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Originally published as Biophys J. BioFAST on December 9, 2005.
doi:10.1529/biophysj.105.066258
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Biophysical Journal 90:1729-1738 (2006)
© 2006 The Biophysical Society

Temperature Dependence of the Volumetric Parameters of Drug Binding to Poly[d(A-T)]·Poly[d(A-T)] and Poly(dA)·Poly(dT)

Xuesong Shi and Robert B. Macgregor, Jr.

Department of Pharmaceutical Sciences, University of Toronto, Toronto, Ontario, Canada

Correspondence: Address reprint requests to Robert B. Macgregor Jr., Dept. of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, 19 Russell St., Toronto, Ontario M5S 2S2, Canada. Tel.: 416-978-7332; Fax: 416-978-8511. E-mail: rob.macgregor{at}utoronto.ca.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
We report the temperature and salt dependence of the volume change ({Delta}Vb) associated with the binding of ethidium bromide and netropsin with poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)]. The {Delta}Vb of binding of ethidium with poly(dA)·poly(dT) was much more negative at temperatures ~70°C than at 25°C, whereas the difference is much smaller in the case of binding with poly[d(A-T)]·poly[d(A-T)]. We also determined the volume change of DNA-drug interaction by comparing the volume change of melting of DNA duplex and DNA-drug complex. The DNA-drug complexes display helix-coil transition temperatures (Tm) several degrees above those of the unbound polymers, e.g., the Tm of the netropsin complex with poly(dA)poly(dT) is 106°C. The results for the binding of ethidium with poly[d(A-T)]·poly[d(A-T)] were accurately described by scaled particle theory. However, this analysis did not yield results consistent with our data for ethidium binding with poly(dA)·poly(dT). We hypothesize that heat-induced changes in conformation and hydration of this polymer are responsible for this behavior. The volumetric properties of poly(dA)·poly(dT) become similar to those of poly[d(A-T)]·poly[d(A-T)] at higher temperatures.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
Over the past four decades, noncovalent interactions between DNA and drugs have been studied intensively; much of the impetus for these studies has arisen from the goal of rational drug design (1Go,2Go). Despite the research dedicated to understanding these interactions, the role of hydration in determining their affinity and specificity has been largely ignored. The interactions of the DNA binding site and the drug with water change upon formation of a complex; disregarding these changes limits the effectiveness and credibility of rational drug design. Although hydration changes are thermodynamically important, the quantitative assessment of the role of hydration in the energetics of the complexes presents a significant experimental challenge: hydration is difficult to detect structurally, it is generally too complex to be adequately simulated by computation, and it is not straightforward to separate the effect of hydration from other factors that influence the thermodynamics of a complex.

To a good approximation, the most important contribution to the volume change accompanying the formation of a noncovalent complex involving biological molecules arises from the accompanying changes in hydration. The difference between the partial molar volume of water in the hydration shell of the complex and of bulk water is the major source of the volume change. Thus, the thermodynamic parameters that provide the most information about hydration are the molar volume, expansivity, and compressibility changes. To date, research aimed at measuring the volume change associated with DNA-drug interactions has met with limited success (3Go–6Go). The two most successful methods employed to date are densitometry (4Go,5Go,7Go) and the spectrophotometric (3Go,6Go) measurement of the dependence of the equilibrium constant on pressure.

In this work, we measured the volume change arising from the formation of DNA-drug complexes using two methods. In the first method, the equilibrium between the drug and DNA at a given temperature and pressure was altered by changing the hydrostatic pressure and then determining the new equilibrium constant at the same temperature. In the second method, we measured the change in the DNA helix-coil transition temperature with and without bound drug at different pressures. The principal advantage of the second method is that it does not require the drug to have any difference in its spectroscopic properties between the free and bound states. The temperature range of these two methods is complementary; by combining them we can determine the effect of temperature on the volume change over the full temperature range in which the complex is stable. We have used these approaches to study the effect of pressure on the interaction of poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] with the intercalator ethidium bromide and netropsin a drug that noncovalently binds in the minor groove of DNA.

