Calculations of the Absolute Free Energies of Binding between RNA and Metal Ions Using Molecular Dynamics Simulations and Continuum Electrostatics

Sensitivity of the RNA Structure to Ion Conditions as Probed by Molecular Dynamics Simulations of Common Canonical RNA Duplexes

RNA molecules play a key role in countless biochemical processes. RNA interactions, which are of highly diverse nature, are determined by the fact that RNA is a highly negatively charged polyelectrolyte, which leads to intimate interactions with an ion atmosphere. Although RNA molecules are formally single-stranded, canonical (Watson-Crick) duplexes are key components of folded RNAs. A double-stranded (ds) RNA is also important for the design of RNA-based nanostructures and assemblies. Despite the fact that the description of canonical dsRNA is considered the least problematic part of RNA modeling, the imperfect shape and flexibility of dsRNA can lead to imbalances in the simulations of larger RNAs and RNA-containing assemblies. We present a comprehensive set of molecular dynamics (MD) simulations of four canonical A-RNA duplexes. Our focus was directed toward the characterization of the influence of varying ion concentrations and of the size of the solvation box. We compared several water models and four RNA force fields. The simulations showed that the A-RNA shape was most sensitive to the RNA force field, with some force fields leading to a reduced inclination of the A-RNA duplexes. The ions and water models played a minor role. The effect of the box size was negligible, and even boxes with a small fraction of the bulk solvent outside the RNA hydration sphere were sufficient for the simulation of the dsRNA.

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.

Thermodynamics of Transition Metal Ion Binding to Proteins

Modeling the thermodynamics of a transition metal (TM) ion assembly be it in proteins or in coordination complexes affords us a better understanding of the assembly and function of metalloclusters in diverse application areas including metal organic framework design, TM-based catalyst design, the trafficking of TM ions in biological systems, and drug design in metalloprotein platforms. While the structural details of TM ions bound to metalloproteins are generally well understood via experimental and computational approaches, accurate studies describing the thermodynamics of TM ion binding are rare. Herein, we demonstrate that we can obtain accurate structural and absolute binding free energies of Co²⁺ and Ni²⁺ to the enzyme glyoxalase I using an optimized 12-6-4 (m12-6-4) potential. Critically, this model simultaneously reproduces the solvation free energy of the individual TM ions and reproduces the thermodynamics of TM ion-ligand coordination as well as the thermodynamics of TM ion binding to a protein active site unlike extant models. We find the incorporation of the thermodynamics associated with protonation state changes for the TM ion (un)binding to be crucial. The high accuracy of m12-6-4 potential in this study presents an accurate route to explore more complicated processes associated with TM cluster assembly and TM ion transport.

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 ΔΔG_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 ΔΔG_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.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

Ursolic acid and carvacrol may be potential inhibitors of dormancy protein small heat shock protein16.3 of Mycobacterium tuberculosis

Small heat shock protein16.3 (sHSP16.3) is a crucial protein for survival of Mycobacterium tuberculosis (MTB) in its host. Besides, this protein acts as a molecular chaperone during stress and is indispensable for MTB's growth, virulence and cell-wall thickening. sHSP16.3 is also a promising candidate for vaccine, serodiagnosis and drug design as well. In the present study, we have targeted sHSP16.3 with two phytochemicals, namely ursolic acid and carvacrol using in silico approach. Molecular docking analysis showed that both phytochemicals (ursolic acid and carvacrol) have docked with sHSP16.3 and shown tendency to inhibit the function of this vital protein of MTB. In addition, both compounds have exhibited strong compatibility with sHSP16.3 during whole 60 ns duration of molecular dynamics simulation. Further, the molecular mechanic/generalized Born/Poisson-Boltzmann surface area (MM/G/P/BSA) free energies were calculated which showed that both phytocompounds have stable and favourable binding energies causing strong binding with binding site of sHSP16.3. Taking together, the data of present study suggest that both phytocompounds may be potential inhibitor of sHSP16.3 of MTB and a best alternative to standard anti-tuberculosis drugs.

Structural characterization of CAS SH3 domain selectivity and regulation reveals new CAS interaction partners

CAS is a docking protein downstream of the proto-oncogene Src with a role in invasion and metastasis of cancer cells. The CAS SH3 domain is indispensable for CAS-mediated signaling, but structural aspects of CAS SH3 ligand binding and regulation are not well understood. Here, we identified the consensus CAS SH3 binding motif and structurally characterized the CAS SH3 domain in complex with ligand. We revealed the requirement for an uncommon centrally localized lysine residue at position +2 of CAS SH3 ligands and two rather dissimilar optional anchoring residues, leucine and arginine, at position +5. We further expanded the knowledge of CAS SH3 ligand binding regulation by manipulating tyrosine 12 phosphorylation and confirmed the negative role of this phosphorylation on CAS SH3 ligand binding. Finally, by exploiting the newly identified binding requirements of the CAS SH3 domain, we predicted and experimentally verified two novel CAS SH3 binding partners, DOK7 and GLIS2.

Direct binding of microRNA-21 pre-element with Regorafenib: An alternative mechanism for anti-colorectal cancer chemotherapy?

