Structural Dynamics of the Methyl-Coenzyme M Reductase Active Site Are Influenced by Coenzyme F430 Modifications.

Methyl-coenzyme M reductase (MCR) is a central player in methane biogeochemistry, governing methanogenesis and the anaerobic oxidation of methane (AOM) in methanogens and anaerobic methanotrophs (ANME), respectively. The prosthetic group of MCR is coenzyme F430, a nickel-containing tetrahydrocorphin. Several modified versions of F430 have been discovered, including the 172-methylthio-F430 (mtF430) used by ANME-1 MCR. Here, we employ molecular dynamics (MD) simulations to investigate the active site dynamics of MCR from Methanosarcina acetivorans and ANME-1 when bound to the canonical F430 compared to 172-thioether coenzyme F430 variants and substrates (methyl-coenzyme M and coenzyme B) for methane formation. Our simulations highlight the importance of the Gln to Val substitution in accommodating the 172 methylthio modification in ANME-1 MCR. Modifications at the 172 position disrupt the canonical substrate positioning in M. acetivorans MCR. However, in some replicates, active site reorganization to maintain substrate positioning suggests that the modified F430 variants could be accommodated in a methanogenic MCR. We additionally report the first quantitative estimate of MCR intrinsic electric fields that are pivotal in driving methane formation. Our results suggest that the electric field aligned along the CH3-S-CoM thioether bond facilitates homolytic bond cleavage, coinciding with the proposed catalytic mechanism. Structural perturbations, however, weaken and misalign these electric fields, emphasizing the importance of the active site structure in maintaining their integrity. In conclusion, our results deepen the understanding of MCR active site dynamics, the enzyme's organizational role in intrinsic electric fields for catalysis, and the interplay between active site structure and electrostatics.

Base pair dynamics, electrostatics, and thermodynamics at the LTR-III quadruplex:duplex junction.

G-quadruplexes (GQs) play key regulatory roles within the human genome and have also been identified to play similar roles in other eukaryotes, bacteria, archaea, and viruses. Human immunodeficiency virus 1, the etiological agent of acquired immunodeficiency syndrome, can form two GQs in its long terminal repeat (LTR) promoter region, each of which act to regulate viral gene expression in opposing manners. The major LTR GQ, called LTR-III, is a distinct hybrid GQ containing a 12-nucleotide duplex loop attached to the quadruplex motif. The resulting quadruplex:duplex junction (QDJ) has been hypothesized to serve as a selective drug targeting site. To better understand the dynamics of this QDJ, we performed conventional and enhanced-sampling molecular dynamics simulations using the Drude-2017 force field. We observed unbiased and reversible formation of additional base pairs in the QDJ, between Ade4:Thy14 and Gua3:Thy14. Both base pairs were electrostatically favored, but geometric constraints within the junction may drive the formation of, and preference for, the Ade4:Thy14 base pair. Finally, we demonstrated that the base pairs are separated only by small energy barriers that may enable transitions between both base-paired states. Together, these simulations provide new insights into the dynamics, electrostatics, and thermodynamics of the LTR-III QDJ.

Pyroglutamylation modulates electronic properties and the conformational ensemble of the amyloid ß-peptide.

Alzheimer's disease (AD) is a neurodegenerative disorder that is characterized by the formation of extracellular amyloid-ß (Aß) plaques. The underlying cause of AD is unknown, however, post-translational modifications (PTMs) of Aß have been found in AD patients and are thought to play a role in protein aggregation. One such PTM is pyroglutamylation, which can occur at two sites in Aß, Glu3 and Glu11. This modification of Aß involves the truncation and charge-neutralization of N-terminal glutamate, causing Aß to become more hydrophobic and prone to aggregation. The molecular mechanism by which the introduction of pyroglutamate (pE) promotes aggregation has not been determined. To gain a greater understanding of the role that charge neutralization and truncation of the N-terminus plays on Aß conformational sampling, we used the Drude polarizable force field (FF) to perform molecular dynamics simulations on AßpE3-42 and AßpE11-42 and comparing their properties to previous simulations of Aß1-42. The Drude polarizable FF allows for a more accurate representation of electrostatic interactions, therefore providing novel insights into the role that charge plays in protein dynamics. Here, we report the parametrization of pE in the Drude polarizable FF and the effect of pyroglutamylation on Aß. We found that AßpE3-42 and AßpE11-42 alter the permanent and induced dipoles of the peptide. Specifically, we found that AßpE3-42 and AßpE11-42 have modification-specific backbone and sidechain polarization response and perturbed solvation properties that shift the Aß conformational ensemble.