In an attempt to assess the factors that underlie the changes in volume parameters we used scaled particle theory to analyze temperature dependence of the volume parameters we obtained for ethidium binding with poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)]. Previous applications of scaled particle theory to this problem have met with limited success because the absolute values of the parameters rely upon detailed structural information that is often not available (8Go,9Go). However, the temperature dependence of the volume parameters is expected to be relatively independent of the structural details.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
Materials
Ethidium bromide (EB) and netropsin (nt) were obtained from Sigma-Aldrich (St. Louis, MO) and used without further purification. Other small-molecular-weight chemicals were all reagent grade or better. Poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] were purchased from Amersham Biosciences Corporation. The DNA polymers were dissolved in and then dialyzed against aqueous solutions containing 20 mM Tris-HCl, pH 7.2, 0.1 mM EDTA, and the desired amount of NaCl. The concentration of DNA, in moles of basepairs, was determined spectrophotometrically using molar extinction coefficients: {varepsilon}259 = 12,000 M–1 cm–1 for poly(dA)·poly(dT) and {varepsilon}262 = 13,200 M–1 cm–1 for poly[d(A-T)]·poly[d(A-T)] (10Go,11Go). The concentrations of the ligand solutions were determined using {varepsilon}480 = 5,850 M–1 cm–1 and {varepsilon}296 = 21,500 M–1 cm–1 for EB and netropsin (12Go,13Go), respectively.

Fluorometric titrations
To measure the parameters describing the equilibrium binding of EB with DNA at room temperature we carried out fluorescence titrations. The data were acquired on a Spex FluoroMax 3 spectrofluorometer (Jobin Yvon, Edison, NJ). The excitation and emission wavelengths were 512 and 600 nm, respectively. DNA solutions were titrated with concentrated EB solutions. If r is the fraction of binding sites occupied, i.e., r = [bound EB]/[total DNA basepairs], and [L] is the concentration of unbound EB, then according to the site-exclusion model,

Formula 1A(1)
where Ka is the equilibrium binding constant, n is the size of the binding site in basepairs, and {omega} is a cooperativity parameter (14Go). The value of the parameters, Ka, n, and {omega} were determined by nonlinear fitting using MATLAB with n constrained to be an integer value. In our analysis, we assumed that the fluorescence properties of bound EB are independent of the fraction of sites bound, r; this is similar to other studies on measuring binding parameters of EB binding.

The value of the equilibrium constant for the binding of netropsin with DNA reported in the literature is at least three orders of magnitude larger than that of EB, and the excluded site parameter, n, is equal to 5 (15Go). Due to the larger value of Ka, netropsin binding was considered to be complete under our experimental conditions.

Pressure dependence of the helix-coil transition
The helix-coil transition temperatures, Tm, of DNA and DNA-ligand complexes were determined by monitoring the change in absorbance at 260 nm as the temperature was increased at 0.6°C/min at pressures from 1 to 200 MPa (0.1 MPa = 1 bar = 0.987 atm). The high-pressure equipment has been described previously (16Go). By measuring Tm at different pressures, the volume change of these helix-coil transitions at ambient pressure was calculated using the Clapeyron equation: dTm/dP = Tm1atm{Delta}Vb/{Delta}H. Calorimetrically determined values of {Delta}H (measured at atmospheric pressure) were taken from the literature. The helix-coil transition of the DNA-ligand complex involves unbinding ligand from DNA and DNA melting. The volume of DNA-drug binding was determined from the difference between volume change of the helix-coil transition of DNA ({Delta}VDNA HC) and the DNA-ligand complex ({Delta}Vcomplex HC): {Delta}Vb = {Delta}VDNA HC{Delta}Vcomplex HC. There are two assumptions implicit in this approach:

  1. The extent of binding of EB with single-stranded DNA is negligible. The equilibrium constant for binding to single-stranded DNA is at least 10 times less than that for duplexes (17Go,18Go).
  2. The enthalpy of helix-coil transition of DNA-ligand complex is equal to the sum of the enthalpy of the helix-coil transition of naked DNA and enthalpy of unbinding of ligand.

Fluorescence measurements at high pressure
We also measured the molar volume change of DNA-ligand binding on the basis of the standard thermodynamic relationship: ({partial}lnKa/{partial}P)T = –{Delta}Vb/RT, where R is the gas constant. To determine {Delta}Vb, we measured the change of lnKa with pressure at constant temperature. The molar volume change of the intercalation of EB with the two DNA polymers was determined at four or five temperatures. The experimental settings of the spectrofluorometer were the same as those used in the fluorescence titration experiments. The change of lnKa could be derived from the change of fluorescence signal intensity based on the results from the titration experiments. To determine {Delta}Vb, the data, lnKa versus pressure, fitted with a second-order polynomial (OriginLab, Northampton, MA), were extrapolated to atmospheric pressure.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
Binding data
The equilibrium binding parameters for ethidium bromide binding with poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] at different salt conditions are summarized in Table 1.


