Mathematical and experimental analysis of localization of anti-tumour antibody-enzyme conjugates

Multiscale Modeling of Antibody-Drug Conjugates: Connecting Tissue and Cellular Distribution to Whole Animal Pharmacokinetics and Potential Implications for Efficacy

Antibody-drug conjugates exhibit complex pharmacokinetics due to their combination of macromolecular and small molecule properties. These issues range from systemic concerns, such as deconjugation of the small molecule drug during the long antibody circulation time or rapid clearance from nonspecific interactions, to local tumor tissue heterogeneity, cell bystander effects, and endosomal escape. Mathematical models can be used to study the impact of these processes on overall distribution in an efficient manner, and several types of models have been used to analyze varying aspects of antibody distribution including physiologically based pharmacokinetic (PBPK) models and tissue-level simulations. However, these processes are quantitative in nature and cannot be handled qualitatively in isolation. For example, free antibody from deconjugation of the small molecule will impact the distribution of conjugated antibodies within the tumor. To incorporate these effects into a unified framework, we have coupled the systemic and organ-level distribution of a PBPK model with the tissue-level detail of a distributed parameter tumor model. We used this mathematical model to analyze new experimental results on the distribution of the clinical antibody-drug conjugate Kadcyla in HER2-positive mouse xenografts. This model is able to capture the impact of the drug-antibody ratio (DAR) on tumor penetration, the net result of drug deconjugation, and the effect of using unconjugated antibody to drive ADC penetration deeper into the tumor tissue. This modeling approach will provide quantitative and mechanistic support to experimental studies trying to parse the impact of multiple mechanisms of action for these complex drugs.

A mechanistic compartmental model for total antibody uptake in tumors

Antibodies are under development to treat a variety of cancers, such as lymphomas, colon, and breast cancer. A major limitation to greater efficacy for this class of drugs is poor distribution in vivo. Localization of antibodies occurs slowly, often in insufficient therapeutic amounts, and distributes heterogeneously throughout the tumor. While the microdistribution around individual vessels is important for many therapies, the total amount of antibody localized in the tumor is paramount for many applications such as imaging, determining the therapeutic index with antibody drug conjugates, and dosing in radioimmunotherapy. With imaging and pretargeted therapeutic strategies, the time course of uptake is critical in determining when to take an image or deliver a secondary reagent. We present here a simple mechanistic model of antibody uptake and retention that captures the major rates that determine the time course of antibody concentration within a tumor including dose, affinity, plasma clearance, target expression, internalization, permeability, and vascularization. Since many of the parameters are known or can be estimated in vitro, this model can approximate the time course of antibody concentration in tumors to aid in experimental design, data interpretation, and strategies to improve localization.

A modeling analysis of the effects of molecular size and binding affinity on tumor targeting

A diverse array of tumor targeting agents ranging in size from peptides to nanoparticles is currently under development for applications in cancer imaging and therapy. However, it remains largely unclear how size differences among these molecules influence their targeting properties. Here, we develop a simple, mechanistic model that can be used to understand and predict the complex interplay between molecular size, affinity, and tumor uptake. Empirical relationships between molecular radius and capillary permeability, interstitial diffusivity, available volume fraction, and plasma clearance were obtained using data in the literature. These relationships were incorporated into a compartmental model of tumor targeting using MATLAB to predict the magnitude, specificity, time dependence, and affinity dependence of tumor uptake for molecules across a broad size spectrum. In the typical size range for proteins, the model uncovers a complex trend in which intermediate-sized targeting agents (MW, approximately 25 kDa) have the lowest tumor uptake, whereas higher tumor uptake levels are achieved by smaller and larger agents. Small peptides accumulate rapidly in the tumor but require high affinity to be retained, whereas larger proteins can achieve similar retention with >100-fold weaker binding. For molecules in the size range of liposomes, the model predicts that antigen targeting will not significantly increase tumor uptake relative to untargeted molecules. All model predictions are shown to be consistent with experimental observations from published targeting studies. The results and techniques have implications for drug development, imaging, and therapeutic dosing.

