Long-range Electrostatic Interactions Research Articles

DNA-protamine condensates under low salt conditions: molecular dynamics simulation with a simple coarse-grained model focusing on electrostatic interactions.

Protamine, a small, strongly positively-charged protein, plays a key role in achieving chromatin condensation inside sperm cells and is also involved in the formulation of nanoparticles for gene therapy and packaging of mRNA-based vaccines against viral infection and cancer. The detailed mechanisms of such condensations are still poorly understood especially under low salt conditions where electrostatic interaction predominates. Our previous study, with a refined coarse-grained model in full consideration of the long-range electrostatic interactions, has demonstrated the crucial role of electrostatic interaction in protamine-controlled reversible DNA condensation. Therefore, we herein pay our attention only to the electrostatic interaction and devise a coarser-grained bead-spring model representing the right linear charge density on protamine and DNA chains but treating other short-range interactions as simply as possible, which would be suitable for real-scale simulations. Effective pair potential calculations and large-scale molecular dynamics simulations using this extremely simple model reproduce the phase behaviour of DNA in a wide range of protamine concentrations under low salt conditions, again revealing the importance of the electrostatic interaction in this process and providing a detailed nanoscale picture of bundle formation mediated by a charge disproportionation mechanism. Our simulations also show that protamine length alters DNA overcharging and in turn redissolution thresholds of DNA condensates, revealing the important role played by entropies and correlated fluctuations of condensing agents and thus offering an additional opportunity to design tailored nanoparticles for gene therapy. The control mechanism of DNA-protamine condensates will also provide a better microscopic picture of biomolecular condensates, i.e., membraneless organelles arising from liquid-liquid phase separation, that are emerging as key principles of intracellular organization. Such condensates controlled by post-translational modification of protamine, in particular phosphorylation, or by variations in protamine length from species to species may also be responsible for the chromatin-nucleoplasm patterning observed during spermatogenesis in several vertebrate and invertebrate species.

A step-wise ion hydration model of aqueous electrolyte solution: The 2:2, 2:1 and 1:2 punches

In prior work we showed that the current step-wise hydration framework shows promise for modeling the concentration-activity relationship in aqueous solutions of ions representing 1:1 electrolytes, alcohols, and sugars, and accurately predicting the partitioning of the water between the bound (hydrated) pool and an unbound (free) pool. In the current work, we continue developing this framework by applying it to ions representing 2:2, 2:1 and 1:2 electrolyte in aqueous solutions. Properly treating ion hydration as an ideal solution along with employing mean spherical approximation of the long-range electrostatic interactions yields an accurate model for most electrolytes considered. This simple model of aqueous solutions is robust for electrolytes and organic solutes.

How Does Gecko Keratin Stick to Hydrophilic and Hydrophobic Surfaces in the Presence and Absence of Water? An Atomistic Molecular Dynamics Investigation.

We developed a united-atom model of gecko keratin to investigate the influence of electrostatic and van der Waals contributions to gecko adhesion in scenarios representing gecko's natural habitats. The keratin model assumes that only intrinsically disordered regions directly contact the surface. Contact angles of two generic substrate surfaces that we created match those previously used in AFM experiments on gecko adhesion. Force probe molecular dynamics simulations pulling the keratin from the surface show that the pull-off force increases with increased water content and is inversely related to the water contact angle of the surface. This matches experimental trends. We investigated the number and charge density of keratin and water at the surface, confirming a water-mediating effect and are able to show that keratin folds polar groups to the hydrophilic surface. We decomposed energetic contributions during pull-off, and our computational model shows that in contrast to popular hypotheses, long-range electrostatic interactions determine much of the pull-off process. The contribution of electrostatics to adhesion may be in the order of the van der Waals contributions.