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TABLE 1  Equilibrium binding parameters for ethidium bromide binding with DNA

 
The binding constant, Ka, and cooperativity, {omega}, are obtained by fitting the raw data to the McGhee-von Hippel site-exclusion model using integer values of the binding-site size n (14Go). Binding with the homopolymer, poly(dA)·poly(dT), shows positive cooperativity, whereas no cooperativity is observed for interaction with the alternating polymer, poly[d(A-T)]·poly[d(A-T)]. The equilibrium constant for EB binding to poly[d(A-T)]·poly[d(A-T)] is >24 times larger than that for binding with homopolymer. The binding constants decrease with increasing salt concentration for both polymers.

Volume change of the DNA helix-coil transition
The pressure dependence of the helix-coil transition temperature, Tm, of the two polymers at two different salt concentrations is summarized in Table 2. We calculated the enthalpies of DNA denaturation at each of the transition temperatures given in Table 2 using calorimetrically measured, temperature-dependent enthalpies. Thus, {Delta}Href = 39.2 kJ mol–1 at 58.2°C with {Delta}Cp = 228 J mol–1 K–1 for poly(dA)·poly(dT) and {Delta}Href = 33.7 kJ mol–1 at 50.9°C with {Delta}Cp = 178 J mol–1 K–1 for poly[d(A-T)]·poly[d(A-T)] (19Go). Increasing the salt concentration stabilizes both polymers; the change in Tm upon changing the salt concentration from 25 to 70 mM equals 7.6 and 7.8°C for poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)], respectively.


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TABLE 2  Volume change of DNA melting at different salts concentrations

 
Combining the data in Table 1 with other data describing the transition volume of these polymers (20Go,21Go), one obtains {Delta}V of the helix-coil transition at different temperatures (Fig. 1). For both polymers, the volume change varies linearly with the helix-coil transition temperature at atmospheric pressure. Within the temperature range studied, both polymers exhibit a positive volume change for the helix-coil transition and the magnitude of {Delta}V increases with increasing temperature. The magnitude of {Delta}V for poly[d(A-T)]·poly[d(A-T)] is less than that for poly(dA)poly(dT) at low temperatures; however, the value of {Delta}V for the two polymers becomes similar at higher temperatures. Extrapolating the temperature dependencies shown in Fig. 1, one finds that at 84.6°C the {Delta}V for the helix-coil transition equals +5.6 cm3 (mol bp)–1 for both polymers.


Figure 1
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FIGURE 1  Temperature dependence of the molar volume change of DNA denaturation. The volume change is per mole of basepairs. The open circles are data for poly(dA)·poly(dT) obtained in this work and the solid circles are from the literature (20). The open triangles are data for poly[d(A-T)]·poly[d(A-T)] obtained in this work and the solid triangles are from the literature (21). The lines fit to the data are given by {Delta}V (cm3 mol bp–1) = –1.82 (± 1.04) + (0.088 ± 0.017) x Tm (°C) for poly(dA)·poly(dT) and {Delta}V (cm3 mol bp–1) = –6.64 (± 0.72) + (0.145 ± 0.012) x Tm (°C) for poly[d(A-T)]·poly[d(A-T)].

 
Volume change of denaturing the DNA-ethidium complex
In these experiments, we measured the helix-coil transition temperature of the DNA-ethidium complex at different pressures; the Tm of the complex is greater than that of the polymer alone. The pressure dependence of the Tm for the two polymers and their EB complexes is depicted in Fig. 2 and the data are summarized in Table 3. As expected, the binding of EB stabilizes the helix form of both polymers. As the extent of binding increases, the helix-coil transition temperature increases; thus, the Tm of the 2:1 complexes is greater than that of the 5:1 complexes. The effect of the salt concentration on the Tm is largest for the unbound polymers; the binding of EB decreases the influence of the salt concentration on the Tm. For example, increasing the salt concentration from 25 to 70 mM caused the Tm of poly(dA)·poly(dT) to increase by 7.6°C, whereas the Tm increased by 3.1°C and 0.3°C with low or high levels of bound ethidium, respectively.


Figure 2
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FIGURE 2  Pressure dependence of the helix-coil transition temperature of DNA with or without ethidium bromide at two sodium chloride concentrations. Poly(dA)·poly(dT), circles; poly[d(A-T)]·poly[d(A-T)], triangles; 25 mM NaCl, open symbols; 75 mM NaCl, solid symbols; DNA only, solid line; basepair/drug ratio of ~5:1 (dotted line); and basepair/drug ratio of 2:1 (dashed line). Please refer to the text for details.

