Monte Carlo Simulation of LNCaP Human Prostate Cancer Cell Aggregation in Liquid-Overlay Culture

Neoplastic cells self-assemble in liquid-overlay cultures into multicellular spheroids that resemble micrometastases and avascular regions of larger tumors. A Monte Carlo simulation based on Meakin's cluster - cluster aggregation model resolved the physical mechanisms by which LNCaP human prostate cancer cells aggregate in this environment. The best-fit solution suggests that LNCaP cells aggregate with an adhesion probability of 0.5% when they migrate within a radius of influence between cell centers of 180 μm, 10 times the cell diameter. The sweeping radius of influence is indicative of cell tethering and/or chemotaxis and results in an intrinsic rate of self-aggregation that increases from k_II = 1.5 h^-1 for single cells to k₁₀₁₀ = 17.5 h^-1 for 10-mers. Similar rates are predicted by Smoluchowski's collision theory (1), suggesting that they are inherent properties of LNCaP liquid-overlay culture. Aggregates form more compact structures in culture than during simulation as measured by the fractal dimension: D_F = 1.74 ± 0.04 for 10-mers in culture vs D_F = 1.25 ± 0.10 for simulated 10-mers. Additional restructuring would further extend the radius of influence and diminish adhesion. Applications of this work include the production of highly viable spheroids for drug testing and basic oncological research.