A mathematical model for the rational design of chimeric ligands in selective drug therapies

Mechanistic computational modeling of monospecific and bispecific antibodies targeting interleukin-6/8 receptors

The spread of cancer from organ to organ (metastasis) is responsible for the vast majority of cancer deaths; however, most current anti-cancer drugs are designed to arrest or reverse tumor growth without directly addressing disease spread. It was recently discovered that tumor cell-secreted interleukin-6 (IL-6) and interleukin-8 (IL-8) synergize to enhance cancer metastasis in a cell-density dependent manner, and blockade of the IL-6 and IL-8 receptors (IL-6R and IL-8R) with a novel bispecific antibody, BS1, significantly reduced metastatic burden in multiple preclinical mouse models of cancer. Bispecific antibodies (BsAbs), which combine two different antigen-binding sites into one molecule, are a promising modality for drug development due to their enhanced avidity and dual targeting effects. However, while BsAbs have tremendous therapeutic potential, elucidating the mechanisms underlying their binding and inhibition will be critical for maximizing the efficacy of new BsAb treatments. Here, we describe a quantitative, computational model of the BS1 BsAb, exhibiting how modeling multivalent binding provides key insights into antibody affinity and avidity effects and can guide therapeutic design. We present detailed simulations of the monovalent and bivalent binding interactions between different antibody constructs and the IL-6 and IL-8 receptors to establish how antibody properties and system conditions impact the formation of binary (antibody-receptor) and ternary (receptor-antibody-receptor) complexes. Model results demonstrate how the balance of these complex types drives receptor inhibition, providing important and generalizable predictions for effective therapeutic design.

AI-based identification of therapeutic agents targeting GPCRs: introducing ligand type classifiers and systems biology

Identifying ligands targeting G protein coupled receptors (GPCRs) with novel chemotypes other than the physiological ligands is a challenge for in silico screening campaigns. Here we present an approach that identifies novel chemotype ligands by combining structural data with a random forest agonist/antagonist classifier and a signal-transduction kinetic model. As a test case, we apply this approach to identify novel antagonists of the human adenosine transmembrane receptor type 2A, an attractive target against Parkinson's disease and cancer. The identified antagonists were tested here in a radio ligand binding assay. Among those, we found a promising ligand whose chemotype differs significantly from all so-far reported antagonists, with a binding affinity of 310 ± 23.4 nM. Thus, our protocol emerges as a powerful approach to identify promising ligand candidates with novel chemotypes while preserving antagonistic potential and affinity in the nanomolar range.

Modeling Pharmacokinetics and Pharmacodynamics of Therapeutic Antibodies: Progress, Challenges, and Future Directions

With more than 90 approved drugs by 2020, therapeutic antibodies have played a central role in shifting the treatment landscape of many diseases, including autoimmune disorders and cancers. While showing many therapeutic advantages such as long half-life and highly selective actions, therapeutic antibodies still face many outstanding issues associated with their pharmacokinetics (PK) and pharmacodynamics (PD), including high variabilities, low tissue distributions, poorly-defined PK/PD characteristics for novel antibody formats, and high rates of treatment resistance. We have witnessed many successful cases applying PK/PD modeling to answer critical questions in therapeutic antibodies’ development and regulations. These models have yielded substantial insights into antibody PK/PD properties. This review summarized the progress, challenges, and future directions in modeling antibody PK/PD and highlighted the potential of applying mechanistic models addressing the development questions.

OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

Providing the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. We developed and validated an optimal dosing algorithm (OptiDose) that computes the optimal individualized dosing regimen for pharmacokinetic-pharmacodynamic models in substantially different scenarios with various routes of administration by solving an optimal control problem. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference function by minimizing a cost functional. In pharmacokinetic-pharmacodynamic modeling, the controls are the administered doses and the reference function can be the disease progression. Drug administration at certain time points provides a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease progression. Consequently, rewriting the cost functional gives a finite-dimensional optimal control problem depending only on the doses. Adjoint techniques allow to compute the gradient of the cost functional efficiently. This admits to solve the optimal control problem with robust algorithms such as quasi-Newton methods from finite-dimensional optimization. OptiDose is applied to three relevant but substantially different pharmacokinetic-pharmacodynamic examples.

