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J. Phys. Chem. B 2009, 113, 1738–1742
Helix-Coil Transition of DNA Monitored by Pressure Perturbation Calorimetry Gamal Rayan,*,† Alekos D. Tsamaloukas,† Robert B. Macgregor, Jr.,† and Heiko Heerklotz† Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, UniVersity of Toronto, Toronto ON, M5S 3M2, Canada ReceiVed: September 16, 2008; ReVised Manuscript ReceiVed: December 5, 2008
We report the first use of pressure perturbation calorimetry (PPC) to characterize the heat-induced helix-coil transition of DNA polymers. The alternating copolymer poly[d(A-T)] was studied in aqueous solutions containing 5.2 and 18.2 mM Na+; it exhibited helix-coil transition temperatures of 33.6 and 44.7 °C, respectively. The transition is accompanied by a negative molar volume change, ∆V ) -2.6 and -2.1 mL/ mol (base pair), respectively, and an increase in the coefficient of thermal expansion, ∆R ) +5 × 10-4 K-1 (at both ionic strengths). These values are consistent with a greater hydration of the coil form. The larger water-accessible surface area of the coil causes more water molecules to assume a bound, more densely packed structure that then gradually decreases with increasing temperature, leading to a larger value of R. The magnitude of the volume changes detected by PPC were larger than those deduced from high-pressure UV spectroscopy, shedding light on the effect of pressure on ∆V. The shape of the PPC peak was nearly identical to the shape of the DSC peak, providing direct evidence for the correlation between the molar volume change and enthalpy change for the helix to coil transition of DNA. Introduction Water is essential to the structure and function of virtually all biological macromolecules due to the nature of its interactions with molecular surfaces. In spite of its fundamental importance, even basic issues of hydration remain controversial. Since the mere contact between solute and solvent does not imply a specific, binding interaction, hydration behavior is measured in terms of changes in the physical properties of the solute and the interacting water. Two quantities have been identified to be particularly useful for understanding hydration, the heat capacity of a solution (and its changes upon folding, binding, association, etc.) and the partial volume of biomolecules in aqueous solution. Heat capacity and entropy changes provide information concerning the mobility and orientational freedom of interfacial water; volume and compressibility changes reveal the extent to which biomolecules perturb the space-consuming hydrogenbond network of water molecules at the interface. Much has been learned about DNA hydration from volumetric studies. Spectroscopic measurements at high pressure have been used to obtain values of ∆V (i.e., -0.5%) of the helix-coil transition of DNA polymers and oligonucleotides.1-4 Buckin and co-workers5 have used densimetry and ultrasonic velocimetry to measure partial molar volumes and compressibilities and have concluded that poly(dA) · poly(dT) is more hydrated than poly[d(A-T)]. Chalikian and colleagues6 have reported that the extent of hydration of double-stranded DNA duplexes shows the following order: poly[d(I-C)] > poly[d(G-C)] > poly[d(A-T)] ≈ poly(dA) · poly(dT). The differences in hydration also influence the binding of drugs to DNA. The minor grovebinding drug netorpsin7 and the intercalating agents ethidium bromide and propidium iodide8 bind to poly(dA) · poly(dT) with a large positive ∆V, but the value of this parameter is negative * To whom correspondence should be addressed. Current Address: Laboratoire de Physique Statistique, Ecole Normale Supe´rieure, 24 Rue Lhomond, 75231 Paris, France. Phone: 01 44 32 34 19; fax: 01 44 32 34 33; e-mail:
[email protected]. † University of Toronto.
