Many researchers—and non-researchers alike—are daunted by the sheer number of active molecular factors in biology, and in the molecular biology of aging in particular. Consequently, a rather popular view of aging holds that it is an intractable problem due to the multidimensional, multifactorial nature of the observed phenomenon.

The aim of this essay is to present evidence that the behavior of a multidimensional entity can be represented as the sum or superposition of biological functions that are less complex, or even simple, and defined on the basis of specific variable(s).

One approach to combating aging is based on the so-called "hallmarks of aging." It posits that the human body, its organs, and its tissues age in distinct ways, and that each physiological function requires a unique approach to slow, delay, or even reverse the molecular signs of aging. Human viability is conceptualized as a function f(x1,...,xn), which depends on a vast array of variables; a decline in any one of these may lead to a reduction in organismal fitness and, ultimately, death.

An even more extreme viewpoint suggests that every single cell requires distinct, and likely multiple interventions to mitigate the signs of cellular aging. This perspective has given rise to so-called "combinatorial therapies," which target various signs of functional decline across different organs. This viewpoint has also led to a curious, anti-Darwinian conclusion: that different mammalian species age in fundamentally different ways. Since this approach failed to address the underlying molecular basis of aging, even combinatorial therapies have failed to yield any substantial increase in the chronological lifespan of mice, flies, or worms.

Aging of Mechanical Objects. Our planet, Earth, is currently populated by machines, those found on land (automobiles, etc.), in the air (aircraft, etc.), and in the water (ships, submarines, etc.). From the perspective of "signs of aging," each mechanism ages and dies in a unique way. Entirely distinct components of these mechanisms slowly lose their functionality. Nevertheless, the entire diversity and complexity of aging in mechanical objects can be reduced to the superposition of several functions of a single variable: the oxidation of iron (the material). Virtually all mechanical parts (functions) today are manufactured from iron or plastic. It makes no difference whether a mechanical part originates from an automobile, a submarine, or a stratospheric aircraft. The actual, fundamental, molecular cause of aging in mechanical objects is a chemical reaction between iron (or other metals, or even plastic) and oxygen.

Conclusion: The complex and diverse aging of mechanical objects is explained, in practice, not merely in theory, by a single variable: a single molecular mechanism. The sum of various functions (such as a car engine or a ship's propeller shaft), all dependent upon this variable (material + oxygen), ultimately leads to the functional failure, and demise of the mechanical object.

A Single Variable. Most interestingly, this conclusion has already been thoroughly described and proven within the field of mathematics. It originated with Hilbert's Thirteenth Problem and subsequently evolved into the Kolmogorov–Arnold theorem. This theorem states that any multidimensional continuous function can be decomposed into a finite sum of compositions of continuous functions of a *single* variable, combined with addition.

The Kolmogorov-Arnold representation theorem (often referred to when discussing the Kolmogorov-Arnold equation) demonstrates that any continuous multivariate function can be decomposed into a finite sum of continuous functions of a single variable.

This means: Any function f(x1, x2, ..., xn) can be expressed as a sum of functions, each of which depends on only one variable.

Is this not precisely what I have been describing regarding the world of mechanical "organisms"?

A Biological Interpretation. Let us return to the "signs of aging." We can construct a molecular-biological analogy to the Kolmogorov–Arnold theorem: a regulatory network involving DNA, RNA, and proteins, serving to explain the fundamental molecular mechanism of aging. In any organism, any tissue, or any organ—regardless of that organ's or tissue's functional purpose.

Even if the regulatory process appears incredibly complex and multifaceted, there exists a method to decompose the system into simpler, single-variable modules which, when properly aggregated and combined, faithfully reproduce the behavior of the entire system. The Kolmogorov–Arnold theorem posits something remarkable: we do not need to comprehend the entirety of the multidimensional interactions simultaneously. Instead, these complex functions can be reconstructed by combining several simple responses from a one-dimensional regulator.

However, the primary challenge lies in identifying the specific biological factor responsible for all the "hallmarks of aging" across all eukaryotes, and perhaps even in prokaryotes. As stated at the outset, this sounds utterly impossible; yet, the Kolmogorov–Arnold theorem asserts the contrary: it is mathematically feasible, and this has been proven.

Allow me to present just such a mechanism. The assertions set forth below are grounded in empirical evidence.

