Coarse-grained modeling of the self-association of therapeutic monoclonal antibodies

DeepSP: Deep learning-based spatial properties to predict monoclonal antibody stability

Therapeutic antibody development faces challenges due to high viscosities and aggregation tendencies. The spatial charge map (SCM) and spatial aggregation propensity (SAP) are computational techniques that aid in predicting viscosity and aggregation, respectively. These methods rely on structural data derived from molecular dynamics (MD) simulations, which are computationally demanding. DeepSCM, a deep learning surrogate model based on sequence information to predict SCM, was recently developed to screen high-concentration antibody viscosity. This study further utilized a dataset of 20,530 antibody sequences to train a convolutional neural network deep learning surrogate model called Deep Spatial Properties (DeepSP). DeepSP directly predicts SAP and SCM scores in different domains of antibody variable regions based solely on their sequences without performing MD simulations. The linear correlation coefficient between DeepSP scores and MD-derived scores for 30 properties achieved values between 0.76 and 0.96 with an average of 0.87. DeepSP descriptors were employed as features to build machine learning models to predict the aggregation rate of 21 antibodies, and the performance is similar to the results obtained from the previous study using MD simulations. This result demonstrates that the DeepSP approach significantly reduces the computational time required compared to MD simulations. The DeepSP model enables the rapid generation of 30 structural properties that can also be used as features in other research to train machine learning models for predicting various antibody stability using sequences only. DeepSP is freely available as an online tool via https://deepspwebapp.onrender.com and the codes and parameters are freely available at https://github.com/Lailabcode/DeepSP.

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.

Concentration-Dependent Diffusion of Monoclonal Antibodies: Underlying Mechanisms of Anomalous Diffusion

The development, storage, transport, and subcutaneous delivery of highly concentrated monoclonal antibody formulations pose significant challenges due to the high solution viscosity and low diffusion of the antibody molecules in crowded environments. These issues often stem from the self-associating behavior of the antibody molecules, potentially leading to aggregation. In this work, we used a dissipative particle dynamics-based coarse-grained model to investigate the diffusion behavior of IgG1 antibody molecules in aqueous solutions with 15 and 32 mM NaCl and antibody concentrations ranging from 10 to 400 mg/mL. We determined the coarse-grained interaction parameters by matching the calculated structure factor with the computational and experimental data from the literature. Our results indicate Fickian diffusion for antibody concentrations of 10 and 25 mg/mL and anomalous diffusion for concentrations exceeding 50 mg/mL. The anomalous diffusion was observed for ∼0.33 to 0.4 μs, followed by Fickian diffusion for all antibody concentrations. We observed a strong linear correlation between the diffusion behavior of the antibody molecules (diffusion coefficient D and anomalous diffusion exponent α) and the amount of aggregates present in the solution and between the amount of aggregates and the Coulomb interaction energy. The investigation of underlying mechanisms for anomalous diffusion revealed that in crowded environments at high antibody concentrations, the attractive interaction between electrostatically complementary regions of the antibody molecules could further bring the neighboring molecules closer to one another, ultimately resulting in aggregate formation. Further, the Coulomb attraction can continue to draw more molecules together, forming larger aggregates.

The search for novel proline analogs for viscosity reduction and stabilization of highly concentrated monoclonal antibody solutions

Administration of monoclonal antibodies (mAbs) is currently focused on subcutaneous injection associated with increased patient adherence and reduced treatment cost, leading to sustainable healthcare. The main bottleneck is low volume that can be injected, requiring highly concentrated mAb solutions. The latter results in increased solution viscosity with pronounced mAb aggregation propensity because of intensive protein-protein interactions. Small molecule excipients have been proposed to restrict the protein-protein interactions, contributing to reduced viscosity. The aim of the study was to discover novel compounds that reduce the viscosity of highly concentrated mAb solution. First, the chemical space of proline analogs was explored and 35 compounds were determined. Viscosity measurements revealed that 18 proline analogs reduced the mAb solution viscosity similar to or more than proline. The compounds forming both electrostatic and hydrophobic interactions with mAb reduced the viscosity of the formulation more efficiently without detrimentally effecting mAb physical stability. A correlation between the level of interaction and viscosity-reducing effect was confirmed with molecular dynamic simulations. Structure rigidity of the compounds and aromaticity contributed to their viscosity-reducing effect, dependent on molecule size. The study results highlight the novel proline analogs as an effective approach in viscosity reduction in development of biopharmaceuticals for subcutaneous administration.

A multi-scale numerical approach to study monoclonal antibodies in solution

Developing efficient and robust computational models is essential to improve our understanding of protein solution behavior. This becomes particularly important to tackle the high-concentration regime. In this context, the main challenge is to put forward coarse-grained descriptions able to reduce the level of detail, while retaining key features and relevant information. In this work, we develop an efficient strategy that can be used to investigate and gain insight into monoclonal antibody solutions under different conditions. We use a multi-scale numerical approach, which connects information obtained at all-atom and amino-acid levels to bead models. The latter has the advantage of reproducing the properties of interest while being computationally much faster. Indeed, these models allow us to perform many-protein simulations with a large number of molecules. We can, thus, explore conditions not easily accessible with more detailed descriptions, perform effective comparisons with experimental data up to very high protein concentrations, and efficiently investigate protein-protein interactions and their role in phase behavior and protein self-assembly. Here, a particular emphasis is given to the effects of charges at different ionic strengths.

