Dendritic cells present pieces of engulfed extracellular antigen on MHC class I, priming CD8⁺ killer T cells — a trick called cross-presentation. Inside the phagosome, each antigen molecule faces two competing exit routes, modelled here as independent Poisson processes exactly as in the 3D twin:
Cytosolic route: Sec61 translocon exports antigen (rate k1)
→ proteasome cleaves it into peptides
→ TAP1/TAP2 pumps peptides into the ER
→ loaded onto MHC-I (tapasin/calreticulin)
Vacuolar route: Cathepsin S degrades antigen in situ (rate k2)
→ peptides load directly onto phagosomal MHC-I
→ TAP- and proteasome-independent, fewer steps
Because both are memoryless exponential processes, the identity of whichever fires first follows the classic competing-risks result:
P(cytosolic route) = k1 / (k1 + k2)
P(vacuolar route) = k2 / (k1 + k2)
- k1 (Sec61 export) — how fast antigen escapes the phagosome into the cytosol for proteasomal processing.
- k2 (cathepsin S) — how fast antigen is degraded directly inside the phagosome/endosome.
- TAP activity — scales how quickly cytosolic peptides reach the ER loading complex; low TAP activity is a well-documented bottleneck that throttles the cytosolic route even when k1 is high.
- Pharmacological block — toggling "Block cytosolic" mimics a proteasome inhibitor (lactacystin/MG132) or a TAP-deficient cell line; "Block vacuolar" mimics bafilomycin A1 collapsing the phagosomal pH gradient cathepsins need. Crucially, the branch decision (which route an antigen molecule is committed to) still happens upstream at the real k1/k2 competing rates — a block does not reroute committed antigen to the surviving pathway, it destroys the fraction already committed to the blocked one. That is why blocking either pathway measurably lowers total surface pMHC-I throughput rather than leaving it unchanged, matching real cross-presentation knockdown experiments.
Predicted steady-state efficiency (fraction of released antigen that reaches the surface) is 1 with both routes open, k2/(k1+k2) with cytosolic blocked, k1/(k1+k2) with vacuolar blocked, and 0 with both blocked — watch the measured "Lost to blocked route" counter and "Predicted efficiency" readout track this live.