Incorporation of Hard and Soft Protein-Protein Interactions into Models for Crowding Effects in Binary and Ternary Protein Mixtures. Comparison of Approximate Analytical Solutions with Numerical Simulation

Polyethylene Glycol Impacts Conformation and Dynamics of Escherichia coli Prolyl-tRNA Synthetase Via Crowding and Confinement Effects

Polyethylene glycol (PEG) is a flexible, nontoxic polymer commonly used in biological and medical research, and it is generally regarded as biologically inert. PEG molecules of variable sizes are also used as crowding agents to mimic intracellular environments. A recent study with PEG crowders revealed decreased catalytic activity of Escherichia coli prolyl-tRNA synthetase (Ec ProRS), where the smaller molecular weight PEGs had the maximum impact. The molecular mechanism of the crowding effects of PEGs is not clearly understood. PEG may impact protein conformation and dynamics, thus its function. In the present study, the effects of PEG molecules of various molecular weights and concentrations on the conformation and dynamics of Ec ProRS were investigated using a combined experimental and computational approach including intrinsic tryptophan fluorescence spectroscopy, atomic force microscopy, and atomistic molecular dynamic simulations. Results of the present study suggest that lower molecular weight PEGs in the dilute regime have modest effects on the conformational dynamics of Ec ProRS but impact the catalytic function primarily via the excluded volume effect; they form large clusters blocking the active site pocket. In contrast, the larger molecular weight PEGs in dilute to semidilute regimes have a significant impact on the protein's conformational dynamics; they wrap on the protein surface through noncovalent interactions. Thus, lower-molecular-weight PEG molecules impact protein dynamics and function via crowding effects, whereas larger PEGs induce confinement effects. These results have implications for the development of inhibitors for protein targets in a crowded cellular environment.

Simplified Equilibrium Model for Exploring the Combined Influences of Concentration, Aggregate Shape, Excluded Volume, and Surface Adsorption upon Aggregation Propensity and Distribution of Globular Macromolecules

A mesoscopic model for the equilibrium self-association of a globular macromolecule that may form oligomers of various shapes and unlimited sizes is presented. Allowance is made within this model for the effects of variation in the free energy of subunit contact within an oligomer of specified size and different shapes, the free energy of adsorption of an oligomer of specified size and shape to a planar surface, and the free energy of nonspecific excluded volume interaction between an oligomer of specified size and shape and an inert species occupying a specified fraction of total volume. The model is analytically soluble and permits rapid calculation and analysis of the effects of variation in each of the three free energy parameters upon the concentration dependence of the weight-average stoichiometry of the oligomer, the fraction of total macromolecule that is adsorbed, and the fraction of differently shaped oligomers that are adsorbed and in free solution.

Influence of Nonspecific Interactions on Protein Associations: Implications for Biochemistry In Vivo

The cellular interior is composed of a variety of microenvironments defined by distinct local compositions and composition-dependent intermolecular interactions. We review the various types of nonspecific interactions between proteins and between proteins and other macromolecules and supramolecular structures that influence the state of association and functional properties of a given protein existing within a particular microenvironment at a particular point in time. The present state of knowledge is summarized, and suggestions for fruitful directions of research are offered. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Modeling protein association from homogeneous to mixed environments: A reaction-diffusion dynamics approach

Protein-protein association in vivo occur in a crowded and complex environment. Theoretical models based on hard-core repulsion predict stabilization of the product under crowded conditions. Soft interactions, on the contrary, can either stabilize or destabilize the product formation. Here we modeled protein association in presence of crowders of varying size, shape, interaction potential and used different mixing parameters for constituent crowders to study the influence on the association reaction. It was found that size is a more dominant factor in crowder-induced stabilization than the shape. Furthermore, in a mixture of crowders having different sizes but identical interaction potential, the change of free energy is additive of the free energy changes produced by individual crowders. However, the free energy change is not additive if two crowders of same size interact via different interaction potentials. These findings provide a systematic understanding of crowding influences in heterogeneous medium.