Modeling dynamic changes in type 1 diabetes progression: quantifying beta-cell variation after the appearance of islet-specific autoimmune responses

Type 1 diabetes (T1DM) is a chronic autoimmune disease with a long prodrome, which is characterized by dysfunction and ultimately destruction of pancreatic beta-cells. Because of the limited access to pancreatic tissue and pancreatic lymph nodes during the normoglycemic phase of the disease, little is known about the dynamics involved in the chain of events leading to the clinical onset of the disease in humans. In particular, during T1DM progression there is limited information about temporal fluctuations of immunologic abnormalities and their effect on pancreatic beta-cell function and mass. Therefore, our understanding of the pathoetiology of T1DM relies almost entirely on studies in animal models of this disease. In an effort to elucidate important mechanisms that may play a critical role in the progression to overt disease, we propose a mathematical model that takes into account the dynamics of functional and dysfunctional beta-cells, regulatory T cells, and pathogenic T cells. The model assumes that all individuals carrying susceptible HLA haplotypes will develop variable degrees of T1DM-related immunologic abnormalities. The results provide information about the concentrations and ratios of pathogenic T cells and regulatory T cells, the timing in which beta-cells become dysfunctional, and how certain kinetic parameters affect the progression to T1DM. Our model is able to describe changes in the ratio of pathogenic T cells and regulatory T cells after the appearance of islet antibodies in the pancreas. Finally, we discuss the robustness of the model and its ability to assist experimentalists in designing studies to test complicated theories about the disease.

On the mechanochemical theory of biological pattern formation with application to vasculogenesis

We first describe the Murray-Oster mechanical theory of pattern formation, the biological basis of which is experimentally well documented. The model quantifies the interaction of cells and the extracellular matrix via the cell-generated forces. The model framework is described in quantitative detail. Vascular endothelial cells, when cultured on gelled basement membrane matrix, rapidly aggregate into clusters while deforming the matrix into a network of cord-like structures tessellating the planar culture. We apply the mechanical theory of pattern formation to this culture system and show that neither strain-biased anisotropic cell traction nor cell migration are necessary for pattern formation: isotropic, strain-stimulated cell traction is sufficient to form the observed patterns. Predictions from the model were confirmed experimentally.

Selective activation of anticancer prodrugs by monoclonal antibody-enzyme conjugates

A great deal of interest has surrounded the activities of monoclonal antibodies (mAbs), and mAb-drug, toxin and radionuclide conjugates for the treatment of human cancers. In the last few years, a number of new mAb-based reagents have been clinically approved (Rituxan, Herceptin, and Panorex), and several others are now in advanced clinical trials. Successful therapeutic treatment of solid tumors with drug conjugates of such macromolecules must overcome the barriers to penetration within tumor masses, antigen heterogeneity, conjugated drug potency, and efficient drug release from the mAbs inside tumor cells. An alternative strategy for drug delivery involves a two-step approach to cancer therapy in which mAbs are used to localize enzymes to tumor cell surface antigens. Once the conjugate binds to the cancer cells and clears from the systemic circulation, antitumor prodrugs are administered that are catalytically converted to active drugs by the targeted enzyme. The drugs thus released are capable of penetrating within the tumor mass and eliminating both cells that have and have not bound the mAb-enzyme conjugate. Significant therapeutic effects have been obtained using a broad range of enzymes along with prodrugs that are derived from both approved anticancer drugs and highly potent experimental agents. This review focuses on the activities of several mAb-enzyme/prodrug combinations, with an emphasis on those that have provided mechanistic insight, clinical activity, novel protein constructs, and the potential for reduced immunogenicity.

Pattern formation in integrative biology--a marriage of theory and experiment

The interdisciplinary challenge to discover the underlying mechanisms in the generation of biological pattern and form are central issues in development. In this review we briefly discuss the philosophy of such an integrative biology approach. We then describe one pattern formation approach which has intimate ties to experiment, namely the mechano-chemical theory. We discuss, by way of example, the successful use of such a framework in the formation of cell-matrix networks, intimately associated with angiogenesis. All of the model parameters are estimated from experiment and the results of the model analysis compare well with experiment. We conclude with some general views on the use of models in biology.