The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 59:B449-B454 (2004)
© 2004 The Gerontological Society of America
Biorepair Mechanisms and Longevity
Robert A. Weale
Institute of Gerontology, King's College London, United Kingdom.
Address correspondence to Professor Robert A. Weale, Institute of Gerontology, King's College London, Franklin-Wilkins Building, Waterloo Rd., London SE1 9NN. E-mail: robert.weale{at}kcl.ac.uk
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Abstract
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The purpose of the study was to find out whether a link could be established between hypothetical biological repair mechanisms, their decay, and longevity. Human biological functions (biomarkers) can be classified accordingly as their generally linear age-related decline starts at birth or in adulthood (
1% per annum), or occurs at a rate of less than 0.5% per annum Sums of exponentially declining functions representing the decline of repair mechanisms are fitted to the averages of each of the above groups. The time constants of the mechanisms are lowest for those ceasing normal function at the age of 35–40 years, i.e., approximately at twice the maximal age at which puberty is reached. An extrapolation of the overall loss of the mechanisms, postulated to account for the declining biomarkers, is, at present, such as to reach zero in the twelfth decade of life.
MORE than 20 years ago, Shock (1) drew attention to three points relating to the decline of human biological functions. First, declines tended to start at about the age of 30 years. Secondly, they inclined to be linear. Thirdly, while the greatest rate of decline was approximately 1% per annum, others, such as nervous conductivity, declined at as low as one third that rate. Point 1 was questionable, since the African tribe of the Masai appeared to maintain their optimum vigor up to the age of 40 (2); however, points 2 and 3 may bear on our understanding of aging in general.
Shock's idea was developed when the fastest rate of decline was found to relate mainly, if not wholly, to functions linked to dividing cells (3). Extrapolation of the linear declines showed that the intersections of the rectilinear decrements with the age axis clustered around a value of 123 ± 26 years. This was noteworthy since the bracket encompasses the increasing number of centenarians now on record in many countries (4). Moreover, the cumulative distribution of the intersections with the age axis (i.e., complete failure) provided a good match for mortality functions of the longest-lived member states of the United Nations. Hence the rate of decline of our functions might have evolved to sustain a currently possible longevity of some 120 years.
Since the time of Shock's publication, some biomarkers have been found to start declining even at birth, as exemplified by the melanin content of the retinal pigment epithelium (5). It was, therefore, thought of interest to discover if the onset of the functional human biological decline might be variable, and whether it could be described by some tentative framework.
Of necessity, the following analysis rests on published sets of data obtained at different times on different participants and numbers of participants, allegedly free of any known pathology, without information having been provided on possible persistent smoking habits or dietary peculiarities.
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A TEST OF SHOCK'S HYPOTHESIS
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A literature search revealed the existence of a number of studies of age-related human biomarkers—the decline of which could, indeed, be set within the age span of 25–30 years. However, there exists also a large number starting much earlier. Are the two groups different, or extremes of a continually varying sample?
Procedure
Linear regressions were fitted to the data in the sets of publications, classified by their age of onset in the Appendix. To make the rates of decline comparable, the data were normalized by dividing each set by its intercept on the ordinate. The values of the regressions at the age of 25 years provided the normalizing constants when declines began at or around that age. In each group, the normalized entries for each age were averaged, yielding mean values forming the basis of the analysis.
The use of an analysis of variance (ANOVA) required equal numbers of mean values in the two groups. Some data years showed no entry. Thus, while there were 71 data-years available for the 25-year group between the ages of 25 and 98 years, the range for the "at birth" group had to be extended from 28 to 100 years to yield an equal number of 71 data (Figure 1). The data are comparable, and, as Figure 1 shows, the biomarkers compatible with falling into Shock's notion decline faster than those declining from birth.
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Figure 1. Decline at two ages of onset [p(F) <<.01]. A comparison of group averages for sets of biomarkers linearly declining from birth and the age of 25 years, respectively. y = years
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The ANOVA yielded an F value of 10.116; the threshold value for N (71,71; p =.01) is 1.80, making it probable that the two groups differ, and that the early onset functions need distinguishing from those pinpointed by Shock.
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AN EXPLANATORY HYPOTHESIS
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There is a great deal of evidence to support the view that our biological functions are amenable to repair when they have suffered some injury. DNA, to quote one example, is liable to be damaged when irradiated by ultraviolet radiation; however, it recovers its function with an efficiency that decreases linearly with age (6). The probable existence of the above two biomarker groups suggests that some of the human repair mechanisms maintain their efficiency longer than others. In this connection, it may be noted that such mechanisms have not recently been linked to longevity, even though a recent review refers to DNA repair (7). Could their cumulative failure account for the decline of some biomarkers? If that were so, it could lead to some interesting consequences. For example, human longevity was, in the wild, appreciably shorter than it is now. Even so, if the species was to survive, parents would have to provide for their offspring up to at least the age at which the young could look after themselves [it may be recalled that Buffon (8) attempted to relate life span to puberty]. The age of onset of self-sufficiency might be placed at the time when puberty was complete. Note also that the age of menarche is variable, being 17 years or more in communities suffering from malnutrition or disease (9). Hence the successful maintenance of functional repair mechanisms might have extended to an age at least twice as long as that needed to complete puberty both for the parents and their offspring, i.e., to some 30 years or more. Can this notion be related to our potential for a longevity possibly extending at present to over 100 years?