A kinetic proofreading model for bispecific protein degraders

Bispecific protein degraders (BPDs) engage the ubiquitin-proteasome system (UPS) to catalytically degrade intracellular proteins through the formation of ternary complexes with the target protein and E3 ubiquitin ligases. Here, we describe the development of a mechanistic modeling framework for BPDs that includes the reaction network governing ternary complex formation and degradation via the UPS. A critical element of the model framework is a multi-step process that results in a time delay between ternary complex formation and protein degradation, thereby balancing ternary complex stability against UPS degradation rates akin to the kinetic proofreading concept that has been proposed to explain the accuracy and specificity of biological processes including protein translation and T cell receptor signal transduction. Kinetic proofreading likely plays a central role in the cell's ability to regulate substrate recognition and degradation by the UPS, and the model presented here applies this concept in the context of a quantitative pharmacokinetic (PK)-pharmacodynamic (PD) framework to inform the design of potent and selective BPDs.

Mechanistic Quantitative Pharmacology Strategies for the Early Clinical Development of Bispecific Antibodies in Oncology

Bispecific antibodies (bsAbs) have become an integral component of the therapeutic research strategy to treat cancer. In addition to clinically validated immune cell re‐targeting, bsAbs are being designed for tumor targeting and as dual immune modulators. Explorative preclinical and emerging clinical data indicate potential for enhanced efficacy and reduced systemic toxicity. However, bsAbs are a complex modality with challenges to overcome in early clinical trials, including selection of relevant starting doses using a minimal anticipated biological effect level approach, and predicting efficacious dose despite nonintuitive dose response relationships. Multiple factors can contribute to variability in the clinic, including differences in functional affinity due to avidity, receptor expression, effector to target cell ratio, and presence of soluble target. Mechanistic modeling approaches are a powerful integrative tool to understand the complexities and aid in clinical translation, trial design, and prediction of regimens and strategies to reduce dose limiting toxicities of bsAbs. In this tutorial, the use of mechanistic modeling to impact decision making for bsAbs is presented and illustrated using case study examples.

Target-Mediated Drug Disposition Model for Bispecific Antibodies: Properties, Approximation, and Optimal Dosing Strategy

Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno-oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here, we have presented a general target-mediated drug disposition (TMDD) model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAbs, turnover of the targets, and internalization of the complexes. In addition, a quasi-equilibrium (QE) approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAbs, which will immediately create and maintain maximal possible TC concentration, is presented.

Drug treatment efficiency depends on the initial state of activation in nonlinear pathways

An accurate prediction of the outcome of a given drug treatment requires quantitative values for all parameters and concentrations involved as well as a detailed characterization of the network of interactions where the target molecule is embedded. Here, we present a high-throughput in silico screening of all potential networks of three interacting nodes to study the effect of the initial conditions of the network in the efficiency of drug inhibition. Our study shows that most network topologies can induce multiple dose-response curves, where the treatment has an enhanced, reduced or even no effect depending on the initial conditions. The type of dual response observed depends on how the potential bistable regimes interplay with the inhibition of one of the nodes inside a nonlinear pathway architecture. We propose that this dependence of the strength of the drug on the initial state of activation of the pathway may be affecting the outcome and the reproducibility of drug studies and clinical trials.

Trispecific antibodies for CD16A-directed NK cell engagement and dual-targeting of tumor cells

Bispecific antibodies that redirect the lytic activity of cytotoxic immune effector cells, such as T- and NK cells, onto tumor cells have emerged as a highly attractive and clinically validated treatment modality for hematological malignancies. Advancement of this therapeutic concept into solid tumor indications, however, is hampered by the scarcity of targetable antigens that are surface-expressed on tumor cells but demonstrate only limited expression on healthy tissues. To overcome this limitation, the concept of dual-targeting, i.e. the simultaneous targeting of two tumor-expressed surface antigens with limited co-expression on non-malignant cells, with multispecific antibodies has been proposed to increase tumor selectivity of antibody-induced effector cell cytotoxicity. Here, a novel CD16A (FcγRIIIa)-directed trispecific, tetravalent antibody format, termed aTriFlex, is described, that is capable of redirecting NK cell cytotoxicity to two surface-expressed antigens. Using a BCMA/CD200-based in vitro model system, the potential use of aTriFlex antibodies for dual-targeting and selective induction of NK cell-mediated target cell lysis was investigated. Bivalent bispecific target cell binding was found to result in significant avidity gains and up to 17-fold increased in vitro potency. These data suggest trispecific aTriFlex antibodies may support dual-targeting strategies to redirect NK cell cytotoxicity with increased selectivity to enable targeting of solid tumor antigens.

