Ghost Dynamics in Receptor Signalling Networks: A Fast--Slow Adaptive Extension of Competitive Cancer Inhibition Models
Abstract
Receptor occupancy models quantify inhibition of cancer signalling, often treating target occupancy as a proxy for downstream activity. Although this simplification yields low-dimensional models, it cannot represent delayed pathway shutdown, transient resistance, or non-monotone viability responses generated by intracellular networks. We formulate a fast--slow framework that distinguishes drug--target occupancy from downstream signalling activity. The fast variable X represents occupancy, the activity variable A represents pro-survival signalling, and the slow variable B represents adaptive feedback including phosphatase induction, stress adaptation, or signalling rewiring. Rapid occupancy relaxation permits a quasi-steady reduction, while weak feedback guarantees global convergence to a unique equilibrium. Stronger feedback may bring the frozen activity subsystem near a saddle-node fold, producing a ghost regime in which trajectories linger near the remnant of a vanished high-activity equilibrium. We determine when slow adaptive passage preserves the inverse-square-root ghost law or, under transverse crossing, produces the dynamic delay scale O(ε−1/3). Coupling activity to viability translates these delays into shoulders in dose--response curves, while adaptive lag may generate early-time overshoot without ad hoc forcing. A proof-of-concept fit to time-resolved viability data reproduces patterns across measured concentrations and observation times and reveals practical identifiability limitations. The framework also predicts exposure-time-dependent shifts in apparent potency, including IC50(t), because viability integrates signalling activity over time rather than receptor occupancy alone.
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BibTeX
@misc{manjunath2026ghost,
title = {{Ghost Dynamics in Receptor Signalling Networks: A Fast--Slow Adaptive Extension of Competitive Cancer Inhibition Models}},
author = {G Manjunath and Roumen Anguelov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.15300},
eprint = {2608.15300},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15300},
}
RIS
TY - UNPB
TI - Ghost Dynamics in Receptor Signalling Networks: A Fast--Slow Adaptive Extension of Competitive Cancer Inhibition Models
AU - G Manjunath
AU - Roumen Anguelov
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2608.15300
UR - https://arxiv.org/abs/2608.15300
AB - Receptor occupancy models quantify inhibition of cancer signalling, often treating target occupancy as a proxy for downstream activity. Although this simplification yields low-dimensional models, it cannot represent delayed pathway shutdown, transient resistance, or non-monotone viability responses generated by intracellular networks. We formulate a fast--slow framework that distinguishes drug--target occupancy from downstream signalling activity. The fast variable X represents occupancy, the activity variable A represents pro-survival signalling, and the slow variable B represents adaptive feedback including phosphatase induction, stress adaptation, or signalling rewiring. Rapid occupancy relaxation permits a quasi-steady reduction, while weak feedback guarantees global convergence to a unique equilibrium. Stronger feedback may bring the frozen activity subsystem near a saddle-node fold, producing a ghost regime in which trajectories linger near the remnant of a vanished high-activity equilibrium. We determine when slow adaptive passage preserves the inverse-square-root ghost law or, under transverse crossing, produces the dynamic delay scale O(ε^−1/3). Coupling activity to viability translates these delays into shoulders in dose--response curves, while adaptive lag may generate early-time overshoot without ad hoc forcing. A proof-of-concept fit to time-resolved viability data reproduces patterns across measured concentrations and observation times and reveals practical identifiability limitations. The framework also predicts exposure-time-dependent shifts in apparent potency, including IC_50(t), because viability integrates signalling activity over time rather than receptor occupancy alone.
ER -