Counterion Condensation Theory Research Articles

Enhancement of the Rates for Insertion of Zinc(II) Ions into a Cationic Porphyrin Catalyzed by Poly(glutamate).

The self-assembly of porphyrins onto polyelectrolytes could lead to interesting changes in their reactivity with respect to the bulk solution. Here, we investigated the kinetics of Zn2+ incorporation into tetra-cationic water-soluble 5,10,15,20-tetrakis-(N-methylpyridinium-4-yl)porphyrin (TMpyP(4)) in the presence of poly(L-glutamic acid) (PGA) in a pH range from 4 to 6.5. Under these conditions, the porphyrin electrostatically interacted with the polymer, which gradually switched from an α-helical to a random coil structure. The profile of the logarithm of the observed rate constant (kobs) versus the pH was sigmoidal with an inflection point close to the pH of the conformation transition for PGA. At a pH of 5.4, when PGA was in its highly charged random coil conformation, an almost 1000-fold increase in the reaction rates was observed. An increase in the ionic strength of the bulk solution led to a decrease in the metal insertion rates. The role of the charged matrix was explained in terms of its ability to assemble both reagents in proximity, in agreement with the theory of counter-ion condensation around polyelectrolytes in an aqueous solution.

Mono-valent salt corrections for RNA secondary structures in the ViennaRNA package

BackgroundRNA features a highly negatively charged phosphate backbone that attracts a cloud of counter-ions that reduce the electrostatic repulsion in a concentration dependent manner. Ion concentrations thus have a large influence on folding and stability of RNA structures. Despite their well-documented effects, salt effects are not handled consistently by currently available secondary structure prediction algorithms. Combining Debye-Hückel potentials for line charges and Manning’s counter-ion condensation theory, Einert et al. (Biophys J 100: 2745-2753, 2011) modeled the energetic contributions of monovalent cations on loops and helices.ResultsThe model of Einert et al. is adapted to match the structure of the dynamic programming recursion of RNA secondary structure prediction algorithms. An empirical term describing the salt dependence of the duplex initiation energy is added to improve co-folding predictions for two or more RNA strands. The slightly modified model is implemented in the ViennaRNA package in such way that only the energy parameters but not the algorithmic structure is affected. A comparison with data from the literature show that predicted free energies and melting temperatures are in reasonable agreement with experiments.ConclusionThe new feature in the ViennaRNA package makes it possible to study effects of salt concentrations on RNA folding in a systematic manner. Strictly speaking, the model pertains only to mono-valent cations, and thus covers the most important parameter, i.e., the NaCl concentration. It remains a question for future research to what extent unspecific effects of bi- and tri-valent cations can be approximated in a similar manner.AvailabilityCorrections for the concentration of monovalent cations are available in the ViennaRNA package starting from version 2.6.0.

Modeling salt adsorption in electrical double layer for capacitive deionization

AbstractThis work presents an electrical double layer (EDL) model for capacitive deionization (CDI) by intercorrelating the salt adsorption, the electrode voltage, and the surface charge density. The counterion condensation is considered a crucial contribution to salt adsorption because of the high surface charge density in the charged micropores. The counterions condense when the surface charge density exceeds a critical value, which is predicted by the counterion condensation theory. The EDL model accurately correlates the NaCl salt adsorption and electrode voltage with various surface charge densities and well predicts the salt adsorption in a wide range of external salt concentrations. The EDL model reproduces the non‐monotonic relationship between the salt adsorption and the specific surface area observed in experiments and provides an explanation from the modeling perspective. Exhibiting superior accuracy and predictability for salt adsorption, the EDL model could serve as an enabling tool contributing to the development of CDI processes.