Differences in Conformational Sampling and Intrinsic Electric Fields Drive Ion Binding in Telomeric and TERRA G-Quadruplexes.

The formation of G-quadruplexes (GQs) occurs in guanine-rich sequences of DNA and RNA, producing highly stable and structurally diverse noncanonical nucleic acid structures. GQs play crucial roles in regulating transcription, translation, and replication and maintaining the genome, among others; thus, changes to their structures can lead to diseases such as cancer. Previous studies using polarizable molecular dynamics simulations have shown differences in ion binding properties between telomeric and telomeric repeat-containing RNA GQs despite architectural similarities. Here, we used volume-based metadynamics and repulsive potential simulations in conjunction with polarizable force fields to quantify the impact of ion binding on the GQ dynamics and ion binding free energies. Furthermore, we describe how GQs exert electric fields on their surroundings to link dynamics with variations in the electronic structure. Our findings provide new insights into the energetic, physical, and conformational properties of GQs and expose subtle but important differences between DNA and RNA GQs with the same fold.

Differences in Conformational Sampling and Intrinsic Electric Fields Drive Ion Binding in Telomeric and TERRA G-Quadruplexes.

The formation of G-quadruplexes (GQs) occurs in guanine-rich sequences of DNA and RNA, producing highly stable and structurally diverse noncanonical nucleic acid structures. GQs play crucial roles in regulating transcription, translation, and replication; and maintaining the genome, among others, thus changes to their structures can lead to diseases such as cancer. Previous studies using polarizable molecular dynamics simulations have shown differences in ion binding properties between telomeric and TERRA GQs despite architectural similarities. Here, we used volume-based metadynamics and repulsive potential simulations in conjunction with polarizable force fields to quantify the impact of ion binding on GQ dynamics and ion binding free energies. Furthermore, we describe how GQs exert electric fields on their surroundings to link dynamics with variations in electronic structure. Our findings provide new insights into the energetic, physical, and conformational properties of GQs and expose subtle, but important, differences between DNA and RNA GQs with the same fold.

charmm2gmx: An Automated Method to Port the CHARMM Additive Force Field to GROMACS.

CHARMM is one of the most widely used biomolecular force fields. Although developed in close connection with a dedicated molecular simulation engine of the same name, it is also usable with other codes. GROMACS is a well-established, highly optimized, and multipurpose software for molecular dynamics, versatile enough to accommodate many different force field potential functions and the associated algorithms. Due to conceptional differences related to software design and the large amount of numeric data inherent to residue topologies and parameter sets, conversion from one software format to another is not straightforward. Here, we present an automated and validated means to port the CHARMM force field to a format read by the GROMACS engine, harmonizing the different capabilities of the two codes in a self-documenting and reproducible way with a bare minimum of user interaction required. Being based entirely on the upstream data files, the presented approach does not involve any hard-coded data, in contrast with previous attempts to solve the same problem. The heuristic approach used for perceiving the local internal geometry is directly applicable for analogous transformations of other force fields.

Monomeric and dimeric states of human ZO1-PDZ2 are functional partners of the SARS-CoV-2 E protein.

The Envelope (E) protein of SARS-CoV-2 plays a key role in virus maturation, assembly, and virulence mechanisms. The E protein is characterized by the presence of a PDZ-binding motif (PBM) at its C-terminus that allows it to interact with several PDZ-containing proteins in the intracellular environment. One of the main binding partners of the SARS-CoV-2 E protein is the PDZ2 domain of ZO1, a protein with a crucial role in the formation of epithelial and endothelial tight junctions (TJs). In this work, through a combination of analytical ultracentrifugation analysis and equilibrium and kinetic folding experiments, we show that ZO1-PDZ2 domain is able to fold in a monomeric state, an alternative form to the dimeric conformation that is reported to be functional in the cell for TJs assembly. Importantly, surface plasmon resonance (SPR) data indicate that the PDZ2 monomer is fully functional and capable of binding the C-terminal portion of the E protein of SARS-CoV-2, with a measured affinity in the micromolar range. Moreover, we present a detailed computational analysis of the complex between the C-terminal portion of E protein with ZO1-PDZ2, both in its monomeric conformation (computed as a high confidence AlphaFold2 model) and dimeric conformation (obtained from the Protein Data Bank), by using both polarizable and nonpolarizable simulations. Together, our results indicate both the monomeric and dimeric states of PDZ2 to be functional partners of the E protein, with similar binding mechanisms, and provide mechanistic and structural information about a fundamental interaction required for the replication of SARS-CoV-2.

