Application of Polyelectrolyte Theories for Analysis of DNA Melting in the Presence of Na+ and Mg2+ Ions

Korolev, Nikolay; Lyubartsev, Alexander P.; Nordenskiöld, Lars

doi:10.1016/s0006-3495(98)77745-8

Cited by 57 publications

(65 citation statements)

References 62 publications

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“…Diffuse magnesium ions are thought to be bound through "outer-sphere" complexes where magnesium ions coordinate six water molecules, [Mg(H 2 O) 6 ] 2+ , and the water molecules establish a network of hydrogen bonds. This was observed using 25 Mg NMR (57) and crystallographic studies (58,59).…”

Section: Discussionmentioning

confidence: 99%

Predicting Stability of DNA Duplexes in Solutions Containing Magnesium and Monovalent Cations

et al. 2008

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Accurate predictions of DNA stability in physiological and enzyme buffers are important for the design of many biological and biochemical assays. We therefore investigated the effects of magnesium, potassium, sodium, Tris ions, and deoxynucleoside triphosphates on melting profiles of duplex DNA oligomers and collected large melting data sets. An empirical correction function was developed that predicts melting temperatures, transition enthalpies, entropies, and free energies in buffers containing magnesium and monovalent cations. The new correction function significantly improves the accuracy of predictions and accounts for ion concentration, G-C base pair content, and length of the oligonucleotides. The competitive effects of potassium and magnesium ions were characterized. If the concentration ratio of [Mg 2+ ] 0.5 /[Mon + ] is less than 0.22 M -1/2 , monovalent ions (K + , Na + ) are dominant. Effects of magnesium ions dominate and determine duplex stability at higher ratios. Typical reaction conditions for PCR and DNA sequencing (1.5-5 mM magnesium and 20-100 mM monovalent cations) fall within this range. Conditions were identified where monovalent and divalent cations compete and their stability effects are more complex. When duplexes denature, some of the Mg 2+ ions associated with the DNA are released. The number of released magnesium ions per phosphate charge is sequence dependent and decreases surprisingly with increasing oligonucleotide length.Interactions of magnesium, sodium and potassium ions with DNA 1 and RNA molecules are important for essential functions of living cells and for molecular biology applications. Both divalent and monovalent cations bind to nucleic acid molecules and affect their physical properties (1). Magnesium cations stabilize nucleic acid duplexes and facilitate their folding into secondary and tertiary structures (2), which are biologically active. Mg 2+ ions are also necessary cofactors of many enzymatic reactions involving nucleic acids (3). The total magnesium concentrations in various cells range from 5 to 30 mM; however, free Mg 2+ concentrations are tightly controlled between 0.4 and 1.2 mM (4). Binding of monovalent cations also increases duplex stability. The major intracellular monovalent cation is K + , while the major monovalent cation in extracellular fluid is Na + .Several theoretical models have been proposed to describe the complex phenomena of associations between cations and nucleic acids. The most widely used approaches are the mean-field approximation of the Poisson-Boltzmann equation (5-8), the counterion condensation model (9, 10), and Monte Carlo simulations (11,12). There have been few experimental studies addressing effects of Mg 2+ ion on the stability of short DNA duplexes (13-16), and comprehensive experimental melting data are not available. The majority of melting studies in magnesium buffers investigated genomic DNAs (e.g., calf thymus) (5,(17)(18)(19), long polymeric repeats (20-22), or biologically active RNA molecules (2, 23). Pione...

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Section: Discussionmentioning

confidence: 99%

Predicting Stability of DNA Duplexes in Solutions Containing Magnesium and Monovalent Cations

et al. 2008

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“…The electrostatic effects in DNA melting are two-fold: an entropic contribution arising from the difference in electrostatic energy between states U and B and an an enthalpic contribution arising from counterion release. At equilibrium the two effects partially compensate and the remaining contribution is, using a simple thermodynamic approach in the low salt limit [48,49], approximately equal to ∆G el = k B T ℓ b (τ B − τ U ) ln(I/I 0 ), where I is the ionic strength (I 0 = 1 M), ℓ b = e 2 /(4πǫk B T ) the Bjerrum length (e is the elementary charge and ǫ the water dielectric permittivity) and τ U and τ B are the linear charge densities of the pure U and B chains, respectively. Although this is an approximate result and the determination of τ B − τ U remains controversial, these two contributions should be included in a more refined model.…”

Section: Discussionmentioning

confidence: 99%

Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

2008

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Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a 1D Ising model, which describes the internal base pair states, coupled to a discrete worm like chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of polydA-polydT and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square-radius as a function of temperature leads to a coherent novel explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulae, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square-radius, all as a function of temperature and DNA length.

