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.     

Competitive Binding of Mg2+ and Na+ Ions to Nucleic Acids: From Helices to Tertiary Structures

Nucleic acids generally reside in cellular aqueous solutions with mixed divalent/monovalent ions, and the competitive binding of divalent and monovalent ions is critical to the structures of nucleic acids because of their polyanionic nature. In this work, we first proposed a general and effective method for simulating a nucleic acid in mixed divalent/monovalent ion solutions with desired bulk ion concentrations via molecular dynamics (MD) simulations and investigated the competitive binding of Mg²⁺/Na⁺ ions to various nucleic acids by all-atom MD simulations. The extensive MD-based examinations show that single MD simulations conducted using the proposed method can yield desired bulk divalent/monovalent ion concentrations for various nucleic acids, including RNA tertiary structures. Our comprehensive analyses show that the global binding of Mg²⁺/Na⁺ to a nucleic acid is mainly dependent on its structure compactness, as well as Mg²⁺/Na⁺ concentrations, rather than the specific structure of the nucleic acid. Specifically, the relative global binding of Mg²⁺ over Na⁺ is stronger for a nucleic acid with higher effective surface charge density and higher relative Mg²⁺/Na⁺ concentrations. Furthermore, the local binding of Mg²⁺/Na⁺ to a phosphate of a nucleic acid mainly depends on the local phosphate density in addition to Mg²⁺/Na⁺ concentrations.     

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.     

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.     

The ionic atmosphere around A-RNA: Poisson-Boltzmann and molecular dynamics simulations

The distributions of different cations around A-RNA are computed by Poisson-Boltzmann (PB) equation and replica exchange molecular dynamics (MD). Both the nonlinear PB and size-modified PB theories are considered. The number of ions bound to A-RNA, which can be measured experimentally, is well reproduced in all methods. On the other hand, the radial ion distribution profiles show differences between MD and PB. We showed that PB results are sensitive to ion size and functional form of the solvent dielectric region but not the solvent dielectric boundary definition. Size-modified PB agrees with replica exchange molecular dynamics much better than nonlinear PB when the ion sizes are chosen from atomistic simulations. The distribution of ions 14 Å away from the RNA central axis are reasonably well reproduced by size-modified PB for all ion types with a uniform solvent dielectric model and a sharp dielectric boundary between solvent and RNA. However, this model does not agree with MD for shorter distances from the A-RNA. A distance-dependent solvent dielectric function proposed by another research group improves the agreement for sodium and strontium ions, even for shorter distances from the A-RNA. However, Mg²⁺ distributions are still at significant variances for shorter distances.     

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.     

Ion Competition in Condensed DNA Arrays in the Attractive Regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt³⁺ Hexammine, or Co³⁺Hex) and one nonDNA-condensing ion (Mg²⁺) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co³⁺Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg²⁺, the Co³⁺Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg²⁺ and Co³⁺Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co³⁺Hex. It is also observed that only ∼20% DNA charge neutralization by Co³⁺Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.     

Effect of Mg<Superscript>2+</Superscript> versus Ca<Superscript>2+</Superscript> on the behavior of Annexin A5 in a membrane-bound state

Annexin A5 (AnxA5) binds to negatively charged phospholipid membranes in a Ca²⁺ dependent manner. Several studies already demonstrate that Mg²⁺ ions cannot induce the binding. In this paper, quartz crystal microbalance with dissipation monitoring (QCM-D), Brewster angle microscopy (BAM), polarization modulation infrared reflection absorption spectroscopy (PMIRRAS) and molecular dynamics (MD) were performed to elucidate the high specificity of Ca²⁺ versus Mg²⁺ on AnxA5 binding to membrane models. In the presence of Ca²⁺, AnxA5 showed a strong interaction with lipids, the protein is adsorbed mainly in α-helix under the DMPS monolayer, with an orientation of the α-helices axes slightly tilted with respect to the normal of the phospholipid monolayer as revealed by PMIRRAS. The Ca²⁺ ions interact strongly with the phosphate group of the phospholipid monolayer. In the presence of Mg²⁺, instead of Ca²⁺, no interaction of AnxA5 with lipids was detected. Molecular dynamics simulations allow us to explain the high specificity of calcium. Ca²⁺ ions are well exposed and surrounded by labile water molecules at the surface of the protein, which then favour their binding to the phosphate group of the membrane, explaining their specificity. To the contrary, Mg²⁺ ions are embedded in the protein structure, with a smaller number of water molecules strongly bound. We conclude that the embedded Mg²⁺ ions inside the AnxA5 structure are not able to link the protein to the phosphate group of the phospholipids for this reason.     

