Coarse-grained strategy for modeling protein stability in concentrated solutions. II: phase behavior

Anisotropic coarse-grain Monte Carlo simulations of lysozyme, lactoferrin, and NISTmAb by precomputing atomistic models

We develop a multiscale coarse-grain model of the NIST Monoclonal Antibody Reference Material 8671 (NISTmAb) to enable systematic computational investigations of high-concentration physical instabilities such as phase separation, clustering, and aggregation. Our multiscale coarse-graining strategy captures atomic-resolution interactions with a computational approach that is orders of magnitude more efficient than atomistic models, assuming the biomolecule can be decomposed into one or more rigid bodies with known, fixed structures. This method reduces interactions between tens of thousands of atoms to a single anisotropic interaction site. The anisotropic interaction between unique pairs of rigid bodies is precomputed over a discrete set of relative orientations and stored, allowing interactions between arbitrarily oriented rigid bodies to be interpolated from the precomputed table during coarse-grained Monte Carlo simulations. We present this approach for lysozyme and lactoferrin as a single rigid body and for the NISTmAb as three rigid bodies bound by a flexible hinge with an implicit solvent model. This coarse-graining strategy predicts experimentally measured radius of gyration and second osmotic virial coefficient data, enabling routine Monte Carlo simulation of medically relevant concentrations of interacting proteins while retaining atomistic detail. All methodologies used in this work are available in the open-source software Free Energy and Advanced Sampling Simulation Toolkit.

Flow Activation Energy of High-Concentration Monoclonal Antibody Solutions and Protein-Protein Interactions Influenced by NaCl and Sucrose

The solution viscosity and protein-protein interactions (PPIs) as a function of temperature (4-40 °C) were measured at a series of protein concentrations for a monoclonal antibody (mAb) with different formulation conditions, which include NaCl and sucrose. The flow activation energy (Eη) was extracted from the temperature dependence of solution viscosity using the Arrhenius equation. PPIs were quantified via the protein diffusion interaction parameter (kD) measured by dynamic light scattering, together with the osmotic second virial coefficient and the structure factor obtained through small-angle X-ray scattering. Both viscosity and PPIs were found to vary with the formulation conditions. Adding NaCl introduces an attractive interaction but leads to a significant reduction in the viscosity. However, adding sucrose enhances an overall repulsive effect and leads to a slight decrease in viscosity. Thus, the averaged (attractive or repulsive) PPI information is not a good indicator of viscosity at high protein concentrations for the mAb studied here. Instead, a correlation based on the temperature dependence of viscosity (i.e., Eη) and the temperature sensitivity in PPIs was observed for this specific mAb. When kD is more sensitive to the temperature variation, it corresponds to a larger value of Eη and thus a higher viscosity in concentrated protein solutions. When kD is less sensitive to temperature change, it corresponds to a smaller value of Eη and thus a lower viscosity at high protein concentrations. Rather than the absolute value of PPIs at a given temperature, our results show that the temperature sensitivity of PPIs may be a more useful metric for predicting issues with high viscosity of concentrated solutions. In addition, we also demonstrate that caution is required in choosing a proper protein concentration range to extract kD. In some excipient conditions studied here, the appropriate protein concentration range needs to be less than 4 mg/mL, remarkably lower than the typical concentration range used in the literature.

A molecular dynamics study of protein denaturation induced by sulfonate-based surfactants

Microsecond timescale explicit-solvent atomistic simulations were carried out to investigate how anionic surfactants modulate protein structure and dynamics. We found that lysozyme undergoes near-complete denaturation at the high concentration (> 0.1 M) of sodium pentadecyl sulfonate (SPDS), while only partial denaturation occurs at the concentration slightly below 0.1 M. In large part, protein denaturation is structurally manifested by disappearance of helical segments and loss of tertiary interactions. The computational prediction of the extent of burial of cysteine residues was experimentally validated by measuring the accessibility of the respective sulfhydryl groups. Overall, our work indicates an interesting synergy between electrostatic and hydrophobic contributions to lysozyme's denaturation process by anionic surfactants. In fact, first disulfide bridges and hydrogen bonds from protein surface to SPDS head groups loosen the protein globule followed by fuller denaturation via insertion of the surfactant's hydrophobic tails into the protein core.