for binding to poly[d(A-T)]. This difference arises from the a spine of hydration of poly(dA) · poly(dT); the interaction of the water molecules comprising the spine is diminished upon drug binding. The alternating polymer, poly[d(A-T)], is less hydrated in the first place.9,10 Pressure perturbation calorimetry (PPC) is a promising addition to the available volumetric techniques.11,12 It has been successfully applied to study changes in hydration accompanying heat-induced transitions such as the coil-to-globule transition of the polymer PNIPAM (∆V/V ) +1%),13 the sphere-to-rod transition of surfactant micelles (≈ +0.2%),12 the denaturation and aggregation of proteins (typically within ( 0.2%),14-16 the melting of gel phases of lipids (≈ +3%),17-19 and the condensation of lipids upon interaction with cholesterol (up to 1%).20 Here we present the first application of PPC to DNA polymers. We have reproduced previously published highpressure data on the heat-induced helix-coil transition of poly[d(A-T)] at different ionic strengths and show which additional information can be obtained by PPC measurements. We report values the partial volume change, ∆V, expansivity change, ∆R, transition temperature, TM, and van‘t Hoff enthalpy, ∆HvH, of the transition. We discuss the effect of high pressure on the observed thermodynamic parameters and the coupling between enthalpy and volume changes. Materials and Methods Materials. Poly[d(A-T)] was purchased from Amersham/GE Healthcare (Piscataway, NJ). Sodium cacodylate trihydrate and sodium chloride were obtained from Sigma-Aldrich Canada (Oakville, ON, Canada). Disodium EDTA was purchased from Bio-Rad Laboratories (Hercules, CA). The polymers were dialyzed thrice at 4 °C in 5 mM sodium cacodylate and 0.1 mM Na2EDTA, pH 6.7, at Na+ concentrations of 5.2 and 18.2 mM. The higher Na+ concentration was attained by adding NaCl to the buffer. The dialysis tubing (molecular weight cutoff of 1000 Da) was obtained from Genotech, Inc. (St. Louis, MO). The concentration of the stock poly[d(A-T)] solution was
10.1021/jp808253t CCC: $40.75 2009 American Chemical Society Published on Web 01/21/2009
Helix-Coil Transition of DNA determined spectrophotometrically using ε262 ) 13 300 (M cm)-1.21 An AVIV model 14 DS UV spectrophotometer (Aviv associates, Lakewood, NJ) was used to measure the absorption. Pressure Perturbation Calorimetry (PPC) and Differential Scanning Calorimetry (DSC). Calorimetry experiments were conducted in a VP-DSC microcalorimeter (Microcal, Northampton, MA), equipped with a PPC accessory from the same manufacturer. For both DSC and PPC measurements, the sample cell was filled with the DNA buffer solution; the reference cell was filled with buffer. The DNA concentrations ranged from around 0.38 to 0.75 mM. Details about both techniques can be found in the pertinent literature.13,14,18,22-24 DSC data were recorded in a series of five to seven scans at heating and cooling rates of 0.5 and 1 K/min. Because of the reversibility of the helix-coil transition of the studied DNA samples, no significant deviations between any of the helix-coil transitions were detected even after multiple denaturations. The DSC curves obtained in corresponding buffer versus buffer scans were subtracted, and the curves were normalized with respect to DNA concentration to yield the correct shape of the molar heat capacity peak,Capp P (T). Data evaluation was performed using Origin for DSC package supplied with the instrument. The automatic PPC routine of the accessory was used for the PPC measurements.14,22Briefly, it runs the calorimeter in isothermal mode at a series of temperatures and performs a selected number of small pressure jumps between ambient pressure and 5 bar above ambient at each temperature. Typically, we recorded data between 20 and 60 °C. At temperatures within the thermal transition, two up and down jumps were carried out at intervals of 0.1 K; outside this temperature range the jumps were carried out at intervals of 0.5 K. The system measures the power required to maintain a constant temperature after each pressure change, dQ/dP|T; for a reversible process, knowledge of dQ/dP|T allows one to calculate the thermal volume and expansivity, dV/dT|P. A complete PPC experiment consists of four runs.14,15 Differential measurements with solution versus buffer and buffer versus water are necessary in order to calculate the difference in expansivity between solute and water. One can then find the absolute, partial molar expansivity of the solute because the temperature-dependent expansivity of water is precisely known. Control measurements consisting of bufferversus-buffer and water-versus-water are performed to correct the raw data for technical imperfections, for example, minute differences in the size of the cells. Because the buffer-buffer, buffer-water, and, water-water controls show only gradual changes with temperature, they are recorded with a moderate temperature resolution and fitted by fourth-order polynomials for interpolation as needed. The up- and down-heat peaks, dQ/ dP|T, were completed within 60 s, each, and showed no systematic differences in their absolute values. This provided evidence of complete re-equilibration after the pressure jumps and increased the precision of the measurement by allowing the two, independently measured values to be averaged. The instrument software reads the sample and blank data and performs all necessary conversions and corrections to derive the coefficient of thermal expansivity, R(T). In a manner analogous to the analysis of data from DSC measurements, the PPC peak of a heat-induced transition is integrated from a progress baseline. The area under the peak of the R(T)-curve corresponds to the relative volume change of the transition, ∆V/V. The value of ∆V is obtained using the relation: ∆V ) VC(∆V/V), where C is the concentration of the DNA sample (given in mg/mL). The position of the peak maximum is TM, and ∆R is the step height between pre- and
