Binding of ionic ligands to polyelectrolytes

Cooperative kinetics of ligand binding to linear polymers

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Cooperative kinetic equation for large ligands binding to long polymers.

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Cooperativity in general affects binding and release rates.

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Appropriate counting of the available binding sites for a ligand to a linear polymer.

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Positive cooperativity increases polymer coverage by the ligand.

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Large ligand size reduces cooperativity effects.

Ligands change the chemical and mechanical properties of polymers. In particular, single strand binding protein (SSB) non-specifically bounds to single-stranded DNA (ssDNA), modifying the ssDNA stiffness and the DNA replication rate, as recently measured with single-molecule techniques. SSB is a large ligand presenting cooperativity in some of its binding modes. We aim to develop an accurate kinetic model for the cooperative binding kinetics of large ligands. Cooperativity accounts for the changes in the affinity of a ligand to the polymer due to the presence of another bound ligand. Large ligands, attaching to several binding sites, require a detailed counting of the available binding possibilities. This counting has been done by McGhee and von Hippel to obtain the equilibrium state of the ligands-polymer complex. The same procedure allows to obtain the kinetic equations for the cooperative binding of ligands to long polymers, for all ligand sizes. Here, we also derive approximate cooperative kinetic equations in the large ligand limit, at the leading and next-to-leading orders. We found cooperativity is negligible at the leading-order, and appears at the next-to-leading order. Positive cooperativity (increased affinity) can be originated by increased binding affinity or by decreased release affinity, implying different kinetics. Nevertheless, the equilibrium state is independent of the origin of cooperativity and only depends on the overall increase in affinity. Next-to-leading approximation is found to be accurate, particularly for small cooperativity. These results allow to understand and characterize relevant ligand binding processes, as the binding kinetics of SSB to ssDNA, which has been reported to affect the DNA replication rate for several SSB-polymerase pairs.

Dissecting Dynamic and Hydration Contributions to Sequence-Dependent DNA Minor Groove Recognition

Sequence selectivity is a critical attribute of DNA-binding ligands and underlines the need for detailed molecular descriptions of binding in representative sequence contexts. We investigated the binding and volumetric properties of DB1976, a model bis(benzimidazole)-selenophene diamidine compound with emerging therapeutic potential in acute myeloid leukemia, debilitating fibroses, and obesity-related liver dysfunction. To sample the scope of cognate DB1976 target sites, we evaluated three dodecameric duplexes spanning >10³-fold in binding affinity. The attendant changes in partial molar volumes varied substantially, but not in step with binding affinity, suggesting distinct modes of interactions in these complexes. Specifically, whereas optimal binding was associated with loss of hydration water, low-affinity binding released more hydration water. Explicit-atom molecular dynamics simulations showed that minor groove binding perturbed the conformational dynamics and hydration at the termini and interior of the DNA in a sequence-dependent manner. The impact of these distinct local dynamics on hydration was experimentally validated by domain-specific interrogation of hydration with salt, which probed the charged axial surfaces of oligomeric DNA preferentially over the uncharged termini. Minor groove recognition by DB1976, therefore, generates dynamically distinct domains that can make favorable contributions to hydration release in both high- and low-affinity binding. Because ligand binding at internal sites of DNA oligomers modulates dynamics at the termini, the results suggest both short- and long-range dynamic effects along the DNA target that can influence their effectiveness as low-MW competitors of protein binding.

Dynamics of Ionic Interactions at Protein-Nucleic Acid Interfaces

Molecular association of proteins with nucleic acids is required for many biological processes essential to life. Electrostatic interactions via ion pairs (salt bridges) of nucleic acid phosphates and protein side chains are crucial for proteins to bind to DNA or RNA. Counterions around the macromolecules are also key constituents for the thermodynamics of protein–nucleic acid association. Until recently, there had been only a limited amount of experiment-based information about how ions and ionic moieties behave in biological macromolecular processes. In the past decade, there has been significant progress in quantitative experimental research on ionic interactions with nucleic acids and their complexes with proteins. The highly negatively charged surfaces of DNA and RNA electrostatically attract and condense cations, creating a zone called the ion atmosphere. Recent experimental studies were able to examine and validate theoretical models on ions and their mobility and interactions with macromolecules. The ionic interactions are highly dynamic. The counterions rapidly diffuse within the ion atmosphere. Some of the ions are released from the ion atmosphere when proteins bind to nucleic acids, balancing the charge via intermolecular ion pairs of positively charged side chains and negatively charged backbone phosphates. Previously, the release of counterions had been implicated indirectly by the salt-concentration dependence of the association constant.