Toward a Suite of Coarse-Grained Models for Molecular Simulation of Monoclonal Antibodies and Therapeutic Proteins

A series of coarse-grained models for molecular simulation of proteins are considered, with emphasis on the application of predicting protein-protein self-interactions for monoclonal antibodies (MAbs). As an illustrative example and for quantitative comparison, the models are used to predict osmotic virial coefficients over a broad range of attractive and repulsive self-interactions and solution conditions for a series of MAbs where the second osmotic virial coefficient has been experimentally determined in prior work. The models are compared based on how well they can predict experimental behavior, their computational burdens, and scalability. An intermediate-resolution model is also introduced that can capture specific electrostatic interactions with improved efficiency and similar or improved accuracy when compared to the previously published models. Guidance is included for the selection of coarse-grained models more generally for capturing a balance of electrostatic, steric, and short-ranged nonelectrostatic interactions for proteins from low to high concentrations.

Transferable Coarse-Grained Models of Liquid-Liquid Equilibrium Using Local Density Potentials Optimized with the Relative Entropy

Bottom-up coarse-grained (CG) models are now regularly pursued to enable large length and time scale molecular simulations of complex, often macromolecular systems. However, predicting fluid phase equilibria using such models remains fundamentally challenging. A major problem stems from the typically low transferability of CG models beyond the densities and/or compositions at which they are parametrized, which is necessary if they are to describe distinct structural and thermodynamic properties unique to each phase. CG model transferability is compounded by the representation of the inherently multibody coarse interactions using pair potentials that neglect higher order effects. Here, we propose to construct transferable single site CG models of liquid mixtures by supplementing traditional CG pair interactions with local density potentials, which constitute a computationally inexpensive mean-field approach to describe many-body effects, in that site energies are modulated by the local solution environment. To illustrate the approach, we use intra- and interspecies local density potentials to develop CG models of benzene-water solutions that show impressive transferability in structural metrics (pair correlation functions, density profiles) throughout composition space, in contrast to pair-only CG representations. While further refinement may be necessary to represent more complex thermodynamic properties, like the liquid-liquid interfacial tension, the generality and improvement offered by the local density approach are highly encouraging for enabling complex phase equilibrium modeling using CG models.

Predicting low-temperature free energy landscapes with flat-histogram Monte Carlo methods

We present a method for predicting the free energy landscape of fluids at low temperatures from flat-histogram grand canonical Monte Carlo simulations performed at higher ones. We illustrate our approach for both pure and multicomponent systems using two different sampling methods as a demonstration. This allows us to predict the thermodynamic behavior of systems which undergo both first order and continuous phase transitions upon cooling using simulations performed only at higher temperatures. After surveying a variety of different systems, we identify a range of temperature differences over which the extrapolation of high temperature simulations tends to quantitatively predict the thermodynamic properties of fluids at lower ones. Beyond this range, extrapolation still provides a reasonably well-informed estimate of the free energy landscape; this prediction then requires less computational effort to refine with an additional simulation at the desired temperature than reconstruction of the surface without any initial estimate. In either case, this method significantly increases the computational efficiency of these flat-histogram methods when investigating thermodynamic properties of fluids over a wide range of temperatures. For example, we demonstrate how a binary fluid phase diagram may be quantitatively predicted for many temperatures using only information obtained from a single supercritical state.

Multicomponent adsorption in mesoporous flexible materials with flat-histogram Monte Carlo methods

We demonstrate an extensible flat-histogram Monte Carlo simulation methodology for studying the adsorption of multicomponent fluids in flexible porous solids. This methodology allows us to easily obtain the complete free energy landscape for the confined fluid-solid system in equilibrium with a bulk fluid of any arbitrary composition. We use this approach to study the adsorption of a prototypical coarse-grained binary fluid in "Hookean" solids, where the free energy of the solid may be described as a simple spring. However, our approach is fully extensible to solids with arbitrarily complex free energy profiles. We demonstrate that by tuning the fluid-solid interaction ranges, the inhomogeneous fluid structure inside the pore can give rise to enhanced selective capture of a larger species through cooperative adsorption with a smaller one. The maximum enhancement in selectivity is observed at low to intermediate pressures and is especially pronounced when the larger species is very dilute in the bulk. This suggest a mechanism by which the selective capture of a minor component from a bulk fluid may be enhanced.

