Interactions of cationic ligands and proteins with small nucleic acids: analytic treatment of the large coulombic end effect on binding free energy as a function of salt concentration

Impact of bound ssRNA length on allostery in the Dengue Virus NS3 helicase

The presence of ATP is known to stimulate helicase activity of the Dengue Virus Non-structural protein 3 helicase (NS3h), and the presence of RNA stimulates NS3h ATPase activity, however this coupling is still mechanistically unclear. Here we use atomistic models and molecular dynamics simulations to evaluate the single-stranded RNA (ssRNA)-length dependence of the NS3h-ssRNA binding affinity and its modulation by bound ATP. Considering complexes with 7, 11, 16 and 26 nucleotides (nts), we observe that both the binding affinity and its modulation by bound ATP are augmented with increased ssRNA lengths. In models with at least 11 nts bound, the binding of ATP results in a shift from a tightly bound to a weakly bound state. We find that the weakly bound state persists during both the ADP-Pi- and ADP-bound stages of the catalytic cycle. We obtain the equilibrium association constants for NS3h binding to an ssRNA 10-mer in vitro, both in the absence and presence of ADP, which further support the alternation between tightly and weakly bound states during the catalytic cycle. The length of bound ssRNA is critical for understanding the NS3h-RNA interaction as well as how it is modulated during the catalytic cycle.

Free energy of cylindrical polyions: Analytical results

Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for low salt concentration. We obtain the exact analytical low-salt asymptotic expression for the grand potential, derived from the known properties of the exact solutions to the cylindrical PB equation. These results are relevant for understanding nucleic acid processes. In practice, our expressions are accurate for arbitrary polyion charges, provided their radius is smaller than the Debye length defined by the electrolyte.

Thermodynamic study of the effect of ions on the interaction between dengue virus NS3 helicase and single stranded RNA

Dengue virus nonstructural protein 3 (NS3) fulfills multiple essential functions during the viral replication and constitutes a prominent drug target. NS3 is composed by a superfamily-2 RNA helicase domain joined to a serine protease domain. Quantitative fluorescence titrations employing a fluorescein-tagged RNA oligonucleotide were used to investigate the effect of salts on the interaction between NS3 and single stranded RNA (ssRNA). We found a strong dependence of the observed equilibrium binding constant, K_obs, with the salt concentration, decreasing at least 7-fold for a 1-fold increase on cation concentration. As a result of the effective neutralization of ~10 phosphate groups, binding of helicase domain of NS3 to ssRNA is accompanied by the release of 5 or 7 monovalent cations from an oligonucleotide or a polynucleotide, respectively and of 3 divalent cations from the same oligonucleotide. Such estimates are not affected by the type of cation, either monovalent (KCl, NaCl and RbCl) or divalent (MgCl₂ and CaCl₂), nor by the presence of the protease domain or the fluorescein label. Combined effect of mono and divalent cations was well described by a simple equilibrium binding model which allows to predict the values of K_obs at any concentration of cations.

Competitive Binding of Mg2+ and Na+ Ions to Nucleic Acids: From Helices to Tertiary Structures

Nucleic acids generally reside in cellular aqueous solutions with mixed divalent/monovalent ions, and the competitive binding of divalent and monovalent ions is critical to the structures of nucleic acids because of their polyanionic nature. In this work, we first proposed a general and effective method for simulating a nucleic acid in mixed divalent/monovalent ion solutions with desired bulk ion concentrations via molecular dynamics (MD) simulations and investigated the competitive binding of Mg²⁺/Na⁺ ions to various nucleic acids by all-atom MD simulations. The extensive MD-based examinations show that single MD simulations conducted using the proposed method can yield desired bulk divalent/monovalent ion concentrations for various nucleic acids, including RNA tertiary structures. Our comprehensive analyses show that the global binding of Mg²⁺/Na⁺ to a nucleic acid is mainly dependent on its structure compactness, as well as Mg²⁺/Na⁺ concentrations, rather than the specific structure of the nucleic acid. Specifically, the relative global binding of Mg²⁺ over Na⁺ is stronger for a nucleic acid with higher effective surface charge density and higher relative Mg²⁺/Na⁺ concentrations. Furthermore, the local binding of Mg²⁺/Na⁺ to a phosphate of a nucleic acid mainly depends on the local phosphate density in addition to Mg²⁺/Na⁺ concentrations.