Computational Screening for mAb Colloidal Stability with Coarse-Grained, Molecular-Scale Simulations

Monoclonal antibodies (mAbs) are an important modality of protein therapeutics with broad applications for numerous diseases. However, colloidal instabilities occurring at high protein concentrations can limit the ability to develop stable, high-concentration liquid dosage forms that are required for patient-centric, device-mediated products. Therefore, it is advantageous to identify colloidally stable mAbs early in the discovery process to ensure that they are selected for development. Experimental screening for colloidal stability can be time- and resource-consuming and is most feasible at the later stages of drug development due to material requirements. Alternatively, computational approaches have emerging potential to provide efficient screening and focus developmental efforts on mAbs with the greatest developability potential, while providing mechanistic relationships for colloidal instability. In this work, coarse-grained, molecular-scale models were fine-tuned to screen for colloidal stability at amino-acid resolution. This model parameterization provides a framework to screen for mAb self-interactions and extrapolate to bulk solution behavior. This approach was applied to a wide array of mAbs under multiple buffer conditions, demonstrating the utility of the presented computational approach to augment early candidate screening and later formulation strategies for protein therapeutics.

Molecular Dynamics Simulation of an Iron(III) Binding Site on the Fc Domain of IgG1 Relevant for Visible Light-Induced Protein Fragmentation

Molecular dynamics simulations were employed to investigate the interaction between Fe(III) and an iron-binding site composed of THR259, ASP252, and GLU261 on the Fc domain of an IgG1. The goal was to provide microscopic mechanistic information for the photochemical, iron-dependent site-specific oxidative fragmentation of IgG1 at THR259 reported in our previous paper. The distance between Fe(III) and residues of interest as well as the binding pocket size was examined for both protonated and deprotonated THR259. The Fe(III) binding free energy (ΔG) was estimated by using an umbrella sampling approach. The pKa shift of the THR259 hydroxyl group caused by the presence of nearby Fe(III) was estimated based on a thermodynamic cycle. The simulation results show that Fe(III) resides inside the proposed binding pocket and profoundly changes the pocket configuration. The ΔG values indicate that the pocket possesses a strong binding affinity for Fe(III). Furthermore, Fe(III) profoundly lowers the pKa value of the THR259 hydroxyl group by 5.4 pKa units.

Antibody association in solution: cluster distributions and mechanisms

Understanding factors that affect the clustering and association of antibodies molecules in solution is critical to their development as therapeutics. For 19 different monoclonal antibody (mAb) solutions, we measured the viscosities, the second virial coefficients, the Kirkwood-Buff integrals, and the cluster distributions of the antibody molecules as functions of protein concentration. Solutions were modeled using the statistical-physics Wertheim liquid-solution theory, representing antibodies as Y-shaped molecular structures of seven beads each. We found that high-viscosity solutions result from more antibody molecules per cluster. Multi-body properties such as viscosity are well predicted experimentally by the 2-body Kirkwood-Buff quantity, G22, but not by the second virial coefficient, B22, and well-predicted theoretically from the Wertheim protein-protein sticking energy. Weakly interacting antibodies are rate-limited by nucleation; strongly interacting ones by propagation. This approach gives a way to relate micro to macro properties of solutions of associating proteins.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Characterizing Protein-Protein Interactions and Viscosity of a Monoclonal Antibody from Low to High Concentration Using Small-Angle X-ray Scattering and Molecular Dynamics Simulations

Understanding protein-protein interactions and formation of reversible oligomers (clusters) in concentrated monoclonal antibody (mAb) solutions is necessary for designing stable, low viscosity (η) concentrated formulations for processing and subcutaneous injection. Here we characterize the strength (K) of short-range anisotropic attractions (SRA) for 75-200 mg/mL mAb2 solutions at different pH and cosolute conditions by analyzing structure factors (Seff(q)) from small-angle X-ray scattering (SAXS) using coarse-grained molecular dynamics simulations. Best fit simulations additionally provide cluster size distributions, fractal dimensions, cluster occluded volume, and mAb coordination numbers. These equilibrium properties are utilized in a model to account for increases in viscosity caused by occluded volume in the clusters (packing effects) and dissipation of stress across lubricated fractal clusters. Seff(q) is highly sensitive to K at 75 mg/mL where mAbs can mutually align to form SRA contacts but becomes less sensitive at 200 mg/mL as steric repulsion due to packing becomes dominant. In contrast, η at 200 mg/mL is highly sensitive to SRA and the average cluster size from SAXS/simulation, which is observed to track the cluster relaxation time from shear thinning. By analyzing the distribution of sub-bead hot spots on the 3D mAb surface, we identify a strongly attractive hydrophobic patch in the complementarity determining region (CDR) at pH 4.5 that contributes to the high K and consequently large cluster sizes and high η. Adding NaCl screens electrostatic interactions and increases the impact of hydrophobic attraction on cluster size and raises η, whereas nonspecific binding of Arg attenuates all SRA, reducing η. The hydrophobic patch is absent at higher pH values, leading to smaller K, smaller clusters, and lower η. This work constitutes a first attempt to use SAXS and CG modeling to link both structural and rheological properties of concentrated mAb solutions to the energetics of specific hydrophobic patches on mAb surfaces. As such, our work opens an avenue for future research, including the possibility of designing coarse-grained models with physically meaningful interacting hot spots.

