RNA G-quadruplex folding is a multi-pathway process driven by conformational entropy.

The kinetics of folding is crucial for the function of many regulatory RNAs including RNA G-quadruplexes (rG4s). Here, we characterize the folding pathways of a G-quadruplex from the telomeric repeat-containing RNA by combining all-atom molecular dynamics and coarse-grained simulations with circular dichroism experiments. The quadruplex fold is stabilized by cations and thus, the ion atmosphere forming a double layer surrounding the highly charged quadruplex guides the folding process. To capture the ionic double layer in implicit solvent coarse-grained simulations correctly, we develop a matching procedure based on all-atom simulations in explicit water. The procedure yields quantitative agreement between simulations and experiments as judged by the populations of folded and unfolded states at different salt concentrations and temperatures. Subsequently, we show that coarse-grained simulations with a resolution of three interaction sites per nucleotide are well suited to resolve the folding pathways and their intermediate states. The results reveal that the folding progresses from unpaired chain via hairpin, triplex and double-hairpin constellations to the final folded structure. The two- and three-strand intermediates are stabilized by transient Hoogsteen interactions. Each pathway passes through two on-pathway intermediates. We hypothesize that conformational entropy is a hallmark of rG4 folding. Conformational entropy leads to the observed branched multi-pathway folding process for TERRA25. We corroborate this hypothesis by presenting the free energy landscapes and folding pathways of four rG4 systems with varying loop length.

pH-dependent structural transitions in cationic ionizable lipid mesophases are critical for lipid nanoparticle function.

Lipid nanoparticles (LNPs) are advanced core-shell particles for messenger RNA (mRNA) based therapies that are made of polyethylene glycol (PEG) lipid, distearoylphosphatidylcholine (DSPC), cationic ionizable lipid (CIL), cholesterol (chol), and mRNA. Yet the mechanism of pH-dependent response that is believed to cause endosomal release of LNPs is not well understood. Here, we show that eGFP (enhanced green fluorescent protein) protein expression in the mouse liver mediated by the ionizable lipids DLin-MC3-DMA (MC3), DLin-KC2-DMA (KC2), and DLinDMA (DD) ranks MC3 ≥ KC2 > DD despite similar delivery of mRNA per cell in all cell fractions isolated. We hypothesize that the three CIL-LNPs react differently to pH changes and hence study the structure of CIL/chol bulk phases in water. Using synchrotron X-ray scattering a sequence of ordered CIL/chol mesophases with lowering pH values are observed. These phases show isotropic inverse micellar, cubic Fd3m inverse micellar, inverse hexagonal [Formula: see text] and bicontinuous cubic Pn3m symmetry. If polyadenylic acid, as mRNA surrogate, is added to CIL/chol, excess lipid coexists with a condensed nucleic acid lipid [Formula: see text] phase. The next-neighbor distance in the excess phase shows a discontinuity at the Fd3m inverse micellar to inverse hexagonal [Formula: see text] transition occurring at pH 6 with distinctly larger spacing and hydration for DD vs. MC3 and KC2. In mRNA LNPs, DD showed larger internal spacing, as well as retarded onset and reduced level of DD-LNP-mediated eGFP expression in vitro compared to MC3 and KC2. Our data suggest that the pH-driven Fd3m-[Formula: see text] transition in bulk phases is a hallmark of CIL-specific differences in mRNA LNP efficacy.

Efficient and accurate binding free energy calculation of Aß9-40 protofilament propagation.

