J. Phys. Chem. B 2007, 111, 5999-6005
5999
Electrostatic Attraction between DNA and a Cationic Surfactant Aggregate. The Screening Effect of Salt Cecı´lia Leal,*,† Elham Moniri,‡ Luis Pegado,*,† and Håkan Wennerstro1 m† Physical Chemistry1, Lund UniVersity, PO Box 124, SE-221 00 Lund, Sweden, and Department of Science, Varamin (pishVa) branch, Islamic Azad UniVersity, Varamin, Iran ReceiVed: August 18, 2006; In Final Form: February 2, 2007
Anionic DNA and cationic surfactants form charge neutral complexes that contain finite amounts of water. There is a strong electrostatic attraction between the oppositely charged species, and the finite swelling is caused by an opposing repulsive force. Adding NaCl to the complexes provides an opportunity to modulate the strength of the electrostatic attraction. The thermodynamics of the isothermal swelling process has been experimentally characterized using a calorimetric technique monitoring both the free energy and the enthalpy. The experimental results are quantitatively analyzed in calculations using the Poisson-Boltzmann equation to describe the electrostatic effects. The main findings are as follows: (i) Addition of salt results in an increased swelling at a given water activity. (ii) The effect of the salt can be quantitatively modeled on the basis of the Poisson-Boltzmann equation with a dielectric description of the water. (iii) There exists a short-range repulsive force between DNA double helices and surfactant aggregates. (iv) Solid NaCl dissolves in the complex at water activities in the range 0.5-0.6 rather than at 0.74 as in a saturated aqueous solution. (v) The heat of solution of NaCl in the complexes is around +1.6 ( 0.5 kJ/mol, surprisingly close to the values found for the dissolution into bulk aqueous solutions.
Introduction In a cell, unselective aggregation between the many proteins, nucleic acids, and membrane elements is prevented through the action of repulsive interactions. These are due to the repulsion between negative surface charges, a short-range repulsion between lipids, and an entropic repulsion from polymeric degrees of freedom. Conversely, the organization of the cellular processes is promoted by a more specific attraction between the relevant species. The attractive forces are primarily due to a hydrophobic interaction and an attraction between species of opposite electrical charge. A DNA double helix is highly negatively charged and it strongly associates with basic proteins. This applies to regulating repressor proteins and to the histones responsible for the compaction of DNA into nucleosomes. Also in colloidal systems one finds the same interplay between repulsion and attraction, and seen from a molecular perspective, the mechanisms are largely the same. It is in practice easier to experimentally study repulsive rather than attractive interactions. In the latter case the system collapses spontaneously into a compact state and one can possibly determine the net change in free energy. It requires special care to find out how the interaction varies with distance. In a mechanical force measurement, one can with some effort apply a compensating pulling force; this can be done using the surface force apparatus and atomic force microscopy techniques. An alternative is to have a balancing repulsive force and then modulate either the repulsion or the attraction to obtain quantitative information on the attractive component provided one can ensure additivity between the different effects. Due to * Corresponding authors. E-mail:
[email protected] (experimental part) and
[email protected] (calculations part). † Lund University. ‡ Islamic Azad University.