An in silico approach to determine inter-subunit affinities in human septin complexes.

The septins are a conserved family of filament-forming guanine nucleotide binding proteins, often named the fourth component of the cytoskeleton. Correctly assembled septin structures are required for essential intracellular processes such as cytokinesis, vesicular transport, polarity establishment, and cellular adhesion. Structurally, septins belong to the P-Loop NTPases but they do not mediate signals to effectors through GTP binding and hydrolysis. GTP binding and hydrolysis are believed to contribute to septin complex integrity, but biochemical approaches addressing this topic are hampered by the stability of septin complexes after recombinant expression and the lack of nucleotide-depleted complexes. To overcome this limitation, we used a molecular dynamics-based approach to determine inter-subunit binding free energies in available human septin dimer structures and in their apo forms, which we generated in silico. The nucleotide in the GTPase active subunits SEPT2 and SEPT7, but not in SEPT6, was identified as a stabilizing element in the G interface. Removal of GDP from SEPT2 and SEPT7 results in flipping of a conserved Arg residue and disruption of an extensive hydrogen bond network in the septin unique element, concomitant with a decreased inter-subunit affinity. Based on these findings we propose a singular "lock-hydrolysis" mechanism stabilizing human septin filaments.

Effects of Familial Alzheimer's Disease Mutations on the Folding Free Energy and Dipole-Dipole Interactions of the Amyloid ß-Peptide.

Familial Alzheimer's disease (FAD) mutations of the amyloid ß-peptide (Aß) are known to lead to early onset and more aggressive Alzheimer's disease. FAD mutations such as "Iowa" (D23N), "Arctic" (E22G), "Italian" (E22K), and "Dutch" (E22Q) have been shown to accelerate Aß aggregation relative to the wild-type (WT). The mechanism by which these mutations facilitate increased aggregation is unknown, but each mutation results in a change in the net charge of the peptide. Previous studies have used nonpolarizable force fields to study Aß, providing some insight into how this protein unfolds. However, nonpolarizable force fields have fixed charges that lack the ability to redistribute in response to changes in local electric fields. Here, we performed polarizable molecular dynamics simulations on the full-length Aß42 of WT and FAD mutations and calculated folding free energies of the Aß15-27 fragment via umbrella sampling. By studying both the full-length Aß42 and a fragment containing mutations and the central hydrophobic cluster (residues 17-21), we were able to systematically study how these FAD mutations impact secondary and tertiary structure and the thermodynamics of folding. Electrostatic interactions, including those between permanent and induced dipoles, affected side-chain properties, salt bridges, and solvent interactions. The FAD mutations resulted in shifts in the electronic structure and solvent accessibility at the central hydrophobic cluster and the hydrophobic C-terminal region. Using umbrella sampling, we found that the folding of the WT and E22 mutants is enthalpically driven, whereas the D23N mutant is entropically driven, arising from a different unfolding pathway and peptide-bond dipole response. Together, the unbiased, full-length, and umbrella sampling simulations of fragments reveal that the FAD mutations perturb nearby residues and others in hydrophobic regions to potentially alter solubility. These results highlight the role electronic polarizability plays in amyloid misfolding and the role of heterogeneous microenvironments that arise as conformational change takes place.

Ion-Dependent Conformational Plasticity of Telomeric G-Hairpins and G-Quadruplexes.