Predicting unfolding thermodynamics and stable intermediates for alanine-rich helical peptides with the aid of coarse-grained molecular simulation

This report focuses on the molecular-level processes and thermodynamics of unfolding of a series of helical peptides using a coarse-grained (CG) molecular model. The CG model was refined to capture thermodynamics and structural changes as a function of temperature for a set of published peptide sequences. Circular dichroism spectroscopy (CD) was used to experimentally monitor the temperature-dependent conformational changes and stability of published peptides and new sequences introduced here. The model predictions were quantitatively or semi-quantitatively accurate in all cases. The simulations and CD results showed that, as expected, in most cases the unfolding of helical peptides is well described by a simply 2-state model, and conformational stability increased with increased length of the helices. A notable exception in a 19-residue helix was when two Ala residues were each replaced with Phe. This stabilized a partly unfolded intermediate state via hydrophobic contacts, and also promoted aggregates at higher peptide concentrations.

Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome's Facet

Bacterial microcompartments, BMCs, are organelles that exist within wide variety of bacteria and act as nanofactories. Among the different types of known BMCs, the carboxysome has been studied the most. The carboxysome plays an important role in the light-independent part of the photosynthesis process, where its icosahedral-like proteinaceous shell acts as a membrane that controls the transport of metabolites. Although a structural model exists for the carboxysome shell, it remains largely unknown how the shell proteins self-assemble. Understanding the self-assembly process can provide insights into how the shell affects the carboxysome's function and how it can be modified to create new functionalities, such as artificial nanoreactors and artificial protein membranes. Here, we describe a theoretical framework that employs Monte Carlo simulations with a coarse-grain potential that reproduces well the atomistic potential of mean force; employing this framework, we are able to capture the initial stages of the 2D self-assembly of CcmK2 hexamers, a major protein-shell component of the carboxysome's facet. The simulations reveal that CcmK2 hexamers self-assemble into clusters that resemble what was seen experimentally in 2D layers. Further analysis of the simulation results suggests that the 2D self-assembly of carboxysome's facets is driven by a nucleation-growth process, which in turn could play an important role in the hierarchical self-assembly of BMC shells in general.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.

Concentrated dispersions of equilibrium protein nanoclusters that reversibly dissociate into active monomers

Stabilizing proteins at high concentration is of broad interest in drug delivery, for treatment of cancer and many other diseases. Herein, we create highly concentrated antibody dispersions (up to 260 mg/mL) comprising dense equilibrium nanoclusters of protein (monoclonal antibody 1B7, polyclonal sheep immunoglobulin G, and bovine serum albumin) molecules which, upon dilution in vitro or administration in vivo, remain conformationally stable and biologically active. The extremely concentrated environment within the nanoclusters (∼700 mg/mL) provides conformational stability to the protein through a novel self-crowding mechanism, as shown by computer simulation, while the primarily repulsive nanocluster interactions result in colloidally stable, transparent dispersions. The nanoclusters are formed by adding trehalose as a cosolute which strengthens the short-ranged attraction between protein molecules. The protein cluster diameter was reversibly tuned from 50 to 300 nm by balancing short-ranged attraction against long-ranged electrostatic repulsion of weakly charged protein at a pH near the isoelectric point. This behavior is described semiquantitatively with a free energy model which includes the fractal dimension of the clusters. Upon dilution of the dispersion in vitro, the clusters rapidly dissociated into fully active protein monomers as shown with biophysical analysis (SEC, DLS, CD, and SDS-PAGE) and sensitive biological assays. Since the concept of forming nanoclusters by tuning colloid interactions is shown to be general, it is likely applicable to a variety of biological therapeutics, mitigating the need to engineer protein stability through amino acid modification. In vivo subcutaneous injection into mice results in indistinguishable pharmacokinetics versus a standard antibody solution. Stable protein dispersions with low viscosities may potentially enable patient self-administration by subcutaneous injection of antibody therapeutics being discovered and developed.

