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8 • Antibody Structural Dynamics 211
B
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B
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B
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B
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B
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B
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At these high concentrations, protein‑protein interactions between mAbs drive self‑ association and determine viscosity.
60,61
As a result of differences in their self‑interaction proles, some mAbs may have poor solubility and not reach the required concentration for effective delivery; some may demonstrate prohibitively high viscosity for comfortable injection; yet others may aggregate irreversibly.
In the development pipeline, experimental methods are used to assess a mAb’s physical and chemical properties and response to environmental conditions like salt concentration
55,62,63
to judge its “developability”. These methods are, however, time con‑ suming and consumptive of mAb material. In response, computational ways to both predict and understand what mAb structures give rise to the properties of concentrated mAb solutions have been developed in the academic literature. Some of these meth‑ ods leverage information from available experimental structures of known therapeutic antibodies to dene developability guidelines.64 These methods do not, however, pro‑ vide information about what structures these antibodies populate that give rise to their behavior in solution. Simulation methods have also been designed to address this short‑ coming.
55,59,65
Some of these methods take a small amount of experimental data as input and extrapolate to diverse solution conditions. Yet other methods are designed to work in tandem with experimental methods to answer the inverse question of what structures give rise to an observed experimental signal. As their goal is predicting protein‑protein interaction‑based parameters, these methods typically consider multiple copies of the mAb of interest at a CG resolution to control computational costs. In the following three case studies, we describe important lessons learned from CG models of concentrated antibody solutions.
Case Study 8.1: Predicting the response
ofmAb solutions to salt and pH
The propensity of mAbs to self‑interact in low‑concentration regimes can be assessed experimentally through the second osmotic virial coefcient,
.55 Its values are a commonly used proxy for protein‑protein interactions in a dilute solution, with positive values indicating repulsive interactions and negative values indicating attractive interac‑ tions. In situations in which a mAb displays strong protein‑protein interactions, such as at higher concentrations, higher‑order virial coefcients that report on the formation of higher‑order oligomers may also be computed. Shahfar and co‑workers55 compared the ability of four different CG models (Figure8.2a) to predict
as a function of the total
ionic strength (TIS) for mAb1, mAbB, mAb2, and mAbC.
Diverse qualitative behavior in experimental
versus TIS curves is observed; mAb1, mAbB, and mAb2 can serve as exemplars of the different behaviors displayed by mAb solutions as TIS changes (Figure8.2b). mAb1 at pH 5 displays large positive
values at low values of TIS in the solution, with a monotonic decrease observed as TIS increases (Figure8.2b, blue). mAbB at pH 5 displays values near zero at low TIS, negative values at intermediate TIS, and then increases monotonically with increasing TIS to a plateau near zero (Figure8.2b, green). Finally, mAb2 at pH 6.5 displays large magnitude negative values of TIS increases (Figure8.2b, yellow). In each of these examples,
at low TIS that increase monotonically toward zero as
versus TIS curves
212 Biopharmaceutical Informatics
B
22
B
22,ST
y
GB/2
22 22,ST
−
FIGURE8.2 (a) All-atom and CG models from Shahfar etal. (2021). (b) Experimental sec­ond virial coefcient versus TIS curves for mAb1 at pH 5 (blue), mAbB at pH 5 (green), and mAb2 at pH 6.5 (yellow). (c) Experimental (black symbols) and CG model predicted second virial coefcient versus TIS curves for the HEXA (blue), DODECA (green), 1bC/D (yellow), and 1bAA (purple) for mAb1 at pH 5. (d) Same as (c) but for mAbB. (e) Same as (c) but for mAb2 at pH 6.5. (f) Same as (c) but for mAbC.
is the second virial coefcient and
is the second virial coefcient under the assumption of steric-only interactions. The
-axis in panel F is denoted
because the large values suggest the formation of higher-order oligomers. (g) DODECA models used by Wang etal. for mAb1 (left) and mAb2 (right). Red and blue beads indicate negative and positive net charges, respectively. Panels A-F reprinted with permission from Shahfar, H.; Forder, J. K.; Roberts, C. J. J. Phys. Chem. B 2021, 125 (14), 3574–3588. Copyright 2023 American Chemical Society. Panel G reprinted with permission from Wang, G. etal. J. Phys. Chem. B 2018, 122 (11), 2867–2880. Copyright 2023 American Chemical Society.
