Free energy calculations are routinely used to study molecular processes inaccessible to unbiased molecular dynamics, but their utility ultimately depends on knowing when and how much their predictions can be trusted. Uncertainty estimation is therefore essential for distinguishing genuine physical features of a free energy profile from artifacts arising from limited simulation data or inadequate sampling. Gaussian processes have emerged as a powerful framework for reconstructing free energy profiles together with predictive uncertainties. However, existing implementations typically condition on fixed hyperparameters and observation noise, preventing predictive uncertainties from adapting to the information content of the simulation data. Here, we develop a generalized hierarchical Gaussian process framework that accounts for these neglected sources of uncertainty. Applications to umbrella sampling and extended Lagrangian metadynamics of peptide-lipid membrane interactions demonstrate that the resulting uncertainty estimates track reconstruction errors across a wide range of sampling and data conditions.

Vesicle internalization proceeds through a series of multivesicular topologies essential for endocytic transport and cellular compartmentalization. The energetic landscapes of related transitions, including vesicle budding and pearling, are known to be governed by the coupling of spontaneous curvature, leaflet area asymmetry, and reduced volume. However, the physical principles driving the structural transformation of hemifused intermediates remain unresolved. Using a continuum elastic model, we identify a morphological phase transition in hemifused invaginating vesicles, from an initial "eye" (lens-like) geometry to an elongated "kettle" geometry. This transition is discontinuous as long as the invaginating vesicle's reduced volume is below a critical threshold, but continuous otherwise. The kettle-like morphology is metastable across a broad range of leaflet area asymmetries, potentially enabling a hysteretic externalization pathway. Increasing either the spontaneous curvature of the shared outer leaflet or the size of the invaginating vesicle, alone or in tandem with the host vesicle, turns the kettle morphology into the global free energy minimum. Notably, simply scaling up the size of both vesicles does not eliminate the free energy barrier. This quantitative characterization provides a structural reference for identifying internalization intermediates witnessed in experimental imaging, and maps the morphological evolution of the internalization pathway across its physical parameter space.

Like-charge pairing is a physical manifestation of the unique solvation properties of certain ion pairs in water. Water's high dielectric constant and related charge screening capability significantly influence the interaction between like-charged ions, with the possibility to transform it-in exceptional cases when noncovalent interactions are involved-from repulsion to attraction. Guanidinium cations (Gdm(+) ) represent a quintessential example of such like-charge pairing due to their specific geometry and electronic structure. In this work, we present experimental validation and quantification of Gdm+ -Gdm+ contact ion pairing in water utilizing nuclear magnetic resonance (NMR) spectroscopy complemented by molecular dynamics (MD) simulations and density functional theory (DFT) calculations. The observed Gdm(+) -Gdm(+) interaction is attractive albeit weak-about -0.5 kJ & sdot;mol(-1) -which aligns with theoretical estimation from MD simulations. We contrast the behavior of Gdm+ with that of NH4 (+) cations, which exhibit no contact ion pairing in water. DFT calculations predict that the NMR chemical shift of Gdm(+) dimers is different than that of monomers, in agreement with NMR titration curves that display a nonlinear Langmuir-like behavior. Additionally, we conducted cryo-electron microscopy-to our knowledge, for the first time-on concentrated oligoarginines R-9, which, unlike nona-lysines K-9, exhibit aggregation in water. These results point to like charge pairing of the guanidinium side chain groups, as corroborated also by MD simulations and free energy calculations.

Hydrated electrons of opposite spins pair to form dielectrons at sufficiently high concentrations that can be achieved by dissolution of alkali metals in water. While experimental investigations of these systems are challenging due to their vigorous, even explosive, reactivity, simulations open the possibility to characterize the structure and reactivity of hydrated dielectrons and the effects of alkali cations thereon. Here, we present ab initio molecular dynamics simulations of a hydrated dielectron without or with explicit Li^+ or Cs^+ counterions. While the overall solvation structure is preserved in all these systems, the presence of cations has a distinct effect of increasing the dielectron gyration radius by about 10