Molecular dynamics of an embedded-charge model of lysozyme aqueous solutions

The onset of liquid-vapor separation in an interaction site model of a lysozyme aqueous solution is investigated by means of molecular dynamics (MD). Calculations are performed for a soft-core version of a potential early introduced by Carlsson et al. (J. Phys. Chem. B 2001, 105, 9040; 2001, 105, 12189.) whose liquid-vapor coexistence was studied by Rosch and Errington (J. Phys. Chem. B 2007, 111, 12591.); our modified model preserves the tailoring onto the experimental lysozyme solution properties embodied by those descriptions. We first show that the structural results obtained by Carlsson et al. at ambient conditions are quite well reproduced by our approach. Then, we cool the system along an isochoric path by monitoring the structural and dynamical properties at various temperatures. We thus show that a fluid-fluid separation takes place at a temperature 15% below the presumed binodal; in particular, we observe that density inhomogeneities develop rather early in the MD run and evolve over tens of nanoseconds into two dense aggregates that eventually merge, after approximately 100 ns more, into a single liquid phase separated from a vapor region by a well-defined planar interface. The densities of the two coexisting fluids are compatible with previous determinations of the binodal line. The connections of this work to the overall scenario of phase stability investigations in protein solutions, as well as possible developments based on the use of more refined models, are discussed.

A didactic model of macromolecular crowding effects on protein folding

A didactic model is presented to illustrate how the effect of macromolecular crowding on protein folding and association is modeled using current analytical theory and discrete molecular dynamics. While analytical treatments of crowding may consider the effect as a potential of average force acting to compress a polypeptide chain into a compact state, the use of simulations enables the presence of crowding reagents to be treated explicitly. Using an analytically solvable toy model for protein folding, an approximate statistical thermodynamic method is directly compared to simulation in order to gauge the effectiveness of current analytical crowding descriptions. Both methodologies are in quantitative agreement under most conditions, indication that both current theory and simulation methods are capable of recapitulating aspects of protein folding even by utilizing a simplistic protein model.

Kinetic studies of cAMP-induced propagation of the allosteric signal in the cAMP receptor protein from Escherichia coli with the use of site-directed mutagenesis

The cyclic AMP receptor protein (CRP) - general transcription factor in Escherichia coli - changes their conformation after the cAMP binding. For CRP mutants bearing the amino acids substitutions in position 138 located within the hinge region, the fluorescence stopped-flow measurements have been employed to study the kinetics of the conformational changes. By using two naturally appearing Tryptophan residues (W13, W85) localized nearby the ligand binding pocket and 1,5-I-AEDANS-labeled C178 localized in the helix-turn-helix (HTH) motif within the C-terminal domain as a fluorescence probes, we observed a first and a consensus steps of CRP-cAMP association, respectively. The collected data suggest that the kinetic parameters determined for mutants, reflect a component of the conformational change occurring in the native protein. Therefore, the independent association of two cAMP molecules to the wt protein is followed by at least a three-step conformational change which alters the surroundings of HTH motifs.

Insights Into Crowding Effects on Protein Stability From a Coarse-Grained Model

Proteins aggregate and precipitate from high concentration solutions in a wide variety of problems of natural and technological interest. Consequently, there is a broad interest in developing new ways to model the thermodynamic and kinetic aspects of protein stability in these crowded cellular or solution environments. We use a coarse-grained modeling approach to study the effects of different crowding agents on the conformational equilibria of proteins and the thermodynamic phase behavior of their solutions. At low to moderate protein concentrations, we find that crowding species can either stabilize or destabilize the native state, depending on the strength of their attractive interaction with the proteins. At high protein concentrations, crowders tend to stabilize the native state due to excluded volume effects, irrespective of the strength of the crowder-protein attraction. Crowding agents reduce the tendency of protein solutions to undergo a liquid-liquid phase separation driven by strong protein-protein attractions. The aforementioned equilibrium trends represent, to our knowledge, the first simulation predictions for how the properties of crowding species impact the global thermodynamic stability of proteins and their solutions.

