1.3. NONLINEARITY OF THE AGING PROCESS
During their lifespans, organisms undergo a wide variety of changes (93). Some of these, such as graying of hair, are clearly not intrinsic features of the aging process. This is a relatively simple example that is not difficult to analyze. Even in a simple eukaryote, there are many age changes that occur (Table 1.I).
Morphological and physiological changes during yeast aging
|Granular appearance|| |
|Surface wrinkles|| |
|Loss of turgor|| |
|Cell fragility (prior to death)||None|
|Cell lysis|| |
|Bud scar number||Increase|
|Cell wall chitin||Increase|
|Generation (cell cycle) time||Increase|
|Response to pheromones (haploids)||None|
| ||Decrease (111)|
|Mating ability (haploids)||Decrease|
|Sporulation ability (diploids)||Increase|
|Cell cycle arrest at Gi/S boundary (putative)|| |
|Senescence factor|| |
|Mutability of mtDNA||Decrease|
|Random budding (98)||Increase|
|Specific gene expression||Altered|
|rDNA circles (112)||Increase|
|Cellular rRNA concentration||Decrease|
|Ribosome activity, polysome recruitment||Decrease|
|Transcriptional silencing (105, 111)||Decrease|
It is not always easy to decide which of these may be intrinsic to aging. In some cases, a genetic manipulation can dissociate the age change from longevity. Yeast cells increase in size as they age. We have shown that the overexpression of an activated allele of RAS extends yeast lifespan, while at the same time causing a rapid initial increase m cell size (94). This indicates that increase m size is not an essential feature of the aging process in yeast. Indeed, individual yeast cells, which constitute the aging organism, vary substantially in the rate of size change during aging. Of course, one may argue that a larger size change for one yeast cell may be equivalent to a smaller change in another in terms of its functional significance. This presupposes a difference in the magnitude of the response to the size change at the level of the individual. Other examples of this sort can be found.
There is no reason to suspect that the response to the size change mentioned above would result in aging. However, we could entertain a chain of events that might well culminate in causing aging to occur. The more pronounced the "ripple effect" in an ever-broadening panorama of change, the higher the probability is that this would take place. A recognition of the impact of change may be difficult to assess when it is averaged over the entire aging population. Instead, it must be evaluated at the level of the individual aging system. In other words, the averaged magnitude may be small.
Several genes have been shown to determine longevity in genetic model systems (reviewed in 95). These genes participate in at least one of four broad physiological responses: metabolism, resistance to stress, integrity of gene regulation, and genetic stability. The example of the yeast RAS2 gene is particularly illuminating. RAS2 is a longevity determining gene (96), and it modulates each of these physiological responses (95-98). Thus, RAS2 has pleiotropic effects on the aging process. Not surprisingly, it is a regulatory gene. It is difficult to decide which of the many processes that RAS2 modulates plays a primary role in the effect of this gene on longevity. Indeed, there may be no primary role as such. All of these processes may require coordination, with one or more coming to the fore due to genetic background and environmental and other epigenetic factors. Some balance must be struck, as evidenced by the biphasic effect of RAS overexpression on yeast longevity (94).
It may be the ability of RAS2 to affect a variety of aging processes that allows us to discern its impact on an aging cohort composed of variously presenting and responding individuals. Further, it may be the ability of this gene to promote a ripple effect of many changes at once. Many of the other genes that determine lifespan in yeast, worms, and fruit flies would have pleiotropic effects on aging.
It follows that genes that are located low in genetic hierarchies, that is, genes that function proximally to the final response in genetic pathways, would be unlikely to modulate the aging process and to alter lifespan. Such genes would also suffer from the redundancy present in the gene hierarchies that affect the broad physiological responses important in aging. In other words, other pathways could substitute for them. These genes, however, might well be involved in certain age-related diseases. An exception to this limited role of genes that reside at the end of pathways might occur if the pathway impinged on a structure or function whose alteration could have diverse physiological consequences.
1.3.1. NONLINEARITY OF YEAST AGING
Individual yeast age, while the population lives on. This is because each generation starts anew. Yeast lifespan is measured by the number of daughter cells produced or, in other words, the number of cell divisions completed (99, 100). Lifespans of individual yeast are determined microscopically (101).
