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

Abstract

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.

FIG. 1.

The experimental mAbs structure at atomic resolution (leftmost, gray) is first relaxed using MD simulations, where-after it is coarse-grained at five different levels shown in the middle, in red. This includes models with 1, 6, 9, or 12 interaction sites, as well as a model where each amino acid is treated as a (charged) sphere. The coarse-grained models are subsequently used in many-body MC simulations to explore the effect of varying mAb concentration and salt concentrations (rightmost).

FIG. 2.

Root mean squared deviation (RMSD) and radius of gyration (R_g) obtained from all-atom MD simulations for the condition I = 7 mM [(a) and (b)] and I = 57 mM [(c) and (d)]. The equilibrated part of the trajectory over which the average R_g is calculated is highlighted in red.

FIG. 3.

mAb structure before and after MD simulations. At the leftmost, the initial mAb structure at atomic resolution overlaps with its coarse-grained representation at the amino acid level. On the center and rightmost, the representative mAb conformations obtained from MD simulations, respectively, for the conditions at 7 and 57 mM of ionic strength. Red, blue, and gray beads represent negatively charged, positively charged, and neutral amino acids, respectively.

FIG. 4.

Effective structure factors, $S_{\mathit{\text{eff}}}(q)$, obtained from simulations of N_p = 20 mAbs coarse-grained at an amino acid level in comparison with experimental data. The left and right columns refer to, respectively, the 7 and 57 mM ionic strength conditions, while on each graph the mAb concentration is indicated. The gray circles in the background represent the experimental data obtained by SAXS experiments together with their error bars, while the open symbols are the simulation results. Each of the colors indicates a different value of the depth of the attractive well in the Lennard–Jones term of Eq. (3), ε_ij. The explored range is $\Delta {\epsilon }_{ij}=$ 0.05–0.085  $k_{B}T$ with steps of 0.005  $k_{B}T$.

FIG. 5.

Effective structure factors, $S_{\mathit{\text{eff}}}(q)$, obtained from simulations of N_p = 20 mAbs coarse-grained at an amino acid level and at low ionic strength (7 mM). Comparison with initial and relaxed structure. The explored range is $\Delta {\epsilon }_{ij}=0.05-0.085k_{B}T$ with steps of 0.005  $k_{B}T$ for both cases.

FIG. 6.

${\chi }^2$ table for the 1-bead (a), 6-bead (b), 9-bead (c), and 12-bead (d) models related to the condition at low mAb concentration (20 mg/mL) and low ionic strength (7 mM) for several combinations of the potential parameters (Q_eff, ε_ij). Each ${\chi }^2$ value is associated with a color. A logarithmic scale is used to highlight differences among the values which are rounded to two decimal places.

FIG. 7.

Effective structure factors, $S_{\mathit{\text{eff}}}(q)$, obtained from experimental data (gray circles) at low ionic strength (7 mM) and 20 mg/mL (left) and 150 mg/mL (right) mAb concentrations in comparison with the 1-bead model (dashed orange line) and an effective charge of Q_eff = 20 e and the 6-bead model (open circles) and an effective charge in the range $\Delta Q_{\mathit{\text{eff}}}=26\hspace{0.17em}\pm \hspace{0.17em}2$e.

FIG. 8.

Values of Q_eff best reproducing the experimental data for the different bead models used as judged from the -tables shown in Figs. 6 and S6–S9 in the supplementary material.

FIG. 9.

Effective structure factors $S_{\mathit{\text{eff}}}(q)$, obtained from simulations with the 9-bead model and an effective charge in the range of $\Delta Q_{\mathit{\text{eff}}}=26-30$e in comparison with experimental data (gray circles). Here, the attractive term is van der Waals-like with ${ϵ}_{ij}=0.8$k_BT.