difficulties of this character, much less is known experimentally about attractive interactions in comparison with repulsive ones. It is commonly found that the attraction between oppositely charged aggregates/macromolecules results in complexes with a residual aqueous film in the contact area.1 This can be caused by a charge mismatch2,3 but also by a nonelectrostatic repulsive short-range force. The net free energy of association is highly dependent on the character of the short-range interaction. It is a major problem in a quantitative description of association in both biological and colloidal systems to reliably describe this short-range part of the interaction curve. In this paper we report a combined experimental and theoretical study of the balance between an attractive electrostatic and a short-range repulsive force in complexes between DNA and two different cationic surfactants. When precipitated from a pure aqueous system the complexes contain around 14 water molecules per charged group despite the fact that there is a strong electrostatic attraction between the anionic and cationic groups. We have previously, using a calorimetric technique, characterized the free energy and enthalpy of the swelling from a dry state to maximum hydration.4 Here we extend this study to include the effect of a screening electrolyte by adding known amounts of NaCl(s) to the complexes. The salt should primarily affect the electrostatic attraction and thus allow for a more extensive swelling of the complexes. There are two main questions: (i) What are the forces involved in the hydration of a DNA-surfactant complex? (ii) To what extent can the electrostatic interactions be described by a continuum dielectric model of the solvent? Materials and Methods Materials. Na-DNA from calf thymus was purchased from Sigma and used as received. DNA concentration (in terms of
10.1021/jp065358h CCC: $37.00 © 2007 American Chemical Society Published on Web 05/09/2007
6000 J. Phys. Chem. B, Vol. 111, No. 21, 2007 base) was determined by UV using the molar extinction coefficient 260 ) 6600 L mol-1 cm-1 at 260 nm.5 The protein contamination indicator, A260/A280, was found to be 1.8, suggesting that the DNA solution was protein-free.5 Sodium bromide and sodium chloride (Riedel-deHaen extra pure quality) were used as received. The cationic surfactants didodecyldimethylammonium bromide, DDAB (Tokyo Kasei Kogyo Co., Ltd, >98% pure), and the hexadecyltrimethylammonium bromide, CTAB (Tokyo Kasei Kogyo Co., Ltd, >98% pure), were used without further purification. The water used was from a Milli-Q filtration system (Millipore). Sample Preparation. DNA solutions were prepared by weighing the desired amount and dissolving it in 5 mM NaBr in a cold room over 1-2 days. Charge neutral DNA-surfactant samples were prepared by mixing matching charge solutions of cationic surfactant (5 mM) and DNA under stirring. The precipitates formed were equilibrated in solution for 2 days, filtered, and washed extensively with pure water. Chemical analysis using optical emission spectrometry with inductively coupled plasma (ICP-AES) was used to determine the traces of sodium (Na) and bromide (Br) in the complex after extensive washing. In terms of sensitivity, the ICP-AES detection limit is typically at the µg/L level. No Na or Br could be detected in the solid DNA-surfactant complex, although we do not exclude a presence of salt at the 0.5 mol % level, with respect to charged species. The complex will be referred to throughout the paper as DNA-CTA or DNA-DDA implying DNA (without counterion Na) and CTA or DDA (without counterion Br). Inclusion of Salt in the Electroneutral DNA-Surfactant Aggregates. Twenty samples of each resulting complex salt (DNA-CTA and DNA-DDA) free of small ions were dried in high vaccum for 3 days and then rehydrated during 5 days in a chamber equilibrated at 25 °C and relative humidity of 99.5% (just slightly below 100% to avoid water condensation). Different amounts of NaCl grains were added to the rehydrated samples in a closed environment to avoid water evaporation from the DNA-CTA complex. NaCl was allowed to diffuse to the DNA-CTA complex over 5 days. The DNA-CTA samples now containing NaCl were once more dried in vaccum over 3 days to remove all the water and hydrated again at 99.5% relative humidity. The water content was measured by weighing after and before salt inclusion. The same procedure was done for desiccators at 75% and 95% relative humidity. Experimental Sorption Isotherms. Sorption isotherms for the complexes with different salt content were determined with a twin double microcalorimeter described by Wadso¨ and Markova.6 The instrument consists of two thermally isolated vessels, one with solid sample and one with pure water. The vessels communicate by vapor water diffusion. Combining Fick’s law with the measured thermal powers of sorption and evaporation on the sample and water vessels makes it possible to determine the amount of sorbed water as a function of water activity (or equivalent water chemical potential). Simultaneously, the partial molar enthalpy of water in the sample is also measured. Small-Angle X-ray Diffraction (SAXd). To verify that the water uptake was occurring in a properly mixed system, the lattice spacing at different relative humidities of the complexes containing different salt content was measured by SAXd. The measurements were performed on a Kratky compact small-angle system. Cu KR radiation of wavelength 1.542 Å was provided by a Seifert ID300 X-ray generator operating at 50 kV and 40 mA. The temperature was kept constant at 25 °C ((0.1 °C) with a Peltier element. The structural features of fully hydrated
Leal et al.
Figure 1. Synchrotron SAX diffraction pattern for fully hydrated DNA-CTA. The two Bragg peaks are consistent with a 2D hexagonal arrangement in the complex salt.
