HYPOTHESES ON LONGEVITY HORMESIS 7gradualist, uniform view of aging. Although it is possible that another
function may be deemed more consistent in the future (e.g., the Weibull
function4142), it seems unlikely that it will deviate significantly from the
linear Gompertz form.
Hypothesis V: Increases and/or decreases in mammalian injury elicited by
nonessential, exogenous agents or stimuli are superimposable with senes
cent injury.
Once again, we are indebted to Sacher and colleagues5’36’39’43 44 for the
unfolding of this hypothesis. The principle of superimposition may be pos
ited as follows:45 If yx is the system response to an input x1? and y2 is the
response to input x2, and kx and k2 are arbitrary coefficients, then the
response to input kjXj 4- k2x2 is k^, + k2y2. Viewed informally, the princi
ple of superimposition requires that the whole be the sum of its individual
parts.
With the introduction of this hypothesis, we are able to propose interest
ing alterations to Gompertz functions that characterize homogeneous popu
lations.71418’21’24’25’27’28’33’46’47 For purposes of simplification, assume aging or
senescent injury accrues in accordance with a linear Gompertz function.
In the first case, assume a single dose of a toxic insult produces an
instantaneous and constant residue of irreparable (permanent) injury. Irrep
arable or irrecoverable injury is damage that is inextricably embedded in the
cellular/subcellular fabric of the organism.43 The Gompertz function
becomes:
where e represents the increment of irreversible injury. It matters not if the
injury is qualitatively dissimilar to aging injury; all that is required is that
the added injury alters system states so as to enhance the probability of
death. If exposure is continued at a zero-order rate at intervals of x units,
and injury is accrued at an age-independent rate, the function becomes:
where 7 is a first-order toxicity rate constant. If the injury is instantaneous
but repaired by a first-order process, we have:
where K is the first-order rate constant specifying repair. If the injury is
continuous (zero-order) but repaired at a first-order rate, the function is:
(7)( 8 )(9)( 10 )