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Quantifying Coulombic and Solvent PolarizationMediated Forces Between DNA Helices Zhaojian He, and Shi-Jie Chen J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 24 May 2013 Downloaded from http://pubs.acs.org on May 24, 2013
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Quantifying Coulombic and Solvent Polarization-Mediated Forces Between DNA Helices Zhaojian He and Shi-Jie Chen∗ Department of Physics and Department of Biochemistry University of Missouri, Columbia, MO 65211
Abstract One of the fundamental problems in nucleic acids biophysics is to predict the different forces that stabilize nucleic acid tertiary folds. Here we provide a quantitative estimation and analysis for the forces between DNA helices in an ionic solution. Using the generalized Born (GB) model and the improved atomistic tightly binding ions (TBI) model, we evaluate ion correlation and solvent polarization effects in inter-helix interactions. The results suggest that hydration, Coulomb correlation and ion entropy act together to cause the repulsion and attraction between nucleic acid helices in Mg2+ and Mn2+ solutions, respectively. The theoretical predictions are consistent with experimental findings. Detailed analysis further suggests that solvent polarization and ion correlation both are crucial for the inter-helix interactions. The theory presented here may provide a useful framework for systematic and quantitative predictions of the forces in nucleic acids folding.
Keywords: RNA folding; Ion effects; Tightly Bound Ion theory; DNA double helices
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to whom correspondence should be addressed; E-mail:
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1. Introduction Nucleic acids are charged polymers. Nucleic acid folding requires cations to neutralize the backbone charges. The cations in the solution can effectively screen Coulomb repulsion between the nucleotides.1, 2 Ion-mediated interactions between nucleic acids play crucial roles in cellular activities such as DNA condensation, packaging1, 2 and RNA folding.3, 4 Understanding the physical mechanism for ion-mediated nucleic acid interactions can have far-reaching impact on our ability to predict and analyze nucleic acid-related cellular functions. One of the intriguing ion effects is the ion-induced attraction between like-charged nucleic acid helices and triplexes.5–14, 16–30 Previous studies showed that the attractive force cannot be explained by Poisson-Boltzmann (PB)-like mean-field interactions between the charges, where fluctuations of ion distribution and correlations between the ions are ignored.31, 32 The result suggests that other effects, such as the fluctuations of charge density with the distance from the nucleic acid surface6 and the two-dimensional (2D) ordering of ions on the nucleic acid surface,7 may be responsible for the attractive force. Further investigations suggest that discrete DNA charges can lead to specific ion binding properties such as binding to the grooves (vs. binding to phosphate charges) and the resultant charge modulation may cause attraction between nucleic acids.8–13 A series of excellent biophysical experiments such as osmotic stress measurements suggest that hydration effect may be responsible for the nucleic acids attractions.14, 16, 17 However, due to the complex interplay between the different forces such as the Coulombic force, the hydration force and the ionic entropic force, a detailed quantitative analysis of the mechanism remains a challenge.1, 5, 16–25 One of the key issues is how to quantify the different forces. The objective of this paper is to provide a quantitative analysis for the physical mechanism of the forces responsible for the possible inter-helix attraction. Previous theoretical studies have suggested that correlations and fluctuations of multivalent ions around the nucleic acids could induce an attractive force between the nucleic acids.8–11 However, the previous theories were mostly based on various simplified structural models for nucleic acids. Recently, a new theory, called “the tightly bound ion” (TBI) theory,33 was developed to account for ion correlations and fluctuations. Compared with the previous simpli-
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fied models for ion correlation, the TBI theory has the advantage to treat realistic 3D structures of the nucleic acids. The TBI theory predicted that DNA double helices can attract each other in divalent ion solutions such as Mg2+ solutions.10 The conclusion is not fully consistent with the experimental finding, which showed a repulsive interaction between helices in a Mg2+ solution.14 This theory-experiment difference may provide insights into the mechanism for the interplay between the different forces between the helices. Two possible problems with the previous TBI predictions are (a) the use of a coarse-grained structural model for the nucleic acids and (b) lack of the hydration effect. To find out the dominant reason that causes the inconsistency between the previous theoretical predictions and the experimental results, we performed calculations using the all-atom (instead of coarse-grained) structure-based TBI model.15, 34 The all atom-based theory again predicts an attractive force in a Mg2+ solution (see below), which shows that lack of hydration effect (instead of the use of coarse grained structure) may be the dominant reason. The above test result points to the possible indispensable role of the hydration effect, along with other effects such as the ion correlation effect, in the interactions between nucleic acids. The conclusion about the importance of the hydration effect is consistent with the findings from the previous biophysical experiments.16, 17, 20 In this paper, through an atomistic structure-based analysis for the solvent hydration and the ion correlation effects, we quantify the different components of the ion-mediated forces between DNA helices and investigate how the integration of the above effects leads to the experimentally observed forces between DNA helices.
2. Method and Results Prediction of the electrostatic free energy through integration of the Tightly Bound Ion (TBI) model and the Generalized Born (GB) model We consider a pair of 24-base pair double-stranded DNA helices (dsDNAs) immersed in an ionic solution (Fig. 1a); See the Supporting Information (SI) “Helix24.pdb” for the PDB coordinates of the structure. The all-atom dsDNAs are generated by the software X3DNA.35 To evaluate the interaction between the helices, we compute the free energy of the system as a function of helix-helix distance x. We use the recently developed atomistic improved
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TBI model34 to treat the electrostatic correlation effect in multivalent ionic solution; see the SI for a description of the TBI model. Briefly, in the TBI model, we separate out a region, called the “tightly bound” (TB) region, from the rest region (called the “diffusive” region) in the solution. The TB and the diffusive regions are defined as regions where Coulomb correlation between ions is strong and weak, respectively. The TB region, depending on the ionic condition of the solution, is usually a thin layer around the nucleic acid structure. For ions in the TB region (“TB ions”), we enumerate all the discrete modes for the many-ion distributions and account for ion correlation through many-ion Coulomb energy for each mode. For ions in the diffusive region, we apply the Poisson-Boltzmann (PB) theory.10 The statistical average over all the ion binding modes determines the thermodynamic stability of the system. We consider both the nonpolar and polar contributions to the hydration effect. As a crude approximation, we use the generalized Born (GB) model36–38 and the solvent accessible surface area-based model39–42 to estimate the polar and the nonpolar free energies, respectively. We first include the polar contribution in the atomistic TBI model. We will then evaluate the importance of the nonpolar effect through quantitative estimations, which suggest that the inclusion of the nonpolar contribution does not alter the conclusions. The electrostatic energy for the charges (phosphates, TB ions) in the TB region for a given binding mode M of ion distribution is given by (T B)
GM
1 ∑ qi2 1 1 ∑ qi qj ∑ qi qj 1 1 − ) −( − ) + (x) = − ( 2 ϵin ϵw Bi ϵin ϵw fij ϵin rij i
i