The Regorafenib is a broad-spectrum kinase inhibitor that has been approved to treat colorectal cancer (CRC). However, evidences have shown that the agent is also implicated in drug interaction with microRNA-21 (miR-21), an oncogenic miRNA which plays a key role in resisting programmed cell death in CRC cells. Here, we supposed that, instead of kinase inhibition, Regorafenib can directly bind to and then stabilize miR-21 pre-element, thus preventing RNase Dicer-meditated cleavage of the pre-element to mature miR-21. In order to verify the notion, an in silico-in vitro integrated investigation of the direct intermolecular interaction between Regorafenib and miR-21 pre-element was performed by using active pocket identification, RNA-ligand docking, molecular dynamics (MD) simulation, binding energetic analysis, and fluorescence-based assay. It was revealed that the Regorafenib can bind at the major groove-like stem region of miR-21 pre-element through three geometrically satisfactory hydrogen bonds (H-bonds) as well as a number of hydrophobic forces and π-π stacking, conferring strong specificity and high stability to the RNA-ligand complex system (K_d=0.73μM). Separate inversion mutation of two base pairs (G6C, C12G) and (A13U, U4A) that are involved in the H-bonding can considerably impair the affinity of Regorafenib to miR-21 pre-element, with K_d increase to 27 and 96μM, respectively. All these supported that Regorafenib can directly bind to miR-21 pre-element at molecular level and the binding mode can be properly modeled by using the proposed integrated strategy. This study would provide a potential, alternative mechanism for anti-colorectal cancer chemotherapy with Regorafenib.

The impact of surface area, volume, curvature, and Lennard-Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

Understanding the kinetic mechanism of RNA single base pair formation

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model.

A novel implicit solvent model for simulating the molecular dynamics of RNA

Although molecular dynamics simulations can be accelerated by more than an order of magnitude by implicitly describing the influence of the solvent with a continuum model, most currently available implicit solvent simulations cannot robustly simulate the structure and dynamics of nucleic acids. The difficulties become exacerbated especially for RNAs, suggesting the presence of serious physical flaws in the prior continuum models for the influence of the solvent and counter ions on the nucleic acids. We present a novel, to our knowledge, implicit solvent model for simulating nucleic acids by combining the Langevin-Debye model and the Poisson-Boltzmann equation to provide a better estimate of the electrostatic screening of both the water and counter ions. Tests of the model involve comparisons of implicit and explicit solvent simulations for three RNA targets with 20, 29, and 75 nucleotides. The model provides reasonable agreement with explicit solvent simulations, and directions for future improvement are noted.

Differential geometry based solvation model II: Lagrangian formulation

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.

Accurate prediction of the binding free energy and analysis of the mechanism of the interaction of replication protein A (RPA) with ssDNA

The eukaryotic replication protein A (RPA) has several pivotal functions in the cell metabolism, such as chromosomal replication, prevention of hairpin formation, DNA repair and recombination, and signaling after DNA damage. Moreover, RPA seems to have a crucial role in organizing the sequential assembly of DNA processing proteins along single stranded DNA (ssDNA). The strong RPA affinity for ssDNA, K(A) between 10(-9)-10(-10) M, is characterized by a low cooperativity with minor variation for changes on the nucleotide sequence. Recently, new data on RPA interactions was reported, including the binding free energy of the complex RPA70AB with dC(8) and dC(5), which has been estimated to be -10 ± 0.4 kcal mol(-1) and -7 ± 1 kcal mol(-1), respectively. In view of these results we performed a study based on molecular dynamics aimed to reproduce the absolute binding free energy of RPA70AB with the dC(5) and dC(8) oligonucleotides. We used several tools to analyze the binding free energy, rigidity, and time evolution of the complex. The results obtained by MM-PBSA method, with the use of ligand free geometry as a reference for the receptor in the separate trajectory approach, are in excellent agreement with the experimental data, with ±4 kcal mol(-1) error. This result shows that the MM-PB(GB)SA methods can provide accurate quantitative estimates of the binding free energy for interacting complexes when appropriate geometries are used for the receptor, ligand and complex. The decomposition of the MM-GBSA energy for each residue in the receptor allowed us to correlate the change of the affinity of the mutated protein with the ΔG(gas+sol) contribution of the residue considered in the mutation. The agreement with experiment is optimal and a strong change in the binding free energy can be considered as the dominant factor in the loss for the binding affinity resulting from mutation.

DESIGN OF HYBRID INHIBITORS TO HIV-1 PROTEASE

A series of HIV-1 protease (PR) inhibitors are designed to increase the binding affinity with PR subsites based on the quantum analysis of the contributions of molecular fragments in six FDA-approved PR drugs to the total binding interaction. The binding free energies were estimated by modified linear interaction energy approach [Zoete H, Michielin O, Karplus M, J Comput Aided Mol Des17:861, 2003], in which the binding free energy is written as a linear combination of the electrostatic interaction energy between PR and the ligand, Eelec, the van der Waals interaction energy between PR and the ligand, E vdW , and the difference of the solvation free energies of the complex, the receptor and the isolated ligand, ΔG solv . The parameters of these energy terms were fitted for a training set of 14 HIV-1 protease–inhibitor complexes of known 3D structure with a correlation coefficient of 0.91 and an unsigned mean error of 0.83 kcal/mol.

