Spontaneous Formation of KCl Aggregates in Biomolecular Simulations: A Force Field Issue?

Osmotic Force Balance Evaluation of Aqueous Electrolyte Osmotic Pressures and Chemical Potentials

Concentrated aqueous salt solutions are ubiquitous in problems of biological and environmental relevance. The development of accurate force fields that capture the interactions between dissolved species in solution is crucial to simulating these systems to gain molecular insights into the underlying processes under saline conditions. The osmotic pressure is a relatively simple thermodynamic property connecting the experimental and simulation measurements of the associative properties of the ions in solution. Milner [C. Gillespie and S. T. Milner, Soft Matter, 16, 9816 (2020)] proposed a simulation approach to evaluate the osmotic pressures of salts in solution by applying a restraint potential to the ions alone in solution and determining the resulting pressure required to balance that potential, referred to here as the osmotic force balance. Here, we expand Milner's approach, demonstrating that the chemical potentials of the salts in solution as a function of concentration can be fitted to the concentration profiles determined from simulation, additionally providing an analytical expression for the osmotic pressure. This approach is used to determine the osmotic pressures of 15 alkali halide salts in water from simulations. The cross interactions between cations and anions in solution are subsequently optimized to capture their experimental osmotic pressures.

Can molecular dynamics be used to simulate biomolecular recognition?

There are many problems in biochemistry that are difficult to study experimentally. Simulation methods are appealing due to direct availability of atomic coordinates as a function of time. However, direct molecular simulations are challenged by the size of systems and the time scales needed to describe relevant motions. In theory, enhanced sampling algorithms can help to overcome some of the limitations of molecular simulations. Here, we discuss a problem in biochemistry that offers a significant challenge for enhanced sampling methods and that could, therefore, serve as a benchmark for comparing approaches that use machine learning to find suitable collective variables. In particular, we study the transitions LacI undergoes upon moving between being non-specifically and specifically bound to DNA. Many degrees of freedom change during this transition and that the transition does not occur reversibly in simulations if only a subset of these degrees of freedom are biased. We also explain why this problem is so important to biologists and the transformative impact that a simulation of it would have on the understanding of DNA regulation.

Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.

Scaled charges for ions: An improvement but not the final word for modeling electrolytes in water

In this work, we discuss the use of scaled charges when developing force fields for NaCl in water. We shall develop force fields for Na⁺ and Cl^- using the following values for the scaled charge (in electron units): ±0.75, ±0.80, ±0.85, and ±0.92 along with the TIP4P/2005 model of water (for which previous force fields were proposed for q = ±0.85 and q = ±1). The properties considered in this work are densities, structural properties, transport properties, surface tension, freezing point depression, and maximum in density. All the developed models were able to describe quite well the experimental values of the densities. Structural properties were well described by models with charges equal to or larger than ±0.85, surface tension by the charge ±0.92, maximum in density by the charge ±0.85, and transport properties by the charge ±0.75. The use of a scaled charge of ±0.75 is able to reproduce with high accuracy the viscosities and diffusion coefficients of NaCl solutions for the first time. We have also considered the case of KCl in water, and the results obtained were fully consistent with those of NaCl. There is no value of the scaled charge able to reproduce all the properties considered in this work. Although certainly scaled charges are not the final word in the development of force fields for electrolytes in water, its use may have some practical advantages. Certain values of the scaled charge could be the best option when the interest is to describe certain experimental properties.

Computer Aided Development of Nucleic Acid Applications in Nanotechnologies

Utilization of nucleic acids (NAs) in nanotechnologies and nanotechnology-related applications is a growing field with broad application potential, ranging from biosensing up to targeted cell delivery. Computer simulations are useful techniques that can aid design and speed up development in this field. This review focuses on computer simulations of hybrid nanomaterials composed of NAs and other components. Current state-of-the-art molecular dynamics simulations, empirical force fields (FFs), and coarse-grained approaches for the description of deoxyribonucleic acid and ribonucleic acid are critically discussed. Challenges in combining biomacromolecular and nanomaterial FFs are emphasized. Recent applications of simulations for modeling NAs and their interactions with nano- and biomaterials are overviewed in the fields of sensing applications, targeted delivery, and NA templated materials. Future perspectives of development are also highlighted.

