Investigation of the phase behavior of an embedded charge protein model through molecular simulation

Biophysical Principles Emerging from Experiments on Protein-Protein Association and Aggregation

Protein-protein association and aggregation are fundamental processes that play critical roles in various biological phenomena, from cellular signaling to disease progression. Understanding the underlying biophysical principles governing these processes is crucial for elucidating their mechanisms and developing strategies for therapeutic intervention. In this review, we provide an overview of recent experimental studies focused on protein-protein association and aggregation. We explore the key biophysical factors that influence these processes, including protein structure, conformational dynamics, and intermolecular interactions. We discuss the effects of environmental conditions such as temperature, pH and related buffer-specific effects, and ionic strength and related ion-specific effects on protein aggregation. The effects of polymer crowders and sugars are also addressed. We list the techniques used to study aggregation. We analyze emerging trends and challenges in the field, including the development of computational models and the integration of multidisciplinary approaches for a comprehensive understanding of protein-protein association and aggregation.

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.

Molecular modelling techniques for predicting liquid-liquid interfacial properties of methanol plus alkane (n-hexane, n-heptane, n-octane) mixtures

In this work, the liquid-liquid interfacial properties of methanol plus n-alkane (n-hexane, n-heptane, n-octane) mixtures are investigated at atmospheric pressure by two complementary molecular modelling techniques; namely, molecular dynamic simulations (MD) and density gradient theory (DGT) coupled with the PC-SAFT (perturbed-chain statistical associating fluid theory) equation of state. Furthermore, two molecular models of methanol are used, which are based on a non-polarisable three site approach. On the one hand, is the original (flexible) TraPPE-UA model force field. On the other hand, is the rigid approximation denoted as OPLS/2016. In both cases, n-alkanes are modelled using the TraPPE-UA model. Simulations are performed using the direct coexistence technique in the ensemble. Special attention is paid to the comparison between the estimations obtained from different methanol models, the available experimental data and theoretical calculations. In all cases, the rigid model is capable of predicting the experimental phase equilibrium and interfacial properties accurately. Unsurprisingly, the methanol-rich density and interfacial tension are overestimated using the TraPPE model combined with Lorentz-Berthelot mixing rules for predicting the mixture behaviour. Accurate comparison between MD and DGT plus PC-SAFT requires consideration of the cross-interactions between individual influence parameters and fitting the βij values. This latter aspect is particularly important because it allows the exploitation of the link between the EOS model and the direct molecular simulation of the corresponding fluid. At the same time, it was demonstrated that the key property defining the interfacial tension value is the absolute concentration of methanol in the methanol-rich phase. This behaviour indicates that there are more hydrogens bonded with each other, and they interact favourably with an increasing number of carbon atoms in the alkane.

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.

Protein folding, binding, and droplet formation in cell-like conditions

The many bystander macromolecules in the crowded cellular environments present both steric repulsion and weak attraction to proteins undergoing folding or binding and hence impact the thermodynamic and kinetic properties of these processes. The weak but nonrandom binding with bystander macromolecules may facilitate subcellular localization and biological function. Weak binding also leads to the emergence of a protein-rich droplet phase, which has been implicated in regulating a variety of cellular functions. All these important problems can now be addressed by realistic modeling of intermolecular interactions. Configurational sampling of concentrated protein solutions is an ongoing challenge.

Softness and non-spherical shape define the phase behavior and the structural properties of lysozyme in aqueous solutions

In this study, Boltzmann inversion is applied in conjunction with molecular dynamics simulations to derive inter-molecular potential for protein lysozyme in aqueous solution directly from experimental static structure factor. The potential has a soft repulsion at short distances and an attraction well at intermediate distances that give rise to the liquid-liquid phase separation. Moreover, Gibbs ensemble Monte Carlo simulations demonstrate that a non-spherical description of lysozyme is better suited to correctly reproduce the experimentally observed properties of such a phase separation. Our findings shed new light on the common problem in molecular and cell biology: "How to model proteins in their natural aqueous environments?"

