Fig 1.
A. Aging is characterized by two distinct and consecutive phases. Phase 1 is characterized by a time-dependent increase in the probability of at least one organ–the intestine–to fail. Phase 2 is the terminal phase of life during which a large number of so-called age-related phenotypes occur concomitantly. B. Each phase can be described by a distinct equation. Phase 1 is defined by a linear equation (y = a t + b–left panel) describing the time-dependent increase of the probability for an individual to turn Smurf. Phase 2 is characterized by a 1-phase exponential decay equation (y = e-kt)–right panel) describing the survival of an isolated Smurf subpopulation. C. The longevity curve of a homogenous population (green line) of flies is the sum of the number of non-Smurfs flies (blue line) and living Smurfs (red line). The mathematical equations that lead to the different curves are given in the right panel. The model uses 3 parameters; a is the rate of apparition of the Smurfs in the whole population, t0 = -b/a is the age at which the Smurfs appear in the population and k is the rate constant defining the Smurf longevity.
Fig 2.
Effects of the different parameters of the model on lifespan.
A, B. As a increases, lifespan decreases and Smurf Increase Rate (SIR) increases. C, D. When b increases, lifespan increases without affecting the SIR but the first Smurfs appear later. E, F. An increase of k decreases both lifespan and the SIR. Thus, by measuring lifespan and SIR of flies in two distinct conditions indicates which parameter is affected by the treatment.
Fig 3.
Smurf death rate can be considered as chronological-age independent in drsGFP females.
A. Median life expectancy of 10 days old females (left panel, 21.29 days) is significantly different the median survival time of Smurfs (right panel, 2.04 days) (*****, p < 10−5). B. The majority of Smurfs grouped by 48 hours (746 out of 1146 individuals) shows a median ‘survival time as Smurfs’ that is not significantly different from the ‘Smurf survival time’ calculated using the whole Smurf population (p > 0.05, no *). Thus we will use this distribution to generate an average ‘Smurf survival curve’. C. Survival curves of Smurf flies from a population of mated drsGFP females monitored daily for their Smurf status and death. The equation of that average ‘Smurf survival curve’ was then determined using non-linear regression based on a 1-phase exponential equation e-kt with k = 0.1911 (IC95 [0.1694 to 0.2129]) R2 = 0.9158. D-E. The 2PAC model allows to fit the experimental longevity curve with a precision (a2PAC = 0.0039; b2PAC = -0.019; R2 = 0.9963) similar to the fits obtained with either the Gompertz model (AGompertz = 0.0053; kGompertz = 0.0942, R2 = 0.9908) or the Weibull model (aWeibull = 0.000485; kWeibull = 2.4746; R2 = 0.9949). F. Comparison of the experimental (0.01607 ± 0.0004693; R2 = 0.9221) and theoretical (0.01512 ± 0.0003713; R2 = 0.9976) SIRs. The goodness of fit was calculated with both Pearson (p < 0.0001) and Spearman tests (p < 0.005). The theoretical SIR calculated with the 2PAC model adjusted parameters is not significantly different from the experimental one (p = 0.5578).
Fig 4.
The remaining lifespan of individuals in phase 2 is similar in different drosophila strains.
A. Mated females from populations of 6 different genetic backgrounds show significant different lifespan curves, DGRP_83 (T50 = 42 days; n = 128), DGRP_88 (T50 = 39.6 days; n = 127), DGRP_91 (T50 = 52.7 days; n = 340), DGRP_105 (T50 = 57.1 days; n = 286), DGRP_136 (T50 = 53.4 days; n = 243) and DGRP_195 (T50 = 32.9 days; n = 262). B, C. The life expectancies of Smurfs from the 6 DGRP lines are highly similar, DGRP_83 (T50 = 4.0 days; n = 31), DGRP_88 (T50 = 2.3 days; n = 45), DGRP_91 (T50 = 5.0 days; n = 96), DGRP_105 (T50 = 3.1 days; n = 75), DGRP_136 (T50 = 3.0 days; n = 56) and DGRP_195 (T50 = 2.9 days; n = 63). In addition, none is different from the one measured using 1146 drsGFP individual flies (p > 0.05, 1-way ANOVA using the drsGFP as reference) although the Smurf survival measurement protocol was different. Error bars represent median ± s.e.m. D-F. Although SIRs of DGRP_195 (0.01832 ± 0.001602; R2 = 0.5612) and DGRP_105 (0.003623 ± 0.001602; R2 = 0.8127) are significantly different (p = 0.01579, N > 5 vials per genotype), it is possible to model the longevity curves of the two genotypes using the same k (phase 2) parameter (calculated from drsGFP Smurf flies–Fig 3C) with R2 > 0.99. Error bars represent mean ± s.e.m. Note concerning Fig 4B and 4C: the T50 are higher in fig C than B and this is due to averaging individual vials for the ANOVA test instead of calculating one T50 using the whole population.