Viscosity Prediction of High-Concentration Antibody Solutions with Atomistic Simulations

The computational prediction of the viscosity of dense protein solutions is highly desirable, for example, in the early development phase of high-concentration biopharmaceutical formulations where the material needed for experimental determination is typically limited. Here, we use large-scale atomistic molecular dynamics (MD) simulations with explicit solvation to de novo predict the dynamic viscosities of solutions of a monoclonal IgG1 antibody (mAb) from the pressure fluctuations using a Green-Kubo approach. The viscosities at simulated mAb concentrations of 200 and 250 mg/mL are compared to the experimental values, which we measured with rotational rheometry. The computational viscosity of 24 mPa·s at the mAb concentration of 250 mg/mL matches the experimental value of 23 mPa·s obtained at a concentration of 213 mg/mL, indicating slightly different effective concentrations (or activities) in the MD simulations and in the experiments. This difference is assigned to a slight underestimation of the effective mAb-mAb interactions in the simulations, leading to a too loose dynamic mAb network that governs the viscosity. Taken together, this study demonstrates the feasibility of all-atom MD simulations for predicting the properties of dense mAb solutions and provides detailed microscopic insights into the underlying molecular interactions. At the same time, it also shows that there is room for further improvements and highlights challenges, such as the massive sampling required for computing collective properties of dense biomolecular solutions in the high-viscosity regime with reasonable statistical precision.

Role of Domain-Domain Interactions on the Self-Association and Physical Stability of Monoclonal Antibodies: Effect of pH and Salt

Monoclonal antibodies (mAbs) make up a major class of biotherapeutics with a wide range of clinical applications. Their physical stability can be affected by various environmental factors. For instance, an acidic pH can be encountered during different stages of the mAb manufacturing process, including purification and storage. Therefore, understanding the behavior of flexible mAb molecules in acidic solution environments will benefit the development of stable mAb products. This study used small-angle X-ray scattering (SAXS) and complementary biophysical characterization techniques to investigate the conformational flexibility and protein-protein interactions (PPI) of a model mAb molecule under near-neutral and acidic conditions. The study also characterized the interactions between Fab and Fc fragments under the same buffer conditions to identify domain-domain interactions. The results suggest that solution pH significantly influences mAb flexibility and thus could help mAbs remain physically stable by maximizing local electrostatic repulsions when mAbs become crowded in solution. Under acidic buffer conditions, both Fab and Fc contribute to the repulsive PPI observed among the full mAb at a low ionic strength. However, as ionic strength increases, hydrophobic interactions lead to the self-association of Fc fragments and, subsequently, could affect the aggregation state of the mAb.

Minimal Coarse-Grained Model for Immunoglobulin G: Diffusion and Binding under Crowding

Immunoglobulin G (IgG) is the most common type of antibody found in blood and extracellular fluids and plays an essential role in our immune response. However, studies of the dynamics and reaction kinetics of IgG-antigen binding under physiological crowding conditions are scarce. Herein, we develop a coarse-grained model of IgG consisting of only six beads that we find minimal for a coarse representation of IgG's shape and a decent reproduction of its flexibility and diffusion properties measured experimentally. Using this model in Brownian dynamics simulations, we find that macromolecular crowding affects only slightly the IgG's flexibility, as described by the distribution of angles between the IgG's arms and stem. Our simulations indicate that, contrary to expectations, crowders slow down the translational diffusion of an IgG less strongly than they do for a smaller Ficoll 70, which we relate to the IgG's conformational size changes induced by crowding. We also find that crowders affect the binding kinetics by decreasing the rate of the first binding step and enhancing the second binding step.

IgG1 and IgG4 antibodies sample initial structure dependent local conformational states and exhibit non-identical Fab dynamics

We have investigated the dynamics of two [Formula: see text]-immunoglobulin molecules, IgG1 and IgG4, using long all atom molecular dynamics simulations. We first show that the de novo structures of IgG1 and IgG4 predicted using AlphaFold, with no interactions between the fragment crystallizable (Fc) domain and the antigen fragment binding domain (Fab), eventually relaxes to a state with persistent Fc-Fab interactions that mirrors experimentally resolved structures. We quantified the conformational space sampled by antibody trajectories spawned from six different initial structures and show that the individual trajectories only sample states bound by a local minimum and display very little mixing in their conformational states. Furthermore, the dynamics of the individual Fab domains are strongly dependent on the initial crystal structure and isotype. In all conditions, we observe non-identical dynamics between the Fab arms in an antibody. For a six-bead coarse grained model, we show that non-covalent Fc-Fab interactions can modulate the stiffnesses associated with Fc-Fab distances, angles, and dihedral angles by up to three orders of magnitude. Our results clearly illustrate the inherent complexities in studying antibody dynamics and highlight the need to include non-identical Fab dynamics as an inherent feature in computational models of therapeutic antibodies.