Telomeric DNA is guanine-rich and can adopt structures such as G-quadruplexes (GQs) and G-hairpins. Telomeric GQs influence genome stability and telomerase activity, making understanding of enzyme-GQ interactions and dynamics important for potential drug design. GQs have a characteristic tetrad core, which is connected by loop regions. Within this architecture are G-hairpins, fold-back motifs that are thought to represent the first intermediate in GQ folding. To better understand the relationship between G-hairpin motifs and GQs, we performed polarizable simulations of a two-tetrad telomeric GQ and an isolated SC11 telomeric G-hairpin. The telomeric GQ contains a G-triad, which functions as part of the tetrad core or linker regions, depending on local conformational change. This triad and another motif below the tetrad core frequently bound ions and may represent druggable sites. Further, we observed the unbiased formation of a G-triad and a G-tetrad in simulations of the SC11 G-hairpin and found that cations can be partially hydrated while facilitating the formation of these motifs. Finally, we demonstrated that K+ ions form specific interactions with guanine bases, while Na+ ions interact nonspecifically with bases in the structure. Together, these simulations provide new insights into the influence of ions on GQs, G-hairpins, and G-triad motifs.

Impact of Electronic Polarization on Preformed, ß-Strand Rich Homogenous and Heterogenous Amyloid Oligomers.

Amyloids are a subset of intrinsically disordered proteins (IDPs) that self-assemble into cross-ß oligomers and fibrils. The structural plasticity of amyloids leads to sampling of metastable, low-molecular-weight oligomers that contribute to cytotoxicity. Of interest are amyloid-ß (Aß) and islet amyloid polypeptide (IAPP), which are involved in the pathology of Alzheimer's disease and Type 2 Diabetes Mellitus, respectively. In addition to forming homogenous oligomers and fibrils, these species have been found to cross-aggregate in heterogeneous structures. Biophysical properties, including electronic effects, that are unique or conserved between homogenous and heterogenous amyloids oligomers are thus far unexplored. Here, we simulated homogenous and heterogenous amyloid oligomers of Aß16-22 and IAPP20-29 fragments using the Drude oscillator model to investigate the impact of electronic polarization on the structural morphology and stability of preformed hexamers. Upon simulation of preformed, ß-strand rich oligomers with Drude, structural rearrangement occurred causing some loss of ß-strand structure in favor of random coil content for all oligomers. Homogenous Aß16-22 was the most stable system, deriving stability from low polarization in hydrophobic residues and through salt bridge formation. Changes in polarization were observed primarily for Aß16-22 residues in heterogenous cross-amyloid systems, displaying a decrease in charged residue dipole moments and an increase in hydrophobic sidechain dipole moments. This work is the first study utilizing the Drude-2019 force field with amyloid oligomers, providing insight into the impact of electronic effects on oligomer structure and highlighting the importance of different microenvironments on amyloid oligomer stability.

Electronic Polarization at the Interface between the p53 Transactivation Domain and Two Binding Partners.

Intrinsically disordered proteins (IDPs) are an abundant class of highly charged proteins that participate in numerous crucial biological processes, often in regulatory roles. IDPs do not have one major free energy minimum with a dominant structure, instead existing as conformational ensembles of multiple semistable conformations. p53 is a prototypical protein with disordered regions and binds to many structurally diverse partners, making it a useful model for exploring the role of electrostatic interactions at IDP binding interfaces. In this study, we used the Drude-2019 force field to simulate the p53 transactivation domain with two protein partners to probe the role of electrostatic interactions in IDP protein-protein interactions. We found that the Drude-2019 polarizable force field reasonably reproduced experimental chemical shifts of the p53 transactivation domain (TAD) in one complex for which these data are available. We also found that the proteins in these complexes displayed dipole response at specific residues of each protein and that residues primarily involved in binding showed a large percent change in dipole moment between the unbound and complexed states. Probing the role of electrostatic interactions in IDP binding can allow us greater fundamental understanding of these interactions and may help with targeting p53 or its partners for drug design.

TUPÃ: Electric field analyses for molecular simulations.

We introduce TUPÃ, a Python-based algorithm to calculate and analyze electric fields in molecular simulations. To demonstrate the features in TUPÃ, we present three test cases in which the orientation and magnitude of the electric field exerted by biomolecules help explain biological phenomena or observed kinetics. As part of TUPÃ, we also provide a PyMOL plugin to help researchers visualize how electric fields are organized within the simulation system. The code is freely available and can be obtained at https://mdpoleto.github.io/tupa/.

Integration of Experimental Data and Use of Automated Fitting Methods in Developing Protein Force Fields.

