Electrostatic Forces at Helix-Coil Boundaries in DNA R. D. BLAKE and SCOTT C. DELCOURT

Department of Biochemistry, University of Maine, Orono, Maine 04469

SYNOPSIS

The T,, of internal loop-forming (dA . dT), domains in pBR322 DNA has been measured over a tenfold range of "a+]. The slopes SN = dT,/d log"a+] are linear and decrease in magnitude with decreasing loop size N, signaling a reduction in Na' released during the transition of these domains to the coil state. Values of SN decrease linearly with increasing N-' in accordance with the expectation of a simple model for the occurrence of a gradient of long-range electrostatic forces at helix-coil boundaries, and extrapolate almost precisely to the value of S, observed for (dA . dT),. These results indicate (1) less counterion is released per phosphate residue from the finite loop than from the infinitesized loop, and (2) the difference in binding is constant for each boundary formed and independent of the size of the loop within the range examined: 350 base pair (bp) > N > 71 bp. The slope of the dependence of SN n: N-' indicates the region of highe! charge density at the boundary extends at least 18 A into the coil and probably 40-50 A before dropping to a value characteristic of the unperturbed coil. The free energy for excess counterion binding at boundaries can be expressed by

-

-AG/RT

= 10.47log[Na']

+ 5.234

When the loop entropy function in a statistical mechanicalalgorithm for the dissociation of DNA is weighted by this quantity, calculated T, are seen to vary by only f0.09"C from observed.

I NTRODUCTlON In its active roles in the cell the two strands of DNA undergo total or partial separation. A knowledge of the thermodynamics of partial strand separation is needed to appreciate the full dimensions of these biological processes. Our most recent approach to this question has been through examination of the energetics of internal loop formation,' using as specimens for study a series of homopoly(dA . dT), inserts in the plasmid pBR322, following loop formation by high-resolutionmelting.2*3 Results indicate that the (dA dT), inserts, dissociating as well-resolved subtransitions at temperatures well below those for the remaining DNA of

-

Q

1990 John Wiley & Sons, Inc.

CCC OOOS-3525/90/020393-13 $04.00 Biopolymers, Vol. 29,393-405 (1990)

the plasmid, are more stable than expected for hypothetical inserts exhibiting ideal behavior, and consisting of freely jointed, Gaussian chains.' Under the solvent conditions of our earlier study, a (dA dT),, insert melts at a temperature expected for a domain of only 91 base pairs (bp) suggesting that polydeoxynucleotide chains are less elastic than expected of Gaussian chains of the same length. This apparent difference in elasticity coincides closely with the extent of residual single-strand stacking in the dissociated loop; it was therefore proposed that an incipient helical orientation of some residues might provide a small thermodynamic advantage for reclosure, and thereby account for the greater stability and apparent stiffness of internal loop domains. It remains to be demonstrated that residual stacking is a significant factor in increasing the loop energy.

-

393

394

BLAKE AND DELCOURT

There is another possible reason for the altered stability of loop-forming domains that has as its basis the existence of atypical properties in coil regions where they interface with helix. Coil strands in the region of interface with helix are subject to the effects of more intense long-range electrostatic forces than are found in interior regions. Electrostatic forces extending beyond nearest neighbors are known to contribute to the altered stability of short he lice^.^,^ In our previous study it was assumed that such forces would be screened to a considerable extent by the moderately high ionic condition of those studies. It was further assumed that since the insert sizes were quite large ( > 60 bp), boundary effects would be negligible. Those studies were carried out in a fixed ionic environment; therefore electrostatic contributions could not be identified. In the present study we have measured the electrostatic effect a t helix-coil boundaries by determination of the energetics of loop formation for three well-characterized sizes of internal loop over a tenfold range of "a+]: 0.03-0.30 molar. This is the maximum range that could be examined. Below 0.03M Na reassociation of DNA is too slow, so that it is difficult to obtain equilibrium melting curves a t reasonable heating rates ( > 3"C/h), while above 0.3M NaCl the high C1- concentration begins to contribute significantly to the energetics of dissociation. +

MATERIALS A N D M E T H O D S DNA Specimens

Recombinant pBR322, containing (dA . dT), inserts of varying lengths N , was prepared and characterized as previously described.' Stretches of (A . T) base pairs were inserted a t the locus for restriction endonuclease PvuII in pBR322 a t position 2069, directly opposite and a t good distance from the locus for restriction endonuclease EcoRI, used for scission and linearization of the circular form in the preparation of DNA for high-resolution melting. The insert locus occurs in a comparatively (G C)-rich region of pBR322 that melts a t very high temperature and therefore acts as stable boundaries for the insert. The fractional (G + C) content (Fee) of the 150 bp downstream from the insert locus is 0.52, and 0.62 upstream. Spectroscopic and thermodynamic analyses indicate that melting is limited to just the (dA . dT)," insert for sizes > 40 10 bp when the insert is in the PvuII

