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

Abstract

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.

Figure 1. The minimum stability analysis model for a gene network.

At any given time the genome consists of a number of normally expressed and dysregulated genes. The proteome accumulates “defects”, such as the proteins over- or under-expressed by dysregulated genes, which are removed via the protein quality-control or turnover systems. DNA repair machinery controls epigenetic states of the genes and restores normal expression levels. On top of this, interactions with the environment damage both the proteome and the genome subsystems, increasing the load on the protein-turnover and DNA-repair components. Parameters f, β, δ, p and c appear in Eqs. (1) and (2), and are interpreted in the text below. The figure was drawn by Peter Fedichev.

Figure 2. Principal components analysis of gene expression profiles in aging flies (data from20), fed on control (ad lib) and Calorically Restricted (CR) diets.

Every point represents a transcriptome for flies of a specific age and diet. As the animals age, the genetic network accumulates regulation errors and the transcription levels change in a single direction, up to a limit beyond which viability cannot be maintained.

Figure 3

(a) ΔM₀, the mortality change as wild-type flies are exposed to N traumatic insults, is plotted as a function of N. (b) Average lifespan, t_avg, is plotted as a function of N. In both panels (a,b), the solid lines indicate the theoretical prediction based on Eq. (6) and parameters estimated from experimental data. Grey symbols are experimental mortality data points.

Figure 4. Stability diagram of the model gene network.

Below the separatrix defined by Eq. (6) the solutions of Eqs. (1,2) are unstable and correspond to “normally” aging animals. The stable solutions exist above the separatrix and may describe “negligible senescence”.