 

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TABLE 3  Volume change of melting of DNA-ethidium complexes

 
In Table 3, the enthalpy of the transition was calculated as the sum of the enthalpy of the helix-coil transition of naked DNA and unbinding of ethidium per basepair at the transition temperature: {Delta}Htot = {Delta}Hhc + r{Delta}Huneb. The enthalpy of helix-coil transition of naked DNA, {Delta}Hhc, was calculated as described before. The enthalpy change resulting from the unbinding of EB, {Delta}Huneb, was calculated using Formula 1A at 20°C, and {Delta}Cp {approx} 0 J K–1 mol–1 for poly(dA)·poly(dT) (22Go), and Formula 1A and {Delta}Cp {approx} –285 J K–1 mol–1 at 20°C for poly[d(A-T)]·poly[d(A-T)] (3Go). At each temperature, r is calculated using the van 't Hoff relationship, the values of the binding parameters at 298 K (Table 1), and literature values of the binding enthalpy (3Go). The cooperativity and binding-site size were assumed not to vary with temperature. This assumption appears reasonable because the magnitude of {Delta}Hhc is several times greater that that of r{Delta}Huneb. Thus, any temperature dependence of these two parameters would not significantly change {Delta}Htot. The last column of Table 3 shows the volume change of melting of DNA-ethidium complexes per basepair of DNA. We do not report data in the case of intermediate amounts of bound ethidium (basepair/ligand ratio of ~5) with poly[d(A-T)]·poly[d(A-T)] at low salt concentration (25 mM), because the transitions are biphasic. All other transitions were monophasic.

Table 4 summarizes the volume change of DNA-EB binding ({Delta}Vb) obtained at the helix-coil transition temperature, which we calculated according to {Delta}Vb = ({Delta}VDNA HC{Delta}Vcomplex HC)/r. In all cases, we observed a negative volume change; thus, higher pressure stabilizes the complex. For the intercalation of EB with poly(dA)·poly(dT), {Delta}Vb ranges from –5.0 to –16.8 cm3mol–1 and is more negative at higher salt concentration and at lower degrees of binding. Note that if the cooperativity of binding of EB with poly(dA)·poly(dT) is completely lost at helix-coil transition temperature, the calculated value of r will be different and the resulting {Delta}Vb will be slightly more negative with an average decrease of ~3 cm3 mol–1. The volume change arising from the interaction of EB with poly[d(A-T)] equals ~–13 cm3 mol–1; this value was not influenced by salt concentration or degree of binding.


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TABLE 4  Volume change of DNA-ligand binding

 
Volume change of denaturing the DNA-netropsin complex
The pressure dependence of the Tm of the two polymers and their netropsin complexes is shown in Fig. 3; the data are summarized in Table 5. The Tm increases significantly, ~40°C, upon the binding of nt; this is much greater than the change caused by the binding of EB, because nt binds more strongly to DNA. The binding of nt with poly(dA)·poly(dT) is energetically more favorable than with poly[d(A-T)]·poly[d(A-T)]; ethidium displays the opposite preference for these polymers. There is no significant difference between the data obtained at 25 and 75 mM salt; this is expected for positively charged ligands at high degrees of binding. Under experimental conditions where the ratio of DNA basepairs to nt was >2:1, we observed a biphasic transition.


Figure 3
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FIGURE 3  Pressure dependence of the helix-coil transition temperature of DNA with or without netropsin at various salt concentrations. Poly(dA)·poly(dT), circles; poly[d(A-T)]·poly[d(A-T)], triangles; 25 mM salt, open symbols; 75 mM salt, solid symbols; DNA only, solid line; basepair/drug ratio of 2:1, dotted line).

 

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TABLE 5  Volume change of melting of DNA-netropsin complexes

 
The enthalpy of the helix-coil transition of the DNA-nt complex was calculated as described above for EB; the results are shown in Table 5. For the binding of nt with poly(dA)·poly(dT), poly[d(A-T)]·poly[d(A-T)], Formula 1A and Formula 1A respectively (14Go), assuming {Delta}Cp {approx} 0 for complex formation with either polymer (23Go). Each bound nt molecule is considered to occupy five consecutive basepairs with a binding constant ~109 M–1 (15Go). Saturation was reached in the four cases we studied with ~0.2 bound nt molecules per basepair.