Counterion condensation theory for finite polyelectrolyte and salt concentrations

In the present work we analyze the physical fundamentals of Manning’s counterion condensation using his charged line model in a simple salt solution. We extend the theory for the cases of finite saline concentration and polymeric concentration tending to zero and the case of both finite concentrations. To find the equilibrium between the phases of free and condensed counterions, besides minimizing the free energy, we deduce an auxiliary equation to determine the two characteristic parameters of the theory, the fraction of condensed counterions and the volume of condensation. We compare the obtained results in the present work for only one infinite charged line with the ones of counterion condensation theory by Schurr and Fujimoto. We find that the linear density of critical charge depends on the concentration of added salt and takes values higher than one, instead of the unitary value predicted by Manning. We obtain the equations by the activity and osmotic coefficients in function of the critical charge density. We compare them with the corresponding equations by Manning for these parameters. We extend the counterion condensation theory to solutions of linear polyelectrolytes for finite saline and polymeric concentrations using a cell model. We modify the electrostatic contribution to the Gibbs energy adding, to the traditional one calculated by Manning, the energy excess due to the macroion present in a cylindrical cell. We apply the theory to obtain the osmotic coefficient and we compare our results with experimental data of DNA osmotic coefficient and with theoretical adjustment using the Poisson–Boltzmann equation.

Counterion atmosphere around DNA double helix: trapping of counterions at the nanoscale

DNA is a strong polyelectrolyte macromolecule making metal ions (counterions) condense to a cloud around the double helix. The counterions may be localized outside the macromolecule and inside the minor and major grooves of the double helix. In the present work, the distribution of condensed counterions between inner and outer regions of DNA has been studied using the approaches of counterion condensation theory. The results have shown that the number of counterions trapped inside the macromolecule should be greater than 0.16 per one phosphate group. The maximal number of counterions that may be localized inside the DNA double helix is limited to about 0.4 per one phosphate group and it is much lower than the total number of condensed counterions. To analyze the structure of counterion cloud the molecular dynamics simulations of B-DNA with K+ counterions have been performed. The obtained number of the counterions trapped inside the grooves of the double helix is about 0.22 ± 0.06 per one phosphate group that agree with the model estimations. The developed model describes general features of the structure of counterion cloud around DNA and is able to predict the number of counterions inside the grooves of the double helix.

DNA Electrostatics: From Theory to Application

AbstractNumerous DNA biosensor platforms developed in the last decades rely on DNA electrostatics as the basis for detection. However, the overwhelming number of theoretical studies and computational models of DNA electrostatics poses a barrier to leveraging our deeper mechanistic understanding in this area for the development of new technologies that will push the field towards more sensitive, quantitative, and reliable DNA‐based sensors. In this review, we will bridge the gap between the theory and applications of DNA charge and electrical surfaces to overcome this barrier. We will discuss key theories such as Manning's counterion condensation theory, the Poisson‐Boltzmann equation, and the Gouy‐Chapman model, and provide examples of technological applications that rely on these theories.

Mutual effects between single-stranded DNA conformation and Na+-Mg2+ ion competition in mixed salt solutions.

The ion-dependence of single-stranded DNA (ssDNA) conformational changes has attracted growing attention because of its biological and technological importance. Although single-species ion effects have been extensively explored, it is challenging to study the ssDNA conformational properties under mixed monovalent/divalent ion conditions due to the complications of ssDNA flexibility and ion-ion competition. In this study, we apply Langevin dynamics simulations to investigate mixed Na+/Mg2+ ion-dependent ssDNA conformations. The ssDNA structure is described using a coarse-grained model, in which the phosphate, base, and sugar of each nucleotide are represented by three different beads. A novel improvement in our simulation model is that mixed-salt-related electrostatic interactions are computed via combining Manning counterion condensation (MCC) theory with the Monte Carlo tightly bound ion (MCTBI) model. Based on this MCC-MCTBI combination, we report new empirical functions to describe the ion-concentration-dependent and ssDNA conformation/structure-dependent electrostatic effects. The calculation results relating to the ion binding properties and the simulation results relating to the ssDNA conformational properties are validated against experimental results. In addition, our simulation results suggest a quantitative relationship between the ssDNA conformation and Na+-Mg2+ competition; this in turn reveals their mutual impact in the ion atmosphere.

