Theoretical aspects of self-assembly of proteins: A Kirkwood-Buff-theory approach

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

Electrostatically Driven Protein-Protein Interactions: Quantitative Prediction of Second Osmotic Virial Coefficients to Aid Antibody Design

Electrostatically driven attractions between proteins can result in issues for therapeutic protein formulations such as solubility limits, aggregation, and high solution viscosity. Previous work showed that a model monoclonal antibody displayed large and potentially problematic electrostatically driven attractions at typical pH (5-8) and ionic strength conditions (∼10-100 mM). Molecular simulations of a hybrid coarse-grained model (1bC/D, one bead per charged site and per domain) were used to predict potential point mutations to identify key charge changes (charge-to-neutral or charge-swap) that could greatly reduce the net attractive protein-protein self-interactions. A series of variants were tested experimentally with static and dynamic light scattering to quantify interactions and compared to model predictions at low and intermediate ionic strength. Differential scanning calorimetry and circular dichroism confirmed minimal impact on structural or thermal stability of the variants. The model provided quantitative/semiquantitative predictions of protein self-interactions compared to experimental results as well as showed which amino acid pairings or groups had the most impact.

Solubility, Solution Thermodynamics, and Preferential Solvation of Amygdalin in Ethanol + Water Solvent Mixtures

The equilibrium solubility of amygdalin in [ethanol (1) + water (2)] mixtures at 293.15 K to 328.15 K was reported. The thermodynamic properties (standard enthalpy Δ_solnH°, standard entropy Δ_solnS°, and standard Gibbs energy of solution Δ_solnG°) were computed using the generated solubility data via van't Hoff and Gibbs equations. The dissolution process of amygdalin is endothermic and the driving mechanism in all mixtures is entropy. Maximal solubility was achieved in 0.4 mole fraction of ethanol at 328.15 K and the minimal one in neat ethanol at 293.15 K. Van't Hoff, Jouyban-Acree-van't Hoff, and Buchowski-Ksiazczak models were used to simulate the obtained solubility data. The calculated solubilities deviate reasonably from experimental data. Preferential solvation parameters of amygdalin in mixture solvents were analyzed using the inverse Kirkwood-Buff integrals (IKBI) method. Amygdalin is preferentially solvated by water in ethanol-rich mixtures, whereas in water-rich mixtures, there is no clear evidence that determines which of water or ethanol solvents would be most likely to solvate the molecule.

Thermodynamic Analysis of n-Hexane-Ethanol Binary Mixtures Using the Kirkwood-Buff Theory

A complete thermodynamic analysis of mixtures consisting of molecules with complex chemical constitution can be rather demanding. The Kirkwood-Buff theory of solutions allows the estimation of thermodynamic properties, which cannot be directly extracted from atomistic simulations, such as the Gibbs energy of mixing (Δ_mix G). In this work, we perform molecular dynamics simulations of n-hexane-ethanol binary mixtures in the liquid state under two temperature-pressure conditions and at various mole fractions. On the basis of the recently published methodology of Galata [ Fluid Phase Equilib. 2018 , 470 , 25 - 37 ] , we first calculate the Kirkwood-Buff integrals in the isothermal-isobaric ( NpT) ensemble, identifying how system size affects their estimation. We then extract the activity coefficients, excess Gibbs energy, excess enthalpy, and excess entropy for the n-hexane-ethanol binary mixtures we simulate. We employ two approaches for quantifying composition fluctuations: one based on counting molecular centers of mass and a second one based on counting molecular segments. Results from the two approaches are practically indistinguishable. We compare our results against predictions of vapor-liquid equilibria obtained in a previous simulation work using the same force field, as well as with experimental data, and find very good agreement. In addition, we develop a simple methodology to identify the hydrogen bonds between ethanol molecules and analyze their effects on mixing properties.

