88 Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamic simulation and Poisson–Boltzmann approach

Ion interactions with nucleic acids (both DNA and RNA) are an important and evolving field of investigation. Positively charged cations may interact with highly negatively charged nucleic acids via simple electrostatic interactions to help screen the electrostatic repulsion along the nucleic acids and assist their folding and/or compaction. Cations may also bind at specific sites and become integral parts of the structures, possibly playing important enzymatic roles. Two popular methods for computationally exploring a nucleic acid’s ion atmosphere are atomistic molecular dynamics (MD) simulations and the Poisson–Boltzmann (PB) equation. In general, monovalent ion results obtained from MD simulations and the PB equation agree well with experiment. However, Bai et al. (2007) observed discrepancies between experiment and the PB equation while examining the competitive binding of monovalent and divalent ions, with more significant discrepancies for divalent ions. The goal of this project was to thoroughly investigate monovalent (Na⁺) and divalent (Mg²⁺) ion distributions formed around a DNA duplex with MD simulations and the PB equation. We simulated three different cation concentrations, and matched the equilibrated bulk ion concentration for our theoretical calculations with the PB equation. Based on previous work, our Mg²⁺ ions were fully solvated, the expected state of Mg²⁺ ions when interacting with a duplex, when the production simulations began and remained throughout the simulations (Kirmizialtin, 2010; Robbins, 2012). Na⁺ ion distributions and number of Na⁺ ions within 10?Å of the DNA obtained from our two methods agreed well. However, results differed for Mg²⁺ ions, with a lower number of ions within the cut-off distance obtained from the PB equation when compared to MD simulations. The Mg²⁺ ion distributions around the DNA obtained via the two methods also differed. Based on our results, we conclude that the PB equation will systematically underestimate Mg²⁺ ions bound to DNA, and much of this deviation is attributed to dielectric saturation associated with high valency ions.     

Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamics simulation and a Poisson‐Boltzmann approach

The ion atmosphere created by monovalent (Na⁺) or divalent (Mg²⁺) cations surrounding a B‐form DNA duplex were examined using atomistic molecular dynamics (MD) simulations and the nonlinear Poisson‐Boltzmann (PB) equation. The ion distributions predicted by the two methods were compared using plots of radial and two‐dimensional cation concentrations and by calculating the total number of cations and net solution charge surrounding the DNA. Na⁺ ion distributions near the DNA were more diffuse in PB calculations than in corresponding MD simulations, with PB calculations predicting lower concentrations near DNA groove sites and phosphate groups and a higher concentration in the region between these locations. Other than this difference, the Na⁺ distributions generated by the two methods largely agreed, as both predicted similar locations of high Na⁺ concentration and nearly identical values of the number of cations and the net solution charge at all distances from the DNA. In contrast, there was greater disagreement between the two methods for Mg²⁺ cation concentration profiles, as both the locations and magnitudes of peaks in Mg²⁺ concentration were different. Despite experimental and simulation observations that Mg²⁺ typically maintains its first solvation shell when interacting with nucleic acids, modeling Mg²⁺ as an unsolvated ion during PB calculations improved the agreement of the Mg²⁺ ion atmosphere predicted by the two methods and allowed for values of the number of bound ions and net solution charge surrounding the DNA from PB calculations that approached the values observed in MD simulations. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 834–848, 2014.     

Mechanism of μ-Opioid Receptor-Magnesium Interaction and Positive Allosteric Modulation

