A multi-scale numerical approach to study monoclonal antibodies in solution.

Developing efficient and robust computational models is essential to improve our understanding of protein solution behavior. This becomes particularly important to tackle the high-concentration regime. In this context, the main challenge is to put forward coarse-grained descriptions able to reduce the level of detail, while retaining key features and relevant information. In this work, we develop an efficient strategy that can be used to investigate and gain insight into monoclonal antibody solutions under different conditions. We use a multi-scale numerical approach, which connects information obtained at all-atom and amino-acid levels to bead models. The latter has the advantage of reproducing the properties of interest while being computationally much faster. Indeed, these models allow us to perform many-protein simulations with a large number of molecules. We can, thus, explore conditions not easily accessible with more detailed descriptions, perform effective comparisons with experimental data up to very high protein concentrations, and efficiently investigate protein-protein interactions and their role in phase behavior and protein self-assembly. Here, a particular emphasis is given to the effects of charges at different ionic strengths.

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.

Salt Effects on Caffeine across Concentration Regimes.

Salts affect the solvation thermodynamics of molecules of all sizes; the Hofmeister series is a prime example in which different ions lead to salting-in or salting-out of aqueous proteins. Early work of Tanford led to the discovery that the solvation of molecular surface motifs is proportional to the solvent accessible surface area (SASA), and later studies have shown that the proportionality constant varies with the salt concentration and type. Using multiscale computer simulations combined with vapor-pressure osmometry on caffeine-salt solutions, we reveal that this SASA description captures a rich set of molecular driving forces in tertiary solutions at changing solute and osmolyte concentrations. Central to the theoretical work is a new potential energy function that depends on the instantaneous surface area, salt type, and concentration. Used in, e.g., Monte Carlo simulations, this allows for a highly efficient exploration of many-body interactions and the resulting thermodynamics at elevated solute and salt concentrations.

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.

Anisotropic protein-protein interactions in dilute and concentrated solutions.

Interactions between biomolecules are ubiquitous in nature and crucial to many applications including vaccine development; environmentally friendly textile detergents; and food formulation. Using small angle X-ray scattering and structure-based molecular simulations, we explore protein-protein interactions in dilute to semi-concentrated protein solutions. We address the pertinent question, whether interaction models developed at infinite dilution can be extrapolated to concentrated regimes? Our analysis is based on measured and simulated osmotic second virial coefficients and solution structure factors at varying protein concentration and for different variants of the protein Thermomyces Lanuginosus Lipase (TLL). We show that in order to span the dilute and semi-concentrated regime, any model must carefully capture the balance between spatial and orientational correlations as the protein concentration is elevated. This requires consideration of the protein surface morphology, including possible patch interactions. Experimental data for TLL is most accurately described when assuming a patchy interaction, leading to dimer formation. Our analysis supports that the dimeric proteins predominantly exist in their open conformation where the active site is exposed, thereby maximising hydrophobic attractions that promote inter-protein alignment.

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.

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.

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.

Conformation- and phosphorylation-dependent electron tunnelling across self-assembled monolayers of tau peptides.

We report on charge transport across self-assembled monolayers (SAMs) of short tau peptides by probing the electron tunneling rates and quantum mechanical simulation. We measured the electron tunneling rates across SAMs of carboxyl-terminated linker molecules (C6H12O2S) and short cis-tau (CT) and trans-tau (TT) peptides, supported on template-stripped gold (AuTS) bottom electrode, with Eutectic Gallium-Indium (EGaIn)(EGaIn) top electrode. Measurements of the current density across thousands of AuTS/linker/tau//Ga2O3/EGaIn single-molecule junctions show that the tunneling current across CT peptide is one order of magnitude lower than that of TT peptide. Quantum mechanical simulation demonstrated a wider energy bandgap of the CT peptide, as compared to the TT peptide, which causes a reduction in its electron tunneling current. Our findings also revealed the critical role of phosphorylation in altering the charge transport characteristics of short peptides; more specifically, we found that the presence of phosphate groups can reduce the energy band gap in tau peptides and alter their electrical properties. Our results suggest that conformational and phosphorylation of short peptides (e.g., tau) can significantly change their charge transport characteristics and energy levels.

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.

Electrostatics Drive Oligomerization and Aggregation of Human Interferon Alpha-2a.

Aggregation is a common phenomenon in the field of protein therapeutics and can lead to function loss or immunogenic patient responses. Two strategies are currently used to reduce aggregation: (1) finding a suitable formulation, which is labor-intensive and requires large protein quantities, or (2) engineering the protein, which requires extensive knowledge about the protein aggregation pathway. We present a biophysical characterization of the oligomerization and aggregation processes by Interferon alpha-2a (IFNα-2a), a protein drug with antiviral and immunomodulatory properties. This study combines experimental high throughput screening with detailed investigations by small-angle X-ray scattering and analytical ultracentrifugation. Metropolis Monte Carlo simulations are used to gain insight into the underlying intermolecular interactions. IFNα-2a forms soluble oligomers that are controlled by a fast pH and concentration-dependent equilibrium. Close to the isoelectric point of 6, IFNα-2a forms insoluble aggregates which can be prevented by adding salt. We show that monomer attraction is driven mainly by molecular anisotropic dipole-dipole interactions that increase with increasing pH. Repulsion is due to monopole-monopole interactions and depends on the charge of IFNα-2a. The study highlights how combining multiple methods helps to systematically dissect the molecular mechanisms driving oligomer formation and to design ultimately efficient strategies for preventing detrimental protein aggregation.