Computational study of bindings of HL9, a nonapeptide fragment of human lysozyme, to HIV-1 fusion protein gp41

HL9 is a nonapeptide fragment of human lysozyme which has been shown to have anti-HIV-1 activity in nanomolar concentration. This study aims to explain this inhibitory activity by using molecular dynamics (MD) simulation, focusing on the ectodomain of gp41, the envelope glycoprotein of HIV-1 crucial to membrane fusion. It was found that in HL9, two Trp residues separated by two others occupy the conserved hydrophobic pocket on gp41 and thus inhibit fusion in dominant-negative manner. Detailed HL9-gp41 binding interactions and free energies of binding were obtained through MD simulation and solvated interaction energies (SIE) calculation, giving a binding free energy of -8.25 kcal/mol which is in close agreement with the experimental value of -9.96 kcal/mol. Since C-helical region (C34) of gp41 also has two Trp residues separated by two others, this arrangement may be generalised and used to scan peptide library and to find those having similar manner of inhibition.

Bidentate RNA-magnesium clamps: on the origin of the special role of magnesium in RNA folding

Magnesium plays a special role in RNA function and folding. Although water is magnesium's most common first-shell ligand, the oxyanions of RNA have significant affinity for magnesium. Here we provide a quantum mechanical description of first-shell RNA-magnesium and DNA-magnesium interactions, demonstrating the unique features that characterize the energetics and geometry of magnesium complexes within large folded RNAs. Our work focuses on bidentate chelation of magnesium by RNA or DNA, where multiple phosphate oxyanions enter the first coordination shell of magnesium. These bidentate RNA clamps of magnesium occur frequently in large RNAs. The results here suggest that magnesium, compared to calcium and sodium, has an enhanced ability to form bidentate clamps with RNA. Bidentate RNA-sodium clamps, in particular, are unstable and spontaneously open. Due to magnesium's size and charge density it binds more intimately than other cations to the oxyanions of RNA, so that magnesium clamps are stabilized not only by electrostatic interactions, but also by charge transfer, polarization, and exchange interactions. These nonelectrostatic components of the binding are quite substantial with the high charge and small interatomic distances within the magnesium complexes, but are less pronounced for calcium due to its larger size, and for sodium due to its smaller charge. Additionally, bidentate RNA clamps of magnesium are more stable than those with DNA. The source of the additional stability of RNA complexes is twofold: there is a slightly attenuated energetic penalty for ring closure in the formation of RNA bidentate chelation complexes and elevated electrostatic interactions between the RNA and cations. In sum, it can be seen why sodium and calcium cannot replicate the structures or energetics of RNA-magnesium complexes.

Differential geometry based solvation model I: Eulerian formulation

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

MIBPB: a software package for electrostatic analysis

The Poisson-Boltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This article presents a matched interface and boundary (MIB)-based PBE software package, the MIBPB solver, for electrostatic analysis. The MIBPB has a unique feature that it is the first interface technique-based PBE solver that rigorously enforces the solution and flux continuity conditions at the dielectric interface between the biomolecule and the solvent. For protein molecular surfaces, which may possess troublesome geometrical singularities, the MIB scheme makes the MIBPB by far the only existing PBE solver that is able to deliver the second-order convergence, that is, the accuracy increases four times when the mesh size is halved. The MIBPB method is also equipped with a Dirichlet-to-Neumann mapping technique that builds a Green's function approach to analytically resolve the singular charge distribution in biomolecules in order to obtain reliable solutions at meshes as coarse as 1 Å--whereas it usually takes other traditional PB solvers 0.25 Å to reach similar level of reliability. This work further accelerates the rate of convergence of linear equation systems resulting from the MIBPB by using the Krylov subspace (KS) techniques. Condition numbers of the MIBPB matrices are significantly reduced by using appropriate KS solver and preconditioner combinations. Both linear and nonlinear PBE solvers in the MIBPB package are tested by protein-solvent solvation energy calculations and analysis of salt effects on protein-protein binding energies, respectively.

Computational exploration of mobile ion distributions around RNA duplex

Atomically detailed distributions of ions around an A-form RNA are computed. Different mixtures of monovalent and divalent ions are considered explicitly. Studies of tightly bound and of diffusive (but bound) ions around 25 base pairs RNA are conducted in explicit solvent. Replica exchange simulations provide detailed equilibrium distributions with moderate computing resources (20 ns of simulation using 64 replicas). The simulations show distinct behavior of single and double charged cations. Binding of Mg(2+) ion includes tight binding to specific sites while Na(+) binds only diffusively. The tight binding of Mg(2+) is with a solvation shell while Na(+) can bind directly to RNA. Negative mobile ions can be found near the RNA but must be assisted by proximate and mobile cations. At distances larger than 16 A from the RNA center, a model of RNA as charged rod in a continuum of ionic solution provides quantitative description of the ion density (the same as in atomically detailed simulation). At shorter distances, the structure of RNA (and ions) has a significant impact on the pair correlation functions. Predicted binding sites of Mg(2+) at the RNA surface are in accord with structures from crystallography. Electric field relaxation is investigated. The relaxation due to solution rearrangements is completed in tens of picoseconds, while the contribution of RNA tumbling continues to a few nanoseconds.