Recently, direct detection of counterion release by NMR spectroscopy has become possible and enabled more accurate and quantitative analysis of the counterion release and its entropic impact on the thermodynamics of protein–nucleic acid association. Recent studies also revealed the dynamic nature of ion pairs of protein side chains and nucleic acid phosphates. These ion pairs undergo transitions between two major states. In one of the major states, the cation and the anion are in direct contact and form hydrogen bonds. In the other major state, the cation and the anion are separated by water. Transitions between these states rapidly occur on a picosecond to nanosecond time scale. When proteins interact with nucleic acids, interfacial arginine (Arg) and lysine (Lys) side chains exhibit considerably different behaviors. Arg side chains show a higher propensity to form rigid contacts with nucleotide bases, whereas Lys side chains tend to be more mobile at the molecular interfaces. The dynamic ionic interactions may facilitate adaptive molecular recognition and play both thermodynamic and kinetic roles in protein–nucleic acid interactions.

Noncooperative thermodynamics and kinetic models of ligand binding to polymers: Connecting McGhee-von Hippel model with the Tonks gas model

Ligand binding to polymers modifies the physical and chemical properties of the polymers, leading to physical, chemical, and biological implications. McGhee and von Hippel obtained the equilibrium coverage as a function of the ligand affinity, through the computation of the possible binding sites for the ligand. Here, we complete this theory deriving the kinetic model for the ligand-binding dynamics and the associated equilibrium chemical potential, which turns out to be of the Tonks gas model type. At low coverage, the Tonks chemical potential becomes the Fermi chemical potential and even the ideal gas chemical potential. We also discuss kinetic models associated with these chemical potentials. These results clarify the kinetic models of ligand binding, their relations with the chemical potentials, and their range of validity. Our results highlight the inaccuracy of ideal and simplified kinetic approaches for medium and high coverages.

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.

Mechanics, thermodynamics, and kinetics of ligand binding to biopolymers

Ligands binding to polymers regulate polymer functions by changing their physical and chemical properties. This ligand regulation plays a key role in many biological processes. We propose here a model to explain the mechanical, thermodynamic, and kinetic properties of the process of binding of small ligands to long biopolymers. These properties can now be measured at the single molecule level using force spectroscopy techniques. Our model performs an effective decomposition of the ligand-polymer system on its covered and uncovered regions, showing that the elastic properties of the ligand-polymer depend explicitly on the ligand coverage of the polymer (i.e., the fraction of the polymer covered by the ligand). The equilibrium coverage that minimizes the free energy of the ligand-polymer system is computed as a function of the applied force. We show how ligands tune the mechanical properties of a polymer, in particular its length and stiffness, in a force dependent manner. In addition, it is shown how ligand binding can be regulated applying mechanical tension on the polymer. Moreover, the binding kinetics study shows that, in the case where the ligand binds and organizes the polymer in different modes, the binding process can present transient shortening or lengthening of the polymer, caused by changes in the relative coverage by the different ligand modes. Our model will be useful to understand ligand-binding regulation of biological processes, such as the metabolism of nucleic acid. In particular, this model allows estimating the coverage fraction and the ligand mode characteristics from the force extension curves of a ligand-polymer system.

Coating of single DNA molecules by genetically engineered protein diblock copolymers

Coating DNA is an effective way to modulate its physical properties and interactions. Current chemosynthetic polymers form DNA aggregates with random size and shape. In this study, monodisperse protein diblock copolymers are produced at high yield in recombinant yeast. They carry a large hydrophilic colloidal block (≈400 amino acids) linked to a short binding block (≈12 basic amino acids). It is demonstrated that these protein polymers complex single DNA molecules as highly stable nanorods, reminiscent of cylindrical viruses. It is proposed that inter- and intramolecular bridging of DNA molecules are prevented completely by the small size of the binding block attached to the large colloidal stability block. These protein diblocks serve as a scaffold that can be tuned for application in DNA-based nanotechnology.

Isothermal titration calorimetry study of the polyelectrolyte complexation of xanthan and chitosan samples of different degree of polymerization

Mixing oppositely charged polyelectrolytes in aqueous solutions leads to the spontaneous formation of polyelectrolyte complexes. Here, we characterize the interaction between xanthan of two different chain lengths, a tri-glucosamine and a chitosan polymer by isothermal titration calorimetry (ITC). Analysis of the experimental thermodynamic data assuming a single set of identical sites indicated both enthalpic and entropic contributions to the overall interaction in the interaction between xanthan and tri-glucosamine. The relative contribution of entropy compared to enthalpy was found to be largest for the shortest chain length of xanthan. Using a chitosan polymer instead of tri-glucosamine gave rise to two different stages in the interaction process. A model where the first stage of the ITC curve represent an initial polyelectrolyte complexation stage followed by aggregation on further titration of chitosan to the xanthan is suggested. Ultrastructure images by applying atomic force microscopy at some selected extents of titration are consistent with the two-stage interpretation of the thermodynamic data.