J. Phys. Chem. B, Vol. 113, No. 6, 2009 1739 post-transition baselines at TM. For the analysis of both DSC and PPC data we have used the molecular weight of 663.4 Da per base pair25 and the partial molar volume of 326.8 mL/mol (base pair) for the sodium salt of poly[d(A-T)].26 This value is corrected for the Donnan membrane equilibrium effect. High-pressure UV Spectroscopy. The instrumentation for measuring the helix-coil transition curves at elevated hydrostatic pressure has been described previously.27 Briefly, a highpressure cell filled with silicon oil as the pressure-transmitting medium is placed in the optical path of a Uvikon model 860 spectrophotometer. The sample is loaded into a quartz cuvette of ∼300 µL volume, which is positioned in the high-pressure cell so that it is in the optical path of the spectrophotometer. The pressure cell is connected to a pressure-generating pump and a circulating temperature bath, which regulate the pressure and temperature, respectively. The temperature, pressure, and absorption of the solution are measured and controlled in real time. Pressures generated by this equipment range from 0.1 MPa (atmospheric pressure) to 250 MPa. The samples were heated at a rate of 0.1 K/min. The biopolymer concentration in the UV melting experiments was approximately 0.07 mM. Melting Curves Analysis. The parameter θ(T), representing the fraction of biopolymers in the coil form at a temperature T, was calculated using the following equation:
θ(T) )
OD(T) - L(T) H(T) - L(T)
(1)
where OD(T) is the optical density of the sample at 262 nm at temperature T, H(T) is the equation for the line describing the high-temperature/post-transitional baseline as a function of temperature, and L(T) is the equation for the line corresponding to the low-temperature/pretransitional baseline. The biopolymer is assumed to be in double stranded (helix) form if θ ) 0, whereas at θ ) 1 the biopolymer is assumed to be entirely in the single stranded (coil) form. The helix-coil transition temperature, TM, is the temperature at which θ ) 0.5. Assuming a single-step biomolecular reaction between the single stranded and double stranded species, the enthalpy change, ∆HvH, of the helix-coil transition was calculated using the van’t Hoff equation:1,28 where
∆HVH ) 6RTM2(dθ/dT)
|
(2) T)TM
R is the gas constant, and dθ/dT is the slope of a θ versus T curve at TM.28 Results PPC and DSC. The top panel of Figure 1 illustrates the experimentally obtained differential heats, Q, as a function of temperature for two consecutive DNA scans in an aqueous buffer solution containing 18.2 mM Na+, and the data for buffer-buffer, buffer-water, and water-water runs. Note the excellent agreement of the two DNA scans consistent with the reversibility of the helix-coil transition of poly[d(A-T)] under these conditions (18.2 mM Na+, pH 6.7). The conversion from Q(T) to R(T) inverses the peak, indicating that the partial molar volume of the DNA decreases as a consequence of the helix-coil transition. The value of R increases from 2 × 10-4 K-1 for the helix to 6 × 10-4 K-1 for the coil; neither value depends strongly on temperature. The maximum of the peak indicates a TM of 44.7 °C. Integration from the baseline yields a relative volume change of ∆V/V )
1740 J. Phys. Chem. B, Vol. 113, No. 6, 2009
Rayan et al.
Figure 1. Differential heats after pressure jumps, Q (top, see plot for details) and resulting coefficients of thermal expansion (bottom, black circles right axis) as a function of temperature. The data were obtained by a PPC experiment with poly[d(A-T)] in 18.2 mM Na+, pH 6.7 at a concentration of 0.40 mM. The bottom panel also shows the DSC curve (blue solid line, left axis) on an inverse scale, illustrating that DSC and PPC curves match in shape and position.
Figure 3. Helix-coil transition temperature, TM, of poly[d(A-T)] as a function of pressure at 5.2 mM Na+ (O) and 18.2 mM Na+ (0) and a DNA concentration of 0.07 mM. The solid lines are linear regressions to the data. The numerical values ∆TM/∆P are listed in Table 1.
of the helix-coil transition. The ∆Vvalues are given in Table 1. It ought to be mentioned that the ∆V accompanying the helix-coil transition of DNA polymers can be positive or negative depending on the conditions,3 and this study was performed under conditions at which the ∆V values are negative. Discussion
Figure 2. Temperature dependence of the baseline-corrected coefficient of thermal expansion, R(T), of 0.40 mM poly[d(A-T)] in 18.2 mM Na+, pH 6.7.
