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.     

Electrostatic contributions to oligonucleotide transitions

In a previous paper we employed Monte Carlo techniques to calculate distribution functions for distances between charged phosphates of randomly coiled oligonucleotides in solution. The average energy of the random coil, as well as the loop weighting function and bimolecular nucleation parameter, was obtained as a function of chain length and salt concentration. In the present paper we apply the results to a consideration of the electrostatic dependence of the helix–coil transition in oligonucleotides. By considering the equilibrium among three species: hairpin, dimer, and random coil, we have calculated (1) the variation in melting temperature of dimer, hairpin, and the dimer-hairpin mixture with salt concentration and chain length, (2) the variation in the equilibrium between dimer and hairpin as a function of salt concentration, temperature, and length, (3) the variation in the transition breadth with salt concentration and chain length.     

Polyelectrolyte theory. I. Counterion accumulation,site-binding,and their insensitivity to polyelectrolyte shape in solutions containing finite salt concentrations

We have computed the Poisson-Boltzmann distribution of counterions around polyelectrolytes in solutions containing finite salt concentrations. The polyelectrolytes considered here are highly charged in the sense that ξ > 1, ξ being the linear charge density parameter for cylinders, which is generalized by us to other shapes. Contrary to the situation at zero salt concentration, the counterion distribution is not strongly shape dependent, being similar for cylinders or spheres which have the same superficial charge density and radius of curvature R_c. The distribution resembles that in the neighborhood of a plane with the same charge density. Three regions are distinguished. (1) In the “inner region” which extends up to a distance R_c/2ξ from the surface, the counterion distribution is essentially salt independent. The counterion concentration in the immediate vicinity of the polyelectrolyte surface (CIV) is quite high, typically 1–10M, and proportional to the square of the surface charge density, which is its main determinant. (2) An intermediate region extends out to a distance where the electrostatic potential is equal to κT/e. This distance is comparable to λ for plane and cylinder, and smaller for the sphere. (3) In the outer region, the distribution is hardly influenced by the details of the inner region, on which it cannot, therefore, give much information. Colligative properties are dependent on the distribution in the outer region and are fairly well predicted even by a rudimentary theory. The large value of the CIV implies that site binding must often be significant. It can be computed by applying the mass-action law to site-bound counterions in equilibrium with the counterions in the neighborhood, whose concentration is the CIV, the relevant equilibrium constant being that for the binding of counterions to isolated monomer sites. Because the CIV is insensitive to salt concentration, this will also be the case for site binding. With the graphs provided, one can compute the extent of sitebinding within the Poisson-Boltzmann framework. The “condensation radius,” i.e., the radius encompassing a counterionic charge 1 ? ξ^?1 around a cylinder, is found to be large. It varies with salt concentration and tends to infinity as the salt is diluted. Neither this radius nor the charge fraction 1 ? ξ^?1 of condensation theory plays any special role in the counterion distribution. The “finite-salt” results apply to salt concentrations, typically as low as 1–10 mM. This encompasses, among others, all experiments on biological polyelectrolytes.     

Deoxydodecanucleotide heteroduplex d(TTTTATAATAAA). d(TTTATTATAAAA) containing the promoter Pribnow sequence TATAAT. I. Double-helix stability by UV spectrophotometry and calorimetry

Thermally induced structural transition in the d(TTTTATAATAAA) d(TTTATTATAAAA) heteroduplex is characterized by UV-spectroscopy and differential scanning calorimetry. At low salt (less than 0.1 M) the occurrence of a cooperative transition in the lower temperature range, followed by a broad transition connected with small increase in absorbance is observed. At high salt (greater than or equal to 0.2 M) a single, monophasic transition appears. Linear dependence of the latter on log of salt concentration (dTm:dlogM = 14.2 degrees C) and of 1/Tm on log of oligomer concentration [derived therefrom delta H (v.H.) = 77.1 kcal/mole (duplex)] allows relating it to the melting of the heteroduplex helix. The non-cooperative transition, independent of oligomer concentration and similar to that of the single chain, was attributed to melting of short hairpin helices upon heteroduplex dissociation. Calorimetric enthalpy: 75.6 kcal/mole (duplex) proved significantly lower than predicted from known calorimetric data for poly[d(AT)] and poly d(A) X poly d(T).     