DNA-CTA and DNA-DDA complexes without any salt were investigated at the Maxlab synchrotron facility in Lund at operating electron energy of 1.5 GeV, wavelength 1.07 Å, and wavelength resolution, E/dE ∼ 103. Results and Discussion Aggregate Geometry. The DNA-surfactant complexes are prepared by precipitation from an aqueous solution, so the resulting complex is a rather compact aggregate where the DNA molecules and the surfactant aggregates are separated by a thin water layer. Figure 1 shows the small-angle X-ray diffraction pattern for a fully hydrated DNA-CTA system without salt. This demonstrates that there is a two-dimensional (2D) hexagonal packing. Even though the detailed structure has not been unequivocally established, we have previously argued that, taking into consideration the size versus charge density of DNA and surfactant rods as well as the requirement of charge neutrality, the packing most consistent with the data is a hexagonally distorted CTA cylinder surrounded by six near neighbor DNA double helices as shown in Figure 2.4 As the water content decreases from full hydration, the characteristic 2D packing distance is expected to decrease, since the water film gets thinner and this was indeed observed. By the addition of salt, the swelling should increase at a given relative humidity since the attractive part of the interaction is made weaker. As shown in Table 1 this qualitative effect is indeed observed at the relative humidities of 75% and 99.5%. These experiments also demonstrate that the NaCl is incorporated into the complexes rather than forming a separate solution. In the table are also included the d spacings obtained for the thermodynamic model described below. Experimental Sorption Isotherms. At the start of the sorption experiments the DNA-surfactant complex is extensively dried to remove as much water as possible. The sample is then mounted in the calorimeter, and both the sorption isotherm and the sorption enthalpy are measured simultaneously. Figure 3a shows the measured sorption isotherms for four different molar ratios salt/DNA-CTA. The maximum swelling was obtained by the desiccator experiment at 0.995 water activity (or 99.5% relative humidity) and these values are incorporated in the figure. The points obtained in the control desiccator experiments at 75% and 95% relative humidity are also included. The main feature is that at low water activity (0.50) the salt does not have any measurable effect on the
DNA-Surfactant Aggregate
J. Phys. Chem. B, Vol. 111, No. 21, 2007 6001
Figure 2. Suggested supramolecular arrangement in stoichiometric DNA-CTA complexes. The inherently cylindrical surfactant rods (cationic headgroups,blue; hydrocarbon tails, yellow) are hexagonally deformed as a response to the interaction with the DNA helices (negatively charged backbone, red; sugar bases, black).4 A 2D projection of a smaller symmetry element of the structure is illustrated in Figure 5
swelling. Then there is a gradual onset of increased swelling, which increases as the salt content becomes higher. The maximum swelling for the sample with the highest salt content is approximately twice as large as that without salt. One can identify three stages in the sorption experiment in the presence of salt. Under dry conditions we expect that the DNA-CTA and NaCl are present as two separate solid phases at equilibrium. These have been formed during a rather rapid drying process so that the separated solid domains might be small. At a small increase of the water activity, it is only the DNA-CTA system that has the ability to take up water. A saturated NaCl solution corresponds to a relative humidity of ≈74%, and for a sorption experiment with pure NaCl there should be a steplike water uptake at this value of the water activity, which has been observed with our equipment in an experiment on an analogous system.7 In the presence of the complex, we observe a more gradual salt-dependent increase in water uptake with an onset around a relative humidity of 50-60%. In agreement with the measurements of d-spacing this implies that the salt is preferably incorporated into the complex rather than forming a separate solution. The driving force for this incorporation is most likely the electrostatic interaction with Na+ preferring DNA and Cl- preferring the CTA part. The starting of salt dissolution should be independent of the total amount of salt, since it is determined by the chemical potential of the crystalline salt. After the onset there is a stage when the sorption process continues at constant chemical potential of NaCl as long as there still is a reservoir of solid salt. In the last stage of the sorption process there is a gradual dilution of the salt in the complex, at a constant amount of salt. The higher the salt concentration, the lower the electrostatic attraction and additionally the higher the contribution from the salt to the osmotic pressure or, equivalently, to the water activity. This promotes the swelling, and for sufficiently high salt contents, the sorption leads to dissolution/disintegration of the DNA-CTA complex. The sorption isotherm was also measured for another aggregate, DNA-DDA that differs from DNA-CTA with respect to geometry. The DNA-DDA complex has a lamellar structure with DDA surfactant bilayers intercalated with DNA molecules.8 In Figure 4 is shown the sorption isotherm at different molar
Figure 3. (a) Experimental sorption isotherm (water content, CW, as a function of water activity) for DNA-CTA loaded with different amounts of salt. From bottom to top in nNaCl/nDNA-CTA: 0 (solid line), 0.36 (dash line), 0.60 (dot line), 0.95 (dash dot line). The individual data points are from independent experiments in desiccators for nNaCl/ nDNA-CTA: (circle) 0, (triangle pointing up) 0.36, (square) 0.60, and (triangle pointing left) 0.95. The full lines at the end of the curves are guidelines to the eye to relate the individual data points with the isotherm lines. (b) Experimental partial molar enthalpy of water (∆Hsorp) vs water content (CW) for DNA-CTA without salt (black line) and DNA-CTA incorporated with NaCl at nNaCl/nDNA-CTA ) 0.60 (line with the arrow).