Abstract Arginine-rich peptides are short amino acid chains capable of spontaneously crossing cellular membranes, with great potential for drug or other cargo delivery. Yet, the mechanisms underlying their cellular penetration are not fully understood. Here, we investigate the modes of action of nonaarginine (R 9 ) across membranes of increasing compositional and biological complexity. We combine computational, fluorescence microscopy, and cryo-EM approaches to both visualize the membrane structural changes arising from peptide-lipid interactions and provide a molecular rationale for the observed effects. In large unilamellar vesicles, R 9 binds preferentially to anionic and PE-rich membranes, induces lipid reorganization, and drives pronounced remodelling, including budding, bifurcations, and time-dependent formation of multilamellar stacks. In cell-derived extracellular vesicles, R 9 -induced remodelling is largely confined to bilamellar bifurcations. In live cells, fluorescent R 9 forms surface puncta that precede cytosolic entry. Correlative cryo-fluorescence and electron tomography reveals that these puncta correspond to strongly folded, multilamellar membrane structures. We propose that these seemingly contrasting observations can be reconciled within a single R 9 mechanism of action, involving membrane folding and stacking, where the different observed morphologies arise from the size of the accessible membrane reservoir.

Molecular dynamics is a valuable tool to probe biological processes at the atomistic level - a resolution often elusive to experiments. However, the credibility of molecular models is limited by the accuracy of the underlying force field, which is often parametrized relying on ad hoc assumptions. To address this gap, we present a Bayesian framework for learning physically grounded parameters directly from ab initio molecular dynamics data. By representing both model parameters and data probabilistically, the framework yields interpretable, statistically rigorous models in which uncertainty and transferability emerge naturally from the learning process. This approach provides a transparent, data-driven foundation for developing predictive molecular models and enhances confidence in computational descriptions of biophysical systems. We demonstrate the method using 18 biologically relevant molecular fragments that capture key motifs in proteins, nucleic acids, and lipids, and, as a proof of concept, apply it to calcium binding to troponin - a central event in cardiac regulation.

Electrolyte-to-metal transitions in liquids represent a critical process in the evolution of excess electrons from localized species into a delocalized conduction band. Alkali metal--ammonia solutions are the textbook example, displaying a gradual progression from blue electrolytes to metallic gold liquids. In contrast, preparing the analogous aqueous solutions was long deemed impossible as alkali metals ignite or even explode on contact with water. Moreover, individual electrons solvated in water are more strongly bound than in liquid ammonia, which suggests that electrolyte-to-metal transitions may be inhibited, or only occur at very high alkali metal concentrations. Here we combine optical spectroscopy with ab initio molecular dynamics to show that aqueous alkali metal solutions can not only be prepared by adsorbing water vapor on alkali metal alloys of varying compositions but that they also undergo a dynamic, fluctuating electrolyte-to-metal transition. Simulations reveal femtosecond-scale flipping between electrolyte and metallic states, while experiments confirm the evolution of the metallic character via plasmonic signatures of distinct colors. Water can thus not only form a metallic solution but also exhibits a dynamic, rapidly fluctuating non-metal-to-metal transition.

The first experimental evidence of quantum Drude oscillator behavior in liquids is uncovered using probabilistic machine learning-augmented iterative Boltzmann inversion applied to noble gas radial distribution functions. Furthermore, classical force fields for noble gases are shown to be reduced to a single parameter through simple empirical relations linked to atomic dipole polarizability. These findings highlight how neutron scattering data can inspire innovative force field design and offer insight into interatomic forces to advance molecular simulations.

Nonmetal-to-metal transitions are among the most fascinating phenomena in material science, associated with strong correlations, large fluctuations, and related features relevant to applications in electronics, spintronics, and optics. Dissolving alkali metals in liquid ammonia results in the formation of solvated electrons, which are localised in dilute solutions but exhibit metallic behaviour at higher concentrations, forming a disordered liquid metal. The electrolyte-to-metal transition in these systems appears to be gradual, but its microscopic origins remain poorly understood. Here, we provide a detailed time-resolved picture of the electrolyte-to-metal transition in solutions of lithium in liquid ammonia, employing ab initio molecular dynamics and many-body perturbation theory, which are validated against photoelectron spectroscopy experiments. We find a rapid flipping between metallic and electrolyte states that persist only on a sub-picosecond timescale within a broad range of concentrations. These flips, occurring within femtoseconds, are characterised by abrupt opening and closing of the band gap, which is connected with only minute changes in the solution structure and the associated electron density.