Self-assembled aggregation of peptides and proteins into regular amyloid fibrils is associated with several neurodegenerative diseases. In case of Alzheimer's disease proteolytic cleavage products of the amyloid precursor protein form pathological amyloid-beta fibrils in a nucleation and propagation phase. The molecular details and thermodynamic driving forces of amyloid formation are not well understood, but are of high relevance for potential pharmacological interference. We used atomistic binding free energy simulations to calculate the free energy of protofilament propagation by an additional Aß9-40 peptide binding to the protofilament tip. It requires sampling of relevant conformational transitions which is challenging since the monomeric Aß9-40 peptide is intrinsically disordered. However, the convergence of umbrella simulations can be enhanced by applying additional restraining potentials on the axial, orientational and conformational degrees of freedom. The improved convergence leads to a much closer agreement with experimental binding free energy data compared to unrestrained umbrella sampling. Moreover, the restraining approach results in a separation of contributions to the total binding free energy. The calculated contributions indicate that the free energy change associated with the restriction of conformational freedom upon propagation makes a large opposing contribution of higher magnitude than the total binding free energy. Finally, optimization of the approach leads to further significant reduction of the computational demand which is crucial for systematic studies on mutations, denaturants and inhibitors in the fibril propagation step.

Remembering the Work of Phillip L. Geissler: A Coda to His Scientific Trajectory.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers.

Twisting DNA by salt.

The structure and properties of DNA depend on the environment, in particular the ion atmosphere. Here, we investigate how DNA twist -one of the central properties of DNA- changes with concentration and identity of the surrounding ions. To resolve how cations influence the twist, we combine single-molecule magnetic tweezer experiments and extensive all-atom molecular dynamics simulations. Two interconnected trends are observed for monovalent alkali and divalent alkaline earth cations. First, DNA twist increases monotonously with increasing concentration for all ions investigated. Second, for a given salt concentration, DNA twist strongly depends on cation identity. At 100 mM concentration, DNA twist increases as Na+ < K+ < Rb+ < Ba2+ < Li+ ≈ Cs+ < Sr2+ < Mg2+ < Ca2+. Our molecular dynamics simulations reveal that preferential binding of the cations to the DNA backbone or the nucleobases has opposing effects on DNA twist and provides the microscopic explanation of the observed ion specificity. However, the simulations also reveal shortcomings of existing force field parameters for Cs+ and Sr2+. The comprehensive view gained from our combined approach provides a foundation for understanding and predicting cation-induced structural changes both in nature and in DNA nanotechnology.

Adsorbing DNA to Mica by Cations: Influence of Valency and Ion Type.

Ion-mediated attraction between DNA and mica plays a crucial role in biotechnological applications and molecular imaging. Here, we combine molecular dynamics simulations and single-molecule atomic force microscopy experiments to characterize the detachment forces of single-stranded DNA at mica surfaces mediated by the metal cations Li+, Na+, K+, Cs+, Mg2+, and Ca2+. Ion-specific adsorption at the mica/water interface compensates (Li+ and Na+) or overcompensates (K+, Cs+, Mg2+, and Ca2+) the bare negative surface charge of mica. In addition, direct and water-mediated contacts are formed between the ions, the phosphate oxygens of DNA, and mica. The different contact types give rise to low- and high-force pathways and a broad distribution of detachment forces. Weakly hydrated ions, such as Cs+ and water-mediated contacts, lead to low detachment forces and high mobility of the DNA on the surface. Direct ion-DNA or ion-surface contacts lead to significantly higher forces. The comprehensive view gained from our combined approach allows us to highlight the most promising cations for imaging in physiological conditions: K+, which overcompensates the negative mica charge and induces long-ranged attractions. Mg2+ and Ca2+, which form a few specific and long-lived contacts to bind DNA with high affinity.

Combining molecular dynamics simulations and x-ray scattering techniques for the accurate treatment of protonation degree and packing of ionizable lipids in monolayers.

The pH-dependent change in protonation of ionizable lipids is crucial for the success of lipid-based nanoparticles as mRNA delivery systems. Despite their widespread application in vaccines, the structural changes upon acidification are not well understood. Molecular dynamics simulations support structure prediction but require an a priori knowledge of the lipid packing and protonation degree. The presetting of the protonation degree is a challenging task in the case of ionizable lipids since it depends on pH and on the local lipid environment and often lacks experimental validation. Here, we introduce a methodology of combining all-atom molecular dynamics simulations with experimental total-reflection x-ray fluorescence and scattering measurements for the ionizable lipid Dlin-MC3-DMA (MC3) in POPC monolayers. This joint approach allows us to simultaneously determine the lipid packing and the protonation degree of MC3. The consistent parameterization is expected to be useful for further predictive modeling of the action of MC3-based lipid nanoparticles.