can be understood in terms of the interactions that predominate in each mAb solution as TIS changes. For mAb1, the behavior is as predicted for a colloid‑like system in which high net surface charge leads to repulsive interactions at low ionic strength that become screened as TIS increases, leading to a plateau near zero at high TIS. mAbB contains both positive and negative charges that can interact attractively, leading to attractive
8 • Antibody Structural Dynamics 213
B
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B
22
B
22
B
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B
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interactions at intermediate TIS when screening is at a favorable level. In the case of mAb2, the results are consistent with a mAb with a low net charge but with charged patches that can strongly attract one another at low TIS and become screened as TIS increases.55 These experimental curves indicate that a CG model must be able to account for various behaviors in order to accurately predict the different behaviors of mAbs.
To predict the
versus TIS curves for mAb1, mAbB, mAb2, and mAbC, Shahfar and co‑workers constructed CG models with (i) one bead per amino acid (1bAA), (ii) 12 beads total with one each per domain in the mAb and the net charge of its constituent amino acids applied to each site (DODECA), (iii) 12 beads total with charged amino acids represented as charged patches on the beads (1bC/D), and (iv) six beads total with two for each Fab and the Fc and the net charge applied to each bead (HEXA). Simulations were run using the Mayer sampling method66 with the overlap sampling algorithm to compute values of
and higher‑order virial coef‑ cients; this amounts to a specialized MC sampler that biases the simulations to preferentially explore states that contribute most to the nal value of a given virial coefcient. Within each of these CG models, solvent is considered implicitly, and similar functions are used to represent their short‑range non‑electrostatic and elec‑ trostatic interactions as functions of SR and strength (well‑depth) of non‑electrostatic interactions between sites and
, respectively. SR sets the maximum
is an adjustment factor that scales the theoretical charges of CG sites. Values of SR and were selected based on test simulations for each CG model until pairs of parameters that minimize the average relative deviation from the experimental
versus TIS
curves were determined.
For mAb1, which displays standard colloid‑like behavior, each of the four CG models provides a reasonably good t at pH 5, with the 1bAA model displaying the small‑ est deviation from the experiment (Figure 8.2c). In the case of mAbB at pH 5, the DODECA and HEXA models fail to predict the correct shape of
at low TIS, while the 1bC/D and 1bAA models both provide strong predictions of the experimental data (Figure8.2d). With mAb2 at pH 6.5, each of the four models again makes reasonable predictions, while for mAbC at pH 5, the HEXA and DODECA models completely fail to capture the shape of the experimental curve (Figure8.2e and f). These results indi‑ cate that a bespoke modeling process for understanding the inuence of salt is required, with some mAbs proving to be less tractable than others and requiring more expensive, higher‑resolution CG models. Shahfar etal. provide a table of CG model parameters for their different mAbs that can help choose reasonable parameters for simulations even in the absence of experimental data (see Ref. 55 Table1).
This MC investigation of the inuence of pH on low‑concentration mAb solutions highlights the challenges and future directions for such predictive models. Strong ts to experimental data tend to be obtained when at least 12 CG interaction sites are con‑ sidered with amino‑acid‑specic charge representations rather than domain‑level net charge electrostatics (i.e., 1bC/D). Models using one CG interaction site per amino acid also provide strong predictions, though at a higher computational cost. Even in some more difcult cases, CG simulations can reproduce the ne structure of experimental
curves.
214 Biopharmaceutical Informatics
Aα= HVI*
H
V
Case Study 8.2: Predictive models for the properties
of high‑concentration mAb solutions
Signicant interest in recent years has been focused on the development of CG models coupled with either MD or MC sampling methods to predict mAb solution viscosity. Wang and co‑workers67 ran Brownian Dynamics simulations using 12‑bead CG representations of two mAbs, mAb1 and mAb2, that have 92% sequence similarity. Despite their highly similar sequences, these mAbs have disparate rheological behavior, with the viscosity of mAb1 varying much more strongly in response to changes in its concentration, pH, and the ionic strength of the solution.61 The initial simulations of Wang and co‑workers were in poor agreement with experimental relative viscosity measurements. Inthese initial simu‑ lations, CG beads within a single mAb molecule interact through bond, angle, dihedral, and Urey‑Bradley terms (additional forceeld terms to account for angle bending), and each CG bead is assigned a charge equal to the net charge of the particles it represents (Figure8.2g). The spring constants and equilibrium values for the CG bead interactions were computed from all‑atom MD simulations of a single mAb molecule.
