[Homeostatic model of aging: state and perspectives].

The homeostatic model of aging formalizing the concept of oxidative damage to the body was proposed in 2001. This formalization led to extensive opportunities for using the model to analyze reproduction and longevity of living organisms. Currently, the simulation of life processes in fruit flies gives much attention to the distribution of resources, taking into account the action of genetic noise. The result is arising of individual heterogeneity, in which unbalanced allocation of resources ends with the death from reproductive overload. The article considers the model of the mechanism of individual reproduction of stochasticity and possibility of its use to assess the maximally tolerated changes in the external environment.

[Health, homeostasis and longevity].

Concepts of health and homeostasis are discussed and their connection to longevity is analyzed. Homeostasis is one of cardinal properties of the organism, which arises in evolution basing on mechanisms maintaining stationarity. Health represents the organisms' ability to sustain homeostasis and return to it after action of external disturbances. Maintaining the health of a human determines longevity. The factors affecting the health, aging and longevity are discussed. Potential reserves of longevity are estimated and possible ways to achieve them are provided.

[Basic principles of creation of multilevel multistage mathematical model of aging].

Current knowledge on the aging allows to elaborate approaches to the creation of multilevel model of multistage of human aging taking into consideration events during the aging at various levels of integration: molecular, cellular, tissue, organ, systemic, organism. The present paper have deals with main states of the mathematical model of multistage aging, principles of its construction, applicability and evaluation of its prognostic power. There are 3 levels of integrative systems: homeostatic (organismal), systemic and cellular-molecular. The definitions of normal and pathological aging are given. The samples of various patterns of aging under the influence of factors accelerating aging (constant illumination or alimentary obesity) or under the factors slowing down aging (treatment with metformin or melatonin) are discussed.

[Caloric restriction increases life span in sterile and non-sterile D. melanogaster females: systems analysis].

Experiments show that moderate caloric restriction in normal (non-sterile) fruit flies results in the increase of life span. It has been found recently that life span increases under caloric restriction also in sterile Drosophila females. This fact was explained by remodeling of metabolism due to insulin signaling. In this paper a hypothesis is put forward that under caloric restriction in the organism, the energy arrival decreases so that the stationary state must be restored. To achieve this, reproduction is reducing, remodeling of metabolism and the increasing of substrates output from the gastrointestinal tract start. The increase of life span can be just a side effect of these processes. Simulation demonstrates that the experimentally observed life span increasing in non-sterile fly females under caloric restriction can be explained exclusively by the reducing reproduction.

[Reproductive overload in D. melanogaster females--its connection with longevity].

The conception of individual reproduction is that fruit flies are genetically designed to oviposit at the highest possible rate. This rate is maintained right up to the moment when the organism begins to age, and the senescence is characterized by the reproduction rate falling exponentially. The population can be divided into z, s, m, and l-phenotypes depending on their resource allocation. The main part of the population consists of m-phenotype flies with a balanced resource allocation. The flies with z-phenotype are infecund; s flies do not reach senility; and l flies, in which the allocation is biased toward somatic organism maintenance, outlast the period of oviposition and die only after they have completely used up their reproductive potential. Individual reproductive patterns and reproductive phenotypes are analyzed for two D. melanogaster populations consisting of 493 and 474 flies. It is shown that there is a mortality curve for each phenotype, and that a part of the population dies out "prematurely" due to reproductive overload.

[Testing of optimality hypothesis for longevous flies D. melanogaster under artificial selection].

In agree with evolutionary principles the fitness of the organisms to environmental condition in a course of natural evolution moves to the optimum in the sense of maximization of reproductive success. Nonetheless, the optimality problem practically was never risen as regards to artificial selection. In the paper a Drosophila strain is analyzed which was subjected to artificial selection for longevity. Beforehand, mathematical modeling showed that natural Drosophila population held in captured condition was evolutionary optimal in the sense of maximization of reproductive success when resource allocation has been fixed between different functions of the organism. In the paper the less laborious analytical technique to analyze the optimality problem is proposed and it is shown that under artificial selection the resource allocation between the reproduction and somatic maintenance changes towards diminution of the resource devoted to reproduction. Such a population from the point of view of maximization of reproductive success loses the optimality characteristics and becomes non-optimal.