On the Molecular Mechanism of the Calcium-Induced Gelation of Pectate. Different Steps in the Binding of Calcium Ions by Pectate.

Pectic acid/sodium pectate is one of the most widespread hydrocolloid used in the food industry. It is able to form strong ionotropic gels by the addition of ions, in particular, calcium ions. The initial steps of binding Ca2+ ions to a sample of sodium pectate with a composition close to 90% of ideal Na+-poly(galacturonate) were investigated by means of circular dichroism (CD), microcalorimetry, dilatometry, viscosity, and membrane osmometry, as a function of increasing Rj, Rj being the ratio of the molar concentrations of Ca2+ and pectate repeating units. Data were collected in aqueous NaClO4 at 25 °C. The key instrument of interpretation has been the counterion condensation theory (CCT) of linear polyelectrolytes, modified to include the presence of both specific affinity of the divalent counterion for the polysaccharide ("territorial binding"), and, very importantly, strong chemical bonding (not a covalent bonding, though) of Ca2+ on conformationally well-defined sites on the polymer, with local charge annihilation. Intrinsic viscosity and number-average molar mass data as a function of Rj showed that calcium bonding brings about chain association right from the beginning of addition to pectate. The analysis of the microcalorimetric curve using the modified CCT revealed two types of bonding. In the order of development as a function of Rj, the first mode (type 1) could be reconciled with the "tilted egg-box" type, recently proposed for Ca2+ binding to alginate and the second mode (type 2) with the "shifted egg-box" proposed for calcium pectate on the basis of conformational analysis investigation. Likewise, the two types of bonding turned out to be superimposable with similar bonding categories proposed for alginate and low-methoxyl pectin (LMP), on the one side, and for the association of semiflexible polyelectrolytes, on the other. The analysis allowed us to obtain standard Gibbs free energy, enthalpy, entropy, and volume molar values both for the affinity and the chemical bonding processes. Interestingly, the analysis of the dependence of the gelation temperatures, Tg, of LMP upon increasing additions of calcium ions provided the values of Tg and standard Gibbs free-energy of calcium-to-pectate association coinciding with those obtained from calorimetry for the type-2 bonding process. This finding corroborated previously reported evidence on the enthalpic nature of the elasticity of Ca2+-pectate gels. Finally, comparative analysis of different techniques, but of CD in particular, enabled proposing a "loose-21-helix" as the starting conformation of sodium pectate in aqueous solution.

Aqueous ion partitioning in Nafion: Applicability of Manning's counter-ion condensation theory

Nafion is a well-studied polymer of significant interest as a fuel cell membrane due to rapid transport of protons, which is often ascribed, at least in part, to its phase-separated morphology. The literature detailing ion sorption and transport in Nafion diverges considerably from that of water purification membranes, with contrasting analyses and models. To help bridge these gaps and facilitate comparisons of membranes with various structures, this study presents measurements of ion activity coefficients and sorption in Nafion 117 equilibrated with aqueous solutions of NaCl, MgCl2, and Na2SO4, which are relevant to water purification. The experimental data are compared to a theoretical framework based on Manning's counter-ion condensation theory and Donnan theory. Good agreement between the model and data is observed for NaCl and MgCl2, using no adjustable parameters. However, the model significantly underpredicts Na2SO4 solubility, which is attributed to ion pairing effects. The results highlight the general applicability of counter-ion condensation theory to highly charged polymers, including those exhibiting nanoscale ordering, while revealing fundamental limitations related to ion pairing.