In the era of opioid abuse epidemics, there is an increased demand for understanding how opioid receptors can be allosterically modulated to guide the development of more effective and safer opioid therapies. Among the modulators of the μ-opioid (MOP) receptor, which is the pharmacological target for the majority of clinically used opioid drugs, are monovalent and divalent cations. Specifically, the monovalent sodium cation (Na⁺) has been known for decades to affect MOP receptor signaling by reducing agonist binding, whereas the divalent magnesium cation (Mg²⁺) has been shown to have the opposite effect, notwithstanding the presence of sodium chloride. Although ultra-high-resolution opioid receptor crystal structures have revealed a specific Na⁺ binding site and molecular dynamics (MD) simulation studies have supported the idea that this monovalent ion reduces agonist binding by stabilizing the receptor inactive state, the putative binding site of Mg²⁺ on the MOP receptor, as well as the molecular determinants responsible for its positive allosteric modulation of the receptor, are unknown. In this work, we carried out tens of microseconds of all-atom MD simulations to investigate the simultaneous binding of Mg²⁺ and Na⁺ cations to inactive and active crystal structures of the MOP receptor embedded in an explicit lipid-water environment and confirmed adequate sampling of Mg²⁺ ion binding with a grand canonical Monte Carlo MD method. Analyses of these simulations shed light on 1) the preferred binding sites of Mg²⁺ on the MOP receptor, 2) details of the competition between Mg²⁺ and Na⁺ cations for specific sites, 3) estimates of binding affinities, and 4) testable hypotheses of the molecular mechanism underlying the positive allosteric modulation of the MOP receptor by the Mg²⁺ cation.     

Salt contribution to the flexibility of single‐stranded nucleic acid of finite length

Nucleic acids are negatively charged macromolecules and their structure properties are strongly coupled to metal ions in solutions. In this article, the salt effects on the flexibility of single‐stranded (ss) nucleic acid chain ranging from 12 to 120 nucleotides are investigated systematically by the coarse‐grained Monte Carlo simulations where the salt ions are considered explicitly and the ss chain is modeled with the virtual‐bond structural model. Our calculations show that, the increase of ion concentration causes the structural collapse of ss chain and multivalent ions are much more efficient in causing such collapse, and both trivalent/small divalent ions can induce more compact state than a random relaxation state. We found that monovalent, divalent, and trivalent ions can all overcharge ss chain, and the dominating source for such overcharging changes from ion‐exclusion‐volume effect to ion Coulomb correlations. In addition, the predicted Na⁺ and Mg²⁺‐dependent persistence length l_p’s of ss nucleic acid are in accordance with the available experimental data, and through systematic calculations, we obtained the empirical formulas for l_p as a function of [Na⁺], [Mg²⁺] and chain length. © 2012 Wiley Periodicals, Inc. Biopolymers 99: 370–381, 2013.     

Threshold Occupancy and Specific Cation Binding Modes in the Hammerhead Ribozyme Active Site are Required for Active Conformation

The relationship between formation of active in-line attack conformations and monovalent (Na⁺) and divalent (Mg²⁺) metal ion binding in hammerhead ribozyme (HHR) has been explored with molecular dynamics simulations. To stabilize repulsions between negatively charged groups, different requirements of the threshold occupancy of metal ions were observed in the reactant and activated precursor states both in the presence and in the absence of a Mg²⁺ in the active site. Specific bridging coordination patterns of the ions are correlated with the formation of active in-line attack conformations and can be accommodated in both cases. Furthermore, simulation results suggest that the HHR folds to form an electronegative recruiting pocket that attracts high local concentrations of positive charge. The present simulations help to reconcile experiments that probe the metal ion sensitivity of HHR catalysis and support the supposition that Mg²⁺, in addition to stabilizing active conformations, plays a specific chemical role in catalysis.     

Characterisation of charge distribution and stability of aptamer-thrombin binding interaction

Aptamers are single stranded nucleic acids with specific target-binding functionalities, biophysical and biochemical properties. The binding performance of aptamers to their cognate targets is influenced by the physicochemical conditions of the binding system particularly in relation to biomolecular charge distribution and hydrodynamic conformations in solution. Herein, we report the use of zeta potential measurements to characterise the surface charge distribution, biomolecular hydrodynamic size and the binding performance of a 15-mer thrombin binding aptamer (TBA) to thrombin under various physicochemical conditions of pH, temperature, monovalent (K⁺) and divalent (Mg²⁺) cation concentrations. Charge distribution analysis demonstrated time dependence in the formation of stable TBA-thrombin and TBA-thrombin-metal ion complexes. TBA was characterised to be most stable in pH above 9. The presence of monovalent and divalent metal ions reduced the electronegativity of TBA through electrostatic interactions, and this demonstrated to improve binding characteristics. TBA-thrombin complexes generated under different physicochemical conditions showed varying surface charge distributions. The stability of TBA-thrombin complex investigated using Scatchard analysis showed that the presence of K⁺ increased the binding performance by displaying a positive cooperativity relationship. The presence of Mg²⁺ showed a concave upward trend, potentially caused by heterogeneity in binding.     