68
Wang and co‑workers noted that in scattering experiments, mAb1 has been found to form reversible dimers and higher‑order oligomers.
60,69
These dynamically forming and breaking groups of self‑associated mAbs are referred to as clusters. Upon adding additional constraints to their CG simulations that cause groups of self‑associated CG mAbs to move together rigidly, simulation results for both mAb1 and mAb2 signi‑ cantly improve. In these new results, mAb2’s viscosity as a function of concentration is predicted well, while the prediction of mAb1’s viscosity is improved but still inaccurate at high concentrations. These simulation results indicate the importance of considering soluble clusters of mAbs in simulations for the prediction of mAb viscosity.
In a follow‑up to the work of Wang etal., Lai and co‑workers attempted to improve this 12‑bead CG model’s ability to capture changes in viscosity with mAb concentra‑ tion by making a key modication to interactions within the model.70 Rather than using a single constant interaction energy between all CG beads regardless of the part of the mAb they represent, they incorporate separate Fv and Fc interaction terms. Interaction strengths between Fv regions are determined using the high‑viscosity index (HVI), a parameter relative to viscosity developed using a machine‑learning approach,71 and then scaled by a tting parameter specic term
. Interactions between mAbs depend, then, on an Fv‑Fv
, an Fc‑Fc specic term set to a constant for all Fcs, and electrostatic forces dependent on the net charge of the CG interaction site. Equilibrium values and force constants for CG interactions were determined from all‑atom simula‑ tions of each mAb, as in the work of Wang etal. Values for
and the strength of Fc interactions were determined using a grid search to nd the pair of parameters that best predicts the viscosity of a 150‑mg/mL mAb solution over all 20 mAbs studied. This simple tting procedure generates models that provide accurate relative viscosity predictions for [mAb] = {50, 100, 125, 150} mg/mL for a set of 20mAbs. In comparison to the original model of Wang etal., the root‑mean‑square deviation improves from 1 to 0.68 and the correlation coefcient improves from 0.63 to 0.87. Despite better per‑ formance on the data set overall, the original model of Wang and co‑workers performs better than that of Lai and co‑workers on mAb2.
8 • Antibody Structural Dynamics 215
A
H
V
= 1
Pq
()
q
π
λ
θ
 
 
4
2
Lai and co‑workers also, for the rst time, explored the inuence of the size of the simulated system on the calculated relative viscosity. In principle, an innite number of simulation boxes with different volumes can be designed and then lled with an appro‑ priate number of mAb representations to reach a desired concentration. All publications investigating mAb solution viscosity prior to this simulated only a single box size. Lai and co‑workers, however, demonstrated that changing the size of the simulation box inuences the calculated relative viscosity. With
, the simulations predict a 3‑fold larger viscosity when run with a box containing N = 4,096monomers versus a smaller box with N = 512monomers. This result breaks one of our basic intuitions for how a chemical system should behave: if we have 10 mL of 1.0 M NaCl and split the solution into two 5‑mL aliquots, we expect each of them to have identical intensive properties like viscosity to the initial solution before it was split. In the case at hand, this illogical result is a simulation artifact that arises due to the dependence of viscosity on the size of self‑associated clusters formed in the nite simulation box. The calculation of the vis‑ cosity can only consider the clusters formed within the simulation box—for large cluster sizes and small periodic boxes, however, the effective cluster extends through the peri‑ odic boundary conditions. This leads to computed viscosities that depend on the size of the simulation box with mAb concentration held constant. When interactions between mAbs are weak and clusters tend to be small, this dependence disappears.
These studies of high‑concentration mAb solutions highlight that Fv‑specic interac‑ tions are crucial for predicting protein‑protein interactions in high‑concentration mAb solutions. The dependence of the cluster‑size distribution on the simulation box dimen‑ sions is a particularly troubling simulation challenge.