Table 4 summarizes the values of {Delta}Vb for the DNA-netropsin complex at the helix-coil transition temperature. Under the conditions studied, the binding of nt exhibits small negative {Delta}Vb values ranging from –4.0 to –7.7 cm3 mol–1. The {Delta}Vb values are slightly more negative for binding with poly(dA)·poly(dT) than with poly[d(A-T)]·poly[d(A-T)] and slightly more negative at higher salt concentrations, but the difference is not significant.

Temperature dependence of {Delta}Vb for EB binding with DNA
Due to the nature of the method employed, the values reported above are obtained at temperatures much higher than those at which most literature data have been reported, i.e., 20–25°C. We also measured {Delta}Vb of EB binding with the two polymers at different temperatures by monitoring the effect of pressure on the fluorescence of the EB-DNA complex; this enabled us to make direct comparisons between the data obtained at the helix-coil transition temperature and literature results obtained at ~25°C. The binding parameters of EB intercalation summarized in Table 1 are similar to those reported by Marky and Macgregor (3Go).

The volume change associated with EB binding with the two polymers at different temperatures is shown in Fig. 4. The binding constant, Ka, at different temperatures was calculated from the fluorescence intensity; the temperature dependence of Ka is shown in Fig. 5. We calculated the enthalpies of binding from the slopes in Fig. 5 using the van 't Hoff equation. The data are summarized in Table 6.


Figure 4
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FIGURE 4  Temperature dependence of volume change of ethidium binding with poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] in 20 mM Tris-HCl, 50 mM NaCl, pH 7.2.

 

Figure 5
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FIGURE 5  Temperature dependence of equilibrium constant of ethidium binding with poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] in 20 mM Tris-HCl, 50 mM NaCl, pH 7.2. A typical plot of lnKa versus pressure (poly[d(A-T)]·poly[d(A-T)], 26.2°C) is shown in the inset.

 

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TABLE 6  Temperature dependence of ethidium-DNA binding

 
The data in Fig. 4 show that the {Delta}Vb of poly[d(A-T)]·poly[d(A-T)] complexation with EB remains negative at all temperatures. For this system, {Delta}Vb becomes more negative with increasing temperature; the coefficient of expansivity, {Delta}E = –0.15 cm3 mol–1 K–1. In the case of the formation of the complex between poly(dA)·poly(dT) and EB, {Delta}Vb changes sign from negative to positive at ~41°C and {Delta}E = –0.49 cm3 mol–1 K–1. The value of {Delta}E is 3–4 times larger for EB binding to poly(dA)·poly(dT) than to poly[d(A-T)]·poly[d(A-T)]. The trends observed in all of the data for the two experimental methods agree well. As seen in Fig. 4, it is evident that at higher temperatures the {Delta}Vb becomes similar for these two polymers.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
We report the temperature and salt dependence of the equilibrium volume parameters for the complexes formed by ethidium bromide and netropsin and poly[d(A-T)]·poly[d(A-T)] and poly(dA)·poly(dT). Our data greatly extend the temperature range of these values for these two DNA-binding ligands. For many noncovalent interactions, a large fraction of the net free energy change results from the differential hydration of the free and bound states. The volume parameters of the binding interaction are the values most directly related to changes in hydration. By extending the temperature range of the volumetric parameters, we can better understand the thermodynamic origins of the stability of the complexes.

We can decompose the volume change that results from formation of a complex, {Delta}Vb, into a sum of three components: {Delta}Vb = {Delta}VI + {Delta}VT + {Delta}VH, where {Delta}VI is the intrinsic volume change, {Delta}VT is the thermal volume change, and {Delta}VH is the hydration volume change. The intrinsic volume, VI, is the geometric volume of the solute molecules (9Go); {Delta}VI will be negligible because the DNA and the DNA-ligand complex are tightly packed and have no significant internal voids. The thermal volume, VT, is the volume of the layer of void space surrounding the solvent accessible surface of the solute molecules. This volume arises from the thermal motion of solute and solvent molecules. Because the thickness of this void layer depends primarily on the solvent, the thermal volume is proportional to the accessible surface area of the solutes to a first approximation.

Intercalation and binding to the minor groove result in a loss of solvent-accessible surface area, hence a loss of VT and a negative {Delta}VT. Hydration volume, VH, is the change in solvent volume arising from the interactions between the solute and the solvent; in water, these interactions lead to the formation of a hydration shell composed of molecules with a higher density than bulk water. The hydration volume change, {Delta}VH, is the volume change generated from exchange between relatively high-density water in the hydration shell of solutes and lower-density bulk water. Both intercalation and minor-groove binding require that the ligands lose some solvent accessibility and some fraction of their hydration shell. Binding may also disrupt specific hydration structures, for example, the specific hydration in the minor-groove DNA. The release of counterions upon binding may have a small negative contribution to {Delta}VH, although this effect may be offset by the uptake of a similarly charged ligand.