Lipid21: Complex Lipid Membrane Simulations with AMBER

We extend the modular AMBER lipid force field to include anionic lipids, polyunsaturated fatty acid (PUFA) lipids, and sphingomyelin, allowing the simulation of realistic cell membrane lipid compositions, including raft-like domains. Head group torsion parameters are revised, resulting in improved agreement with NMR order parameters, and hydrocarbon chain parameters are updated, providing a better match with phase transition temperature. Extensive validation runs (0.9 μs per lipid type) show good agreement with experimental measurements. Furthermore, the simulation of raft-like bilayers demonstrates the perturbing effect of increasing PUFA concentrations on cholesterol molecules. The force field derivation is consistent with the AMBER philosophy, meaning it can be easily mixed with protein, small molecule, nucleic acid, and carbohydrate force fields.

Influence of Monovalent Salts on α-Glycine Crystal Growth from Aqueous Solution: Molecular Dynamics Simulations at Constant Supersaturation Conditions

The growth of α-glycine crystals from aqueous solution is investigated at constant supersaturations by utilizing the constant chemical potential molecular dynamics method. The study considers two faces (010) and (011) that predominantly determine the α-glycine crystal morphology. The general Amber force field (GAFF) with two different charge sets derived from semi-empirical calculations using the complete neglect of differential overlap method (CNDO) and from density functional calculations using the double-numerical plus d- and p-polarization basis set (DNP) is applied to describe α-glycine. The extended simple point charge model is used to simulate water. It is observed that the GAFF/DNP set leads to a much slower integration of glycine molecules into the crystal structure than the GAFF/CNDO set. The GAFF/CNDO set, however, causes the growth even at concentrations well below the experimental solubility. For the GAFF/DNP set, the influence of potassium chloride (KCl) and sodium chloride (NaCl) on the face growth rates is investigated. The parameters recently proposed by Yagasaki et al. [J. Chem. Theory Comput. 2020, 16, 2460-2473] are used to describe salt ions, as standard GAFF parameters lead to the unexpected formation of salt clusters at a concentration lower than the experimental solubility value. According to our simulation results, both salts suppress the growth of the (011) and (010) faces. The inhibiting effect of NaCl is much stronger than that of KCl for the (011) face, while both salts have a similar inhibiting effect on the (010) face. The results are in line with the experimental observations of the impact of salt ions on the α-glycine growth rates for the (011) face reported in literature.

Molecular Dynamics Simulations of Nanostructures Formed by Hydrophobins and Oil in Seawater

Classical molecular dynamics simulations using the Martini coarse-grained force field were performed to study oil nanodroplets surrounded by fungal hydrophobin (HP) proteins in seawater. The class I EAS and the class II HFBII HPs were studied along with two model oils, namely, benzene and n-decane. Both HPs exhibit free energy minima at the oil-seawater interface, which is deeper in benzene compared to the n-decane systems. Larger constraint forces are required to keep both HPs within the n-decane phase compared to inside benzene, with HFBII being more affine to benzene compared to EAS. Smaller surface tensions are observed at benzene-seawater interfaces coated with HPs compared to their n-decane counterparts. In the latter the surface tension remains unchanged upon increases in the concentration of HPs, whereas in benzene systems adding more HPs lead to decreases in surface tension. EAS has a larger tendency to cluster together in the interface compared to HFBII, with both HPs having larger coordination numbers when surrounding benzene droplets compared to when they are around n-decane nanoblobs. The HP-oil nanostructures in seawater examined have radii of gyration ranging between 2 and 12 nm, where the n-decane structures are larger and have more irregular shapes compared to the benzene systems. The n-decane molecules within the nanostructures form a compact spherical core, with the HPs partially covering its surface and clustering together, conferring irregular shapes to the nanostructures. The EAS with n-decane structures are larger and have more irregular shapes compared to their HFBII counterparts. In contrast, in the HP-benzene structures both HPs tend to penetrate the oil part of the droplet. The HFBII-benzene structures having the larger oil/HP ratios examined tend to be more compact and spherical compared to their EAS counterparts; however, some of the HFBII-benzene systems that have smaller oil/HP ratios have a more elongated structure compared to their EAS counterparts. This simulation study provides insights into HP-oil nanostructures that are smaller than the oil droplets and gas bubbles recently studied in experiments and, thus, might be challenging to examine with experimental techniques.