-0.0055, which corresponds to a change in molar volume equal to -2.1 mL/mol. The bottom panel of Figure 1 shows the apparent heat capacity curve obtained by DSC after subtraction of a buffervs-buffer blank. The scale is inverted to emphasize the agreement between the PPC and DSC data. The peak position of the DSC curve implies TM ) 44.7 °C, the baseline offset at TM is ∆CP ) -0.61 kcal mol-1 K-1, and integration of the peak from the baseline yields the calorimetric enthalpy change of ∆Hcal ) 6.5 kcal mol-1. Assuming a two-state helix-coil transition, the van’t Hoff analysis yields the model dependent enthalpy change of the transition. Thus, the van’t Hoff enthalpy can be obtained by fitting either the DSC or the PPC curve. In Figure 2 one can see that the PPC peak after baseline subtraction agrees well with the van’t Hoff fit; from either data set, the resulting ∆HvH equals 710 kcal mol-1. High-pressure UV Spectroscopy. The pressure dependence of TM for poly[d(A-T)] in 5.2 and 18.2 mM Na+ is illustrated in Figure 3. The molar volume change of the helix-coil transition ∆V was calculated from the slopes of the data shown in Figure 3 via the Clapeyron equation:
∆TM ∆V ) TM ∆P ∆Hcal
(3)
where ∆Hcal is the calorimetrically determined enthalpy change
We have shown here that PPC is a precise and convenient new method to characterize volumetric changes accompanying the helix-coil transition of DNA. Let us compare the results of PPC with those from high-pressure UV and other methods. This will not only show advantages of PPC but demonstrate that combination of the two methods may provide additional insight into the hydration behavior of DNA. PPC Operates at Low Pressure. It is very important to note that PPC uses very low pressure for technical purposes and is not a method for studying the effect of pressure on the state of biomolecules. The maximum pressure used in the experiments presented here was 5 bar; this is 2 or 3 orders of magnitude less than the pressure needed for pressure-induced denaturation of DNA or proteins at room temperature. However, to change the native-denatured equilibrium by an extremely small, yet experimentally detectable amount, the measurement must be made at, or very close to, the helix-coil transition temperature at ambient pressure. The coil state in a PPC measurement is identical to that observed for thermally induced denaturation at ambient pressure. In our study, PPC yielded values for ∆V that are 1.5-2 mL/ molmorenegativethanthoseobtainedfromtheClausius-Clapeyron evaluation of the high-pressure UV data. This deviation exceeds the experimental uncertainties of the two methods. This suggests that the methods do not detect exactly the same quantity and that there is a difference between either the native or the denatured state, or both, at high pressure and at ambient pressure. Structurally, it is not surprising that the properties of the helix and coil states depend on pressure. The residual structure and properties of temperature- and pressure-denatured lipids and proteins may differ substantially from each other.29,30 A highpressure FTIR study of the DNA monomers poly(dA) and poly(dT) illustrated that elevated pressure resulted in increased stacking of the single strands.31 Increased stacking would presumably decrease the solvent-accessible surface area of the polymer in the coil state, which in turn would lead to decreased
Helix-Coil Transition of DNA
J. Phys. Chem. B, Vol. 113, No. 6, 2009 1741
TABLE 1: Thermodynamic Parameters for the Helix-Coil Transition of poly[d(A-T)] as Obtained by PPC, DSC, and Pressure-dependent UV Spectroscopy PPC and DSC [Na+] (mM)
TM (°C)
∆TM PPC (°C)
∆Hcal (kcal/mol)
∆HvH DSC (kcal/mol)
∆HvH PPC (kcal/mol)
∆V (mL/mol)
5.2 18.2
33.6 ( 0.1 44.7 ( 0.1
0.6 ( 0.1 1.0 ( 0.1
7.0 ( 0.2 5.0 ( 0.5
920 ( 40 580 ( 20
1100 ( 200 730 ( 50
-2.6 ( 0.1 -2.1 ( 0.1
UV [Na+] (mM)
TM (°C)*
100xdTM/dP (°C/MPa)
∆HvH (kcal/mol)
N (b.p.)