The development of accurate protein force fields has been the cornerstone of molecular simulations for the past 50 years. During this period, many lessons have been learned regarding the use of experimental target data and parameter fitting procedures. Here, we review recent advances in protein force field development. We discuss the recent emergence of polarizable force fields and the role of electronic polarization and areas in which additive force fields fall short. The use of automated fitting methods and the inclusion of additional experimental solution data during parametrization is discussed as a means to highlight possible routes to improve the accuracy of force fields even further.

CHARMM-GUI Drude prepper for molecular dynamics simulation using the classical Drude polarizable force field.

Explicit treatment of electronic polarizability in empirical force fields (FFs) represents an extension over a traditional additive or pairwise FF and provides a more realistic model of the variations in electronic structure in condensed phase, macromolecular simulations. To facilitate utilization of the polarizable FF based on the classical Drude oscillator model, Drude Prepper has been developed in CHARMM-GUI. Drude Prepper ingests additive CHARMM protein structures file (PSF) and pre-equilibrated coordinates in CHARMM, PDB, or NAMD format, from which the molecular components of the system are identified. These include all residues and patches connecting those residues along with water, ions, and other solute molecules. This information is then used to construct the Drude FF-based PSF using molecular generation capabilities in CHARMM, followed by minimization and equilibration. In addition, inputs are generated for molecular dynamics (MD) simulations using CHARMM, GROMACS, NAMD, and OpenMM. Validation of the Drude Prepper protocol and inputs is performed through conversion and MD simulations of various heterogeneous systems that include proteins, nucleic acids, lipids, polysaccharides, and atomic ions using the aforementioned simulation packages. Stable simulations are obtained in all studied systems, including 5 µs simulation of ubiquitin, verifying the integrity of the generated Drude PSFs. In addition, the ability of the Drude FF to model variations in electronic structure is shown through dipole moment analysis in selected systems. The capabilities and availability of Drude Prepper in CHARMM-GUI is anticipated to greatly facilitate the application of the Drude FF to a range of condensed phase, macromolecular systems.

Preparing and Analyzing Polarizable Molecular Dynamics Simulations with the Classical Drude Oscillator Model.

Molecular dynamics (MD) simulations performed with force fields that include explicit electronic polarization are becoming more prevalent in the field. The increasing emergence of these simulations is a result of continual refinement against a range of theoretical and empirical target data, optimization of software algorithms for higher performance, and availability of graphical processing unit hardware to further accelerate the simulations. Polarizable MD simulations are likely to be most impactful in biomolecular systems in which heterogeneous environments or unique microenvironments exist that would lead to inaccuracies in simulations performed with fixed-charge, nonpolarizable force fields. The further adoption of polarizable MD simulations will benefit from tutorial material that specifically addresses preparing and analyzing their unique features. In this chapter, we introduce common protocols for preparing routine biomolecular systems containing proteins, including both a globular protein in aqueous solvent and a transmembrane model peptide in a phospholipid bilayer. Details and example input files are provided for preparation of the simulation system using CHARMM, performing the simulations with OpenMM, and analyzing interesting dipole moment properties in CHARMM.

Cation competition and recruitment around the c-kit1 G-quadruplex using polarizable simulations.

Nucleic acid-ion interactions are fundamentally important to the physical, energetic, and conformational properties of DNA and RNA. These interactions help fold and stabilize highly ordered secondary and tertiary structures, such as G-quadruplexes (GQs), which are functionally relevant in telomeres, replication initiation sites, and promoter sequences. The c-kit proto-oncogene encodes for a receptor tyrosine kinase and is linked to gastrointestinal stromal tumors, mast cell disease, and leukemia. This gene contains three unique GQ-forming sequences that have proposed antagonistic effects on gene expression. The dominant GQ, denoted c-kit1, has been shown to decrease expression of c-kit transcripts, making the c-kit1 GQ a promising drug target. Toward disease intervention, more information is needed regarding its conformational dynamics and ion binding properties. Therefore, we performed molecular dynamics simulations of the c-kit1 GQ with K+, Na+, Li+, and mixed salt solutions using the Drude-2017 polarizable force field. We evaluated GQ structure, ion sampling, core energetics, ion dehydration and binding, and ion competition and found that each analysis supported the known GQ-ion specificity trend (K+ > Na+ > Li+). We also found that K+ ions coordinate in the tetrad core antiprismatically, whereas Na+ and Li+ align coplanar to guanine tetrads, partially because of their attraction to surrounding water. Further, we showed that K+ occupancy is higher around the c-kit1 GQ and its nucleobases than Na+ and Li+, which tend to interact with backbone and sugar moieties. Finally, we showed that K+ binding to the c-kit1 GQ is faster and more frequent than Na+ and Li+. Such descriptions of GQ-ion dynamics suggest the rate of dehydration as the dominant factor for preference of K+ by DNA GQs and provide insight into noncanonical nucleic acids for which little experimental data exist.

