Immune evasion in prostate cancer: resolving the cold tumour paradox via a hybrid discrete-continuum computational framework.

Background: Prostate cancer (PCa) presents a formidable clinical paradox. It is immunologically cold and resistant to immune checkpoint blockade (ICB), yet bulk genomic analyses consistently reveal low and non-prognostic expression of CD274 (PD-L1), the primary molecular target of such therapies. We hypothesised that this paradox arises from a failure of current methodologies to account for two critical, interacting dimensions: the granular heterogeneity of basal gene expression (the static engine) and the spatiotemporal dynamics of adaptive resistance mediated by interferon-gamma (the adaptive engine). Methods: We developed a rigorous, multi-phase computational framework integrating clinical genomics with hybrid agent-based modelling. In Phase I, we extracted and normalized CD274 mRNA expression from the TCGA-PRAD cohort (n = 554) to define the empirical landscape of basal resistance. In Phase II, we developed a spatial Agent-Based Model (ABM) parameterized by this distribution to simulate clonal selection. In Phase III, we extended this into a Hybrid Discrete-Continuum model, coupling discrete agents with a reaction-diffusion Partial Differential Equation (PDE) representing the IFN-{gamma} field. We simulated 50 stochastic replicates per arm across four experimental arms, including Diffusion and Induction knockouts. Results: Bulk TCGA analysis confirmed low average PD-L1 expression (Median Transcripts Per Million (TPM) = 1.48; Interquartile Range (IQR): 0.91-2.14) with no prognostic value (Hazard Ratio (HR) = 1.15; 95% Confidence Interval (CI): 0.67-1.97; log-rank p = 0.605). However, the static ABM revealed that rare, high-expressing genomic outliers (>9.0 TPM) drive persistence through Darwinian immunoediting, enriching the surviving population's resistance by 3.86-fold. The hybrid adaptive model demonstrated a far superior survival strategy: the IFN-{gamma}/PD-L1 feedback loop facilitated the emergence of "protective sanctuaries"-localised regions of high resistance at the tumour-immune interface. This mechanism increased final tumour burden by ~4.5-fold compared to static selection alone (p<0.001). Spatiotemporal analysis confirmed that resistance is not a fixed trait but a dynamic state induced by immune pressure. Diffusion knockout (D = 0) abolished sanctuary formation, reducing final burden by 65% (p<0.001), while induction knockout (Pmax = 0) reverted to static outcomes. Conclusions: This study resolves the cold tumour paradox by demonstrating that PCa resistance is driven by a twin engine of rare genomic outliers and adaptive spatial dynamics. The failure of biomarkers in PCa is due to their inability to capture the dynamic mirage of adaptive sanctuaries. Our validated framework offers a platform for testing synchronised therapeutic disruptions targeting both the static genomic landscape and the dynamic cytokine signalling axis.