Case Study 8.3: Tandem experimental and
simulation studies of mAb solutions
While the previous two case studies have focused on using CG methods to predict the solution properties of mAbs with minimal reliance on experimental data in their parameterization procedures, other CG models have been designed to work exclusively in tandem with experiments.
59,62
In such studies, experimental small‑angle X‑ray scat‑ tering (SAXS) or small‑angle neutron scattering (SANS) data are used as a target during CG model optimization and parameters chosen that minimize the deviation between simulated and experimental scattering data.
59,62
The scattering data may also be rened into an all‑atom model, from which a CG representation is then constructed.59 While these methods are not, strictly speaking, predictive models for viscosity, the best‑t simulations can provide a wealth of information about cluster‑size distributions and help understand the dynamic oligomeric states populated by mAbs in solution.
In the work of Dear and co‑workers,62 SAXS experiments at [mAb] = 5 mg/mL
were used to assign a mAb shape by tting to
=
a function of
sin
where λ is the wavelength of the incident X‑ray and
, the normalized form factor, as
216 Biopharmaceutical Informatics
Pq
()
is the scattering angle. The scattering pattern represented by the form factor is related to the size and shape of the protein in the solution.72 In general, low concen‑ trations of 1–10 mg/mL are used to provide a compromise between the increase in signal‑to‑noise ratio and the decrease in interparticle distances that both accompany increased solution concentration. While the former is always favorable, the latter can inuence the scattering pattern. In practice, proles collected at different con‑ centrations may be merged into a single representative curve. Solutions of mAb2 at [NaCl] = 0, 50, 250 mM and with [Arg] = 250 mM and mAb4 with either 250‑mM NaCl or Arg were all assayed with SAXS, and the resulting 12‑bead CG models with various interaction proles. While each of the CG mod‑ els for a particular mAb and solution condition have identical bead sizes and loca‑ tions, they differ in terms of how many beads experience attractive interactions and where these attractive beads are placed within the CG model. MD simulations were run with 6,000 identical mAb CG representations in a periodic box with a constant number of particles, system volume, and system temperature for each mAb and CG model. They nd that models with only three attractive beads per mAb are frequently detected bound to more than three neighbors. This result appears to invalidate theo‑ retical models that only allow one interaction partner per binding site. low‑up paper, Chowdhury and co‑workers investigated the inuence of short‑range, non‑electrostatic attractive and electrostatic repulsive interactions. Using a similar tting and simulation procedure to Dear etal., Chowdhury and coworkers59manipu‑ lated the parameters within the CG model to best t the experimental structure factor curves under various conditions for mAb2. These simulations found that including uniform VDW interactions between all model beads allows predictions of structure factor curves to become more accurate.
These simulation results highlight the ability of CG simulations to aid in understand‑ ing the difcult inverse question that accompanies spectroscopic assays of biomolecules: what ensemble of structures gives rise to the observed signal? In this case, exploring various CG models and rationalizing which models provide the best predictions for which system provides a wealth of additional information beyond the experiment alone. As computational power increases and model accuracy continues to improve, the use of CG simulations to understand the ne structure of experimental scattering curves may become more commonplace.
curves used to build
73,74
In a fol‑
8.4.2 Predicting and Understanding Binding
Mechanisms, Energetics, and Aggregation
The following three case studies highlight the use of all‑atom simulations to understand and predict the mechanisms and energetics of mAbs interacting with their targets as well as the aggregation propensity of mAbs. While all‑atom simulations have become more common in the academic literature, their high computational cost limits their applica‑ tion across the development pipeline. As enhanced sampling techniques and simulation
8 • Antibody Structural Dynamics 217
speeds continue to improve, however, we expect to see an ever‑increasing reliance on the predictions of all‑atom MD.
Case Study 8.4: Predicting the binding mechanism
and oligomeric preference of solanezumab
Bekker etal. (2020) ran multicanonical MD simulations, in which structures from tra‑ jectories run at different temperatures may be reweighted to provide better sampling at a specic temperature of interest, of solanezumab binding to the monomeric form of its target peptide amyloid‑β (Aβ, Figure8.3a).75 In these simulations, the Fv region of solanezumab was held partially restrained, and the center of mass of Aβ was then allowed to explore conformations within a cylinder positioned normal to the solane‑ zumab binding site. This combination of multicanonical MD with positional restraints increases the speed of the conformational search relative to single‑temperature simu‑ lations and reduces the number of accessible conformations for the solanezumab/Aβ system, enhancing sampling.