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.

Activity, folding and Z-DNA formation of the 8-17 DNAzyme in the presence of monovalent ions

The effect of monovalent ions on both the reactivity and global folding of the 8-17 DNAzyme is investigated, and the results are compared with those of the hammerhead ribozyme, which has similar size and secondary structure. In contrast to the hammerhead ribozyme, the 8-17 DNAzyme activity is not detectable in the presence of 4 M K(+), Rb(+), or Cs(+) or in the presence of 80 mM, [Co(NH(3))(6)](3+). Only 4 M Li(+), NH(4)(+) and, to a lesser extent, Na(+) conferred detectable activity. The observed rate constants (k(obs) approximately 10(-3) min(-1) for Li(+) and NH(4)(+)) are approximately 1000-fold lower than that in the presence of 10 mM Mg(2+), and approximately 200,000-fold slower than that in the presence of 100 microM Pb(2+). Since the hammerhead ribozyme displays monovalent ion-dependent activity that is often within approximately 10-fold of divalent metal ion-dependent activity, these results suggest that the 8-17 DNAzyme, obtained by in vitro selections, has evolved to have a more stringent divalent metal ion requirement for high activity as compared to the naturally occurring ribozymes, making the 8-17 DNAzyme an excellent choice as a Pb(2+) sensor with high selectivity. In contrast to the activity data, folding was observed in the presence of all the monovalent ions investigated, although those monovalent ions that do not support DNAzyme activity have weaker binding affinity (K(d) approximately 0.35 M for Rb(+) and Cs(+)), while those that confer DNAzyme activity possess stronger affinity (K(d) approximately 0.22 M for Li(+), Na(+) and NH(4)(+)). In addition, a correlation between metal ion charge density, binding affinity and enzyme activity was found among mono- and divalent metal ions except Pb(2+); higher charge density resulted in stronger affinity and higher activity, suggesting that the observed folding and activity is at least partially due to electrostatic interactions between ions and the DNAzyme. Finally, circular dichroism (CD) study has revealed Z-DNA formation with the monovalent metal ions, Zn(2+) and Mg(2+); the K(d) values obtained using CD were in the same range as those obtained from folding studies using FRET. However, Z-DNA formation was not observed with Pb(2+). These results indicate that Pb(2+)-dependent function follows a different mechanism from the monovalent metal ions and other divalent metal ions; in the presence of latter metal ions, metal-ion dependent folding and structural changes, including formation of Z-DNA, play an important role in the catalytic function of the 8-17 DNAzyme.

Full-length hepatitis B virus core protein packages viral and heterologous RNA with similarly high levels of cooperativity

A critical feature of a viral life cycle is the ability to selectively package the viral genome. In vivo, phosphorylated hepatitis B virus (HBV) core protein specifically encapsidates a complex of pregenomic RNA (pgRNA) and viral polymerase; it has been suggested that packaging is specific for the complex. Here, we test the hypothesis that core protein has intrinsic specificity for pgRNA, independent of the polymerase. For these studies, we also evaluated the effect of core protein phosphorylation on assembly and RNA binding, using phosphorylated core protein and a phosphorylation mimic in which S155, S162, and S170 were mutated to glutamic acid. We have developed an in vitro system where capsids are disassembled and assembly-active core protein dimer is purified. With this protein, we have reassembled empty capsids and RNA-filled capsids. We found that core protein dimer bound and encapsidated both the HBV pregenomic RNA and heterologous RNA with high levels of cooperativity, irrespective of phosphorylation. In direct competition assays, no specificity for pregenomic RNA was observed. This suggests that another factor, such as the viral polymerase, is required for specific packaging. These results also beg the question of what prevents HBV core protein from assembling on nonviral RNA, preserving the protein for virus production.

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.

RNA helix stability in mixed Na+/Mg2+ solution

A recently developed tightly bound ion model can account for the correlation and fluctuation (i.e., different binding modes) of bound ions. However, the model cannot treat mixed ion solutions, which are physiologically relevant and biologically significant, and the model was based on B-DNA helices and thus cannot directly treat RNA helices. In the present study, we investigate the effects of ion correlation and fluctuation on the thermodynamic stability of finite length RNA helices immersed in a mixed solution of monovalent and divalent ions. Experimental comparisons demonstrate that the model gives improved predictions over the Poisson-Boltzmann theory, which has been found to underestimate the roles of multivalent ions such as Mg2+ in stabilizing DNA and RNA helices. The tightly bound ion model makes quantitative predictions on how the Na+-Mg2+ competition determines helix stability and its helix length-dependence. In addition, the model gives empirical formulas for the thermodynamic parameters as functions of Na+/Mg2+ concentrations and helix length. Such formulas can be quite useful for practical applications.

