On Life Longevity Problems

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There are two main theories of cellular aging (L. Hayflick [78], J. Medina [133]): Error Accumulation, explaining aging as an imperfect ability to repair all the breakdowns that normally occur and Programmed Death, explaining aging by much more deliberate breakdowns with the help of 'suicide genes" that turn on at specific times.


Let us focus on the mitochondria of cells as an example. Like most manufacturing processes, this energy-production factory also produces toxic waste. The waste consists of excess electrons. Occasionally, those electrons do not crash into molecular oxygen and do make water. Instead, the electrons crash into other atoms creating molecules with unpaired electrons called free radicals. Free radicals are highly reactive and cause a lot of internal cellular damage. Oxygenated free radicals are also called ROS (Reactive Oxygen Species) molecules. Like a lot of industrial waste, ROS molecules can damage anything that they encounter in their way, including proteins, fats, RNA, and even DNA.

On the other hand, there are the molecules that destroy free radicals, including vitamin E. They are called anti-oxidants. There is evidence [78] that in spite of anti-oxidants and some products of genes that destroy free radicals, ROS molecules damage DNA as we age. Similar processes take place not only in mitochondria, but also in other parts of cells. The similar processes of error accumulation take place not only in mitochondria, but


Cytogerontologists now can remove the nuclei from cultured normal cells and then insert nuclei from young cells into old cytoplasts and nuclei from old cells into young cytoplasts. The number of times that both types of hybrid cells divided led them to conclude that the age of the nucleus governed how long the hybrid cell divided in culture.

A cell clock might actually work due to telomeres, DNA sequences that are located on the tips of human chromosomes and that consist of repeating sub-unite. With each cell division die repeated sequence in the telomeres is reduced. Because it happens at a fixed rate, die length of telomeres behaves like a clock. Immortalized tumor cells found a way to keep their telomers the same length. There is the enzyme called telomerase that can replicate

In most non-tumor cells, the genes that encode telomerase are turned off and the cells subsequendy age and die. Is this turn-off an error or the beginning of programmed death? It

When young cells are given a growth factor, it stimulates gene, called fos, expression. This gene expression makes the transcription factor Fos. Aging cells do not make the Fos protein. Actually, there are other genes that act in similar manner as the/as gene and control

Among newly discovered genes is the gene apo-\. The respective protein Apo-1 is known as a receptor. The hands that bind to this molecular lever are called ligands. As soon as Apo-1 binds to its ligand, the cell begins to undergo apoptosis. Another death protein is BAX. If a cell has enough Bax die cell will die, otherwise the cell will survive. Thus, the idea of regulating the amount of deadly molecules is real.

Are there also life genes? The answer is yes and the data came from cancer research. One of these genes is bcl-2. If this gene is placed into a cell that normally has a death sentence the cell will not undergo apoptosis. The respective protein Bsl-2 inhibits formation of ROS molecules. As to BAX protein, Bsl-2 will bind to all the BAX, if there is enough Bsl-2. Thus, die decision to die or live depends on the ratio between these two gene

The world of death-dealing and life-saving genes is complex and ever growing. Various laboratories studied not only particular gene products (among these products is senstatine protein that can reverse the aging process in skin cells, in nerves within the brain, and in certain blood vessel cells), but also how multiple interactions between many genes can cause die cell to live or die (longevity assurance genes (LAG genes), miscellaneous genes including multiple aging genes (the final total may run into the thousands)).

While we are beginning to understand how cells commit to growth or to suicide, "we have found two extraordinary properties: 1. By blocking the death genes, we extend not only the life of die cell where the block occurred, but also the life of the organism that contains the cell. 2, Genes that control these life-and-death decisions in humans work just as effectively in worms. This means that the process is conserved, and gives greater weight to the data we see in animals when we think of our own bodies." [133], p. 312.

Among many factors, the human growth hormone, hGH, has a great deal to do with human longevity. After the age of 60, this hormone begins to shut down. The process is called hGH menopause. The certain procedures of injecting this hormone have resulted in not only stopping normal march toward aging, but also reversing certain biological functions. In conclusion, we would like to quote from Dr. Michael Jazwinski, Louisiana

"Possibly in 30 years we will have in hand the major genes that determine longevity, and will be in a position to double, triple, even quadruple our maximum life span of 120

2. Modeling of Cell Longevity Problems

We consider modeling of cell longevity with regard to the error accumulation theory that explains aging as an imperfect ability to repair all the breakdowns that normally occur and the programmed death theory that explains aging with the help of "suicide genes" turning on at specific times. The main prospective conventional way to overcome aging is handling the

Below, we also consider, in short, a possible application of our class MM to modeling 2.1. MODELING OF ERROR ACCUMULATION

Error accumulation factors (see s. 1.1) can be mapped in die models by decreasing values of the main functions of the type a(i,.s) and $(t,s) while t is increasing. The reason of that decrease is the influence of toxic waste, produced in most manufacturing processes.

On the abstract level of the function of o£jt,s) and p(/,s)-types, a failure to accumulate results of all restoration efforts can be explained by necessity of maintaining and restoring, in turn, those restoration efforts themselves. This convergent recursive chain practically has to be stopped somewhere, and sometimes this occurs after the process of development had

The simplest MM of degradation ofa£t>s) and P(M) have die form

Let us consider the influence of decreased value of a on an example of the MM of

M(t) = M*/{ 1+Cexp {~aryR(t-t*)]h m* = CaA}*M*/(l+e)2, (2)

where M* is the desired limiting value of the enzyme-substrate complex quantity M(t), mA is the initial rate of creation of the enzyme-substrate complex, aA" is the decreased initial value

Under small aA" in the relation (2), the constant C has to be rather large and hence the desired value M* practically cannot be achieved.

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