Lipid shape and packing are key for optimal design of pH-sensitive mRNA lipid nanoparticles.

The ionizable-lipid component of RNA-containing nanoparticles controls the pH-dependent behavior necessary for an efficient delivery of the cargo-the so-called endosomal escape. However, it is still an empirical exercise to identify optimally performing lipids. Here, we study two well-known ionizable lipids, DLin-MC3-DMA and DLin-DMA using a combination of experiments, multiscale computer simulations, and electrostatic theory. All-atom molecular dynamics simulations, and experimentally measured polar headgroup pKa values, are used to develop a coarse-grained representation of the lipids, which enables the investigation of the pH-dependent behavior of lipid nanoparticles (LNPs) through Monte Carlo simulations, in the absence and presence of RNA molecules. Our results show that the charge state of the lipids is determined by the interplay between lipid shape and headgroup chemistry, providing an explanation for the similar pH-dependent ionization state observed for lipids with headgroup pKa values about one-pH-unit apart. The pH dependence of lipid ionization is significantly influenced by the presence of RNA, whereby charge neutrality is achieved by imparting a finite and constant charge per lipid at intermediate pH values. The simulation results are experimentally supported by measurements of α-carbon 13C-NMR chemical shifts for eGFP mRNA LNPs of both DLin-MC3-DMA and DLin-DMA at various pH conditions. Further, we evaluate the applicability of a mean-field Poisson-Boltzmann theory to capture these phenomena.

Chemometrics in Protein Formulation: Stability Governed by Repulsion and Protein Unfolding.

Therapeutic proteins can be challenging to develop due to their complexity and the requirement of an acceptable formulation to ensure patient safety and efficacy. To date, there is no universal formulation development strategy that can identify optimal formulation conditions for all types of proteins in a fast and reliable manner. In this work, high-throughput characterization, employing a toolbox of five techniques, was performed on 14 structurally different proteins formulated in 6 different buffer conditions and in the presence of 4 different excipients. Multivariate data analysis and chemometrics were used to analyze the data in an unbiased way. First, observed changes in stability were primarily determined by the individual protein. Second, pH and ionic strength are the two most important factors determining the physical stability of proteins, where there exists a significant statistical interaction between protein and pH/ionic strength. Additionally, we developed prediction methods by partial least-squares regression. Colloidal stability indicators are important for prediction of real-time stability, while conformational stability indicators are important for prediction of stability under accelerated stress conditions at 40 °C. In order to predict real-time storage stability, protein-protein repulsion and the initial monomer fraction are the most important properties to monitor.

Counterintuitive Electrostatics upon Metal Ion Coordination to a Receptor with Two Homotopic Binding Sites.

The consecutive binding of two potassium ions to a bis(18-crown-6) analogue of Tröger's base (BCETB) in water was studied by isothermal titration calorimetry using four different salts, KCl, KI, KSCN, and K2SO4. A counterintuitive result was observed: the enthalpy change associated with the binding of the second ion is more negative than that of the first (ΔHbind,2° < ΔHbind,1°). This remarkable finding is supported by continuum electrostatic theory as well as by atomic scale replica exchange molecular dynamics simulations, where the latter robustly reproduces experimental trends for all simulated salts, KCl, KI, and KSCN, using multiple force fields. While an enthalpic K+-K+ attraction in water poses a small, but fundamentally important, contribution to the overall interaction, the probability of the collapsed conformation (COL) of BCETB, where both crown ether moieties (CEs) of BCETB are bent in toward the cavity, was found to increase successively upon binding of the first and second potassium ions. The promotion of the COL conformation reveals favorable intrinsic interactions between the potassium coordinated CEs, which further contribute to the observation that ΔHbind,2° < ΔHbind,1°. While the observed trend is independent of the counterion, the origin of the significantly larger magnitude of the difference ΔHbind,2° - ΔHbind,1° observed experimentally for KSCN was studied in light of the weaker hydration of the thiocyanate anion, resulting in an enrichment of thiocyanate ions close to BCETB compared to the other studied counterions.