Charge density of divalent metal cations determines RNA stability

RNA molecules are exquisitely sensitive to the properties of counterions. The folding equilibrium of the Tetrahymena ribozyme is measured by nondenaturing gel electrophoresis in the presence of divalent group IIA metal cations. The stability of the folded ribozyme increases with the charge density (zeta) of the cation. Similar scaling is found when the free energy of the RNA folded in small and large metal cations is measured by urea denaturation. Brownian dynamics simulations of a polyelectrolyte show that the experimental observations can be explained by nonspecific ion-RNA interactions in the absence of site-specific metal chelation. The experimental and simulation results establish that RNA stability is largely determined by a combination of counterion charge and the packing efficiency of condensed cations that depends on the excluded volume of the cations.

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

For nonspecific binding of oligopeptides and other cationic ligands, including proteins, to nucleic acid oligomers, we develop a model capable of quantifying and predicting the salt concentration dependence of the binding free energy (deltaG(o)obs) by way of an analytic treatment of the Coulombic end effect (CEE). Ligands, nucleic acids, and their complexes (species j of valence Zj) are modeled as finite lattices with absolute value(Zj) charged residues; the CEE is quantified by its characteristic length Ne (specified in charged residues) and its consequences for the free energy and ion association of the oligomer. Expressions are developed for the individual site binding constants Ki as a function of position (site number i) of a bound ligand on a nucleic acid and for the observed binding constant Kobs as an ensemble average of Ki. Analysis of deltaG(o)obs = -RT ln Kobs and Sa Kobs identical with (partial differential ln Kobs)/(partial differential ln a(+/-)) for binding of the oligopeptide KWK6 (ZL = +8) to single-stranded (ss) dT(pdT)(absolute value(ZD) oligomers (dT-mers) where ZD = {-6, -10, -11, -14, -15} in the range 0.1-0.25 M Na+ yields Ne = 9.0 +/- 0.8 residues at each end, demonstrating that both KWK6 and the above dT-mers are sufficiently short so that the CEE extends over the entire molecule. The dependences of Kobs and of Sa Kobs on absolute value(ZD) for a given ZL are determined by the difference between 2Ne and the net number of charged residues Q in the complex (Q identical with absolute value(ZD) - ZL). For Q < 2Ne, characteristic of complexes of KWK6 with this set of dT-mers, the distribution of binding free energies deltaG(o)obs = -RT ln Ki for sites along the DNA oligomer is parabolic, and Kobs and Sa Kobs are strongly dependent on absolute value(ZD). For Q > or = 2Ne, the distribution of binding free energies deltaG(o)obs is trapezoidal, and the dependence of Kobs and Sa Kobs on absolute value(ZD) is weaker. Application of the model to nonspecific binding of human DNA polymerase beta to ssDNA demonstrates the significance of the CEE in determining Kobs and Sa Kobs of binding of a cationic site on a protein to a DNA oligomer.

Counterion charge density determines the position and plasticity of RNA folding transition states

The self-assembly of RNA structure depends on the interactions of counterions with the RNA and with each other. Comparison of various polyamines showed that the tertiary structure of the Tetrahymena ribozyme is more stable when the counterions are small and highly charged. By monitoring the folding kinetics of the ribozyme as a function of polyamine concentration, we now find that the charge density of the counterions determines the positions of the folding transition states. The transition state ensemble (TSE) between U and N moves away from the native state as the counterion valence and charge density increase, as predicted by the Hammond postulate. The TSE is broader and less structured when the RNA is refolded in polyamines rather than Mg2+. That the charge density of the counterions determines the plasticity of the TSE demonstrates the importance of interactions among condensed counterions for the self-assembly of RNA structures. We propose that the major barrier to RNA folding is dominated by entropy changes when counterion charge density is low and enthalpy differences when it is high.

