An underappreciated peculiarity of late-life human mortality kinetics assessed through the lens of a generalization of the Gompertz-Makeham law

Much attention in biogerontology is paid to the deceleration of mortality rate increase with age by the end of a species-specific lifespan, e.g. after ca. 90 years in humans. Being analyzed based on the Gompertz law µ(t)=µ0e^γt with its inbuilt linearity of the dependency of lnµ on t, this is commonly assumed to reflect the heterogeneity of populations where the frailer subjects die out earlier thus increasing the proportions of those whose dying out is slower and leading to decreases in the demographic rates of aging. Using Human Mortality Database data related to France, Sweden and Japan in five periods 1920, 1950, 1980, 2018 and 2020 and to the cohorts born in 1920, it is shown by LOESS smoothing of the lnµ-vs-t plots and constructing the first derivatives of the results that the late-life deceleration of the life-table aging rate (LAR) is preceded by an acceleration. It starts at about 65 years and makes LAR at about 85 years to become 30% higher than it was before the acceleration. Thereafter, LAR decreases and reaches the pre-acceleration level at ca. 90 years. This peculiarity cannot be explained by the predominant dying out of frailer subjects at earlier ages. Its plausible explanation may be the acceleration of the biological aging in humans at ages above 65-70 years, which conspicuously coincide with retirement. The decelerated biological aging may therefore contribute to the subsequent late-life LAR deceleration. The biological implications of these findings are discussed in terms of a generalized Gompertz-Makeham law µ(t) = C(t)+µ0e^f(t).

A 2D analysis of correlations between the parameters of the Gompertz-Makeham model (or law?) of relationships between aging, mortality, and longevity

When mortality (μ), aging rate (γ) and age (t) are treated according to the Gompertz model μ(t) = μ₀e^γt (GM), any mean age corresponds to a manifold of paired reciprocally changing μ₀ and γ. Therefore, any noisiness of data used to derive GM parameters makes them negatively correlated. Besides this artifactual factor of the Strehler-Mildvan correlation (SMC), other factors emerge when the age-independent mortality C modifies survival according to the Gompertz-Makeham model μ(t) = C+μ₀e^γt (GMM), or body resources are partitioned between survival and protection from aging [the compensation effect of mortality (CEM)]. Theoretical curves in (γ, logμ₀) coordinates show how μ₀ decreases when γ increases upon a constant mean age. Within a species-specific range of γ, such "isoage" curves look as nearly parallel straight lines. The slopes of lines constructed by applying GM to survival curves modeled according to GMM upon changes in C are greater than the isoage slopes. When CEM is modeled, the slopes are still greater. Based on these observations, CEM is shown to contribute to SMC associated with sex differences in lifespan, with the effects of several life-extending drugs, and with recent trends in survival/mortality patterns in high-life-expectancy countries; whereas changes in C underlie differences between even high-life-expectancy countries, not only between high- and low-life-expectancy countries. Such interpretations make sense only if GM is not merely a statistical model, but rather reflects biological realities. Therefore, GM is discussed as derivable by applying certain constraints to a natural law termed the generalized Gompertz-Makeham law.

A Tale of Two Concepts: Harmonizing the Free Radical and Antagonistic Pleiotropy Theories of Aging

SIGNIFICANCE

The two foremost concepts of aging are the mechanistic free radical theory (FRT) of how we age and the evolutionary antagonistic pleiotropy theory (APT) of why we age. Both date from the late 1950s. The FRT holds that reactive oxygen species (ROS) are the principal contributors to the lifelong cumulative damage suffered by cells, whereas the APT is generally understood as positing that genes that are good for young organisms can take over a population even if they are bad for the old organisms. Recent Advances: Here, we provide a common ground for the two theories by showing how aging can result from the inherent chemical reactivity of many biomolecules, not just ROS, which imposes a fundamental constraint on biological evolution. Chemically reactive metabolites spontaneously modify slowly renewable macromolecules in a continuous way over time; the resulting buildup of damage wrought by the genes coding for enzymes that generate such small molecules eventually masquerades as late-acting pleiotropic effects. In aerobic organisms, ROS are major agents of this damage but they are far from alone.

CRITICAL ISSUES

Being related to two sides of the same phenomenon, these theories should be compatible. However, the interface between them is obscured by the FRT mistaking a subset of damaging processes for the whole, and the APT mistaking a cumulative quantitative process for a qualitative switch.

FUTURE DIRECTIONS

The manifestations of ROS-mediated cumulative chemical damage at the population level may include the often-observed negative correlation between fitness and the rate of its decline with increasing age, further linking FRT and APT. Antioxid. Redox Signal. 29, 1003-1017.

Applying parametric models to survival data: tradeoffs between statistical significance, biological plausibility, and common sense

Parametric models for survival data help to differentiate aging from other lifespan determinants. However, such inferences suffer from small sizes of experimental animal samples and variable animals handling by different labs. We analyzed control data from a single laboratory where interventions in murine lifespan were studied over decades. The minimal Gompertz model (GM) was found to perform best with most murine strains. However, when several control datasets related to a particular strain are fitted to GM, strikingly rigid interdependencies between GM parameters emerge, consistent with the Strehler-Mildvan correlation (SMC). SMC emerges even when survival patterns do not conform to GM, as with cancer-prone HER2/neu mice, which die at a log-normally distributed age. Numerical experiments show that SMC includes an artifact whose magnitude depends on dataset deviation from conformance to GM irrespectively of the noisiness of small datasets, another contributor to SMC. Still another contributor to SMC is the compensation effect of mortality (CEM): a real tradeoff between the physiological factors responsible for initial vitality and the rate of its decline. To avoid misinterpretations, we advise checking experimental results against a SMC based on historical controls or on subgroups obtained by randomization of control animals. An apparent acceleration of aging associated with a decrease in the initial mortality is invalid if it is not greater than SMC suggests. This approach applied to published data suggests that the effects of calorie restriction and of drugs believed to mimic it are different. SMC and CEM relevance to human survival patterns is discussed.