Modeling the Cue-Signal-Response Balance of Apoptotic Parameters in Prostate Cancer Cells

Introduction: Pro-survival and apoptotic stimuli coexist in a population of tumor cells, even for receptors that are most frequently known to elicit one response over the other. As an exemplary case, prostate cancer cells express death receptors, the primary mediators of apoptosis activation, along with androgen receptors (AR), a mediator of cell survival. Furthermore, experimental evidence suggests that AR signaling is necessary for Bax-induced apoptosis, indicating a potential overlap between the pro-survival and apoptosis signaling pathways. Thus, it is important to understand how these opposing signaling pathways affect a heterogeneous population of cells in order to promote cell death. In this work, we incorporate experimental data to simulate the cue-signal-response amongst 10,000 in silico lymph node carcinoma of the prostate (LNCaP) cells to understand how temporal dynamics, ligand stimulation, intracellular signaling species, strength of receptor activation, and cell-to-cell heterogeneity can collectively contribute to evasion of cell death in LNCaP cells. Computational modeling offers a practical foundation for understanding how these parameters influence the cells’ decision-making process toward adverse outcomes, like cancer. Therefore, we developed a quantitative understanding of the Fas-mediated signaling of apoptosis to predict the likelihood of the tumor cell choosing one outcome (apoptosis or proliferation) over the other and gain insight into how uncontrolled growth of LNCaP cells can be prevented. In this work, we focus on the ligand-receptor pair of FasL and Fas, which promotes the extrinsic arm of canonical apoptosis signaling.

Materials and

Methods: The effects of FasL and Fas receptor signaling are simulated using ordinary differential equation (ODE) modeling (Mangrum and Finley, 2024. J Theor Biol, in revision), while varying several important features of this interaction such as dissociation of FasL and Fas, receptor degradation, and the rate at which the signal is transduced. We use two distribution types for starting amounts of the intracellular protein levels to cover a wide range of relevant values for each starting protein and further account for cell-to-cell heterogeneity. The LNCaP protein dynamics were calibrated to previously published Western blot analysis. Using these inputs and varying receptor parameters, we simulate the apoptotic efficacy of in silico tumor cells using pre-set apoptotic thresholds to define the level of activated caspase-3 (C3a) required to trigger apoptosis in LNCaP cells.

Results, Conclusions, and Discussions: We developed an in silico model that provides a quantitative foundation for the impacts of apoptotic signaling via Fas on LNCaP cells. The model predicts that apoptotic efficacy is most sensitive to the dissociation constant when the initial amounts are sampled from a uniform distribution. In contrast, the receptor parameters only slightly affect the time the C3a threshold is reached for apoptotic cells with starting amounts sampled from the normal distribution (p>0.05). Over the baseline receptor parameters, the cells that become apoptotic took an average of 195.3 minutes to reach the threshold for the uniform distribution and 167.6 minutes for the normal distribution (Figure 1). The number of non-apoptotic cells increases as the dissociation constant is increased and cells with low receptor levels were predicted to be the most sensitive to varying amounts of ligand. This suggests that as long as more FasL molecules are present in the surrounding extracellular matrix, the Fas receptor molecules are free to bind another ligand, activating new rounds of signaling once the preceding ligand unbinds. While ligand-receptor features are predicted to be necessary to control how cells react to external stimuli given the single causal chain of Fas, future work will assess how multiple receptor pathways, such as pro-survival promoting receptors, cause different patterns of apoptosis alongside Fas receptor.

Hormone-dependent cancer types are the most frequently diagnosed cancers in both males and females, which points to a critical need for further research in this field. Although targeting the male sex hormone, androgen, can be an effective treatment for prostate cancer, some patients do not respond. This might be brought on by a weakened apoptotic signal or by heterogeneity in the Fas-mediated apoptotic signaling pathway. Our model predicts the cell fate decision of tumor cells to commence apoptosis for pre-defined C3a threshold values. Furthermore, we predict the time it takes to reach the C3a threshold, in response to the various conditions of extracellular activation by FasL binding to Fas. This research provides quantitative information that could be leveraged to regulate apoptotic signaling and can be applied to different types of cancer cells and apoptosis-promoting receptors.

Acknowledgements (Optional): Research partially supported by the USC Center for Computational Modeling of Cancer