Toward Biotherapeutics Formulation Composition Engineering using Site-Identification by Ligand Competitive Saturation (SILCS)

Formulation of protein-based therapeutics employ advanced formulation and analytical technologies for screening various parameters such as buffer, pH, and excipients. At a molecular level, physico-chemical properties of a protein formulation depend on self-interaction between protein molecules, protein-solvent and protein-excipient interactions. This work describes a novel in silico approach, SILCS-Biologics, for structure-based modeling of protein formulations. SILCS Biologics is based on the Site-Identification by Ligand Competitive Saturation (SILCS) technology and enables modeling of interactions among different components of a formulation at an atomistic level while accounting for protein flexibility. It predicts potential hotspot regions on the protein surface for protein-protein and protein-excipient interactions. Here we apply SILCS-Biologics on a Fab domain of a monoclonal antibody (mAbN) to model Fab-Fab interactions and interactions with three amino acid excipients, namely, arginine HCl, proline and lysine HCl. Experiments on 100 mg/ml formulations of mAbN showed that arginine increased, lysine reduced, and proline did not impact viscosity. We use SILCS-Biologics modeling to explore a structure-based hypothesis for the viscosity modulating effect of these excipients. Current efforts are aimed at further validation of this novel computational framework and expanding the scope to model full mAb and other protein therapeutics.

Depletion interactions modulate the binding between disordered proteins in crowded environments

The molecular environment in a biological cell is much more crowded than the conditions commonly used in biochemical and biophysical experiments in vitro. It is therefore important to understand how the conformations and interactions of biological macromolecules are affected by such crowding. Addressing these questions quantitatively, however, has been challenging owing to a lack of sufficiently detailed experimental information and theoretical concepts suitable for describing crowding, especially when polymeric crowding agents and biomolecules are involved. Here, we use the combination of extensive single-molecule experiments with established and recent theoretical concepts to investigate the interaction between two intrinsically disordered proteins. We observe pronounced effects of crowding on their interactions and provide a quantitative framework for rationalizing these effects.

Intrinsically disordered proteins (IDPs) abound in cellular regulation. Their interactions are often transitory and highly sensitive to salt concentration and posttranslational modifications. However, little is known about the effect of macromolecular crowding on the interactions of IDPs with their cellular targets. Here, we investigate the influence of crowding on the interaction between two IDPs that fold upon binding, with polyethylene glycol as a crowding agent. Single-molecule spectroscopy allows us to quantify the effects of crowding on a comprehensive set of observables simultaneously: the equilibrium stability of the complex, the association and dissociation kinetics, and the microviscosity, which governs translational diffusion. We show that a quantitative and coherent explanation of all observables is possible within the framework of depletion interactions if the polymeric nature of IDPs and crowders is incorporated based on recent theoretical developments. The resulting integrated framework can also rationalize important functional consequences, for example, that the interaction between the two IDPs is less enhanced by crowding than expected for folded proteins of the same size.

Quantitative Interpretation of Solvent Paramagnetic Relaxation for Probing Protein-Cosolute Interactions

Protein-small cosolute molecule interactions are ubiquitous and known to modulate the solubility, stability, and function of many proteins. Characterization of such transient weak interactions at atomic resolution remains challenging. In this work, we develop a simple and practical NMR method for extracting both energetic and dynamic information on protein-cosolute interactions from solvent paramagnetic relaxation enhancement (sPRE) measurements. Our procedure is based on an approximate (non-Lorentzian) spectral density that behaves exactly at both high and low frequencies. This spectral density contains two parameters, one global related to the translational diffusion coefficient of the paramagnetic cosolute, and the other residue specific. These parameters can be readily determined from sPRE data, and then used to calculate analytically a concentration normalized equilibrium average of the interspin distance, ⟨r^-6⟩_norm, and an effective correlation time, τ_C, that provide measures of the energetics and dynamics of the interaction at atomic resolution. We compare our approach with existing ones, and demonstrate the utility of our method using experimental ¹H longitudinal and transverse sPRE data recorded on the protein ubiquitin in the presence of two different nitroxide radical cosolutes, at multiple static magnetic fields. The approach for analyzing sPRE data outlined here provides a powerful tool for deepening our understanding of extremely weak protein-cosolute interactions.

Simple Calculation of Phase Diagrams for Liquid-Liquid Phase Separation in Solutions of Two Macromolecular Solute Species

A simple method is described for the calculation of two- and three-dimensional phase diagrams describing stability and coexistence curves or surfaces separating one- and two-phase regions in composition/temperature space of a solution containing solute species 1 and 2. The calculation requires a quantitative description of the intermolecular potentials of mean force acting between like (1–1 and 2–2) and unlike (1–2) species. Example calculations are carried out for solutions of species interacting via spherically symmetric square-well potentials as first-order models for protein–protein interaction. When the interaction between species 1 and 2 is more repulsive than those acting between like species, the two-phase region is characterized by an equilibrium between a phase enriched in 1 and depleted in 2 and a phase enriched in 2 and depleted in 1. When the interaction between species 1 and 2 is more attractive than those acting between like species, the two-phase region is characterized by an equilibrium between a phase enriched in both species and a phase depleted in both species. The latter example provides a first-order description of coacervate formation without postulating specific interactions between the two solute species.