+

sequence environment of pBR322 (Ref. 1, and unpublished work of S. Delcourt and R. Blake). The lengths of (dA dT), were determined by three different approaches as previously described.' Results from numerous replicate analyses indicate an uncertainty in the lengths of inserts of f l bp. Three sizes of insert containing 71, 82, and 114 (A . T) base pairs were selected for detailed examination of electrostatic effects. The plasmids containing these inserts are alternately referred to as pBR322(dA . dT), or simply (dA . dT),. The poly(dA . dT) specimen used in this study and sometimes referred to as the "infinite polymer," was of commercial source. The electrophoretic mobility of this specimen in 1%agarose was limited entirely to the compression zone; therefore it can only be said that the length is > 30 kilo bases (kb). Poly(dA . dT) was added to all plasmid specimens undergoing high-resolution melting. Its melting occurs sharply and a t low temperature, well isolated from the melting of the plasmid or of (dA. dT), inserts, and therefore serves as a useful secondary standard, both as an apparent representative of an insert of infinite size in the determination of loop energy and as a sensitive indicator of sodium ion concentration. Full melting of poly(dA . dT) takes place within 0.7"C, while 50% melting occurs within 0.15"C near T,. T, for poly(dA . dT) can usually be determined to within f0.05"C. The T, of poly(dA . dT) has been determined for almost 40 different "a+] over the range of 0.01-1.OM. The log[Na+] dependence is linear over the range of 0.01-0.50M Na+, with r = 0.9994. The least-squares slope and intercept given in the first line of Table I are then used in the confirmation of "a+] for melting results of (dA . dT), inserts. Bacterial DNAs used in this study were obtained from various commercial sources. These DNAs were subjected to CsCl density gradient centrifugation both as check of the (G + C) content and as a further purification step.

"a']

and Buffer

The total "a+] was determined from the weight of added NaCl plus a small contribution from ionized buffer. Before the weighing of NaCl it was dessicated at 150°C for 24 h. A Na cacodylate buffer and Na EDTA chelating agent were present in all solutions in the amount of 2.5 and 0.2 mM, respectively, and together were assumed to contribute 1.75 m M Na' to the total. The depen-

ELECTROSTATIC FORCES

395

Table I Parameters" for the Sodium Ion Dependence of the Melting Temperature

S

Ti,,

4x

20.058 19.852 18.009 17.269 16.845 20.84 20.21 15.839 18.327 17.015 17.3 16.934 18.36 19.29 17.032 15.302 17.142 15.669 16.2 15.431 13.67

88.099 85.935 89.802 91.261 91.827 82.24 85.39 94.787 96.065 97.872 102.2 104.77 107.49 101.45 105.450 103.705 109.350 107.829 109.1 112.31 123.66

0 0 0 0 0 0 0 0.25 0.28 0.33 0.44 0.499 0.50 0.50 0.52 0.527 0.59 0.61 0.62 0.72 1.oo

DNA Specimen Poly(dA . dT) . . (dA . dT), . . . . . (dA . dT),,, . . . . . . (dA . dT),. . . . . . . (dA . dT),, . . . Poly[d(A - T) . d(A (dA . dT}h

-

T)]

pBR322 #1 CLperfringens DNA pBR322 #2 B. subtilis DNA

A-DNA Poly[d(A - C) . d(G - T)] Poly[d(G - A) . d(T - C)] E . coli DNA pBR322 DNA (overall) pBR322 #10 pBR322 # l l Ps. fluorescens DNA M . Zysodeikticus DNA

{dG - dCJh

'IT,! = S log,,,[Na+]+ T,.,,, "C and S

=

dT,,/d log,,,[Na

'1.

"Obtained by extrapolation (cf. Fig. 6).

dence of T,, on log[Na+] was determined for most DNA specimens on a t least six samples, equispaced in log[Na ' ] over the range of 0.03-0.3M Na+. The NaCl was weighed separately for each sample-not added by serial dilution from a single stock concentrate. The T, of poly(dA . dT) that was added to all specimens served as a check of the "a']. Statistical Mechanical Calculations of Melting Curves

The model used for dissociation of DNA was the familiar Ising model for a one-dimensional lattice with loop entropy,2 in which linked nucleotide residues exist in either the paired or disordered state for each configuration of states. The algorithm is a modified version of that described by Fixman and Freire,6 with values for parameters given in our previous report.' Melting Curves

DNA melting was followed by the loss of hypochromicity, by the absorbance differenceapproximation m e t h ~ d ,most ~ often a t 270 nm, where the difference-extinction coefficients for (A . T) and ( G . C) base pairs are equal.3 Values of AA( X ),/AT were digitized a t densities of 100 deg-'.