Effects of flexibility in coarse-grained models for bovine serum albumin and immunoglobulin G

We construct a coarse-grained, structure-based, low-resolution, 6-bead flexible model of bovine serum albumin (BSA, PDB: 4F5S), which is a popular example of a globular protein in biophysical research. The model is obtained via direct Boltzmann inversion using all-atom simulations of a single molecule, and its particular form is selected from a large pool of 6-bead coarse-grained models using two suitable metrics that quantify the agreement in the distribution of collective coordinates between all-atom and coarse-grained Brownian dynamics simulations of solutions in the dilute limit. For immunoglobulin G (IgG), a similar structure-based 12-bead model has been introduced in the literature [Chaudhri et al., J. Phys. Chem. B 116, 8045 (2012)] and is employed here to compare findings for the compact BSA molecule and the more anisotropic IgG molecule. We define several modified coarse-grained models of BSA and IgG, which differ in their internal constraints and thus account for a variation of flexibility. We study denser solutions of the coarse-grained models with purely repulsive molecules (achievable by suitable salt conditions) and address the effect of packing and flexibility on dynamic and static behavior. Translational and rotational self-diffusivity is enhanced for more elastic models. Finally, we discuss a number of effective sphere sizes for the BSA molecule, which can be defined from its static and dynamic properties. Here, it is found that the effective sphere diameters lie between 4.9 and 6.1 nm, corresponding to a relative spread of about ±10% around a mean of 5.5 nm.

Characterizing Experimental Monoclonal Antibody Interactions and Clustering Using a Coarse-Grained Simulation Library and a Viscosity Model

Attractive protein-protein interactions in concentrated monoclonal antibody (mAb) solutions may lead to the formation of clusters that increase viscosity. Here, we propose an analytical model that relates mAb solution viscosity to clustering by accounting for the contributions of suboptimal mAb packing within a cluster and cluster fractal dimension. The influence of short-range, anisotropic attractions and long-range Coulombic repulsion on cluster properties is investigated by analyzing the cluster-size distributions, cluster fractal dimensions, radial distribution functions, and static structure factors from a library of coarse-grained molecular dynamics simulations. The library spans a vast range of mAb charges and attractive interactions in solutions of varying ionic strength. We present a framework for combining the viscosity model and simulation library to successfully characterize the attraction, repulsion, and clustering of an experimental mAb in three different pH and cosolute conditions by fitting the measured viscosity or structure factor from small-angle X-ray scattering. At low ionic strength, the cluster-size distribution is impacted by strong charges, and both the viscosity and net charge or structure factor and net charge must be considered to deconvolute the effects of short-range attraction and long-range repulsion.

High concentration formulation developability approaches and considerations

The growing need for biologics to be administered subcutaneously and ocularly, coupled with certain indications requiring high doses, has resulted in an increase in drug substance (DS) and drug product (DP) protein concentrations. With this increase, more emphasis must be placed on identifying critical physico-chemical liabilities during drug development, including protein aggregation, precipitation, opalescence, particle formation, and high viscosity. Depending on the molecule, liabilities, and administration route, different formulation strategies can be used to overcome these challenges. However, due to the high material requirements, identifying optimal conditions can be slow, costly, and often prevent therapeutics from moving rapidly into the clinic/market. In order to accelerate and derisk development, new experimental and in-silico methods have emerged that can predict high concentration liabilities. Here, we review the challenges in developing high concentration formulations, the advances that have been made in establishing low mass and high-throughput predictive analytics, and advances in in-silico tools and algorithms aimed at identifying risks and understanding high concentration protein behavior.

The influence of excipients on the viscosity of monoclonal antibody solutions

The aggregation propensity of monoclonal antibodies can be modified by adding different cosolutes into the solution. A simple coarse-grained model in the combination with the thermodynamic perturbation theory was used to predict cluster distribution and viscosity of the solutions of IgG4 monoclonal anibody in the presence of L-Arginine Hydrochloride. The data were analysed using binding polynomial to describe the binding of cosolute (Arginine) to the antibody molecule. The results show that by binding to the antibody molecule the cosolute occupies some of the binding sites of the antibody, and in this way reduces the amount of binding sites available to other antibody molecules. The aggregation propensity of the antibody molecules is therefore reduced.

Copolyelectrolyte-Based Nanocapsules for Oral Monoclonal Antibody Therapy: A Mesoscale Modeling Survey

Antibody therapy generally requires parenteral injection to attain the required bioavailability and pharmacokinetics, but improved formulations may slow enzymatic degradation of the antibody in the gastrointestinal tract, permitting the use of noninvasive oral delivery. Rationally designed carrier materials can potentially improve therapeutic activity both by shielding fragile biopharmaceuticals from proteolytic degradation and targeting specific receptors in vivo. One potentially useful class of protein carriers is block copolyelectrolytes, one polyelectrolyte plus one neutral hydrophilic polymer block, that self-assemble into stable micelles, providing a simple and biocompatible nanocapsule separating the protein from the outer medium. Here, we develop and implement an integrated mesoscale model to design molecular structures for block copolyelectrolyte nanocapsules predicted to protect Trastuzumab, an antibody used to treat breast cancer, in the low pH gastrointestinal tract and to selectively release this antibody in the more neutral intestinal environment. The simulations show a tightly packed self-assembled core-shell structure at pH = 3 that is ruptured and dynamically reassembled into a weaker structure at pH = 7. Our model identifies that the designed block copolyelectrolyte characteristics, such as block length ratio, can control the level of drug protection and release in vivo, providing simple design rules for engineering polyelectrolyte-based formulations that may allow oral administration of targeted antibody chemotherapies.

