Journal Article

Antibodies to Modulate Surface Receptor Systems Are Often Bivalent and Must Compete in a Two‐Dimensional Cell Contact Region

Tenney, Daniel J., Han, Minhua, Jing, Yawu, Leil, Tarek A., Cheng, Yougan, Bee, Christine, Schmidt, Brian J.

2019

Overview

Integrated experimental and modeling methods using both surface plasmon resonance–based kinetic measures and cell‐binding data have been used to account for the kinetics of individual receptors, their apparent binding affinity, and more important their cross‐linking behavior. See PDF] Model state variables and parameters Symbol Description Suggested units k a Free antibody association rate with free antigen nM−1 day−1 k r Dissociation rate of monovalent antibody–antigen complexes day−1 k xa Cross‐linking rate for antibody–antigen complexes μm2 molecule−1 day−1 N cell Number of cells in the assay well (often around 1 × 105 for avidity experiments) number N nmole A conversion factor from nanomole to molecules (6.022 × 1014) molecule nanomole−1 r cell Assumed cell radius μm V w Volume of the assay well L X A Amount of free antibody nanomole X B Amount of bound antibody nanomole X C1 Amount of single antigen and antibody complex on the cell surface nanomole X C2 Amount of double antigen and antibody complex on the cell surface nanomole X RT Total amount of antigen on the cell surface nanomole B Density of total antibody bound on the cell surface molecule μm−2 σ Confinement length nanometer k a,lgnd Solution phase association rate of receptor‐ligand complexes nanomolar−1 day−1 k xa,lgnd Two‐dimensional association rate of receptor‐ligand complexes μm2 molecule−1 day−1 V convert Volumetric conversion factor (1 × 10−18) L nm−1 μm−2 f v Vascular fraction for the tumor dimensionless f ICF Fraction of the nonvascular tumor volume that is intracellular dimensionless f ECM,A Fraction of the interstitial tumor volume that is not accessible to antibody due to extracellular matrix dimensionless k in,DAg Rate constant for antigen molecules to diffuse into the synapse day−1 k out,DAg Rate for antigen diffusing out of the synapse day−1 Q prod,contact Production rate of antigen for cells in contact molecule day−1 k sdeg Surface antigen degradation rate day−1 k xr,lgnd Dissociation rate of receptor–ligand complexes day−1 S syn Total surface area directly involved in cell–cell contact in the tumor (synapse), same on antigen‐expressing or ligand‐expressing cells μm2 S Agnonsyn Surface area on antigen‐expressing cells in the tumor that are engaged in cell–cell contacts, but this portion of the surface is not directly involved in the synapse μm2 V t Total tumor volume L X At Amount of free antibody in the tumor nanomole X Agsyn Amount of free antigen in cellular synapses nanomole X Agnonsyn Amount of free antigen on contacting cells but outside of synapses nanomole X C1syn Amount of single‐antigen antibody complexes in cellular synapses nanomole X C2syn Amount of double‐antigen antibody complexes in cellular synapses nanomole X lgndsyn Amount of free ligand in cellular synapses nanomole X CAglgnd Amount of antigen–ligand complexes in cellular synapses nanomole Illustration of models. (a) Cartoon of antibody‐binding minimodel depicting monovalent antibody, first bond formation, and cross‐linking. Note that different regions and characteristics of the curve are differentially sensitive and best able to report different underlying biophysical parameters, such as the cross‐linking, monovalent association rates, and total receptor site densities. (c) Illustration of a bigger model incorporating bivalent antibody–antigen interactions and competition for ligand. To better assess these issues, experimental checks coupled with simulation, such as observing dissociation kinetics of bound antibody preattached to cells with a pulse‐chase incubation, can serve as additional verification for estimated cell‐binding kinetic parameters.

• Publisher: John Wiley & Sons, Inc,John Wiley and Sons Inc,Wiley
• Subject: Antigens / Binding sites / Experiments / Flow cytometry / Immunoglobulins / Kinetics / Ligands / Ordinary differential equations / Variables