Influence of chitosan structure on the formation and stability of DNA-chitosan polyelectrolyte complexes

The interactions between DNA and chitosans varying in fractional content of acetylated units (FA), degree of polymerization (DP), and degree of ionization were investigated by several techniques, including an ethidium bromide (EtBr) fluorescence assay, gel retardation, atomic force microscopy, and dynamic and electrophoretic light scattering. The charge density of the chitosan and the number of charges per chain were found to be the dominating factors for the structure and stability of DNA-chitosan complexes. All high molecular weight chitosans condensed DNA into physically stable polyplexes; however, the properties of the complexes were strongly dependent on FA, and thereby the charge density of chitosan. By employing fully charged oligomers of constant charge density, it was shown that the complexation of DNA and stability of the polyplexes is governed by the number of cationic residues per chain. A minimum of 6-9 positive charges appeared necessary to provide interaction strength comparable to that of polycations. In contrast, further increase in the number of charges above 9 did not increase the apparent binding affinity as judged from the EtBr displacement assay. The chitosan oligomers exhibited a pH-dependent interaction with DNA, reflecting the number of ionized amino groups. The complexation of DNA and the stability of oligomer-based polyplexes became reduced above pH 7.4. Such pH-dependent dissociation of polyplexes around the physiological pH is highly relevant in gene delivery applications and might be one of the reasons for the high transfection activity of oligomer-based polyplexes observed.

DNA-polycation complexation and polyplex stability in the presence of competing polyanions

Polyelectrolyte complex (polyplex) formation was studied by employing tapping mode atomic force microscopy (AFM) and an ethidium bromide fluorescence assay. The polycations chitosan and poly-L-lysine were used to compact DNA and the stability of the polyplexes was evaluated upon exposure to competing polyanions (alginate and xanthan). Furthermore, the relative preference of these polycations for DNA and the competing polyanion was investigated. The results showed that neither poly-L-lysine nor chitosan displayed any selectivity in binding to DNA relative to the competing polyanions, demonstrating the importance of electrostatics in the binding of a polycation to a polyanion. However, the ability of the polyanions to destabilize the DNA-polycation complexes depended on both the polyanion and the polycation employed, indicating that polymer-specific properties are also important for the complexation behavior and polyplex stability. Destabilization experiments further showed that annealing yielded complexes that were less prone to disruption upon subsequent exposure to alginate. Annealing experiments of plasmid DNA-chitosan complexes showed an increased fraction of rods following temperature treatment, indicating that the rods most likely are the more stable morphology for this system.

On the theory of noncovalent binding

It is widely accepted that the binding constant of a receptor and ligand can be written as a two-body integral involving the interaction energy of the receptor and the ligand. Interestingly, however, three different theories of binding in the literature dictate three distinct integrals. The present study uses theory, as well as simulations of binding experiments, to test the validity of the three integrals. When binding is measured by a signal that detects the ligand in the binding site, the most accurate results are obtained by an integral of the Boltzmann factor, where the bound complex is defined in terms of an exclusive binding region. A novel prediction of this approach, that expanding a ligand can increase its binding constant, is borne out by the simulations. The simulations also show that abnormal binding isotherms can be obtained when the region over which the signal is detected deviates markedly from the exclusion zone. Interestingly, the binding constant measured by equilibrium dialysis, rather than by monitoring a localized signal, can yield a binding constant that differs from that obtained from a signal measurement, and that is matched best by the integral of the Mayer factor.

Glycosaminoglycan destabilization of DNA–chitosan polyplexes for gene delivery depends on chitosan chain length and GAG properties

Chitosan-based gene delivery systems are promising candidates for non-viral gene therapy. A wide range of chitosans has been studied to optimize the properties of the DNA-chitosan complexes to yield high transfection efficiencies. An important parameter to control is the polyplex stability to allow transport towards the cells, subsequent internalization and release of DNA intracellularly. The stability of the DNA-chitosan complexes was here studied after exposure to heparin and hyaluronic acid (HA) using atomic force microscopy (AFM) and ethidium bromide (EtBr) fluorescence assay. To study the effect of polycation chain length on the polyplex stability, chitosans with a degree of polymerization (DP) varying from approximately 10 to approximately 1000 were employed for DNA compaction. Whereas HA was unable to dissociate the complexes, the degree of dissociation caused by heparin depended on both the chitosan chain length and the amount of chitosan used for complexation. When increasing the chitosan concentration, larger heparin concentrations were required for polyplex dissociation. Furthermore, increasing the chitosan chain length yielded more stable complexes. Varying the chitosan chain length thus provides a tool for controlling the ability of the polyplex to deliver therapeutic gene vectors to cells.