General principles of binding between cell surface receptors and multi-specific ligands: A computational study

The interactions between membrane receptors and extracellular ligands control cell-cell and cell-substrate adhesion, and environmental responsiveness by representing the initial steps of cell signaling pathways. These interactions can be spatial-temporally regulated when different extracellular ligands are tethered. The detailed mechanisms of this spatial-temporal regulation, including the competition between distinct ligands with overlapping binding sites and the conformational flexibility in multi-specific ligand assemblies have not been quantitatively evaluated. We present a new coarse-grained model to realistically simulate the binding process between multi-specific ligands and membrane receptors on cell surfaces. The model simplifies each receptor and each binding site in a multi-specific ligand as a rigid body. Different numbers or types of ligands are spatially organized together in the simulation. These designs were used to test the relation between the overall binding of a multi-specific ligand and the affinity of its cognate binding site. When a variety of ligands are exposed to cells expressing different densities of surface receptors, we demonstrated that ligands with reduced affinities have higher specificity to distinguish cells based on the relative concentrations of their receptors. Finally, modification of intramolecular flexibility was shown to play a role in optimizing the binding between receptors and ligands. In summary, our studies bring new insights to the general principles of ligand-receptor interactions. Future applications of our method will pave the way for new strategies to generate next-generation biologics.

In order to adapt to surrounding environments, multiple signaling pathways have been evolved in cells. The first step of these pathways is to detect external stimuli, which is conducted by the dynamic interactions between cell surface receptors and extracellular ligands. As a result, recognition of extracellular ligands by cell surface receptors is an indispensable component of many physiological or pathological activities. In both natural selection and drug design, the presence of multiple binding sites in extracellular ligand complexes (so-called multi-specific ligands) is a common strategy to target different receptors on surface of the same cell. Such spatial organization of ligand binding sites can elaborately modulate the downstream signaling pathways. However, our understanding to the interactions between multi-specific ligands and membrane receptors is largely limited by the fact that these interactions are difficult to quantify and they have only been successfully measured in a very small number of cases in vivo. Using a simple computational model, we can realistically simulate the binding process between specially designed multi-specific ligands and membrane receptors on cell surfaces. This study therefore provides a useful pathway to unravel basic mechanisms of ligand-receptor interactions and design principles for new drug candidates.

An experimental and computational framework for engineering multifunctional nanoparticles: designing selective anticancer therapies

A key challenge in the treatment of cancer with nanomedicine is to engineer and select nanoparticle formulations that lead to the desired selectivity between tumorigenic and non-tumorigenic cells. To this aim, novel designed nanomaterials, deep biochemical understanding of the mechanisms of interaction between nanomaterials and cells, and computational models are emerging as very useful tools to guide the design of efficient and selective nanotherapies. This works shows, using a combination of detailed experimental approaches and simulations, that the specific targeting of cancer cells in comparison to non-tumorigenic cells can be achieved through the custom design of multivalent nanoparticles. A theoretical model that provides simple yet quantitative predictions to tune the nanoparticles targeting and cytotoxic properties by their degree of functionalization is developed. As a case study, a system that included a targeting agent and a drug and is amenable to controlled experimental manipulation and theoretical analysis is used. This study shows how at defined functionalization levels multivalent nanoparticles can selectively kill tumor cells, while barely affecting non-tumorigenic cells. This work opens a way to the rational design of multifunctionalized nanoparticles with defined targeting and cytotoxic properties for practical applications.

The application of mathematical modelling to the design of bispecific monoclonal antibodies

Targeting multiple receptors with bispecific antibodies is a novel approach that may prevent the development of resistance to cancer treatments. Despite the initial promise, full clinical benefit of this technology has yet to be realized. We hypothesized that in order to optimally exploit bispecific antibody technology, thorough fundamental knowledge of their pharmacological properties compared to that of single agent combinations was needed. Therefore, we developed a mathematical model for the binding of bispecific antibodies to their targets that accounts for the spatial distribution of the binding receptors and the kinetics of binding, and is scalable for increasing valency. The model provided an adequate description of internal and literature-reported in vitro data on bispecific binding. Simulations of in vitro binding with the model indicated that bispecific antibodies are not always superior in their binding potency to combination of antibodies, and the affinity of bispecific arms must be optimized for maximum binding potency. Our results suggest that this tool can be used for the design and development of the next generation of anti-cancer bispecific compounds.