Recent developments in empirical atomistic force fields for nucleic acids and applications to studies of folding and dynamics.

Nucleic acids play critical roles in carrying genetic information, participating in catalysis, and preserving chromosomal structure. Despite over a century of study, efforts to understand the dynamics and structure-function relationships of DNA and RNA at the atomic level are still ongoing. Molecular dynamics (MD) simulations augment experiments by providing atomistic resolution and quantitative relationships between structure and conformational energy. Steady advancements in computer hardware, software, and atomistic force fields (FFs) over 40 years have facilitated new discoveries. Here, we review nucleic acid FF development with emphasis on recent refinements that have improved descriptions of important nucleic acid properties. We then discuss several key examples of successes and challenges in modeling nucleic acid structure and dynamics using the latest FFs.

Ion Binding Properties and Dynamics of the bcl-2 G-Quadruplex Using a Polarizable Force Field.

G-quadruplexes (GQs) are topologically diverse, highly thermostable noncanonical nucleic acid structures that form in guanine-rich sequences in DNA and RNA. GQs are implicated in transcriptional and translational regulation and genome maintenance, and deleterious alterations to their structures contribute to diseases such as cancer. The expression of the B-cell lymphoma 2 (Bcl-2) antiapoptotic protein, for example, is under transcriptional control of a GQ in the promoter of the bcl-2 gene. Modulation of the bcl-2 GQ by small molecules is of interest for chemotherapeutic development but doing so requires knowledge of the factors driving GQ folding and stabilization. To develop a greater understanding of the electrostatic properties of the bcl-2 promoter GQ, we performed molecular dynamics simulations using the Drude-2017 polarizable force field and compared relevant outcomes to the nonpolarizable CHARMM36 force field. Our simulation outcomes highlight the importance of dipole-dipole interactions in the bcl-2 GQ, particularly during the recruitment of a bulk K+ ion to the solvent-exposed face of the tetrad stem. We also predict and characterize an "electronegative pocket" at the tetrad-long loop junction that induces local backbone conformational change and may induce local conformational changes at cellular concentrations of K+. These outcomes suggest that moieties within the bcl-2 GQ can be targeted by small molecules to modulate bcl-2 GQ stability.

Polarizable Molecular Dynamics Simulations of Two c-kit Oncogene Promoter G-Quadruplexes: Effect of Primary and Secondary Structure on Loop and Ion Sampling.

G-quadruplexes (GQs) are highly ordered nucleic acid structures that play fundamental roles in regulating gene expression and maintaining genomic stability. GQs are topologically diverse and enriched in promoter sequences of growth regulatory genes and proto-oncogenes, suggesting that they may serve as attractive targets for drug design at the level of transcription rather than inhibiting the activity of the protein products of these genes. The c-kit promoter contains three adjacent GQ-forming sequences that have proposed antagonistic effects on gene expression and thus are promising drug targets for diseases such as gastrointestinal stromal tumors, mast cell disease, and leukemia. Because GQ stability is influenced by primary structure, secondary structure, and ion interactions, a greater understanding of GQ structure, dynamics, and ion binding properties is needed to develop novel, GQ-targeting therapeutics. Here, we performed molecular dynamics simulations to systematically study the c-kit2 and c-kit* GQs, evaluating nonpolarizable and polarizable force fields (FFs) and examining the effects of base substitutions and cation type (K+, Na+, and Li+) on the dynamics of their isolated and linked structures. We found that the Drude polarizable FF outperformed the additive CHARMM36 FF in two- and three-tetrad GQs and solutions of KCl, NaCl, and LiCl. Drude simulations with different cations agreed with the known GQ stabilization preference (K+ > Na+ > Li+) and illustrated that tetrad core-ion coordination differs as a function of cation type. Finally, we showed that differences in primary and secondary structure influence loop sampling, ion binding, and core-ion energetics of GQs.