Effects of Na+ and Mg++ ions on the helix–coil transition of DNA

The effects of monovalent (Na⁺) and divalent (Mg⁺⁺) cations on the temperature and breadth of the helix–coil transition of phage DNA have been investigated. The experimental results confirm the findings of Dove and Davidson [J. Mol. Biol. 5 , 467–478 (1962)] for the limiting cases of zero divalent ion concentration and saturating levels of divalent ion, and extend their findings to the intermediate region of Mg⁺⁺ concentrations. A theory for the dependence of transition temperature on the ion concentrations is developed, utilizing the approach of Wyman [Adv. Protein Chem. 19 , 223–286 (1964)], modified to account for electrostatic nonideality of the polyelectrolytes. The theory is in agreement with Manning's treatment of the experiments of Dove and Davidson [Biopolymers 11 , 937–949, 951–955 (1972)] and is in fair agreement with experimental data over the entire range of ion concentrations. Further investigation of the structure and ion-binding properties of the denatured form will be required before a quantitative comparison between theory and experiment can be performed.     

On the application of polyelectrolyte "limiting laws" to the helix-coil transition of DNA. II. The effect of Mg++ counterions

The techniques of the previous article are here applied to the case for which the solution contains, in addition to excess uni–univalent salt, one equivalent of divalent counterions per mole nucleotide. In agreement with the melting temperature measurements of Dove and Davidson for Mg⁺⁺, it is predicted that a region of uni–univalent salt concentration then exists in which (dT _m/^d log m A +) is negative. It is further predicted, in accord with experiment, that in the presence of divalent counterions, the helical form of DNA is much more stable than in their absence.     

Thermodynamics and equilibrium sedimentation analysis of the close approach of DNA molecules and a molecular ordering transition

Measurement of the equilibrium distribution of persistence length fragments of DNA in high concentration in the ultracentrifuge shows that the reduced osmotic pressure rises much faster than linearly. From analysis of the data in terms of the Zimm cluster integral we infer that the net interactions between helices are purely repulsive at all distances. A theoretical equation of state derived from scaled particle theory with one adjustable parameter is in excellent agreement with the experimental data so long as the salt concentration is not excessively low. The parameter represents the hard-core radius in a simplified approximation to the potential function for the electrostatic repulsion between helices. Its value depends on the salt concentration, and it shrinks at high salt to a radius in close agreement with direct structural estimates. At a particular value of the osmotic pressure that is only slightly salt dependent, the solution undergoes a reversible transition to a denser, turbid, optically anisotropic phase. The relation between DNA volume fraction, including the electrostatic radius, at the transition point and the effective asymmetry of the molecules as a function of salt is in approximate correspondence with various theoretical treatments. However, the experimental function extrapolates to the correct limit for spherical particles. The work needed to bring DNA to a high concentration is estimated. The results suggest that the phase transition is first order.     

Salt-dependent conformational transitions in the self-complementary deoxydodecanucleotide d(CGCAATTCGCG): Evidence for hairpin formation

Differential scanning calorimetry (DSC), temperature-dependent uv-absorption spectroscopy, and temperature-dependent CD were used to monitor and characterize the salt-dependent, thermally induced structural transitions in the deoxydodecanucleotide d(CGCGAATTCGCG). At the high oligomer concentrations required for DSC, the calorimetric scans revealed a single, monophasic transition curve at all salt concentrations. Based on previous nmr melting studies under similar conditions, we conclude that these monophasic transitions correspond to the cooperative duplex-to-single-strand conversion of the dodecamer. By contrast, at the lower oligomer concentrations used for the spectroscopic studies, the shapes of the uv and CD melting curves were found to depend on the concentration of the added salt. At high salt (≥0.1M Na⁺), a single, monophasic transition curve was observed. At lower salt (?0.01M Na⁺), the CD and uv melting curves exhibit biphasic behavior. Based on the concentration dependence, the enthalpy, and the cooperativity of each transition in the biphasic curve, we conclude that at low salt and low oligomer concentrations, the dodecamer melts in a sequential manner involving initial disruption of a duplex structure and subsequent disruption of a hairpin structure.     