Assessment of anion exchange membrane selectivity with ionic membrane conductivity, revised with Manning's theory or the Kohlrausch's law

The evaluation of anion exchange membrane (AEM) selectivity towards different anions requires facile characterization methods. The anion selectivity of membranes could principally, but practically not easy to, be extracted from the measured anion transport selectivity in electrodialysis (ED), which is a parameter closely related to the process conditions. According to the classical solution-diffusion model, the membrane anion selectivity could be decoupled into two parts: the partitioning selectivity factor of anions between the membrane and the solution phase; the mobility ratio of anions in the membrane. Alternatively, based on the relationship between the anion composition in the membrane and the mixed-ionic membrane conductivities, these two parts can be calculated from the volumetric swelling ratios and ionic conductivities when the AEMs are in pure and mixed-anion forms, respectively. This relationship is proved to be linear in two commercial AEMs (ASE and ACS) for the NO3−/Cl− and SO42−/Cl− pairs. Further, it is possible to obtain the anion selectivity directly for the ASE membrane from corresponding membrane ionic conductivities, with Manning's counter-ion condensation theory to account for the anion activity coefficients in the membrane. While for the NO3−/Cl− pair in the monovalent-anion selective ACS membrane, the selectivity thus calculated is very different from that obtained in ED. For the nonlinear anion composition-conductivity relationship observed in the commercial FAA membrane, the Kohlrausch's parameter (σ) is successfully introduced to describe the mutual influence of anions in the membrane. In this case, it is also possible to obtain the anion selectivity with the proposed approach. This work provides a different perspective to study the selectivity and conductivity of AEMs.

Numerical simulation of salinity gradient power generation using reverse electrodialysis

Reverse electrodialysis (RED) is a promising technology that directly converts salinity gradient energy into electrical energy through the directional permeation of ions across the ion exchange membranes (IEMs). Fundamental understanding of the multi-physical RED process requires a reliable description of all the related phenomena involved in the process. In this work, a two-dimensional RED model based on the Nernst-Planck framework was developed. The fluid dynamics and ion transport were modelled in a full-length cell pair domain by employing the continuity, Navier-Stokes and Nernst-Planck equations complemented by the Donnan exclusion theory and local electroneutrality. The experimentally inaccessible IEM diffusion coefficients were analytically determined using the counterion condensation theory incorporating the tortuosity effect. A numerical simulation was carried out using the developed model. The solution velocity, ion concentration and electric fields were obtained and the characteristics of ion transport were analyzed. The effects of solution inlet velocity, IEM fixed charge concentration and cell pair length on RED performance were investigated and the mechanisms governing the variations of performance parameters were revealed based on ion transport. The present model contributes to a clearer understanding of the connection between the ion transport behavior and the stack performance.

Modeling aqueous multivalent polyelectrolytes systems with polyelectrolyte NRTL model

Thermodynamic modeling of aqueous polyelectrolyte systems is of great interest in many industrial applications and biological systems. Recently a Polyelectrolyte Nonrandom Two-Liquid activity coefficient model was proposed for aqueous monovalent polyelectrolyte systems. Integrating Manning’s counterion condensation theory, Pitzer-Debye-Hückel theory, and electrolyte Nonrandom Two-Liquid theory, the model accounts for the solution nonideality derived from long-range electrostatic polyion-ion and ion-ion interactions as well as short-range van der Waals molecule–molecule, molecule-ion, and ion-ion interactions. This work extends the model for aqueous multivalent polyelectrolyte systems and shows satisfactory agreement between the model results and the available literature data on thermodynamic properties of varieties of multivalent polyelectrolyte systems.

Contributions and competition of Mg2+ and K+ in folding and stabilization of the Twister ribozyme.

