Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model

Tuning phase compositions of MoS2 nanomaterials for enhanced heavy metal removal: performance and mechanism

Two-dimensional MoS₂ nanosheets have shown great potential in heavy metal remediation due to their unique properties. MoS₂ has two primary phases: 1T and 2H. Each has different physiochemical properties, but the impact of these differences on the overall material's heavy metal removal performance and associated mechanisms is rarely reported. In this study, we synthesized morphologically similar but phase-distinct MoS₂ samples via hydrothermal synthesis, which comprised dominantly either a metallic 1T phase or a semiconducting 2H phase. 1T-MoS₂ samples exhibited higher removal capacities for Ag⁺ and Pb²⁺ cations relative to 2H-MoS₂. In particular, an eight-fold increase in the Pb²⁺ adsorption capacity was observed in the 1T-MoS₂ samples (i.e. ∼632.9 mg g^-1) compared to the 2H-MoS₂ samples (∼81.6 mg g^-1). The mechanisms driving the enhanced performance of 1T-MoS₂ were investigated through detailed characterization of metal-laden MoS₂ samples and DFT modelling. We found that 1T-MoS₂ intrinsically had a larger interlayer spacing than 2H-MoS₂ because water molecules were retained between the hydrophilic 1T nanosheets during hydrothermal synthesis. The widened interlayer spacing in 1T-MoS₂ allowed the diffusion of heavy metal ions into the nanochannels, increasing the number of adsorption sites and total removal capacities. On the other hand, DFT modelling revealed the energy-favorable adsorption complex of Ag⁺ and Pb²⁺ for 1T-MoS₂, in which each metal atom was bonded with three S atoms leading to much higher adsorption energies relative to 2H-MoS₂ for Ag⁺ and Pb²⁺. This study unravels the underlying mechanisms of phase-dependent heavy metal remediation by MoS₂ nanosheets, providing an important guide for the use of 2D nanomaterials in environmental applications which include heavy metal removal, contaminant sensing, and membrane separation.

Theory of Weakly Polydisperse Cytoskeleton Filaments

Cytoskeleton filaments have the extraordinary ability to change conformations dynamically in response to alterations of the number density of actins/tubulin, the number density and type of binding agents, and the electrolyte concentration. This property is crucial for eukaryotic cells to achieve specific biological functions in different cellular compartments. Conventional approaches to biopolymers’ solution break down for cytoskeleton filaments because they entail several approximations to treat their polyelectrolyte and mechanical properties. In this article, we introduce a novel density functional theory for polydisperse, semiflexible cytoskeleton filaments. The approach accounts for the equilibrium polymerization kinetics, length and orientation filament distributions, as well as the electrostatic interaction between filaments and the electrolyte. This is essential for cytoskeleton polymerization in different cell compartments generating filaments of different lengths, sometimes long enough to become semiflexible. We characterized the thermodynamics properties of actin filaments in electrolyte aqueous solutions. We calculated the free energy, pressure, chemical potential, and second virial coefficient for each filament conformation. We also calculated the phase diagram of actin filaments’ solution and compared with the corresponding results in in vitro experiments.

Surface charging parameters of charged particles in symmetrical electrolyte solutions

Surface electric charge of dispersed particles is an essential determinant of physicochemical properties, coagulation and flocculation processes, and stability of colloidal solutions. Size-dependence of surface potential, charge density, and total surface charge of suspended charged particles has recently received attention in the literature. Despite the clear significance of understanding such dependence, very few studies have been devoted to this problem, with contradictory results of the relationship type. Currently, there is no analytical formula to represent explicit relationships between surface charging parameters and particle size. This research work is directed at development of accurate physics-based formulas for quantification of curvature-dependence of surface potential, surface charge density, and total surface charge for cylindrical and spherical charged particles immersed in a symmetrical electrolyte solution. First, a non-dimensional approach is adopted to simplify the problems, overcoming the difficulty of dealing with multiple influential variables. Then, to reduce the degrees of freedom of the problems under consideration, Gauss's law is combined with the condition of electro-neutrality in an electrical double layer (EDL). Next, the resulting complex integral equations are solved to construct characteristic curves and to express the dimensionless surface charging parameters explicitly as a function of the dimensionless particle radius. The new theoretical expressions are founded on approximate analytical and numerical solutions of the nonlinear Poisson-Boltzmann (PB) equation in cylindrical and spherical geometries. Afterwards, the solutions of the non-dimensionalized problems are dimensionalized to derive accurate explicit closed-form expressions, describing how surface charging parameters are related to the radius of a charged particle, properties of the solution, and thermodynamic conditions. These analytical formulas enable researchers to properly determine surface potential, surface charge density, total surface charge, and radius of dispersed particles by characterizing only one of them. Finally, the validity of the commonly-held hypothesis that surface charge density is independent of particle size is examined at the end of this study.