The formation of a DNA-ligand complex may lead to the creation of an extensive multilayer hydration structure surrounding unbound DNA; however, the total number of water molecules involved in hydration will decrease due to the loss of solvent-accessible surface. Thus, the overall result of binding is a net release of high-density hydration water to the bulk phase and a positive {Delta}VH. In sum, {Delta}Vb has a major negative contribution from {Delta}VT and a major positive contribution from {Delta}VH. The sign of {Delta}Vb depends on the relative magnitude of {Delta}VT and {Delta}VH. Both negative and positive {Delta}Vb have been reported (3Go,24Go).

Ideally, one would like to link the thermodynamic values with molecular changes; however, such an interpretation is not straightforward. Thermodynamic values for biological systems are rarely sufficiently detailed to permit a molecular interpretation. Structural methods generally only reveal those water molecules that are strongly associated with the solute while the majority water molecules interacting more weakly are not observed. We considered that, in the present case, theory might provide insight where these two experimental approaches fall short.

The scaled particle theory (SPT) is a statistical mechanical theory of liquids developed to interpret the thermodynamic parameters of aqueous and nonaqueous solutions (8Go,25Go,26Go). With SPT one can generate an approximate expression for the reversible work required to generate a cavity in a fluid of spherical particles to accommodate a new spherical particle (the solute); the volume of the cavity is equal to VI + VT (8Go). According to the assumptions of SPT, the thermal volume, VT, of a spherical solute is given as (8Go,9Go)

Formula 1(1)
where Formula 1 and Formula 1

The parameter d1 is the effective hard-sphere diameter of the solvent; for water d1 = 0.274 nm; Formula 1 is the partial molar volume of the solvent; NA is Avogadro's number, and y is the packing density of the solvent. The parameters B and C depend only on the relative size of the solute and the solvent molecules. It is important to note that the only temperature-dependent parameters are Formula 1 and the coefficient of isothermal compressibility of the solvent Formula 1

SPT has limited utility for predicting the absolute value of VT because most molecules are not well approximated as spheres but the temperature dependence of VT is not expected to depend on shape and should be explained by this theory. The relative temperature dependence of VT can be expressed as a sum of three terms:

Formula 2(2)

The first term on the right-hand side of Eq. 2 contributes to an increase in VT with temperature and is almost constant within our temperature range (1/T ~0.0035 at 10°C and 0.0028 at 80°C). The second term depends on the compressibility of the solvent. For an aqueous NaCl solution, the coefficient of isothermal compressibility, Formula 2 decreases approximately linearly between 0 and 40°C, reaches a minimum, and then increases approximately linearly from 50 to 100°C (27Go). The solution becomes less compressible with increasing salt concentration and the temperature dependence of Formula 2 becomes slightly weaker with increasing salt concentration. For a 70-mM NaCl solution, the second term increases linearly from –0.47% (10°C) to +0.42% (80°C) (27Go).

The third term, Formula 2 is the only one that includes the influence of the relative size of solute molecules to solvent molecules on VT. The solvent and solute are considered to be hard spheres with diameters d1 and d2, respectively; a fivefold change in the ratio of the diameters, d2/d1, from 2 to 10 results in a relatively small (1%) change in Formula 2 at constant temperature. Thus, the relative size of the solute has little influence on temperature dependence of the thermal volume VT. If we take d2/d1 = 3 for ethidium in water, then the third term changes linearly from –0.04% at 10°C to –0.18% at 80°C. Thus, we expect VT to decrease slowly with temperature from 10 to ~25°C and then increase with temperature.

To compare our calculations with the experimentally measured temperature dependence of volume, we must consider the temperature dependence of VH also. The value of VH can be expressed as Formula 2 in which Formula 2 is the free energy of dipole-dipole interactions between solvent water and solute and Formula 2 is the free energy of other van der Waals interactions between solvent water and solute; both terms are negative and, consequently, so is VH (7Go). If Adipole and Gother are approximated to be temperature-independent, the relative temperature dependence of VT can be expressed as a sum of two terms:

Formula 3(3)
in which Formula 3 The first term of the right-hand side of Eq. 3 is the same as the second term of Eq. 2. The second term is similar to the first term of Eq. 2 except for a negative sign and a factor that varies between 0 and 1 depending on the solute molecules. Combining Eqs. 2 and 3 we obtain

Formula 4(4)

Since VH and VH,dipole are negative and VT is positive, the influence of Formula 4 is diminished and the influence of 1/T is strengthened. The overall effect is that dV changes sign from negative to positive at low temperatures, reaches a maximum, and then decreases slowly with temperature. Thus, dV becomes less sensitive to temperature.