Ion Competition in Condensed DNA Arrays in the Attractive Regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt³⁺ Hexammine, or Co³⁺Hex) and one nonDNA-condensing ion (Mg²⁺) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co³⁺Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg²⁺, the Co³⁺Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg²⁺ and Co³⁺Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co³⁺Hex. It is also observed that only ∼20% DNA charge neutralization by Co³⁺Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.     

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.     

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), Mg²⁺ 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 Mg²⁺ ion concentrations. For Mg²⁺ solutions, the TBI model, which accounts for the Mg²⁺ ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg²⁺ 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.     

Microscopic insight to specificity of metal ion cofactor in DNA cleavage by restriction endonuclease EcoRV

Restriction endonucleases protect bacterial cells against bacteriophage infection by cleaving the incoming foreign DNA into fragments. In presence of Mg²⁺ ions, EcoRV is able to cleave the DNA but not in presence of Ca²⁺, although the protein binds to DNA in presence of both metal ions. We make an attempt to understand this difference using conformational thermodynamics. We calculate the changes in conformational free energy and entropy of conformational degrees of freedom, like DNA base pair steps and dihedral angles of protein residues in Mg²⁺(A)-EcoRV-DNA complex compared to Ca²⁺(S)-EcoRV-DNA complex using all-atom molecular dynamics (MD) trajectories of the complexes. We find that despite conformational stability and order in both complexes, the individual degrees of freedom behave differently in the presence of two different metal ions. The base pairs in cleavage region are highly disordered in Ca²⁺(S)-EcoRV-DNA compared to Mg²⁺(A)-EcoRV-DNA. One of the acidic residues ASP90, coordinating to the metal ion in the vicinity of the cleavage site, is conformationally destabilized and disordered, while basic residue LYS92 gets conformational stability and order in Ca²⁺(S) bound complex than in Mg²⁺(A) bound complex. The enhanced fluctuations hinder placement of the metal ion in the vicinity of the scissile phosphate of DNA. Similar loss of conformational stability and order in the cleavage region is observed by the replacement of the metal ion. Considering the placement of the metal ion near scissile phosphate as requirement for cleavage action, our results suggest that the changes in conformational stability and order of the base pair steps and the protein residues lead to cofactor sensitivity of the enzyme. Our method based on fluctuations of microscopic conformational variables can be applied to understand enzyme activities in other protein-DNA systems.     

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na⁺ and Mg²⁺) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na⁺ and Mg²⁺ concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.     

Improved model of hydrated calcium ion for molecular dynamics simulations using classical biomolecular force fields

Calcium ions (Ca²⁺) play key roles in various fundamental biological processes such as cell signaling and brain function. Molecular dynamics (MD) simulations have been used to study such interactions, however, the accuracy of the Ca²⁺ models provided by the standard MD force fields has not been rigorously tested. Here, we assess the performance of the Ca²⁺ models from the most popular classical force fields AMBER and CHARMM by computing the osmotic pressure of model compounds and the free energy of DNA–DNA interactions. In the simulations performed using the two standard models, Ca²⁺ ions are seen to form artificial clusters with chloride, acetate, and phosphate species; the osmotic pressure of CaAc₂ and CaCl₂ solutions is a small fraction of the experimental values for both force fields. Using the standard parameterization of Ca²⁺ ions in the simulations of Ca²⁺‐mediated DNA–DNA interactions leads to qualitatively wrong outcomes: both AMBER and CHARMM simulations suggest strong inter‐DNA attraction whereas, in experiment, DNA molecules repel one another. The artificial attraction of Ca²⁺ to DNA phosphate is strong enough to affect the direction of the electric field‐driven translocation of DNA through a solid‐state nanopore. To address these shortcomings of the standard Ca²⁺ model, we introduce a custom model of a hydrated Ca²⁺ ion and show that using our model brings the results of the above MD simulations in quantitative agreement with experiment. Our improved model of Ca²⁺ can be readily applied to MD simulations of various biomolecular systems, including nucleic acids, proteins and lipid bilayer membranes. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 752–763, 2016.     

