Mutant Burden

Finite Hayflick limits can reduce expected long-term tumor burden by orders of magnitude. For k=50 and mutation probability 10^-9, the equal-growth asymptotic burden is about eight orders of magnitude smaller with limits. Replication limits can make total expected cell burden much smaller than in the no-limit model. There are regimes where expected mutant counts are strongly affected while variance remains close to the no-limit prediction. The total expected cell burden can still grow without bound when mutants escape replication limits. Variance under replication limits can differ from the expectation because it weights mutant growth with e to twice gamma times elapsed time.