Ion distributions around left- and right-handed DNA and RNA duplexes: a comparative study

The ion atmosphere around nucleic acids is an integral part of their solvated structure. However, detailed aspects of the ionic distribution are difficult to probe experimentally, and comparative studies for different structures of the same sequence are almost non-existent. Here, we have used large-scale molecular dynamics simulations to perform a comparative study of the ion distribution around (5′-CGCGCGCGCGCG-3′)₂ dodecamers in solution in B-DNA, A-RNA, Z-DNA and Z-RNA forms. The CG sequence is very sensitive to ionic strength and it allows the comparison with the rare but important left-handed forms. The ions investigated include Na⁺, K⁺ and Mg^{2 +}, with various concentrations of their chloride salts. Our results quantitatively describe the characteristics of the ionic distributions for different structures at varying ionic strengths, tracing these differences to nucleic acid structure and ion type. Several binding pockets with rather long ion residence times are described, both for the monovalent ions and for the hexahydrated Mg[(H₂O)₆]²⁺ ion. The conformations of these binding pockets include direct binding through desolvated ion bridges in the GpC steps in B-DNA and A-RNA; direct binding to backbone oxygens; binding of Mg[(H₂O)₆]²⁺ to distant phosphates, resulting in acute bending of A-RNA; tight ‘ion traps’ in Z-RNA between C-O2 and the C-O2′ atoms in GpC steps; and others.     

Predicting Ion Binding Properties for RNA Tertiary Structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg²⁺ 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 Mg²⁺ 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 Mg²⁺/Na⁺ ion-binding to various RNA and DNA structures over a wide range of Mg²⁺ and Na⁺ concentrations.     

Surface potential of phosphatidylserine monolayers. I. Divalent ion binding effect

Surface potentials of phosphatidylserine monolayers have been measured in the presence of different divalent ion concentrations in order to determine the way in which divalent ions bind to the membrane surface. The association constants for divalent ions (Mg²⁺, Ca²⁺ and Mn²⁺) with the phosphatidylserine membrane have been obtained from the experimental data and simple ion binding theory. The order of divalent ion binding to the membrane is Mn²⁺ > Ca²⁺ > Mg²⁺. However, none of the divalent ions used completely neutralized the negative charge of phosphatidylserine even at relatively high concentrations. The amounts of the divalent ions bound depended upon the concentration of the monovalent ions present in the subphase. It is suggested that the amounts of bound ions obtained from the use of radioisotope tracer methods may include a considerable contribution from the excess free ions in the double layer region of the phosphatidylserine membrane.     

Symmetric K+ and Mg2+ ion-binding sites in the 5S rRNA loop E inferred from molecular dynamics simulations