Native folded and compact intermediate states of RNA typically involve tertiary structures in the presence of divalent ions such as Mg2+ in a background of monovalent ions. In a recent study, we have shown how the presence of Mg2+ impacts the transition from partially unfolded to folded states through a “push-pull” mechanism where the ion both favors and disfavors the sampling of specific phosphate-phosphate interactions. To further understand the ion atmosphere of RNA in folded and partially folded states results from atomistic umbrella sampling and oscillating chemical potential grand canonical Monte Carlo/molecular dynamics (GCMC/MD) simulations are used to obtain atomic-level details of the distributions of Mg2+ and K+ ions around Twister RNA. Results show the presence of 100 mM Mg2+ to lead to increased charge neutralization over that predicted by counterion condensation theory. Upon going from partially unfolded to folded states, overall charge neutralization increases at all studied ion concentrations that, while associated with an increase in the number of direct ion-phosphate interactions, is fully accounted for by the monovalent K+ ions. Furthermore, K+ preferentially interacts with purine N7 atoms of helical regions in partially unfolded states, thereby potentially stabilizing the helical regions. Thus, both secondary helical structures and formation of tertiary structures leads to increased counterion condensation, thereby stabilizing those structural features of Twister. Notably, it is shown that K+ can act as a surrogate for Mg2+ by participating in specific interactions with nonsequential phosphate pairs that occur in the folded state, explaining the ability of Twister to self-cleave at submillimolar Mg2+ concentrations.

Modeling and validation of concentration dependence of ion exchange membrane permselectivity: Significance of convection and Manning's counter-ion condensation theory

Electrodialysis, reverse electrodialysis, and related electrochemical processes are increasingly important technologies for water purification and renewable energy generation and storage. The electrical efficiency of these processes is directly related to the permselectivity of the ion exchange membranes (IEMs) – defined as the extent to which the membrane permits the passage of counter-ions (ions of opposite charge to the membrane, e.g., cations for a cation exchange membrane) while blocking passage of co-ions. Permselectivity is not a material constant, but rather depends on the concentration and composition of the electrolyte solutions in contact with the IEM. Thus, even though permselectivity is routinely measured at standardized conditions (usually 0.5 M/0.1 M NaCl or KCl), the practical utility of such data is limited because we lack an accurate, quantitative way of using it to predict permselectivity under relevant process conditions. Moreover, the concentration dependence of IEM permselectivity has historically been studied primarily by evaluating the performance of (reverse) electrodialysis stacks rather than individual membranes, which has made it difficult to relate the concentration dependence of permselectivity to specific membrane characteristics. In this study, we measured the permselectivity of four commercial IEMs in six different concentration gradients employing 4 M and 0.5 M NaCl as the high salt concentration. We then constructed a predictive model of membrane permselectivity based on the extended Nernst-Planck equation and investigated how accounting for convection and electrostatic effects (via Manning's counter-ion condensation theory) affected model accuracy. We demonstrate that accurate, quantitative predictions of IEM permselectivity as a function of external salt concentrations are possible and require knowledge of only four easily measured membrane properties: water uptake, water permeability, charge, and thickness.

Describing ion exchange membrane-electrolyte interactions for high electrolyte concentrations used in electrochemical reactors

In this work we describe the application of thermodynamic approaches to evaluate the uptake of acids into ion exchange membranes under conditions of equilibration of the membranes with concentrated solutions. This situation is encountered in practical electrochemical reactor systems such as redox flow batteries (RFBs). First, we collect data describing that uptake for a series of acids in contact with perfluorosulfonic acid membranes. We then develop a treatment of the activity coefficients in such systems with a standard thermodynamic analysis of equilibrium between the solution and membrane phases. This is augmented by the Freeman-Manning counterion condensation approach. The latter fails to capture the behavior. As an alternative, based on the first part of the Freeman-Manning analysis we estimate the Donnan potential difference at the membrane surface. This parameter reliably captures the membrane behavior, with the potential tending toward the same constant value for the membrane exposed to different acids. The counterion condensation theory may provide insight into the evolution of the Donnan potential as a function of concentration in the low concentration regime. Finally, we comment on the possible development of this approach as a useful predictive parameter for membrane behavior in RFBs.