DeepSCM: An efficient convolutional neural network surrogate model for the screening of therapeutic antibody viscosity

Predicting high concentration antibody viscosity is essential for developing subcutaneous administration. Computer simulations provide promising tools to reach this aim. One such model is the spatial charge map (SCM) proposed by Agrawal and coworkers (mAbs. 2015, 8(1):43-48). SCM applies molecular dynamics simulations to calculate a score for the screening of antibody viscosity at high concentrations. However, molecular dynamics simulations are computationally costly and require structural information, a significant application bottleneck. In this work, high throughput computing was performed to calculate the SCM scores for 6596 nonredundant antibody variable regions. A convolutional neural network surrogate model, DeepSCM, requiring only sequence information, was then developed based on this dataset. The linear correlation coefficient of the DeepSCM and SCM scores achieved 0.9 on the test set (N = 1320). The DeepSCM model was applied to screen the viscosity of 38 therapeutic antibodies that SCM correctly classified and resulted in only one misclassification. The DeepSCM model will facilitate high concentration antibody viscosity screening. The code and parameters are freely available at https://github.com/Lailabcode/DeepSCM.

Effects of Monovalent Salt on Protein-Protein Interactions of Dilute and Concentrated Monoclonal Antibody Formulations

In this study, we used sodium chloride (NaCl) to extensively modulate non-specific protein-protein interactions (PPI) of a humanized anti-streptavidin monoclonal antibody class 2 molecule (ASA-IgG2). The changes in PPI with varying NaCl (C_NaCl) and monoclonal antibody (mAb) concentration (C_mAb) were assessed using the diffusion interaction parameter k_D and second virial coefficient B₂₂ measured from solutions with low to moderate C_mAb. The effective structure factor S(q)_eff measured from concentrated mAb solutions using small-angle X-ray and neutron scattering (SAXS/SANS) was also used to characterize the PPI. Our results found that the nature of net PPI changed not only with C_NaCl, but also with increasing C_mAb. As a result, parameters measured from dilute and concentrated mAb samples could lead to different predictions on the stability of mAb formulations. We also compared experimentally determined viscosity results with those predicted from interaction parameters, including k_D and S(q)_eff. The lack of a clear correlation between interaction parameters and measured viscosity values indicates that the relationship between viscosity and PPI is concentration-dependent. Collectively, the behavior of flexible mAb molecules in concentrated solutions may not be correctly predicted using models where proteins are considered to be uniform colloid particles defined by parameters derived from low C_mAb.

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.

Impact of IgG subclass on molecular properties of monoclonal antibodies

Immunoglobulin G-based monoclonal antibodies (mAbs) have become a dominant class of biotherapeutics in recent decades. Approved antibodies are mainly of the subclasses IgG1, IgG2, and IgG4, as well as their derivatives. Over the decades, the selection of IgG subclass has frequently been based on the needs of Fc gamma receptor engagement and effector functions for the desired mechanism of action, while the effect on drug product developability has been less thoroughly characterized. One of the major reasons is the lack of systematic understanding of the impact of IgG subclass on the molecular properties. Several efforts have been made recently to compare molecular property differences among these IgG subclasses, but the conclusions from these studies are sometimes obscured by the interference from variable regions. To further establish mechanistic understandings, we conducted a systematic study by grafting three independent variable regions onto human IgG1, an IgG1 variant, IgG2, and an IgG4 variant constant domains and evaluating the impact of subclass and variable regions on their molecular properties. Structural and computational analysis revealed specific molecular features that potentially account for the differential behavior of the IgG subclasses observed experimentally. Our data indicate that IgG subclass plays a significant role on molecular properties, either through direct effects or via the interplay with the variable region, the IgG1 mAbs tend to have higher solubility than either IgG2 or IgG4 mAbs in a common pH 6 buffer matrix, and solution behavior relies heavily on the charge status of the antibody at the desirable pH.

Molecular Flexibility of Antibodies Preserved Even in the Dense Phase after Macroscopic Phase Separation

Antibody therapies are typically based on high-concentration formulations that need to be administered subcutaneously. These conditions induce several challenges, inter alia a viscosity suitable for injection, sufficient solution stability, and preservation of molecular function. To obtain systematic insights into the molecular factors, we study the dynamics on the molecular level under strongly varying solution conditions. In particular, we use solutions of antibodies with poly(ethylene glycol), in which simple cooling from room temperature to freezing temperatures induces a transition from a well-dispersed solution into a phase-separated and macroscopically arrested system. Using quasi-elastic neutron scattering during in situ cooling ramps and in prethermalized measurements, we observe a strong decrease in antibody diffusion, while internal flexibility persists to a significant degree, thus ensuring the movement necessary for the preservation of molecular function. These results are relevant for a more dynamic understanding of antibodies in high-concentration formulations, which affects the formation of transient clusters governing the solution viscosity.

New Model to Predict the Concentration-Dependent Viscosity of Monoclonal Antibody Solutions

Concentrated monoclonal antibody solutions exhibit high solution viscosity, which is experimentally measured to be ∼1-2 orders of magnitude higher than the viscosity of water. However, physical processes responsible for the high antibody viscosity are not fully understood. We show that fluid occlusion due to the trapped solvent molecules within the boundaries formed by the aggregated antibodies is responsible for the elevated solution viscosity. We develop a theory to predict the viscosity of monoclonal antibodies based on the geometry of the antibody molecule and the aggregate morphology. We validate our theory with experiments and highlight useful insights obtained from the viscosity equation which could help in controlling the drug viscosity at the molecular design stage itself.