Cluster expansions of multicomponent ionic materials: Formalism and methodology

The cluster expansion (CE) method has seen continuous and increasing use in the study of configuration-dependent properties of crystalline materials. The original development of the CE method along with the underlying mathematical formalism and assumptions was focused on the study of metallic alloys. Since then the methodology has been actively and successfully used in the study of ionic materials as well. In this work, we present a cohesive reformulation of the mathematical formalism underlying the CE method based on a synthesis of its original formulation, several additions and extensions that have been proposed since, and a revised representation of its constituent mathematical objects. We then proceed to describe some of the formal implications of using the methodology for charge-neutral configurations in ionic systems. In particular, we discuss the reduction of the size of configuration spaces and the resulting linear dependencies that arise among correlation functions that span the larger unconstrained configuration space. Additionally, we explore the effects of long-range electrostatic interactions. We also demonstrate how the previously proposed use of a point electrostatic term successfully accounts for the majority of the longer-range electrostatic interactions, and leaves the cluster expansion terms to capture mostly short-range interactions. Finally, we present and discuss a variety of recently developed methodologies, including training structure selection, oxidation state assignment, structure mapping, and regression algorithms, that are necessary to address these formal mathematical notions for a practical implementation of the CE method in the study of multicomponent ionic materials.

Biomolecular Complexation on the "Wrong Side": A Case Study of the Influence of Salts and Sugars on the Interactions between Bovine Serum Albumin and Sodium Polystyrene Sulfonate.

In the protein purification, drug delivery, food industry, and biotechnological applications involving protein–polyelectrolyte complexation, proper selection of co-solutes and solution conditions plays a crucial role. The onset of (bio)macromolecular complexation occurs even on the so-called “wrong side” of the protein isoionic point where both the protein and the polyelectrolyte are net like-charged. To gain mechanistic insights into the modulatory role of salts (NaCl, NaBr, and NaI) and sugars (sucrose and sucralose) in protein–polyelectrolyte complexation under such conditions, interaction between bovine serum albumin (BSA) and sodium polystyrene sulfonate (NaPSS) at pH = 8.0 was studied by a combination of isothermal titration calorimetry, fluorescence spectroscopy, circular dichroism, and thermodynamic modeling. The BSA–NaPSS complexation proceeds by two binding processes (first, formation of intrapolymer complexes and then formation of interpolymer complexes), both driven by favorable electrostatic interactions between the negatively charged sulfonic groups (−SO3–) of NaPSS and positively charged patches on the BSA surface. Two such positive patches were identified, each responsible for one of the two binding processes. The presence of salts screened both short-range attractive and long-range repulsive electrostatic interactions between both macromolecules, resulting in a nonmonotonic dependence of the binding affinity on the total ionic strength for both binding processes. In addition, distinct anion-specific effects were observed (NaCl < NaBr < NaI). The effect of sugars was less pronounced: sucrose had no effect on the complexation, but its chlorinated analogue, sucralose, promoted it slightly due to the screening of long-range repulsive electrostatic interactions between BSA and NaPSS. Although short-range non-electrostatic interactions are frequently mentioned in the literature in relation to BSA or NaPSS, we found that the main driving force of complexation on the “wrong side” are electrostatic interactions.

Far-Field Electrostatic Signatures of Macromolecular 3D Conformation.

In solution as in vacuum, the electrostatic field distribution in the vicinity of a charged object carries information on its three-dimensional geometry. We report on an experimental study exploring the effect of molecular shape on long-range electrostatic interactions in solution. Working with DNA nanostructures carrying approximately equal amounts of total charge but each in a different three-dimensional conformation, we demonstrate that the geometry of the distribution of charge in a molecule has substantial impact on its electrical interactions. For instance, a tetrahedral structure, which is the most compact distribution of charge we tested, can create a far-field effect that is effectively identical to that of a rod-shaped molecule carrying half the amount of total structural charge. Our experiments demonstrate that escape-time electrometry (ETe) furnishes a rapid and facile method to screen and identify 3D conformations of charged biomolecules or molecular complexes in solution.

Understanding Supramolecular Assembly of Supercharged Proteins.

