Speaker
Description
We present a mathematical framework to describe tumor growth under PROTAC treatment, integrating PK, PD, and tumor growth inhibition. PROTACs are a new class of drugs that promote selective degradation of oncogenic proteins \cite{1}. Although preclinical studies show tumor shrinkage, relapse often occurs, suggesting resistance mechanisms \cite{2}. The model links PROTAC-induced protein degradation to tumor growth inhibition. To account for reduced treatment efficacy, we introduce a cumulative resistance mechanism, allowing a progressive reduction of drug efficacy over repeated dosing \cite{3}. The model combines a two-compartment PK model, a protein turnover module with constant synthesis and drug-stimulated degradation \cite{4}, and classical tumor growth laws (Linear, Exponential, Logistic, Gompertz) \cite{5}. After calibration on in-vivo xenograft data, the model accurately reproduces both initial regression and subsequent regrowth observed experimentally. A key contribution is the mathematical analysis. By treating the remaining protein level as a bifurcation parameter, we identify a critical threshold separating tumor eradication from relapse. Crossing this threshold induces a qualitative change in system stability, marking the transition from regression to tumor outgrowth. This analysis provides a predictive tool to anticipate resistance onset from protein dynamics, supporting adaptive therapeutic strategies aimed at delaying relapse while optimizing drug exposure.
Bibliography
@article{1,
title = {{PK/PD modeling of targeted protein degraders: Charting new waters and navigating the shallows}},
journal = {Drug Discovery Today},
volume = {30},
number = {3},
pages = {104311},
year = {2025},
url = {https://doi.org/10.1016/j.drudis.2025.104311},
author = {R.T.U. Haid and A. Reichel},
}
@article{2,
author = {Ottis, Philipp and Palladino, Chiara and Thienger, Phillip and Britschgi, Adrian and Heichinger, Christian and Berrera, Marco and Julien-Laferriere, Alice and Roudnicky, Filip and Kam-Thong, Tony and Bischoff, James R. and Martoglio, Bruno and Pettazzoni, Piergiorgio},
title = {Cellular Resistance Mechanisms to Targeted Protein Degradation Converge Toward Impairment of the Engaged Ubiquitin Transfer Pathway},
journal = {ACS Chemical Biology},
volume = {14},
number = {10},
pages = {2215-2223},
year = {2019},
URL = { https://doi.org/10.1021/acschembio.9b00525},
}
@article{3,
author = {Panetta, J.C.},
journal = {Applied Mathematics Letters},
number = {1},
pages = {123--127},
title = {{A logistic model of periodic chemotherapy with drug resistance}},
volume = {10},
year = {1997},
url = {https://doi.org/10.1016/s0893-9659(96)00123-1},
}
@article{4,
author = {Vetma, V. and Perez, L. C. and Elias, J. and Stingu, A. and Kombara, A.
and Gmaschitz, T. and Braun, N. and Ciftci, T. and Dahmann, G.
and Diers, E. and Gerstberger, T. and Greb, P. and Kidd, G.
and Kofink, C. and Puoti, I. and Spiteri, V. and Trainor, N.
and Weinstabl, H. and Westermaier, Y. and Whitworth, C.
and Ciulli, A. and Farnaby, W. and McAulay, K. and Frost, A. B.
and Chessum, N. and Koegl, M.},
title = {Confounding Factors in Targeted Degradation of Short-Lived Proteins},
journal = {ACS Chemical Biology},
year = {2024},
volume = {19},
number = {7},
pages = {1484--1494},
url = {https://doi.org/10.1021/acschembio.4c00152}
}
@article{5,
author = {Murphy, H. and Jaafari, H. and Dobrovolny, H.M.},
title = {Differences in predictions of ODE models of tumor growth: a cautionary example},
journal = {BMC Cancer},
volume = {16},
number = {1},
pages = {163},
year = {2016},
url = {https://doi.org/10.1186/s12885-016-2164-x}
}