Figure 4. Experimental sorption isotherm for DNA-DDA incorporated with different salt contents. From bottom to top in nNaCl/nDNA-DDA: 0 (solid line), 0.41 (dash line), 0.68 (dot line), 1.04 (dash dot line). The individual data points are from independent experiments in desiccators at nNaCl/nDNA-DDA: (circle) 0, (triangle pointing up) 0.41, (square) 0.68, and (triangle pointing left) 1.04. The full lines at the end of the curves are guidelines to the eye to relate the individual data points with the isotherm lines.
ratios salt/DNA-DDA. Also for the lamellar DNA-DDA complex the isotherm displays essentially the same features as
6002 J. Phys. Chem. B, Vol. 111, No. 21, 2007
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TABLE 1: Calculated and Experimental d Spacings for the Aggregates at Different Salt Content and Relative Humidity d spacing (Å) DNA-CTA
DNA-DDA
RH (%)
nsalt/naggregate )0
nsalt/naggregate ) 0.36
nsalt/naggregate ) 0.6
nsalt/naggregate ) 0.95
75 80 (model) 95 (model) 99.5
41.7 52.6 58.4 45.8
50.6 54.4 62.7 54.6
53.2 55.5 66.1 56.5
57.1 69.2 69.8
for the DNA-CTA case. There is a small increase of the water activity for DNA-DDA water uptake followed by a gradual salt-dependent increase in water uptake with an onset around a water activity of 0.50-0.60 due to salt dissolution in the water reservoir of the DNA-DDA aggregate. This seems to be a general effect, not dependent on aggregate geometry. Sorption Enthalpies. It is an advantage of the sorption calorimetric technique we use that at the same time as the sorption isotherm is acquired the enthalpy associated with the water sorption process is also monitored. Provided the sorption process is slow enough to ensure equilibrium conditions, this enthalpy is equivalent to the partial molar enthalpy of water. This quantity is shown in Figure 3b as a function of water content for DNA-CTA without salt and at salt/aggregate molar ratio of 0.6. The two curves are similar for the major part of the isotherms. The small quantitative deviations at low water contents can be explained by the fact that the initial state is generated by a nonspecific drying process which introduces a certain lack of control in the beginning of the experiment. The deviations observed at high water contents are within the experimental uncertainty with the exception that in the presence of salt a small peak appears at around seven to eight water molecules per DNA-CTA pair. In all cases the partial molar enthalpy goes from distinctly negative at low water contents to positive values at high water contents. In previous studies,4,9 we have concluded that the major source of the positive enthalpy at high water contents is due to a gradual increase in the conformational freedom of the alkyl chains of the amphiphile. For samples containing salt, the distinct positive enthalpy peak occurs at water activities 0.550.60. The higher the salt content, the larger the peak. By integration we estimate that the area under the peak corresponds to +1.6 ( 0.5 kJ/mol NaCl. The dissolution of NaCl in water, NaCl(s) f Na+(aq, cNaCl ≈ 0) + Cl-(aq), is an endothermic process with ∆H ) +3.89 kJ/mol10 and for the dissolution of solid NaCl in pure water with formation of a saturated solution, ∆H ) +1.85 kJ/mol.11,12 Thus we find that in the complex the enthalpy of dissolution not only has the same sign but also the magnitude is very close to what is found for dissolution into bulk aqueous phase. These enthalpy values have a magnitude that is only a small fraction of the cohesive energy of a NaCl crystal (787 kJ/mol).10 In the dissolved state, the direct interaction between Na+ and Cl- is much smaller than that in the solid and the enthalpy values show that this interaction is nearly compensated by hydration. In the complex there is the additional possibility for the interaction of Na+ and Cl- with the charged surfaces. In this perspective, it is remarkable that in the confined environment of the DNA-surfactant complex the amount of energy associated in the dissolution is similar to that in pure water. The ions appear to exist in an immediate aqueous environment also in the complex. The enthalpy data support the interpretation that dissolution of the salt occurs in the range between ≈0.50 and 0.60 water activity. Once the salt is in solution, there are no large enthalpy