Towards an improved prediction of concentrated antibody solution viscosity using the Huggins coefficient

The viscosity of a monoclonal antibody solution must be monitored and controlled as it can adversely affect product processing, packaging and administration. Engineering low viscosity mAb formulations is challenging as prohibitive amounts of material are required for concentrated solution analysis, and it is difficult to predict viscosity from parameters obtained through low-volume, high-throughput measurements such as the interaction parameter, k_D, and the second osmotic virial coefficient, B₂₂. As a measure encompassing the effect of intermolecular interactions on dilute solution viscosity, the Huggins coefficient, k_h, is a promising candidate as a parameter measureable at low concentrations, but indicative of concentrated solution viscosity. In this study, a differential viscometry technique is developed to measure the intrinsic viscosity, [η], and the Huggins coefficient, k_h, of protein solutions. To understand the effect of colloidal protein-protein interactions on the viscosity of concentrated protein formulations, the viscometric parameters are compared to k_D and B₂₂ of two mAbs, tuning the contributions of repulsive and attractive forces to the net protein-protein interaction by adjusting solution pH and ionic strength. We find a strong correlation between the concentrated protein solution viscosity and the k_h but this was not observed for the k_D or the b₂₂, which have been previously used as indicators of high concentration viscosity. Trends observed in [η] and k_h values as a function of pH and ionic strength are rationalised in terms of protein-protein interactions.

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.

Calculation of therapeutic antibody viscosity with coarse-grained models, hydrodynamic calculations and machine learning-based parameters

High viscosity presents a challenge for manufacturing and drug delivery of therapeutic antibodies. The viscosity is determined by protein-protein interactions among many antibodies. Molecular simulation is a promising method to study protein-protein interactions; however, all-atom models do not allow the simulation of multiple molecules, which is necessary to compute viscosity directly. Coarse-grained models, on the other hand can do this. In this work, a 12-bead coarse-grained model based on Swan and coworkers (J. Phys. Chem. B 2018, 122, 2867-2880) was applied to study antibody interactions. Two adjustable parameters related to the short-range interactions on the variable and constant regions were determined by fitting experimental data of 20 IgG1 monoclonal antibodies at 150 mg/mL. The root-mean-square deviation improved from 1 to 0.68, and the correlation coefficient improved from 0.63 to 0.87 compared to that of a previous model that assumed the short-range interactions were the same for all the beads. Our model is also able to calculate the viscosity over a wide range of concentrations without additional parameters. A tabulated viscosity based on our model is provided to facilitate antibody screening in early-stage design.

Monoclonal Antibody Aggregation near Silicone Oil-Water Interfaces

In this work, we study the hydrodynamic behavior of monoclonal antibodies in the presence of silicone oil-water interfaces. We model the antibody molecules using a coarse-grained 24-bead model, where two beads are used to represent each antibody domain. We consider the spatial variation of the antibody polarity in our model as each bead represents a set of hydrophilic or hydrophobic amino acids. We use the dissipative particle dynamics scheme to represent the coarse-grained force field which governs the motion of the beads. In addition, interprotein interactions are modeled using an electrostatic force field. The model parameters are determined by comparing the structure factor against experimental structure factor data ranging from a low concentration regime (10 mg/mL) to a high concentration regime (150 mg/mL). Next, we conduct simulations for a suspension of antibody molecules in the presence of silicone oil-water interfaces. Protein loss from the bulk solution is noticed as the molecules adsorb at the interface. We observe dynamic cluster formation in the solution bulk and at the interface, as the antibody molecules self-associate along their trajectories. We quantify the aggregation using a density clustering algorithm and investigate the effect of the antibody concentration on the diffusivity of the antibody solution, aggregation propensity, and protein loss from the bulk. Our study shows that numerical simulations can be an important tool for understanding the molecular mechanisms driving protein aggregation near hydrophobic interfaces.

Machine Learning Applied to Determine the Molecular Descriptors Responsible for the Viscosity Behavior of Concentrated Therapeutic Antibodies

Predicting the solution viscosity of monoclonal antibody (mAb) drug products remains as one of the main challenges in antibody drug design, manufacturing, and delivery. In this work, the concentration-dependent solution viscosity of 27 FDA-approved mAbs was measured at pH 6.0 in 10 mM histidine-HCl. Six mAbs exhibited high viscosity (>30 cP) in solutions at 150 mg/mL mAb concentration. Combining molecular modeling and machine learning feature selection, we found that the net charge in the mAbs and the amino acid composition in the Fv region are key features which govern the viscosity behavior. For mAbs whose behavior was not dominated by charge effects, we observed that high viscosity is correlated with more hydrophilic and fewer hydrophobic residues in the Fv region. A predictive model based on the net charges of mAbs and a high viscosity index is presented as a fast screening tool for classifying low- and high-viscosity mAbs.

Electrostatic interactions modulate the differential aggregation propensities of IgG1 and IgG4P antibodies and inform charged residue substitutions for improved developability

Native state aggregation is an important concern in the development of therapeutic antibodies. Enhanced knowledge of mAb native state aggregation mechanisms would permit sequence-based selection and design of therapeutic mAbs with improved developability. We investigated how electrostatic interactions affect the native state aggregation of seven human IgG1 and IgG4P mAb isotype pairs, each pair having identical variable domains that are different for each set of IgG1 and IgG4P constructs. Relative aggregation propensities were determined at pH 7.4, representing physiological conditions, and pH 5.0, representing commonly used storage conditions. Our work indicates that the net charge state of variable domains relative to the net charge state of the constant domains is predominantly responsible for the different native state aggregation behavior of IgG1 and IgG4P mAbs. This observation suggests that the global net charge of a multi domain protein is not a reliable predictor of aggregation propensity. Furthermore, we demonstrate a design strategy in the frameworks of variable domains to reduce the native state aggregation propensity of mAbs identified as being aggregation-prone. Importantly, substitution of specifically identified residues with alternative, human germline residues, to optimize Fv charge, resulted in decreased aggregation potential at pH 5.0 and 7.4, thus increasing developability.

