Theoretical approach to biological aging

We employ the framework of multitype Galton-Watson processes to model a population of dividing cells. The cellular type is represented by its biological age, defined as the count of harmful proteins in the cell body. The stochastic evolution of the biological age of a generic cell is modeled as a discrete Markov chain with a finite set of states $\{0,1,\ldots,n\}$, where $n$ signifies the absorbing state corresponding to the senescence state of the cell. In our setting, cells...

We represent a process of learning by using bit strings, where 1-bits represent the knowledge acquired by individuals. Two ways of learning are considered: individual learning by trial-and-error; and social learning by copying knowledge from other individuals, or from parents in the case of species with parental care. The age-structured bit string allows us to study how knowledge is accumulated during life and its influence over the genetic pool of a population after many gen...

In this paper the Penna model is reconsidered. With computer simulations we check how the control parameters of the model influence the size of the stable population.

What is aging? Mechanistic answers to this question remain elusive despite decades of research. Here, we propose a mathematical model of cellular aging based on a model gene interaction network. Our network model is made of only non-aging components - the biological functions of gene interactions decrease with a constant mortality rate. Death of a cell occurs in the model when an essential gene loses all of its interactions to other genes, equivalent to the deletion of an ess...

Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a...

A large amount of population models use the concept of a carrying capacity. Simulated populations are bounded by invoking finite resources through a survival probability, commonly referred to as the Verhulst factor. The fact, however, that resources are not easily accounted for in actual biological systems makes the carrying capacity parameter ill-defined. Henceforth, we deem it essential to consider cases for which the parameter is unnecessary. This work demonstrates the pos...

We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die, keeping the population constant. An offspring has the same genome as its (randomly chosen) parent, except for a small amount of (also random) mutations. Chance may thus generate a newborn with a genome that is better than that of its parent, an...

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent death probability, as well as a variable reproduction probability for each individual as a function of age. We first solve for the steady-state of the model in mean field theory, before developing analytic techniques to compute Gaussian fluctu...

In these lecture notes I describe some of the main theoretical ideas emerged to explain the aging dynamics. This is meant to be a very short introduction to aging dynamics and no previous knowledge is assumed. I will go through simple examples that allow one to grasp the main results and predictions.

In this work we check the occurrence of the Azbel assumption of mortality within the framework of a bit string model for biological ageing. We reproduced the observed feature of linear correspondence between the fitting parameters of the death rate as obtained by Azbel with demographic data.