A mathematical model is used to describe the increase in generation time with age of mother cells in the asymmetrically dividing yeast Saccharomyces cerevisiae. It is postulated that the generation time increases linearly with the amount of a senescence factor present in each cell. The senescence factor, which inhibits cell division is produced continuously. Although it is not degraded or destroyed, it may be diluted by cell division. The model is formally identical to one which was successful in describing waste dilution in populations of aging human diploid fibroblasts (Hirsch, 1978). The relation between aging in yeast and in fibroblasts is explored. Agreement between calculated results and yeast cell generation-time data is adequate. The results indicate that the senescence factor accumulates with little or no dilution in aging yeast mother cells.

Cell Division↗

PubMedDate not supplied

Do intersections of mortality-rate and survival functions have significance?

Common points of intersections have frequently been reported among members of families of linearized mortality-rate and survival functions. A general condition for the existence of such intersections is derived. It is shown that a common point of intersection between straight-line functions exists if and only if the intercepts of the functions are linearly related to their slopes. This slope-intercept condition is applied to a didactic model to illustrate its generality and to three models, the Gompertz-Makeham, the Weibull, and the logistic, which are often used in the analysis of mortality data. The slope-intercept condition for the Gompertz-Makeham mortality-rate model proves to be the well-known Strehler-Mildvan correlation. Families of mortality-rate functions or of the corresponding survival functions but not both may display common points of intersection. Differences between the ages at which survival functions intersect and those at which the associated mortality-rate functions intersect are calculated to be of the order of magnitude of 10 to 20 years. Survival function intersections lie close to the limit of human life span but often arise in consequence of unsupported extrapolations of data obtained at younger ages. These and other results lead to the conclusion that, in themselves, the intersections of survival and mortality-rate functions are not of great importance. To the extent that significance can be attributed to the intersections, it lies in the existence of linear relationships between their slopes and intercepts.

Data Interpretation, Statistical↗

PubMedDate not supplied

Can an improved environment cause maximum lifespan to decrease? Comments on lifespan criteria and longitudinal Gompertzian analysis.

Longitudinal Gompertzian analysis yields the counterintuitive conclusion that an improved environment can cause a decrease in maximum lifespan. The basis for this conclusion is examined. Results include the following: 1) The use of a specified high mortality rate as a criterion for maximum lifespan is arbitrary and leads to a calculated lifespan which is quite sensitive to the value of the criterion. 2) The definition of lifespan as the age to which a specified small population fraction survives is less arbitrary and less sensitive to the chosen criterion value. 3) However, the use of a survival criterion for lifespan in place of a mortality-rate criterion does not eliminate the seeming contradiction between environmental improvement and decreased lifespan. 4) Mortality rates can be approximated in semilogarithmic coordinates by three straight-line segments. The first segment, applicable through age 85, is the conventional Gompertz function. The second segment, representing ages 85 through 96, has a lower slope than the first, while the third segment, representing ages 96 through 124, has a negative slope. 5) The mortality rate obtained by extrapolating the first segment to a nominal age of maximum lifespan differs markedly from the true mortality rate at that age. 6) The conclusion that an improved environment is associated with a reduction in lifespan arises as a consequence of such an extrapolation.

Adult↗