Temperature was increased at 6.3"C h I , whch is less than half the rate leading to nonequilibrium melting curves in the lowest salt region of these studies,',8 and controlled to within kO.5 mdeg as previously de~cribed.~ The melting temperature (T,) was determined by a nonlinear regression fit of a derivative "cosh" function for a two-state transition to the experimental ~ubtransition,'~~ or from the temperature corresponding to (& A ) / I( dT The latter method was used, for example, for obtaining T, of poly(dA . dT), which exhibits an asymmetric derivative melting profile. ~

RESULTS Melting temperatures of subtransitions in DNA depend on nucleotide sequence and domain size, particularly if the domain is internal. In addition, we may expect long-range electrostatic forces to affect melting temperatures. The magnitude of such forces will depend upon the structure of bordering domains and the counterion concentration. Given the (dA . dT), specimens we have constructed, the first three conditions (domain sequence, size, and bordering domains) can be specified as independent variables, and stability can be examined against the dependent variable counterion concentration.

396

BLAKE AND DELCOURT

dWdT

1

I

8

I

1

I

5

I

I

‘ 6

t

I

60

I

I

I

I

70

I

80

temperature

I

J

30

,OC

o.o*[ dWdT

82

Figure 1. (a) High-resolution melting curve of pBR322 (dA . dT),, DNA in 0.0418M N a + , containing 5 pg/mL of poly(dA . dT) as secondary standard. (b) High-resolution melting curves of (dA . dV7,, (dA . dT),,, and (dA . dT)l,, in 0.0750M Na+. The axes have been magnified fivefold. The noisy curves represent experimental results, obtained as described in the materials and methods section. The smooth lines represent coincident theoretical curves obtained by two different methods as described in the text.

The rationale for expecting an altered dependence of T, on counterion concentration for loops of different size is that the atypical coil structure a t the interface with helix should experience more intense long-range electrostatic forces than usual. Such forces should be constant for a loop, independent of loop size, and modulated to a different extent than internal loop regions by an increase in the counterion concentration. Accordingly, the dependence of T, on [Nail has been measured for three different loop-forming domains, (dA * dT),,,

(dA . dT),,, and (dA . dT),,, in pBR322 DNA. Figure l(a) shows an illustrative melting curve of pBR322(dA . dT),, in 0.0418M Na+, containing a small amount of poly(dA . dT) as a secondary standard. The T, of the latter is 60.69OC, indicating a “a+] of 0.0430M (see the materials and methods section), and a combined error of 3% in the measurement of “a+] and temperature for this experiment, which is slightly above the average ( 52%) for all melting experiments. The ordinate in Fig. l(a) represents the derivative of the fraction of

ELECTROSTATIC FORCES

base pairs dissociated 6 with temperature. Discrete bands for subtransitions emanating from domains in the original pBR322 plasmid are clustered a t higher temperatures between 73"-87°C in Fig. l(a), and are numbered. Most but not all of these bands represent the superposition of more than one subtransition (S. Delcourt and R. D. Blake, in preparation). The subtransition for the (dA * dT),, insert is plainly visible in Fig. l(a) a t 67.79"C. The noisy curves in Fig. l(b) then represent a greatly enlarged composite of the observed subtransitions for all three (dA dT), inserts examined in this study in 0.0750M Na+. Several effects of loop size are evident from these curves. As loop size increases there is, as expected, a corresponding increase in peak height and integrated area. There is also a decrease in the range of melting and decrease in melting temperature, both reflecting a high level of cooperativity. Assuming transitions are two state, these curves may be described by the cosh equations

-

dd/dT

=

( A HJ4RT ') X

{ cosh' [ ( A H J 2 RTT,)

where the unit enthalpy per (A . T) base pair is given by

AE = AHJ(

N

+ 1)

(2)

Given experimental values for d6/dT and T, from results such as those in Fig. l(b), AH were determined from Eq. (1) by nonlinear regression. (Enthalpies determined by the van't Hoff method were essentially identical, although the analysis was limited to a more narrow range of temperature and was more cumbersome.) More than 40 experiments on insert domains over the range of 128 > N > 63 bp were analyzed in this fashion. The dependence of AH on N was nil, with correlation coefficient < 0.2. The entire collection of curves was best satisfied by a single value of AH = 8.5 k 0.8 kcal/mol(A . T)bp. The standard deviation was slightly greater for smaller inserts. Therefore, a fourfold larger number of curves for N 9 80 bp were examined than for the larger inserts. The smooth curves in Fig. l(b) were produced by Eq. (1) with AH = 8.5 kcal/mol(A. T)bp, and T, from the melting temperature for the infinite polymer