Preparation of alkylated chitosan-based polyelectrolyte hydrogels: The effect of monomer charge on polymerization

The objective of this work was to study the effect of the loading of monomers (cationic, anionic and ampholytes) in the preparation of polyelectrolyte hydrogels (PEHG) based on alkylated vinylated chitosan, in order to improve the understanding of the effect of ionic monomers on the polymerization of alkylated vinyl chitosan to obtain PEHGs. To achieve this, sequential synthesis of PEHGs was carried out starting from chitosan, glycidyl methacrylate (GMA) and ionic monomers: sodium 4-styrenesulfonate, [3-(methacryloylamino)propyl]dimethyl(3-sulfopropyl)ammonium hydroxide and 4-(vinylbenzyl)trimethylammonium chloride. The stages of synthesis were (a) chemical modification of the chitosan with N-(3-chloro-2-hydroxypropyl)-trimethylammonium chloride as an alkylating agent to obtain chitosan with positive charges, (b) insertion of vinyl side groups by opening the epoxide ring at pH 3.8 using GMA and (c) in situ polymerization of vinyl monomers in a polyelectrolyte aqueous solution (ACh-vinyl solution). Characterizations of the intermediate and PEHGs were performed. It was concluded that the different solution processes occurring in the reactor can be explained by counterion condensation theory in conjunction with Gibbs-Donnan equilibrium. The water absorption capacities of PEHGs were 144.6, 42.7, and 92.5 g H2O/g of dried HG for cationic, ampholyte, and anionic hydrogels, respectively.

Multi-block versus random quaternary ammonium Poly(arylene ether sulfone) membrane dependent water and alcohol mass uptake, directionally-dependent swelling and ion conductivity, and alcohol transport

Quaternary ammonium poly(arylene ether sulfone) copolymer random and multi-block ionomers were synthesized using multiple condensation reactions. Hydrophilic and hydrophobic block-length relationships were investigated with respect to directionally-dependent water swelling, hydroxyl conductivity, percolation-dependent properties, and alcohol transport. 1H nuclear magnetic resonance was used to evaluate brominated multi-block poly(arylene ether sulfone) composition, degree of functionalization, and ion-exchange capacity (IEC). These highly aminated ionomers did not display any counterion condensation associated with their conductivity as predicted by Oosawa-Manning Counterion Condensation Theory. Water-swollen quaternary ammonium poly(arylene ether sulfone) copolymer random and multi-block ionomers; and Nafion 117 membrane conductivity was modeled using Percolation Theory. In general, multi-block ionomer in-plane hydroxide conductivity was greater than its randomly functionalized counterpart at a similar IEC. Multi-block ionomer films with the largest hydrophilic block length (24k) exhibited a hydroxide conductivity of 62.1 mS/cm. An equivalent random copolymer's conductivity was 1.25 times lower. Multi-block and random copolymer's in-plane conductivity was 23.5% lower than its through-plane conductivity at an IEC greater than 2.02 meq/g. This decrease was strongly coupled with its swelling ratio and water uptake (WU). Increased swelling and water dilutes the available charge carriers responsible for through-plane conductivity. A percolation threshold at an IEC of 1.75 was observed for the random copolymer. Its maximum WU was 223 wt%. The multi-block ionomer's WU ranged between 172 wt% and 78.6 wt% at a similar IEC. Swelling suppression at high IEC was attributed to the sequential hydrophilic-hydrophobic block architecture. Multi-block ionomers with smaller hydrophilic block lengths appeared to inhibit alcohol transport more effectively than larger ones at the same IEC. Increasing block length led to greater water and alcohol uptake that was related to ion-domain size, alcohol polarity, and ionomer solubility parameter. Smaller hydrophilic block size was more effective at decreasing alcohol permeation at a similar ion-group concentration. This was attributed to reduced ion-domain cluster size not achievable with larger hydrophilic multiblock ionomers. These results suggest that block length has an important role in controlling ionomer swelling, and ion and alcohol transport, which is critical to fuel cells, and solid-state electrochemical devices.