The aqueous environment as an active participant in the protein folding process

Existing computational models applied in the protein structure prediction process do not sufficiently account for the presence of the aqueous solvent. The solvent is usually represented by a predetermined number of H₂O molecules in the bounding box which contains the target chain. The fuzzy oil drop (FOD) model, presented in this paper, follows an alternative approach, with the solvent assuming the form of a continuous external hydrophobic force field, with a Gaussian distribution. The effect of this force field is to guide hydrophobic residues towards the center of the protein body, while promoting exposure of hydrophilic residues on its surface. This work focuses on the following sample proteins: Engrailed homeodomain (RCSB: 1enh), Chicken villin subdomain hp-35, n68h (RCSB: 1yrf), Chicken villin subdomain hp-35, k65(nle), n68h, k70(nle) (RCSB: 2f4k), Thermostable subdomain from chicken villin headpiece (RCSB: 1vii), de novo designed single chain three-helix bundle (a3d) (RCSB: 2a3d), albumin-binding domain (RCSB: 1prb) and lambda repressor-operator complex (RCSB: 1lmb).

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood–Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard–Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions.

Kirkwood-Buff integrals for hard-core Yukawa fluids

The Kirkwood-Buff (KB) theory of solution is employed to investigate several macroscopic properties of the one-component hard-core Yukawa (HCY) fluid, where the key physical quantities are the KB integrals (KBIs). For both repulsive and attractive HCY fluids, the radial distribution functions are calculated by using the classical density functional theory, and then the corresponding KBIs are carried out. Since the local structure and global properties of a fluid can be related by KBI, we presented the isothermal compressibility and the derivative of the chemical potential with respect to bulk density for both repulsive and attractive HCY fluids. It is found that a transition of the affinity of particles in an attractive HCY fluid exists. The corresponding phase diagrams on the affinity are illustrated, which consist of repulsive and attractive regions with the boundary line of KBIs being zero. These results show that the aggregated structure of a HCY fluid can be effectively regulated by the screening parameter, bulk density and interaction energy, while KBIs can provide a quantitative reliable description on the properties of HCY fluids.

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.

Kirkwood-Buff Approach Rescues Overcollapse of a Disordered Protein in Canonical Protein Force Fields

Understanding the function of intrinsically disordered proteins is intimately related to our capacity to correctly sample their conformational dynamics. So far, a gap between experimentally and computationally derived ensembles exists, as simulations show overcompacted conformers. Increasing evidence suggests that the solvent plays a crucial role in shaping the ensembles of intrinsically disordered proteins and has led to several attempts to modify water parameters and thereby favor protein-water over protein-protein interactions. This study tackles the problem from a different perspective, which is the use of the Kirkwood-Buff theory of solutions to reproduce the correct conformational ensemble of intrinsically disordered proteins (IDPs). A protein force field recently developed on such a basis was found to be highly effective in reproducing ensembles for a fragment from the FG-rich nucleoporin 153, with dimensions matching experimental values obtained from small-angle X-ray scattering and single molecule FRET experiments. Kirkwood-Buff theory presents a complementary and fundamentally different approach to the recently developed four-site TIP4P-D water model, both of which can rescue the overcollapse observed in IDPs with canonical protein force fields. As such, our study provides a new route for tackling the deficiencies of current protein force fields in describing protein solvation.

Hydrotropy: monomer-micelle equilibrium and minimum hydrotrope concentration

Drug molecules with low aqueous solubility can be solubilized by a class of cosolvents, known as hydrotropes. Their action has often been explained by an analogy with micelle formation, which exhibits critical micelle concentration (CMC). Indeed, hydrotropes also exhibit "minimum hydrotrope concentration" (MHC), a threshold concentration for solubilization. However, MHC is observed even for nonaggregating monomeric hydrotropes (such as urea); this raises questions over the validity of this analogy. Here we clarify the effect of micellization on hydrotropy, as well as the origin of MHC when micellization is not accompanied. On the basis of the rigorous Kirkwood-Buff (KB) theory of solutions, we show that (i) micellar hydrotropy is explained also from preferential drug-hydrotrope interaction; (ii) yet micelle formation reduces solubilization effeciency per hydrotrope molecule; (iii) MHC is caused by hydrotrope-hydrotrope self-association induced by the solute (drug) molecule; and (iv) MHC is prevented by hydrotrope self-aggregation in the bulk solution. We thus need a departure from the traditional view; the structure of hydrotrope-water mixture around the drug molecule, not the structure of the aqueous hydrotrope solutions in the bulk phase, is the true key toward understanding the origin of MHC.