2D companion to the 3D scene: the same one-compartment bioenergetic (Thomann-type) model, drawn as a chain diagram and a live burden chart instead of rendered spheres. Engineered nanoparticles are far too large to partition passively across membranes the way lipophilic organics like PCBs do, so uptake is dominated by gut-mediated dietary assimilation:
Producer (level 0):
dC0/dt = ku·Cwater − ke·C0
Consumers (levels 1..N-1):
dCi/dt = AE·IR·C(i-1) − (ke+kg)·Ci
TMF = C_top / C_bottom (steady state)
AE = assimilation efficiency (fraction of ingested nanoparticle mass crossing the gut epithelium), IR = ingestion rate as a fraction of body mass per day, ke = elimination/depuration rate, kg = growth-dilution rate (held small and fixed here).
- Biomagnification (TMF > 1) requires AE·IR to exceed the combined loss rate (ke+kg) at every step — the classic behaviour of fat-soluble pollutants that lodge in tissue and barely clear.
- Trophic dilution (TMF < 1) is what most published feeding studies actually find for engineered nanoparticles: low gut translocation (AE typically 1-10%), fast faecal egestion and lysosomal processing keep ke high, so burden falls at each step up the chain — the opposite of mercury or PCBs.
- Adding more trophic levels compounds the same per-step ratio AE·IR/(ke+kg), so a chain with more links dilutes (or magnifies) further by the time it reaches the top.
- Drag AE and ke toward the biological extremes (very high AE, very low ke) to see the rare case where a nanoparticle formulation would behave like a magnifying pollutant instead.