Mechanism of microRNA-target interaction: molecular dynamics simulations and thermodynamics analysis

MicroRNAs (miRNAs) are endogenously produced ∼21-nt riboregulators that associate with Argonaute (Ago) proteins to direct mRNA cleavage or repress the translation of complementary RNAs. Capturing the molecular mechanisms of miRNA interacting with its target will not only reinforce the understanding of underlying RNA interference but also fuel the design of more effective small-interfering RNA strands. To address this, in the present work the RNA-bound (Ago-miRNA, Ago-miRNA-target) and RNA-free Ago forms were analyzed by performing both molecular dynamics simulations and thermodynamic analysis. Based on the principal component analysis results of the simulation trajectories as well as the correlation analysis in fluctuations of residues, we discover that: 1) three important (PAZ, Mid and PIWI) domains exist in Argonaute which define the global dynamics of the protein; 2) the interdomain correlated movements are so crucial for the interaction of Ago-RNAs that they not only facilitate the relaxation of the interactions between residues surrounding the RNA binding channel but also induce certain conformational changes; and 3) it is just these conformational changes that expand the cavity of the active site and open putative pathways for both the substrate uptake and product release. In addition, by thermodynamic analysis we also discover that for both the guide RNA 5′-end recognition and the facilitated site-specific cleavage of the target, the presence of two metal ions (of Mg²⁺) plays a predominant role, and this conclusion is consistent with the observed enzyme catalytic cleavage activity in the ternary complex (Ago-miRNA-mRNA). Our results find that it is the set of arginine amino acids concentrated in the nucleotide-binding channel in Ago, instead of the conventionally-deemed seed base-paring, that makes greater contributions in stabilizing the binding of the nucleic acids to Ago.

One of the biggest surprises at the beginning of the ‘post-genome era’ was the discovery of numerous genes encoding microRNAs. The number of microRNA genes is estimated to be nearly 1% of that of protein-coding genes, which were found in genomes of such diverse organisms as Caenorhabditis elegans, Drosophila melanogaster, Arabidopsis thaliana, and Homo sapiens. Their products, tiny RNAs (miRNAs and siRNAs), are thought to bind to Argonaute (Ago) proteins and form effector complexes to direct mRNA cleavage or repress translation of complementary RNAs, during development, organogenesis, and very likely during many other processes. The cellular interactions between the miRNAs and their target RNAs associating with Ago are only beginning to be revealed, and details of this interaction mechanism at molecular level are still poorly understood. In this article we propose the possible mechanisms of miRNA-target interaction with special emphasis on their structural dynamic and thermodynamic aspects. The results of our model suggest the chemical and physical factors and effects that may be responsible for the miRNA-Ago assembly and miRNA-target recognition.

Binding selectivity of RecA to a single stranded DNA, a computational approach

Homologous recombination (HR) is the major DNA double strand break repair pathway which maintains the genomic integrity. It is fundamental for the survivability and functionality of all organisms. One of the initial steps in HR is the formation of the nucleoprotein filament composed by a single stranded DNA chain surrounded by the recombinases protein. The filament orchestrates the search for an undamaged homologue, as a template for the repair process. Our theoretical study was aimed at elucidating the selectivity of the interaction between a monomer of the recombinases enzyme in the Escherichia coli, EcRecA, the bacterial homologue of human Rad51, with a series of oligonucleotides of nine bases length. The complex, equilibrated for 20 ns with Langevian dynamics, was inserted in a periodic box with a 8 Å buffer of water molecules explicitly described by the TIP3P model. The absolute binding free energies are calculated in an implicit solvent using the Poisson-Boltzmann (PB) and the generalized Born (GB) solvent accessible surface area, using the MM-PB(GB)SA model. The solute entropic contribution is also calculated by normal mode analysis. The results underline how a significant contribution of the binding free energy is due to the interaction with the Arg196, a critical amino acid for the activity of the enzyme. The study revealed how the binding affinity of EcRecA is significantly higher toward dT₉ rather than dA₉, as expected from the experimental results.

A detailed binding free energy study of 2:1 ligand-DNA complex formation by experiment and simulation

In 2004, we used NMR to solve the structure of the minor groove binder thiazotropsin A bound in a 2:1 complex to the DNA duplex, d(CGACTAGTCG)2. In this current work, we have combined theory and experiment to confirm the binding thermodynamics of this system. Molecular dynamics simulations that use polarizable or non-polarizable force fields with single and separate trajectory approaches have been used to explore complexation at the molecular level. We have shown that the binding process invokes large conformational changes in both the receptor and ligand, which is reflected by large adaptation energies. This is compensated for by the net binding free energy, which is enthalpy driven and entropically opposed. Such a conformational change upon binding directly impacts on how the process must be simulated in order to yield accurate results. Our MM-PBSA binding calculations from snapshots obtained from MD simulations of the polarizable force field using separate trajectories yield an absolute binding free energy (-15.4 kcal mol(-1)) very close to that determined by isothermal titration calorimetry (-10.2 kcal mol(-1)). Analysis of the major energy components reveals that favorable non-bonded van der Waals and electrostatic interactions contribute predominantly to the enthalpy term, whilst the unfavorable entropy appears to be driven by stabilization of the complex and the associated loss of conformational freedom. Our results have led to a deeper understanding of the nature of side-by-side minor groove ligand binding, which has significant implications for structure-based ligand development.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Theoretical studies on the interaction of modified pyrimidines and purines with purine riboswitch

