Viscosity Prediction of High-Concentration Antibody Solutions with Atomistic Simulations

Abstract

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.

Figure 1

(A) Padlan IgG1 mAb is shown in cartoon representation, with light and heavy chains colored orange and cyan, respectively. The glycan in the Fc domain is shown as red spheres. (B) MD simulation system composed of four mAbs solvated by water and 150 mM NaCl.

Figure 2

Pressure autocorrelation functions (ACFs) for the mAb solutions at 200 mg/mL (black) and 250 mg/mL (blue) concentrations. The ACFs shown were averaged over all nondiagonal elements of the pressure tensor and over the combinations of diagonal elements (see the Methods Section) and were also averaged over all 63 individual trajectories. The inset shows the short-time behavior of the ACFs (linear time axis).

Figure 3

Green–Kubo integrals of the two mAb solutions studied. (A, B) Plotted are the running GK integrals of the N = 63 individual MD trajectories for the mAb concentrations of 200 (A) and 250 mg/mL (B), together with the average (thick lines). (C) The average GK integrals from panels (A, B) are plotted together with the triexponential fits (eq 4, dashed red lines). The averages over the three sets of repeats (each with N = 21 trajectories) are plotted as thin lines. (D) The standard deviations eq 2 are plotted together with the fits (eq 3, dashed red lines).

Figure 4

Experimentally determined dynamic viscosities at different mAb concentrations and Ross–Minton fit to the data. The black dots and orange triangles show the data from the filtered and unfiltered samples, respectively. The error bars reflect an uncertainty in the sample concentrations of ca. 10%. The Ross–Minton fit to the combined data (filtered and unfiltered) is shown as a blue line. The error range, resulting from the min–max values of the concentration uncertainties, is depicted by the blue shaded area. The viscosities from the MD simulations are shown as blue dots.

Figure 5

Bootstrap analysis of the statistical convergence of the viscosity estimate as a function of the number of MD trajectories. The black and blue lines represent the average viscosity obtained for 200 and 250 mg/mL concentration by randomly drawing the indicated number of trajectories from the full set. Each draw was repeated 100 times; the shaded areas show the standard deviation.