Potassium binding to the 5 S rRNA loop E motif has been studied by molecular dynamics at high (1.0 M) and low (0.2 M) concentration of added KCl in the presence and absence of Mg²⁺. A clear pattern of seven deep groove K⁺ binding sites or regions, in all cases connected with guanine N7/O6 atoms belonging to GpG, GpA, and GpU steps, was identified, indicating that the LE deep groove is significantly more ionophilic than the equivalent groove of regular RNA duplexes. Among all, two symmetry-related sites (with respect to the central G·A pair) were found to accommodate K⁺ ions with particularly long residence times. In a preceding molecular dynamics study by Auffinger et al. in the year 2003, these two sites were described as constituting important Mg²⁺ binding locations. Altogether, the data suggest that these symmetric sites correspond to the loop E main ion binding regions. Indeed, they are located in the deep groove of an important ribosomal protein binding motif associated with a fragile pattern of non-Watson-Crick pairs that has certainly to be stabilized by specific Mg²⁺ ions in order to be efficiently recognized by the protein. Besides, the other sites accommodate monovalent ions in a more diffuse way pointing out their lesser significance for the structure and function of this motif. Ion binding to the shallow groove and backbone atoms was generally found to be of minor importance since, at the low concentration, no well defined binding site could be characterized while high K⁺ concentration promoted mostly unspecific potassium binding to the RNA backbone. In addition, several K⁺ binding sites were located in positions equivalent to water molecules from the first hydration shell of divalent ions in simulations performed with magnesium, indicating that ion binding regions are able to accommodate both mono- and divalent ionic species. Overall, the simulations provide a more precise but, at the same time, a more intricate view of the relations of this motif with its ionic surrounding.     

Counterion exchange reactions on DNA: Monte Carlo and Poisson-Boltzmann analysis

In solutions containing DNA and cations of more than one type, the competitive interactions of these cations with DNA can be modeled as an ion exchange process that can be described quantitatively by means of the theoretical approach reported in this paper. Under conditions of experimental interest the radial distribution function of each type of counterion is calculated from the results of canonical Monte Carlo (MC) simulations using the primitive model for DNA (having a helical charge distribution) and for the electrolyte ions. These ions consist of monovalent coions, monovalent counterions intended to represent Na⁺, and counterions of a second type designated M^z+, having variable size and charge (z ≥ 1). The competitive association of these counterions with DNA is described in terms of D, a parameter analogous to an ion exchange equilibrium quotient. Values of D are calculated from the results of our MC simulations and compared with corresponding predictions of the Poisson–Boltzmann (PB) cell model and with results inferred from analyses of previously published nmr measurements. Over typical experimental concentration ranges (0.02M < [Na⁺] < 0.20M, 0.001 < [M^z+] < 0.160M), D^MC and D^PB both are predicted to be relatively independent of the bulk ion concentrations. For various specifications of the size and charge of the competing cation (M^z+), D^MC and D^PB exhibit similar trends, although the MC simulations consistently predict that the cations bearing a higher charge density than that of Na⁺ are somewhat stronger competitors than indicated by the PB calculations. For monovalent and divalent competitors of varying radii, theoretical predictions of D are compared with values obtained by fitting nmr measurements. If the hard-sphere radii specified in the simulations are the (hydrated) ionic radii determined from conductance measurements, then the MC predictions and the corresponding nmr results are in reasonable agreement for various monovalent competitors and for a divalent polyamine, but not for Ca²⁺ and Mg²⁺.     

Microsecond Molecular Dynamics Simulations of Mg2+- and K+- Bound E1 Intermediate States of the Calcium Pump

We have performed microsecond molecular dynamics (MD) simulations to characterize the structural dynamics of cation-bound E1 intermediate states of the calcium pump (sarcoendoplasmic reticulum Ca²⁺-ATPase, SERCA) in atomic detail, including a lipid bilayer with aqueous solution on both sides. X-ray crystallography with 40 mM Mg²⁺ in the absence of Ca²⁺ has shown that SERCA adopts an E1 structure with transmembrane Ca²⁺-binding sites I and II exposed to the cytosol, stabilized by a single Mg²⁺ bound to a hybrid binding site I′. This Mg²⁺-bound E1 intermediate state, designated E1•Mg²⁺, is proposed to constitute a functional SERCA intermediate that catalyzes the transition from E2 to E1•2Ca²⁺ by facilitating H⁺/Ca²⁺ exchange. To test this hypothesis, we performed two independent MD simulations based on the E1•Mg²⁺ crystal structure, starting in the presence or absence of initially-bound Mg²⁺. Both simulations were performed for 1 µs in a solution containing 100 mM K⁺ and 5 mM Mg²⁺ in the absence of Ca²⁺, mimicking muscle cytosol during relaxation. In the presence of initially-bound Mg²⁺, SERCA site I′ maintained Mg²⁺ binding during the entire MD trajectory, and the cytosolic headpiece maintained a semi-open structure. In the absence of initially-bound Mg²⁺, two K⁺ ions rapidly bound to sites I and I′ and stayed loosely bound during most of the simulation, while the cytosolic headpiece shifted gradually to a more open structure. Thus MD simulations predict that both E1•Mg²⁺ and E•2K⁺ intermediate states of SERCA are populated in solution in the absence of Ca²⁺, with the more open 2K⁺-bound state being more abundant at physiological ion concentrations. We propose that the E1•2K⁺ state acts as a functional intermediate that facilitates the E2 to E1•2Ca²⁺ transition through two mechanisms: by pre-organizing transport sites for Ca²⁺ binding, and by partially opening the cytosolic headpiece prior to Ca²⁺ activation of nucleotide binding.     

