## Computer Model Of Rdna Circle Accumulation

Monte Carlo computational methods can be used to estimate the magnitude of changes in experimentally measured ERC levels that would be produced by modifications in processes that influence ERC generation in cells. Computationally, the behavior of ERCs within a population of yeast cells can be modeled using a minimal set of the following six parameters:

P°ir: Probability that an ERC will be formed from the rDNA array in any generation.

Emax: Maximum number of ERCs that a cell will tolerate. When ERCs accumulate in a cell beyond this level, the cell stops dividing.

Prep: Probability that an ERC will replicate.

Pseg: Probability that an ERC will segregate to a daughter cell.

Paim: Probability that a yeast cell dies due to age-independent factors.

Spost: Number of generations a postmitotic yeast cell remains intact and can be recovered for analysis.

All time-dependent parameters are expressed per generation. Only the first five parameters affect the life span in an ERC model of yeast aging. Old yeast cells that have stopped dividing do not live indefinitely; they eventually lyse and are lost to analysis. Although it does not affect the life span as defined as number of cell divisions, the post-mitotic survival of cells does affect the number of ERCs that are recovered from age-sorted populations.

A minimal ERC model of yeast aging can be described:

1. Daughter cells may be produced with ERCs. The probability that any ERC in a dividing mother cell will segregate to the newly produced daughter cells is Prep, and is assumed to be independent of segregation of any other ERCs in the mother cell, and is assumed to be unaffected by the age of the mother or total number of ERCs. The asymmetrical segregation of ERCs to daughter cells is not 100% (60).

2. An ERC is generated by recombination from the rDNA array with fixed probability Pcir.

3. ERCs accumulate exponentially in the mother cell at a rate determined by Prep. The ARS present in the rDNA may not be sufficient to replicate an ERC once per cell division (92).

4. When ERCs reach some fixed level within the cell, cell replication ceases (60) at the ERC level given by Emax.

Yeast cells can die owing to non-ERC related and non-age dependent factors at a fixed rate given by Paim. This parameter is necessary as the age-independent mortality rate is likely increased in sgsl mutants (91).

Many assumptions are necessary to create even a simple model of the behavior of ERCs in yeast aging. Factors such as the recombination of ERCs back into the chromosomal rDNA array, ERC-ERC recombination producing multimers with greater number of ARSs, and the possible effects of growth or other conditions on generating ERCs are ignored. The purpose of this analysis is not to try and fit the data to obtain accurate estimates of what the values of parameters may be but rather to estimate what magnitude of change in parameters may produce what magnitude of change in the life span and levels of ERC accumulation and in what direction those changes will be.

Table 1 and Figure 5 give the output of the Monte Carlo simulation of yeast aging. For a given set of values for the input parameters, the output of the model is the predicted life span of the yeast strain, the predicted steady-state level of circles in a logarithmically growing population, and the predicted level of circles in age-sorted populations.

The most obvious result of the computer analysis of ERC accumulation is that the increase in the expected number of ERCs—either in logarithmically growing or age-sorted populations—is not great. A three-fold increase in the rate of circle formation is predicted to cause only a three-fold increase in the expected number of ERCs in an unsorted or sorted to seven-generation population (compare Table 1, row b to row a; Fig. 5b to 5a). Initially, one might believe that if ERCs are being produced and are accumulating at a faster rate, then the difference in ERC levels should continue to increase with successive generations. Although the absolute difference in the ERC level will increase with successive generations, the relative levels (the measure that can be experimentally determined) remain constant or decrease with successive generations.

Some factors that clearly affect the life span, even within an ERC model of yeast aging, will not be reflected in ERC levels that are measured. How ERCs might cause mitotic arrest is not known; it is believed that when they reach a sufficient level they may titrate essential cellular factors (60,93). It is likely that the sensitivity of cells to ERC accumulation (Emax) may vary in different strains. Given the exponential kinetics of ERC accumulation, changes in Emax have a minor effect on life span but no measurable effect on ERC accumulation (see Table 1, row c; Fig. 5c).

With several parameters, changes that cause an increase in the life span cause a corresponding decrease in predicted ERC levels, and changes that cause a decrease in the life span cause an increase in predicted ERC levels. This is not true for all parameters. Like SGS1 (91), other single-gene mutations are likely to cause alterations in more than one parameter of the model. As discussed above, increasing the ability of cells to tolerate ERCs (Emax) can extend the life span and leave unchanged or minimally increase the measured levels of ERCs in cells (see Fig. 5c). Increasing the rate that ERCs segregate to daughter cells (Pseg) can greatly extend the life span and also increase the ERC level in an unsorted population (see

Table 1 Predicted Life Span and ERC Accumulation

ERCs/Cell

Sorted to 7 generations Sorted to 15 generations

Input parameters

Life span

Postmitotic Survival

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