The osmotic second virial coefficient for protein self-interaction: Use and misuse to describe thermodynamic nonideality

Hydrodynamic and thermodynamic analysis of PEGylated human serum albumin

Covalent labeling of therapeutic drugs and proteins with polyethylene glycol (PEGylation) is an important modification for improving stability, solubility, and half-life. PEGylation alters protein solution behavior through its impact on thermodynamic nonideality by increasing the excluded volume, and on hydrodynamic nonideality by increasing the frictional drag. To understand PEGylation's impact, we investigated the thermodynamic and hydrodynamic properties of a model system consisting of PEGylated human serum albumin derivatives using analytical ultracentrifugation (AUC) and dynamic light scattering (DLS). We constructed PEGylated human serum albumin derivatives of single, linear 5K, 10K, 20K, and 40K PEG chains and a single branched-chain PEG of 40K (2 × 20K). Sedimentation velocity (SV) experiments were analyzed using SEDANAL direct boundary fitting to extract ideal sedimentation coefficients so, hydrodynamic nonideality ks, and thermodynamic nonideality 2BM1SV terms. These quantities allow the determination of the Stokes radius Rs, the frictional ratio f/fo, and the swollen or entrained volume Vs/v, which measure size, shape, and solvent interaction. We performed sedimentation equilibrium experiments to obtain independent measurements of thermodynamic nonideality 2BM1SE. From DLS measurements, we determined the interaction parameter, kD, the concentration dependence of the apparent diffusion coefficient, D, and from extrapolation of D to c = 0 a second estimate of Rs. Rs values derived from SV and DLS measurements and ensemble model calculations (see complementary study) are then used to show that ks + kD = theoretical 2B22M1. In contrast, experimental BM1 values from SV and sedimentation equilibrium data collectively allow for similar analysis for protein-PEG conjugates and show that ks + kD = 1.02-1.07∗BM1, rather than the widely used ks + kD = 2BM1 developed for hard spheres. The random coil behavior of PEG dominates the colloidal properties of PEG-protein conjugates and exceeds the sum of a random coil and hard-sphere volume due to excess entrained water.

Amino Acids and Their Biological Derivatives Modulate Protein-Protein Interactions in an Additive Way

Protein-protein interactions (PPIs) differ when measured in test tubes and cells due to the complexity of the intracellular environment. Free amino acids (AAs) and their derivatives constitute a significant fraction of the intracellular volume and mass. Recently, we have found that AAs have a generic property of rendering protein dispersions more stable by reducing the net attractive part of PPIs. Here, we study the effects on PPIs of different AA derivatives, AA mixtures, and short peptides. We find that all the tested AA derivatives modulate PPIs in solution as effectively as AAs. Furthermore, we show that the modulation effect is additive when AAs form mixtures or are bound into short peptides. Therefore, this study demonstrates the additive effects of a class of small molecules (i.e., AAs and their biological derivatives) on PPIs and provides insights into rationally designing biocompatible molecules for stabilizing protein interactions and consequently tuning protein functions.

Direct prediction of intermolecular interactions driven by disordered regions

Intrinsically disordered regions (IDRs) are critical for a wide variety of cellular functions, many of which involve interactions with partner proteins. Molecular recognition is typically considered through the lens of sequence-specific binding events. However, a growing body of work has shown that IDRs often interact with partners in a manner that does not depend on the precise order of the amino acid order, instead driven by complementary chemical interactions leading to disordered bound-state complexes. Despite this emerging paradigm, we lack tools to describe, quantify, predict, and interpret these types of structurally heterogeneous interactions from the underlying amino acid sequences. Here, we repurpose the chemical physics developed originally for molecular simulations to develop an approach for predicting intermolecular interactions between IDRs and partner proteins. Our approach enables the direct prediction of phase diagrams, the identification of chemically-specific interaction hotspots on IDRs, and a route to develop and test mechanistic hypotheses regarding IDR function in the context of molecular recognition. We use our approach to examine a range of systems and questions to highlight its versatility and applicability.