A free‑energy landscape projected onto the two principal components (PC1 and PC2) of this simulation suggested that the solanezumab Fv explores a diverse conformational landscape at 300 K around the experimental structure (Figure8.3b, experimental struc‑ ture indicated by a white X). Bekker etal. 2020 then selected a set of ten structures from the free‑energy landscape representing steps along the binding reaction and performed path‑sampling simulations to characterize the binding mechanism. These path‑sam‑ pling simulations revealed the mechanism of interaction between solanezumab and Aβ. As the peptide approaches the antibody, transient non‑specic interactions begin to form. Once it reaches 8–10 Å from the binding pocket center of mass, the hydrophobic core of the pocket begins to interact via CDRH1 and CDRL1 (observed as a metastable plateau in the potential of mean force, Figure8.3c). Many individual native contacts are made as the peptide nears the core, with non‑specic interactions gradually becoming stabilized by salt bridges. Bekker etal. 2020 conclude by simulating Aβ in isolation, revealing (consistent with previous work76) that Aβ explores disordered structures in the unbound state.
Comparing their results to the three typical binding models of (i) lock and key, (ii) population shift, and (iii) induced t, Bekker and co‑workers determined that their results are most consistent with what they term a “mutual population shift”. Each mol‑ ecule undergoes random structural perturbations until it is in a native‑like state, which allows it to rapidly bind if its partner is nearby and also in a native‑like state. In other words, if a molecule of both the mAb and the peptide are both in native‑like states in close proximity, they form a bound complex. Their structure and mechanism of inter‑ action also provide an explanation for the substrate selection of solanezumab: only the monomeric form of Aβ is able to t deep enough within the solanezumab binding pocket to induce a conformational shift away from the random states it populates in solution. These all‑atom MD simulations highlight the strengths of this technique, providing a detailed binding mechanism along the chosen order parameter.
218 Biopharmaceutical Informatics
(Continued)
8 • Antibody Structural Dynamics 219
FIGURE8.3 (Continued) (a) Simulation setup of Bekker etal. 2020. (b) Free-energy land­scape from all-atom simulations of solanezumab (labeled L and H for variable light and variable heavy) and Aβ peptide at 300 K. (c) Potential of mean force over the order param- eter λ′, the distance between the peptide and binding pocket. (d) Fractional contributions to total receptor free energy from the peptide, α1, and α2 helices. (e) Fractional contributions of CDR loops to total ligand-free energy. (f) The temperature at which a set of ten Fvs pass below solubility thresholds during temperature-ramp all-atom MD. (g) Percent change in aggregation for 13mAb solutions after 3 months of storage at 40°C. Panels a–c: Reprinted with permission from Bekker, G. J. etal. Sci. Rep. 2020, 10 (1), 1–9 (Creative Commons Attribution 4.0, https://creativecommons.org/licenses/by/4.0/). Panels f and g: Reprinted with permission from Berner, C. et al. Mol. Pharm. 2021, 18 (6), 2242–2253. Copyright 2023 American Chemical Society.
Case Study 8.5: Predicting and understanding the energetics
of interactions between antibodies and their targets
All‑atom simulations allow for the energetic interactions between molecules to be inves‑ tigated at levels of detail inaccessible by experiment. This advantage has been high‑ lighted by two recent studies of the differences between how T‑cell receptors (TCRs) and TCR‑mimetic antibodies (TCRms) bind their targets. TCRs are the natural immune system’s method of identifying peptide fragments presented by human leukocyte anti‑ gens (pHLAs), in which the peptide binds the groove between the α1 and α2 helices of the HLA. The TCR variable region recognizes pHLAs exposing non‑self peptides, while the membrane‑bound constant region, alongside crucial co‑receptors, enables downstream immune activation. The pharmaceutical industry is increasingly interested in translating TCR specicity to solubilized drug formats, which require stronger target binding. This necessitates engineering efforts to “afnity enhance” the TCR variable domain, or the use of immune recognition domains that were not evolutionarily selected to bind pHLAs, such as antibodies (TCRms), but which can routinely achieve binding in the nM‑pM range.