Folding of the Tetrahymena ribozyme by polyamines: importance of counterion valence and size

Polyamines are abundant metabolites that directly influence gene expression. Although the role of polyamines in DNA condensation is well known, their role in RNA folding is less understood. Non-denaturing gel electrophoresis was used to monitor the equilibrium folding transitions of the Tetrahymena ribozyme in the presence of polyamines. All of the polyamines tested induce near-native structures that readily convert to the native conformation in Mg(2+). The stability of the folded structure increases with the charge of the polyamine and decreases with the size of the polyamine. When the counterion excluded volume becomes large, the transition to the native state does not go to completion even under favorable folding conditions. Brownian dynamics simulations of a model polyelectrolyte suggest that the kinetics of counterion-mediated collapse and the dimensions of the collapsed RNA chains depend on the structure of the counterion. The results are consistent with delocalized condensation of polyamines around the RNA. However, the effective charge of the counterions is lowered by their excluded volume. The stability of the folded RNA is enhanced when the spacing between amino groups matches the distance between adjacent phosphate groups. These results show how changes in intracellular polyamine concentrations could alter RNA folding pathways.

Effect of the number of nucleic acid oligomer charges on the salt dependence of stability (DeltaG 37degrees) and melting temperature (Tm): NLPB analysis of experimental data

For nucleic acid oligomers with variable chain lengths, the salt concentration ([salt]) dependences of the denaturation temperature (T(m)) and of the free energy of helix formation at 37 degrees C (Delta) are predicted using nonlinear Poisson-Boltzmann (NLPB) calculations. Analysis of experimental data reveals that the ratio of the [salt] derivative of melting temperature (ST(m) = dT(m)/d log[salt]) to the value for a polymer with the same base composition (ST(m)/ST(m, infinity)) is independent of base composition but strongly dependent on the number of DNA charges (/Z/) below approximately 8 bp for two-strand helices (formed from association of two complementary strands) and below approximately 18 bp for hairpin helices (formed from folding of one self-complementary strand). We interpret these ST(m)/ST(m, infinity) ratios in terms of the ratio of thermodynamic ion release from the oligomer (Deltan(u), per charge) to that from the same oligomer embedded in polymeric DNA (Deltan(u, infinity), per charge). Experimental values of ST(m)/ST(m, infinity) and its dependence on /Z/ are in good agreement with NLPB predictions for a preaveraged (essential structural) model of DNA. In particular, the NLPB calculations describe the stronger /Z/ dependence of ST(m) observed for melting of oligomeric hairpin helices than for melting of two-strand helices. These calculations predict an experimentally detectable (>or=10%) difference between ST(m) and ST(m, infinity) which increases strongly with decreasing length for two-strand helix lengths of <15 bp and for hairpin helix lengths of <30 bp. From NLPB values of Deltan(u)/Deltan(u, infinity), we predict Delta as a function of [salt] and /Z/. Predictions of thermodynamic and thermal stabilities of oligomeric helices as functions of length and [salt] are consistent with and represent a significant refinement of the average oligomer salt effect currently in use in nearest neighbor stability predictions.

Structural Analysis of Chitosan Mediated DNA Condensation by AFM: Influence of Chitosan Molecular Parameters

Chitosan is a nontoxic and biodegradable polysaccharide that has recently emerged as a promising candidate for gene delivery. Here the ability of various chitosans, differing in the fractional content of acetylated units (F(A)) and the degree of polymerization (DP), to compact DNA was studied. Polyplexes made from mixing plasmid DNA with chitosan yielded a blend of toroids and rods, as observed by AFM. The ratios between the fractions of toroids and rods were observed to decrease with increasing F(A) of the chitosan, indicating that the charge density of chitosan, proportional to (1 - F(A)), is important in determining the shape of the compacted DNA. The amount of chitosan required to fully compact DNA into well-defined toroidal and rodlike structures were found to be strongly dependent on the chitosan molecular weight, and thus its total charge. A higher charge ratio (+/-) was needed for the shorter chitosans, showing that an increased concentration of the low DP chitosan could compensate for the reduced interaction strength of the individual ligands with DNA. Employing chitosans with different molecular parameters offers the possibility of designing DNA-chitosan polyplexes with various geometries, reflecting various chitosan-DNA interaction strengths, which is necessary for the evaluation of efficient gene delivery vehicles.

Adsorption of monovalent and multivalent cations and anions on DNA molecules

Adsorption of monovalent and multivalent cations and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modeled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modeled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major-groove cationic charge is independent of the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salts. Simulations for larger ion radii, which mimic the effect of ion hydration, indicate an increased adsorbtion of cations in the major groove.