Over the course of our studies of yeast longevity, we have frequently encountered nonlinearities. One such nonlinearity was mentioned above. It is the biphasic increase in longevity observed on overexpression of an activated allele of RAS, evidenced by an increase in longevity followed by the loss of the effect at higher levels of overexpression. We have also found that the ultraviolet radiation (UV) resistance profile is biphasic as a function of age (97). UV resistance first increases through mid-life and then declines. Induction of thermal tolerance results in a transient decline in mortality rate in yeast (S. Shama, C.-Y. Lai, and S.M. Jazwinski, unpublished). This induction can be repeated throughout the lifespan, resulting in an increase in yeast longevity that is greater, the greater the number of heat stresses. However, this is efficacious only up to a point. The response peaks followed by a decline, another example of a biphasic response.
Nonlinearities of this sort reflect an output that is not proportional to the input into the system. They suggest that the dynamics of the system are nonlinear. This lends a degree of stochasticity to the system. This fits aging admirably, because the lifespan of the individual is virtually impossible to predict with any certainty even in the presence of extensive age changes.
1.3.2. CHANGE AS THE CAUSE OF AGING
The variability of age changes from individual to individual makes it difficult to contend that such changes are uniformly the effect of an aging process. We have postulated that, in contrast, change is the cause of aging, and that it is intrinsic to aging (98). This intrinsic aspect of change simply means that it occurs without any reference to any other parameters. It does not require any heterogeneity of any sort to occur. Even simple chemical reactions display periodic fluctuations (reference is made to the Belousov-Zhabotinsky reaction (102)). The flux of physiological processes in living organisms is all the more likely to exhibit change.
The probability of change is given by the exponential expression exp(-x), where x≥0. We introduce the factor A to account for the effect of aging on this probability, since we perceive aging to involve increasing change. We then write the difference equation.
Fig. 1.3. Computational solution of Pn+1 = A · exp(Pn) ) by iteration for four values of A.
Pn+1 = A · exp(-Pn), for n ∈ [0, +∞);
P replaces x here, and it is a parameter that describes the state of the aging system. It expresses the propensity of the system to age on a relative scale, with P=0 indicating no aging. The precise derivation of this equation and its rationale have been described (98). This equation models the aging process.
P1 = A · exp(P0)
P2 = A · exp(P1);
P3 = A · exp(P2);
The solution to this equation for consecutive states of the system, n, and any given A is an iterative computation, such that a family of such solutions is shown in Fig. 1.3. With each iteration, the result oscillates until a constant result called a stable fixed point is obtained. These stable fixed points converge on 1 as A increases. However, two stable fixed points result when A reaches a certain value between 2 and 3, resulting in a stable two-cycle. As A increases, these two solutions diverge further and further. One of them increases constantly, while the other converges on 0. The former indicates an increasing propensity to age resulting in death, while the latter indicates a decreasing tendency to age. Quite paradoxically, the greater the influence of aging on the change, that is, the larger A is, the more likely that lack of aging will appear. Since change is intrinsic to aging, the only way that genes and environment can affect aging is through the factor A.
1.3.3. EVIDENCE FOR CHANGE AT THE LEVEL OF THE INDIVIDUAL
There are many changes that occur during yeast aging, some of which can be readily observed by simple microscopic observation (Table I). One of these is global spatial organization, which in S. cerevisiae is seen as budding pattern. Haploid yeast, with which we are dealing here, bud axially; that is, each bud emerges in the vicinity of the previous bud site. This is distinct from the polar budding pattern of diploid yeast, in which the cell buds alternately from its opposite poles (103). It is possible to score the sites of bud emergence during the yeast lifespan by allowing an incipient bud to form prior to removal of the previous bud with the micromanipulator (98). Any budding that is neither clearly axial nor clearly polar is scored as random. We have rarely found polar budding in haploid yeast as they progress through their lifespans (98).
Individual yeast cell switch from an axial budding pattern to a random one as they age. However, the timing of this event is apparently random (Fig. 1.4). Furthermore, the yeast switch back to an axial pattern quite unpredictably. Indeed, these switching events can be quite frequent in some cases. This change at the level of the individual yeast provides firm support for the thesis that change is intrinsic to aging. It also suggests that this change is stochastic. Thus, it is reasonable to describe it by an expression of probability.