Hairpin Formation In d-AAGCTTAAGCTT Under High Salt Conditions Shows Unusual Properties

Abstract

The hairpin-duplex equillibria of the dodecamer d-AAGCTTAAGCTT and interaction of the duplex form with a pentapeptide, KGWGK, has been studied. UV thermal transitions are monophasic at low salt but biphasic at higher salt concentrations. At 10^?5M or less oligomer concentration biphasic melting curves persist till 900 mM NaCl. The d(Tm)/d log(Na⁺) for the duplex form is 12 °C and for the hairpin is 18 °C. The ΔH and ΔS values for duplex formation are low(-25 Kcal/mole and—59 Cal/mole respectively). KGWGK binds to the duplex form with a binding constant K = 3.4×10⁵M^?1measured from fluorescence quenching of tryptophan. These unusual results are markedly different from that reported for d-AGATCT- AGATCT (Biochemistry 31, 6241–6245) and are discussed in ternis of sequence dependence of loop folding and cruciform extrusion pathway of hairpin formation.     

Energetics of the hairpin to mismatched duplex transition of d(GCCGCAGC) on NaCl solution

We report Potential of Mean Force studies to describe the relative thermodynamic stabilities of d(GCCGCAGC) in a mismatched duplex and a hairpin monomer conformation in NaCl solution. The PMF calculations are combined with previous molecular mechanics and normal mode analysis in order to estimate the role of different components of the free energy in determining the relative stability of the duplex and hairpin structures. The high entropy associated with the loop region and the lack of minor groove phosphate-phosphate interactions in the hairpin compete against the gain in enthalpic contribution to the free energy due to base pairing in the mismatched duplex. The combined free energy calculations show that the hairpin is the most stable conformation at low salt and that a hairpin to duplex transition takes place at approximately 0.47 M NaCl. In addition, we studied the hairpin to partially stacked single helical conformation equilibrium at low salt. We found a small variation in transition temperature in salt concentration, delta Tm/delta log10(cs) approximately 2-3 degrees K/decade, in contrast to the duplex to hairpin or duplex to partially stacked single helix transition where the transition temperature exhibited marked dependence on salt concentration. This is in qualitative agreement with experimental data. Based on the Potential of Mean Force free energy calculation, the order of relative stability of the three-conformations studied varies with salt concentration. We observed the following orders of stability: stacked single helix greater than hairpin greater than duplex for cs less than 0.77 M NaCl; single helix greater than duplex greater than hairpin for 0.77 less than Cs less than 2.1 M; and duplex greater than hairpin greater than single strand for cs greater than 2.1 M. From the calculated PMF free energy curves in the NaCl concentration range, 0.012 less than cs less than 5.0 M, we can assign upper and lower bounds for the non-ionic differences in free energy between the duplex, hairpin, and stacked single helical states (at standard conditions: cs = 1.0 M, T = 25 degrees C, and 1 M oligomer concentration). We found that for delta G duplex single helix = G duplex - 2 x G single helix less than -7.38 Kcal/mol, the single helix is the least stable state. For the duplex-to-hairpin free energy difference in the range, -1.87 less than delta G duplex-hairpin less than 0.03 Kcal/mol, there will always be a salt-induced hairpin-to-duplex transition for 0.01 less than cs less than 1.6 M NaCl. If delta G duplex-hairpin less than -1.87, the duplex is always more stable than the hairpin; and for delta G duplex-hairpin greater than Kcal/mol, the hairpin state is always more stable than the duplex, for all salt concentrations.     

Kinetics of synthesesis of polymeric dAT on oligomeric templates

A model is developed to explain the following experimental observations: oligomers of the alternating DNA copolymer dAT serve as templates for the enzymatic synthesis of macromolecular dAT; the rate of polymer synthesis with a template oligomer of given length increases to a maximum and then decreases as the temperature increases; the temperature for the maximum rate of synthesis increases with the length of the template. These observations were interpreted in terms of the repeated “slipping” of the oligomer along the product strand to expose template sites. This communication extends this idea. We suppose that the rate-limiting step in the polymerization is either the attachment of the substrate to the exposed template site or the synthesis of the phosphodiester bond. Then the rate of synthesis is proportional to the equilibrium concentration either of exposed template sites or of template sites occupied by substrate molecules. These concentrations are evaluated in terms of a simple theory of the helix–coil transition. The model qualitatively reproduces the dependence of the rate of synthesis on template length and temperature and predicts rates of synthesis in approximate agreement with experiment.     