A thermodynamic framework for the magnesium-dependent folding of RNA

The goal of this review is to present a unified picture of the relationship between ion binding and RNA folding based on recent theoretical and computational advances. In particular, we present a model describing how the association of magnesium ions is coupled to the tertiary structure folding of several well-characterized RNA molecules. This model is developed in terms of the nonlinear Poisson-Boltzmann (NLPB) equation, which provides a rigorous electrostatic description of the interaction between Mg(2+) and specific RNA structures. In our description, most of the ions surrounding an RNA behave as a thermally fluctuating ensemble distributed according to a Boltzmann weighted average of the mean electrostatic potential around the RNA. In some cases, however, individual ions near the RNA may shed some of their surrounding waters to optimize their Coulombic interactions with the negatively charged ligands on the RNA. These chelated ions are energetically distinct from the surrounding ensemble and must be treated explicitly. This model is used to explore several different RNA systems that interact differently with Mg(2+). In each case, the NLPB equation accurately describes the stoichiometric and energetic linkage between Mg(2+) binding and RNA folding without requiring any fitted parameters in the calculation. Based on this model, we present a physical description of how Mg(2+) binds and stabilizes specific RNA structures to promote the folding reaction.

Asymptotic solution of the cylindrical nonlinear Poisson-Boltzmann equation at low salt concentration: analytic expressions for surface potential and preferential interaction coefficient

The analytic solution to the nonlinear Poisson-Boltzmann equation describing the ion distributions surrounding a nucleic acid or other cylindrical polyions as a function of polyion structural quantities and salt concentration ([salt]) has been sought for more than 80 years to predict the effect of these quantities on the thermodynamics of polyion processes. Here we report an accurate asymptotic solution of the cylindrical nonlinear Poisson-Boltzmann equation at low to moderate concentration of a symmetrical electrolyte (< or = 0.1 M 1:1 salt). The approximate solution for the potential is derived as an asymptotic series in the small parameter var epsilon(-1), where var epsilon identical with kappa(-1)/a, the ratio of the Debye length (kappa(-1)) to the polyion radius (a). From the potential at the polyion surface, we obtain the coulombic contribution to the salt-polyelectrolyte preferential interaction (Donnan) coefficient (Gamma(u)coul) per polyion charge at any reduced axial charge density xi. Gamma(u)coul is the sum of the previously recognized low-salt limiting value and a salt-dependent contribution, analytically derived here in the range of low-salt concentrations. As an example of the application of this solution, we obtain an analytic expression for the derivative of the midpoint temperature of a nucleic acid conformational transition with respect to the logarithm of salt concentration (dT(m)/d ln[salt]) in terms of [salt] and nucleic acid structural quantities. This expression explains the experimental observation that this derivative is relatively independent of salt concentration but deviates significantly from its low-salt limiting value in the range 0.01-0.1 M.

The effect of monovalent ions on polyphosphate binding to Escherichia coli exopolyphosphatase

The thermodynamic driving force for the interaction of Escherichia coli exopolyphosphatase (PPX) with polyphosphate was investigated by varying salt choice and concentration. This interaction was found to be cation concentration independent but weakly dependent on the concentration of certain anions. Both of these traits are very uncommon for nonspecific protein-polyelectrolyte interactions. Interpretation of these results based on theory indicated that binding was not entropy driven due to release of polyelectrolyte-condensed counterions, as is the case for nearly all protein-polyelectrolyte interactions. The thermodynamics of the PPX-polyphosphate interaction showed similarity only to the interaction of polynucleotides with single stranded binding proteins.

The interpretation of Mg(2+) binding isotherms for nucleic acids using Poisson-Boltzmann theory

Magnesium ions play a crucial role in the structural integrity and biological activity of nucleic acids. Experimental thermodynamic descriptions of Mg(2+) interactions with nucleic acids in solution have generally relied on the analyses of binding polynomials to estimate the energetic contributions of diffuse and site-bound ions. However, since ion binding is dominated by long-range electrostatic forces, such models provide only a phenomenological description of the experimental Mg(2+) binding data and provide little insight into the actual mechanism of the binding equilibria. Here, we present a rigorous theoretical framework based on the non-linear Poisson-Boltzmann (NLPB) equation for understanding diffuse ion interactions that can be used to interpret experimental Mg(2+) binding isotherms. As intuitively expected, in the NLPB model binding is simply the total accumulation of the ion around the nucleic acid. Comparing the experimental data to the calculated curves shows that the NLPB equation provides a remarkably accurate description of Mg(2+) binding to linear polynucleotides like DNA and poly(A x U) without any fitted parameters. In particular, the NLPB model explains two general features of magnesium binding; the strong dependence on univalent salt concentration, and its substantial anticooperativity. Each of these effects can be explained by changes in the Mg(2+) distribution around the polyion under different solution conditions. In order to more fully understand these different aspects of magnesium binding, the free energy of Mg(2+) binding, DeltaGMg, is calculated and partitioned into several salt-dependent contributions: the change in the electrostatic interaction free energy of the charges, DeltaDeltaGE.D (including Mg(2+)-phosphate, Mg(2+)-Mg(2+), Mg(2+)-Na(+), Na(+)-Na(+), Na(+)-phosphate interactions, and similar contributions for Cl(-)) and the cratic free energies of (re)organizing the MgCl2 and NaCl atmospheres, DeltaG(Mg)org and DeltaDeltaG(Na)org, respectively. For the systems studied here, DeltaGMg is strongly influenced by entropic free energy changes in the distributions of both NaCl and MgCl2, DeltaG(Mg)org and DeltaDeltaG(Na)org. From this analysis, we also raise the possibility that coions added with the magnesium salt might play an important role in the overall stability of nucleic acids under some conditions.