Ordered supramolecular assemblies have recently been created using electrostatic interactions between oppositely charged proteins. Despite recent progress, the fundamental mechanisms governing the assembly of oppositely supercharged proteins are not fully understood. Here, we use a combination of experiments and computational modeling to systematically study the supramolecular assembly process for a series of oppositely supercharged green fluorescent protein variants. We show that net charge is a sufficient molecular descriptor to predict the interaction fate of oppositely charged proteins under a given set of solution conditions (e.g., ionic strength), but the assembled supramolecular structures critically depend on surface charge distributions. Interestingly, our results show that a large excess of charge is necessary to nucleate assembly and that charged residues not directly involved in interprotein interactions contribute to a substantial fraction (∼30%) of the interaction energy between oppositely charged proteins via long-range electrostatic interactions. Dynamic subunit exchange experiments further show that relatively small, 16-subunit assemblies of oppositely charged proteins have kinetic lifetimes on the order of ∼10–40 min, which is governed by protein composition and solution conditions. Broadly, our results inform how protein supercharging can be used to create different ordered supramolecular assemblies from a single parent protein building block.

Electrokinetic Janus micromotors moving on topographically flat chemical patterns

Ionic and molecular selectivity are considered unique for the nanoscale and not realizable in microfluidics. This is due to the scale-matching problem—a difficulty to match the dimensions of ions and electrostatic potential screening lengths with micron-sized confinements. Here, we demonstrate a microscale realization of ionic transport processes closely resembling those specific to ionic channels or in nanofluidic junctions, including selectivity, guidance and flow focusing. As a model system, we explore electrokinetic spherical Janus micromotors moving over charged surfaces with complex charge distribution and without any topographical wall. We discuss peculiarities of the long-range electrostatic interaction on the behavior of the system including interface crossing and reflection of positively charged particles from negatively charged interfaces. These results are crucial for understanding the electrokinetic transport of biochemical species under confinement, have the potential to increase the precision of lab-on-chip-based assays, as well as broadening use cases and control strategies of nano-/micromachinery.

Enthalpy of solvation of alkali metal salts in a protic ionic liquid: Effect of cation charge and size

• Experimental and theoretical study of solution and solvation of mono- and divalent alkaline metal cations. • MD simulations provided coordination numbers, which showed an interesting similarity in IL and water environments. • Solvation of alkali and alkaline earth nitrate metal salts ((LiNO 3 , KNO 3 , RbNO 3 , CsNO 3 , Mg(NO 3 ) 2 and Ca(NO 3 ) 2 ) in EAN. • Analysis of the energetics and structure of solvation confirms the well-known water-like solvation properties of EAN. An experimental and theoretical study of solution and solvation of mono- and divalent alkali metal cations in the protic ionic liquid (IL) ethylammonium nitrate (EAN) is reported. High precision solution-reaction calorimetry was used to obtain the heat of solvation, which was used for the analysis of the thermodynamics. A close relation between the structure of the salts in the crystalline phase and its enthalpy of solvation in the IL is reported. A detailed picture of the molecular environments in the solvation shells around the metal cations is provided by means of molecular dynamics simulations. The analysis of the energetics and structure of solvation confirms the well-known water-like solvation properties of EAN, with the solvation shell around the metal cations in both media being very similar. On the other hand, the results show that it is energetically more favourable to solvate smaller cations with higher valence. Indeed, the simulations show that the long-range electrostatic interactions are the main contribution to solvation interaction, with the electric field at the surface of the alkali metal cations as the basic magnitude controlling it.

Software for Evaluating Long-Range Electrostatic Interactions Based on the Ewald Summation and Its Application to Electrochemical Energy Storage Materials.