nsalt/naggregate )0
nsalt/naggregate ) 0.41
nsalt/naggregate ) 0.68
37.4
45.4
47.7
41.6
47.8
49.8
effects although one can envisage distinct changes in the electrostatics. One source of this insensitivity of the enthalpy is that for aqueous ionic systems the electrostatics is typically dominated by the entropy contributions due to the unusual temperature dependence of the dielectric constant of water.13 Thermodynamic Model. The main purpose of studying the salt dependence of the sorption process is to probe the attractive electrostatic interaction between the constituents of the DNAsurfactant complex. The nature of the electrostatic interaction in similar systems has previously been discussed by Ben-Shaul and co-workers.14-17 Adding a simple salt, which primarily should affect the electrostatic component, provides additional quantitative information on the interactions. It is our previous experience that modeling the aqueous part as a dielectric provides a surprisingly accurate description of electrostatic interactions also at short range.18,19 In the present system we have two oppositely charged surfaces separated by only a thin aqueous layer over which there is a strong electric field. We cannot expect a priori that a dielectric description should work under such circumstances, and the case has not to our knowledge been tested previously. In previous studies of interactions of charged systems, we have studied systems of high symmetry and this provides substantial simplifications in the description. Due to that we are here dealing with two types of charged molecules/aggregates, the system necessarily is less symmetric. Below we will model the DNA-CTA system as a hexagonally distorted CTA cylinder surrounded by six near neighbor DNA double helices as shown in Figure 2. A smaller adequate symmetry element in such a structure is an equilateral triangle, representing a sixth of a hexagonal unit cell as shown in Figure 5. In this cell there is a fixed uniform negative charge distribution on the surfaces of the DNA cylinders. Similarly there is a uniform compensating positive charge density on the surface of the CTA cylinders. DNA is modeled in a very simplistic way as robust cylinders of radius 10.5 Å and surface charge density σ )-0.0119 e/Å2. The geometry of the molecule with minor and major grooves as well as distinct conformations at different hydration and salt levels is not included. The CTA cylinders are allowed to deform according to
r ) r0(1 + δ sin(6θ))
(1)
where δ is the degree of deformation and θ the polar angle. We work at constant volume for the CTA cylinders (or constant cross sectional area in 2D), so r0 is calculated as follows: For each deformation parameter (δ), r0 is such that the cross sectional area equals the one for a cylinder of radius 21.5 Å (non-deformed CTA radius in the hexagonal phase). The surface charge density, σ, on these deformed cylinders is such that it neutralizes the DNA charges. Increasing deformation increases the surface area and both r0 and σ go down. The surface charge density on a CTA cylinder in its own hexagonal phase is around σ ) 0.020 e/Å2.20 In the model, this value is reduced by about 20% when the deformation is included. The total volume of a
DNA-Surfactant Aggregate
J. Phys. Chem. B, Vol. 111, No. 21, 2007 6003 To obtain a formally complete model, nonelectrostatic contributions have to be included. The free energy cost associated with the deformation of the CTA cylinders is given by
Gdef ) Kdefδ2
(4)
where Kdef is a deformation constant and δ the variable deformation parameter explained above. This can be considered as the first term in an expansion in even powers of δ. We finally have a short-rage repulsion contribution which, in accordance with a previous study22 we describe as
Gsr ) K1nc exp(-nH2O/(K2nc)) Figure 5. Model of the DNA-CTA aggregate. The triangle contains robust DNA half cylinders with negative surface charge (red line) and an interior with an electric permittivity, ) 2. The CTA rods (blue lines) are distorted and positively charged, in the interior ) 2. The rest of the space is filled with water described as ) 78.5. The distances are in angstroms.
