Unsupervised learning of aging principles from longitudinal data.

Age is the leading risk factor for prevalent diseases and death. However, the relation between age-related physiological changes and lifespan is poorly understood. We combined analytical and machine learning tools to describe the aging process in large sets of longitudinal measurements. Assuming that aging results from a dynamic instability of the organism state, we designed a deep artificial neural network, including auto-encoder and auto-regression (AR) components. The AR model tied the dynamics of physiological state with the stochastic evolution of a single variable, the "dynamic frailty indicator" (dFI). In a subset of blood tests from the Mouse Phenome Database, dFI increased exponentially and predicted the remaining lifespan. The observation of the limiting dFI was consistent with the late-life mortality deceleration. dFI changed along with hallmarks of aging, including frailty index, molecular markers of inflammation, senescent cell accumulation, and responded to life-shortening (high-fat diet) and life-extending (rapamycin) treatments.

Longitudinal analysis of blood markers reveals progressive loss of resilience and predicts human lifespan limit.

We investigated the dynamic properties of the organism state fluctuations along individual aging trajectories in a large longitudinal database of CBC measurements from a consumer diagnostics laboratory. To simplify the analysis, we used a log-linear mortality estimate from the CBC variables as a single quantitative measure of the aging process, henceforth referred to as dynamic organism state indicator (DOSI). We observed, that the age-dependent population DOSI distribution broadening could be explained by a progressive loss of physiological resilience measured by the DOSI auto-correlation time. Extrapolation of this trend suggested that DOSI recovery time and variance would simultaneously diverge at a critical point of 120 - 150 years of age corresponding to a complete loss of resilience. The observation was immediately confirmed by the independent analysis of correlation properties of intraday physical activity levels fluctuations collected by wearable devices. We conclude that the criticality resulting in the end of life is an intrinsic biological property of an organism that is independent of stress factors and signifies a fundamental or absolute limit of human lifespan.

A universal transcriptomic signature of age reveals the temporal scaling of Caenorhabditis elegans aging trajectories.

We collected 60 age-dependent transcriptomes for C. elegans strains including four exceptionally long-lived mutants (mean adult lifespan extended 2.2- to 9.4-fold) and three examples of lifespan-increasing RNAi treatments. Principal Component Analysis (PCA) reveals aging as a transcriptomic drift along a single direction, consistent across the vastly diverse biological conditions and coinciding with the first principal component, a hallmark of the criticality of the underlying gene regulatory network. We therefore expected that the organism's aging state could be characterized by a single number closely related to vitality deficit or biological age. The "aging trajectory", i.e. the dependence of the biological age on chronological age, is then a universal stochastic function modulated by the network stiffness; a macroscopic parameter reflecting the network topology and associated with the rate of aging. To corroborate this view, we used publicly available datasets to define a transcriptomic biomarker of age and observed that the rescaling of age by lifespan simultaneously brings together aging trajectories of transcription and survival curves. In accordance with the theoretical prediction, the limiting mortality value at the plateau agrees closely with the mortality rate doubling exponent estimated at the cross-over age near the average lifespan. Finally, we used the transcriptomic signature of age to identify possible life-extending drug compounds and successfully tested a handful of the top-ranking molecules in C. elegans survival assays and achieved up to a +30% extension of mean lifespan.

Strehler-Mildvan correlation is a degenerate manifold of Gompertz fit.

Gompertz empirical law of mortality is often used in practical research to parametrize survival fraction as a function of age with the help of just two quantities: the Initial Mortality Rate (IMR) and the Gompertz exponent, inversely proportional to the Mortality Rate Doubling Time (MRDT). The IMR is often found to be inversely related to the Gompertz exponent, which is the dependence commonly referred to as Strehler-Mildvan (SM) correlation. In this paper, we address fundamental uncertainties of the Gompertz parameters inference from experimental Kaplan-Meier plots and show, that a least squares fit often leads to an ill-defined non-linear optimization problem, which is extremely sensitive to sampling errors and the smallest systematic demographic variations. Therefore, an analysis of consequent repeats of the same experiments in the same biological conditions yields the whole degenerate manifold of possible Gompertz parameters. We find that whenever the average lifespan of species greatly exceeds MRDT, small random variations in the survival records produce large deviations in the identified Gompertz parameters along the line, corresponding to the set of all possible IMR and MRDT values, roughly compatible with the properly determined value of average lifespan in experiment. The best fit parameters in this case turn out to be related by a form of SM correlation. Therefore, we have to conclude that the combined property, such as the average lifespan in the group, rather than IMR and MRDT values separately, may often only be reliably determined via experiments, even in a perfectly homogeneous animal cohort due to its finite size and/or low age-sampling frequency, typical for modern high-throughput settings. We support our findings with careful analysis of experimental survival records obtained in cohorts of C. elegans of different sizes, in control groups and under the influence of experimental therapies or environmental conditions. We argue that since, SM correlation may show up as a consequence of the fitting degeneracy, its appearance is not limited to homogeneous cohorts. In fact, the problem persists even beyond the simple Gompertz mortality law. We show that the same degeneracy occurs exactly in the same way, if a more advanced Gompertz-Makeham aging model is employed to improve the modeling. We explain how SM type of relation between the demographic parameters may still be observed even in extremely large cohorts with immense statistical power, such as in human census datasets, provided that systematic historical changes are weak in nature and lead to a gradual change in the mean lifespan.

Stability analysis of a model gene network links aging, stress resistance, and negligible senescence.

Several animal species are considered to exhibit what is called negligible senescence, i.e. they do not show signs of functional decline or any increase of mortality with age. Recent studies in naked mole rat and long-lived sea urchins showed that these species do not alter their gene-expression profiles with age as much as other organisms do. This is consistent with exceptional endurance of naked mole rat tissues to various genotoxic stresses. We conjectured, therefore, that the lifelong transcriptional stability of an organism may be a key determinant of longevity. We analyzed the stability of a simple genetic-network model and found that under most common circumstances, such a gene network is inherently unstable. Over a time it undergoes an exponential accumulation of gene-regulation deviations leading to death. However, should the repair systems be sufficiently effective, the gene network can stabilize so that gene damage remains constrained along with mortality of the organism. We investigate the relationship between stress-resistance and aging and suggest that the unstable regime may provide a mathematical basis for the Gompertz "law" of aging in many species. At the same time, this model accounts for the apparently age-independent mortality observed in some exceptionally long-lived animals.