Recent experimental study [S.D. Gilbert, S.J. Mediatore, R.T. Batey, Modified pyrimidine specifically bind the purine riboswitch, J. Am. Chem. Soc. 128 (2006) 14214-14215] demonstrated that the purine riboswitch could specifically bind some ligands other than purines such as amino-pyrimidines, and the authors proposed that the five-membered ring of purine was not required for recognition. To get insight into the interaction details, we used molecular docking method to investigate the interactions of a mutant form of guanine riboswitch with a series of amino-purines, amino-pyrimidines and imidazole derivatives, and employed molecular simulation method to study the dynamic behavior of the selected complexes. The calculation results reveal that (1) all the amino-purines and amino-pyrimidines bind in a same cavity composed of four nucleobases including U22, U47, U51 and U74, which is consistent with the experimental results, while the two imidazole derivatives adopt other binding modes; (2) the purines are engulfed within three-way junction motifs, but most pyrimidines only form two-way junctions with the riboswitch; (3) the number and position of amino substituents could seriously affect the binding of pyrimidines. As riboswitches are potentially excellent candidates for antibiotic therapeutics, these findings may be useful for understanding the range of compounds that riboswitch can specifically recognize.

Assessing the performance of implicit solvation models at a nucleic acid surface

Implicit solvation models are popular alternatives to explicit solvent methods due to their ability to "pre-average" solvent behavior and thus reduce the need for computationally-expensive sampling. Previously, we have demonstrated that Poisson-Boltzmann models for polar solvation and integral-based models for nonpolar solvation can reproduce explicit solvation forces in a low-charge density protein system. In the present work, we examine the ability of these continuum models to describe solvation forces at the surface of a RNA hairpin. While these models do not completely describe all of the details of solvent behavior at this highly-charged biomolecular interface, they do provide a reasonable description of average solvation forces and therefore show significant promise for developing more robust implicit descriptions of solvent around nucleic acid systems for use in biomolecular simulation and modeling. Additionally, we observe fairly good transferability in the nonpolar model parameters optimized for protein systems, suggesting its robustness for modeling general nonpolar solvation phenomena in biomolecular systems.

Energetics of the human Tel-22 quadruplex-telomestatin interaction: a molecular dynamics study

The formation and stabilization of telomeric quadruplexes has been shown to inhibit the activity of telomerase, thus establishing telomeric DNA quadruplex as an attractive target for cancer therapeutic intervention. In this context, telomestatin, a G-quadruplex-specific ligand known to bind and stabilize G-quadruplex, is of great interest. Knowledge of the three-dimensional structure of telomeric quadruplex and its complex with telomestatin in solution is a prerequisite for structure-based rational drug design. Here, we report the relative stabilities of human telomeric quadruplex (AG3[T2AG3]3) structures under K+ ion conditions and their binding interaction with telomestatin, as determined by molecular dynamics simulations followed by energy calculations. The energetics study shows that, in the presence of K+ ions, mixed hybrid-type Tel-22 quadruplex conformations are more stable than other conformations. The binding free energy for quadruplex-telomestatin interactions suggests that 1:2 binding is favored over 1:1 binding. To further substantiate our results, we also calculated the change in solvent-accessible surface area (DeltaSASA) and heat capacity (DeltaCp) associated with 1:1 and 1:2 binding modes. The extensive investigation performed for quadruplex-telomestatin interaction will assist in understanding the parameters influencing the quadruplex-ligand interaction and will serve as a platform for rational drug design.

Binding of antifusion peptides with HIVgp41 from molecular dynamics simulations: quantitative correlation with experiment

Peptides based on C-terminal regions of the human immunodeficiency virus (HIV) viral protein gp41 represent an important new class of antiviral therapeutics called peptide fusion inhibitors. In this study, computational methods were used to model the binding of six peptides that contain residues that pack into a conserved hydrophobic pocket on HIVgp41, an attractive target site for the development of small molecule inhibitors. Free energies of binding were computed using molecular mechanics Generalized Born surface area (MM-GBSA) methods from molecular dynamics (MD) simulations, which employed either explicit (TIP3P) or continuum Generalized Born (GB) water models and strong correlations between experimental and computational affinities were obtained in both cases. Energy decomposition of the TIP3P-MD results (r2 = 0.75) reveals that variation in experimental affinity is highly correlated with changes in intermolecular van der Waals energies (deltaE(vdw)) on both a local (residue-based, r2 = 0.94) and global (peptide-based, r2 = 0.84) scale. The results show that differential association of C-peptides with HIVgp41 is driven solely by changes within the conserved pocket supporting the hypothesis that this region is an important drug target site. Such strong agreement with experiment is notable given the large size of the ligands (34 amino-acids) relative to the small range of experimental affinities (2 kcal/mol) and demonstrates good sensitivity of this computational method for simulating peptide fusion inhibitors. Finally, inspection of simulation trajectories identified a highly populated pi-type hydrogen bond, which formed between Gln575 on the receptor and the aromatic ring of peptide ligand Phe631, which could have important implications for drug design.