Electrochemical characteristics such as open-circuit voltage and ionic conductivity of electrochemical energy storage materials are easily affected, typically negatively, by mobile ion/vacancy ordering. Ordered phases can be identified based on the lattice gas model and electrostatic energy screening. However, the evaluation of long-range electrostatic energy is not straightforward because of the conditional convergence. The Ewald method decomposes the electrostatic energy into a real space part and a reciprocal space part, achieving a fast convergence in each. Due to its high computational efficiency, Ewald-based techniques are widely used in analyzing characteristics of electrochemical energy storage materials. In this work, we present software not only integrating Ewald techniques for two-dimensional and three-dimensional periodic systems but also combining the Ewald method with the lattice matching algorithm and bond valence. It is aimed to become a useful tool for screening stable structures and interfaces and identifying the ionic transport channels of cation conductors.

Preferential Regulation of Transient Protein-Protein Interaction by the Macromolecular Crowders.

The environmental condition is a critical regulation factor for protein behavior in solution. Several studies have shown that macromolecular crowders can modulate protein structures, interactions, and functions. Recent publications described the regulation of specific interaction by macromolecular crowders. However, the other category of protein-protein interaction, namely, the transient interaction, is rarely investigated, especially from the perspective of protein structure to study transient interactions between proteins. Here, we used nuclear magnetic resonance and small-angle X-ray/neutron scattering methods to structurally investigate the ensemble of the protein complex in dilute buffer and crowded environments. Histidine phosphocarrier protein (HPr) and the N-terminal domain of enzyme I (EIN) are the important components of the bacterial phosphotransfer system. Our results show that the addition of Ficoll-70 promotes HPr molecules to form the encounter complex with EIN maintained by long-range electrostatic interaction. However, when macromolecular crowder BSA is used, the soft interaction between BSA and HPr perturbs the active site of HPr, driving HPr to form an encounter complex with EIN at the weakly charged interface. Our results indicate that different macromolecular crowders could influence transient EIN-HPr interaction through different mechanisms and provide new insights into protein-protein interaction regulation in native environments.

Modulating interfacial polymerization with phytate as aqueous-phase additive for highly-permselective nanofiltration membranes

Modulating interfacial polymerization (IP) process has been recognized as an effective way to optimize the physicochemical structure of polyamide membranes and thus elevating nanofiltration performance. Herein, phytic acid dodecasodium salt (PADS), a small molecule salt with high solubility, is used as an aqueous-phase additive to modulate the piperazine (PIP) monomers diffusion behavior via electrostatic interaction during the IP process. The PADS with a high charge density can form long-range electrostatic interaction with the PIP molecules to retard their diffusion. The diffusion coefficient of PIP can be effectively modulated within an order of magnitude (∼10−5-10−6 cm2 s−1) by varying the amount of PADS. Accordingly, the growth of polyamide layer is inhibited and the membrane thickness is reduced from 95 nm to 50 nm. The optimized membrane presents a two-fold increase in water permeance while maintaining excellent salt rejection performance (Na2SO4 rejection >97%), outperforming the benchmark commercial nanofiltration membranes.

Second Coordination Sphere Effects on the Mechanistic Pathways for Dioxygen Activation by a Ferritin: Involvement of a Tyr Radical and the Identification of a Cation Binding Site.

Ferritins are ubiquitous diiron enzymes involved in iron(II) detoxification and oxidative stress responses and can act as metabolic iron stores. The overall reaction mechanisms of ferritin enzymes are still unclear, particularly concerning the role of the conserved, near catalytic center Tyr residue. Thus, we carried out a computational study of a ferritin using a large cluster model of well over 300 atoms including its first‐ and second‐coordination sphere. The calculations reveal important insight into the structure and reactivity of ferritins. Specifically, the active site Tyr residue delivers a proton and electron in the catalytic cycle prior to iron(II) oxidation. In addition, the calculations highlight a likely cation binding site at Asp65, which through long‐range electrostatic interactions, influences the electronic configuration and charge distributions of the metal center. The results are consistent with experimental observations but reveal novel detail of early mechanistic steps that lead to an unusual mixed‐valent iron(III)‐iron(II) center.

Colloidal Systems in Concentrated Electrolyte Solutions Exhibit Re-entrant Long-Range Electrostatic Interactions due to Underscreening.