Surface Charge Can Modulate Phase Separation of Multidomain Proteins

Phase separation has emerged as an important mechanism explaining the formation of certain biomolecular condensates. Biological phase separation is often driven by the multivalent interactions of modular protein domains. Beyond valency, the physical features of folded domains that promote phase separation are poorly understood. We used a model system─the small ubiquitin modifier (SUMO) and its peptide ligand, the SUMO interaction motif (SIM)─to examine how domain surface charge influences multivalency-driven phase separation. Phase separation of polySUMO and polySIM was altered by pH via a change in the protonation state of SUMO surface histidines. These effects were recapitulated by histidine mutations, which modulated SUMO solubility and polySUMO-polySIM phase separation in parallel and were quantitatively explained by atomistic modeling of weak interactions among proteins in the system. Thus, surface charge can tune the phase separation of multivalent proteins, suggesting a means of controlling phase separation biologically, evolutionarily, and therapeutically.

Retrospective rationalization of disparities between the concentration dependence of diffusion coefficients obtained by boundary spreading and dynamic light scattering

This study establishes the existence of substantial agreement between published results from traditional boundary spreading measurements (including synthetic boundary measurements in the analytical ultracenrifuge) on two globular proteins (bovine serum albumin, ovalbumin) and the concentration dependence of diffusion coefficient predicted for experiments conducted under the operative thermodynamic constraints of constant temperature and solvent chemical potential. Although slight negative concentration dependence of the translational diffusion coefficient is the experimentally observed as well as theoretically predicted, the extent of the concentration dependence is within the limits of experimental uncertainty inherent in diffusion coefficient measurement. Attention is then directed toward the ionic strength dependence of the concentration dependence coefficient ([Formula: see text]) describing diffusion coefficients obtained by dynamic light scattering, where, in principle, the operative thermodynamic constraints of constant temperature and pressure preclude consideration of results in terms of single-solute theory. Nevertheless, good agreement between predicted and published experimental ionic strength dependencies of [Formula: see text] for lysozyme and an immunoglobulin is observed by a minor adaptation of the theoretical treatment to accommodate the fact that thermodynamic activity is monitored on the molal concentration scale because of the constraint of constant pressure that pertains in dynamic light scattering experiments.

Experimental support for reclassification of the light scattering second virial coefficient from macromolecular solutions as a hydrodynamic parameter

This investigation examines the source of the disparity between experimental values of the light scattering second virial coefficient [Formula: see text] (mL.mol/g2) for proteins and those predicted on the statistical mechanical basis of excluded volume. A much better theoretical description of published results for lysozyme is obtained by considering the experimental parameters to monitor the difference between the thermodynamic excluded volume term and its hydrodynamic counterpart. This involves a combination of parameters quantifying concentration dependence of the translational diffusion coefficient obtained from dynamic light scattering measurements. That finding is shown to account for observations of a strong correlation between [Formula: see text] (mL/g), where M2 is the molar mass (molecular weight) of the macromolecule and the diffusion concentration parameter [Formula: see text] (mL/g). On the grounds that [Formula: see text] is regarded as a hydrodynamic parameter, the same status should be accorded the light scattering second virial coefficient rather than its current incorrect thermodynamic designation as [Formula: see text] (mL.mol/g2), or just B, the osmotic second virial coefficient for protein self-interaction.

Molecular-Based Description of the Osmotic Second Virial Coefficients of Electrolytes: Rigorous Formal Links to Solute-Solvent Interaction Asymmetry, Virial Expansion Paths, and Experimental Evidence

We introduce a molecular-based route to the evaluation of the osmotic second virial coefficients of dissociative solutes in dilute binary solutions, according to a general molecular thermodynamic solvation formalism of electrolyte solutions. We discuss the underlying solvation fundamentals and derive rigorous expressions leading to (i) the functional relationship among the osmotic second virial coefficients and the limiting composition behavior of the non-Coulombic contribution to the Kirkwood-Buff integral of the solute-solute interactions, the corresponding composition slope of the mean activity coefficient of the electrolyte solute, and a precisely defined solute-solvent intermolecular interaction asymmetry that characterizes unambiguously the solution non-ideality; (ii) the self-consistent calculation of the osmotic second virial coefficients of electrolytes as defined by the composition expansion along different thermodynamic paths and/or composition variables; (iii) the microstructural interpretation of Hill's isobaric-isothermal osmotic second virial coefficient in terms of Kirkwood-Buff correlation function integrals and its relationships to other osmotic coefficients from composition expansions along alternative thermodynamic paths; and (iv) the identification of drawbacks in the implementation of previous methods, originally intended for non-electrolyte systems, to systems involving dissociative solutes. The proposed formalism provides the fundamentally based foundations to the determination of the osmotic second virial coefficients of any type of electrolyte solute, whose thermodynamic expressions converge naturally to the non-electrolyte ones by setting to unity the solute stoichiometric coefficient ν. Following the formal results, we illustrate the formalism with the calculation of a variety of osmotic second virial coefficients involving a wide selection of aqueous solutions at ambient conditions and comprising a wide range of anion-cation type combinations characterized by 2 ≤ ν ≤ 6. Finally, we interpret the behavior of the resulting osmotic virial coefficients in terms of the solute-solvent intermolecular interaction asymmetry, discuss the experimental data requirements for the accurate evaluation of the osmotic second virial coefficients, and provide some observations as well as their modeling implications.