Multiscale Coarse-Grained Approach to Investigate Self-Association of Antibodies

Self-association of therapeutic monoclonal antibodies (mabs) are thought to modulate the undesirably high viscosity observed in their concentrated solutions. Computational prediction of such a self-association behavior is advantageous early during mab drug candidate selection when material availability is limited. Here, we present a coarse-grained (CG) simulation method that enables microsecond molecular dynamics simulations of full-length antibodies at high concentrations. The proposed approach differs from others in two ways: first, charges are assigned to CG beads in an effort to reproduce molecular multipole moments and charge asymmetry of full-length antibodies instead of only localized charges. This leads to great improvements in the agreement between CG and all-atom electrostatic fields. Second, the distinctive hydrophobic character of each antibody is incorporated through empirical adjustments to the short-range van der Waals terms dictated by cosolvent all-atom molecular dynamics simulations of antibody variable regions. CG simulations performed on a set of 15 different mabs reveal that diffusion coefficients in crowded environments are markedly impacted by intermolecular interactions. Diffusion coefficients computed from the simulations are in correlation with experimentally measured observables, including viscosities at a high concentration. Further, we show that the evaluation of electrostatic and hydrophobic characters of the mabs is useful in predicting the nonuniform effect of salt on the viscosity of mab solutions. This CG modeling approach is particularly applicable as a material-free screening tool for selecting antibody candidates with desirable viscosity properties.

Coarse-Grained Molecular Dynamics Simulations for Understanding the Impact of Short-Range Anisotropic Attractions on Structure and Viscosity of Concentrated Monoclonal Antibody Solutions

Understanding protein-protein interactions in concentrated therapeutic monoclonal antibody (mAb) solutions is desirable for improved drug discovery, processing, and administration. Here, we deduce both the net protein charge and the magnitude and geometry of short-ranged, anisotropic attractions of a mAb across multiple concentrations and cosolute conditions by comparing structure factors S(q) obtained from small-angle X-ray scattering experiments with those from molecular dynamics (MD) simulations. The simulations, which utilize coarse-grained 12-bead models exhibiting a uniform van der Waals attraction, uniform electrostatic repulsion, and short-range attractions between specific beads, are versatile enough to fit S(q) of a wide range of protein concentrations and ionic strength with the same charge on each bead and a single anisotropic short-range attraction strength. Cluster size distributions (CSDs) obtained from best fit simulations reveal that the experimental structure is consistent with small reversible oligomers in even low viscosity systems and help quantify the impact of these clusters on viscosity. The ability to systematically use experimental S(q) data together with MD simulations to discriminate between different possible protein-protein interactions, as well as to predict viscosities from protein CSDs, is beneficial for designing mAbs and developing formulation strategies that avoid high viscosities and aggregation at high concentration.

Self-diffusion of a highly concentrated monoclonal antibody by fluorescence correlation spectroscopy: insight into protein-protein interactions and self-association

The dynamic behavior of monoclonal antibodies (mAbs) at high concentration provides insight into protein microstructure and protein-protein interactions (PPI) that influence solution viscosity and protein stability. At high concentration, interpretation of the collective-diffusion coefficient Dc, as determined by dynamic light scattering (DLS), is highly challenging given the complex hydrodynamics and PPI at close spacings. In contrast, self-diffusion of a tracer particle by Brownian motion is simpler to understand. Herein, we develop fluorescence correlation spectroscopy (FCS) for the measurement of the long-time self-diffusion of mAb2 over a wide range of concentrations and viscosities in multiple co-solute formulations with varying PPI. The normalized self-diffusion coefficient D0/Ds (equal to the microscopic relative viscosity ηeff/η0) was found to be smaller than η/η0. Smaller ratios of the microscopic to macroscopic viscosity (ηeff/η) are attributed to a combination of weaker PPI and less self-association. The interaction parameters extracted from fits of D0/Ds with a length scale dependent viscosity model agree with previous measurements of PPI by SLS and SAXS. Trends in the degree of self-association, estimated from ηeff/η with a microviscosity model, are consistent with oligomer sizes measured by SLS. Finally, measurements of collective diffusion and osmotic compressibility were combined with FCS data to demonstrate that the changes in self-diffusion between formulations are due primarily to changes in the protein-protein friction in these systems, and not to protein-solvent friction. Thus, FCS is a robust and accessible technique for measuring mAb self-diffusion, and, by extension, microviscosity, PPI and self-association that govern mAb solution dynamics.