Mg2+ Impacts the Twister Ribozyme through Push-Pull Stabilization of Nonsequential Phosphate Pairs

RNA molecules perform a variety of biological functions for which the correct three-dimensional structure is essential, including as ribozymes where they catalyze chemical reactions. Metal ions, especially Mg²⁺, neutralize these negatively charged nucleic acids and specifically stabilize RNA tertiary structures as well as impact the folding landscape of RNAs as they assume their tertiary structures. Specific binding sites of Mg²⁺ in folded conformations of RNA have been studied extensively; however, the full range of interactions of the ion with compact intermediates and unfolded states of RNA is challenging to investigate, and the atomic details of the mechanism by which the ion facilitates tertiary structure formation is not fully known. Here, umbrella sampling combined with oscillating chemical potential Grand Canonical Monte Carlo/molecular dynamics simulations are used to capture the energetics and atomic-level details of Mg²⁺-RNA interactions that occur along an unfolding pathway of the Twister ribozyme. The free energy profiles reveal stabilization of partially unfolded states by Mg²⁺, as observed in unfolding experiments, with this stabilization being due to increased sampling of simultaneous interactions of Mg²⁺ with two or more nonsequential phosphate groups. Notably, these results indicate a push-pull mechanism in which the Mg²⁺-RNA interactions actually lead to destabilization of specific nonsequential phosphate-phosphate interactions (i.e., pushed apart), whereas other interactions are stabilized (i.e., pulled together), a balance that stabilizes unfolded states and facilitates the folding of Twister, including the formation of hydrogen bonds associated with the tertiary structure. This study establishes a better understanding of how Mg²⁺-ion interactions contribute to RNA structural properties and stability.     

Reduced Model Captures Mg-RNA Interaction Free Energy of Riboswitches

The stability of RNA tertiary structures depends heavily on Mg²⁺. The Mg²⁺-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ₂₊, the number of excess Mg²⁺ associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg²⁺ ions interact closely and strongly with the RNA, unlike monovalent ions such as K⁺, suggesting that an explicit treatment of Mg²⁺ is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg²⁺-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg²⁺ through the explicit representation of Mg²⁺ ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K⁺ and models its competition with condensed Mg²⁺. The model contains one fitted parameter, the number of condensed K⁺ ions in the absence of Mg²⁺. Values of Γ₂₊ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ₂₊ to the Mg²⁺-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg²⁺ and RNA dynamics.     

Reduced Model Captures Mg2+-RNA Interaction Free Energy of Riboswitches

The stability of RNA tertiary structures depends heavily on Mg²⁺. The Mg²⁺-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ₂₊, the number of excess Mg²⁺ associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg²⁺ ions interact closely and strongly with the RNA, unlike monovalent ions such as K⁺, suggesting that an explicit treatment of Mg²⁺ is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg²⁺-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg²⁺ through the explicit representation of Mg²⁺ ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K⁺ and models its competition with condensed Mg²⁺. The model contains one fitted parameter, the number of condensed K⁺ ions in the absence of Mg²⁺. Values of Γ₂₊ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ₂₊ to the Mg²⁺-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg²⁺ and RNA dynamics.     

Determining the Functions of HIV-1 Tat and a Second Magnesium Ion in the CDK9/Cyclin T1 Complex: A Molecular Dynamics Simulation Study

The current paradigm of cyclin-dependent kinase (CDK) regulation based on the well-established CDK2 has been recently expanded. The determination of CDK9 crystal structures suggests the requirement of an additional regulatory protein, such as human immunodeficiency virus type 1 (HIV-1) Tat, to exert its physiological functions. In most kinases, the exact number and roles of the cofactor metal ions remain unappreciated, and the repertoire has thus gained increasing attention recently. Here, molecular dynamics (MD) simulations were implemented on CDK9 to explore the functional roles of HIV-1 Tat and the second Mg²⁺ ion at site 1 (Mg₁ ²⁺). The simulations unveiled that binding of HIV-1 Tat to CDK9 not only stabilized hydrogen bonds (H-bonds) between ATP and hinge residues Asp104 and Cys106, as well as between ATP and invariant Lys48, but also facilitated the salt bridge network pertaining to the phosphorylated Thr186 at the activation loop. By contrast, these H-bonds cannot be formed in CDK9 owing to the absence of HIV-1 Tat. MD simulations further revealed that the Mg₁ ²⁺ ion, coupled with the Mg₂ ²⁺ ion, anchored to the triphosphate moiety of ATP in its catalytic competent conformation. This observation indicates the requirement of the Mg₁ ²⁺ ion for CDK9 to realize its function. Overall, the introduction of HIV-1 Tat and Mg₁ ²⁺ ion resulted in the active site architectural characteristics of phosphorylated CDK9. These data highlighted the functional roles of HIV-1 Tat and Mg₁ ²⁺ ion in the regulation of CDK9 activity, which contributes an important complementary understanding of CDK molecular underpinnings.