Self-Interactions of Two Monoclonal Antibodies: Small-Angle X-ray Scattering, Light Scattering, and Coarse-Grained Modeling.

Using light scattering (LS), small-angle X-ray scattering (SAXS), and coarse-grained Monte Carlo (MC) simulations, we studied the self-interactions of two monoclonal antibodies (mAbs), PPI03 and PPI13. With LS measurements, we obtained the osmotic second virial coefficient, B22, and the molecular weight, Mw, of the two mAbs, while with SAXS measurements, we studied the mAbs' self-interaction behavior in the high protein concentration regime up to 125 g/L. Through SAXS-derived coarse-grained representations of the mAbs, we performed MC simulations with either a one-protein or a two-protein model to predict B22. By comparing simulation and experimental results, we validated our models and obtained insights into the mAbs' self-interaction properties, highlighting the role of both ion binding and charged patches on the mAb surfaces. Our models provide useful information about mAbs' self-interaction properties and can assist the screening of conditions driving to colloidal stability.

Electronic polarization effects on membrane translocation of anti-cancer drugs.

Free-energy calculations are crucial for investigating biomolecular interactions. However, in theoretical studies, the neglect of electronic polarization can reduce predictive capabilities, specifically for free-energy calculations. To effectively mimick polarization, we explore a Charge Switching (CS) model, aiming to narrow the gap between computational and experimental results. The model requires quantum-level partial charge calculations of the molecule in different environments, combined with atomistic MD simulations. Studying three different anti-cancer drug molecules with three different phospholipid membranes, we show that the method significantly improves agreement with available experimental data. In contrast, using conventional fixed charge atomistic methods, qualitative discrepancies with experiments are observed, and we show that neglecting polarization may lead to an unphysical free energy sign inversion. While the CS method is here applied to anti-cancer drug-membrane translocation, it could be used more generally to study processes considering solvent effects.

A modified Jarzynski free-energy estimator to eliminate non-conservative forces and its application in nanoparticle-membrane interactions.

Computational methods to understand interactions in bio-complex systems are however limited to time-scales typically much shorter than in Nature. For example, on the nanoscale level, interactions between nanoparticles (NPs)/molecules/peptides and membranes are central in complex biomolecular processes such as membrane-coated NPs or cellular uptake. This can be remedied by the application of e.g. Jarzynski's equality where thermodynamic properties are extracted from non-equilibrium simulations. Although, the out of equilibrium work leads to non-conservative forces. We here propose a correction Pair Forces method, that removes these forces. Our proposed method is based on the calculation of pulling forces in backward and forward directions for the Jarzynski free-energy estimator using steered molecular dynamics simulation. Our results show that this leads to much improvement for NP-membrane translocation free energies. Although here we have demonstrated the application of the method in molecular dynamics simulation, it could be applied for experimental approaches.

Anion-cation contrast of small molecule solvation in salt solutions.

The contributions from anions and cations from salt are inseparable in their perturbation of molecular systems by experimental and computational methods, rendering it difficult to dissect the effects exerted by the anions and cations individually. Here we investigate the solvation of a small molecule, caffeine, and its perturbation by monovalent salts from various parts of the Hofmeister series. Using molecular dynamics and the energy-representation theory of solvation, we estimate the solvation free energy of caffeine and decompose it into the contributions from anions, cations, and water. We also decompose the contributions arising from the solute-solvent and solute-ions interactions and that from excluded volume, enabling us to pin-point the mechanism of salt. Anions and cations revealed high contrast in their perturbation of caffeine solvation, with the cations salting-in caffeine via binding to the polar ketone groups, while the anions were found to be salting-out via perturbations of water. In agreement with previous findings, the perturbation by salt is mostly anion dependent, with the magnitude of the excluded-volume effect found to be the governing mechanism. The free-energy decomposition as conducted in the present work can be useful to understand ion-specific effects and the associated Hofmeister series.

