Contribution of Quantitative Methods of Estimating Mortality Dynamics to Explaining Mechanisms of Aging

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 (CVLS) 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, CVLS 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).

Evolution of Longevity in Tetrapods: Safety Is More Important than Metabolism Level

Various environmental morphological and behavioral factors can determine the longevity of representatives of various taxa. Long-lived species develop systems aimed at increasing organism stability, defense, and, ultimately, lifespan. Long-lived species to a different extent manifest the factors favoring longevity (gerontological success), such as body size, slow metabolism, activity of body's repair and antioxidant defense systems, resistance to toxic substances and tumorigenesis, and presence of neotenic features. In continuation of our studies of mammals, we investigated the characteristics that distinguish long-lived ectotherms (crocodiles and turtles) and compared them with those of other ectotherms (squamates and amphibians) and endotherms (birds and mammals). We also discussed mathematical indicators used to assess the predisposition to longevity in different species, including standard indicators (mortality rate, maximum lifespan, coefficient of variation of lifespan) and their derivatives. Evolutionary patterns of aging are further explained by the protective phenotypes and life history strategies. We assessed the relationship between the lifespan and various studied factors, such as body size and temperature, encephalization, protection of occupied ecological niches, presence of protective structures (for example, shells and osteoderms), and environmental temperature, and the influence of these factors on the variation of the lifespan as a statistical parameter. Our studies did not confirm the hypothesis on the metabolism level and temperature as the most decisive factors of longevity. It was found that animals protected by shells (e.g., turtles with their exceptional longevity) live longer than species that have poison or lack such protective adaptations. The improvement of defense against external threats in long-lived ectotherms is consistent with the characteristics of long-lived endotherms (for example, naked mole-rats that live in underground tunnels, or bats and birds, whose ability to fly is one of the best defense mechanisms).

Evolution of Longevity as a Species-Specific Trait in Mammals

From the evolutionary point of view, the priority problem for an individual is not longevity, but adaptation to the environment associated with the need for survival, food supply, and reproduction. We see two main vectors in the evolution of mammals. One is a short lifespan and numerous offspring ensuring reproductive success (r-strategy). The other one is development of valuable skills in order compete successfully (K-strategy). Species with the K-strategy should develop and enhance specific systems (anti-aging programs) aimed at increasing the reliability and adaptability, including lifespan. These systems are signaling cascades that provide cell repair and antioxidant defense. Hence, any arbitrarily selected long-living species should be characterized by manifestation to a different extent of the longevity-favoring traits (e.g., body size, brain development, sociality, activity of body repair and antioxidant defense systems, resistance to xenobiotics and tumor formation, presence of neotenic traits). Hereafter, we will call a set of such traits as the gerontological success of a species. Longevity is not equivalent to the evolutionary or reproductive success. This difference between these phenomena reaches its peak in mammals due to the development of endothermy and cephalization associated with the cerebral cortex expansion, which leads to the upregulated production of oxidative radicals by the mitochondria (and, consequently, accelerated aging), increase in the number of non-dividing differentiated cells, accumulation of the age-related damage in these cells, and development of neurodegenerative diseases. The article presents mathematical indicators used to assess the predisposition to longevity in different species (including the standard mortality rate and basal metabolic rate, as well as their derivatives). The properties of the evolution of mammals (including the differences between modern mammals and their ancestral forms) are also discussed.

Ants as Object of Gerontological Research

Social insects with identical genotype that form castes with radically different lifespans are a promising model system for studying the mechanisms underlying longevity. The main direction of progressive evolution of social insects, in particular, ants, is the development of the social way of life inextricably linked with the increase in the colony size. Only in a large colony, it is possible to have a developed polyethism, create large food reserves, and actively regulate the nest microclimate. The lifespan of ants hugely varies among genetically similar queens, workers (unproductive females), and males. The main advantage of studies on insects is the determinism of ontogenetic processes, with a single genome leading to completely different lifespans in different castes. This high degree of determinacy is precisely the reason why some researchers (incorrectly) call a colony of ants the "superorganism", emphasizing the fact that during the development, depending on the community needs, ants can switch their ontogenetic programs, which influences their social roles, ability to learn (i.e., the brain [mushroom-like body] plasticity), and, respectively, the spectrum of tasks performed by a given individual. It has been shown that in many types of food behavior, older ants surpass young ones in both performing the tasks and transferring the experience. The balance between the need to reduce the "cost" of non-breeding individuals (short lifespan and small size of workers) and the benefit from experienced long-lived workers possessing useful skills (large size and "non-aging") apparently determines the differences in the lifespan and aging rate of workers in different species of ants. A large spectrum of rigidly determined ontogenetic trajectories in different castes with identical genomes and the possibility of comparison between "evolutionarily advanced" and "primitive" subfamilies (e.g., Formicinae and Ponerinae) make ants an attractive object in the studies of both normal aging and effects of anti-aging drugs.

