Computergest├╝tzte Epidemiologie
Mathematische Modellierung
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Modelling senescence in ciliates

Asexually reproducing hypotrichous ciliates undergo senescence, which is in general attributed to degenerative processes in the macronucleus, assuming that a loss of viability is based on a loss of genetic elements. It is generally accepted that the genetic elements in the macronucleus of Hypotrichs segregate randomly, a process which potentially can lead to aneuploid imbalances in the distribution of gene copies. It is, however, unclear whether there are mechanisms which compensate for such imbalances such that each genetic element regains its predetermined copy number (regulatory model, conserving euploidy), or if the genetic elements only double, so that genetic imbalances can be inherited to further generations (stochastic model, allowing aneuploidy).

Results: We have investigated the regulatory and the stochastic model with respect to the number of generations a lineage of Hypotrichs can survive under asexual conditions (Duerr et al., 2004; Abstract). Simple prediction formulae for the approximate survival time of asexually reproducing ciliates are provided for both models. Whereas the regulatory model cannot explain senescence in Hypotrichs, the stochastic model provides plausible results which, however, strongly depend on the assumed distribution of copy numbers. Our modeling approach shows that we can only speculate about reasons of senescence in ciliates until the distribution of copy numbers in their macronucleus is unknown.

Survival times (left column, A1-C1) of asexually reproducing Hypotrichs under three different distributions of copy numbers (right column, A2-C2) resulting from 1,000 simulated experiments. In all three cases A-C, the number of different macronucleus chromosomes is G=15,000 and the initial mean number of pre-replication copies per macronucleus chromosome is mn=15,000, yielding a total number of chromosomes of N=2.25*108. In the right column, the distribution of copy numbers of the initial cell is shown in gray bars and the distribution of copy numbers of the last viable cell is shown in black bars (* in A2 points at the highest, observed copy number). A: all macronucleus chromosomes initially have an identical pre-replication copy number of n=15,000. B: copy numbers initially are uniformly distributed in the intervall [1,000 ; 29,000]. C: the initial pre-replication copy number is n=15,000 for all macronucleus chromosomes except for one rare chromosome with 1,000 copies (indicated by an arrow in C2). Curves in (A) and (B) represent normal distributions fitted to the simulation results.

Methods: In contrast to the regulatory model, which can be easily formulated by a binomial expression, the stochastic model has been explored by computer simulations.


  • Duerr, HP, Eichner M, Ammermann D, 2004. Modeling senescence in hypotrichous ciliates. Protist 155: 45-52 (Abstract)