Charge Regulation during Amyloid Formation of α-Synuclein.

Electrostatic interactions play crucial roles in protein function. Measuring pKa value perturbations upon complex formation or self-assembly of e.g. amyloid fibrils gives valuable information about the effect of electrostatic interactions in those processes. Site-specific pKa value determination by solution NMR spectroscopy is challenged by the high molecular weight of amyloid fibrils. Here we report a pH increase during fibril formation of α-synuclein, observed using three complementary experimental methods: pH electrode measurements in water; colorimetric changes of a fluorescent indicator; and chemical shift changes for histidine residues using solution state NMR spectroscopy. A significant pH increase was detected during fibril formation in water, on average by 0.9 pH units from 5.6 to 6.5, showing that protons are taken up during fibril formation. The pH upshift was used to calculate the average change in the apparent pKaave value of the acidic residues, which was found to increase by at least 1.1 unit due to fibril formation. Metropolis Monte Carlo simulations were performed on a comparable system that also showed a proton uptake due to fibril formation. Fibril formation moreover leads to a significant change in proton binding capacitance. Parallel studies of a mutant with five charge deletions in the C-terminal tail revealed a smaller pH increase due to fibril formation, and a smaller change (0.5 units on average) in the apparent pKaave values of the acidic residues. We conclude that the proton uptake during the fibril formation is connected to the high density of acidic residues in the C-terminal tail of α-synuclein.

Impact of Arginine-Phosphate Interactions on the Reentrant Condensation of Disordered Proteins.

Re-entrant condensation results in the formation of a condensed protein regime between two critical ion concentrations. The process is driven by neutralization and inversion of the protein charge by oppositely charged ions. Re-entrant condensation of cationic proteins by the polyvalent anions, pyrophosphate and tripolyphosphate, has previously been observed, but not for citrate, which has similar charge and size compared to the polyphosphates. Therefore, besides electrostatic interactions, other specific interactions between the polyphosphate ions and proteins must contribute. Here, we show that additional attractive interactions between arginine and tripolyphosphate determine the re-entrant condensation and decondensation boundaries of the cationic, intrinsically disordered saliva protein, histatin 5. Furthermore, we show by small-angle X-ray scattering (SAXS) that polyvalent anions cause compaction of histatin 5, as would be expected based solely on electrostatic interactions. Hence, we conclude that arginine-phosphate-specific interactions not only regulate solution properties but also influence the conformational ensemble of histatin 5, which is shown to vary with the number of arginine residues. Together, the results presented here provide further insight into an organizational mechanism that can be used to tune protein interactions in solution of both naturally occurring and synthetic proteins.

Virtual cell model for osmotic pressure calculation of charged biomolecules.

The osmotic pressure of dilute electrolyte solutions containing charged macro-ions as well as counterions can be computed directly from the particle distribution via the well-known cell model. Originally derived within the Poisson-Boltzmann mean-field approximation, the cell model considers a single macro-ion centered into a cell, together with counterions needed to neutralize the total cell charge, while it neglects the phenomena due to macro-ion correlations. While extensively applied in coarse-grained Monte Carlo (MC) simulations of continuum solvent systems, the cell model, in its original formulation, neglects the macro-ion shape anisotropy and details of the surface charge distribution. In this paper, by comparing one-body and two-body coarse-grained MC simulations, we first establish an upper limit for the assumption of neglecting correlations between macro-ions, and second, we validate the approximation of using a non-spherical macro-ion. Next, we extend the cell model to all-atom molecular dynamics simulations and show that protein concentration-dependent osmotic pressures can be obtained by confining counterions in a virtual, spherical subspace defining the protein number density. Finally, we show the possibility of using specific interaction parameters for the protein-ion and ion-ion interactions, enabling studies of protein concentration-dependent ion-specific effects using merely a single protein molecule.

Self-association of a highly charged arginine-rich cell-penetrating peptide.