Procedure
Assume that life is supported by the activity of repair mechanisms evolved to maintain homeostasis, that these have not changed significantly since our emergence from "the wild," and that they start decaying exponentially at different ages. Their rate of decay is constrained by the observation that biological functions are found to decline mostly linearly with a slope of somewhat less than 1% per annum, suggesting that, at present, the most probable maximum longevity is well over 100 years. Since Madame Calment has reached 122 years, this age must be biologically possible, and cannot be dismissed as a one-off. As mentioned above, the notion that we may potentially live until the 12th decade or so is consistent with current mortality data for the longest-lived nations on Earth. Whereas life expectancy depends both on genetic and on environmental factors, both also are likely to affect biomarkers. While mortality statistics are published frequently in many countries, their potential link to lifestyle has not yet been explored universally, as a result of which the link between the two is bound to contain a speculative element.
For simplicity's sake, onsets of decay were postulated to occur in groups of 5 years up to the age of 90 years, higher ages of onset of decay being found unnecessary. Use of a trial-and-error method determined their several decay constants. Two conditions needed to be fulfilled: the sum of the functions were to fit their linear regression optimally, and the regression was originally required to reach zero at the age of 123 ± 26 years. This figure was based on a histogram that had been constructed as follows. Regressions were fitted to published cross-sectional data on biomarkers selected for their apparent reliability and relevance. Extrapolation of the regressions to the x (age) axis yielded ages of complete failure, which were measures of the rates of decline of the biomarkers. Collected into age groups of 10 years, 74 sets of unweighted data yielded a histogram on a base of 60 to 180 years, peaking at the above value of 123 years (3,10). While it is conceivable to link mortality to a life-preserving factor that is the first to fail, a probabilistic approach resting on system failure resulting from a combination of functional terminations is buttressed by the evidence: As mentioned above, it leads to an acceptable description of the current age-related mortality data for the longest-lived member states of the United Nations. The present more rigorous and updated collection of functions, listed in the Appendix, showed that both the 0years and 25years onset groups point to the figure of 123years being replaced by 128years.
Illustrating the procedure, Figure 2 traces the exponential decline functions F(D), used in the present analysis, against the age of onset of the cessation of normal maintenance. The extreme functions are shown both with data points and curves in order to emphasise that both rate of decay and age of its onset are variable. The rates of decay were determined by trial and error so that the residual between the normalized sum of all the exponentials and its regression should be a minimum provided that the regression intersected the x (age) axis at 128 years in accordance with the figure quoted in the previous paragraph.
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Figure 2. Exponential decay functions for the hypothetical repair mechanisms. Plots of the probable efficiencies of hypothetical exponentially declining repair mechanisms ceasing the maintenance of normal functioning at intervals in groups of 5 years, and used to support a hypothetical description of the declines of biomarkers, grouped as set out in the text. Note the minimum of the rate constants at 35–40 years
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The analysis was next extended to experimental results, namely the two groups mentioned above in "A Test of Shock's Hypothesis," and another including very slow rates of decline. The borderline between this group and the other two is a slope of –0.0056 normalized units per annum (= 1/180; see paragraph 2 of "Procedure" section under heading "An Explanatory Hypothesis" above).
Following the desirability of economy in explanatory hypotheses, the selection of F(D)s available from Figure 2 was to be kept to a minimum. This was arrived at by determining the Schwarz Criterion (SC) (11), which represents a development of the long-established likelihood function (12,13). It provides a measure between the most probable fit between the average of the residual formed by a set of data and, in the present case, the sum SUM(E) of a number of exponentials used to describe the data. SC is a minimum, determined by trial and error, and expressed as a natural logarithm.
The procedure was applied to each of the three groups of data in turn. Table 1 lists the values of SC for the data having an onset at birth, at 25years, and the slow data. This last SUM(E) rests on the earliest 3 F(D)s, each index being multiplied by an empirical slow-down factor of 0.0718. Most of the functions in this group relate to nerves or the brain.
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RESULTS
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The columns of Table 1 contain the results for each of the above groups of data. It will be seen that the number of exponentials used is smaller in each group than is available on the basis of Figure 2, which in turn contains only the exponentials F(D) employed in the current analysis as a whole.