Aging is a phenomenon observed in all eukaryotic organisms. Over the course of evolution, across a wide variety of habitats, eukaryotes have acquired numerous adaptive traits, which manifest as the multitude of functions ascribed to differentiated cells, tissues, and organs. This has led to the diversity of aging phenotypes observed in both multicellular and unicellular eukaryotic species, as well as to the formulation of numerous hypotheses regarding the mechanisms of aging. Although aging may be a universal feature of all eukaryotes, its underlying mechanism remains obscured by approximately two billion years of evolution. Consequently, a biochemical or cellular trait common to all evolutionary lineages could serve as a promising candidate for explaining the diversity of cytological and biochemical changes observed in various eukaryotic tissues during aging, as well as for targeting via direct pharmacological intervention.

Typically, aging cells are characterized by unbalanced mitochondrial dynamics, skewed toward a preponderance of punctate mitochondria. Genetic and pharmacological manipulations of mitochondrial fission-fusion cycles can contribute to either accelerated or decelerated aging in cells or organisms. Mitochondria originated from autotrophic alpha-proteobacteria during the early stages of eukaryotic evolution. To escape their host cells, dividing alpha-proteobacteria would initiate the lysis of the host cell; apoptosis is a product of this primordial program for the lytic exit of the symbiont cell. Over the course of evolution, the eukaryotic host cell mitigated the detrimental effects of these symbiotic proto-mitochondria; consequently, modern mitochondria are now functionally interdependent with their eukaryotic host cells, while retaining their own circular genomes and independent replication timing. An imbalance between cellular and mitochondrial proliferation generates intracellular stress, ultimately leading to a gradual decline in host cell performance and age-related pathology.

The basal mechanism of aging is the conflict between mtDNA replication and mRNA transcription. This variable underlies all biological functions manifested in cells, tissues, organs, and organisms with diverse physiological roles.

1. mtDNA replication counteracts mRNA transcription and takes precedence over it.
2. The total number of mtDNA copies may not increase over time, yet mtDNA can become stalled in a replicative mode, thereby blocking transcription from that specific mtDNA.
3. Consequently, a gradual loss of function occurs in any cell, regardless of its specialization.

Thus, aging evolved from a conflict between maintaining a quiescent, non-proliferative state and an evolutionarily conserved reproductive program governing the life cycle of former symbiotic organisms: mitochondria.

1. mtDNA replication coincides with transcription in both time and space;
2. Collisions between transcription and replication machinery exert a deleterious effect on mtDNA gene expression;
3. DNA helicases facilitate replication through obstacles such as transcriptional complexes;
4. mtDNA replication is equivalent to the reproduction of an endosymbiont within a host cell;
5. mtDNA replication is invariably associated with the mitochondrial membrane, and the mtDNA forms a so-called nucleoid;
6. The "endosymbiont" intends to exit the host cell; Therefore, it prepares for potentially harsh conditions outside the host cell and begins to form amyloid, one of the most robust biological structures.
7. Amyloid-like proteins are extremely rigid and can support the survival of endosymbionts outside the host cell.
8. mtDNA replication is linked to the formation of amyloid deposits; the ultimate goal is the protection of the "symbionts."
9. This pro-amyloid state propagates throughout the host cell's proteome.
10. The result is the accumulation of proteins in a low-energy state, which is unable to support all essential protein functions.
11. Consequently: aging.

There is a pharmacological approach that has been tested sucsesfully on C. elegans, normal human cells and some very preliminary data on mice:

• to stimulate mtDNA transcription;
• to suppress mtDNA replication;
• to counteract the deleterious effect of amyloid propagation originating from within the mitochondria.

Best,

Sergei Vatolin

1. Kolmogorov. On the representation of continuous functions of several variables in the form of superpositions of continuous functions of one variable and addition. Dokl. Akad. Nauk SSSR 114, 953–956 (1957).

2. Greenberg, E. F. & Vatolin, S. Symbiotic Origin of Aging. Rejuvenation Res. 21, 225–231 (2018).

3. Agaronyan, K., Morozov, Y. I., Anikin, M. & Temiakov, D. Mitochondrial biology. Replication-transcription switch in human mitochondria. Science 347, 548–551 (2015).

4. Pomerantz, R. T. & O’Donnell, M. What happens when replication and transcription complexes collide? Cell Cycle 9, 2537–2543 (2010).