Старение: различие между смертью клеток и смертью организма с позиции математической модели

Abstract

Смерть клеток в стареющем организме не вызывает сомнения и, по умолчанию, признается следствием старения самих клеток. Однако здесь присутствует парадокс, который не был замечен раньше: смерть клеток, которые являются постоянными структурными элементами тканей и органов, не допускается с позиции математического закона, характеризующий динамику популяционной смертности. Использование математической модели старения, основанное на законе смертности Гомперца, позволяет провести анализ фактических данных, отражающих динамику клеточной численности. В частности, на примере возрастных изменений плотности (численности) клеток в эндотелии роговицы можно оценить реальную модель старения организма, в основе которой лежит возрастнезависимая потеря клеток – стохастический механизм элиминации клеток из тканевой системы, не связанный со старением самих клеток.

In nature there is nothing eternal, and the death of any living being is perceived as for granted. Nevertheless, aging, which is the main reason for this, remains one of the mysteries of natural science, because through the inevitability of the death of organisms it is difficult to explain the infinity of life on the whole. This paradox is known from ancient times, as evidenced by one of Socrates' dialogues: «if everything that had been involved in life grew old, and if it died, it would remain dead and not come to life again, is it not absolutely clear that in the end everything would be dead and life would disappear». In other words, natural science from ancient times meant that the aging organism must contain ageless elements, i.e. there must be a level of structural organization that ensures the infinity of life. This philosophical thought is metaphysical in its essence, since no actual evidence that an object cannot grow old can be proved. Indeed, if death is proved by the fact of the deceased's presence, then the absence of aging is an observer's problem, but not a proof that it is impossible in principle. This is important to consider when we address to aging of the cell. The use of the mathematical model of aging, based on the Gompertz mortality law, allows an analysis of actual data reflecting the dynamics of cellular abundance. In particular, with the example of age-related changes in the density (number) of cells in the corneal endothelium, we have the opportunity to see a real model of aging of an organism based on age-independent cell loss – a stochastic mechanism for eliminating cells from the tissue system that is not associated with the aging of the cells themselves. The question of how cells in the tissue system are eliminated without previous aging, that is, in fact, being in physiological conditions, requires special discussion. However, ignorance of the mechanism is not an obstacle to the creation of an aging model that relies both on a mathematical law based on demographic observations and on data on the dynamics of elimination of endothelial cells detected with endothelial microscopy. Loss of endothelial cells leads to a decrease in the functional and adaptive abilities of the cornea, which in the end may result in complete loss of function, i.e. functional death of this tissue, as it is well known in ophthalmology. In this case, the loss of cells is not due to their age, i.e. is not associated with the alleged, although not proven, cellular aging. Following the mathematical model, we can conclude that the aging of the body is the aging of tissues, which is not the result of the aging of the cells that form them. To accept this statement, it is necessary to renounce the dogmatic view of aging, which is usually associated with human aging, rectilinearly projected onto the cell. Starting from the mathematical principle, we should strive to analyze medical and biological data from the position of exact science, and not to drive them into the dogmatic framework. The mathematical approach to the study of the age-related elimination of endothelial cells in the cornea allows one to obtain a formula by which the aging of the cornea can be represented as the disintegration of the tissue system, with the same pattern that is characteristic of the phenomenon of nature such as radioactive decay. Based on this formula, you can calculate the life expectancy, including the highest possible. However, for this, it will be necessary to obtain similar data on the dynamics of cell abundance in tissue systems that provide the contractile capacity of the heart and other life-supporting functions, which so far exist only for the corneal endothelium.

Смерть клітин в організмі, що старіє не викликає сумніву і, за замовчуванням, визнається наслідком старіння самих клітин. Однак тут присутній парадокс, який не був помічений раніше: смерть клітин, які є постійними структурними елементами тканин і органів, не припустима з позиції математичного закону, що характеризує динаміку популяційної смертності. Використання математичної моделі старіння, що грунтується на законі смертності Гомперца, дозволяє провести аналіз фактичних даних, що відображають динаміку клітинної чисельності. Зокрема, на прикладі вікових змін щільності (чисельності) клітин в ендотелії рогівки можна оцінити реальну модель старіння організму, в основі якої лежить вік-незалежна втрата клітин – стохастичний механізм елімінації клітин з тканинної системи, не пов'язаний зі старінням самих клітин.