Crowder-Induced Conformational Ensemble Shift in Escherichia coli Prolyl-tRNA Synthetase

The effect of molecular crowding on the structure and function of Escherichia coli prolyl-transfer RNA synthetase (Ec ProRS), a member of the aminoacyl-transfer RNA synthetase family, has been investigated using a combined experimental and theoretical method. Ec ProRS is a multidomain enzyme; coupled-domain dynamics are essential for efficient catalysis. To gain insight into the mechanistic detail of the crowding effect, kinetic studies were conducted with varying concentrations and sizes of crowders. In parallel, spectroscopic and quantum chemical studies were employed to probe the "soft interactions" between crowders and protein side chains. Finally, the dynamics of the dimeric protein was examined in the presence of crowders using a long-duration (70 ns) classical molecular dynamic simulations. The results of the simulations revealed a shift in the conformational ensemble, which is consistent with the preferential exclusion of cosolutes. The "soft interactions" model of the crowding effect also explained the alteration in kinetic parameters. In summary, the study found that the effects of molecular crowding on both conformational dynamics and catalytic function are correlated in the multidomain Ec ProRS, an enzyme that is central to protein synthesis in all living cells. This study affirmed that large and small cosolutes have considerable impacts on the structure, dynamics, and function of modular proteins and therefore must be considered for stabilizing protein-based pharmaceuticals and industrial enzymes.

On the nature of the optimal form of the holdase-type chaperone stress response

The holdase paradigm of chaperone action involves preferential binding by the chaperone to the unfolded protein state, thereby preventing it from either, associating with other unstable proteins (to form large dysfunctional aggregates), or being degraded by the proteolytic machinery of the cell/organism. In this paper, we examine the necessary physical constraints imposed upon the holdase chaperone response in a cell-like environment and use these limitations to comment on the likely nature of the optimal form of chaperone response in vivo.

Transfer Free Energies of Test Proteins Into Crowded Protein Solutions Have Simple Dependence on Crowder Concentration

The effects of macromolecular crowding on the thermodynamic properties of test proteins are determined by the latter's transfer free energies from a dilute solution to a crowded solution. The transfer free energies in turn are determined by effective protein-crowder interactions. When these interactions are modeled at the all-atom level, the transfer free energies may defy simple predictions. Here we investigated the dependence of the transfer free energy (Δμ) on crowder concentration. We represented both the test protein and the crowder proteins atomistically, and used a general interaction potential consisting of hard-core repulsion, non-polar attraction, and solvent-screened electrostatic terms. The chemical potential was rigorously calculated by FMAP (Qin and Zhou, 2014), which entails expressing the protein-crowder interaction terms as correlation functions and evaluating them via fast Fourier transform (FFT). To high accuracy, the transfer free energy can be decomposed into an excluded-volume component (Δμ_e−v), arising from the hard-core repulsion, and a soft-attraction component (Δμ_s−a), arising from non-polar and electrostatic interactions. The decomposition provides physical insight into crowding effects, in particular why such effects are very modest on protein folding stability. Further decomposition of Δμ_s−a into non-polar and electrostatic components does not work, because these two types of interactions are highly correlated in contributing to Δμ_s−a. We found that Δμ_e−v fits well to the generalized fundamental measure theory (Qin and Zhou, 2010), which accounts for atomic details of the test protein but approximates the crowder proteins as spherical particles. Most interestingly, Δμ_s−a has a nearly linear dependence on crowder concentration. The latter result can be understood within a perturbed virial expansion of Δμ (in powers of crowder concentration), with Δμ_e−v as reference. Whereas the second virial coefficient deviates strongly from that of the reference system, higher virial coefficients are close to their reference counterparts, thus leaving the linear term to make the dominant contribution to Δμ_s−a.

Non-specific Interactions Between Macromolecular Solutes in Concentrated Solution: Physico-Chemical Manifestations and Biochemical Consequences

A general thermodynamic formulation of the effect of hard and soft non-specific intermolecular interactions upon reaction equilibria is summarized. A highly simplified quantitative model for non-specific intermolecular interaction is introduced. This model is used to illustrate how the magnitudes of attractive and repulsive components of the overall intermolecular interaction, and the balance between them, influence the concentration-dependent properties of a highly concentrated solution of a single macromolecular solute. The properties calculated using the results of computer simulation and an approximate analytical model are found to agree qualitatively with the results of experimental measurements on protein solutions over a broad range of concentration.

