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DNA Duplex Length and Salt Concentration Dependence of Enthalpy-Entropy Compensation Parameters for DNA Melting E. B. Starikov*,† and Bengt Norde´n‡,§ Institute for Nanotechnology, Research Center Karlsruhe, Post Box 3640, D-76021 Karlsruhe, Germany, and Department of Physical Chemistry, Chalmers UniVersity of Technology, SE-412 96 Gothenburg, Sweden ReceiVed: April 28, 2009; ReVised Manuscript ReceiVed: July 10, 2009
Systematical differential calorimetry experiments on DNA oligomers with different lengths and placed in water solutions with various added salt concentrations may, in principle, unravel important information about the structure and dynamics of the DNA and their water-counterion surrounding. With this in mind, to reinterpret the most recent results of calorimetric experiments on DNA oligomers of such a kind, the recent enthalpy-entropy compensation theory has been used. It is demonstrated that the application of the latter could enable direct estimation of thermodynamic parameters of the microphase transitions connected to the changes in DNA dynamical regimes versus the length of the biopolymers and the ionic strengths of their water solutions, and this calls for much more systematical experimental and theoretical studies in this field. In their very most recent systematical study, Benight et al.1 have investigated melting of DNA duplexes, with their lengths ranging from 6 to 35 nucleotide pairs, using differential scanning calorimetry (DSC). They have determined the complete set of thermodynamic parameters for the DNA melting process and suggested a very interesting new explanation for the long and well-known phenomenon of “helix initiation/nucleation” during DNA duplex formation. Indeed, they have succeeded in estimating the free-energy cost of the “hypothetical duplex” possessing no base pairs but occupying precisely the same molar volume as the fully base-paired DNA duplex. This free-energy cost increases with decreasing salt concentration of the DNA solution, which is in qualitative agreement with earlier results for the free energies of DNA duplex initiation/nucleation (that is, formation of the first nucleotide pair). In the present Letter, we would like to demonstrate that the linear enthalpy-entropy correlation (EEC), as published (but not discussed in detail) in ref 1, should allow a wider physical-chemical interpretation if the EEC theory proposed inref 2 is applied. Specifically, here, we use the enthalpy ∆H and entropy ∆S data, as published in Table 2 of ref 1, to apply the theory2 in two ways, (A) estimating parameters a and b in the general EEC relationship ∆H ) a∆S + b for different salt concentrations and (B) do the same analysis for different DNA duplex lengths. Whereas the former estimation appears to deliver self-consistent quantitative statistics for the a and b parameters but only qualitative conclusions regarding their salt dependence, the latter bears exclusively a qualitative character, owing to the scarcity of the salt concentration values studied in ref 1. * To whom correspondence should be addressed. E-mail: starikow@ chemie.fu-berlin.de. † Research Center Karlsruhe. ‡ Chalmers University of Technology. § E-mail:
[email protected].
10.1021/jp903924j CCC: $40.75
TABLE 1: EEC Parameters Estimated at Different Na+ Salt Concentrations Using Data of Reference 1 for 19 DNA Duplex Sequences (estimated errors in parentheses)a Na+ concentration, mM
a, compensation temperature, K
b, compensation free energy, kcal/mol
b/a, entropic parameter, cal/(mol · K)
1000 600 300 85
372 (3) 372 (2) 372 (2) 361 (4)
10.58 (1.58) 10.39 (0.95) 11.54 (0.71) 7.42 (1.70)
28.44 (4.17) 27.92 (2.56) 31.05 (1.92) 20.57 (4.71)
a For explanations of the physical meaning of parameters, see ref 2.
Nonetheless, the results of our estimations are nontrivial and can hopefully stimulate more systematic DSC studies on DNA melting. The estimation (A) delivers the a and b parameter values shown in Table 1. Statistical Student tests (together with the Welsh’s nonparametric tests) demonstrate that there is a significant difference between the a and b values at [Na+] ) 85 mM and those at higher salt concentrations. Interestingly, the a value at the latter corresponds to the water boiling point, whereas that at the former is significantly lower. Furthermore, the b value at [Na+] ) 300 mM is significantly different from those at higher and lower salt concentrations, which holds for the b/a ratio as well. Finally, there are no significant differences between the EEC parameters at [Na+] ) 600 mM and 1 M. Thus, the salt dependence of the EEC parameters might be explained by the imaginary process of gradual depletion of the counterion shell3 around the DNA duplexes with the increase of salt concentration. The apparent peak in the entropic parameter at [Na+] ) 300 mM might be assigned to a kind of enhancement in the motility of the counterion-water shell as a whole with respect to the DNA duplex (the so-called DNA plasmon4-8) at this salt concentration. Some support of such a viewpoint is provided by a recent study of translocation of DNA 2009 American Chemical Society
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J. Phys. Chem. B, Vol. 113, No. 33, 2009
Letters
Figure 1. DNA duplex length dependence of the (a) compensation temperature (parameter a in the general EEC relationship ∆H ) a∆S + b) and (b) compensation free energy (parameter b in the general EEC relationship).