Coefficient of Variation of Lifespan Across the Tree of Life: Is It a Signature of Programmed Aging?

Measurements of variation are of great importance for studying the stability of pathological phenomena and processes. For the biology of aging, it is very important not only to determine average mortality, but also to study its stability in time and the size of fluctuations that are indicated by the variation coefficient of lifespan (CV_LS). It is believed that a relatively small (~20%) value of CV_LS in humans, comparable to the coefficients of variation of other events programmed in ontogenesis (for example, menarche and menopause), indicates a relatively rigid determinism (N. S. Gavrilova et al. (2012) Biochemistry (Moscow), 77, 754-760). To assess the prevalence of this phenomenon, we studied the magnitude of CV_LS, as well as the coefficients of skewness and kurtosis in diverse representatives of the animal kingdom using data provided by the Institute for Demographic Research (O. R. Jones et al. (2014) Nature, 505, 169-173). We found that, unlike humans and laboratory animals, in most examined species the values of CV_LS are rather high, indicating heterogeneity of the lifespan in the cohorts studied. This is probably due to the large influence of background mortality, as well as the non-monotonicity of total mortality in the wild, especially at the earliest ages. One way to account for this influence is to "truncate" the data (removing the earliest and latest ages from consideration). To reveal the effect of this procedure, we proposed a new indicator, the stability coefficient of mortality dynamics, which indicates how quickly CV_LS is reduced to values that characterize a relatively homogeneous population (33%) when the data are "truncated". Such indicators facilitate the use of the parameters of survival curves for analysis of the effects of geroprotectors, lifestyle, and other factors on lifespan, and for the quantification of relative contributions of genetic and environmental factors to the dynamics of aging in human and animal populations, including those living in the wild.

Is It Possible to Prove the Existence of an Aging Program by Quantitative Analysis of Mortality Dynamics?

Accumulation of various types of lesions in the course of aging increases an organism's vulnerability and results in a monotonous elevation of mortality rate, irrespective of the position of a species on the evolutionary tree. Stroustrup et al. (Nature, 530, 103-107) [1] showed in 2016 that in the nematode Caenorhabditis elegans, longevity-altering factors (e.g. oxidative stress, temperature, or diet) do not change the shape of the survival curve, but either stretch or shrink it along the time axis, which the authors attributed to the existence of an "aging program". Modification of the accelerated failure time model by Stroustrup et al. uses temporal scaling as a basic approach for distinguishing between quantitative and qualitative changes in aging dynamics. Thus we analyzed data on the effects of various longevity-increasing genetic manipulations in flies, worms, and mice and used several models to choose a theory that would best fit the experimental results. The possibility to identify the moment of switch from a mortality-governing pathway to some other pathways might be useful for testing geroprotective drugs. In this work, we discuss this and other aspects of temporal scaling.

Temporal Scaling of Age-Dependent Mortality: Dynamics of Aging in Caenorhabditis elegans Is Easy to Speed Up or Slow Down, but Its Overall Trajectory Is Stable

The dynamics of aging is often described by survival curves that show the proportion of individuals surviving to a given age. The shape of the survival curve reflects the dependence of mortality on age, and it varies greatly for different organisms. In a recently published paper, Stroustrup and coauthors ((2016) Nature, 530, 103-107) showed that many factors affecting the lifespan of Caenorhabditis elegans do not change the shape of the survival curve, but only stretch or compress it in time. Apparently, this means that aging is a programmed process whose trajectory is difficult to change, although it is possible to speed it up or slow it down. More research is needed to clarify whether the "rule of temporal scaling" is applicable to other organisms. A good indicator of temporal scaling is the coefficient of lifespan variation: similar values of this coefficient for two samples indicate similar shape of the survival curves. Preliminary results of experiments on adaptation of Drosophila melanogaster to unfavorable food show that temporal scalability of survival curves is sometimes present in more complex organisms, although this is not a universal rule. Both evolutionary and environmental changes sometimes affect only the average lifespan without changing the coefficient of variation (in this case, temporal scaling is present), but often both parameters (i.e. both scale and shape of the survival curve) change simultaneously. In addition to the relative stability of the coefficient of variation, another possible argument in favor of genetic determination of the aging process is relatively low variability of the time of death, which is sometimes of the same order of magnitude as the variability of timing of other ontogenetic events, such as the onset of sexual maturation.