Ion Condensation onto Ribozyme Is Site Specific and Fold Dependent

The highly charged RNA molecules, with each phosphate carrying a single negative charge, cannot fold into well-defined architectures with tertiary interactions in the absence of ions. For ribozymes, divalent cations are known to be more efficient than monovalent ions in driving them to a compact state, although Mg2+ ions are needed for catalytic activities. Therefore, how ions interact with RNA is relevant in understanding RNA folding. It is often thought that most of the ions are territorially and nonspecifically bound to the RNA, as predicted by the counterion condensation theory. Here, we show using simulations of Azoarcus ribozyme, based on an accurate coarse-grained three-site interaction model with explicit divalent and monovalent cations, that ion condensation is highly specific and depends on the nucleotide position. The regions with high coordination between the phosphate groups and the divalent cations are discernible even at very low Mg2+ concentrations when the ribozyme does not form tertiary interactions. Surprisingly, these regions also contain the secondary structural elements that nucleate subsequently in the self-assembly of RNA, implying that ion condensation is determined by the architecture of the folded state. These results are in sharp contrast to interactions of ions (monovalent and divalent) with rigid charged rods, in which ion condensation is uniform and position independent. The differences are explained in terms of the dramatic nonmonotonic shape fluctuations in the ribozyme as it folds with increasing Mg2+ or Ca2+ concentration.

Structure-Based Model of RNA Pseudoknot Captures Magnesium-Dependent Folding Thermodynamics.

We develop a simple, coarse-grained approach for simulating the folding of the Beet Western Yellow Virus (BWYV) pseudoknot toward the goal of creating a transferable model that can be used to study other small RNA molecules. This approach combines a structure-based model (SBM) of RNA with an electrostatic scheme that has previously been shown to correctly reproduce ionic condensation in the native basin. Mg2+ ions are represented explicitly, directly incorporating ion-ion correlations into the system, and K+ is represented implicitly, through the mean-field generalized Manning counterion condensation theory. Combining the electrostatic scheme with a SBM enables the electrostatic scheme to be tested beyond the native basin. We calibrate the SBM to reproduce experimental BWYV unfolding data by eliminating overstabilizing backbone interactions from the molecular contact map and by strengthening base pairing and stacking contacts relative to other native contacts, consistent with the experimental observation that relative helical stabilities are central determinants of the RNA unfolding sequence. We find that this approach quantitatively captures the Mg2+ dependence of the folding temperature and generates intermediate states that better approximate those revealed by experiment. Finally, we examine how our model captures Mg2+ condensation about the BWYV pseudoknot and a U-tail variant, for which the nine 3' end nucleotides are replaced with uracils, and find our results to be consistent with experimental condensation measurements. This approach can be easily transferred to other RNA molecules by eliminating and strengthening the same classes of contacts in the SBM and including generalized Manning counterion condensation.

Separation and Characterization of Highly Charged Polyelectrolytes Using Free-Solution Capillary Electrophoresis.

The characterization of statistical copolymers of various charge densities remains an important and challenging analytical issue. Indeed, the polyelectrolyte (PE) effective electrophoretic mobility tends to level off above a certain charge density, due to the occurrence of Manning counterion condensation. Surprisingly, we demonstrate in this work that it is possible to get highly resolutive separations of charged PE using free-solution capillary electrophoresis, even above the critical value predicted by the Manning counterion condensation theory. Full separation of nine statistical poly(acrylamide-co-2-acrylamido-2-methylpropanesulfonate) polymers of different charge densities varying between 3% and 100% was obtained by adjusting the ionic strength of the background electrolyte (BGE) in counter electroosmotic mode. Distributions of the chemical charge density could be obtained for the nine PE samples, showing a strong asymmetry of the distribution for the highest-charged PE. This asymmetry can be explained by the different reactivity ratios during the copolymerization. To shed more light on the separation mechanism, effective and apparent selectivities were determined by a systematic study and modeling of the electrophoretic mobility dependence according to the ionic strength. It is demonstrated that the increase in resolution with increasing BGE ionic strength is not only due to a closer matching of the electroosmotic flow magnitude with the PE electrophoretic effective mobility, but also to an increase of the dependence of the PE effective mobility according to the charge density.