Content advisory
This digitised material is free to access, but contains information or visuals that may:
- include personal details of living individuals
- be upsetting or distressing
- be explicit or graphic
- include objects and images of objects decontextualised in a way that is offensive to the originating culture.
Licence: In copyright
Credit: "Szilard's Theory of Aging". Source: Wellcome Collection.
3/46
![V ol . 45, 1959 GENETICS: SZILARD o i OX a somatic cell suffer such hits is a characteristic of the species and does not vary appreciably from individual to individual. As a result of an aging process of this nature, the number of the somatic cells of an individual organism which have survived up to a given age (in the sense of remaining able to fulfil their function in the organism) decreases with age. On the basis of our assumptions, spelled out below, the surviving fraction of the somatic cells decreases with age at an accelerating rate. Our theory postulates that when/, the surviving fraction of the somatic cells of an individual, approaches a certain critical value, /*, then the probability that that individual may die within a period of one year will come close to 1. On this basis, the theory establishes a relationship between the surviving fraction of the somatic cells and the age of death of the individual. Because the young mammalian organism may be assumed to have a large func tional reserve, we shall assume that the surviving fraction of the somatic cells of an individual may fall substantially before the organism loses its capacity to live, per haps to a value somewhere between 1 / 3 and 1 / i2 . The precise meaning of the term critical value, /*, will shift as we go from the crudest form of the theory, which we shall discuss first, to a less crude form of the theory, which we shall discuss thereafter. In the crudest form of the theory, we shall assume that an adult does not die of natural causes until the surviving fraction of his somatic cells comes very close to the critical fraction /* and that he dies at the critical age, i.e., within the year in which this surviving fraction reaches the critical fraction /*. Thus, in its crudest form, the theory postulates that the age at death is uniquely determined by the genetic makeup of the individual. Clearly, this cannot be strictly true, for, if it were true, identical twins would die within one year of each other. In fact, the mean difference between the ages at death of female identical twins can be estimated to be about 3.5 years. The discrepancy arises from the failure of the crude theory to take into account that in a cohort of identical individuals the number of deaths per year may be expected to rise as a continuous function with advancing age and that an appreciable number of deaths may be expected to occur at ages lower than the critical age. If not otherwise stated, our discussion here relates to man and, in particular, to the female of the species. In the case of man, the somatic cells of the female con tain m = 23 pairs of homologous chromosomes. There may be in man perhaps 15,000 genes. There may be a larger number of specific DNA molecules which are inherited from generation to generation, but we designate as genes here only those DNA molecules which would handicap the individual if present in a mu tant form. An individual who is a heterozygote for a mutant gene might not necessarily be handicapped under the conditions prevailing at present in the United States, where essentially no adult dies for lack of food or shelter and no adult has a reduced propensity to procreate because of his inability to provide food or shelter for his offspring. But such a heterozygote would have been handicapped (accord ing to our definition of the term gene) under conditions which were prevalent in the past—up to recent times. The present abundance of mutant forms of genes in the population may not correspond to the steady state under present conditions. We may assume that the genes somehow affect differentiation and morpho genesis during the embryonic development of the individual and that a mutant form 32 GENETICS: SZILARD P roc. N. A. S of a gene may cause, with a certain probability—appreciable even in the hetero zygote—a developmental abnormality of the individual. We assume that among the 15,000 genes, there are perhaps 3,000 genes which are important for the functioning of the somatic cells of the adult. We shall call these genes vegetative genes, and a mutant form of such a gene we shall desig nate as a fault. Of the remainder of the genes, we shall assume that they are irrelevant for the functioning of the somatic cells of the adult organism. We postulate that, in the course of aging, a somatic cell remains functional as long as, out of each pair of homologous vegetative genes, at least one of the two genes is competent and active and that the cell ceases to be functional when both genes are out of action. Accordingly when a chromosome suffers an aging hit, the cell will cease to be functional if the homologous chromosome has either previously suffered an aging hit or if it carries a fault. According to the views here adopted, the main reason why some adults live shorter lives and others live longer is the difference in the number of faults they have inherited. If we assume that faults are distributed in the population at ran dom, then we can compute the distribution of the faults, from the mean value of faults per person (which we shall designate by n). From the observed distribution of the ages at death, between seventy and ninety years of age, we shall be led to conclude that we have n > 2. For n = 2 we would obtain from the crude theory for the critical surviving fraction of the somatic cells f* œ 1 / 4 . For n = 4 we would obtain /* Vi 2 . On this basis we shall be led to conclude that we have n < 4. We shall, for the purposes of our discussion, adopt, as a reasonable value, n = 2.5, and then we obtain/* œ l / 6 , which would seem to be a reasonable value. The Surviving Fraction of the Somatic Cells. —We shall now proceed to com pute the surviving fraction of the somatic cells of a female who has inherited r faults, as a function of her age. We designate by £ the average number of aging hits that have been suffered by a chromosome of a somatic cell, and we may write £ = (1) 2m T where r is the average time interval between two subsequent aging hits suffered in toto by the m pairs of homologous chromosomes contained in a somatic cell. We may call this average time interval r the basic time interval of the aging- process. Let us now consider a female who has inherited r faults. If none of the pairs of homologous chromosomes contain more than one fault—a condition likely to be fulfilled if r is small compared to m —then we may write for the surviving frac tion of her somatic cells at a given age / = [1 - (1 - e-^] m ~ r .e~ ri (2) or In / = (m — r) In [1 — (1 — e~*) 2 ] — r£. (3) For £ 1 we may write, from equation (3), neglecting m£ A and r£ 3 , etc., In 1 = - e) + ~ ?)■ (4)](https://iiif.wellcomecollection.org/image/b18184078_PP_CRI_H_2_29_0003.jp2/full/800%2C/0/default.jpg)