Cation-π interactions involving the tetramethylammonium motif are prevalent in biological systems, playing crucial roles in membrane protein function, DNA expression regulation, and protein folding. However, accurately modeling cation-π interactions where electronic polarization plays a critical role is computationally challenging, especially in large biomolecular systems. This study implements a physically justified electronic continuum correction (ECC) to the CHARMM36 force field, scaling ionic charges by a factor of 0.75 to effectively account for electronic polarization without additional computational overhead. This approach, while not specifically designed for cation-π interactions, is shown here to significantly improve predictions of the structure of an aqueous tetramethylammonium-pyridine complex as compared to neutron diffraction data. This result, together with computational predictions for the structure of the aqueous tetramethylammonium-phenol complex, underscores the potential of ECC as a versatile method to improve the description of cation-π interactions in biomolecular simulations.

Tetramethylammonium (TMA) is a ubiquitous cationic motif in biochemistry, found in the charged choline headgroup of membrane phospholipids and in tri-methylated lysine residues, which modulates histone-DNA interactions and impacts epigenetic mechanisms. TMA interactions with anionic species, particularly carboxylate groups of amino acid residues and extracellular sugars, are of substantial biological relevance, as these interactions mediate a wide range of cellular processes. This study investigates the molecular interactions between TMA and acetate, representing carboxylate-containing groups, using neutron scattering experiments complemented by force fields and ab initio molecular dynamics (MD) simulations. Neutron diffraction with isotopic substitution reveals specific ion pairing signatures between TMA and acetate, with simulations providing a detailed interpretation of the ion pairing structures. Force fields, notably CHARMM36 with the electronic continuum correction (ECC) (by a factor of 0.85) and AMBER99SB, capture essential pairing characteristics, but only revPBE-based ab initio MD simulations accurately model specific experimental features such as the low Q peak intensity in reciprocal space. Our study delivers a refined molecular model of TMA-carboxylate interactions, guiding the selection of force fields for complex biological systems where such interactions are of significant importance.

Salt bridges are ionic interactions that are of great importance in protein recognition. However, their structural description using X-ray crystallography or NMR may be inconclusive. Classical molecular dynamics (MD) used for the interpretation neglects electronic polarization, which results in artifactual overbinding. Here, we resolve the problem via charge scaling, which accounts for electronic polarization in a mean-field way. We study three salt bridges in insulin analogue. New NMR ensembles are generated via NOE-restrained MD using ff19SB and CHARMM36m force fields and the scaled-charge prosECCo75. Tens of μs of unrestrained MD show in a statistically converged manner that ff19SB induces a non-native salt bridge. This behavior is quantified via umbrella sampling of salt bridge dissociation, which indicates a rather high strength of up to 4 and 5 kcal mol-1 for CHARMM36m and ff19SB, respectively. In contrast, prosECCo75 gives a biologically reasonable dissociation barrier of 1 kcal mol-1. Our results indicate that a physically justified description of charge-charge interactions within a nonpolarizable MD framework reliably describes aqueous biomolecular systems.

Charge scaling, also denoted as the electronic continuum correction, has proven to be an efficient method for effectively including electronic polarization in force field molecular dynamics simulations without additional computational costs. However, scaling charges in existing force fields, fitted at least in part to experimental data, lead to inconsistencies, such as overscaling. We have, therefore, recently developed a four-site water model consistent with charge scaling, i.e., possessing the correct low-frequency dielectric constant of 45. Here, we build on top of this water model to develop charge-scaled models of biologically relevant Li+, Na+, K+, Ca2+, and Mg2+ cations as well as Cl-, Br-, and I- anions, employing machine learning to streamline and speed up the parametrization process. On the one hand, we show that the present model outperforms the best existing charge scaled model of aqueous ions. On the other hand, the present work points to a future need for consistently and simultaneously improving the water and ion models within the electronic continuum correction framework.

Simple water models with fixed partial charges, particularly 4-site models such as TIP4P/2005, TIP4P-FB, and OPC, have proven to be highly accurate in reproducing many experimental properties of liquid water. It is intriguing that dielectric constants of these models, together with those of popular 3-site models, such as SPC/E and TIP3P, cover a wide range of values, often very far from the experimental one. Here, we address the issue of the surprising insensitivity of the quality of a water model to its dielectric constant. We build upon our recently developed machine learning-assisted methodology for water model development to construct and analyze a large set of high-quality water models with dielectric constants varying from ∼45 to ∼75. We confirm the weak sensitivity of the water model quality on the dielectric constant in this broad range, with optimal values for classical 4-site fixed charge water models lying between 55 and 70. We also identified a set of correlations between parameters of high quality water models at a given value of the dielectric constant.