To assess our results, we are interested in evaluating the volume change, {Delta}V, instead of V in Eq. 4; thus, all of the terms change signs: {Delta}VT is negative; {Delta}VH is positive; and d{Delta}V is likely negative for our temperature range. For EB intercalation with poly[d(A-T)]·poly[d(A-T)], the loss of solvent-accessible surface of EB predominates {Delta}VT.

In the absence of structural data for the DNA-ethidium complex we have estimated the fraction of solvent-accessible surface area lost in the following manner. First, the thermal volume of EB is found by multiplying the Connolly molecular area of ethidium, 296.2 Å2, by 0.51 Å, as outlined in Lee and Chalikian (28Go), which results in {Delta}VT = –91 cm3 mol–1 (note the change in units). If three of the four aromatic rings of EB are partially covered by basepairs above and below, then VT will be reduced by ~50% upon intercalation, thus, {Delta}VT = –45.5 cm3 mol–1. For this system, {Delta}V = {Delta}VT + {Delta}VH, to a good approximation, and the value of {Delta}V ranges from –10.7 to –16.1 cm3 mol–1 between 12.7 and 48.9°C. Using our estimate of {Delta}VT we find that {Delta}VH is ~32 cm3 mol–1.

Since dipole-dipole interactions are the major force in causing extraction of hydration water (29Go), {Delta}VH,dipole makes a significant contribution to {Delta}VH. Suppose {Delta}VH,dipole represents ~60% of {Delta}VH or ~19 cm3 mol–1, then d{Delta}V is ~–0.16 cm3 mol–1 at 12.7°C and ~–0.15 cm3 mol–1 at 48.9°C. This is in agreement with our experiment result of –0.15 cm3 mol–1. Changing the ratio of {Delta}VH,dipole to {Delta}VH to 40% or 80% only slightly broadens d{Delta}V to ~–0.13 (40%) or –0.18 (80%) cm3/mol, respectively. Thus, the slight decrease in {Delta}V observed with increasing temperature for EB binding with poly[d(A-T)]·poly[d(A-T)] is mainly due to the predictable changes of solvent properties and solvent-solute interactions.

Despite this apparent quantitative success, SPT does not yield credible results for analysis of EB binding with poly(dA)·poly(dT). For this system, the experimentally measured value of d{Delta}V is –0.49 cm3 mol–1 between 19° and 49°C; this is three times larger than the value of –0.20 ± 0.04 cm3 mol–1 calculated using SPT as outlined above. The difference in d{Delta}V appears too large to be explained by error; it implies some changes of the system, other than in thermal motion, with temperature. Thermodynamic measurements do not provide insight into the molecular processes leading to binding and there are no data on the structure of these systems at high temperatures. Our observations may arise as a consequence of a temperature-dependent loss of specific structures involved in the hydration of poly(dA)·poly(dT) or a heat-induced conformational change. We hypothesize that the change occurs with the unbound polymer and not with the complex. The polymer is less hydrated at higher temperatures so that it loses fewer water molecules at higher temperatures, resulting in a more negative value of {Delta}Vb. The alternating polymer, poly[d(A-T)]·poly[d(A-T)], does not undergo the same temperature-dependent changes as poly(dA)·poly(dT) and does not have irregular temperature dependence of {Delta}Vb. Although there is good agreement between our results and the analysis based on SPT for EB binding to poly[d(A-T)]·poly[d(A-T)], it may be fortuitous. The assumptions we made for the parameters appear reasonable and the fact that the theory does not adequately describe the behavior of EB binding to poly(dA)·poly(dT) is not altogether surprising considering the generally anomalous properties of this polymer.

In our analyses, we have assumed that the intrinsic volume change is independent of temperature. Although this assumption appears reasonable, it is possible that the rise per basepair could increase significantly with temperature. Such an increase would contribute to the intrinsic volume and change the relative contribution of the volume components to the observed volume change. We are not aware of any measurements of the temperature dependence of intrinsic volume in the literature that would permit us to estimate the magnitude of this effect.