Determination of Ion Atmosphere Effects on the Nucleic Acid Electrostatic Potential and Ligand Association Using AH+·C Wobble Formation in Double-Stranded DNA

The high charge density of nucleic acids and resulting ion atmosphere profoundly influence the conformational landscape of RNA and DNA and their association with small molecules and proteins. Electrostatic theories have been applied to quantitatively model the electrostatic potential surrounding nucleic acids and the effects of the surrounding ion atmosphere, but experimental measures of the potential and tests of these models have often been complicated by conformational changes and multisite binding equilibria, among other factors. We sought a simple system to further test the basic predictions from electrostatics theory and to measure the energetic consequences of the nucleic acid electrostatic field. We turned to a DNA system developed by Bevilacqua and co-workers that involves a proton as a ligand whose binding is accompanied by formation of an internal AH⁺·C wobble pair [Siegfried, N. A., et al. Biochemistry, 2010, 49, 3225]. Consistent with predictions from polyelectrolyte models, we observed logarithmic dependences of proton affinity versus salt concentration of −0.96 ± 0.03 and −0.52 ± 0.01 with monovalent and divalent cations, respectively, and these results help clarify prior results that appeared to conflict with these fundamental models. Strikingly, quantitation of the ion atmosphere content indicates that divalent cations are preferentially lost over monovalent cations upon A·C protonation, providing experimental indication of the preferential localization of more highly charged cations to the inner shell of the ion atmosphere. The internal AH⁺·C wobble system further allowed us to parse energetic contributions and extract estimates for the electrostatic potential at the position of protonation. The results give a potential near the DNA surface at 20 mM Mg²⁺ that is much less substantial than at 20 mM K⁺ (−120 mV vs −210 mV). These values and difference are similar to predictions from theory, and the potential is substantially reduced at higher salt, also as predicted; however, even at 1 M K⁺ the potential remains substantial, counter to common assumptions. The A·C protonation module allows extraction of new properties of the ion atmosphere and provides an electrostatic meter that will allow local electrostatic potential and energetics to be measured within nucleic acids and their complexes with proteins.

Studies of the B-Z transition of DNA: The temperature dependence of the free-energy difference, the composition of the counterion sheath in mixed salt, and the preparation of a sample of the 5'-d[T-(m(5) C-G)12 -T] duplex in pure B-DNA or Z-DNA form

It is often envisioned that cations might coordinate at specific sites of nucleic acids and play an important structural role, for instance in the transition between B-DNA and Z-DNA. However, nucleic acid models explicitly devoid of specific sites may also exhibit features previously considered as evidence for specific binding. Such is the case of the "composite cylinder" (or CC) model which spreads out localized features of DNA structure and charge by cylindrical averaging, while sustaining the main difference between the B and Z structures, namely the better immersion of the B-DNA phosphodiester charges in the solution. Here, we analyze the non-electrostatic component of the free-energy difference between B-DNA and Z-DNA. We also compute the composition of the counterion sheath in a wide range of mixed-salt solutions and of temperatures: in contrast with the large difference of composition between the B-DNA and Z-DNA forms, the temperature dependence of sheath composition, previously unknown, is very weak. In order to validate the model, the mixed-salt predictions should be compared to experiment. We design a procedure for future measurements of the sheath composition based on Anomalous Small-Angle X-ray Scattering and complemented by (31) P NMR. With due consideration for the kinetics of the B-Z transition and for the capacity of generating at will the B or Z form in a single sample, the 5'-d[T-(m(5) C-G)12 -T] 26-mer emerges as a most suitable oligonucleotide for this study. Finally, the application of the finite element method to the resolution of the Poisson-Boltzmann equation is described in detail. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 369-384, 2016.