∆V (mL/mol)
5.2 18.2
34.3 ( 0.1 46.1 ( 0.1
-1.64 ( 0.01 -0.11 ( 0.05
990 ( 88 530 ( 19
141 ( 13 106 ( 4
-1.1 ( 0.01 -0.1 ( 0.05
* Extrapolated to atmospheric pressure.
hydration. The native states of proteins32,33 and DNA34 are also effected by elevated hydrostatic pressure, becoming more hydrated in both cases. Both these effects, increased hydration of the native state as well as decreased hydration of the coil, reduce the increase in hydration upon denaturation, rendering ∆V less negative at high pressure. PPC Detects ∆r, Which in Turn Tells Us More about Hydration. PPC measurements yield the expansivity change directly, providing another key parameter for assessing hydration of biopolymers. Thermal expansivity results from the release of molecules from tightly packed, low-entropy states driven by thermal energy. An example of such an effect is the gradual breakdown of low-density, ice-like clusters of water between 0 and 4 °C, a process that has a negative value of R. The condensation of lipids by cholesterol at low temperature causes an anomalously high R due to the weakening of this condensation at increasing temperature.20 For DNA, the more extensive hydration of the coil state gives rise to an increased expansion. Thus, the results of this study illustrate that the coil state is more hydrated than the helix state and are qualitatively in agreement with previous volumetric studies.3,35,36 Much insight into the hydration of DNA has been elucidated by the densimetric and ultrasonic velocimetric experiments performed by Chalikian and collaborators.35-37 The consensus of those studies is that the coil state is more hydrated than the helix state, as witnessed by positive changes in expansibility, ∆E, and negative changes in adiabatic compressibility, ∆KS, accompanying the helix-coil transition of DNA. PPC/DSC Demonstrate the Correlation of r(T) and Cp(T). A comparison of the DSC and PPC peaks in Figure 1 show that both have the same shape and position. This provides an experimental confirmation of the previous finding that the volume change and enthalpy change for the formation of nucleic acid duplexes are correlated and that the correlation is linked to the hydration change of the process.38,39 Thus, the values of ∆Hcal and ∆V for the helix-coil transition of poly[d(A-T)] are dominated by the same process, the hydration change. This is qualitatively analogous to the relationship observed and discussed between ∆H and ∆V of lipid chain melting,17,40 which accounts for the similarity of the value of dTM/dP for a wide variety of saturated chain lipids.18,29 Both peak shapes can independently be fitted by the van’t Hoff equation for the progress of a heat-induced, two-state transition, yielding an excellent fit as illustrated for PPC in Figure 2. This is an important and interesting finding; Haq and colleagues41 have demonstrated by singular value decomposition that the helix-coil transition of several synthetic polynucleotides, including poly[d(A-T)], points to the existence of 4-5 significant spectral species. However, for the system studied here, PPC/DSC shows that there is no significantly populated
intermediate; thus, all molecular species can be grouped into one of two thermodynamically distinct states. The application of the van’t Hoff analysis yields the enthalpy and volume changes of a cooperative unit undergoing the transition. Comparison with the calorimetrically determined enthalpy change per base pair yields the cooperative unit, N ) ∆HvH/∆Hcal, as shown in Table 1. It should be noted that the cooperative length decreases as the ionic strength of the medium is increased, as previously documented also for poly[d(A-T)].3,42 This is consistent with the observed increase in the width of the melting transition, which increases from 0.6 to 1.0 K as the ionic strength increases from 5.2 to 18.2 mM Na+. PPC is Precise and Little Dependent on Critical Assumptions. One of the assumptions of the PPC technique is that the system equilibrates within the time between the pressure jumps so that Q corresponds to the complete volume change and a reversible process (dS ) Q/dT in PPC theory). The fulfilment of this assumption is directly tested and established in terms of the agreement of |Q| obtained after up- and down-jumps in P. Another assumption is that temperature changes are precisely compensated by the instrument; this is critical for extremely narrow (half-width 0.1 K) or intense (∆V/V ) 3%) transitions such as lipid melting43 but poses no issue here. A potential error source for PPC data is the relatively large heat of the buffer-water blank; this is reduced by avoiding solutions with very high ionic strength and by using the dialysis buffer of the sample for blank and reference cell. A method to assess systematic errors induced by the buffer correction is to repeat the experiment at different DNA concentrations. We have established that the resulting PPC curve was independent of [DNA] in the range 0.20-0.75 mM (data not shown). A major assumption of the UV method utilizing the ClausiusClapeyron equation is that the enthalpy is not markedly dependent on pressure. Recently, a differential scanning calorimeter has become available that can experimentally test this assumption up to 200 MPa;44 however, it has not yet been used for DNA. Model-dependent enthalpies calculated from heatinduced helix-coil transitions at high pressure do not display any marked pressure dependence over this pressure. 1,3 Conclusion We have used PPC to obtain the molar volume change, ∆V and expansivity change, ∆R, of the helix-coil transition of poly[d(A-T)]. The values are consistent with a substantial increase in DNA hydration upon this transition. The near perfect overlap of the PPC and DSC peaks directly illustrates that the enthalpy change, ∆Hcal, and volume change, ∆V, of the helix-coil transition are correlated. This study illustrates that PPC is a versatile technique for volumetric studies of biopolymers at low pressures.