Protein-protein recognition and interaction hot spots in an antigen-antibody complex: free energy decomposition identifies "efficient amino acids"

The molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) method was applied to the study of the protein-protein complex between a camelid single chain variable domain (cAb-Lys3) and hen egg white lysozyme (HEL), and between cAb-Lys3 and turkey egg white lysozyme (TEL). The electrostatic energy was estimated by solving the linear Poisson-Boltzmann equation. A free energy decomposition scheme was developed to determine binding energy hot spots of each complex. The calculations identified amino acids of the antibody that make important contributions to the interaction with lysozyme. They further showed the influence of small structural variations on the energetics of binding and they showed that the antibody amino acids that make up the hot spots are organized in such a way as to mimic the lysozyme substrate. Through further analysis of the results, we define the concept of "efficient amino acids," which can provide an assessment of the binding potential of a particular hot spot interaction. This information, in turn, can be useful in the rational design of small molecules that mimic the antibody. The implications of using free energy decomposition to identify regions of a protein-protein complex that could be targeted by small molecules inhibitors are discussed.

Dynamics and assembly of the cytolethal distending toxin

The cytolethal distending toxin (CDT) is a widespread bacterial toxin that consists of an active subunit CdtB with nuclease activity and two ricin-like lectin domains, CdtA and CdtC, that are involved in the delivery of CdtB into the host cell. The three subunits form a tripartite complex that is required to achieve the fully active holotoxin. In the present study we investigate the assembly and dynamic properties of the CDT holotoxin using molecular dynamics simulations and binding free energy calculations. The results have revealed that CdtB likely adopts a different conformation in the unbound state with a closed DNA binding site. The two characterized structural elements of the aromatic patch and groove on the CdtA and CdtC protein surfaces exhibit high mobility, and free energy calculations show that the heterodimeric complex CdtA-CdtC, as well as the CdtA-CdtB and CdtB-CdtC sub-complexes are less energetically stable as compared to the binding in the tripartite complex. Analysis of the dynamical cross-correlation map reveals information on the correlated motions and long-range interplay among the CDT subunits associated with complex formation. Finally, the estimated binding free energies of subunit interactions are presented, together with the free energy decomposition to determine the contributions of residues for both binding partners, providing insight into the protein-protein interactions in the CDT holotoxin.

Molecular dynamics simulations of RNA: an in silico single molecule approach

RNA molecules are now known to be involved in the processing of genetic information at all levels, taking on a wide variety of central roles in the cell. Understanding how RNA molecules carry out their biological functions will require an understanding of structure and dynamics at the atomistic level, which can be significantly improved by combining computational simulation with experiment. This review provides a critical survey of the state of molecular dynamics (MD) simulations of RNA, including a discussion of important current limitations of the technique and examples of its successful application. Several types of simulations are discussed in detail, including those of structured RNA molecules and their interactions with the surrounding solvent and ions, catalytic RNAs, and RNA-small molecule and RNA-protein complexes. Increased cooperation between theorists and experimentalists will allow expanded judicious use of MD simulations to complement conceptually related single molecule experiments. Such cooperation will open the door to a fundamental understanding of the structure-function relationships in diverse and complex RNA molecules. .

Potential influence of Asp in the Ca2+ coordination position 5 of parvalbumin on the calcium-binding affinity: A computational study

Parvalbumins (PV) are calcium-binding proteins, all sharing the common helix-loop-helix (EF-hand) motif. This motif contains a central twelve-residue Ca(2+)-binding loop with the flanking helices positioned roughly perpendicular to each other. The precise role of these coordination residues has been the subject of intense studies. In this work, we focus on the coordination position 5 in the CD Ca(2+)-binding site of silver hake parvalbumin isoform B (SHPV-B). The most common residue at site 5 of calcium-binding loop in canonical EF-hands is Asp [B.J. Marsden, G.S. Shaw, B.D. Sykes, Biochem. Cell Biol. 68 (1990) 587-601], but in the CD site of PV, this position is almost always serine (Ser). The substitution of Ser with Asp will add the 5th carboxylate residue in the CD coordination sphere. However, as predicted by the acid pair hypothesis, the Ca(2+)-binding affinity would be maximized in an EF-hand motif that has four carboxylate ligands paired along the +/-x, and +/-z-axes [R.E. Reid, R.S. Hodges, J. Theor. Biol. 84 (1980) 401-444]. Molecular dynamics simulations and free energy calculations were employed to investigate the influence of Ser to Asp mutation at position 5 on calcium-binding affinity. We found that the Asp variant exhibited remarkable stability during the entire molecular dynamics simulation, with not only the retention of the Ca(2+)-binding site, but also increased compactness in the coordination sphere. The S55D fragment also accommodated Ca(2+) well. We conclude that the reason why Asp which is the most common residue at site 5 of calcium-binding loop in canonical EF-hands has never been identified at this position experimentally for PVs might be related to its physiological functions.