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.     

ADP binding to (Na + K)-activated ATPase

[¹⁴C]ADP binding to EDTA-washed ox brain cell membranes was increased by Na⁺, but decreased by K⁺, Mg²⁺ and Ca²⁺. Na⁺ abolished the effect of K⁺ on ADP binding by a competitive mechanism, but could not reverse the inhibitory action of Mg²⁺ and Ca²⁺. It is concluded that the cation-induced changes in ADP binding reflect properties of (Na⁺ + K⁺)-activated ATPase.     

Divalent cations and the phosphatase activity of the (Na + K)-dependent ATPase

Phosphatase activity of a kidney (Na + K)-ATPase preparation was optimally active with Mg²⁺ plus K⁺. Mn²⁺ was less effective and Ca²⁺ could not substitute for Mg²⁺. However, adding Ca²⁺ with Mg²⁺ or substituting Mn²⁺ for Mg²⁺ activated it appreciably in the absence of added K⁺, and all three divalent cations decreased apparent affinity for K⁺. Inhibition by Na⁺ decreased with higher Mg²⁺ concentrations, when Ca²⁺ was added, and when Mn²⁺ was substituted for Mg²⁺. Dimethyl sulfoxide, which favorsE ₂ conformations of the enzyme, increased apparent affinity for K⁺, whereas oligomycin, which favorsE ₁ conformations, decreased it. These observations are interpretable in terms of activation through two classes of cation sites. (i) At divalent cation sites, Mg²⁺ and Mn²⁺, favoring (under these conditions)E ₂ conformations, are effective, whereas Ca²⁺, favoringE ₁, is not, and monovalent cations complete. (ii) At monovalent cation sites divalent cations compete with K⁺, and although Ca²⁺ and Mn²⁺ are fairly effective, Mg²⁺ is a poor substitute for K⁺, while Na⁺ at these sites favorsE ₁ conformations. K⁺ increases theK _m for substrate, but both Ca²⁺ and Mn²⁺ decrease it, perhaps by competing with K⁺. On the other hand, phosphatase activity in the presence of Na⁺ plus K⁺ is stimulated by dimethyl sulfoxide, by higher concentrations of Mg²⁺ and Mn²⁺, but not by adding Ca²⁺; this is consistent with stimulation occurring through facilitation of an E₁ to E₂ transition, perhaps an E₁-P to E₂-P step like that in the (Na + K)-ATPase reaction sequence. However, oligomycin stimulates phosphatase activity with Mg²⁺ plus Na⁺ alone or Mg²⁺ plus Na⁺ plus low K⁺: this effect of oligomycin may reflect acceleration, in the absence of adequate K⁺, of an alternative E₂-P to E₁ pathway bypassing the monovalent cation-activated steps in the hydrolytic sequence.     