In the work of Holland et al. (2020), all‑atom simulations were used to generate ensembles of conformations for a set of TCRs, TCRms, and afnity‑enhanced TCRs.77 The molecular mechanic Poisson‑Boltzmann surface area (MMPBSA) method was then used to predict the free energy difference between the bound and unbound states for each complex, and the result decomposed into the per‑residue contributions.78 In brief, this method uses all‑atom MD structures in concert with implicit solvent calculations to predict free energy differences between states. Decomposition of the free energy revealed that while afnity‑enhanced TCRs tend to have a broad binding signature char‑ acterized by strong interactions with up to three residues in the peptide antigen, TCRms tend to have only one or two strong energetic contacts with the peptide.
Raybould et al. (2022), leveraging the increasing numbers of MX structures for TCRms, performed a similar MD study comparing TCR, TCRm, and afnity‑enhanced
79
TCR interactions with their targets.
To provide the best comparisons possible, Raybould and co‑workers simulated three different peptide antigens, Wilms’ Tumor 1 (WT1), New York esophageal squamous cell carcinoma 1 (NY‑ESO‑1), and p53_R175H
220 Biopharmaceutical Informatics
neoantigen (p53 R175H) bound by the same HLA in contact with various TCR, TCRm, and afnity‑enhanced TCRs. The contributions of the peptide, α1 helix, and α2 helix to the total free‑energy change of the pHLA were computed using the molecular mechanic Generalized‑Born surface area approach, a technique related to MMPBSA but using a different representation of the protein for surface area calculations. These calculations revealed that natural and afnity‑enhanced TCRs tend to gain a larger proportion of their binding energy from the peptide than any of the TCRms (Figure8.3d). Further, these calculations suggested that some peptide antigens are easier to bind than others, with WT1 peptides notably all ranking at the bottom in terms of fraction contribution to the total free energy change in the receptor. Similar calculations carried out on the residues in the CDRs (Figure8.3e) indicated that while the CDR[H/B]3 and CDR[L/A]3 predominate across the board, the pattern changes depending on the context. While TCRms tend to gain more energy from CDRH3 than CDRL3, in TCRs, there is no clear preference.
These studies into the energetics of antibody‑antigen and TCR‑antigen interactions highlight one of the key uses of MD and molecular simulations in general: gaining more detailed analysis than is possible experimentally. By determining which residues contribute most strongly to binding, studies like these can serve as the beginnings of a computational basis for mutational studies.
Case Study 8.6: Predicting aggregation‑prone
antibody therapeutics with all‑atom MD
The formation of aggregates within mAb solutions during processing and storage can lead to the rejection of otherwise promising candidate molecules; aggregation has there‑ fore been called the “most common and troubling manifestation of protein instabil‑ ity, encountered in almost all stages of protein drug development”.80 Predicting this behavior with small amounts of mAb material at an early stage of development is therefore highly desirable, and computational methods have been developed to identify and interrogate regions prone to aggregation.
81–83
Aggregation‑prone regions are spe‑ cic short‑sequence motifs that appear to be able to modulate aggregation, leading to extensive computational investigations of their dynamics. For example, a recent study of aggregation‑prone pentapeptides revealed that they can begin to form aggregates within 20 ns at a concentration of 0.1 M, with mutations strongly inuencing the kinetics of aggregate assembly.83 In a recent paper, Berner and co‑workers used a combination of two experimental unfolding reversibility methods and one simulation technique to inter‑ rogate a set of 13 candidate mAbs, including some aggregation‑prone examples.82 They note that their work is inspired by the observation that antibodies with domains that undergo reversible thermal unfolding also tend to be resistant to aggregation and that antibodies that refold to monomers after unfolding with denaturant aggregate less in formulations. In the following section, we describe the insights into aggregation they gained from all‑atom simulations of antibody Fv regions.
82
Berner and co‑workers
performed all‑atom MD simulations of the Fv segments of the ten antibodies for which they had access to experimental structures (Figure8.3f) and experimental assay data. These data show the temperatures at which each of the ten