Designing cell-targeted therapeutic proteins reveals the interplay between domain connectivity and cell binding

The therapeutic efficacy of cytokines is often hampered by severe side effects due to their undesired binding to healthy cells. One strategy for overcoming this obstacle is to tether cytokines to antibodies or antibody fragments for targeted cell delivery. However, how to modulate the geometric configuration and relative binding affinity of the two domains for optimal activity remains an outstanding question. As a result, many antibody-cytokine complexes do not achieve the desired level of cell-targeted binding and activity. Here, we address these design issues by developing a computational model to simulate the dynamics and binding kinetics of natural and engineered fusion proteins such as antibody-cytokine complexes. To verify the model, we developed a modular system in which an antibody fragment and a cytokine are conjugated via a DNA linker that allows for programmable linker geometry and protein spatial configuration. By assembling and testing several anti-CD20 antibody fragment-interferon ? complexes, we showed that varying the linker length and cytokine binding affinity controlled the magnitude of cell-targeted signaling activation in a manner that agreed with the model predictions, which were expressed as dose-signaling response curves. The simulation results also revealed that there is a range of cytokine binding affinities that would achieve optimal therapeutic efficacy. This rapid prototyping platform will facilitate the rational design of antibody-cytokine complexes for improved therapeutic outcomes.

Synergistic interaction between selective drugs in cell populations models

The design of selective drugs and combinatorial drug treatments are two of the main focuses in modern pharmacology. In this study we use a mathematical model of chimeric ligand-receptor interaction to show that the combination of selective drugs is synergistic in nature, providing a way to gain optimal selective potential at reduced doses compared to the same drugs when applied individually. We use a cell population model of proliferating cells expressing two different amounts of a target protein to show that both selectivity and synergism are robust against variability and heritability in the cell population. The reduction in the total drug administered due to the synergistic performance of the selective drugs can potentially result in reduced toxicity and off-target interactions, providing a mechanism to improve the treatment of cell-based diseases caused by aberrant gene overexpression, such as cancer and diabetes.

A tunable coarse-grained model for ligand-receptor interaction

Cell-surface receptors are the most common target for therapeutic drugs. The design and optimization of next generation synthetic drugs require a detailed understanding of the interaction with their corresponding receptors. Mathematical approximations to study ligand-receptor systems based on reaction kinetics strongly simplify the spatial constraints of the interaction, while full atomistic ligand-receptor models do not allow for a statistical many-particle analysis, due to their high computational requirements. Here we present a generic coarse-grained model for ligand-receptor systems that accounts for the essential spatial characteristics of the interaction, while allowing statistical analysis. The model captures the main features of ligand-receptor kinetics, such as diffusion dependence of affinity and dissociation rates. Our model is used to characterize chimeric compounds, designed to take advantage of the receptor over-expression phenotype of certain diseases to selectively target unhealthy cells. Molecular dynamics simulations of chimeric ligands are used to study how selectivity can be optimized based on receptor abundance, ligand-receptor affinity and length of the linker between both ligand subunits. Overall, this coarse-grained model is a useful approximation in the study of systems with complex ligand-receptor interactions or spatial constraints.

The current importance of cell surface receptors as primary targets for drug treatment explains the increasing interest in a mathematical and quantitative description of the process of ligand-receptor interaction. Recently, a new generation of synthetic chimeric ligands has been developed to selectively target unhealthy cells, without harming healthy tissue. To understand these and other types of complex ligand-receptor systems, conventional chemical interaction models often rely on simplifications and assumptions about the spatial characteristics of the system, while full atomistic molecular dynamics simulations are too computationally demanding to perform many particle statistical analysis. In this paper, we describe a novel approach to model the interaction between ligands and receptors based on a coarse grained approximation that includes explicitly both spatial and kinetic details of the interaction, while allowing many-particle simulations and therefore, statistical analysis at biologically relevant time scales. The model is used to study the binding properties of generic chimeric ligands to understand how cell specificity is achieved, its dependence on receptor concentration and the influence of the distance between subunits of the chimera. Overall, this approach proves optimal to study other ligand-receptor systems with complex spatial regulation, such as receptor clustering, multimerization and multivalent asymmetric ligand binding.