(5)
It is particularly convenient to describe the short-range repulsion in this form when one deals with systems of low symmetry. Here K1 and K2 are parameters to be determined; nc represents the number of charges in DNA and CTA aggregates and nH2O represents the number of water molecules. When salt is added to the system, we additionally have a free energy term representing the entropy of mixing of the ions
-TSmix ) NAkBT
∑i ∫ ci{ln(ci/c0) - 1} dV
(6)
This term contains the ideal entropy of mixing, also present in the absence of electrostatic interactions. c0 is the water concentration set to ∼55 M and ci represent the ion concentration profiles. The deformation term in eq 4 could only influence the water chemical potential indirectly, since it does not explicitly depend on the number of water molecules. By differentiation of eq 5, the contribution to the water chemical potential from the shortrange repulsion term is
(µH2O)sr ) -K1/K2 exp(-nH2O/(K2nc)) Figure 6. Experimental sorption isotherms, from bottom to top in nNaCl/ nDNA-CTA: 0 (solid line), 0.36 (dash line), 0.60 (dot line), 0.95 (dash dot line). Calculated isotherms (individual points) at different salt/ aggregate molar ratios, nNaCl/nDNA-CTA: (circle) 0, (triangle pointing up) 0.36, (square) 0.60, and (triangle pointing left) 0.95.
prism with an equilateral triangle cross section (or, equivalently, its side length) is given by the sum of the volumes of the DNA, CTA, and water domains. The volume of the aqueous region is determined by the number of water molecules multiplied by a volume of 30 Å3. For simplicity we neglect ion volume in our model. The length of the side of the triangle goes from 61 to 84 Å when the water content varies from 10 to 50 water molecules/DNA-CTA pair, respectively. The quantity of interest in order to reproduce the experimental data is the chemical potential of water in the DNA-CTA complex given by
µH2O )
∂Gtot ∂nH2O
(2)
where Gtot is the total free energy. There are three components to the free energy in our thermodynamic model (i) electrostatic energy, (ii) deformation energy, and (iii) short-range repulsion. The electrostatic energy is obtained through integration of the electric field squared over the volume of the water domains21
Eel ) 1/20
∫(∇Φ)2 dV
(3)
(7)
We are left with the problem of obtaining the electrostatic contribution to the chemical potential
(µH2O)el )
∂Gel ∂nH2O
(8)
Gel is either the energy term in eq 3 (salt-free case) or the sum of the terms in eqs 3 and 6 (salt case). In the calculations the electrostatic chemical potentials are obtained numerically from finite differences. The slope of a plot of electrostatic free energy vs water content is the chemical potential. To obtain the electrostatic free energies, one has to solve the following secondorder elliptic partial differential equation
-∇0∇Φ ) F
(9)
which relates the electrostatic potential Φ to the spatial charge density F via Poisson’s equation. In the salt-free case F ) 0 while when salt is added, F is described by assuming that the ions are distributed according to the Boltzmann distribution law. We then arrive at the nonlinear Poisson-Boltzmann equation
-∇0∇Φ ) NA
∑i zici0 exp(-zieΦ/kBT)
(10)
where ci0 is the concentration of ion i at a reference point where the electric potential Φ is set to zero and zi is its valency. The ion distribution ci is
ci ) ci0 exp(-zieΦ/kBT)
(11)
6004 J. Phys. Chem. B, Vol. 111, No. 21, 2007 By solving eq 9, one acquires both the potentials and ion concentration profiles needed in eqs 3 and 6, respectively. In the present case we have to solve a 2D partial differential equation with boundary conditions reflecting a complex geometry. This is conveniently done with finite element methods. In this work we employed the Femlab software package and its electrostatics module.23 Due to symmetry and overall electroneutrality, we impose the normal component of the electrical field to be zero at the sides of the triangle. The field (but not ions) penetrates into the DNA and CTA domains where we assigned a dielectric permittivity of 2 while for the water domain we used )78.5. Equation 9 is then solved inside the triangle for a certain deformation, water, and salt content. In the salt-free case, F is only due to the fixed surface charges. In the salt case, F in the water domain is