397

weighted by the loop entropy function as previously described.l Thus, while small enthalpic effects of domain size and temperature might have been expected, they are below the sensitivity of our experiments. The magnitude of the electrostatic end effect was determined from the dependence of T, on "a+] for the three sizes of insert over a tenfold range of "a+]. Some results are shown in Fig. 2. It should be mentioned that poly(dA. dT) was present in all experiments as indicator of the precise solvent conditions. Thirty-eight determinations of T, for poly(dA. dT) over the range 0.01-1.0 M Na+ (Fig. 2) fit the first-order expression

T,

=

S . log,,[Na+]

+ T,,"

(3)

with correlation of 0.9994 and standard error of 0.12"C. Slope and intercept are recorded in Table 1. The level of precision in the fit of (dA . dT), insert results to Eq. (3) was equivalent to that for poly(dA . dT) and was only marginally improved if the T, of the marker poly(dA . dT) was used to indicate "a+]. The average standard error for fit of insert results to Eq. (3) was 0.08"C. The slopes S, = dT,/d log[Na+], recorded in Table I, decrease with decreasing length N. This signals a reduction in the amount of Na+ released from loop-forming domains during the transition to coil state. Less counterion is being released from regions of higher charge density a t boundaries with helix. As shown by Manningg and Record," the fraction of counterion condensed to a polyelectrolyte plus that involved in screening is given by the ion association parameter

+

=

1- (20-l

(4)

where [, the charge density parameter, is given by [ = e2/fkTb

(5)

The quantity e 2 / c kT represents the characteristic length and b the mean spacing of charges along the contour axis of the polyelectrolyte. The fraction of counterions thermodynamically released when the charge density of the helix is reduced to that of the coil, given by A+ = (+he'x - +'Oil), is proportional to measured slopes:

=

2.3RT2, ArNA+/0.5( N

+ 1)AE

(6)

398

BLAKE AND DELCOURT

L I-* -2

I

8

I

1

I

I

I

log,,[Nat

I

I

1

I

I

I

I

J

-I

Figure 2. Variation of T,, with log[Na-] for a variety of different DNAs and domains of pBR322 DNA. The uppermost curve ( C )represents the variation for the pBR322 peak represents the variation for A-DNA; labeled # l l in Fig. l(a). The next curve down (0) the next (a)is for pBR322 peak #3; (0):pBR322 peak #l; (9):CZ.perfringens DNA; ( 0 ) :(dA . dT),,; (a):(dA . dT),,,; and the bottom most curve (0) is for poly(dA . dT). Values for the least-squares slopes and temperature intercepts a t 1.OM Na' for these and other DNAs are listed in Table I.

where S = dT,,, N / d log[Na+] in Table I. As shown above, the unit transition enthalpy is constant for loops of different size; therefore under conditions when T,,, are approximately equal we may write

represents a minimum distance for the higher counterion binding a t the ends of the loop. The average fraction of counterion bound to the entire loop is then given by

represent characteristics of the where S, and infinite polymer, presumably but not necessarily poly(dA . dT). S, and A#, represent values of the same characteristics for finite loop domains. The Record-Lohman approach in the treatment of oligoelectrolyte behavior then serves as an excellent theoretical foundation for the analysis of (dA . dT), behavior, and where possible we have preserved their notation. The model partitions charge density of the loop domain between ,$:: for ! n residue pairs a t either end of the domain, and ,$::; for the interior region. The latter is assumed to be the same as for a coil of infinite length, where bcoil 4.12 A, and the fraction of bound counterion given by #:,$' = 1 - ( 2 [ ) - l . The length over which applies is assumed to be constant over a distance of n residue pairs and independent of the size of the loop. I t is further assumed that ::6: = in these end regions. These simplifications are made in the absence of more detailed knowledge of the molecular structure and electrostatic field gradient a t the interface of helix to coil. Under these assumptions, n clearly

while that for the same segment in the helical state is given by

-

A$:,

(zix

so that

and from Eqs. (7) and (10) we obtain

Thus, S, is predicted to increase linearly with decreasing 1 / N , with a slope equal to S X 2 n , extrapolating to S, as 1 / N + 0. The plot of S, for (dA . dT), in Fig. 3 shows results to be quite linear with 1 / N ( r = - 0.9997), extrapolating to a value for S, = 19.83, which is virtually identical to that obtained for (dA . dT), (see below) and just 1% below that observed for poly(dA . dT) (Table 1). From the slope of the plot in Fig. 3 we obtain a distance equivalent to 5.50 residue pairs for n , the

ELECTROSTATIC FORCES

0

0.01

I/N

399

0.02 ,[bpi'

Figure 3. Variation of slopes dT,, ,/d log,,[Na+], obtained from results such as shown in Fig. 2 with reciprocal loop size for the three (dA . dT), specimens. The solid circle ( 0 ) at the x axis origin represents the slope for poly(dA . dT). The datum indicated by (a)is for generic (dA . dT) neighbors obtained by extrapolation (see text), while the value indicated by (a)represents the behavior of poly[(dA - dT) . (dA - dT)].