High-Throughput Screening for Colloidal Stability of Peptide Formulations Using Dynamic and Static Light Scattering

Selection of an appropriate formulation to stabilize therapeutic proteins against aggregation is one of the most challenging tasks in early-stage drug product development. The amount of aggregates is more difficult to quantify in the case of peptides due to their small molecular size. Here, we investigated the suitability of diffusion self-interaction parameters (k_D) and osmotic second virial coefficients (B₂₂) for high-throughput (HT) screening of peptide formulations regarding their aggregation risk. These parameters were compared to the effect of thermal stress on colloidal stability. The formulation matrix comprised six buffering systems at two selected pH values, four tonicity agents, and a common preservative. The results revealed that electrostatic interactions are the main driver to control colloidal stability. Preferred formulations consisted of acetate and succinate buffer at pH 4.5 combined with glycerol or mannitol and optional m-cresol. k_D proved to be a suitable surrogate for B₂₂ as an indicator of high colloidal stability in the case of peptides as was previously described for globular proteins and antibodies. Formulation assessment solely based on k_D obtained by HT methods offers important insights into the optimization of colloidal stability during the early development of peptide-based liquid formulations and can be performed with a limited amount of peptide (∼360 mg).

Experimental determination of second virial coefficients by small-angle X-ray scattering: a problem revisited

This investigation examines the validity of employing single-solute theory to interpret SAXS measurements on buffered protein solutions-the current practice despite the necessity to regard the buffer components as additional non-scattering solutes rather than as part of the solvent. The present study of bovine serum albumin in phosphate-buffered saline supplemented with 20-100 g/L sucrose as small cosolute has certainly verified the prediction that the experimentally obtained second virial coefficient should contain protein-cosolute contributions. Nevertheless, the second virial coefficient determined for protein solutions supplemented with high cosolute concentrations on the basis of single-solute theory remains a valid means for identifying conditions conducive to protein crystallization, because the return of a slightly negative second virial coefficient based on single-solute theory [Formula: see text] still establishes the existence of slightly associative interactions between protein molecules, irrespective of the molecular source-protein self-interactions and/or protein-cosolute contributions.

Use of molecular crowding for the detection of protein self-association by size-exclusion chromatography

The feasibility of employing molecular crowding cosolutes to facilitate the detection of protein self-association by zonal size exclusion chromatography is investigated. Theoretical considerations have established that although the cosolute-induced displacement of a self-association equilibrium towards the oligomeric state invariably occurs in the mobile phase of the column, that displacement is only manifested as a decreased protein elution volume for cosolutes sufficiently small to partition between the mobile and stationary phases. Indeed, the use of a crowding agent sufficiently large to be confined to the mobile phase gives rise to an increased elution volume that could be misconstrued as evidence of cosolute-induced protein dissociation. Those theoretical considerations are reinforced by experimental studies of α-chymotrypsin (a reversibly dimerizing enzyme) on Superdex 200. The use of cosolutes such as sucrose and small polyethylene glycol fractions such as PEG-2000 is therefore recommended for the detection of protein self-association by molecular crowding effects in size exclusion chromatography.

Spectroscopic methods for assessing the molecular origins of macroscopic solution properties of highly concentrated liquid protein solutions