determined from eq 10. We did not optimize the deformation and made the calculations for the constant value, δ ) 0.1.24 It is yet essential to include a deformation, otherwise it is impossible to remove water below about 18 water molecules per DNA/surfactant pair in the cell model. Furthermore, packing is not feasible below about 10 water molecules per DNA-CTA pair using the deformation model of eq 1, regardless of the deformation constant. This puts a lower limit to the concentrations for which calculations could be performed. Calculated Sorption Isotherms. In the model, three factors influence the chemical potential of the water. For a specified geometry the electrostatic contribution is uniquely determined. It is particularly clear that the effect of added salt is calculated in a parameter-free way. We adopted a procedure to ensure a constant salt content for each point in the isotherms. The other important contribution comes from the short-range force. We have used a previously developed description for this contribution.21 The two parameters K1 (5.1 kBT) and K2 (8.2 kBT) of eq 5 are chosen so that we reproduce the curve for the salt-free case. It is an essential assumption that this part of the free energy is unaffected by the presence of salt. In Figure 6 we show the calculated salt dependence of the sorption isotherms. The figure also includes the experimental results. The agreement between calculated and experimental values is clearly satisfactory. This result brings about a number of conclusions: (i) The description of a continuum model appears to work well in a concentrated system at high electric fields and with a rather complicated geometry. In such a model the molecular degrees of freedom of the water molecules are suppressed and the water is replaced by an incompressible medium of given electric permittivity (ii) The formation of a thin aqueous layer separating the DNA and the CTA is caused by a short-range repulsive force. (iii) The inclusion of a deformation constant for the surfactant is required to obtain agreement between calculated and observed values. In the salt-free case, we observe that the electrostatic contribution to the water chemical potential is relatively insensitive to water content. This observation can be qualitatively understood by considering a simple planar capacitor situation. With fixed and opposite charges on the planar walls, the force between the plates, and thus the chemical potential of the intervening medium, is independent of the separation between the plates. When a fixed amount of electrolyte is added to such a system, the respective counterions tend to condense on the charged surfaces and the primary effect of the electrolyte is to reduce the effective charge on the walls. To a first approximation, a modest amount of electrolyte then gives a smaller attraction and a moderately distance-dependent force
Leal et al. due to the osmotic effect of the ions. In the presence of a strongly distance dependent pushing force, the system finds an equilibrium, zero force, further out in the presence of electrolyte. Conclusions In this investigation we have shown that the addition of salt to a DNA-CTA complex results in an increased uptake of water at a given water activity. This swelling can be quantitatively modeled using a combination of (i) an attractive electrostatic interaction described through the Poisson-Boltzmann equation, (ii) a repulsive short-range force, and (iii) a deformation of the CTA aggregate. It is worth noting that the dielectric description of the water appears to be valid even under the rather extreme conditions found in the confined water space in the complexes. The enthalpy curve in the calorimetric measurements shows an endothermic heat of dissolution ∆H) +1.6 ( 0.5 kJ/mol for NaCl(s) in the complex. This is remarkably close to the value +3.89 kJ/mol for the dissolution into pure water. This is a further indication that the ions experience an immediate aqueous environment also within the complexes. The dissolution of the NaCl(s) occurs in the range of 0.5-0.6 in water activity, which is substantially lower than that for a saturated salt solution (0.74 water activity). This is most likely due to the electrostatic attraction between the charged aggregates and their respective counterions. In a previous