Coulombic free energy and salt ion association per phosphate of all-atom models of DNA oligomer: dependence on oligomer size

We investigate how the coulombic Gibbs free energy and salt ion association per phosphate charge of DNA oligomers vary with oligomer size (i.e. number of charged residues ∣Z_D∣) at 0.15 M univalent salt by non-linear Poisson Boltzmann (NLPB) analysis of all-atom DNA models. Calculations of these quantities ([Formula: see text], [Formula: see text]) are performed for short and long double-stranded (ds) and single-stranded (ss) DNA oligomers, ranging from 4 to 118 phosphates (ds) and from 2 to 59 phosphates (ss). Behaviors of [Formula: see text] and [Formula: see text] as functions of ∣Z_D∣ provide a measure of the range of the coulombic end effect and determine the size of an oligomer at which an interior region with the properties (per charge) of the infinite-length polyelectrolyte first appears. This size (10-11 phosphates at each end for ds DNA and 6-9 for ss DNA at 0.15 M salt) is in close agreement with values obtained previously by Monte Carlo and NLPB calculations for cylindrical models of polyions, and by analysis of binding of oligocations to DNA oligomers. Differences in [Formula: see text] and in [Formula: see text] between ss and ds DNA are used to predict effects of oligomeric size and salt concentration on duplex stability in the vicinity of 0.15 M salt. Results of all-atom calculations are compared with results of less structurally detailed models and with experimental data.

Nonspecific DNA binding and bending by HUαβ: interfaces of the three binding modes characterized by salt-dependent thermodynamics

Previous isothermal titration calorimetry (ITC) and Förster resonance energy transfer studies demonstrated that Escherichia coli HU(αβ) binds nonspecifically to duplex DNA in three different binding modes: a tighter-binding 34-bp mode that interacts with DNA in large (>34 bp) gaps between bound proteins, reversibly bending it by 140(o) and thereby increasing its flexibility, and two weaker, modestly cooperative small site-size modes (10 bp and 6 bp) that are useful for filling gaps between bound proteins shorter than 34 bp. Here we use ITC to determine the thermodynamics of these binding modes as a function of salt concentration, and we deduce that DNA in the 34-bp mode is bent around-but not wrapped on-the body of HU, in contrast to specific binding of integration host factor. Analyses of binding isotherms (8-bp, 15-bp, and 34-bp DNA) and initial binding heats (34-bp, 38-bp, and 160-bp DNA) reveal that all three modes have similar log-log salt concentration derivatives of the binding constants (Sk(i)) even though their binding site sizes differ greatly; the most probable values of Sk(i) on 34-bp DNA or larger DNA are -7.5±0.5. From the similarity of Sk(i) values, we conclude that the binding interfaces of all three modes involve the same region of the arms and saddle of HU. All modes are entropy-driven, as expected for nonspecific binding driven by the polyelectrolyte effect. The bent DNA 34-bp mode is most endothermic, presumably because of the cost of HU-induced DNA bending, while the 6-bp mode is modestly exothermic at all salt concentrations examined. Structural models consistent with the observed Sk(i) values are proposed.

Understanding the physical basis of the salt dependence of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes

The predictions of the derivative of the electrostatic binding free energy of a biomolecular complex, ΔG(el), with respect to the logarithm of the 1:1 salt concentration, d(ΔG(el))/d(ln[NaCl]), SK, by the Poisson-Boltzmann equation, PBE, are very similar to those of the simpler Debye-Hückel equation, DHE, because the terms in the PBE's predictions of SK that depend on the details of the dielectric interface are small compared to the contributions from long-range electrostatic interactions. These facts allow one to obtain predictions of SK using a simplified charge model along with the DHE that are highly correlated with both the PBE and experimental binding data. The DHE-based model developed here, which was derived from the generalized Born model, explains the lack of correlation between SK and ΔG(el) in the presence of a dielectric discontinuity, which conflicts with the popular use of this supposed correlation to parse experimental binding free energies into electrostatic and nonelectrostatic components. Moreover, the DHE model also provides a clear justification for the correlations between SK and various empirical quantities, like the number of ion pairs, the ligand charge on the interface, the Coulomb binding free energy, and the product of the charges on the complex's components, but these correlations are weak, questioning their usefulness.