Another manifestation of individual change is the epigenetic switch in silencing status at the silent mating type locus which occurs with a low probability in every cell division in yeast (104). This is a change at the molecular level. The loss of telomeric silencing during yeast aging has been demonstrated (105). This determination was performed in a cross-sectional manner and presented as an average over all of the individuals in the population. We would predict that different individuals would markedly vary in the pattern of silencing loss at telomeres, with some even regaining silencing. This prediction is based on the conclusions regarding cell polarity change that have been studied already, as indicated earlier.
Fig. 1.4. Cell polarity changes in individual cells during aging. The budding patterns (axial, random, and unknown) for randomly chosen S. cerevisiae SP1-1 cells were determined throughout their lifespans (98). Three are shown here. Out of 200 examined, none displayed identical patterns of polarity change. Unknown designates a budding that cannot be scored because the previous bud had fallen off.
Changes in silencing status at telomeres during aging are not surprising given the requirement of rebuilding heterochromatin following each cycle of DNA replication. The possible involvement of silencing changes in aging has been documented in genetic studies (reviewed in 98). With respect to the importance of cellular spatial organization in determining longevity, it is worth noting that the global spatial order gene teal in Schizosaccharomyces pombe (106) is a homologue of the Caenorhabditis elegans spe-26 gene (107), a determinant of longevity in that organism (198).
1.3.4. EPIGENETIC STRATIFICATION
Given a sufficiently large A, the solution of our equation indicates that, paradoxically, lack of aging should emerge. In the first instance, we should be able to observe this by examming an aging yeast cohort. The expectation is not that immortal yeast could be detected nor that yeast that remained young through-out their lifespans would be found. The determination of the mortality rate for a large yeast cohort showed that, following an exponential increase at early ages, there was a clear and significant plateau in mortality rate at later ages (98). The oldest yeast showed no further increase in mortality rate. Thus, they experienced no further acceleration of the aging process. Such acceleration is considered the hallmark of aging. Instead, they remained as they were. The cause of the mortality rate plateau is individual change (109). The net result is the epigenetic stratification of the population into two groups.
This is not the only evidence for epigenetic stratification. We have also detected it at the level of cell polarity. Genes and environment can only operate through factor A, according to the model. Thus, they cannot eliminate the changes in cell polarity that occur during the lifespan. Instead, they modulate them. Overexpres-sion of RAS2 extends lifespan (96). It also delays the process of loss of cell polarity during the lifespan (Fig. 1.5). More specifically, overexpression of RAS2 produces a singularity in the cell polarity profile, partitioning it into two regions (98). The first of these displays no significant change in polarity, followed by the second, in which random budding increases in frequency at the same rate as in the control. The singularity described above occurs in mid-life.
RAS2 can modulate the age-dependent change in cell polarity, indicating that it acts through or is a component of factor A. To verify this conclusion, we have also tested whether RAS2 can affect age-dependent change at the molecular level. We focused our attention on telomeric silencing. We found that deletion of the RAS2 gene, a manipulation which curtails lifespan (96), dramatically reduced silencing (98). Such a reduction in basal silencing would readily accentuate the loss of silencing that normally occurs during aging (105). Indeed, it may be the loss of expression of RAS2 during the yeast lifespan (96) that may be the cause of loss of telomeric silencing during yeast aging.
Fig. 1.5. Effect of RAS2 on loss of cell polarity during the lifespan. The budding patterns, expressed as percent random, are shown for S. cerevisiae SPl control cells or cells overexpressing RAS2 (998), grouped into three age classes.
Nonlinear dynamic modeling of aging m the form of the simple difference equation presented here provides a deterministic rule that can be used to describe the state of an aging system, which is driven by change possessing a probabilistic character. The epigenetic stratification that this model specifies when the effect of aging becomes intense is counterintuitive and therefore a strong feature of this model. The equation describes the biological aging process at levels of organization spanning the molecular to the organism by virtue of the scale invariance of this process at all of these levels.
The premise on which the model is based, and the essential element in the equation, is that change is the cause of aging first of all and secondly its result. The natural result of the change inherent in the model is loss of organization at various levels. The disruption of homeostasis that this portends can be viewed as a fundamental feature of the biological aging process.