publication we have suggested that aggregate deformations provide the repulsive component balancing the electrostatic attraction. Although deformations are important in the system, there has to be an additional explicit repulsive force for the system to find a balance at a finite swelling. It is thus necessary to explicitly include a short-range repulsive force in the quantitative description. We have characterized the short-range repulsion in terms of two parameters, whose values are consistent with what has been found previously.21 There has been a considerable debate about the molecular origin of this interaction.25-30 We note that the present study is fully compatible with the view that the repulsion is caused by local excitations at the surface of the aggregates. Our system is asymmetric with respect to both the nature of the interacting polar surfaces and their charge. It thus takes additional assumptions to argue that they induce similar surface polarizations of the water molecules, which is a necessary step if one wants to explain the repulsion in terms of a decaying surface polarization.27 Acknowledgment. This work was supported by the Swedish Research Council (VR) (C.L., H.W.) and the Fundac¸ a˜o para a Cieˆncia e a Tecnologia (FCT), Portugal, (L.P., SFRH/BD/21462/ 2005). Bengt Jo¨nsson is greatly acknowledged for helpful discussions. Maxlab in Lund is acknowledged for allowing measurements during the setup of the new SAXS synchrotron beamline. Daniel Topgaard is acknowledged for rendering Figure 2. References and Notes (1) Israelachvili, J.; Wennerstro¨m, H. Nature 1996, 379, 219. (2) Stahlberg, J.; Jo¨nsson, B. Anal. Chem. 1996, 68, 1536. (3) Stahlberg, J.; Appelgren, U.; Jo¨nsson, B. J. Colloid Interface Sci. 1995, 176, 397. (4) Leal, C.; Wadso¨, L.; Olofsson, G.; Miguel, M.; Wennerstro¨m, H. J. Phys. Chem. B 2004, 108, 3044. (5) Saenger, W. Principles of Nucleic Acid Structure; SpringerVerlag: New York, 1984. (6) Wadso¨, L.; Markova, N. Thermochim. Acta 2000, 360, 101. (7) Silva, C. L.; Topgaard, D.; Kocherbitov, V.; Pais, A. C.; Sousa, J. J.; Sparr, E. Submitted for publication in Biochim. Biophys. Acta Biomembr. (8) Ra¨dler, J. O.; Koltover, I.; Salditt, T.; Safinya, C. R. Science 1997, 275, 810.
DNA-Surfactant Aggregate (9) Leal, C.; Topgaard, D.; Martin, R. W.; Wennerstro¨m, H. J. Phys. Chem. B 2004, 108, 15392. (10) Atkins, P. W. Physical Chemistry, 5th ed.; W H Freeman & Co: London, 1994. (11) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Data, Suppl. 1982, 11 (S1), 1. (12) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Data 1982, 11, 1. (13) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Biology and Technology Meet; VCH: New York, 1998. (14) May, S.; Harries, D.; Ben-Shaul, A. Biophys. J. 2000, 78, 1681. (15) Bruinsma, R. Eur. Phys. J. B 1998, 4, 75. (16) Harries, D.; May, S.; Gelbart, W. M.; Ben-Shaul, A. Biophys. J. 1998, 75, 159. (17) Harries, D.; May, S.; Ben-Shaul, A. J. Phys. Chem. B 2003, 107, 3624. (18) Wennerstro¨m, H.; Jo¨nsson, B.; Linse, P. J. Chem. Phys. 1982, 76, 4665.
J. Phys. Chem. B, Vol. 111, No. 21, 2007 6005 (19) Wennerstro¨m, H.; Jo¨nsson, B. J. Phys. 1988, 49, 1033. (20) Fontell, K.; Khan, A.; Lindstro¨m, B.; Maciejewska, D.; PuangNgern, S. Colloid Polym. Sci. 1991, 269, 727. (21) Jo¨nsson, B.; Wennerstro¨m, H. J. Phys. Chem. 1987, 91, 338. (22) Jo¨nsson, B.; Wennerstro¨m, H. J. Phys. Chem. 1987, 91, 338. (23) Femlab; 3.1 ed.; Comsol AB, 2004. (24) An optimization of the deformation constant would of course have been desirable in a full theoretical study of this question. It is our opinion anyway that this would involve a level of detail and calculation outside the scope of this work. Nevertheless, preliminary calculations during the implementation of our procedures lead us to think that the effect of geometry optimization could only be small, and the qualitative picture obtained here should not be changed. (25) Parsegian, V. A.; Rand, R. P.; Fuller, N. L. J. Phys. Chem. 1991, 95, 4777. (26) Parsegian, V. A.; Rand, R. P. Langmuir 1991, 7, 1299. (27) Marcelja, S.; Radic, N. Chem. Phys. Lett. 1976, 42, 129. (28) Israelachvili, J. N.; Wennerstro¨m, H. J. Phys. Chem. 1992, 96, 520. (29) Israelachvili, J. N.; Wennerstro¨m, H. Langmuir 1990, 6, 873. (30) Faraudo, J.; Bresme, F. Phys. ReV. Lett. 2005, 94, 077802.