Pressure in Molecular Simulations with Scaled Charges. 1. Ionic Systems

Charge scaling, rationalized as MDEC (molecular dynamics in electronic continuum) or ECC (electronic continuum correction), has become a widely used simple approach to how to avoid self-consistent induced dipoles yet approximately take into account the effects of electronic polarizability. It has been assumed that the continuum permittivity does not depend on density; in turn, pressure is calculated by standard formulas. In this work, we elaborate a complementary approximation of density-independent molecular polarizability and derive formulas for pressure corrections within the MDEC framework; real behavior lies between these two extremes. The pressure corrections for test ionic systems are huge and negative, leading to sizable densities in constant-pressure MDEC simulations. A comparison of MDEC results with equivalent polarizable systems gives a good pressure match for a crystal but very low MDEC pressures for ionic liquids. These results witness about the importance of a correct density dependence not only of continuum permittivity in MDEC simulations but also of polarizability in polarizable simulations.

Dielectric constant and density of aqueous alkali halide solutions by molecular dynamics: A force field assessment

The concentration dependence of the dielectric constant and the density of 11 aqueous alkali halide solutions (LiCl, NaCl, KCl, RbCl, CsCl, LiI, NaI, KI, CsI, KF, and CsF) is investigated by molecular simulation. Predictions using eight non-polarizable ion force fields combined with the TIP4P/ε water model are compared to experimental data. The influence of the water model and the temperature on the results for the NaCl brine are also addressed. The TIP4P/ε water model improves the accuracy of dielectric constant predictions compared to the SPC/E water model. The solution density is predicted well by most ion models. Almost all ion force fields qualitatively capture the decline of the dielectric constant with the increase of concentration for all solutions and with the increase of temperature for NaCl brine. However, the sampled dielectric constant is mostly in poor quantitative agreement with experimental data. These results are related to the microscopic solution structure, ion pairing, and ultimately the force field parameters. Ion force fields with excessive contact ion pairing and precipitation below the experimental solubility limit generally yield higher dielectric constant values. An adequate reproduction of the experimental solubility limit should therefore be a prerequisite for further investigations of the dielectric constant of aqueous electrolyte solutions by molecular simulation.

Lennard-Jones Parameters Determined to Reproduce the Solubility of NaCl and KCl in SPC/E, TIP3P, and TIP4P/2005 Water

Most classical nonpolarizable ion potential models underestimate the solubility values of NaCl and KCl in water significantly. We determine Lennard-Jones parameters of Na⁺, K⁺, and Cl^- that reproduce the solubility as well as the hydration free energy in dilute aqueous solutions for three water potential models, SPC/E, TIP3P, and TIP4P/2005. The ion-oxygen distance in the solution and the cation-anion distance in salt are also considered in the parametrization. In addition to the target properties, the hydration enthalpy, hydration entropy, self-diffusion coefficient, coordination number, lattice energy, enthalpy of solution, density, viscosity, and number of contact ion pairs are calculated for comparison with 17 frequently used or recently developed ion potential models. The overall performance of each ion model is represented by a global score using a scheme that was originally developed for comparison of water potential models. The global score is better for our models than for the other 17 models not only because of the quite good prediction for the solubility but also because of the relatively small deviation from the experimental value for many of the other properties.

A force field of Li+, Na+, K+, Mg2+, Ca2+, Cl-, and SO4 2- in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions

In this work, a force field for several ions in water is proposed. In particular, we consider the cations Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ and the anions Cl^- and SO₄ ^2-. These ions were selected as they appear in the composition of seawater, and they are also found in biological systems. The force field proposed (denoted as Madrid-2019) is nonpolarizable, and both water molecules and sulfate anions are rigid. For water, we use the TIP4P/2005 model. The main idea behind this work is to further explore the possibility of using scaled charges for describing ionic solutions. Monovalent and divalent ions are modeled using charges of 0.85 and 1.7, respectively (in electron units). The model allows a very accurate description of the densities of the solutions up to high concentrations. It also gives good predictions of viscosities up to 3 m concentrations. Calculated structural properties are also in reasonable agreement with the experiment. We have checked that no crystallization occurred in the simulations at concentrations similar to the solubility limit. A test for ternary mixtures shows that the force field provides excellent performance at an affordable computer cost. In summary, the use of scaled charges, which could be regarded as an effective and simple way of accounting for polarization (at least to a certain extend), improves the overall description of ionic systems in water. However, for purely ionic systems, scaled charges will not adequately describe neither the solid nor the melt.