Fast Method for Computing Chemical Potentials and Liquid-Liquid Phase Equilibria of Macromolecular Solutions

Chemical potential is a fundamental property for determining thermodynamic equilibria involving exchange of molecules, such as between two phases of molecular systems. Previously, we developed the fast Fourier transform (FFT)-based method for Modeling Atomistic Protein-crowder interactions (FMAP) to calculate excess chemical potentials according to the Widom insertion. Intermolecular interaction energies were expressed as correlation functions and evaluated via FFT. Here, we extend this method to calculate liquid-liquid phase equilibria of macromolecular solutions. Chemical potentials are calculated by FMAP over a wide range of molecular densities, and the condition for coexistence of low- and high-density phases is determined by the Maxwell equal-area rule. When benchmarked on Lennard-Jones fluids, our method produces an accurate phase diagram at 18% of the computational cost of the current best method. Importantly, the gain in computational speed increases dramatically as the molecules become more complex, leading to many orders of magnitude in speed up for atomistically represented proteins. We demonstrate the power of FMAP by reporting the first results for the liquid-liquid coexistence curve of γII-crystallin represented at the all-atom level. Our method may thus open the door to accurate determination of phase equilibria for macromolecular mixtures such as protein-protein mixtures and protein-RNA mixtures, that are known to undergo liquid-liquid phase separation, both in vitro and in vivo.

Protein aggregation in salt solutions

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein-protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim's thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid-liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer-salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

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.

Thermodynamic versus conformational metastability in fibril-forming lysozyme solutions

The role of intermolecular interaction in fibril-forming protein solutions and its relation with molecular conformation is a crucial aspect for the control and inhibition of amyloid structures. Here, we study the fibril formation and the protein-protein interactions of lysozyme at acidic pH and low ionic strength. The amyloid formation occurs after a long lag time and is preceded by the formation of oligomers, which seems to be off-pathway with respect to fibrillation. By measuring the osmotic isothermal compressibility and the collective diffusion coefficient of lysozyme in solution, we observe that the monomeric solution is kept in a thermodynamically metastable state by strong electrostatic repulsion, even in denaturing conditions. The measured repulsive interaction between monomers is satisfactorily accounted for by classical polyelectrolyte theory. Further, we observe a slow conformational change involving both secondary and tertiary structure, which drives the proteins toward a more hydrophobic conformation. Denatured proteins are driven out of metastability through conformational substates, which are kinetically populated and experience a lower activation energy for fibril formation. Thus, our results highlight the role of electrostatic repulsion, which hinders the aggregation of partially denatured proteins and operates as a gatekeeper favoring the association of those monomers whose conformation is capable of forming amyloid structure.

Anisotropic Interactions in Protein Mixtures: Self Assembly and Phase Behavior in Aqueous Solution

Recent experimental studies show that oppositely charged proteins can self-assemble to form seemingly stable microspheres in aqueous salt solutions. We here use parallel tempering Monte Carlo simulations to study protein phase separation of lysozyme/α-lactalbumin mixtures and show that anisotropic electrostatic interactions are important for driving protein self-assembly. In both dilute and concentrated protein phases, the proteins strongly align according to their charge distribution. While this alignment can be greatly diminished by a single point mutation, phase separation is completely suppressed when neglecting electrostatic anisotropy. The results highlight the importance of subtle electrostatic interactions even in crowded biomolecular environments where other short-ranged forces are often thought to dominate.

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.

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.

Phase behavior of model confined fluids. Influence of substrate-fluid interaction strength

We examine the relationship between the macroscopic phase behavior of nanoconfined fluids and the nature of microscopic interactions between a confining substrate and fluid. Two model slit-pore systems are explored using grand canonical transition-matrix Monte Carlo simulation. One system consists of a square-well fluid interacting with a square-well substrate, and the other contains an embedded point charge model of lysozyme interacting with a mica surface. Fluid phase diagrams are constructed for a broad range of substrate conditions. Our results indicate that one observes a maximum in the critical temperature of the fluid phase envelope upon variation of substrate strength for a given slit width. Both systems studied exhibit such maxima at intermediate wall strength. The physical rationale for this observation suggests that this behavior should be generally expected. We introduce two metrics that enable one to predict conditions that produce maxima in critical temperature. The first is related to the contact angle a fluid develops at a single confining substrate. The second is based upon virial coefficient information and requires knowledge of the substrate-fluid and fluid-fluid interaction potentials only.