region of higher charge density a t the ends. This (minimum) distance, corresponding to 4.5 residues or 18.5 A in the coil state, is a region where coil strands approach both one another and the helix, with a corresponding local increase in charge density. The higher charge density may actually extend 10-15 nucleotide residues into the coil before reaching a value characteristic of the loop interior. From examination of Eqs. (6), (7), and (11) it is apparent that the limit to precision in the measurement of n , the size of the affected region, is subject to the precision of contributing factors, primarily the unit enthalpy associated with dissociation of loop domains, AH = AHd/( N + 1). The size of n , obtained from the slope of data in Fig. 3, is constant (kO.01 bp) over the range of sizes examined, and is a further indication that the dependence of A p on N is very small or nil. The net increase in counterion bound to the coil because of this greater charge density leads to an increase in the loop free energy. Loop energy, represented b.y the second term in the following expression' :

is seen to be proportional to the difference between

Tm,Nand Tm+ for finite and infinite size loops, respectively. Loop energy is characterized by a helix interruption parameter a, and by the loopclosure probability,6, l 2

'',

1.7

f ( N ) = ( N + 0)-

* 0.2

(13)

where D represents an empirical stiffness parameter. Plots of l/Tm, against 1/( N + 1) shown in Fig. 4 are linear ( r = 0.9994). Variations in the slopes of these curves with "a'], representing variations in loop energy, can be clearly discerned, indicating the need for explicit recognition of electrostatic contributions in Eq. (12). The equilibrium reaction for disturbance of counterion binding a t the ends of the ith internal domain during melting can be represented by the reaction

+ ( A r - 8Ar)Na'

(14)

where subscripts h and c refer to helix and coil states, where A r represents the fraction of counterion per nucleotide lost from a loop of infinite proportions and, where SAr is that extra fraction of Na+ that remains bound a t loop ends when domains ( z - 1) and ( z + 1) remain helical. The

400

BLAKE AND DELCOURT

0

102/(N+I)

I

Figure 4. The dependence of l/Tm, on 1/( N + 1) as described by Eq. (12). The solid lines were produced from linear regression analysis on the experimental results (open circles). The solid circles represent values of l/Tm for poly(dA . dT) in the corresponding “a’]. The dashed curves, labeled “Gaussian chain,” were obtained by Eq. (12) with the extrapolated value of Tm,= ( T z k ) ; a value of unity for the stiffness parameter, D; A H = 8.5 kcal/mol (A . T) bp; and a, = 2 x

-

1.5

- 1.0

log[Na’]

Figure 5. The dependence on “a’] of the equilibrium constant for the excess counterion binding at loop ends of coil regions.

EIJXTROSTATIC FORCES

equilibrium constant Ke: then accounts for the excess counterion binding at loop ends of coil regions, due to the higher charge density over those regions. [The corresponding weighting factor for the electrostatic end effect at the interface of helix and coil during melting from helix ends or for the enlargement of a loop is then given by (K;:)"'). When incorporated into Eq. (12) we obtain

Values of Kr: were evaluated a t six different "a+] from the difference between observed slopes of data such as illustrated in Fig. 4 and those calculated from Eq. (la), represented by the dashed lines. The stiffness parameter for the calculated slopes [Eq. (12)] was assigned a value of unity, so that loop energy for the latter curves corresponds to that expected of freely jointed Gaussian chains. Values used for T,,+ in Eq. (12) were those obtained by extrapolation of regression lines through experimentally determined T,, N , such as illustrated in Fig. 4 and indicated as TZ:. Figure 5 shows a plot of 1nK: determined in this fashion against log[Na+]. The results are linear, and may be described by the least-squares expression logK;;

=

4 . 5 5 . log[Na+]

+ 2.27

(16)

From this expression we calculate that K 2 + 1 at - 0.4M Na +,above which AG?: 0, and electrostatic loop-end effects are nil. The electrostatic end effect at helix-coil junctions observed here is almost tenfold greater than was observed by Elson et al.4 for helix ends. When values for Kei from Eq. (16) are applied to the loop energy term of Eq. (15) we obtain a standard error of only 0.09"C for the difference between observed and calculated T,, N . Curves calculated for (dA . dT), domains by statistical mechanics that include this weighting factor are identical to the smooth lines through experimental results in Fig. l(b). These results, therefore, account quantitatively for the difference noted previously between observed properties of singlestrand coil regions in loops and those expected for freely jointed chains. There is no apparent need to invoke a reduced chain elasticity to explain the difference. The T,, for poly(dA . dT), indicated in Fig. 4 by solid circles, fall well off the line for T,, N , being higher by more than 2°C than TZk obtained by extrapolation. Coefficients describing the depen-

-

'