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“…We show, via a well-defined coupled Ising-Heisenberg statistical model, that an entropy driven denaturation transition emerges by integrating out chain fluctuations, due to the entropic lowering of the energetic barrier for bubble nucleation. This minimal model neglects all other (residual) interactions between bases arising from, e.g., electrostatics [14], self-avoidance [6], and helical twist [15].We begin by considering a worm like chain (WLC) Hamiltonian H[r 1 , r 2 ] for two interacting ssDNA homopolymers of length L: where s is the curvilinear index, r i (s) is the position of chain i at base position s, and ρ(s) ≡ r 1 (s) − r 2 (s) is the relative (internal) coordinate (β = 1/k B T andṙ(s) = ∂r ∂s ). The coefficient κ b is a bending elastic modulus that is proportional to the short distance cut-off ℓ 0 ≈ 0.34 nm…”

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confidence: 99%

Thermal Denaturation of Fluctuating DNA Driven by Bending Entropy

2007

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A statistical model of homopolymer DNA, coupling internal base pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-square-radius, are also explicitly calculated, leading, e.g., to a coherent explanation for the experimentally observed thermal viscosity transition.PACS numbers: 87.10.+e, 87.15.Ya, 82.39.Pj Double-stranded DNA (dsDNA) is made up of two intertwined interacting semi-flexible single-strand DNA (ssDNA) chains. Over fifty years ago it was recognized that the intracellular unwinding of DNA at physiological temperature has as counterpart the thermally induced denaturation above physiological temperature of purified DNA solutions where dsDNA completely separates into two ssDNA. Despite the differences between the two mechanisms, this observation has led to an intensive study of thermal denaturation [1,2]. The stability of dsDNA at physiological temperature is due to the selfassembly of neighboring base pairs within a same strand via base-stacking interactions and of both strands via hydrogen bonds between complementary bases. The bonding energy is, however, on the order of k B T (thermal energy) [3] and thermal fluctuations can lead, even at physiological temperature, to local and transitory unzipping of dsDNA [1]. The cooperative opening of consecutive base pairs leads to denaturation bubbles and the melting temperature, T m , above which bubbles proliferate, depends on sequence, chain length, and ionic strength. Experiments show, for example, that there exist a bubble initiation barrier of ∼ 10k B T and free energy cost of ∼ 0.1k B T for breaking an additional base pair in an existing A-T bubble [4]. A detailed understanding of equilibrium [1] and dynamical [5] properties of DNA in solution is still being sought and a consensus concerning the physical mechanism behind the denaturation transition has not yet been reached.A variety of mesoscopic models have been proposed to account for the thermodynamical properties of denaturation bubbles in DNA. They range from i) simple effective Ising-like two-state models [1] to more detailed ones such as ii) loop entropy models (with or without chain selfavoidance) [1,2,6,7], and iii) non-linear phonon models, where the shape of the interaction potential between base pairs is more precisely taken into account [8,9]. To get a transition in models i) and ii), an effective temperature dependent base-pair chemical potential must be inserted by hand. For finite chains, type (ii) models simply refine the sharpness of the transition [1], but do not attempt to provide a deeper explanation of the ...

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Application of Polyelectrolyte Theories for Analysis of DNA Melting in the Presence of Na+ and Mg2+ Ions

Cited by 57 publications

References 62 publications

Predicting Stability of DNA Duplexes in Solutions Containing Magnesium and Monovalent Cations

Predicting Stability of DNA Duplexes in Solutions Containing Magnesium and Monovalent Cations

Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

Thermal Denaturation of Fluctuating DNA Driven by Bending Entropy

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