Mechanism of the difference in the binding affinity of E. coli tRNAGln to glutaminyl-tRNA synthetase caused by noninterface nucleotides in variable loop

Aminoacyl-tRNA synthetases (ARSs) distinguish their cognate tRNAs from many other kinds of tRNAs, despite the very similar tertiary structures of tRNAs. Many researchers have supported the view that this recognition is achieved by intermolecular interactions between tRNA and ARS. However, one of the aptamers of Escherichia coli glutamine specific tRNA, var-AGGU, has a higher affinity to ARS than the wild-type, although the sequence difference only lies in the variable loop located on the opposite side of the binding interface with ARS. To understand the reason for the difference in affinity, we did molecular dynamics simulations on tRNAs and their complexes with ARS. We calculated the enthalpic and entropic contributions to the binding free energy with the molecular mechanics-Poisson-Boltzmann/surface area method and found that the entropic difference plays an important role in the difference in binding free energies. During the molecular dynamics simulations, dynamic rearrangements of hydrogen bonds occurred in the tertiary core region of the wild-type tRNA, whereas they were not observed in the free var-AGGU simulation. Since the internal mobility was suppressed upon complex formation with ARS, the entropy loss in the wild-type was larger than that of the aptamer. We therefore concluded that the sequence difference in the variable loop caused the difference in the internal mobility of the tertiary core region tRNAs and led to the difference in the affinity to ARS through the entropy term.

Reducing CDK4/6-p16(INK4a) interface. Computational alanine scanning of a peptide bound to CDK6 protein

The tumor suppressor gene p16INK4a is commonly found altered in numerous and different types of cancer. The encoded protein arrests cell cycle in G1 phase by binding to CDK4 and CDK6, inhibiting their kinase function. In 1995, a 20-residue peptide, extracted from p16INK4a protein sequence, was discovered that retains the cell cycle inhibition properties of the endogenous tumor suppressor. However, its structure has not been determined yet. In this article, the features of a theoretical structure of the peptide bound to CDK6 are reported. The complex was modeled from CDK6-p16INK4a X-ray crystal structure and through molecular dynamics. Final structure was assessed by comparing computed binding free energy changes, when single-alanine substitutions were brought about on the peptide, to experimental data. Better concordance was obtained when including a high level of solvation effects. Solute-solvent vdW energy and electrostatic energy between solute and first shells of water, computed through a force field and considering explicit waters, were also to be included to achieve reasonably good concordance between theoretical and experimental data.

A molecular dynamics study and free energy analysis of complexes between the Mlc1p protein and two IQ motif peptides

The Mlc1p protein from the budding yeast Saccharomyces cerevisiae is a Calmodulin-like protein, which interacts with IQ-motif peptides located at the yeast's myosin neck. In this study, we report a molecular dynamics study of the Mlc1p-IQ2 protein-peptide complex, starting with its crystal structure, and investigate its dynamics in an aqueous solution. The results are compared with those obtained by a previous study, where we followed the solution structure of the Mlc1p-IQ4 protein-peptide complex by molecular dynamics simulations. After the simulations, we performed an interaction free-energy analysis using the molecular mechanics Poisson-Boltzmann surface area approach. Based on the dynamics of the Mlc1p-IQ protein-peptide complexes, the structure of the light-chain-binding domain of myosin V from the yeast S. cerevisiae is discussed.

Multiple binding modes of the camptothecin family to DNA oligomers

The binding constants of camptothecin, topotecan and its lactone ring-opened carboxylate derivative to DNA octamers were measured by UV and NMR spectroscopy. The self-association of topotecan (TPT) was also measured. The carboxylate form of TPT binds in the same way as the lactone, but more weakly. Titration of TPT into d(GCGATCGC)2 shows a preferred location stacked onto the terminal G1 base. However, the intermolecular NOEs cannot be reconciled with a single conformation of the complex, and suggest a model of a limited number of conformations in fast exchange. MD calculations on four pairs of starting structures with TPT stacked onto the G1-C8 base pair in different orientations were therefore performed. The use of selected experimental "docking" restraints yielded ten MD trajectories covering a wide conformational space. From a combination of calculated free energies, NOEs and chemical shifts, some of the structures produced could be eliminated, and it is concluded that the data are consistent with two major families of conformations in fast exchange. One of these is the conformation found in a crystal of a TPT/DNA/topoisomerase I ternary complex [Proc. Natl. Acad. Sci. USA 2002, 99, 15 387-15 392].

Structure and dynamics of an RNA tetraloop: a joint molecular dynamics and NMR study

Molecular dynamics simulations of the RNA tetraloop 5'-CGCUUUUGCG-3' with high melting temperature and significant conformational heterogeneity in explicit water solvent are presented and compared to NMR studies. The NMR data allow for a detailed test of the theoretical model, including the quality of the force field and the conformational sampling. Due to the conformational heterogeneity of the tetraloop, high temperature (350 K) and locally enhanced sampling simulations need to be invoked. The Amber98 force field leads to a good overall agreement with experimental data. Based on NMR data and a principal component analysis of the 350 K trajectory, the dynamic structure of the tetraloop is revealed. The principal component free energy surface exhibits four minima, which correspond to well-defined conformational structures that differ mainly by their base stacking in the loop region. No correlation between the motion of the sugar rings and the stacking dynamics of the loop bases is found.