Magnesium force fields for OPC water with accurate solvation, ion-binding, and water-exchange properties: Successful transfer from SPC/E.

Magnesium plays a vital role in a large variety of biological processes. To model such processes by molecular dynamics simulations, researchers rely on accurate force field parameters for Mg2+ and water. OPC is one of the most promising water models yielding an improved description of biomolecules in water. The aim of this work is to provide force field parameters for Mg2+ that lead to accurate simulation results in combination with OPC water. Using 12 different Mg2+ parameter sets that were previously optimized with different water models, we systematically assess the transferability to OPC based on a large variety of experimental properties. The results show that the Mg2+ parameters for SPC/E are transferable to OPC and closely reproduce the experimental solvation free energy, radius of the first hydration shell, coordination number, activity derivative, and binding affinity toward the phosphate oxygens on RNA. Two optimal parameter sets are presented: MicroMg yields water exchange in OPC on the microsecond timescale in agreement with experiments. NanoMg yields accelerated exchange on the nanosecond timescale and facilitates the direct observation of ion binding events for enhanced sampling purposes.

Kinetic pathways of water exchange in the first hydration shell of magnesium: Influence of water model and ionic force field.

Water exchange between the first and second hydration shell is essential for the role of Mg2+ in biochemical processes. In order to provide microscopic insights into the exchange mechanism, we resolve the exchange pathways by all-atom molecular dynamics simulations and transition path sampling. Since the exchange kinetics relies on the choice of the water model and the ionic force field, we systematically investigate the influence of seven different polarizable and non-polarizable water and three different Mg2+ models. In all cases, water exchange can occur either via an indirect or direct mechanism (exchanging molecules occupy different/same position on the water octahedron). In addition, the results reveal a crossover from an interchange dissociative (Id) to an associative (Ia) reaction mechanism dependent on the range of the Mg2+-water interaction potential of the respective force field. Standard non-polarizable force fields follow the Id mechanism in agreement with experimental results. By contrast, polarizable and long-ranged non-polarizable force fields follow the Ia mechanism. Our results provide a comprehensive view on the influence of the water model and the ionic force field on the exchange dynamics and the foundation to assess the choice of the force field in biomolecular simulations.

Extended magnesium and calcium force field parameters for accurate ion-nucleic acid interactions in biomolecular simulations.

Magnesium and calcium play an essential role in the folding and function of nucleic acids. To correctly describe their interactions with DNA and RNA in biomolecular simulations, an accurate parameterization is crucial. In most cases, the ion parameters are optimized based on a set of experimental solution properties such as solvation free energies, radial distribution functions, water exchange rates, and activity coefficient derivatives. However, the transferability of such bulk-optimized ion parameters to quantitatively describe biomolecular systems is limited. Here, we extend the applicability of our previous bulk-optimized parameters by including experimental binding affinities toward the phosphate oxygen on nucleic acids. In particular, we systematically adjust the combination rules that are an integral part of the pairwise interaction potentials of classical force fields. This allows us to quantitatively describe specific ion binding to nucleic acids without changing the solution properties in the most simple and efficient way. We show the advancement of the optimized Lorentz combination rule for two representative nucleic acid systems. For double-stranded DNA, the optimized combination rule for Ca2+ significantly improves the agreement with experiments, while the standard combination rule leads to unrealistically distorted DNA structures. For the add A-riboswitch, the optimized combination rule for Mg2+ improves the structure of two specifically bound Mg2+ ions as judged by the experimental distance to the binding site. Including experimental binding affinities toward specific ion binding sites on biomolecules, therefore, provides a promising perspective to develop a more accurate description of metal cations for biomolecular simulations.

Hofmeister Series for Metal-Cation-RNA Interactions: The Interplay of Binding Affinity and Exchange Kinetics.

