Calculating Aging: Analysis of Survival Curves in the Norm and Pathology, Fluctuations in Mortality Dynamics, Characteristics of Lifespan Distribution, and Indicators of Lifespan Variation.

The article describes the history of studies of survival data carried out at the Research Institute of Physico-Chemical Biology under the leadership of Academician V. P. Skulachev from 1970s until present, with special emphasis on the last decade. The use of accelerated failure time (AFT) model and analysis of coefficient of variation of lifespan (CV) in addition to the Gompertz methods of analysis, allows to assess survival curves for the presence of temporal scaling (i.e., manifestation of accelerated aging), without changing the shape of survival curve with the same coefficient of variation. A modification of the AFT model that uses temporal scaling as the null hypothesis made it possible to distinguish between the quantitative and qualitative differences in the dynamics of aging. It was also shown that it is possible to compare the data on the survival of species characterized by the survival curves of the original shape (i.e., "flat" curves without a pronounced increase in the probability of death with age typical of slowly aging species), when considering the distribution of lifespan as a statistical random variable and comparing parameters of such distribution. Thus, it was demonstrated that the higher impact of mortality caused by external factors (background mortality) in addition to the age-dependent mortality, the higher the disorder of mortality values and the greater its difference from the calculated value characteristic of developed countries (15-20%). For comparison, CV for the Paraguayan Ache Indians is 100% (57% if we exclude prepuberty individuals as suggested by Jones et al.). According to Skulachev, the next step is considering mortality fluctuations as a measure for the disorder of survival data. Visual evaluation of survival curves can already provide important data for subsequent analysis. Thus, Sokolov and Severin [1] found that mutations have different effects on the shape of survival curves. Type I survival curves generally retains their standard convex rectangular shape, while type II curves demonstrate a sharp increase in the mortality which makes them similar to a concave exponential curve with a stably high mortality rate. It is noteworthy that despite these differences, mutations in groups I and II are of a similar nature. They are associated (i) with "DNA metabolism" (DNA repair, transcription, and replication); (ii) protection against oxidative stress, associated with the activity of the transcription factor Nrf2, and (iii) regulation of proliferation, and (or these categories may overlap). However, these different mutations appear to produce the same result at the organismal level, namely, accelerated aging according to the Gompertz's law. This might be explained by the fact that all these mutations, each in its own unique way, either reduce the lifespan of cells or accelerate their transition to the senescent state, which supports the concept of Skulachev on the existence of multiple pathways of aging (chronic phenoptosis).