Coulombic free energy of polymeric nucleic acid: low- and high-salt analytical approximations for the cylindrical Poisson-Boltzmann model

An accurate analytical expression for the Coulombic free energy of DNA as a function of salt concentration ([salt]) is essential in applications to nucleic acid (NA) processes. The cylindrical model of DNA and the nonlinear Poisson-Boltzmann (NLPB) equation for ions in solution are among the simplest approaches capable of describing Coulombic interactions of NA and salt ions and of providing analytical expressions for thermodynamic quantities. Three approximations for Coulombic free energy G(u,infinity)(coul) of a polymeric nucleic acid are derived and compared with the numerical solution in a wide experimental range of 1:1 [salt] from 0.01 to 2 M. Two are obtained from the two asymptotic solutions of the cylindrical NLPB equation in the high-[salt] and low-[salt] limits: these are sufficient to determine G(u,infinity)(coul) of double-stranded (ds) DNA with 1% and of single-stranded (ss) DNA with 3% accuracy at any [salt]. The third approximation is experimentally motivated Taylor series up to the quadratic term in ln[salt] in the vicinity of the reference [salt] 0.15 M. This expression with three numerical coefficients (Coulombic free energy and its first and second derivatives at 0.15 M) predicts dependence of G(u,infinity)(coul) on [salt] within 2% of the numerical solution from 0.01 to 1 M for ss (a = 7 A, b = 3.4 A) and ds (a = 10 A, b = 1.7 A) DNA. Comparison of cylindrical free energy with that calculated for the all-atom structural model of linear B-DNA shows that the cylindrical model is completely sufficient above 0.01 M of 1:1 [salt]. The choice of two cylindrical parameters, the distance of closest approach of ion to cylinder axis (radius) a and the average axial charge separation b, is discussed in application to all-atom numerical calculations and analysis of experiment. Further development of analytical expression for Coulombic free energy with thermodynamic approaches accounting for ionic correlations and specific effects is suggested.

Ensemble methods for monitoring enzyme translocation along single stranded nucleic acids

We review transient kinetic methods developed to study the mechanism of translocation of nucleic acid motor proteins. One useful stopped-flow fluorescence method monitors arrival of the translocase at the end of a fluorescently labeled nucleic acid. When conducted under single-round conditions the time courses can be analyzed quantitatively using n-step sequential models to determine the kinetic parameters for translocation (rate, kinetic step size and processivity). The assay and analysis discussed here can be used to study enzyme translocation along a linear lattice such as ssDNA or ssRNA. We outline the methods for experimental design and two approaches, along with their limitations, that can be used to analyze the time courses. Analysis of the full time courses using n-step sequential models always yields an accurate estimate of the translocation rate. An alternative semi-quantitative "time to peak" analysis yields accurate estimates of translocation rates only if the enzyme initiates translocation from a unique site on the nucleic acid. However, if initiation occurs at random sites along the nucleic acid, then the "time to peak" analysis can yield inaccurate estimates of even the rates of translocation depending on the values of other kinetic parameters, especially the rate of dissociation of the translocase. Thus, in those cases analysis of the full time course is needed to obtain accurate estimates of translocation rates.

Contributions of the histidine side chain and the N-terminal alpha-amino group to the binding thermodynamics of oligopeptides to nucleic acids as a function of pH

Interactions of histidine with nucleic acid phosphates and histidine pK(a) shifts make important contributions to many protein-nucleic acid binding processes. To characterize these phenomena in simplified systems, we quantified binding of a histidine-containing model peptide HWKK ((+)NH(3)-His-Trp-Lys-Lys-NH(2)) and its lysine analogue KWKK ((+)NH(3)-Lys-Trp-Lys-Lys-NH(2)) to a single-stranded RNA model, polyuridylate (polyU), by changes in tryptophan fluorescence as a function of salt concentration and pH. For both HWKK and KWKK, equilibrium binding constants, K(obs), and magnitudes of log-log salt derivatives, SK(obs) identical with (partial differential logK(obs)/partial differential log[Na(+)]), decreased with increasing pH in the manner expected for a titration curve model in which deprotonation of the histidine and alpha-amino groups weakens binding and reduces its salt-dependence. Fully protonated HWKK and KWKK exhibit the same K(obs) and SK(obs) within uncertainty, and these SK(obs) values are consistent with limiting-law polyelectrolyte theory for +4 cationic oligopeptides binding to single-stranded nucleic acids. The pH-dependence of HWKK binding to polyU provides no evidence for pK(a) shifts nor any requirement for histidine protonation, in stark contrast to the thermodynamics of coupled protonation often seen for these cationic residues in the context of native protein structure where histidine protonation satisfies specific interactions (e.g., salt-bridge formation) within highly complementary binding interfaces. The absence of pK(a) shifts in our studies indicates that additional Coulombic interactions across the nonspecific-binding interface between RNA and protonated histidine or the alpha-amino group are not sufficient to promote proton uptake for these oligopeptides. We present our findings in the context of hydration models for specific vs nonspecific nucleic acid binding.