Intrinsic viscosities of cyclic and linear lamda DNA

The ratio of the intrinsic viscosities of the linear and circular forms of λ DNA, [η]L /[η]c, has been measured as a function of ionic strength in the range [Na⁺] = 0.6. M–0.03MCorrections were made for the presence of uncyclizable linear contaminant in circular preparations. By combining data in the literature on the ionic strength dependence of linear DNA of various molecular weights with that obtained here, it was possible to determine the expansion parameter εL as a function of [Na⁺]. εL is defined by the relation 〈L²〉 = b²N^1+εL, where 〈L¹〉 is the mean-square end-to-end distance of a chain of N segments of length b. The empirical relation εL = 0.05 ? 0.11 log [Na⁺] for native NaDNA at 25°C is found. When εL = 0, [η]L /[η]c extrapolates to 1.6, in good agreement with the theoretical prediction of 1.55. As εL increases, [η]L /[η]c increases, in agreement with a theory of Bloomfield and Zimm.     

Importance of oligoelectrolyte end effects for the thermodynamics of conformational transitions of nucleic acid oligomers: a grand canonical Monte Carlo analysis.

Effects of salt concentration on the stabilities of oligonucleotide helices are analyzed directly in terms of delta gamma N----yN identical to gamma denyN - gamma natN, the difference in the salt-nucleotide phosphate preferential interaction coefficients for the denatured state, having yN phosphate charges, and for the native state, having N phosphate charges (y = 1 for hairpin denaturation and y = 0.5 for dimer denaturation). Previous experimental studies of the denaturation of hairpin oligonucleotides (having 18 less than N less than 44) indicate significant differences between delta gamma N----N and delta gamma infinity, the value determined for the denaturation of the corresponding polynucleotide. These differences are thermodynamic manifestations of the oligoelectrolyte end effect. In contrast, the available data on the denaturation of oligonucleotide dimer helices (N less than or equal to 22) imply that differences between delta gamma infinity and delta gamma N----0.5N, and hence oligoelectrolyte end effects, are small or negligible. To determine the origin of these apparently conflicting implications concerning the importance of oligoelectrolyte end effects, we have calculated the N dependence of gamma N from grand canonical Monte Carlo simulations for an idealized model of the structure and charge distribution of each oligomer conformation. Our calculations are in quantitative agreement with the experimental finding for d(TA) hairpin oligomers that -delta gamma N----N decreases linearly as N-1 increases, and with the extant experimental determinations of delta gamma N----0.5N. These results provide an illustration of how the large electrostatic end effects exhibited by the hairpin denaturation data are masked when delta gamma infinity is compared with values of delta gamma N----0.5N for short dimer helices (N less than or equal to 22). For 0.5N greater than 24, -delta gamma N----0.5N is predicted to be a linear function of N-1 whose slope has the opposite sign from, and is more salt-concentration dependent than, the corresponding slope of -delta gamma N----N as a function of N-1. Our calculations also yield predictions about the N dependences of the individual values of gamma N that can be tested by determining Donnan coefficients from membrane dialysis equilibrium experiments. For long enough hairpin and dimer oligonucleotides (yN greater than or equal to 24), in either native or denatured forms, we predict that the (positive) difference gamma infinity - gamma N increases linearly with increasing N-1. For smaller values of N the difference gamma infinity - gamma N continues to increase with increasing N-1.     

Kinetic and thermodynamic characterization of DNA duplex–hairpin interconversion for two DNA decamers: d(CAACGGGTTG) and d(CAACCCGTTG)