Small-angle X-ray scattering (SAXS) measurements reveal a striking difference in intermolecular interactions between two short highly charged peptides-deca-arginine (R10) and deca-lysine (K10). Comparison of SAXS curves at high and low salt concentration shows that R10 self-associates, while interactions between K10 chains are purely repulsive. The self-association of R10 is stronger at lower ionic strengths, indicating that the attraction between R10 molecules has an important electrostatic component. SAXS data are complemented by NMR measurements and potentials of mean force between the peptides, calculated by means of umbrella-sampling molecular dynamics (MD) simulations. All-atom MD simulations elucidate the origin of the R10-R10 attraction by providing structural information on the dimeric state. The last two C-terminal residues of R10 constitute an adhesive patch formed by stacking of the side chains of two arginine residues and by salt bridges formed between the like-charge ion pair and the C-terminal carboxyl groups. A statistical analysis of the Protein Data Bank reveals that this mode of interaction is a common feature in proteins.

Arginine "Magic": Guanidinium Like-Charge Ion Pairing from Aqueous Salts to Cell Penetrating Peptides.

It is a textbook knowledge that charges of the same polarity repel each other. For two monovalent ions in the gas phase at a close contact this repulsive interaction amounts to hundreds of kilojoules per mole. In aqueous solutions, however, this Coulomb repulsion is strongly attenuated by a factor equal to the dielectric constant of the medium. The residual repulsion, which now amounts only to units of kilojoules per mole, may be in principle offset by attractive interactions. Probably the smallest cationic pair, where a combination of dispersion and cavitation forces overwhelms the Coulomb repulsion, consists of two guanidinium ions in water. Indeed, by a combination of molecular dynamics with electronic structure calculations and electrophoretic, as well as spectroscopic, experiments, we have demonstrated that aqueous guanidinium cations form (weakly) thermodynamically stable like-charge ion pairs. The importance of pairing of guanidinium cations in aqueous solutions goes beyond a mere physical curiosity, since it has significant biochemical implications. Guanidinium chloride is known to be an efficient and flexible protein denaturant. This is due to the ability of the orientationally amphiphilic guanidinium cations to disrupt various secondary structural motifs of proteins by pairing promiscuously with both hydrophobic and hydrophilic groups, including guanidinium-containing side chains of arginines. The fact that the cationic guanidinium moiety forms the dominant part of the arginine side chain implies that the like-charge ion pairing may also play a role for interactions between peptides and proteins. Indeed, arginine-arginine pairing has been frequently found in structural protein databases. In particular, when strengthened by a presence of negatively charged glutamate, aspartate, or C-terminal carboxylic groups, this binding motif helps to stabilize peptide or protein dimers and is also found in or near active sites of several enzymes. The like-charge pairing of the guanidinium side-chain groups may also hold the key to the understanding of the arginine "magic", that is, the extraordinary ability of arginine-rich polypeptides to passively penetrate across cellular membranes. Unlike polylysines, which are also highly cationic but lack the ease in crossing membranes, polyarginines do not exhibit mutual repulsion. Instead, they accumulate at the membrane, weaken it, and might eventually cross in a concerted, "train-like" manner. This behavior of arginine-rich cell penetrating peptides can be exploited when devising smart strategies how to deliver in a targeted way molecular cargos into the cell.

On short-ranged pair-potentials for long-range electrostatics.

In computer simulations, long-range electrostatic interactions are surprisingly well approximated by truncated, short-ranged pair potentials. Examples are reaction field methods; the Wolf method; and a number of schemes based on cancellation of electric multipole moments inside a cut-off region. These methods are based on the assumption that the polarization of the neglected surroundings can be inferred from a local charge distribution. Multipole moments themselves are only approximations to the true charge distribution, approximations which many times are needed to simplify calculations in complex systems. In this work we investigate a new, generalized pair-potential based on the idea of moment cancellation that covers interactions between electrostatic moments of any type. We find that moment cancellation in itself is insufficient to generate accurate results and a more restricted formalism is needed, in our case to cancel the virtual charges of the imposed moments. Thus, it is unfeasible to cancel higher-order moments with explicit higher-order moments such as dipoles and instead image charges are needed. The proposed pair-potential is general and straight forwardly implementable for any electrostatic moment - monopole, dipole, quadrupole, etc. - with a computational complexity scaling with the number of particles in the system.

