Effect of Electric Charge on Biotherapeutic Transport, Binding and Absorption: A Computational Study

TL;DR

This work tackles how electric charge modulates subcutaneous monoclonal antibody transport, binding, and absorption. It introduces a multiphysics framework that couples $Nernst$-$Planck$ electromigration with $Darcy$-flow in a three-layer tissue domain and integrates $pH$-dependent binding kinetics to predict spatial drug distributions. The study reveals that injection- and charge-driven processes govern both short-term depot dynamics and long-term absorption, with key dependencies on buffer $pH$, body mass index, injection depth, and formulation concentration, and it shows consistency with depot-clearance experiments. The findings inform formulation and administration strategies to optimize bioavailability and identify directions for extending the model to tissue deformation and a broader set of mAbs.

Abstract

This study explores the effects of electric charge on the dynamics of drug transport and absorption in subcutaneous injections of monoclonal antibodies (mAbs). We develop a novel mathematical and computational model, based on the Nernst-Planck equations and porous media flow theory, to investigate the complex interactions between mAbs and charged species in subcutaneous tissue. The model enables us to study short-term transport dynamics and long-term binding and absorption for two mAbs with different electric properties. We examine the influence of buffer pH, body mass index, injection depth, and formulation concentration on drug distribution and compare our numerical results with experimental data from the literature.

Figures (13)

• Figure 1: Schematic illustration of the injection process at different scales. Monoclonal antibodies (mAbs) carry an electric charge that varies with the pH level. Upon injection into the adipose layer, mAbs interact with the ion species within the extracellular matrix (ECM) of the tissue, which in turn modifies the local electric potential $\Phi$ and pH. These changes influence the binding rate of mAbs to the ECM.
• Figure 2: (A) Isoelectric plots of the mAbs considered in the study, where we mark the isoelectric point (pI). The isoelectric points were computed from the amino acid sequences of the mAbs using the ProteinAnalysis module from Bio.SeqUtils.ProtParam in Biopython cock2009biopython. (B-C) Experimental data and fits of the association $k_a$ and dissociation $k_d$ rate at different pH levels mAb1_expsmAb2_exps.
• Figure 3: Short-term results for Ipilimumab and IgG1 with different buffer pH levels. (A) Time evolution of fluid pressure and velocity averaged 2 mm around the injection point. (B) Time evolution of averaged electric potential, $\langle \Phi \rangle = 1/|\Omega|\int_{\Omega} \Phi \mathrm{d}\Omega$. (C) Time evolution of averaged tissue pH. (D) Time evolution of the average net charge density, $\langle \rho_{\mathrm{mAb}} \rangle =1/|\Omega|\int_{\Omega} z_{\mathrm{mAb}} c_{\mathrm{mAb}} \mathrm{d}\Omega$. The shaded region denotes the injection time interval. The arrows indicate increasing buffer pH.
• Figure 4: Snapshots of the spatial distribution of different quantities 5 seconds after the end of the injection for the Ipilimumab with a buffer pH of $6.0$. (A) Concentration of Na$^+$. The dashed lines indicate the tissue layer interfaces. (B) Concentration of Cl$^-$. (C) Tissue pH. (D) Electric potential. (E) Close-up of electric potential gradient and streamlines at the edge of the drug depot. (F) Fluid velocity in logarithmic scale and velocity streamlines. (G) Net drug charge.
• Figure 5: Effect of buffer pH on the long-term distribution of free, bound, and absorbed drug as a percentage of the total injected volume for two different mAbs.