Glass polymorphism and liquid-liquid phase transition in aqueous solutions: experiments and computer simulations

One of the most intriguing anomalies of water is its ability to exist as distinct amorphous ice forms (glass polymorphism or polyamorphism). This resonates well with the possible first-order liquid-liquid phase transition (LLPT) in the supercooled state, where ice is the stable phase. In this Perspective, we review experiments and computer simulations that search for LLPT and polyamorphism in aqueous solutions containing salts and alcohols. Most studies on ionic solutes are devoted to NaCl and LiCl; studies on alcohols have mainly focused on glycerol. Less attention has been paid to protein solutions and hydrophobic solutes, even though they reveal promising avenues. While all solutions show polyamorphism and an LLPT only in dilute, sub-eutectic mixtures, there are differences regarding the nature of the transition. Isocompositional transitions for varying mole fractions are observed in alcohol but not in ionic solutions. This is because water can surround alcohol molecules either in a low- or high-density configuration whereas for ionic solutes, the water ion hydration shell is forced into high-density structures. Consequently, the polyamorphic transition and the LLPT are prevented near the ions, but take place in patches of water within the solutions. We highlight discrepancies and different interpretations within the experimental community as well as the key challenges that need consideration when comparing experiments and simulations. We point out where reinterpretation of past studies helps to draw a unified, consistent picture. In addition to the literature review, we provide original experimental results. A list of eleven open questions that need further consideration is identified.

Development of Nonbonded Models for Metal Cations Using the Electronic Continuum Correction

The parametrization of classical nonbonded models of metal ions has been widely addressed in the recent years. Despite the continuous development of novel and more physically inspired functional forms, the 12-6 Lennard-Jones plus Coulomb potential is still the most adopted force field in molecular dynamics (MD) codes, owing to its simple form and easy implementation. However, due to the integer formal charge, unpolarizable force fields of ions may suffer from overestimated interatomic electrostatic interactions, leading to nonphysical clustering or repulsion between such full charges. The electronic continuum correction (ECC) can fix this problem through a simple inclusion of solvent polarization effects via ionic charge rescaling. In this work, the development of novel nonbonded models for mono, divalent, and highly charged metal ions is presented. For each metal species, the ionic charge has been scaled, according to the ECC. Lennard-Jones parameters have been optimized using experimental structural and thermodynamic properties as target quantities. Performances of the proposed models are discussed and compared with the literature data, while transferability attitudes among different and well-known water models are evaluated. © 2019 Wiley Periodicals, Inc.

Alkali ion influence on structure and stability of fibrillar amyloid-β oligomers

Alzheimer's disease is characterized by the aggregation of Amyloid-β (Aβ) peptide into oligomers, fibrils and plaques. Many factors influencing this process as well as the stability of the various Aβ aggregates are known to date, and include the concentration and type of metal ions. Most experimental and theoretical studies have concentrated on heavy metal ions, like Fe²⁺, Zn²⁺, or Cu²⁺, while the smaller alkali ions Li⁺, Na⁺, and K⁺ have not gained much attention notwithstanding their role and ubiquity in physiological environments. In this work, we applied atomistic molecular dynamics simulations to investigate the potential role of these alkali ions in stabilizing fibrillar Aβ oligomers of different size and topology, i.e., single and double filament systems comprising 3-24 peptide chains per filament. We find a pronounced difference on the molecular level in the interaction behavior with free carboxylate groups of the Aβ oligomer: Li⁺ forms stable bridged interactions, whereas K⁺ interacts more transiently and lacks bridging. The behavior of Na⁺ is in between, so that this ion-protein interaction obeys the renowned Hofmeister series. These differences are also reflected in the ability of the alkali ions to stabilize the oligomer secondary structure. The stabilizing effect is most pronounced for the smaller fibrillar oligomers, suggesting that the type of alkali ion critically affects the initial stages of fibril formation. Our findings thus offer a molecular explanation for the observation that the polymorphisms of Aβ fibril structures are caused by differences in the surrounding ionic environment. Graphical abstract Influence of alkali ions on the structure and stability of fibrillar amyloid-β oligomers.

