evaluated tra’nsiltion parameters are given in the legend to Figure 3. Figure 3 reveals the plots of In (Kobs) ?)erSuS In [NaCl] for molecules I, II and III clearly display two transition regions. The first transition is rather broad and occurs up to fi = 0.3 while the second transition has a greater slope and takes plabce above fi = @3. Interpretation of the early transitions of molecules I and II is somewhat uneertain d-ue to deviations from linearity of the transition free energy, in conflict with our empirical model, that can be significant at the low salt eoncentra,tions of molecules I and IT over which the first transitions occur. The relatively higher salt concentration over which the first transition of molecule IT1 occurs allows a more meaningful interpretation. The distinctly biphasic transition of molecule III suggests that until the fraction of Z-form reaches 0.3, that is 0.3 x 8 = 2.4 base-pairs (on average) have flipped to the Z-form, B-Z conversion proceeds much less co-operatively. This being so: the lower limit on the critical size of the co-operative unit for the B-Z transition of molecule III must be of the order of 2.4 base-pairs. The shapes of the fi versus NaCli curve6 shown in Figure 2 for molecules I or II and III are quite similar near the transition midpoint (fz =: 0.5) except that the transition of molecule IIT is shifted upward in salt concentration by N 2~5 M-?iaCl. A qualitative interpretation consistent with these observations is: the first transition in molecule III corresponds to the formation of a stable conformational junction between the Z-forming (C*G:), block and the flanking heterogeneous eight base--pair B-form duplex region. Evidence supporting this conjecture obtained from n.m.r. measurements of molecule III at high salt (4.5 M-N&I) indicated the presence of a B-Z junction containing approxi-
M. J. Doktycz et al.
6
mately three base-pairs (Sheardy & Winkle, 1989). The present arguments suggesting formation of a stable B-Z conformational junction composed of between two and three base-pairs are entirely consistent with measurements previously reported (Luthman & Behe, 1988; Klysik et al., 1983; Ellison et al., 1985; Sheardy & Winkle, 1989; Dai et al., 1989). Quantitative verification of the interpretations given above can be obtained from our empirical model by considering the total free energies of molecules I or II, AG::, and molecule III AGF;. Since - RT In (K,,) = AG,,, equations (8) and (10) indicate: AG:li
= rc[NaCl] + AGf;;:
AC:: = Ic[NaCl] + AG::,. IC is a constant that can be evaluated at either [NaCl]: or [NaCl]:” using the graphically evaluated An values obtained from the plots in Figure 3 for each of the molecules. In general, IC is found by equating the derivatives of the expressions on either side of the equals sign in equation (11):
An dln [NaCl] d[NaCl] which
should
rca[NaCl] WCII,
AGj = 1875(355-
1.04) = 47 kcal/mol.
(16)
This value is in excellent agreement with published values of B-Z junction free energy (4 < AGj < 5 kcal/mol junction) evaluated from analysis of B-Z transitions in supercoiled (Singleton et al., 1983) and linear DNA polymers (Luthman & Behe, 1988; Klysik et aZ., 1983). The thermodynamic equivalence of the junction free energy in the 16 base-pair DNA of this study with that of junctions formed in DNA polymers, indicates B-Z junctions have similar structural independent characteristics of the molecular environments in which they reside. Therefore, it immediately appears that the 16 base-pair junctioncontaining molecule of this study is an ideal candidate with which to perform n.m.r. and X-ray erystallographic investigations of the solution structure and at,omic dimensions of a B-Z conformational junction. Such investigations are currently in progress. This work was supported by grants GM-39471 from the National Institutes of Health (ASB), and DMB-8616358 from the National Science Foundation (RDS).
= RTd[NaCl] IINaCI,,’ (13)
yield:
IC = RT(An,,,/[NaCl]~)
gives:
References Car&hers,
= RT(An,,,,/[NaCl]~“). (14)
ICis calculated from the values of An,,,, and An,,, and the mid-point salt concentrations stated above and given in the legend to Figure 3. For molecules I and II, the value of IC at the transition midpoint is found to be 1880 compared to 1869 cal/mol [NaCl] for molecule III (1 cal = 4.184 J). Considering the errors associated with fitting the linear regions on the plots in Figure 3 ( *5%) to obtain An, these IC values evaluated at the midpoints of the transitions of molecules I to III are in exact agreement. Such agreement in conjunction with the actual transition data of Figure 2 provides quantitative proof that the second transition of molecule III indeed obeys the same salt dependence as the transitions of molecules I and II. An explanation consistent with this notion is: molecule III undergoes the same equilibrium conformational transition as molecules I and II shifted to higher salt by the unfavorable free energy cost of forming a B-Z junction. Thus, the junction free energy, AGj can be obtained from the difference of the free energies given in equations (13) and (14). At the respective transition midpoints, [NaCl] = [NaCl]y or [NaCl]:, AGkii = AGi’& = 0, AG:J = rc[NaCl]y and AGFi = rc[NaCl]E. Therefore: AGj = RTk-( [NaCl]$-
[NaCl]p).
M. H. (1982). In Chemical and Enzymatic of Gene Fragments (Gassen, H. 6. 8r. Lang, A., eds), Verlag Chemie, Weinheim. Chen, C., Ringquist, S. & Hanlon, S. (1987). Biochemistiry, 26, 8213-8221. Dai, Z., Thomas, G. A., Evertsz, E. & Petieolas, W. L. (1989). Biochemistry, 28, 6991-6996. Ellison, M. J., Kelleher, R. J. III, Wang, A. II-J., Habener, J. F. & Rich, A. (1985). Proc. Nat. Acad. Synthesis
(W
Substituting in equation (15) the average value of IC given above (- 1875) and the appropriate midpoint salt concentrations provided in the Eigure 3 caption
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Edited by P. van Hippel