Aging and immortality in a cell proliferation model

Abstract

We investigate a model of cell division in which the length of telomeres within a cell regulates its proliferative potential. At each division, telomeres undergo a systematic length decrease as well as a superimposed fluctuation due to exchange of telomere DNA between the two daughter cells. A cell becomes senescent when one or more of its telomeres become shorter than a critical length. We map this telomere dynamics onto a biased branching-diffusion process with an absorbing boundary condition whenever any telomere reaches the critical length. Using first-passage ideas, we find a phase transition between finite lifetime and immortality (infinite proliferation) of the cell population as a function of the influence of telomere shortening, fluctuations, and cell division.

FIG. 1

Schematic illustration of telomere evolution. The telomeres in the initial cell contain x = 15 units. Upon division, each telomere ostensibly shortens by Δx = 5 units, but additional exchange of δx = ±2 units between daughter telomeres (dashed) leads to final lengths of 8 and 12.

FIG. 2

Plot of the number of active cells versus time from the second line of Eq. (7) for the case of M = 1 telomere per cell, with ε₁ = 0.8 (solid) 0.9 (dashed), and 0.99 (dotted).

FIG. 3

Plot of the total number of senescent cells that are produced during the evolution of the cell population as a function of the dimensionless growth rate ε₁ = 4Dk/v².