Thermodynamics of the fourU RNA thermal switch derived from molecular dynamics simulations and spectroscopic techniques

Bacterial 5' untranslated regions of mRNA, termed thermal switches or thermometers, change their structure in response to temperature change. This structural change provides for the regulation of gene expression. One of such thermal switches, called fourU, is present in the Salmonella species. Mutations of fourU were found to abrogate its regulatory properties. We investigated the thermodynamics of the fourU fragment responsible for its structural changes. All-atom molecular dynamics simulations at various temperatures and spectroscopic experiments in solution were performed for the wild-type fourU and its mutants. We found that the U11C and A8C mutations stabilize the fourU structure in comparison to the wild-type fourU, and the double-point G14A/C25U mutant has the most destabilizing effect on the fourU hairpin 2 responsible for temperature sensing. The G14A/C25U mutant is also the easiest to strand-invade by a complementary oligonucleotide as indicated by fluorescence spectroscopy experiments.

Influence of Na+ and Mg2+ ions on RNA structures studied with molecular dynamics simulations

The structure of ribonucleic acid (RNA) polymers is strongly dependent on the presence of, in particular Mg2+ cations to stabilize structural features. Only in high-resolution X-ray crystallography structures can ions be identified reliably. Here, we perform molecular dynamics simulations of 24 RNA structures with varying ion concentrations. Twelve of the structures were helical and the others complex folded. The aim of the study is to predict ion positions but also to evaluate the impact of different types of ions (Na+ or Mg2+) and the ionic strength on structural stability and variations of RNA. As a general conclusion Mg2+ is found to conserve the experimental structure better than Na+ and, where experimental ion positions are available, they can be reproduced with reasonable accuracy. If a large surplus of ions is present the added electrostatic screening makes prediction of binding-sites less reproducible. Distinct differences in ion-binding between helical and complex folded structures are found. The strength of binding (ΔG‡ for breaking RNA atom-ion interactions) is found to differ between roughly 10 and 26 kJ/mol for the different RNA atoms. Differences in stability between helical and complex folded structures and of the influence of metal ions on either are discussed.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Decoupled side chain and backbone dynamics for proton translocation - M2 of influenza A

The 97 amino acid bitopic membrane protein M2 of influenza A forms a tetrameric bundle in which two of the monomers are covalently linked via a cysteine bridge. In its tetrameric assembly the protein conducts protons across the viral envelope and within intracellular compartments during the infectivity cycle of the virus. A key residue in the translocation of the protons is His-37 which forms a planar tetrad in the configuration of the bundle accepting and translocating the incoming protons from the N terminal side, exterior of the virus, to the C terminal side, inside the virus. With experimentally available data from NMR spectroscopy of the transmembrane domains of the tetrameric M2 bundle classical MD simulations are conducted with the protein bundle in different protonation stages in respect to His-37. A full correlation analysis (FCA) of the data sets with the His-37 tetrad either in a fully four times unprotonated or protonated state, assumed to mimic high and low pH in vivo, respectively, in both cases reveal asymmetric backbone dynamics. His-37 side chain rotation dynamics is increased at full protonation of the tetrad compared to the dynamics in the fully unprotonated state. The data suggest that proton translocation can be achieved by decoupled side chain or backbone dynamics. Graphical abstract Visualization of the tetrameric bundle of the transmembrane domains of M2 of influenza A after 200 ns of MD simulations (upper left). The four histidine residues 37 are either not protonated as in M2⁰ or fully protonated is in M2⁴⁺. The asymmetric dynamics of the backbones are shown after a full correlation analysis (FCA) in blue (lower left). The rotational dynamics of the χ2 dihedral angles of the histidines in M2⁰ (upper right) are less than those in M2⁴⁺ (lower right).