duplexes through nanopores under the influence of applied voltage, manifested in measurable changes of electrolytic ionic current through the pore.9 Specifically, the DNA translocation is found to result in a decrease of the measured ionic current if the concentration of the additional salt is less than 400 mM and in an increase for higher salt concentrations. Strikingly, their critical ionic strength of 400 mM agrees well with ours (300 mM), with the difference being possibly explained by the fact that they used potassium chloride as an additional salt,9 whereas the work in ref 1 refers to sodium cations. “Magic” ionic strength values have also been discussed theoretically10,11 in the context of specific ionic-strength-dependent changes in the electrostatic screening of the DNA duplexes by their counterions, just in accordance with the dynamic charge correlation concept of “DNA plasmons”4-8 based on collective modes embodying the dynamical screening of DNA anionic charge. Meanwhile, ref 11 goes even more deeply into the molecular details of the DNA electrokinetics, that is, DNA mobility under application of macroscopic electric fields. It turns out11 that the mobility of counterions around DNA experiences an additional salt-dependent change of sign, which is reflected in the counterion excess conductivity. The authors11 dub this
finding an anomaly and discuss its detailed physical picture; for low salt, counterions stick to the polyelectrolyte and move along in the electric field, in agreement with the canonic viewpoint, whereas for high salt, the motion decouples, and counterions move opposite to the polyelectrolyte. Interestingly, the theoretical estimate of this threshold ionic strength is around 0.1 mM, again comparable to the critical salt level of ref 9 and our result mentioned above, recalling the roughness of the coarse-grained theoretical model employed in ref 11. This discussion suggests that our EEC theory can be capable of revealing the anomalous change in the collective counterion motility as a hidden factor. The latter is clearly not obvious from the calorimetric results1 but becomes visible in other studies, namely, when external macroscopic electric fields are applied to the system. With a more extended set of the microcalorimetric data, our EEC theory might even be helpful in reliably estimating thermodynamical parameters of the hidden factors/processes under study. The second estimation (B) has revealed an interesting dependence of the EEC parameter values on the DNA duplex length; see Figure 1. It should be noted here that the EEC parameter estimates for each of the DNA duplexes under study
Letters in ref 1 have been obtained using solely the four salt concentration data points available from ref 1. For the DNA duplexes longer than 25 nucleotide pairs, no reasonable EEC could be obtained at all. Hence, we may consider this part of our results as a qualitative hint only, which requires further systematical studies. Still, some significant difference can be noted between the a and b values for DNA duplexes shorter than 10 pairs and longer than 20 pairs and those longer than 10 pairs and shorter than 20 pairs. Along with this, the EEC parameter differences between the shortest and longest duplexes studied in ref 1 cannot be proven significant on this extremely scarce set of the four data points. The only tentative conclusions that we may draw for the estimation (B) findings are as follows. The a values for the shortest and longest duplexes are in the temperature range of the usual DNA duplex melting but should be noticeably higher for at least some of the DNA duplexes of the intermediate length. Moreover, the b values for the shortest and longest duplexes are most probably near 0 or rather low but appreciably nonzero for the DNA duplexes of the intermediate length. This could be indicative of some nontrivial collective dynamics in the latter DNA duplexes. With this in mind, it would definitely be interesting to disentangle the contributions of the DNA length and DNA sequence into such dynamics, which would definitely require further systematical studies. Of extreme interest