A next generation mathematical model for the in vitro to clinical translation of T-cell engagers.

T-cell engager (TCE) molecules activate the immune system and direct it to kill tumor cells. The key mechanism of action of TCEs is to crosslink CD3 on T cells and tumor associated antigens (TAAs) on tumor cells. The formation of this trimolecular complex (i.e. trimer) mimics the immune synapse, leading to therapeutic-dependent T-cell activation and killing of tumor cells. Computational models supporting TCE development must predict trimer formation accurately. Here, we present a next-generation two-step binding mathematical model for TCEs to describe trimer formation. Specifically, we propose to model the second binding step with trans-avidity and as a two-dimensional (2D) process where the reactants are modeled as the cell-surface density. Compared to the 3D binding model where the reactants are described in terms of concentration, the 2D model predicts less sensitivity of trimer formation to varying cell densities, which better matches changes in EC50 from in vitro cytotoxicity assay data with varying E:T ratios. In addition, when translating in vitro cytotoxicity data to predict in vivo active clinical dose for blinatumomab, the choice of model leads to a notable difference in dose prediction. The dose predicted by the 2D model aligns better with the approved clinical dose and the prediction is robust under variations in the in vitro to in vivo translation assumptions. In conclusion, the 2D model with trans-avidity to describe trimer formation is an improved approach for TCEs and is likely to produce more accurate predictions to support TCE development.

A Mechanistic Site-Of-Action Model: A Tool for Informing Right Target, Right Compound, And Right Dose for Therapeutic Antagonistic Antibody Programs.

Quantitative modeling is increasingly utilized in the drug discovery and development process, from the initial stages of target selection, through clinical studies. The modeling can provide guidance on three major questions-is this the right target, what are the right compound properties, and what is the right dose for moving the best possible candidate forward. In this manuscript, we present a site-of-action modeling framework which we apply to monoclonal antibodies against soluble targets. We give a comprehensive overview of how we construct the model and how we parametrize it and include several examples of how to apply this framework for answering the questions postulated above. The utilities and limitations of this approach are discussed.

Modeling the effect of blunt impact on mitochondrial function in cartilage: implications for development of osteoarthritis.

OBJECTIVE: Osteoarthritis (OA) is a disease characterized by degeneration of joint cartilage. It is associated with pain and disability and is the result of either age and activity related joint wear or an injury. Non-invasive treatment options are scarce and prevention and early intervention methods are practically non-existent. The modeling effort presented in this article is constructed based on an emerging biological hypothesis-post-impact oxidative stress leads to cartilage cell apoptosis and hence the degeneration observed with the disease. The objective is to quantitatively describe the loss of cell viability and function in cartilage after an injurious impact and identify the key parameters and variables that contribute to this phenomenon. METHODS: We constructed a system of differential equations that tracks cell viability, mitochondrial function, and concentrations of reactive oxygen species (ROS), adenosine triphosphate (ATP), and glycosaminoglycans (GAG). The system was solved using MATLAB and the equations' parameters were fit to existing data using a particle swarm algorithm. RESULTS: The model fits well the available data for cell viability, ATP production, and GAG content. Local sensitivity analysis shows that the initial amount of ROS is the most important parameter. DISCUSSION: The model we constructed is a viable method for producing in silico studies and with a few modifications, and data calibration and validation, may be a powerful predictive tool in the search for a non-invasive treatment for post-traumatic osteoarthritis.

Mathematics as a conduit for translational research in post-traumatic osteoarthritis.

Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:566-572, 2017.

Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model.

Post-traumatic osteoarthritis affects almost 20% of the adult US population. An injurious impact applies a significant amount of physical stress on articular cartilage and can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. In our effort to understand the underlying biochemical mechanisms of this debilitating disease, we have constructed a multiscale mathematical model of the process with three components: cellular, chemical, and mechanical. The cellular component describes the different chondrocyte states according to the chemicals these cells release. The chemical component models the change in concentrations of those chemicals. The mechanical component contains a simulation of a blunt impact applied onto a cartilage explant and the resulting strains that initiate the biochemical processes. The scales are modeled through a system of partial-differential equations and solved numerically. The results of the model qualitatively capture the results of laboratory experiments of drop-tower impacts on cartilage explants. The model creates a framework for incorporating explicit mechanics, simulated by finite element analysis, into a theoretical biology framework. The effort is a step toward a complete virtual platform for modeling the development of post-traumatic osteoarthritis, which will be used to inform biomedical researchers on possible non-invasive strategies for mitigating the disease.