[Gerontology in silico: the emergence of a new discipline].

In this paper the modern views concerning the place of mathematical and computer modeling of aging and aging related pathologies in the current state and in future developments of gerontology are discussed. The review of most perspective directions of research including analyses of demographic, molecular, cellular, and physiological mechanisms of aging, the roles of damage and reparation of DNA, cell proliferation and apoptosis, where application of mathematical modeling is promising is given. Special attention is paid to the results and perspectives of mathematical modeling in experimental gerontology including modeling of aging and longevity in laboratory animals (nematode worms, fruit flies, mice, rats) and humans.

[Life expectancy and its modeling].

Modeling of the limited life span in an individual organism is discussed. Two models are presented in this discussion, a model of "natural technology" and a homeostatic model of aging in an organism. The problem of a transition from a model of an individual organism to a model of cohort and a population is studied. It is shown that it is enough to have only one property in an organism--death occurrence to model a cohort, whereas to model a population with overlapped generations two properties are needed, that is ability to die and ability to produce progenies. Examples of modeling of an individual organism, a cohort and a population are presented.

[Mathematical modeling in gerontology--strategic perspectives]. / Matematicheskoe modelirovanie v gerontologii--strategicheskie perspektivy.

Mathematical description of aging and mortality is presented. A review of tendencies in modeling is discussed and some difficulties related to adequacy and the ways of information presentation in the models are talked about. A short view is given at the two main modeling techniques in biology, namely the models of data and models of a system. Strategic perspectives of modeling in biogerontology are presented in terms of modeling paradigms. One can speak about a general paradigm consisting of postulates, principles and techniques related to a model, which allows a solving different problems with the same model, if the model can be modified to treat the variety of problems. Modification is to be done in the framework of concepts of the model by using a sum of the methods related to it. It is shown how the homeostatic paradigm can be used to predict a specific human longevity.

[Mathematical modeling and simulation of life history and tradeoffs]. / Matematicheskie modeli istorii zhizni i balansa resursov.

General trends in mathematical life history modeling are reviewed. In modern experimental biogerontology life history consists of all traits that affect fecundity and survival. Tradeoffs are of special importance in the theory of life history, studied either as an evolutionary phenomenon or as a feature of individual life history. Tradeoffs between cost of reproduction and survival are mostly studied and modeled. Special attention is given in the review to statistical modeling of life history (Monte-Carlo techniques). A number of modeling paradigms is presented and their perspectives are discussed.

[Checking of some hypotheses of the pathogenesis of diabetes mellitus by mathematical modeling]. / Proverka nekotorykh gipotez patogeneza sakharnogo diabeta putem matematicheskogo modelirovaniia.

A mathematical model of normal regulation of carbohydrate metabolism by the pancreas endocrine apparatus is presented. In a numerical experiment the model imitated changed levels of sucrose, insulin glucagon and gastrointestinal hormones in the blood in response to the ingested 50 g of glucose. The model of normal regulation was damaged in the way which theoretically should result in diabetes development. Then an estimation was made to what extent the disturbances of carbohydrate metabolism characteristic of diabetes were reproduced by the changed model. It has been shown that disturbances specific for diabetes appear when the sensitivity of beta-cells to glucose stimulus or hyperproduction of glucagon decreased. No changes in the behaviour of blood glucose typical of diabetes were obtained in the model when a decrease of the sensitivity of insulin receptors due to hyperinsulinemia in insulin-dependent tissues was imitated, as well as an increased activity of liver insulinase or hyposecretion of gastrointestinal hormones. These results point to the necessity of further development of these hypotheses.