Figure 3 illustrates the procedure of matching sums of F(D)s to experimental data, in this case those starting their decay at 25years. The symbols employed require a comment. It will have been noted that the F(D)s in Figure 2 are distinguished by different symbols. Those in Figure 3 relate to them as follows. The lowest curve is a replica of the F(D) with an age of onset of decay of 20years, this being also the lowest value for those data in Table 1 (data column 2). The next higher symbol in Figure 3 is similar to that of F(D) for the age of onset of 30years; Table 1 shows that the F(D) for 25years was not used, whereas the symbol in Figure 3 represents the normalized sum for F(D) for 20years and 30years, respectively, and so on for the other symbols in Figure 3, which also need to be read in conjunction with Table 1.
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Figure 3. Onset of decline at 25 years and after. Plots of the efficiencies of hypothetical exponentially declining repair mechanisms selected from
Figure 2 by the application of Schwarz' Criterion to describe the family of biological functions declining from the age of 25 years of age. The symbols relate to those in
Figure 2, as explained in the text
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Note that some of F(D)s occur more than once (Table 1). Since this implies that their effect is greater than if they were to occur only once, the amalgamation of the values in Table 1 is shown in Figure 4. The symbols relate to those in Figure 2. A regression determined for this amalgamated failure in efficiency is statistically significant (p <.005), and suggests, within broad limits, an end in the 12th decade of life.
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Figure 4. The overall decay of hypothetical repair mechanisms. Summary of the exponentials F(D) used in the description of the 3 groups of human biological attributes in the Appendix. The symbols relate to those in
Figure 2, as explained in the text. The black circles represent ages of onset that were not utilized
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DISCUSSION
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The considerable variability notwithstanding, a large number of human biomarkers seem to be classifiable according to the age of onset of their decline and their rate of decline, respectively. The former criterion distinguishes functions starting to decline at birth from those according to Shock's notion of a decline once adulthood has been reached. The second, less clear-cut distinction rests on a watershed slope of –0.0056 normalized units per annum Functions decreasing with a slope smaller than this are allocated to the "slow decline" group.
A tentative subdivision of the attributes into metabolic (meta), structural (str), muscular (m), and cerebral/nervous (cn) factors is marked in the Appendix and assembled in Table 2. In order to address the question of whether the preponderance of the cn biomarkers in the slow decline section is significant or not, a 2 x 2 table was constructed by adding the figures in each of the 4 rectangles in Table 2. The chi-square test yielded a significance with p <<.0000. An analogous procedure revealed an association between meta and onset at birth (p =.000027).
The current hypothesis describes all 3 age-of-onset groups in terms of sums of between 3 and 13 exponentially declining functions, culled from a total of 16, the onset of decline increasing in steps of 5 years. The "slow decline" group is, moreover, characterized by an empirical "slow-down" factor, reducing the index of all 3 used components by 13.93. While it has not been possible, at this stage, to identify the hypothesized repair mechanisms, it is reassuring to find their number to be limited.
As mentioned earlier, SC is expressed as a natural logarithm, and its decreasing value from left to right in Table 1 is explicable in terms of the accuracy with which each set of original data can be matched with SUM(E), a sum of the exponentials.
The indices of the exponential decline functions F(D), i.e., the rate constants, vary systematically (Figure 2), being minimal at 35–40 years, i.e., this peak exhibits maximal stability. The significance of this observation relates to the remarks relating to "the wild" made in paragraph 1 of the "Procedure" section under heading "An Explanatory Hypothesis" above.
Conclusion
The hypothesis that the age-related decline of human biomarkers rests on the progressive failure of 16 unspecified repair mechanisms, with an exponentially decreasing efficiency, has yielded two results. First, their time constants (which are reciprocals of rate constants) peak at an age of approximately 35–40 years. This is twice the longest observed age of attaining puberty, i.e., in evolutionary terms, an age higher than this would, in the wild, have become unnecessary insofar as concerns the care of the young: such a period provides for both parents, obviously, and their offspring reaching puberty. Second, in order that this value may materialize, the repair mechanisms should remain functional up to the twelfth decade with a standard error of ±2 decades. Thus, the mechanisms postulated to lose their initial efficiency at the ages of 80 and 85 years will still be 13% efficient at the age of 120 years. The mechanism with the lowest decay constant (–0.021) will have an efficiency of 17%. Although there are occasional references to the possibility that the human life span is limited (14,15), the hypothesis lends no support to that view (cf. 10,16). There are indications that its present extent may be appreciably increased (17,18); however, if valid, the hypothesis indicates that an uphill struggle is likely to be needed to achieve this. Moreover, the hypothesis may be further developed by the procedure being applied to individual biomarkers rather than just to groups of them.
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Acknowledgments
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I thank Mr. M. R. Weale, National Institute of Social and Economic Research, London, for invaluable advice on statistical matters.
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Footnotes
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Decision Editor: James R. Smith, PhD
Received October 31, 2003
Accepted February 12, 2004
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References
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Abstract
A Test of Shock's...