The experimental values of {Delta}Vb for EB binding with poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] converge at high temperatures. We observed the same trend for nt binding and the helix-coil transition of the naked DNA polymers; it appears as though these two polymers become increasingly similar at higher temperatures. The physical and structural properties of poly(dA)·poly(dT) differ from those of other DNA polymers, such as poly[d(A-T)]·poly[d(A-T)] (30Go–32Go). The behavior of poly(dA)·poly(dT) has drawn a great deal of interest and it is tempting to attribute the anomalous properties of this polymer to the structure observed in oligonucleotides with consecutive AT sequences, such as the middle section of the Dickerson dodecamer, d[CGCGAATTCGCG]2 (33Go). The x-ray fiber diffraction study of Alexeev et al. (30Go) showed that poly(dA)·poly(dT) is a B-type double helix with a distinctively narrow minor groove; the narrow minor groove is also a characteristic of oligonucleotides with consecutive adenosine residues (34Go). The narrow minor groove has been linked to formation of a spine-like hydration pattern in the minor groove (35Go). Molecular simulation has shown that it is energetically favorable to form a spine of hydration in poly(dA)·poly(dT) but unfavorable for poly[d(A-T)]·poly[d(A-T)] (36Go,37Go). This may imply that the conformation and hydration differences are partly responsible for the properties of poly(dA)·poly(dT). Unfortunately, unlike oligonucleotides, DNA polymers are not amenable to high-resolution structural studies. In the absence of high-resolution structure data, the exact difference between these two polymers remains unclear.

Premelting transitions have been observed for poly(dA)·poly(dT) using spectroscopic techniques (38Go,39Go). Herrera and Chaires (39Go) showed that ultraviolet absorbance and molar ellipticity of poly(dA)·poly(dT) exhibit a strong temperature dependence; this is not observed for poly[(dAT)]·poly[(dAT)]. It was proposed that the temperature-dependent conformation changes and concomitant disruption of the hydration spine were responsible for the spectroscopic responses. It seems reasonable to propose that similar temperature-dependent changes in structure and hydration are responsible for the volumetric changes we report.

For ethidium intercalation, our results near ambient temperature agree with values in the literature (Table 7). The van 't Hoff enthalpies for binding with poly[d(A-T)]·poly[(dA-T)] and poly(dA)·poly(dT) obtained from the fluorescence method, –7.7 and –0.83 kcal mol–1, respectively, are similar to the calorimetric results, –9.0 and –1.3 kcal mol–1, respectively (3Go), validating the use of the fluorescence method. From these data, the volume change at melting temperature can be predicted to be ~–19 ± 1 cm3 mol–1 and –18 ± 2 cm3 mol–1 for binding with the poly[d(A-T)]·poly[d(A-T)] and poly(dA)·poly(dT), respectively. The melting method gives a similar result for poly(dA)·poly(dT) at –16.8 ± 3.5 cm3 mol–1 and slightly more positive values for binding with poly[d(A-T)]·poly[d(A-T)] at –13.8 ± 2.2 cm3 mol–1. This implies that determining the volume change by observing the coupling between binding and the helix-coil transition yields an accurate value of the volume change at the transition temperature. This value cannot be obtained by other volumetric methods. This method also requires less material than densitometry and can be used for any ligand-DNA system without the need of spectroscopic signal from the ligand.


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TABLE 7  Comparison of volume change data for DNA-ligand binding

 
As shown in Table 7, the densitometry data from literature for netropsin binding with DNA show a much more positive {Delta}Vb for poly(dA)·poly(dT) than poly[d(A-T)]·poly[d(A-T)] at ambient temperature (5Go). The {Delta}Vb measured at melting temperature by melting experiments are similar for both polymers, apparently due to the polymers becoming increasingly similar at high temperature. Unlike simple intercalators, such as EB, nt binding in the minor groove results in the creation of a certain amount of void between netropsin and the minor groove. Thus, it is impossible to predict its volume-change temperature dependence without additional knowledge of the void volume or structure of the complex at high temperatures.

In future studies we intend to apply the scaled particle theory to the analysis of the temperature dependence of volumetric properties of a greater range of molecules and binding events. A theoretical interpretation of the pressure dependence of these parameters will also be investigated. With further improvements, we feel that this approach may be very useful in the dissection of the relative contributions of the thermal and hydration volumes.


    ACKNOWLEDGEMENTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
We are grateful to the Canadian Institutes for Health Research for their financial support of this research.

Submitted on May 10, 2005; accepted for publication November 16, 2005.


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 REFERENCES
 
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