In cases of subcutaneous injection of therapeutic monoclonal antibodies, high protein concentrations (>50 mg/ml) are often required. During the development of these high concentration liquid formulations (HCLF), challenges such as aggregation, gelation, opalescence, phase separation, and high solution viscosities are more prone compared to low concentrated protein formulations. These properties can impair manufacturing processes, as well as protein stability and shelf life. To avoid such unfavourable solution properties, a detailed understanding about the nature of these properties and their driving forces are required. However, the fundamental mechanisms that lead to macroscopic solution properties, as above mentioned, are complex and not fully understood, yet. Established analytical methods for assessing the colloidal stability, i.e. the ability of a native protein to remain dispersed in solution, are restricted to dilute conditions and provide parameters such as the second osmotic virial coefficient, B₂₂, and the diffusion interaction coefficient, k_D. These parameters are routinely applied for qualitative estimations and identifications of proteins with challenging solution behaviours, such as high viscosities and aggregation, although the assays are prepared for low protein concentration conditions, typically between 0.1 and 20 mg/ml ("ideal" solution conditions). Quantitative analysis of samples of high protein concentration is difficult and it is hard to obtain information about the driving forces of such solution properties and corresponding protein-protein self-interactions. An advantage of using specific spectroscopic methods is the potential of directly analysing highly concentrated protein solutions at different solution conditions. This allows for collecting/gaining valuable information about the fundamental mechanisms of solution properties of the high protein concentration regime. In addition, the derived parameters might be more predictive as compared to the parameters originating from assays which are optimized for the low protein concentration range. The provided information includes structural data, molecular dynamics at various timescales and protein-solvent interactions, which can be obtained at molecular resolution. Herein, we provide an overview about spectroscopic techniques for analysing the origins of macroscopic solution behaviours in general, with a specific focus on pharmaceutically relevant high protein concentration and formulation conditions.

Intrinsically disordered sequences enable modulation of protein phase separation through distributed tyrosine motifs

Liquid–liquid phase separation (LLPS) is thought to contribute to the establishment of many biomolecular condensates, eukaryotic cell structures that concentrate diverse macromolecules but lack a bounding membrane. RNA granules control RNA metabolism and comprise a large class of condensates that are enriched in RNA-binding proteins and RNA molecules. Many RNA granule proteins are composed of both modular domains and intrinsically disordered regions (IDRs) having low amino acid sequence complexity. Phase separation of these molecules likely plays an important role in the generation and stability of RNA granules. To understand how folded domains and IDRs can cooperate to modulate LLPS, we generated a series of engineered proteins. These were based on fusions of an IDR derived from the RNA granule protein FUS (fused in sarcoma) to a multivalent poly-Src homology 3 (SH3) domain protein that phase-separates when mixed with a poly-proline–rich-motif (polyPRM) ligand. We found that the wild-type IDR promotes LLPS of the polySH3–polyPRM system, decreasing the phase separation threshold concentration by 8-fold. Systematic mutation of tyrosine residues in Gly/Ser-Tyr-Gly/Ser motifs of the IDR reduced this effect, depending on the number but not on the position of these substitutions. Mutating all tyrosines to non-aromatic residues or phosphorylating the IDR raised the phase separation threshold above that of the unmodified polySH3–polyPRM pair. These results show that low-complexity IDRs can modulate LLPS both positively and negatively, depending on the degree of aromaticity and phosphorylation status. Our findings provide plausible mechanisms by which these sequences could alter RNA granule properties on evolutionary and cellular timescales.

Glargine and degludec: Solution behaviour of higher dose synthetic insulins

Single, double and triple doses of the synthetic insulins glargine and degludec currently used in patient therapy are characterised using macromolecular hydrodynamic techniques (dynamic light scattering and analytical ultracentrifugation) in an attempt to provide the basis for improved personalised insulin profiling in patients with diabetes. Using dynamic light scattering and sedimentation velocity in the analytical ultracentrifuge glargine was shown to be primarily dimeric under solvent conditions used in current formulations whereas degludec behaved as a dihexamer with evidence of further association of the hexamers ("multi-hexamerisation"). Further analysis by sedimentation equilibrium showed that degludec exhibited reversible interaction between mono- and-di-hexamer forms. Unlike glargine, degludec showed strong thermodynamic non-ideality, but this was suppressed by the addition of salt. With such large injectable doses of synthetic insulins remaining in the physiological system for extended periods of time, in some case 24-40 hours, double and triple dose insulins may impact adversely on personalised insulin profiling in patients with diabetes.

Foreword to 'Quantitative and analytical relations in biochemistry'-a special issue in honour of Donald J. Winzor's 80th birthday

The purpose of this special issue is to honour Professor Donald J. Winzor's long career as a researcher and scientific mentor, and to celebrate the milestone of his 80th birthday. Throughout his career, Don has been renowned for his development of clever approximations to difficult quantitative relations governing a range of biophysical measurements. The theme of this special issue, 'Quantitative and analytical relations in biochemistry', was chosen to reflect this aspect of Don's scientific approach.