401

dence of T, on "a'] for poly(dA . d T ) are given in the top row of Table I, while those for TZk are listed in the second row. The slopes are essentially the same but the intercept values differ by 2.1"C. This greater stability of poly(dA . dT) is significant to within 0.08"C and suggests a mean loop size for the latter a t T,,, of only 350-400 bp by interpolation, the precise size being dependent upon "a+]. The Na+ dependence of T, for many of the melting bands arising from the parent pBR322 DNA seen in Fig. l(a) also give evidence of being perturbed by long-range electrostatic effects. The superposition of two or more subtransitions over most of the temperature range of melting in this figure generally means a precise assignment of effects will not be straightforward; nevertheless domains responsible for effects can be localized and often identified from the magnitude of the effect and the sequence characteristics of suspected regions of DNA. Noticeable in Fig. 2 and Fig. 6 is the low "a+] dependence of T, for the band labeled #1 in Fig. l(a). From the area under the curve for this band in more than 20 melting curves on pBR322 DNA we estimate the size of the domain to be 101 f 19 bp. Thermodynamic analysis indicates this peak to represent the superposition of two or more subtransitions. Spectral decompositied indicates the segments involved have an overall (G + C) content of 23 f 2%. These characteristics correspond uniquely to a contiguous segment of 100 bp in pBR322 between #3188-3287 of 24% (G + C). The assignment has been confirmed by the perturbation of domain melting temperature after cleavage at different sites by a wide variety of restriction nucleases (S. Delcourt and R. D. Blake, in preparation). A calculated melting curve also confirms this assignment, indicating the domain responsible for the subtransition is a segment of 90 bp of 23.3% (G + C) over the region 3195-3284 in pBR322. Theory indicates melting occurs by the formation and concomitant enlargement of an internal loop, as was suggested by the thermodynamic analysis of the observed band. The theoretical and experimental temperature ranges of melting of this multistate process are identical. However, the theoretical T, is almost two degrees above the observed. A similar discrepancy was noted originally by Wartell and Benight,2 working with short fragments of pBR322 DNA containing this region. Wartell and Benight suggested that the lack of quantitative agreement between theory and experiment is due to the presence of twofold palindromic sequences that alter T, by forming hairpin

402

BLAKE AND DELCOURT

0

0.5

10 FGC

Figure 6. The variation of slopes dT,/d log,,[Na+] with base composition. Results selected for illustration in this figure include those for CZ.perfringens DNA (O), A-DNA ( O ) , E. coli DNA (O), M . Zysodeikticus DNA (a), poly(dA . dT) (a),and pBR322 DNA (0). Values for distinct peaks in the pBR322 melting curve are represented by the open circles, numbered in accordance with the melting curve shown in Fig. l(a). The line represents a plot of Eq. (18) for the collective results from different bacterial and viral DNAs (see text).

(cruciform) intermediates. There is a 26 bp palindrome at 3236/3237, and the large electrostatic effect could be one consequence of a hairpin structure since new helix-coil boundaries are generated. Unfortunately, the magnitude of the perturbation of T, could not at first be established because of uncertainty in a suitable value for the expected T, oc and of dT,, ,/d log[Na+]. We attempted to use literature values for T,,+ and dT,,,/d log[Na+] to resolve the question of electrostatic effects on melting, but found the level of precision unacceptable. Consequently, we undertook a series of systematic experiments to determine more precise values for the T, of six bacterial DNAs of different (G + C) content in different "a+]. Synthetic DNAs of repeating mono- and dinucleotides were initially included in our study; however, their melting properties were anomalous in one regard or another, and so could not be used in the overall determination of Tm,m.As can be seen in Table I, values of dT,/d log[Na+] for both poly[d(A - C) . d(G - T)] and poly[d(G - A) . d(T - C)] are high-well above values for large natural DNAs of similar (G + C) content, e.g., E . coli and A. It was also noted that data for the large bacterial/viral DNAs were not linear below - 0.03M Na'. We found T, to be significantly lower than expected from results obtained above 0.03M Na+. As can be seen in Fig, 2, the dependence of T, on "a+] for X-DNA is linear only above 0.03M Na+. Below 0.03M Na+ melting oc-

curs a t lower T, reflecting nonequilibrium behavior. A t these lower salt concentrations it is virtually impossible to obtain equilibrium melting curves at reasonable heating l3 Early published TA4-16include many results obtained below 0.03M Na+, and even below 0.01M Na+; therefore, we rejected such data for quantitative analysis of electrostatic effects. A large number of T, were obtained on six bacterial DNAs of 72 > G C > 28% over the range 0.3 > "a+] > 0.03M and fit by regression to a modified Frank-Kamenetskii equation14:

+

T,,

=

203.79

-

(3.09 - F G C )

x (38.34-6.54log,,[Na+])

(17)