Molecular insight into carboxylic acid-alkali metal cations interactions: reversed affinities and ion-pair formation revealed by non-linear optics and simulations.

Specific interactions between the carboxylic acid moiety and the monovalent salts CsCl, NaCl, and LiCl, have been investigated in Langmuir monolayers using vibrational sum frequency spectroscopy (VSFS) and complemented with coarse grained and all-atom molecular dynamics simulations. By exploiting VSFS's intrinsic surface specificity, an emphasis was made on targeting headgroup vibrations of both its charged and uncharged forms as well as water molecules in the interfacial layer. The degree of deprotonation of the monolayer as a function of cation concentration and pH was experimentally determined and theoretically rationalized. Starting from 100 mM, the surface charge was overestimated by the Gouy-Chapman model and varied depending on the identity of the cation, highlighting the appearance of ion specific effects. Agreement could be found using a modified Poisson-Boltzmann model that takes into account steric effects, with a fitted effective ion-size compatible with the hydrated ion diameters. The relative affinity of the cations to the carboxylic acid moiety was pH dependent: at pH 4.5 they arranged in the order Cs+ > Na+ > Li+, but fully reversed (Li+ > Na+ > Cs+) at pH 9. Simulations yielded microscopic insight into the origin of this behavior, with the cations showing contrasting interaction preferences for either the uncharged carboxylic acid or the charged carboxylate. Sum frequency spectra also provided evidence that all cations remained hydrated when interacting with the charged headgroup, forming solvent-separated or solvent-shared ion pairs. However, for the specific case of 1 M Li+ at pH 9, contact ion pairs were formed. Finally, the remarkable effect of trace metal multivalent cations in the interpretation of experiments is briefly discussed. The results provide exciting new insights into the complex interactions of alkali metal cations with the biophysically relevant carboxylic acid moiety.

Aggregate Size Dependence of Amyloid Adsorption onto Charged Interfaces.

Amyloid aggregates are associated with a range of human neurodegenerative disorders, and it has been shown that neurotoxicity is dependent on aggregate size. Combining molecular simulation with analytical theory, a predictive model is proposed for the adsorption of amyloid aggregates onto oppositely charged surfaces, where the interaction is governed by an interplay between electrostatic attraction and entropic repulsion. Predictions are experimentally validated against quartz crystal microbalance-dissipation experiments of amyloid beta peptides and fragmented fibrils in the presence of a supported lipid bilayer. Assuming amyloids as rigid, elongated particles, we observe nonmonotonic trends for the extent of adsorption with respect to aggregate size and preferential adsorption of smaller aggregates over larger ones. Our findings describe a general phenomenon with implications for stiff polyions and rodlike particles that are electrostatically attracted to a surface.

Total Description of Intrinsic Amphiphile Aggregation: Calorimetry Study and Molecular Probing.

Isothermal titration calorimetry (ITC) is an apt tool for a total thermodynamic description of self-assembly of atypical amphiphiles such as anionic boron cluster compounds (COSAN) in water. Global fitting of ITC enthalpograms reveals remarkable features that differentiate COSAN from classical amphiphiles: (i) strong enthalpy and weak entropy contribution to the free energy of aggregation, (ii) low degree of counterion binding, and (iii) very low aggregation number, leading to deviations from the ideal closed association model. The counterion condensation obtained from the thermodynamic model was compared with the results of 7Li DOSY NMR of Li[COSAN] micelles, which allows direct tracking of Li cations. The basic thermodynamic study of COSAN alkaline salt aggregation was complemented by NMR and ITC experiments in dilute Li/NaCl and acetonitrile aqueous solutions of COSAN. The strong affinity of acetonitrile molecules to COSAN clusters was microscopically investigated by all-atomic molecular dynamics simulations. The impact of ionic strength on COSAN self-assembling was comparable to the behavior of classical amphiphiles, whereas even a small amount of acetonitrile cosolvent has a pronounced nonclassical character of COSAN aggregation. It demonstrates that large self-assembling changes are triggered by traces of organic solvents.