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Consensus on the solubility of NaCl in water from computer simulations using the chemical potential route

The solubility of NaCl in water is evaluated by using three force field models: Joung-Cheatham for NaCl dissolved in two different water models (SPC/E and TIP4P/2005) and Smith Dang NaCl model in SPC/E water. The methodology based on free-energy calculations [E. Sanz and C. Vega, J. Chem. Phys. 126, 014507 (2007)] and [J. L. Aragones et al., J. Chem. Phys. 136, 244508 (2012)] has been used, except, that all calculations for the NaCl in solution were obtained by using molecular dynamics simulations with the GROMACS package instead of homemade MC programs. We have explored new lower molalities and made longer runs to improve the accuracy of the calculations. Exploring the low molality region allowed us to obtain an analytical expression for the chemical potential of the ions in solution as a function of molality valid for a wider range of molalities, including the infinite dilute case. These new results are in better agreement with recent estimations of the solubility obtained with other methodologies. Besides, two empirical simple rules have been obtained to have a rough estimate of the solubility of a certain model, by analyzing the ionic pairs formation as a function of molality and/or by calculating the difference between the NaCl solid chemical potential and the standard chemical potential of the salt in solution.

Molecular Dynamics Simulation Study of Parallel Telomeric DNA Quadruplexes at Different Ionic Strengths: Evaluation of Water and Ion Models

Most molecular dynamics (MD) simulations of DNA quadruplexes have been performed under minimal salt conditions using the Åqvist potential parameters for the cation with the TIP3P water model. Recently, this combination of parameters has been reported to be problematic for the stability of quadruplex DNA, especially caused by the ion interactions inside or near the quadruplex channel. Here, we verify how the choice of ion parameters and water model can affect the quadruplex structural stability and the interactions with the ions outside the channel. We have performed a series of MD simulations of the human full-parallel telomeric quadruplex by neutralizing its negative charge with K(+) ions. Three combinations of different cation potential parameters and water models have been used: (a) Åqvist ion parameters, TIP3P water model; (b) Joung and Cheatham ion parameters, TIP3P water model; and (c) Joung and Cheatham ion parameters, TIP4Pew water model. For the combinations (b) and (c), the effect of the ionic strength has been evaluated by adding increasing amounts of KCl salt (50, 100, and 200 mM). Two independent simulations using the Åqvist parameters with the TIP3P model show that this combination is clearly less suited for the studied quadruplex with K(+) as counterions. In both simulations, one ion escapes from the channel, followed by significant deformation of the structure, leading to deviating conformation compared to that in the reference crystallographic data. For the other combinations of ion and water potentials, no tendency is observed for the channel ions to escape from the quadruplex channel. In addition, the internal mobility of the three loops, torsion angles, and counterion affinity have been investigated at varied salt concentrations. In summary, the selection of ion and water models is crucial as it can affect both the structure and dynamics as well as the interactions of the quadruplex with its counterions. The results obtained with the TIP4Pew model are found to be closest to the experimental data at all of the studied ion concentrations.

Asymmetric dynamics of ion channel forming proteins - Hepatitis C virus (HCV) p7 bundles

Protein p7 of hepatitis C virus (HCV) is a short 63 amino acid membrane protein which homo-oligomerises in the lipid membrane to form ion and proton conducting bundles. Two different genotypes (GTs) of p7, 1a and 5a, are used to simulate hexameric bundles of the protein embedded in a fully hydrated lipid bilayer during 400 ns molecular dynamics (MD) simulations. Whilst the bundle of GT 1a is based on a fully computational derived structure, the bundle of GT 5a is based on NMR spectroscopic data. Results of a full correlation analysis (FCA) reveal that albeit structural differences both bundles screen local minima during the simulation. The collective motion of the protein domains is asymmetric. No 'breathing-mode'-like dynamics is observed. The presence of divalent ions, such as Ca-ions affects the dynamics of especially solvent exposed parts of the protein, but leaves the asymmetric domain motion unaffected.

Sodium and Potassium Interactions with Nucleic Acids

Metal ions are essential cofactors for the structure and functions of nucleic acids. Yet, the early discovery in the 70s of the crucial role of Mg(2+) in stabilizing tRNA structures has occulted for a long time the importance of monovalent cations. Renewed interest in these ions was brought in the late 90s by the discovery of specific potassium metal ions in the core of a group I intron. Their importance in nucleic acid folding and catalytic activity is now well established. However, detection of K(+) and Na(+) ions is notoriously problematic and the question about their specificity is recurrent. Here we review the different methods that can be used to detect K(+) and Na(+) ions in nucleic acid structures such as X-ray crystallography, nuclear magnetic resonance or molecular dynamics simulations. We also discuss specific versus non-specific binding to different structures through various examples.