A large variety of physicochemical properties involving RNA depends on the type of metal cation present in solution. In order to gain microscopic insight into the origin of these ion specific effects, we apply molecular dynamics simulations to describe the interactions of metal cations and RNA. For the three most common ion binding sites on RNA, we calculate the binding affinities and exchange rates of eight different mono- and divalent metal cations. Our results reveal that binding sites involving phosphate groups preferentially bind metal cations with high charge density (such as Mg2+) in inner-sphere conformations while binding sites involving N7 or O6 atoms preferentially bind cations with low charge density (such as K+). The binding affinity therefore follows a direct Hofmeister series at the backbone but is reversed at the nucleobases leading to a high selectivity of ion binding sites on RNA. In addition, the exchange rates for cation binding cover almost 5 orders of magnitude, leading to a vastly different time scale for the lifetimes of contact pairs. Taken together, the site-specific binding affinities and the specific lifetime of contact pairs provide the microscopic explanation of ion specific effects observed in a wide variety of macroscopic RNA properties. Finally, combining the results from atomistic simulations with extended Poisson-Boltzmann theory allows us to predict the distribution of metal cations around double-stranded RNA at finite concentrations and to reproduce the results of ion counting experiments with good accuracy.

Kinetic pathways of water exchange in the first hydration shell of magnesium.

Water exchange between the coordination shells of metal cations in aqueous solutions is fundamental in understanding their role in biochemical processes. Despite the importance, the microscopic mechanism of water exchange in the first hydration shell of Mg2+ has not been resolved since the exchange dynamics is out of reach for conventional all-atom simulations. To overcome this challenge, transition path sampling is applied to resolve the kinetic pathways, to characterize the reaction mechanism and to provide an accurate estimate of the exchange rate. The results reveal that water exchange involves the concerted motion of two exchanging water molecules and the collective rearrangement of all water molecules in the first hydration shell. Using a recently developed atomistic model for Mg2+, water molecules remain in the first hydration shell for about 40 ms, a time considerably longer compared to the 0.1 ms predicted by transition state theory based on the coordinates of a single water molecule. The discrepancy between these timescales arises from the neglected degrees of freedom of the second exchanging water molecule that plays a decisive role in the reaction mechanism. The approach presented here contributes molecular insights into the dynamics of water around metal cations and provides the basis for developing accurate atomistic models or for understanding complex biological processes involving metal cations.

Ion-Specific and pH-Dependent Hydration of Mica-Electrolyte Interfaces.

Hydration forces play a crucial role in a wide range of phenomena in physics, chemistry, and biology. Here, we study the hydration of mica surfaces in contact with various alkali chloride solutions over a wide range of concentrations and pH values. Using atomic force microscopy and molecular dynamics simulations, we demonstrate that hydration forces consist of a superposition of a monotonically decaying and an oscillatory part, each with a unique dependence on the specific type of cation. The monotonic hydration force gradually decreases in strength with decreasing bulk hydration energy, leading to a transition from an overall repulsive (Li+, Na+) to an attractive (Rb+, Cs+) force. The oscillatory part, in contrast, displays a binary character, being hardly affected by the presence of strongly hydrated cations (Li+, Na+), but it becomes completely suppressed in the presence of weakly hydrated cations (Rb+, Cs+), in agreement with a less pronounced water structure in simulations. For both aspects, K+ plays an intermediate role, and decreasing pH follows the trend of increasing Rb+ and Cs+ concentrations.

Force fields for monovalent and divalent metal cations in TIP3P water based on thermodynamic and kinetic properties.

Metal cations are essential in many vital processes. In order to capture the role of different cations in all-atom molecular dynamics simulations of biological processes, an accurate parametrization is crucial. Here, we develop force field parameters for the metal cations Li+, Na+, K+, Cs+, Mg2+, Ca2+, Sr2+, and Ba2+ in combination with the TIP3P water model that is frequently used in biomolecular simulations. In progressing toward improved force fields, the approach presented here is an extension of previous efforts and allows us to simultaneously reproduce thermodynamic and kinetic properties of aqueous solutions. We systematically derive the parameters of the 12-6 Lennard-Jones potential which accurately reproduces the experimental solvation free energy, the activity derivative, and the characteristics of water exchange from the first hydration shell of the metal cations. In order to reproduce all experimental properties, a modification of the Lorentz-Berthelot combination rule is required for Mg2+. Using a balanced set of solution properties, the optimized force field parameters aim to capture the fine differences between distinct metal cations including specific ion binding affinities and the kinetics of cation binding to biologically important anionic groups.