Shape dependence of thermodynamics of adsorption on nanoparticles: a theoretical and experimental study

Nanomaterials have excellent adsorption performance, which mainly depends on the adsorption thermodynamics that is related to the shape of the nanoparticles that make up the nanomaterial, but the effects of shape on the thermodynamics of adsorption are not fully clear. In this paper, theoretically, the general formulae of adsorption thermodynamic properties for nanoparticles with different shapes and different sizes were derived, and the influencing regularities and mechanisms on adsorption thermodynamic properties were discussed. Experimentally, the influences of the shape and size of nano-CeO2 on the thermodynamics of adsorption were studied in aqueous solution. The experiment results showed that the shape has significant influences on the thermodynamics of adsorption, and the smaller the particle size, the more significant the effects of shape on the thermodynamics. For the adsorption of nano-CeO2 with different shapes and the same equivalent particle size, compared with the sphere, the equilibrium constant of adsorption for the octahedron is larger, while the molar Gibbs free energy of adsorption , the molar adsorption enthalpy of adsorption and the molar adsorption entropy of adsorption are smaller. For the adsorption of nano-CeO2 with the same shape, with the decreasing particle size, increases, while , and decrease; and , , and are each linearly related to the reciprocal of particle size. The experimental results are consistent with the theoretical relations. The theories can quantitatively describe the adsorption behavior on nanoparticles, explain the regularities and mechanisms of influence of shape, and provide guidance for the research and application of nanoadsorption.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

A how-to approach for estimation of surface/Stern potentials considering ionic size and polarization

Based on the effects of ionic volume in Stern layer and polarization in diffuse layer, the relationship between surface potential and Stern potential is quantified.

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Quantitative assessment of the accuracy of the Poisson-Boltzmann cell model for salty suspensions

The cell model is a ubiquitous, fast, and relatively easily implemented model used to estimate the osmotic pressure of a colloidal dispersion. It has been shown to yield accurate approximations of the pressure in dispersions with a low salt content. It is generally accepted that it performs well when long-ranged interactions are involved and the structure of the dispersion is solidlike. The aim of the present work is to determine quantitatively the error committed by assuming the pressure computed with the cell model is the real osmotic pressure of a dispersion. To this end, cell model pressures are compared to a correct estimation of the actual pressures obtained from Poisson-Boltzmann Brownian dynamics simulations including many-body electrostatics and the thermal motion of the colloids. The comparison is performed for various colloidal sizes and charges, salt contents, and volume fractions. It is demonstrated that the accuracy of the cell model predictions is a function of only the average intercolloid distance scaled by Debye's length κd̅ and the normalized colloidal charge. The cell model is accurate for κd̅ < 1 and not reliable for κd̅ > 5 independently of the colloidal charge. In the 1 < κd̅ < 5 range, covering a wide set of experimental conditions, the colloidal surface charge has a large influence on the error associated with the cell approximation. The results presented in this article should provide a useful reference to determine a priori if the cell model can be expected to predict accurately an equation of state for a given set of physicochemical parameters.

Predicting ion-nucleic acid interactions by energy landscape-guided sampling

The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.

Predicting ion binding properties for RNA tertiary structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.

Salt-dependent folding energy landscape of RNA three-way junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg(2+) ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na(+) and Mg(2+) ion concentrations. For Mg(2+) solutions, the TBI model, which accounts for the Mg(2+) ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg(2+) in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.

A density functional theory for Lennard-Jones fluids in cylindrical pores and its applications to adsorption of nitrogen on MCM-41 materials

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.