Water-Mediated Ion Pairing: Occurrence and Relevance.

We present an overview of the studies of ion pairing in aqueous media of the past decade. In these studies, interactions between ions, and between ions and water, are investigated with relatively novel approaches, including dielectric relaxation spectroscopy, far-infrared (terahertz) absorption spectroscopy, femtosecond mid-infrared spectroscopy, and X-ray spectroscopy and scattering, as well as molecular dynamics simulation methods. With these methods, it is found that ion pairing is not a rare phenomenon only occurring for very particular, strongly interacting cations and anions. Instead, for many salt solutions and their interfaces, the measured and calculated structure and dynamics reveal the presence of a distinct concentration of contact ion pairs (CIPs), solvent shared ion pairs (SIPs), and solvent-separated ion pairs (2SIPs). We discuss the importance of specific ion-pairing interactions between cations like Li(+) and Na(+) and anionic carboxylate and phosphate groups for the structure and functioning of large (bio)molecular systems.

Coarse-grained model of titrating peptides interacting with lipid bilayers.

Molecular-level computer simulations of peptide aggregation, translocation, and protonation at and in biomembranes are impeded by the large time and length scales involved. We present a computationally efficient, coarse-grained, and solvent-free model for the interaction between lipid bilayers and peptides. The model combines an accurate description of mechanical membrane properties with a new granular representation of the dielectric mismatch between lipids and the aqueous phase. All-atom force fields can be easily mapped onto the coarse-grained model, and parameters for coarse-grained monopeptides accurately extrapolate to membrane permeation free energies for the corresponding dipeptides and tripeptides. Acid-base equilibria of titratable amino acid residues are further studied using a constant-pH ensemble, capturing protonation state changes upon membrane translocation. Important differences between histidine, lysine, and arginine are observed, which are in good agreement with experimental observations.

Steering patchy particles using multivalent electrolytes.

Proteins and many recently designed colloids can be regarded as patchy particles where directional interactions strongly influence and govern assembly behavior. Using explicit ion implicit solvent Metropolis Monte Carlo simulations, we investigate spherical model particles, carrying both charge and electric patches, in dilute aqueous 1 : 1, 1 : 3, and 3 : 1 electrolyte solutions. Striking differences in pair interaction free energies and orientational correlations are induced by three different salts which are discussed and rationalized in terms of ion-binding to surface groups, ion-ion correlations, and double layer forces. These findings suggest a general strategy where directional, intermolecular interactions can be invoked and tuned via small amounts of a carefully chosen electrolyte.

Strings and stripes formed by a protein system interacting via a single-patch attraction.

The phase behavior of lactoferrin has been studied as a function of concentration at a pH and ionic strength where lactoferrin is known to interact effectively via a patch-patch attraction. In contrast to isotropic attractive potentials, the directional attraction gives rise to a different phase or solution behavior. At low concentrations, the protein dimerizes. As the concentration is increased, the protein self-assembles into elongated, stripe-like structures at intermediate protein concentrations, a behavior which has been predicted for the case of attractive one-patch colloids. The stripe phase is surprisingly difficult to detect using conventional techniques, i.e. small-angle X-ray scattering, since only a small fraction of the proteins participate in the stripes combined with sedimentation due to micron-sized entities. This is circumvented by monitoring the change in the overall protein concentration by static light scattering and the stripe formation can be followed. For visualization of the structures cryo-TEM is used.