Conformational dynamics of RNA-peptide binding: a molecular dynamics simulation study

Molecular dynamics simulations of the binding of the heterochiral tripeptide KkN to the transactivation responsive (TAR) RNA of HIV-1 is presented, using an all-atom force field with explicit water. To obtain starting structures for the TAR-KkN complex, semirigid docking calculations were performed that employ an NMR structure of free TAR RNA. The molecular dynamics simulations show that the starting structures in which KkN binds to the major groove of TAR (as it is the case for the Tat-TAR complex of HIV-1) are unstable. On the other hand, the minor-groove starting structures are found to lead to several binding modes, which are stabilized by a complex interplay of stacking, hydrogen bonding, and electrostatic interactions. Although the ligand does not occupy the binding position of Tat protein, it is shown to hinder the interhelical motion of free TAR RNA. The latter is presumably necessary to achieve the conformational change of TAR RNA to bind Tat protein. Considering the time evolution of the trajectories, the binding process is found to be ligand-induced and cooperative. That is, the conformational rearrangement only occurs in the presence of the ligand and the concerted motion of the ligand and a large part of the RNA binding site is necessary to achieve the final low-energy binding state.

Dynamic behavior of DNA base pairs containing 8-oxoguanine

The process by which DNA repair enzymes recognize and selectively excise damaged bases in duplex DNA is fundamental to our mechanistic understanding of these critical biological reactions. 8-Oxoguanine (8-oxoG) is the most common form of oxidative DNA damage; unrepaired, this lesion generates a G:C-->T:A mutation. Central to the recognition and repair of DNA damage is base extrusion, a process in which the damaged base lesion or, in some cases, its partner disengages from the helix and is bound to the enzyme's active site where base excision takes place. The conformation adopted by 8-oxoG in duplex DNA is affected by the base positioned opposite this lesion; conformational changes may also take place when the damaged base binds to its cognate repair enzyme. We performed unrestrained molecular dynamics simulations for several 13-mer DNA duplexes. Oligomers containing G:C and 8oxoG:C pairs adopted Watson-Crick geometries in stable B-form duplexes; 8oxoG showed increased local and global flexibility and a reduced barrier to base extrusion. Duplexes containing the G:A mismatch showed much larger structural fluctuations and failed to adopt a well-defined structure. For the 8oxoG:A mismatch that is recognized by the DNA glycosylase MutY, the damaged nucleoside underwent spontaneous and reproducible anti-->syn transitions. The syn conformation is thermodynamically preferred. Steric hindrance and unfavorable electrostatics associated with the 8oxoG O8 atom in the anti conformation were the major driving forces for this transition. Transition events follow two qualitatively different pathways. The overall anti-->syn transition rate and relative probability of the two transition paths were dependent on local sequence context. These simulations indicate that both the dynamic and equilibrium behavior of the duplex change as a result of oxidation; these differences may provide valuable new insight into the selective action of enzymes on damaged DNA.

Ions and RNA Folding

The problem of how ions influence the folding of RNA into specific tertiary structures is being addressed from both thermodynamic (by how much do different salts affect the free energy change of folding) and structural (how are ions arranged on or near an RNA and what kinds of environments do they occupy) points of view. The challenge is to link these different approaches in a theoretical framework that relates the energetics of ion-RNA interactions to the spatial distribution of ions. This review distinguishes three different kinds of ion environments that differ in the extent of direct ion-RNA contacts and the degree to which the ion hydration is perturbed, and summarizes the current understanding of the way each environment relates to the overall energetics of RNA folding.

Calculation of the binding free energy for magnesium-RNA interactions

The nature of the interaction between nucleic acids and divalent ions in solution is complex. It includes long-range electrostatic and short-range nonelectrostatic forces. Water molecules can be in an inner coordination shell that intervenes between the ion and its binding site. This work describes a method for calculating the binding free energy and applies it to a specific Mg-RNA system in the presence of monovalent salt. The approach combines high-level ab initio theory with Poisson-Boltzmann calculations and provides an accurate description of all terms of the binding free energy for magnesium ions located at the RNA surface (including nonelectrostatic interactions). Some alternative macroscopic approaches are also discussed.

Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method

A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment).

Efficiency of a second-generation HIV-1 protease inhibitor studied by molecular dynamics and absolute binding free energy calculations

A subnanomolar inhibitor of human immunodeficiency virus type 1 (HIV-1) protease, designated QF34, potently inhibits the wild-type and drug-resistant enzyme. To explain its broad activity, the binding of QF34 to the wild-type HIV-1 protease is investigated by molecular dynamics simulations and compared to the binding of two inhibitors that are used clinically, saquinavir (SQV) and indinavir (IDV). Analysis of the flexibility of protease residues and inhibitor segments in the complex reveals that segments of QF34 were more mobile during the dynamics studies than the segments of SQV and IDV. The dynamics of hydrogen bonding show that QF34 forms a larger number of stable hydrogen bonds than the two inhibitors that are used clinically. Absolute binding free energies were calculated with molecular mechanics-generalized Born surface area (MM-GBSA) methodology using three protocols. The most consistent results were obtained using the single-trajectory approach, due to cancellation of errors and inadequate sampling in the separate-trajectory protocols. For all three inhibitors, energy components in favor of binding include van der Waals and electrostatic terms, whereas polar solvation and entropy terms oppose binding. Decomposition of binding energies reveals that more protease residues contribute significantly to the binding of QF34 than to the binding of SQV and IDV. Moreover, contributions from protease main chains and side chains are balanced in the case of QF34 (52:48 ratio, respectively), whereas side chain contributions prevail in both SQV and IDV (main-chain:side-chain ratios of 41:59 and 45:55, respectively). The presented results help explain the ability of QF34 to inhibit multiple resistant mutants and should be considered in the design of broad-specificity second-generation HIV-1 protease inhibitors.