might be some kind of periodicity seen in the both panels of Figure 1 and possibly assignable to the actual geomertical periodicity of the DNA duplex. However, the data set reported in ref 1 is statistically too premature to draw some valid conclusions on this theme, as discussed above. Further experimental and theoretical studies on the above topic might be very interesting. Indeed, the nontrivial lengthdependent dynamics in question is also a kind of hidden factor which is not directly observable in microcalorimetric experiments. For example, the earlier work12 revealed clear-cut lengthdependent effects when added salt contained one multivalent and one monovalent counterion type competing with each other for the DNA binding slots. In another vein, both ionic strength and length effects can be theoretically modeled in an explicit way if the conventional Manning model is adequately extended.13 Furthermore, we may recall here the recent communication on some cooperative longitudinal stretching of DNA duplexes ranging from 10 to 35 nucleotide pairs in length (which is unexpected from the standpoint of the conventional elastic rod model of DNA duplex),14 along with other recent findings on the unusual DNA duplex bending rigidity15 and the counterintuitive twist-stretch coupling in DNA duplexes.16 Exploring
J. Phys. Chem. B, Vol. 113, No. 33, 2009 11377 the physical-chemical mechanisms of the length- and sequencedependent collective dynamics of DNA duplexes could be crucially important for detailed understanding of diverse interesting phenomena ranging from the DNA length-dependent electrophoretic mobility (see, for example, ref 17 and the references therein) to various modalities of biologically important protein-DNA complexes (see, for example,refs 18-22 and the references therein). In this respect, our EEC model could help to interpret composite experimental and/or theoretical findings when one and the same complex (bio)(nano)molecular system (or a system set) is explored using a number of different experimental and/or theoretical techniques in parallel. Acknowledgment. B.N. gratefully acknowledges the Award of 2008 from King Abdullah University of Science and Technology. References and Notes (1) Manyanga, F.; Horne, M. T.; Brewood, G. P.; Fish, D. J.; Dickman, R.; Benight, A. S. J. Phys. Chem. B 2009, 113, 2556–2563. (2) Starikov, E. B.; Norde´n, B. J. Phys. Chem. B 2007, 111, 14431– 14435. (3) Schurr, J. M.; Fujimoto, B. S. Biophys. Chem. 2002, 101-102, 425–445. (4) van Zandt, L. L.; Saxena, V. K. Phys. ReV. Lett. 1988, 61, 1788– 1790. (5) Sokoloff, J. B. Phys. ReV. Lett. 1989, 63, 2316. (6) Saxena, V. K.; van Zandt, L. L.; Schroll, W. K. Phys. ReV. A 1989, 39, 1474–1481. (7) van Zandt, L. L.; Saxena, V. K. Phys. ReV. A 1989, 39, 2672– 2674. (8) Saxena, V. K.; van Zandt, L. L. Phys. ReV. A 1992, 45, 7610– 7620. (9) Smeets, R. R. M.; Keyser, U. F.; Krapf, D.; Wu, M.-Y.; Dekker, N. H.; Dekker, C. Nano Lett. 2006, 6, 89–95. (10) Reboux, S.; Capuani, F.; Gonzalez-Segredo, N.; Frenkel, D. J. Chem. Theory Comput. 2006, 2, 495–503. (11) Fischer, S.; Naji, A.; Netz, R. R. Phys. ReV. Lett. 2008, 101, 176103. (12) Li, A. Z.; Marx, K. A. Biophys. J. 1999, 77, 114–122. (13) Manning, G. S. Biophys. J. 2006, 90, 3208–3215. (14) Mathew-Fenn, R. S.; Das, R.; Harbury, P. A. B. Science 2008, 322, 446–449. (15) Cloutier, T. E.; Widom, J. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3645–3650. (16) Gore, J.; Bryant, Z.; No¨llman, M.; Le, M. U.; Cozzarelli, N. R.; Bustamante, C. Nature 2006, 442, 836–839. (17) Elder, J. K.; Southern, E. M. Anal. Biochem. 1983, 128, 227–231. (18) Dieterich, A. E.; Eshaghpour, H.; Crothers, D. M.; Cantor, Ch. R. Nucleic Acids Res. 1980, 8, 2475–2488. (19) Goryushin, I. Yu.; Kil, Yu. V.; Reznikoff, W. S. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 10834–10838. (20) Krebs, J. E.; Dunaway, M. Mol. Cell. Biol. 1996, 16, 5821–5829. (21) Ma, Y.; Lieber, M. R. Biochemistry 2001, 40, 9638–9646. (22) Siino, J. S.; Yau, P. M.; Imai, B. S.; Gatewood, J. M.; Bradbury, E. M. Biochem. Biophys. Res. Commun. 2003, 302, 885–891.
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