Dynamics of Seeded Aß40-Fibril Growth from Atomistic Molecular Dynamics Simulations: Kinetic Trapping and Reduced Water Mobility in the Locking Step.

Filamentous ß-amyloid aggregates are crucial for the pathology of Alzheimer's disease. Despite the tremendous biomedical importance, the molecular pathway of growth propagation is not completely understood and remains challenging to investigate by simulations due to the long time scales involved. Here, we apply extensive all-atom molecular dynamics simulations in explicit water to obtain free energy profiles and kinetic information from position-dependent diffusion profiles for three different Aß9-40-growth processes: fibril elongation by single monomers at the structurally unequal filament tips and association of larger filament fragments. Our approach provides insight into the molecular steps of the kinetic pathway and allows close agreement with experimental binding free energies and macroscopic growth rates. Water plays a decisive role, and solvent entropy is identified as the main driving force for assembly. Fibril growth is disfavored energetically due to cancellation of direct peptide-peptide interactions and solvation effects. The kinetics of growth is consistent with the characteristic dock/lock mechanism, and docking is at least 2 orders of magnitude faster. During initial docking, interactions are mediated by transient non-native hydrogen bonds, which efficiently catch the incoming monomer or fragment already at separations of about 3 nm. In subsequent locking, the dynamics is much slower due to formation of kinetically trapped conformations caused by long-lived non-native hydrogen bonds. Fibril growth additionally requires collective motion of water molecules to create a dry binding interface. Fibril growth is further retarded due to reduced mobility of the involved hydration water, evident from a 2-fold reduction of the diffusion coefficient.

Mechanism of Reversible Peptide-Bilayer Attachment: Combined Simulation and Experimental Single-Molecule Study.

The binding of peptides and proteins to lipid membrane surfaces is of fundamental importance for many membrane-mediated cellular processes. Using closely matched molecular dynamics simulations and atomic force microscopy experiments, we study the force-induced desorption of single peptide chains from phospholipid bilayers to gain microscopic insight into the mechanism of reversible attachment. This approach allows quantification of desorption forces and decomposition of peptide-membrane interactions into energetic and entropic contributions. In both simulations and experiments, the desorption forces of peptides with charged and polar side chains are much smaller than those for hydrophobic peptides. The adsorption of charged/polar peptides to the membrane surface is disfavored by the energetic components, requires breaking of hydrogen bonds involving the peptides, and is favored only slightly by entropy. By contrast, the stronger adsorption of hydrophobic peptides is favored both by energy and by entropy and the desorption forces increase with increasing side-chain hydrophobicity. Interestingly, the calculated net adsorption free energies per residue correlate with experimental results of single residues, indicating that side-chain free energy contributions are largely additive. This observation can help in the design of peptides with tailored adsorption properties and in the estimation of membrane binding properties of peripheral membrane proteins.

Specific ion binding to carboxylic surface groups and the pH dependence of the Hofmeister series.