The standard error in T, was f0.52"C for 27 experiments. T,, values from this expression represent the sum of energetic contributions from all ten nearest neighbor stacking factors in quasirandom proportions corresponding to the FGc of the DNA. Also, these T, represent stabilities of domains of cooperative length^,'^ i.e., not significantly different from T,,,. The derivative with respect to [Nail yields

dT,/d

log,,[Na+]

=

20.21

-

6.54FG, (18)

A plot of Eq. (18) is shown in Fig. 6, represented by the line. The observed slopes for X-DNA and several bacterial DNAs fall close to the line, reflecting

ELECTROSTATIC FORCES

the level of precision in this equation. These results are in good agreement with a relationship determined earlier7 from a study of large domains in A-DNA above 0.04M Na+: dT,,/dlog,,,[Na+]

=

20.16 - 6.82 F,,

(19)

Both Eq. (18) and Eq. (19) are substantially different from older data heavily weighted by results obtained below 0.03M Na+. The extrapolated value of dTJd log,,[Na+] for a “generic” (A . T) bp, that is, the mean value for all A - T nearest neighbor possibilities, is 20.21. This value is slightly higher than the value observed here for (dA . dT),, 19.85. The difference probably reflects a 2% larger stacking enthalpy for the A A ( T T ) nearest neighbor than for the generic A - ‘r neighbor, the mean for AA, TT, AT, and T A . Equation (18) now serves as a means to evaluate electrostatic effects in subtransitions involving domains of different base compositions in DNAs such as pHR322. Alternatively, Eq. 18 can be used to decipher the multistate dissociation of linked domains. The analysis assumes that Eq. 18 is an acceptable approximation of S, over the full range of (G + C ) contents. The multistate dissociation of the domain producing the band labeled #1 in the melting curve for pBR322 DNA shown in Fig. 1 can be analyzed by Eq. (11). The observed value of S, for this subtransition is 15.8 (Table I), which

from Eq. (18) is 15% smaller than expected for an infinite loop, 18.7, with the same base composition. Assuming the electrostatic end effect extends into the coil regions by 5.5 bp, as was seen for the (dA . dT), loops, we estimate the initial size of the loop from Eq. (11) to be 72-75 bp. As noted above, the size estimate for this domain from the integrated area under melting curves is 101 -t 19 bp, while the observed ratio S,,,/S, indicates a domain of only 75 bp. This suggests that a loop of 75 bp forms initially and then enlarges to - 101 bp. Thus, analysis of experimental profiles as well as statistical mechanical analysis of melting of the putative segment responsible for this subtransition both indicate that dissociation is multistate, beginning with the formation of a closed loop of 72-75 bp. This initial loop displays a weak dependence on “a+], as seen in Fig. 6 and Table I, because two new helix-coil boundaries are generated. The formation of the loop is then followed by an enlargement of a further 20-25 bp with no formation of additional boundaries. This interpretation is subject to the uncertainty of whether hairpin structures occur, as noted above. The melting band labeled #11 in Fig. l(a) also displays a noticeably weak dependence of T, on “a+]. A short section of the pBR322 melting curve showing the behavior of #10 and #11 over an eightfold range of “a’] is shown in Fig. 7. Peak #10 is seen to approach and merge with #11. The dependence of T, on “ a ’ ] for the

0.6

004

dQ I dT 0.2

0 84

88

403

90

96

Figure 7. Short sections of the highest temperature region of pHR322 melting, showing t h e dependence of peaks #10 and 11 (cf. Fig. 1) on “a’].

404

BLAKE AND DELCOURT

former band is equivalent to that prescribed by Eq. (18). The latter, #11, represents the dissociation of the last remnant of helix leading to total separation of the two strands, and as such exhibits the obverse electrostatic end effect of loop formation. The structure does not correspond perfectly to that examined by Elson et al.4 working with truncated oligonucleotide helixes. In the present case the helixes have dangling coil strands and represent the loss of two helix-coil boundaries. Further work is in progress to characterize the electrostatic boundary effects and processes of melting of these and other sequence domains in pBR322 in greater detail.

DISCUSSION The simplicity of the Ising nearest neighbor model 2, l8 used in statistical mechanical calculation of the stability of DNA has been preserved by assuming long-range energetic effects are small and can be safely absorbed within the large overall energy of dissociation of entire domains. However, resolution of melting has now improved to the point where the stability of the average domain can be measured with a precision of f0.001% ( k O.l"C), making it possible to study the comparatively small contribution of long-range forces associated with boundary formation in partially dissociated DNAs. Results show that electrostatic forces created a t helix-coil boundaries contribute substantially to the stability of internal domains. These effects are constant for each boundary formed, so that the net effect is seen as a greater than expected increase in stability of loop-forming domains with decreasing loop size. A t low countenon concentrations, loops of 70-80 bp may show an increase in T, of 3-4°C due to these long-range forces. Recognition of these effects in the theoretical model is necessary before meaningful quantitative adjustments in nearest neighbor stacking forces can be made to reconcile theoretical with experimental curves.2-l 8 , I 9 Recognition is important for other studies as well, particularly for more accurate prediction of secondary and tertiary structures in single-stranded DNAs and RNAs, 2"-23 and for understanding the binding of proteins to partially dissociated DNA, such as occurs with SSB protein24x2sand RNA p o l y m e r a ~ e . ~ ~ The charge density of coil regions in close proximity to helixes is substantially higher than in more remote regions of coil. Consequently, when