Neutron scattering and molecular dynamics studies were performed on a concentrated aqueous tetramethylammonium (TMA) chloride solution to gain insight into the hydration shell structure of TMA, which is relevant for understanding its behavior in biological contexts of, e.g., properties of phospholipid membrane headgroups or interactions between DNA and histones. Specifically, neutron diffraction with isotopic substitution experiments were performed on TMA and water hydrogens to extract the specific correlation between hydrogens in TMA (HTMA) and hydrogens in water (HW). Classical molecular dynamics simulations were performed to help interpret the experimental neutron scattering data. Comparison of the hydration structure and simulated neutron signals obtained with various force field flavors (e.g. overall charge, charge distribution, polarity of the CH bonds and geometry) allowed us to gain insight into how sensitive the TMA hydration structure is to such changes and how much the neutron signal can capture them. We show that certain aspects of the hydration, such as the correlation of the hydrogen on TMA to hydrogen on water, showed little dependence on the force field. In contrast, other correlations, such as the ion-ion interactions, showed more marked changes. Strikingly, the neutron scattering signal cannot discriminate between different hydration patterns. Finally, ab initio molecular dynamics was used to examine the three-dimensional hydration structure and thus to benchmark force field simulations. Overall, while neutron scattering has been previously successfully used to improve force fields, in the particular case of TMA we show that it has only limited value to fully determine the hydration structure, with other techniques such as ab initio MD being of a significant help.

Hydration and, in particular, the coordination number of a metal ion is of paramount importance as it defines many of its (bio)physicochemical properties. It is not only essential for understanding its behavior in aqueous solutions but also determines the metal ion reference state and its binding energy to (bio)molecules. In this paper, for divalent metal cations Ca2+, Cd2+, Cu2+, Fe2+, Hg2+, Mg2+, Ni2+, Pb2+, and Zn2+, we compare two approaches for predicting hydration numbers: (1) a mixed explicit/continuum DFT-D3//COSMO-RS solvation model and (2) density functional theory based ab initio molecular dynamics. The former approach is employed to calculate the Gibbs free energy change for the sequential hydration reactions, starting from [M(H2O)(2)](2+) aqua complexes to [M(H2O)(9)](2+), allowing explicit water molecules to bind in the first or second coordination sphere and determining the most stable [M(H2O)(n)](2+) structure. In the latter approach, the hydration number is obtained by integrating the ion-water radial distribution function. With a couple of exceptions, the metal ion hydration numbers predicted by the two approaches are in mutual agreement, as well as in agreement with the experimental data

Calmodulin (CaM) is a ubiquitous calcium-sensitive messenger in eukaryotic cells. It was previously shown that CaM possesses an affinity for diverse lipid moieties, including those found on CaM-binding proteins. These facts, together with our observation that CaM accumulates in membrane-rich protrusions of HeLa cells upon increased cytosolic calcium, motivated us to perform a systematic search for unmediated CaM interactions with model lipid membranes mimicking the cytosolic leaflet of plasma membranes. A range of experimental techniques and molecular dynamics simulations prove unambiguously that CaM interacts with lipid bilayers in the presence of calcium ions. The lipids phosphatidylserine (PS) and phosphatidylethanolamine (PE) hold the key to CaM–membrane interactions. Calcium induces an essential conformational rearrangement of CaM, but calcium binding to the headgroup of PS also neutralizes the membrane negative surface charge. More intriguingly, PE plays a dual role—it not only forms hydrogen bonds with CaM, but also destabilizes the lipid bilayer increasing the exposure of hydrophobic acyl chains to the interacting proteins. Our findings suggest that upon increased intracellular calcium concentration, CaM and the cytosolic leaflet of cellular membranes can be functionally connected.

Charge scaling has proven to be an efficient way to account in a mean-field manner for electronic polarization by aqueous ions in force field molecular dynamics simulations. However, commonly used water models with dielectric constants over 50 are not consistent with this approach leading to "overscaling", i.e., generally too weak ion-ion interactions. Here, we build water models fully compatible with charge scaling, i.e., having the correct low-frequency dielectric constant of about 45. To this end, we employ advanced optimization and machine learning schemes in order to explore the vast parameter space of four-site water models efficiently. As an a priori unwarranted positive result, we find a sizable range of force field parameters that satisfy the above dielectric constant constraint providing at the same time accuracy with respect to experimental data comparable with the best existing four-site water models such as TIP4P/2005, TIP4P-FB, or OPC. The present results thus open the way to the development of a consistent charge scaling force field for modeling ions in aqueous solutions.