Protein-Protein Interactions of Highly Concentrated Monoclonal Antibody Solutions via Static Light Scattering and Influence on the Viscosity

The ability to design and formulate mAbs to minimize attractive interactions at high concentrations is important for protein processing, stability, and administration, particularly in subcutaneous delivery, where high viscosities are often challenging. The strength of protein-protein interactions (PPIs) of an IgG1 and IgG4 monoclonal antibody (mAb) from low to high concentration was determined by static light scattering (SLS) and used to understand viscosity data. The PPI were tuned using NaCl and five organic ionic co-solutes. The PPI strength was quantified by the normalized structure factor S(0)/ S(0)_HS and Kirkwood-Buff integral G₂₂/ G_22,HS (HS = hard sphere) determined from the SLS data and also by fits with (1) a spherical Yukawa potential and (2) an interacting hard sphere (IHS) model, which describes attraction in terms of hypothetical oligomers. The IHS model was better able to capture the scattering behavior of the more strongly interacting systems (mAb and/or co-solute) than the spherical Yukawa potential. For each descriptor of PPI, linear correlations were obtained between the viscosity at high concentration (200 mg/mL) and the interaction strengths evaluated both at low (20 mg/mL) and high concentrations (200 mg/mL) for a given mAb. However, the only parameter that provided a correlation across both mAbs was the oligomer mass ratio ( m_oligomer/ m_{monomer+dimer}) from the IHS model, indicating the importance of self-association (in addition to the direct influence of the attractive PPI) on the viscosity.

Towards developing principles of protein folding and dynamics in the cell

Proteins must fold and function in the immensely complex environment of a cell, i.e. the cytoplasm-this is far from the ideal test-tube setting of a dilute solution. Here we review the advances in protein folding and dynamics inside the cell. In developing principles of protein behavior in vivo, we also begin to understand the organization and dynamics of the cytoplasm, unifying the single protein scale with the many-protein architectures at the subcellular scale. Our group has significantly contributed to this frontier by characterizing the effect of macromolecular crowding on the distribution of protein conformations. Additionally, we provide a personal perspective on becoming a theoretical biological physicist in the era of interdisciplinary research that has been greatly influenced by Dr Kamal Shukla. We also share our view on the future direction of protein folding inside a cell.

Toward an understanding of biochemical equilibria within living cells

Four types of environmental effects that can affect macromolecular reactions in a living cell are defined: nonspecific intermolecular interactions, side reactions, partitioning between microenvironments, and surface interactions. Methods for investigating these interactions and their influence on target reactions in vitro are reviewed. Methods employed to characterize conformational and association equilibria in vivo are reviewed and difficulties in their interpretation cataloged. It is concluded that, in order to be amenable to unambiguous interpretation, in vivo studies must be complemented by in vitro studies carried out in well-characterized and controllable media designed to contain key elements of selected intracellular microenvironments.

In Aqua Veritas: The Indispensable yet Mostly Ignored Role of Water in Phase Separation and Membrane-less Organelles

Despite the common practice of presenting structures of biological molecules on an empty background and the assumption that interactions between biological macromolecules take place within the inert solvent, water represents an active component of various biological processes. This Perspective addresses indispensable, yet mostly ignored, roles of water in biological liquid-liquid phase transitions and in the biogenesis of various proteinaceous membrane-less organelles. We point out that changes in the structure of water reflected in the changes in its abilities to donate and/or accept hydrogen bonds and participate in dipole-dipole and dipole-induced dipole interactions in the presence of various solutes (ranging from small molecules to synthetic polymers and biological macromolecules) might represent a driving force for the liquid-liquid phase separation, define partitioning of various solutes in formed phases, and define the exceptional ability of intrinsically disordered proteins to be engaged in the formation of proteinaceous membrane-less organelles.

Explicit Incorporation of Hard and Soft Protein-Protein Interactions into Models for Crowding Effects in Protein Mixtures. 2. Effects of Varying Hard and Soft Interactions upon Prototypical Chemical Equilibria

Previously derived approximate analytical relations for the activity coefficient of each solute in a mixture of up to three spherical solutes in a highly nonideal solution interacting via square well potentials of mean force (Hoppe, T.; Minton, A. P. J Phys Chem B. 2016, 120, 11866-11872) were used to explore the effect of heterogeneity in volume occupancy and intermolecular interactions upon prototypical schemes representing solubility, partitioning, conformational isomerization, and self-association in crowded solutions. Results generally indicate that all of the equilibria explored are exquisitely sensitive to variations in both volume occupancy and intermolecular interaction and have important implications for the design and execution of more detailed simulations of complex media.

Role of solvent properties of water in crowding effects induced by macromolecular agents and osmolytes

Dipolarity/polarizability of water in polymer mixtures may be additive, reduced or enhanced depending on the composition of the mixture.