Monovalent ion stimulated adenosine triphosphatase from oat roots

Monovalent ion stimulated ATPase activity from oat (Avena sativa) roots has been found to be associated with various membrane fractions (cell wall, mitochondrial and microsomal) of oat roots. The ATPase requires Mg²⁺ (or Mn⁺²) but is further stimulated by K⁺ and other monovalent ions. The monovalent ions are ineffective in the absence of the divalent activating cation. The ATPase has been described with respect to monovalent ion specificity, temperature, pH, substrate specificity, and Mg²⁺ and K⁺ concentrations. It was further shown that oligomycin inhibits a part of the total ATPase activity and on the basis of the oligomycin sensitivity it appears that at least 2 membrane associated ATPases are being measured. The mitochondrial fraction is most sensitive to oligomycin and the microsomal fraction is least sensitive to oligomycin. The oligomycin insensitive ATPase appears to be stimulated more by K⁺ than the oligomycin sensitive ATPase.     

The effect of sodium on inorganic phosphate- and p-nitrophenyl phosphate-facilitated ouabain binding to (Na+ + K+)-activated ATPase

The effect of the hydrolysis product P_i and the artificial substrate p-nitrophenyl phosphate (p-nitrophenyl-P) on ouabain binding to (Na⁺ + K⁺)-activated ATPase was investigated.The hypothesis that (Mg²⁺ + p-nitrophenyl-P)-supported ouabain binding might be due to P_i release and thus (Mg²⁺ + P_i)-supported could not be confirmed.The enzyme · ouabain complexes obtained with different substrates were characterized according to their dissociation rates after removal of the ligands facilitating binding. The character of the enzyme · ouabain complex is determined primarily by the monovalent ion present during ouabain binding, but, qualitatively at least, it is immaterial whether binding was obtained with p-nitrophenyl phosphate or P_i.The presence or absence of Na⁺ during binding has a special influence upon the character of the enzyme · ouabain complex. Without Na⁺ and in the presence of Tris ions the complex obtained with (Mg²⁺ + P_i) and that obtained with (Mg²⁺ + p-nitrophenyl-P) behaved in a nearly identical manner, both exhibiting a slow decay. High Na⁺ concentration diminished the level of P_i-supported ouabain binding, having almost no effect on p-nitrophenyl phosphate-supported binding. Both enzyme · ouabain complexes, however, now resembled the form obtained with (Na⁺ + ATP), as judged from their dissociation rates and the K⁺ sensitivity of their decay. The complexes obtained at a high Na⁺ concentration underwent a very fast decay which could be slowed considerably after adding a low concentration of K⁺ to the resuspension medium. The most stable enzyme · ouabain complex was obtained in the presence of Tris ions only, irrespective of whether p-nitrophenyl phosphate or P_i facilitated complex formation. The presence of K⁺ gave rise to a complex whose dissociation rate was intermediate between those of the complexes obtained in the presence of Tris and a high Na⁺ concentration.It is proposed that the different ouabain dissociation rates reflect different reactive state of the enzyme. The resemblance between the observations obtained in phosphorylation and ouabain binding experiments is pointed out.     

Surface potential of phosphatidylserine monolayers II. Divalent and monovalent ion binding

Ion binding constants for phosphatidylserine membranes have been derived from the variation of the surface potential of phosphatidylserine monolayers with divalent cation concentrations in the presence of various monovalent salts in the aqueous subphase. The observed surface potential data for the monolayers, analyzed by use of the Gouy-Chapman diffuse potential theory, together with a simple binding reaction formula, yield, for Ca²⁺, Mg²⁺, Na⁺ and (Me)₄N⁺ binding constant values of 30 M^?1, 10 M^?1, 0.6 M^?1 and 0.05 M^?1, respectively. The effect of pH on surface potential of phosphatidylserine monolayers was found to be dependent upon ionic species other than H⁺ in the subphase solution. The distinction between apparent and intrinsic dissociation constants of H⁺ for biomolecules was made in terms of ion binding due to other ions at the same site as for H⁺ in biomolecules.     

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that $\text{ΔΔ}{G}_{\text{hyd}},$ the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and $\text{ΔΔ}{G}_{\text{hyd}}$ can reach ?2.0 kcal/mol and ?3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.