Macromolecular crowding modulates folding mechanism of alpha/beta protein apoflavodoxin

Protein dynamics in cells may be different from those in dilute solutions in vitro, because the environment in cells is highly concentrated with other macromolecules. This volume exclusion because of macromolecular crowding is predicted to affect both equilibrium and kinetic processes involving protein conformational changes. To quantify macromolecular crowding effects on protein folding mechanisms, we investigated the folding energy landscape of an alpha/beta protein, apoflavodoxin, in the presence of inert macromolecular crowding agents, using in silico and in vitro approaches. By means of coarse-grained molecular simulations and topology-based potential interactions, we probed the effects of increased volume fractions of crowding agents (phi(c)) as well as of crowding agent geometry (sphere or spherocylinder) at high phi(c). Parallel kinetic folding experiments with purified Desulfovibro desulfuricans apoflavodoxin in vitro were performed in the presence of Ficoll (sphere) and Dextran (spherocylinder) synthetic crowding agents. In conclusion, we identified the in silico crowding conditions that best enhance protein stability, and discovered that upon manipulation of the crowding conditions, folding routes experiencing topological frustrations can be either enhanced or relieved. Our test-tube experiments confirmed that apoflavodoxin's time-resolved folding path is modulated by crowding agent geometry. Macromolecular crowding effects may be a tool for the manipulation of protein-folding and function in living cells.

Coarse-grained strategy for modeling protein stability in concentrated solutions. III: directional protein interactions

We extend our coarse-grained modeling strategy described in parts I and II of this investigation to account for nonuniform spatial distributions of hydrophobic residues on the solvent-exposed surfaces of native proteins. Within this framework, we explore how patchy surfaces can influence the solvent-mediated protein-protein interactions, and the unfolding and self-assembly behaviors of proteins in solution. In particular, we compare the equilibrium unfolding and self-assembly trends for three model proteins that share the same overall sequence hydrophobicity, but exhibit folded configurations with different solvent-exposed native-state surface morphologies. Our model provides new insights into how directional interactions can affect native-state protein stability in solution. We find that strongly-directional attractions between native molecules with patchy surfaces can help stabilize the folded conformation through the formation of self-assembled clusters. In contrast, native proteins with more uniform surfaces are destabilized by protein-protein attractions involving the denatured state. Finally, we discuss how the simulation results provide insights into the experimental solution behaviors of several proteins that display directional interactions in their native states.

Analytical model for studying how environmental factors influence protein conformational stability in solution

We introduce an analytical modeling strategy for probing the conformational stability of globular proteins in aqueous solution. In this approach, the intrinsic (i.e., infinite dilution) thermodynamic stability and coarse structural properties of the proteins, as well as the effective protein-protein interactions, derive from a heteropolymer collapse theory that incorporates predicted temperature- and pressure-dependent hydrophobic interactions. Protein concentration effects are estimated by integrating this information into a molecular thermodynamic model, which is an ad hoc generalization of the exact equilibrium theory of a one-dimensional binary mixture of square-well particles that interconvert through an isomerization (i.e., folding) reaction. The end result is an analytical multiscale modeling approach which, although still schematic, can predict that folded proteins exhibit a closed-loop region of stability in the pressure-temperature plane and that protein concentration has a nonmonotonic effect on protein stability, results consistent with qualitative trends observed in both experiments of protein solutions and simulations of coarse-grained protein models.

Heteropolymer collapse theory for protein folding in the pressure-temperature plane

We revisit a heteropolymer collapse theory originally introduced to explore how the balance between hydrophobic interactions and configurational entropy determines the thermal stability of globular proteins at ambient pressure. We generalize the theory by introducing a basic statistical mechanical treatment for how pressure impacts the solvent-mediated interactions between hydrophobic amino-acid residues. In particular, we estimate the strength of the hydrophobic interactions using a molecular thermodynamic model for the interfacial free energy between liquid water and a curved hydrophobic solute. The model, which also reproduces many of the distinctive thermodynamic properties of aqueous solutions in bulk and interfacial environments, predicts that the water-solute interfacial free energy is significantly reduced by the application of high hydrostatic pressures. This allows water to penetrate into folded heteropolymers at high pressure and break apart their hydrophobic cores, a scenario suggested earlier by information theory calculations. As a result, folded heteropolymers are predicted to display the kind of closed region of stability in the pressure-temperature plane exhibited by native proteins. We compare predictions of the collapse theory with experimental data for several proteins.