The day in conversation for 2026-10-15

The discussion: Ines: I’m still wrestling with that Adenoid Cystic Carcinoma modeling piece; the idea that radiotherapy timing is a critical control variable based on oxygen depletion dynamics feels incredibly tangible, but it relies so heavily on those nonlinear differential equations staying stable across different tissue types. Marcus: That stability is the crux of it, isn't it? I always worry that when we move from deterministic ODEs to these kinds of highly coupled systems in biological settings, we lose the ability to handle genuine stochasticity—the tiny fluctuations in nutrient availability or local oxygen tension that actually drive tumor heterogeneity. It’s a beautiful simplification for a framework, but biologically, it’s a massive blind spot if you ignore the noise. Yuki: I think maybe that's where the comparison to the eDNA work comes in. If we take Marcus's point about stochasticity and apply that lens to those environmental PDE models—the delayed source inputs for river systems—we see how similar the challenges are, even though one is modeling chemical kinetics and the other is molecular diffusion. The underlying issue isn't just solving the equation; it’s correctly parameterizing what we assume is constant versus what we know must be dynamic input.