The duplex–hairpin interconversion of two DNA decamers, d(CAACGGGTTG) and d(CAACCCGTTG), has been characterized thermodynamically and kinetically by using uv-melting and nmr relaxation methods. Separately, each decamer shows slow exchange between hairpin and duplex conformations. The hairpin conformations have melting points of 47 and 50°C, respectively, and exhibit similar thermodynamic stabilities. The enthalpies of duplex formation, measured by nmr, were found to be very similar (ΔH_DH = 26 ± 3 kcal/mole) for both decanters at low salt concentrations (< 50 mM NaCl). However, as the salt concentration was increased the behavior of ΔH_DH, and kinetics is significantly different for each decamer. The d(CAACGGGTTG) decamer forms a duplex containing two central G·G mismatches at high salt and DNA concentration. Based upon the measurement of high interconversion activation energies and a decrease in hairpin formation rate with increasing salt, the interconversion between hairpin and duplex was concluded to proceed by complete strand dissociation. In contrast, the d(CAAC-CCGTTG) decamer was determined to form a duplex with two centrally located C·C mismatches at pH values less than 6.2, consistent with the formation of a hemiprotonated C⁺·C mismatch. At pH values greater than 6.4, the hairpin–duplex equilibrium is almost completely shifted toward the hairpin conformation at DNA concentrations of 0.5–7.0 mM and salt concentrations of 10–100 mM. The interconversion of duplex and hairpin conformations was ascertained by means of both kinetic and thermodynamic measurements to proceed by a slightly different mechanism than its complementary decamer. Although the interconversion proceeds by complete strand separation as suggested by high duplex-hairpin interconversion activation enthalpies, the increasing hairpin formation rate with increasing ionic strength as well as the ΔH_DH, dependence on sail indicate that an intermediate internally bulged duplex (no C⁺·C formation) is stabilized by increasing ionic strength. These data support an interconversion mechanism where an intermediate internally bulged duplex may be the rate limiting step before strand separation. © 1995 John Wiley & Sons, Inc.     

Molecular dynamics simulation of human interleukin-4: comparison with NMR data and effect of pH,counterions and force field on tertiary structure stability

The human protein interleukin-4 (IL-4) has been simulated at two different pH values 2 and 6, with different amounts of counterions present in the aqueous solution, and with two different force-field parameter sets using molecular dynamics simulation with the aim of validation of force field and simulation set-up by comparison to experimental nuclear magnetic resonance data, such as proton–proton nuclear Overhauser effect (NOE) distance bounds, ³ J(HN,HC_α) coupling constants and backbone N–H order parameters. Thirteen simulations varying in the length from 3 to 7 ns are compared.

At pH 6 both force-field parameter sets used do largely reproduce the NOE's and order parameters, the GROMOS 45A3 set slightly better than the GROMOS 53A6 set. ³ J values predicted from the simulation agree less well with experimental values. At pH 2 the protein unfolds, unless counterions are explicitly present in the system, but even then the agreement with experiment is worse than at pH 6. When simulating a highly charged protein, such as IL-4 at pH 2, the inclusion of counterions in the simulation seems mandatory.     

Mechanism for unwinding of double-helical polynucleotides by formaldehyde

We have formulated a mathematical model for the unwinding process of polynucleotides induced by formaldehyde by making use of the master equation approach. Our model assumes that the formaldehyde kinetics follows the helix–coil theory of Zimm and Bragg. The model incorporates experimental features such as the interplay between pH-dependent and -independent reactions and the dependence of the initial and final helix stability on the unwinding. That is, our model incorporates the existence of the critical point such that if the pH of the system is high enough (i.e., pH ? 7), the unwinding of polynucleotides occurs by means of two separate chemical reactions, either by the HCHO–imino reaction alone or by the HCHO–amino reaction alone. The critical point depends on the ionic strength, temperature, and the formaldehyde concentration satisfying the relation s = 1 + K_Uλ, where s is the helix stability parameter, K_U is the binding constant for the HCHO–imino reaction, and λ is the formaldehyde concentration. Thus above the critical point, i.e., s < (1 + K_Uλ), the unwinding is due to the reaction of imino groups with formaldehyde, and below the critical point, i.e., s > (1 + K_Uλ), the unwinding is due to the reaction of amino groups with formaldehyde. Although, below the critical point, the imino group does not participate directly in the rate-determining step, it participates indirectly in such a manner that it reduces the initial helix stability parameter s to s/(1 + K_Uλ) by forming a complex. The kinetic constants in the master equation have been determined by making use of the principle of detailed balance and the breathing mechanism proposed in the past. With this model we have quantitatively explained the anomalous temperature dependence observed in the kinetics of formaldehyde-induced poly[d(A-T)] and the salt dependence observed in poly(A·U).     