Binding of Disordered Peptides to Kelch: Insights from Enhanced Sampling Simulations

Keap1 protein plays an essential role in regulating cellular oxidative stress response and is a crucial binding hub for multiple proteins, several of which are intrinsically disordered proteins (IDP). Among Kelch's IDP binding partners, NRF2 and PTMA are the two most interesting cases. They share a highly similar binding motif; however, NRF2 binds to Kelch with a binding affinity of approximately 100-fold higher than that of PTMA. In this study, we perform an exhaustive sampling composed of 6 μs well-tempered metadynamics and 2 μs unbiased molecular dynamics (MD) simulations aiming at characterizing the binding mechanisms and structural properties of these two peptides. Our results agree with previous experimental observations that PTMA is remarkably more disordered than NRF2 in both the free and bound states. This explains PTMA's lower binding affinity. Our extensive sampling also provides valuable insights into the vast conformational ensembles of both NRF2 and PTMA, supports the hypothesis of coupled folding-binding, and confirms the essential role of linear motifs in IDP binding.

Accelerating the Conformational Sampling of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are a class of proteins lacking a well-defined secondary structure. Instead, they are able to attain multiple conformations, bind to multiple targets, and respond to changes in their surroundings. Functionally, IDPs have been associated with molecular recognition, cell regulation, and signal transduction. The dynamic conformational ensemble of IDPs is highly environmental and binding partner dependent, rendering the characterization of IDPs extremely challenging. Here, we compare the sampling efficiencies of conventional molecular dynamics (MD), well-tempered metadynamics (WT-META), and bias-exchange metadynamics (BE-META). The total simulation time was over 10 μs, and a 20-mer peptide derived from the Neh2 domain of the Nuclear factor erythroid 2-related factor 2 (Nrf2) protein was simulated. BE-META, with a neutral replica and seven biased replicas employing a set of seven relevant collective variables (CVs), provided the most reliable and efficient sampling. Finally, we propose a free-energy reconstruction method based on the probability distribution of the secondary structure contents. This postprocessing analysis confirms the presence of not only the β-hairpin conformation of the free Neh2 peptide but also its rare bound-state-like conformation, both of that have been experimentally observed. In addition, our simulations also predict other possible conformations to be verified with future experiments.

Effect of Force Field Parameters on Sodium and Potassium Ion Binding to Dipalmitoyl Phosphatidylcholine Bilayers

The behavior of electrolytes in molecular dynamics simulations of zwitterionic phospholipid bilayers is very sensitive to the force field parameters used. Here, several 200 ns molecular dynamics of simulations of dipalmitoyl phosphotidylcholine (PC) bilayers in 0.2 M sodium or potassium chloride using various common force field parameters for the cations are presented. All employed parameter sets give a larger number of Na(+) ions than K(+) ions that bind to the lipid heads, but depending on the parameter choice quite different results are seen. A wide range of coordination numbers for the Na(+) and K(+) ions is also observed. These findings have been analyzed and compared to published experimental data. Some simulations produce aggregates of potassium chloride, indicating (in accordance with published simulations) that these force fields do not reproduce the delicate balance between salt and solvated ions. The differences between the force fields can be characterized by one single parameter, the electrostatic radius of the ion, which is correlated to σMO (M represents Na(+)/K(+)), the Lennard-Jones radius. When this parameter exceeds a certain threshold, binding to the lipid heads is no longer observed. One would, however, need more accurate experimental data to judge or rank the different force fields precisely. Still, reasons for the poor performance of some of the parameter sets are clearly demonstrated, and a quality control procedure is provided.

Competitive interaction of monovalent cations with DNA from 3D-RISM

The composition of the ion atmosphere surrounding nucleic acids affects their folding, condensation and binding to other molecules. It is thus of fundamental importance to gain predictive insight into the formation of the ion atmosphere and thermodynamic consequences when varying ionic conditions. An early step toward this goal is to benchmark computational models against quantitative experimental measurements. Herein, we test the ability of the three dimensional reference interaction site model (3D-RISM) to reproduce preferential interaction parameters determined from ion counting (IC) experiments for mixed alkali chlorides and dsDNA. Calculations agree well with experiment with slight deviations for salt concentrations >200 mM and capture the observed trend where the extent of cation accumulation around the DNA varies inversely with its ionic size. Ion distributions indicate that the smaller, more competitive cations accumulate to a greater extent near the phosphoryl groups, penetrating deeper into the grooves. In accord with experiment, calculated IC profiles do not vary with sequence, although the predicted ion distributions in the grooves are sequence and ion size dependent. Calculations on other nucleic acid conformations predict that the variation in linear charge density has a minor effect on the extent of cation competition.

