A Crash Course on Aging

At the physiological level, aging is neither rigid nor unchangeable. Instead, the molecular and mechanisms driving aging are sufficiently plastic that a variety of diverse interventions--dietary, pharmaceutical, and genetic--have been developed to radically manipulate aging. These interventions, shown to increase the health and lifespan of laboratory animals, are now being explored for therapeutic applications in humans. This clinical potential makes it especially important...

Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which characterizes the dynamics of an evolving population with a given maximum age. Remarkably, while the spectrum of eigenvalues that govern the evolution depends on the fitness, how they change with the maximum age is independent of fitness. Thi...

Since its proposition in 1995, the Heumann-Hotzel model has remained as an obscure model of biological aging. The main arguments used against it were its apparent inability to describe populations with many age intervals and its failure to prevent a population extinction when only deleterious mutations are present. We find that with a simple and minor change in the model these difficulties can be surmounted. Our numerical simulations show a plethora of interesting features: t...

Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in amorphous materials (``Glasses'') which pose a challenge to theorist. Aging signals the breaking of time-translational invariance and the violation of the fluctuation dissipation theorem during the relaxation process. But while the origin o...

Motivated by recent research of aging in E. coli, we explore the effects of aging on bacterial fitness. The disposable soma theory of aging was developed to explain how differences in lifespans and aging rates could be linked to life history trade-offs. Although generally applied for multicellular organisms, it is also useful for exploring life history strategies of single celled organisms such as bacteria. Starting from the Euler-Lotka equation, we propose a mathematical mod...

We study and compare equilibrium and aging dynamics on both sides of the ideal glass transition temperature $T_{MCT}$. In the context of a mean field model, we observe that all dynamical behaviors are determined by the energy distance $\epsilon$ to threshold - i.e. marginally stable - states. We furthermore show the striking result that after eliminating age and temperature at the benefit of $\epsilon$, the scaling behaviors above and below $T_{MCT}$ are identical, reconcilin...

This is an extended abstract of lectures delivered at the 4th Warsaw Summer School on Statistical Physics in Kazimierz Dolny, June 25-July 2, 2011.

We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to $|\omega|^{\delta-1}$ at small frequencies, with $0<\delta<2$. The aging properties of the medium are encoded in a frequency dependent effective temperature $T_{\rm eff.}(\omega)$. The latter is modelized by a function propo...

The distribution of a population throughout the physiological age of the individuals is very relevant information in population studies. It has been modeled by the Langevin and the Fokker- Planck equations. A major problem with these equations is that they allow the physiological age to move back in time. This paper proposes an Infinitesimally ratcheted random walk as a way to solve that problem. Two mathematical representations are proposed. One of them uses a non-local scal...

Ignoring the differences between countries, human reproductive and dispersal behaviors can be described by some standardized models, so whether there is a universal law of population growth hidden in the abundant and unstructured data from various countries remains unclear. The age-specific population data constitute a three-dimensional tensor containing more comprehensive information. The existing literature often describes the characteristics of global or regional populatio...