Process optimization and protein engineering mitigated manufacturing challenges of a monoclonal antibody with liquid-liquid phase separation issue by disrupting inter-molecule electrostatic interactions

We report a case study in which liquid-liquid phase separation (LLPS) negatively impacted the downstream manufacturability of a therapeutic mAb. Process parameter optimization partially mitigated the LLPS, but limitations remained for large-scale manufacturing. Electrostatic interaction driven self-associations and the resulting formation of high-order complexes are established critical properties that led to LLPS. Through chain swapping substitutions with a well-behaved antibody and subsequent study of their solution behaviors, we found the self-association interactions between the light chains (L_Cs) of this mAb are responsible for the LLPS behavior. With the aid of in silico homology modeling and charged-patch analysis, seven charged residues in the L_C complementarity-determining regions (CDRs) were selected for mutagenesis, then evaluated for self-association and LLPS properties. Two charged residues in the light chain (K30 and D50) were identified as the most significant to the LLPS behaviors and to the antigen-binding affinity. Four adjacent charged residues in the light chain (E49, K52, R53, and R92) also contributed to self-association, and thus to LLPS. Molecular engineering substitution of these charged residues with a neutral or oppositely-charged residue disrupted the electrostatic interactions. A double-mutation in CDR2 and CDR3 resulted in a variant that retained antigen-binding affinity and eliminated LLPS. This study demonstrates the critical nature of surface charged resides on LLPS, and highlights the applied power of in silico protein design when applied to improving physiochemical characteristics of therapeutic antibodies. Our study indicates that in silico design and effective protein engineering may be useful in the development of mAbs that encounter similar LLPS issues.

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.

Structure, heterogeneity and developability assessment of therapeutic antibodies

Increasing attention has been paid to developability assessment with the understanding that thorough evaluation of monoclonal antibody lead candidates at an early stage can avoid delays during late-stage development. The concept of developability is based on the knowledge gained from the successful development of approximately 80 marketed antibody and Fc-fusion protein drug products and from the lessons learned from many failed development programs over the last three decades. Here, we reviewed antibody quality attributes that are critical to development and traditional and state-of-the-art analytical methods to monitor those attributes. Based on our collective experiences, a practical workflow is proposed as a best practice for developability assessment including in silico evaluation, extended characterization and forced degradation using appropriate analytical methods that allow characterization with limited material consumption and fast turnaround time.

Modeling the depletion effect caused by an addition of polymer to monoclonal antibody solutions

We present a theoretical study of colloidal stability of the model mixtures of monoclonal antibody molecules and non-adsorbing (no polymer-protein attraction) polymers. The antibodies are pictured as an assembly of seven hard spheres assuming a Y-like shape. Polymers present in the mixture are modeled as chain-like molecules having from 32 up to 128 monomers represented as hard spheres. We use Wertheim's thermodynamic perturbation theory to construct the two molecular species and to calculate measurable properties. The calculations are performed in the osmotic ensemble. In view that no direct attractive interaction is present in the model Hamiltonian, we only account for the entropic contribution to the phase equilibrium. We calculate chemical potentials and the equation of state for the model mixture to determine the liquid-liquid part of the phase diagram. We investigate how the critical antibody number density depends on the degree of polymerization and the bead size ratio of the polymer and protein components. The model mixture qualitatively correctly predicts some basic features of real systems. The effects of the model 'protein' geometry, that is the difference in results for the flexible Y-shaped protein versus the rigid spherical one, are also examined.

Controlling the viscosities of antibody solutions through control of their binding sites

For biotechnological drugs, it is desirable to formulate antibody solutions with low viscosities. We go beyond previous colloid theories in treating protein-protein self-association of molecules that are antibody-shaped and flexible and have spatially specific binding sites. We consider interactions either through fragment antigen (Fab-Fab) or fragment crystalizable (Fab-Fc) binding. Wertheim's theory is adapted to compute the cluster-size distributions, viscosities, second virial coefficients, and Huggins coefficients, as functions of antibody concentration. We find that the aggregation properties of concentrated solutions can be anticipated from simpler-to-measure dilute solutions. A principal finding is that aggregation is controllable, in principle, through modifying the antibody itself, and not just the solution it is dissolved in. In particular: (i) monospecific antibodies having two identical Fab arms can form linear chains with intermediate viscosities. (ii) Bispecific antibodies having different Fab arms can, in some cases, only dimerize, having low viscosities. (iii) Arm-to-Fc binding allows for three binding partners, leading to networks and high viscosities.

Theory for the Liquid-Liquid Phase Separation in Aqueous Antibody Solutions

This study presents the theory for liquid-liquid phase separation for systems of molecules modeling monoclonal antibodies. Individual molecule is depicted as an assembly of seven hard spheres, organized to mimic the Y-shaped antibody. We consider the antibody-antibody interactions either through Fab, Fab' (two Fab fragments may be different), or Fc domain. Interaction between these three domains of the molecule (hereafter denoted as A, B, and C, respectively) is modeled by a short-range square-well attraction. To obtain numerical results for the model under study, we adapt Wertheim's thermodynamic perturbation theory. We use this model to calculate the liquid-liquid phase separation curve and the second virial coefficient B2. Various interaction scenarios are examined to see how the strength of the site-site interactions and their range shape the coexistence curve. In the asymmetric case, where an attraction between two sites is favored and the interaction energies for the other sites kept constant, critical temperature first increases and than strongly decreases. Some more microscopic information, for example, the probability for the particular two sites to be connected, has been calculated. Analysis of the experimental liquid-liquid phase diagrams, obtained from literature, is presented. In addition, we calculate the second virial coefficient under conditions leading to the liquid-liquid phase separation and present this quantity on the graph B2 versus protein concentration.