Surface force measurements have revealed that at very high electrolyte concentrations as well as in neat and diluted ionic liquids and deep eutectic solvents, the range of electrostatic interactions is far greater than the Debye length. Here, we explore the consequences of this underscreening for soft-matter and colloidal systems by investigating the stability of nanoparticle dispersions, the self-assembly of ionic surfactants, and the thickness of soap films. In each case, we find clear evidence of re-entrant properties due to underscreening at high salt concentrations. Our results show that underscreening in concentrated electrolytes is a general phenomenon and is not dependent on confinement by macroscopic surfaces. The stability of systems at very high salinity due to underscreening may be beneficially applied to processes that currently use low-salinity water.

A step-wise ion hydration model of aqueous electrolyte solution: The 1:1 punch

In prior work we showed that the current step-wise hydration framework shows promise for modeling the concentration-activity relationship in aqueous solutions of electrolytes, alcohols, and sugars, and accurately predicting the partitioning of the water between the bound (hydrated) pool and an unbound (free) pool. In the current work, we continue developing this framework by applying it to ions in electrolyte solutions. To a large extent, hydration of the ions along with either the mean spherical approximation or the Pitzer-Simon characterization of the long-range electrostatic interactions together yield a decently accurate model of the electrolytes without the need for ion-ion interaction parameters. The accuracy of the model degrades at high concentrations for highly hydrated ions when the number of water molecules per electrolyte in the free water pool becomes depleted.

The first laminin G-like domain of protein S is essential for binding and activation of Tyro3 receptor and intracellular signalling

The homologous proteins Gas6 and protein S (ProS1) are both natural ligands for the TAM (Tyro3, Axl, MerTK) receptor tyrosine kinases. ProS1 selectively activates Tyro3; however, the precise molecular interface of the ProS1-Tyro3 contact has not been characterised. We used a set of chimeric proteins in which each of the C-terminal laminin G-like (LG) domains of ProS1 were swapped with those of Gas6, as well as a set of ProS1 mutants with novel added glycosylations within LG1. Alongside wildtype ProS1, only the chimera containing ProS1 LG1 domain stimulated Tyro3 and Erk phosphorylation in human cancer cells, as determined by Western blot. In contrast, Gas6 and chimeras containing minimally the Gas6 LG1 domain stimulated Axl and Akt phosphorylation. We performed in silico homology modelling and molecular docking analysis to construct and evaluate structural models of both ProS1-Tyro3 and Gas6-Axl ligand-receptor interactions. These analyses revealed a contact between the ProS1 LG1 domain and the first immunoglobulin domain of Tyro3, which was similar to the Gas6-Axl interaction, and involved long-range electrostatic interactions that were further stabilised by hydrophobic and polar contacts. The mutant ProS1 proteins, which had added glycosylations within LG1 but which were all outside of the modelled contact region, all activated Tyro3 in cells with no hindrance. In conclusion, we show that the LG1 domain of ProS1 is necessary for activation of the Tyro3 receptor, involving protein-protein interaction interfaces that are homologous to those of the Gas6-Axl interaction.

Long-range electrostatic interactions significantly modulate the affinity of dynein for microtubules

The dynein family of microtubule minus-end-directed motor proteins drives diverse functions in eukaryotic cells, including cell division, intracellular transport, and flagellar beating. Motor protein processivity, which characterizes how far a motor walks before detaching from its filament, depends on the interaction between its microtubule-binding domain (MTBD) and the microtubule. Dynein’s MTBD switches between high- and low-binding affinity states as it steps. Significant structural and functional data show that specific salt bridges within the MTBD and between the MTBD and the microtubule govern these affinity state shifts. However, recent computational work suggests that nonspecific, long-range electrostatic interactions between the MTBD and the microtubule may also play an important role in the processivity of dynein. To investigate this hypothesis, we mutated negatively charged amino acids remote from the dynein MTBD-microtubule-binding interface to neutral residues and measured the binding affinity using microscale thermophoresis and optical tweezers. We found a significant increase in the binding affinity of the mutated MTBDs for microtubules. Furthermore, we found that charge screening by free ions in solution differentially affected the binding and unbinding rates of MTBDs to microtubules. Together, these results demonstrate a significant role for long-range electrostatic interactions in regulating dynein-microtubule affinity. Moreover, these results provide insight into the principles that potentially underlie the biophysical differences between molecular motors with various processivities and protein-protein interactions more generally.