Thermodynamics of the conformational transition of biopolyelectrolytes: the case of specific affinity of counterions

A formal development of the Counterion Condensation theory (CC) of linear polyelectrolytes has been performed to include specific (chemical) affinity of condensed counterions, for polyelectrolyte charge density values larger than the critical value of condensation. It has been conventionally assumed that each condensed counterion exhibits an affinity free-energy difference for the polymer, (DeltaG(aff)). Moreover, the model assumes that the enthalpic and entropic contributions to DeltaG(aff), i.e., DeltaH(aff) and DeltaS(aff), are both independent of temperature, ionic strength and polymer concentration. Equations have been derived relative to the case of the thermally induced, ionic strength dependent, conformational transition of a biopolyelectrolyte between two conformations for which chemical affinity is supposed to take place. The experimental data of the intramolecular conformational transition of the ionic polysaccharide kappa-carrageenan in dimethylsulfoxide (DMSO) have been successfully compared with the theoretical predictions. This novel approach provides the enthalpic and entropic affinity values for both conformations, together with the corresponding thermodynamic functions of nonpolyelectrolytic origin pertaining to the biopolymer backbone change per se, i.e., DeltaH(n.pol) and DeltaS(n.pol), according to a treatment previously shown to be successful for lower values of the biopolyelectrolyte linear charge density. The ratio of DeltaH(n.pol) to DeltaS(n.pol) was found to be remarkably constant independent of the value of the dielectric constant of the solvent, from formamide to water to DMSO, pointing to the identity of the underlying conformational process.

The importance of coulombic end effects: experimental characterization of the effects of oligonucleotide flanking charges on the strength and salt dependence of oligocation (L8+) binding to single-stranded DNA oligomers

Binding constants Kobs, expressed per site and evaluated in the limit of zero binding density, are quantified as functions of salt (sodium acetate) concentration for the interactions of the oligopeptide ligand KWK6NH2 (designated L8+, with ZL = 8 charges) with three single-stranded DNA oligomers (ss dT-mers, with |ZD| = 15, 39, and 69 charges). These results provide the first systematic experimental information about the effect of changing |ZD| on the strength and salt dependence of oligocation-oligonucleotide binding interactions. In a comparative study of L8+ binding to poly dT and to a short dT oligomer (|ZD| = 10),. Proc. Natl. Acad. Sci. USA. 93:2511-2516) demonstrated the profound thermodynamic effects of phosphate charges that flank isolated nonspecific L8+ binding sites on DNA. Here we find that both Kobs and the magnitude of its power dependence on salt activity (|SaKobs|) increase monotonically with increasing |ZD|. The dependences of Kobs and SaKobs on |ZD| are interpreted by introducing a simple two-state thermodynamic model for Coulombic end effects, which accounts for our finding that when L8+ binds to sufficiently long dT-mers, both DeltaGobso = -RT ln Kobs and SaKobs approach the values characteristic of binding to poly-dT as linear functions of the reciprocal of the number of potential oligocation binding sites on the DNA lattice. Analysis of our L8+-dT-mer binding data in terms of this model indicates that the axial range of the Coulombic end effect for ss DNA extends over approximately 10 phosphate charges. We conclude that Coulombic interactions cause an oligocation (with ZL < |ZD|) to bind preferentially to interior rather than terminal binding sites on oligoanionic or polyanionic DNA, and we quantify the strong increase of this preference with decreasing salt concentration. Coulombic end effects must be considered when oligonucleotides are used as models for polyanionic DNA in thermodynamic studies of the binding of charged ligands, including proteins.

Theory of biomolecular recognition

Specific, noncovalent binding of biomolecules can only be understood by considering structural, thermodynamic, and kinetic issues. The theoretical foundations for such analyses have been clarified in the past year. Computational techniques for both particle-based and continuum models continue to improve and to yield useful insights into an ever wider range of biomolecular systems.