Unusual stability exhibited by (AT)XN12(AT)Y motif associated with high fetal hemoglobin levels

Abstract

Quasi-palindromic sequences (AT)_XN₁₂(AT)_Y present in HS2 (hypersensitive site 2) of the human β-globin locus are known to be significantly associated with increased fetal hemoglobin (HbF) levels. High HbF levels in some adults arise due to pathological conditions such as sickle cell disease and β-thalassemia. However, elevated levels of HbF are also associated with a reducing morbidity and mortality in patients with β-thalassemia and thus ameliorate the severity of the disease. Using gel-electrophoresis, ultraviolet (UV)-thermal denaturation, and circular dichroism (CD) techniques, we demonstrated that it exhibits a hairpin-duplex equilibrium. Intramolecular species (hairpin) were observed in both low and high salt concentrations in gel assay studies displaying the unusual stability of intramolecular species even at the high counter-ion concentration. The unusual stability of hairpin secondary structures was also demonstrated by the monophasic nature of the melting profiles for the oligonucleotides which persisted at low as well as high salt and oligomer concentrations. Change in CD spectra as a function of oligomer concentration indicates that the bimolecular duplex formation is selectively favored over monomolecular hairpin formation at and above 9 µM oligomer concentration. Thus, we hypothesize that imperfect inverted repeat sequence (AT)_XN₁₂(AT)_Y of HS2 of β-globin gene LCR forms the unusually stable hairpins which may result in the formation of a cruciform structure that may be recruited for binding by various nuclear proteins that could result in elevated HbF levels.

Communicated by Ramaswamy H. Sarma.     

Alkyl Substituent in Place of the Thymine Methyl Group Controls the A-X Conformational Bimorphism in Poly(dA-dT)

Abstract

Circular dichroism studies of a family of poly(dA-y⁵dU) polynucleotides (y = H, methyl, ethyl, propyl, butyl or pentyl) were conducted in water-alcohol solutions containing sodium or cesium counterions. The polynucleotides denatured or adopted A- or X-DNA double helices depending on the concentration and type of alcohol, type of counterions and the length of the aliphatic substituent in place of the thymine methyl group. Short aliphatic substituents and sodium cations favored A-DNA while long aliphatic substituents and cesium cations promoted X-DNA. This study demonstrates delicacy of the conformational equilibrium of poly(dA-dT) between the A- and X-DNA double helices which depends on both intramolecular and intermolecular factors.     

Na+ effects on transition of DNA and polynucleotides of variable linear charge density.

A range of linear charge densities of the ordered and disordered forms of DNA or polynucleotides can be obtained experimentally by acid or alkaline titration, or by the investigation of unusual complexes involving protonated bases or three-stranded helices. The variation of melting temperatures with Na⁺ concentration for various of these systems is known and in some cases is complemented by structural and thermodynamic information. We have extended the condensation–screening theory of Manning [Biopolymers, 11 , 937–955 (1972)] to these systems. The stabilizing and destabilizing effects of Na⁺ (condensation and screening, respectively) and be independently varied, and the theory is successful in predicting the qualitative (in some cases, quanittative) behaviour that is observed. Comparison of theory and experiment indicates that the axial phosphate distance b for single-stranded polynucleotides increases with increasing pH. Values of the critical parameter ξ are obtained for the various polynucleotide structures. These values are essential for an understanding of ionic effects on charged ligand–polynucleotide interactions.     

What Drives Amyloid Molecules To Assemble into Oligomers and Fibrils?

We develop a theory for three states of equilibrium of amyloid peptides: the monomer, oligomer, and fibril. We assume that the oligomeric state is a disordered micellelike collection of a few peptide chains held together loosely by hydrophobic interactions into a spherical hydrophobic core. We assume that fibrillar amyloid chains are aligned and further stabilized by steric zipper interactions—hydrogen bonding, steric packing, and specific hydrophobic side-chain contacts. The model makes a broad set of predictions that are consistent with experimental results: 1), Similar to surfactant micellization, amyloid oligomerization should increase with peptide concentration in solution. 2), The onset of fibrillization limits the concentration of oligomers in the solution. 3), The extent of Aβ fibrillization increases with peptide concentration. 4), The predicted average fibril length versus monomer concentration agrees with data on α-synuclein. 5), Full fibril length distributions agree with data on α-synuclein. 6), Denaturants should melt out fibrils. And finally, 7), added salt should stabilize fibrils by reducing repulsions between amyloid peptide chains. It is of interest that small changes in solvent conditions can tip the equilibrium balance between oligomer and fibril and cause large changes in rates through effects on the transition-state barrier. This model may provide useful insights into the physical processes underlying amyloid diseases.