Chemistry specificity of DNA-polycation complex salt response: a simulation study of DNA, polylysine and polyethyleneimine

In this work, the chemistry specific stability determining factors of DNA-polycation complexes are examined by performing all-atom molecular dynamics simulations. To this end, we conduct a systematic variation of polycation line charge through polyethyleneimine (PEI) protonation and polycation chemistry via comparison with poly-l-lysine (PLL). Our simulations show that increasing line charge of the polycation alone does not lead to more salt tolerant complexes. Instead, the effective charge compensation by the polycation correlates with the increased stability of the complex against additional salt. The salt stability of PEI-DNA complexes also links to the proton sponge property of weak polycations, commonly assumed to be behind the effectivity of PEI as a gene delivery vector. Examination of the complexes reveals the mechanism behind this behaviour; more Cl(-) ions are attracted by the protonated complexes but, in contrast to the common depiction of the proton sponge behaviour, the ion influx does not cause swelling of the complex structure itself. However, PEI protonation leads to release of PEI while DNA remains tightly bound to the complex. Jointly, these findings shed light on the stability determining factors of DNA-polycation complexes, raise charge distribution as an important stability determining contributor, and indicate that the effectivity of PEI in gene delivery is likely to result from the freed PEI facilitating gene transfection.

Molecular view of ligands specificity for CAG repeats in anti-Huntington therapy

Huntington's disease is a fatal and devastating neurodegenerative genetic disorder for which there is currently no cure. It is characterized by Huntingtin protein's mRNA transcripts with 36 or more CAG repeats. Inhibiting the formation of pathological complexes between these expanded transcripts and target proteins may be a valuable strategy against the disease. Yet, the rational design of molecules specifically targeting the expanded CAG repeats is limited by the lack of structural information. Here, we use well-tempered metadynamics-based free energy calculations to investigate pose and affinity of two ligands targeting CAG repeats for which affinities have been previously measured. The first consists of two 4-guanidinophenyl rings linked by an ester group. It is the most potent ligand identified so far, with Kd = 60(30) nM. The second consists of a 4-phenyl dihydroimidazole and 4-1H-indole dihydroimidazole connected by a C-C bond (Kd = 700(80) nM). Our calculations reproduce the experimental affinities and uncover the recognition pattern between ligands' and their RNA target. They also provide a molecular basis for the markedly different affinity of the two ligands for CAG repeats as observed experimentally. These findings may pave the way for a structure-based hit-to-lead optimization to further improve ligand selectivity toward CAG repeat-containing mRNAs.

Computational Calorimetry: High-Precision Calculation of Host-Guest Binding Thermodynamics

We present a strategy for carrying out high-precision calculations of binding free energy and binding enthalpy values from molecular dynamics simulations with explicit solvent. The approach is used to calculate the thermodynamic profiles for binding of nine small molecule guests to either the cucurbit[7]uril (CB7) or β-cyclodextrin (βCD) host. For these systems, calculations using commodity hardware can yield binding free energy and binding enthalpy values with a precision of ∼0.5 kcal/mol (95% CI) in a matter of days. Crucially, the self-consistency of the approach is established by calculating the binding enthalpy directly, via end point potential energy calculations, and indirectly, via the temperature dependence of the binding free energy, i.e., by the van't Hoff equation. Excellent agreement between the direct and van't Hoff methods is demonstrated for both host-guest systems and an ion-pair model system for which particularly well-converged results are attainable. Additionally, we find that hydrogen mass repartitioning allows marked acceleration of the calculations with no discernible cost in precision or accuracy. Finally, we provide guidance for accurately assessing numerical uncertainty of the results in settings where complex correlations in the time series can pose challenges to statistical analysis. The routine nature and high precision of these binding calculations opens the possibility of including measured binding thermodynamics as target data in force field optimization so that simulations may be used to reliably interpret experimental data and guide molecular design.