Ion binding to acidic groups is a central mechanism for ion-specificity of macromolecules and surfaces. Depending on pH, acidic groups are either protonated or deprotonated and thus change not only charge but also chemical structure with crucial implications for their interaction with ions. In a two-step modeling approach, we first determine single-ion surface interaction potentials for a few selected halide and alkali ions at uncharged carboxyl (COOH) and charged carboxylate (COO(-)) surface groups from atomistic MD simulations with explicit water. Care is taken to subtract the bare Coulomb contribution due to the net charge of the carboxylate group and thereby to extract the nonelectrostatic ion-surface potential. Even at this stage, pronounced ion-specific effects are observed and the ion surface affinity strongly depends on whether the carboxyl group is protonated or not. In the second step, the ion surface interaction potentials are used in a Poisson-Boltzmann model to calculate the surface charge and the potential distribution in the solution depending on salt type, salt concentration, and solution pH in a self-consistent manner. Hofmeister phase diagrams are derived on the basis of the long-ranged forces between two carboxyl-functionalized surfaces. For cations we predict direct, reversed, and altered Hofmeister series as a function of the pH, qualitatively similar to recent experimental results for silica surfaces. The Hofmeister series reversal for cations is rationalized by a reversal of the single-cation affinity to the carboxyl group depending on its protonation state: the deprotonated carboxylate (COO(-)) surface group interacts most favorably with small cations such as Li(+) and Na(+), whereas the protonated carboxyl (COOH) surface group interacts most favorably with large cations such as Cs(+) and thus acts similarly to a hydrophobic surface group. Our results provide a general mechanism for the pH-dependent reversal of the Hofmeister series due to the different specific ion binding to protonated and deprotonated surface groups.

Cryo-EM Analysis of the Effect of Seeding with Brain-derived Aß Amyloid Fibrils.

Aß amyloid fibrils from Alzheimer's brain tissue are polymorphic and structurally different from typical in vitro formed Aß fibrils. Here, we show that brain-derived (ex vivo) fibril structures can be proliferated by seeding in vitro. The proliferation reaction is only efficient for one of the three abundant ex vivo Aß fibril morphologies, which consists of two peptide stacks, while the inefficiently proliferated fibril morphologies contain four or six peptide stacks. In addition to the seeded fibril structures, we find that de novo nucleated fibril structures can emerge in seeded samples if the seeding reaction is continued over multiple generations. These data imply a competition between de novo nucleation and seed extension and suggest further that seeding favours the outgrowth of fibril morphologies that contain fewer peptide stacks.

Insights into the Structural Basis of Amyloid Resistance Provided by Cryo-EM Structures of AApoAII Amyloid Fibrils.

Amyloid resistance is the inability or the reduced susceptibility of an organism to develop amyloidosis. In this study we have analysed the molecular basis of the resistance to systemic AApoAII amyloidosis, which arises from the formation of amyloid fibrils from apolipoprotein A-II (ApoA-II). The disease affects humans and animals, including SAMR1C mice that express the C allele of ApoA-II protein, whereas other mouse strains are resistant to development of amyloidosis due to the expression of other ApoA-II alleles, such as ApoA-IIF. Using cryo-electron microscopy, molecular dynamics simulations and other methods, we have determined the structures of pathogenic AApoAII amyloid fibrils from SAMR1C mice and analysed the structural effects of ApoA-IIF-specific mutational changes. Our data show that these changes render ApoA-IIF incompatible with the specific fibril morphologies, with which ApoA-II protein can become pathogenic in vivo.

Anionic and cationic Hofmeister effects on hydrophobic and hydrophilic surfaces.

Using a two-step modeling approach, we address the full spectrum of direct, reversed, and altered ionic sequences as the charge of the ion, the charge of the surface, and the surface polarity are varied. From solvent-explicit molecular dynamics simulations, we extract single-ion surface interaction potentials for halide and alkali ions at hydrophilic and hydrophobic surfaces. These are used within Poisson-Boltzmann theory to calculate ion density and electrostatic potential distributions at mixed polar/unpolar surfaces for varying surface charge. The resulting interfacial tension increments agree quantitatively with experimental data and capture the Hofmeister series, especially the anomaly of lithium, which is difficult to obtain using continuum theory. Phase diagrams that feature different Hofmeister series as a function of surface charge, salt concentration, and surface polarity are constructed from the long-range force between two surfaces interacting across electrolyte solutions. Large anions such as iodide have a high hydrophobic surface affinity and increase the effective charge magnitude on negatively charged unpolar surfaces. Large cations such as cesium also have a large hydrophobic surface affinity and thereby compensate an external negative charge surface charge most efficiently, which explains the well-known asymmetry between cations and anions. On the hydrophilic surface, the size-dependence of the ion surface affinity is reversed, explaining the Hofmeister series reversal when comparing hydrophobic with hydrophilic surfaces.