strands of the duplex dissociate the high counterion concentrations from condensation and screening effects are not released to the same extent from boundary regions as from remote regions. The reduction in counterion mixing or cratic entropy a t boundaries is seen as a further boost in the T, for internal domains. The equilibrium constant for excess counterion binding a t loop ends of coil regions has been measured by differences between the observed T, and that calculated for a freely jointed coil lacking in long-range electrostatic forces. When loop energy is weighted by this factor, we find agreement between experimental and theoretical melting temperatures to be quantitative ( & 0.09'C). When this weighting factor is included in the Ising model with loop energy, the resulting calculated melting curves for the parent pBR322 show substantial changes in overall profile and somewhat better correspondence with actual melting experiments. Further work on refinement of values for stacking parameters and the introduction of parameters for such aberrant intermediates as hairpins is needed before quantitative agreement is obtained. We wish to recognize Roseann Cochrane for her patience and diligence in helping us to complete this manuscript. This work was carried out with funds granted by NIH (GM22827) and by MAES (Project No. 08402).

REFERENCES 1. Blake, R. D. & Delcourt, S. G. (1987) Biopolymers 26, 2009-2026. 2. Wartell, R. M. & Benight, A. S. (1985) Phys. Rep. 126, 67-107. 3. Blake, R. D. & Hydorn, T. G. (1985) J . Biochem. Biophys. Methods 11, 307-316. 4. Elson, E. L., Scheffler, I. E. & Baldwin, R. L. (1970) J . Mol. Biol. 54, 401-415. 5. Record, M. T., Jr. & Lohman, T. M. (1978) Biopolymers 17, 159-166. 6. Fixman, M. & Freire, J. J. (1977) Biopolymers 16, 2693-2704. 7. Blake, R. D. & Haydock, P. V. (1979) Biopolymers 18, 3089-3109. 8. Yen, W.-S. & Blake, R. D. (1981) Biopolymers 20, 1161-1181. 9. Manning, G. S. (1969) J . Chem. Phys. 51, 924-933. 10. Record, M. T., Jr., Lohman, T. M. & deHaseth, P. L. (1976) J . Mol. Biol. 107, 145-158. 11. Jacobson, H. & Stockrnayer, W. H. (1950) J . Chem. Phys. 18, 1600-1607. 12. Klotz, L. C. (1969) Biopolymers 7, 265-273.

ELECTROSTATIC FORCES

13. Perelroyzen, M. P., Lyamichev, V. I., Kalambet, A. Y., Lyubchenko, L. Y. & Volgodskii, A. D. (1981) Nucleic Acids Res. 9, 4043-4050. 14. Marrnur, J. & Doty, P. (1960) J. Mol. Biol. 5, 109-131. 15. Mandel, M., Igambi, L., Bargendahl, J., Dodson, M. L., Jr., & Sheltgen, E. (1970) J. Bacterwl. 101, 333-339. 16. Frank-Kamenetskii, M. D. (1971) Biopolymers 10, 2623-2624. 17. Blake, R. D. (1987) Bwpolymers 26, 1063-1074. 18. Gotoh, 0. (1983) Ado. Biophy~.16, 1-52. 19. Gotoh, 0. & Tagashira, Y. (1981) BwpoZymers 20, 1033-1042. 20. Tinoco, I., Jr., Uhlenbeck, 0. C. & Levine, M. D. (1971) Nature 230, 363-367.

405

21. Tinoco, I., Jr., Borer, P. N., Dengler, B., Levine, M. D., Uhlenbeck, 0. C., Crothers, D. M. & Gralla, J. (1973) Nature New Bwl. 246, 40-41. 22. Papanicolaou, C., Gouy, M. & Ninio, J. (1984) Nuckic Acids Res. 12, 31-44. 23. Jacobson, A. B., Good, L., Simonetti, M. & Zuker, M. (1984) Nucleic Acids Res. 12, 45-52. 24. Lohman, T. M., Overman, L. B. & Datta, S. (1986) J . Mol. Bi d . 187, 603-615. 25. Greipel, J., Urbanke, C. & Maass, G. (1990) in press. 26. Record, M. T., Jr., Anderson, C. F., Mills, P., Mossing, M. & Roe, J.-H. (1985) Ado. Biophys. 20, 109-135.

Received December 10, 1988 Accepted February 21, 1989