The effects of hairpin loops on ligand-DNA interactions

Hairpin nucleic acids are frequently used in physical studies due to their greater thermal stability compared to their equivalent duplex structures. They are also good models for more complex loop-containing structures such as quadruplexes, i-motifs, cruciforms, and molecular beacons. Although a connecting loop can increase stability, there is little information on how the loop influences the interactions of small molecules with attached base-paired nucleic acid regions. In this study, the effects of different hairpin loops on the interactions of A/T specific DNA minor groove binding agents with a common stem sequence have been investigated by spectroscopic and surface plasmon resonance (SPR) biosensor methods. The results indicate that the hairpin loop has little influence on the specific site interactions on the stem but significantly affects nonspecific binding. The use of a non-nucleotide loop (with a reduced negative charge) not only enhances the thermal stability of the hairpin but also reduces the nonspecific binding at the loop without compromising the primary binding affinity on the stem.

Formation of a wrapped DNA-protein interface: experimental characterization and analysis of the large contributions of ions and water to the thermodynamics of binding IHF to H' DNA

To characterize driving forces and driven processes in formation of a large-interface, wrapped protein-DNA complex analogous to the nucleosome, we have investigated the thermodynamics of binding the 34-base pair (bp) H' DNA sequence to the Escherichia coli DNA-remodeling protein integration host factor (IHF). Isothermal titration calorimetry and fluorescence resonance energy transfer are applied to determine effects of salt concentration [KCl, KF, K glutamate (KGlu)] and of the excluded solute glycine betaine (GB) on the binding thermodynamics at 20 degrees C. Both the binding constant K(obs) and enthalpy Delta H degrees (obs) depend strongly on [salt] and anion identity. Formation of the wrapped complex is enthalpy driven, especially at low [salt] (e.g., Delta H(o)(obs)=-20.2 kcal x mol(-1) in 0.04 M KCl). Delta H degrees (obs) increases linearly with [salt] with a slope (d Delta H degrees (obs)/d[salt]), which is much larger in KCl (38+/-3 kcal x mol(-1) M(-1)) than in KF or KGlu (11+/-2 kcal x mol(-1) M(-1)). At 0.33 M [salt], K(obs) is approximately 30-fold larger in KGlu or KF than in KCl, and the [salt] derivative SK(obs)=dlnK(obs)/dln[salt] is almost twice as large in magnitude in KCl (-8.8+/-0.7) as in KF or KGlu (-4.7+/-0.6). A novel analysis of the large effects of anion identity on K(obs), SK(obs) and on Delta H degrees (obs) dissects coulombic, Hofmeister, and osmotic contributions to these quantities. This analysis attributes anion-specific differences in K(obs), SK(obs), and Delta H degrees (obs) to (i) displacement of a large number of water molecules of hydration [estimated to be 1.0(+/-0.2)x10(3)] from the 5340 A(2) of IHF and H' DNA surface buried in complex formation, and (ii) significant local exclusion of F(-) and Glu(-) from this hydration water, relative to the situation with Cl(-), which we propose is randomly distributed. To quantify net water release from anionic surface (22% of the surface buried in complexation, mostly from DNA phosphates), we determined the stabilizing effect of GB on K(obs): dlnK(obs)/d[GB]=2.7+/-0.4 at constant KCl activity, indicating the net release of ca. 150 H(2)O molecules from anionic surface.