1742 J. Phys. Chem. B, Vol. 113, No. 6, 2009 Note Added in Proof Dragan and colleagues have utilized PPC to monitor the melting of DNA oligonucleotides, and have reported an increase in the coefficient of thermal expansion,45 which is in agreement with the data obtained in this study. References and Notes (1) Wu, J. Q.; Macgregor, R. B., Jr. Biochemistry 1993, 32 (46), 12531–7. (2) Wu, J. Q.; Macgregor, R. B., Jr. Biopolymers 1995, 35 (4), 369–76. (3) Rayan, G.; Macgregor, R. B., Jr. J. Phys. Chem. B 2005, 109 (32), 15558–65. (4) Macgregor, R. B., Jr. Biopolymers 1996, 38 (3), 321–7. (5) Buckin, V. A.; Kankiya, B. I.; Bulichov, N. V.; Lebedev, A. V.; Gukovsky, I.; Chuprina, V. P.; Sarvazyan, A. P.; Williams, A. R. Nature 1989, 340 (6231), 321–2. (6) Chalikian, T. V.; Volker, J.; Srinivasan, A. R.; Olson, W. K.; Breslauer, K. J. Biopolymers 1999, 50 (5), 459–71. (7) Marky, L. A.; Kupke, D. W. Biochemistry 1989, 28 (26), 9982–8. (8) Marky, L. A.; Macgregor, R. B., Jr. Biochemistry 1990, 29 (20), 4805–11. (9) Kopka, M. L.; Fratini, A. V.; Drew, H. R.; Dickerson, R. E. J. Mol. Biol. 1983, 163 (1), 129–46. (10) Chuprina, V. P. Nucleic Acids Res. 1987, 15 (1), 293–311. (11) (a) Brandts, J.; Lin, L. Thermochim. Acta 2003, 414, 75–80. (b) 2003, 414, 95-100. (12) Heerklotz, H.; Tsamaloukas, A.; Kita-Tokarczyk, K.; Strunz, P.; Gutberlet, T. J. Am. Chem. Soc. 2004, 126 (50), 16544–52. (13) Kujawa, P.; Winnik, F. M. Macromolecules 2001, 34, 4130–4135. (14) Lin, L. N.; Brandts, J. F.; Brandts, J. M.; Plotnikov, V. Anal. Biochem. 2002, 302 (1), 144–60. (15) Mitra, L.; Smolin, N.; Ravindra, R.; Royer, C.; Winter, R. Phys. Chem. Chem. Phys. 2006, 8 (11), 1249–65. (16) Dzwolak, W.; Ravindra, R.; Winter, R. Phys. Chem. Chem. Phys. 2004, 6 (8), 1938–1943. (17) Heerklotz, H. Biophys. J. 2002, 83 (5), 2693–701. (18) Heerklotz, H.; Seelig, J. Biophys. J. 2002, 82 (3), 1445–52. (19) Wang, S. L.; Epand, R. M. Chem. Phys. Lipids 2004, 129 (1), 21– 30. (20) Heerklotz, H.; Tsamaloukas, A. Biophys. J. 2006, 91 (2), 600–7. (21) Inman, R. B.; Baldwin, R. L. J. Mol. Biol. 1962, 5, 172–84. (22) Heerklotz, P. D. Methods Mol. Biol. 2007, 400, 197–206.
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JP808253T