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.

Effects of Heparin and Bivalirudin on Thrombin-Induced Platelet Activation: Differential Modulation of PAR Signaling Drives Divergent Prothrombotic Responses.

Heparin and bivalirudin are widely used as anticoagulants in the setting of acute thrombosis. In this study, we investigated how these drugs affect the ability of thrombin to generate a prothrombotic platelet response via activation of the protease-activated receptors (PARs) 1 and 4. We examined the effects of heparin/antithrombin and bivalirudin on PAR1- and PAR4-mediated intracellular calcium mobilization, aggregation, α-granule release, and procoagulant membrane exposure in platelets exposed to thrombin concentrations likely to be encountered in the thrombus microenvironment during thrombosis. At physiological antithrombin levels, heparin treatment resulted in complete and sustained inhibition of thrombin-induced PAR4-mediated platelet activation, but transient PAR1 signaling was sufficient to elicit significant α-granule release and platelet aggregation. In contrast, bivalirudin treatment resulted in rapid and profound inhibition of signaling from both PAR receptors, followed by a delayed phase of PAR4-mediated platelet activation, resulting in a robust prothrombotic response. Combination treatment with bivalirudin and subtherapeutic concentrations of heparin completely inhibited the residual platelet activation observed with single drug treatment at all time-points. Our results show that heparin and bivalirudin have different and complementary inhibitory effects on the activation of PAR1 and PAR4 by thrombin.

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.

Generalized Moment Correction for Long-Ranged Electrostatics.

Describing long-ranged electrostatics using short-ranged pair potentials is appealing because the computational complexity scales linearly with the number of particles. The foundation of the approach presented here is to mimic the long-ranged medium response by cancelling electric multipoles within a small cutoff sphere. We propose a rigorous and formally exact new method that cancels up to infinitely many multipole moments and is free of operational damping parameters often required in existing theories. Using molecular dynamics simulations of water with and without added salt, we discuss radial distribution functions, Kirkwood-Buff integrals, dielectrics, diffusion coefficients, and angular correlations in relation to existing electrostatic models. We find that the proposed method is an efficient and accurate alternative for handling long-ranged electrostatics as compared to Ewald summation schemes. The methodology and proposed parameterization are applicable also for dipole-dipole interactions.

Integrating All-Atom and Coarse-Grained Simulations-Toward Understanding of IDPs at Surfaces.

We present a scheme for transferring conformational degrees of freedom from all-atom (AA) simulations of an intrinsically disordered protein (IDP) to coarse-grained (CG) Monte Carlo (MC) simulations using conformational swap moves. AA simulations of a single histatin 5 peptide in water were used to obtain a structural ensemble, which is reweighted in a CGMC simulation in the presence of a negatively charged surface. For efficient sampling, the AA trajectory was condensed using two approaches: RMSD clustering (based on the root-mean-square difference in atom positions) and a "naïve" truncation, where only every 100th frame of the trajectory was included in the library. The results show that even libraries with few structures well reproduce the radius of gyration and interaction free energy as functions of the distance from the surface. We further observe that the surface slightly promotes the secondary structure of histatin 5 and more so if using explicit surface charges rather than smeared charges.

Anomalous Salt Dependence Reveals an Interplay of Attractive and Repulsive Electrostatic Interactions in α-synuclein Fibril Formation.

α-Synuclein (α-syn) is an intrinsically disordered protein with a highly asymmetric charge distribution, whose aggregation is linked to Parkinson's disease. The effect of ionic strength was investigated at mildly acidic pH (5.5) in the presence of catalytic surfaces in the form of α-syn seeds or anionic lipid vesicles using thioflavin T fluorescence measurements. Similar trends were observed with both surfaces: increasing ionic strength reduced the rate of α-syn aggregation although the surfaces as well as α-syn have a net negative charge at pH 5.5. This anomalous salt dependence implies that short-range attractive electrostatic interactions are critical for secondary nucleation as well as heterogeneous primary nucleation. Such interactions were confirmed in Monte Carlo simulations of α-syn monomers interacting with surface-grafted C-terminal tails, and found to be weakened in the presence of salt. Thus, nucleation of α-syn aggregation depends critically on an attractive electrostatic component that is screened by salt to the extent that it outweighs the screening of the long-range repulsion between negatively charged monomers and negative surfaces. Interactions between the positively charged N-termini of α-syn monomers on the one hand, and the negatively C-termini of α-syn on fibrils or vesicles surfaces on the other hand, are thus critical for nucleation.

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.