A deep potential model with long-range electrostatic interactions.

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

All-Atom Simulation Method for Zeeman Alignment and Dipolar Assembly of Magnetic Nanoparticles.

Magnetic nanoparticles (MNPs) can organize into novel structures in solutions with excellent order and unique geometries. However, studies of the self-assembly of smaller MNPs are challenging due to a complicated interplay between external magnetic fields and van der Waals, electrostatic, dipolar, steric, and hydrodynamic interactions. Here, we present a novel all-atom molecular dynamics simulation method to enable detailed studies of the dynamics, self-assembly, structure, and properties of MNPs as a function of core sizes and shapes, ligand chemistry, solvent properties, and external field. We demonstrate the use and effectiveness of the model by simulating the self-assembly of oleic acid ligand-functionalized magnetite (Fe3O4) nanoparticles, with spherical and cubic shapes, into rings, lines, chains, and clusters under a uniform external magnetic field. We found that the long-range electrostatic interactions can favor the formation of a chain over a ring, the ligands promote MNP cluster growth, and the solvent can reduce the rotational diffusion of the MNPs. The algorithm has been parallelized to take advantage of multiple processors of a modern computer and can be used as a plugin for the popular simulation software LAMMPS to study the behavior of small MNPs and gain insights into the physics and chemistry of different magnetic assembly processes with atomistic details.

HSMA: An O(N) electrostatics package implemented in LAMMPS

We implement two recently developed fast Coulomb solvers, HSMA3D (Zhao et al. (2018) [49]) and HSMA2D (Liang et al. (2020) [50]), into a new user package HSMA for the molecular dynamics simulation engine LAMMPS. The HSMA package is designed for efficient and accurate modeling of electrostatic interactions in 3D and 2D periodic systems with dielectric effects at O(N) cost. The implementation is hybrid MPI and OpenMP parallelized and compatible with existing LAMMPS functionalities. The vectorization technique following AVX512 instructions is adopted for acceleration. To establish the validity of our implementation, we have presented extensive comparisons to the widely used particle-particle particle-mesh (PPPM) algorithm in LAMMPS and other dielectric solvers. With the proper choice of algorithm parameters and parallelization setup, the package enables calculations of electrostatic interactions that is efficient especially for systems with dielectric mismatch. Program summaryProgram Title: HSMACPC Library link to program files:https://doi.org/10.17632/z39zyh573s.1Developer's repository link:https://github.com/LiangJiuyang/HSMA-Harmonic-surface-mapping-algorithm-in-LAMMPSLicensing provisions: GPLv3Programming language: C++Nature of problem: Evaluation of long-range electrostatic interactions for charged system with fully periodic condition or confined by planar dielectric interfaces.Solution method: We implement the Harmonic Surface Mapping algorithm (HSMA), which combines the image-charge method with the harmonic surface mapping and converts the contribution of infinite images into a finite number of surface charges on an auxiliary sphere, into simulation package LAMMPS. The HSMA package works for both fully periodic systems and partially periodic systems with planar dielectric interfaces, achieving truly linear O(N) complexity by employing fast multipole method. Our package can be applied to general all-atom simulations and a broad range of charged complex fluids under dielectric confinement.Additional comments including restrictions and unusual features: Hybrid MPI plus OpenMP parallelization is used in HSMA package for high-performance computing. We provide vector optimization by using the AVX512 instructions and Intel MKL library for further acceleration. The Intel Parallel Studio is required for these techniques.