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Megaworm: Scientists watch 100,000 worms live and die in a grand lifespan experiment

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From 26 Jan 2016 Nature weekly Podcast (about 07:49 min into the 'cast):

"Megaworm: Scientists watch 100,000 worms live and die in a grand lifespan experiment"

 

http://www.nature.com/nature/podcast/

 

The Podcast episode, particularly, goes into relevance and importance of CR in this megaworm study.

In essence, CR is like a broad-spectrum life extender (i.e., it lessens risk of ALL tested diseases).

 

Other LE interventions (besides CR) were also explored/tested.

 

Not sure Al has posted this paper ;) Would be nice in PDF, as it's full o' infographics, as the thumbnails suggest!

 

http://www.nature.com/nature/journal/vaop/ncurrent/full/nature16550.html

 

The temporal scaling of Caenorhabditis elegans ageing
 
Nicholas Stroustrup, Winston E. Anthony, Zachary M. Nash, Vivek Gowda, Adam Gomez, Isaac F. López-Moyado, Javier Apfeld & Walter Fontana
 
 
Nature (2016) doi:10.1038/nature16550
Received 27 July 2015 Accepted 18 December 2015 Published online 27 January 2016

 

The process of ageing makes death increasingly likely, involving a random aspect that produces a wide distribution of lifespan even in homogeneous populations1, 2. The study of this stochastic behaviour may link molecular mechanisms to the ageing process that determines lifespan. Here, by collecting high-precision mortality statistics from large populations, we observe that interventions as diverse as changes in diet, temperature, exposure to oxidative stress, and disruption of genes including the heat shock factor hsf-1, the hypoxia-inducible factor hif-1, and the insulin/IGF-1 pathway components daf-2, age-1, and daf-16 all alter lifespan distributions by an apparent stretching or shrinking of time. To produce such temporal scaling, each intervention must alter to the same extent throughout adult life all physiological determinants of the risk of death. Organismic ageing in Caenorhabditis elegans therefore appears to involve aspects of physiology that respond in concert to a diverse set of interventions. In this way, temporal scaling identifies a novel state variable, r(t), that governs the risk of death and whose average decay dynamics involves a single effective rate constant of ageing, kr. Interventions that produce temporal scaling influence lifespan exclusively by altering kr. Such interventions, when applied transiently even in early adulthood, temporarily alter kr with an attendant transient increase or decrease in the rate of change in r and a permanent effect on remaining lifespan. The existence of an organismal ageing dynamics that is invariant across genetic and environmental contexts provides the basis for a new, quantitative framework for evaluating the manner and extent to which specific molecular processes contribute to the aspect of ageing that determines lifespan.

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Thanks Khurram!

 

That Nature podcast episode is great! I liked the first segment on Google's AlphaGo program, I posted about earlier today.

 

Not sure Al has posted this paper ;) Would be nice in PDF, as it's full o' infographics, as the thumbnails suggest!

 

http://www.nature.com/nature/journal/vaop/ncurrent/full/nature16550.html

 

I guess you haven't yet learned of sci-hub.io, discussed here. Information wants to be free... Here is a link to the full text. The paper is very interesting, although quite technical and math-oriented.

 

The researchers observed across a range of challenges (temperature, CR, poisons & genetic manipulations) and severity of these challenges, their impact on the lifespan of the little C. elegans worms was a stretching (or shrinking) of the survival curves. Rather than changing the shape of the survival curve (e.g. 'squaring' the survival curve, but not extending the age to which the longest-lived worms survive), all these interventions kept the shape of the survival curve the same but scaled it instead. For example, worms kept in cool conditions lived longer than warm worms, but both groups had the same relative mortality distribution curve. So for example (and I'm making up the numbers), 10% of the worms died >30% earlier than the mean lifespan in a group, and 10% of the worms lived >30% longer than the mean lifespan in a group, regardless of whether it was the cool, long-lived group, or the warm, short-lived group.

 

The authors say this is a surprising result, suggesting the possibility that there is a single, underlying rate constant of aging - which the commentator in the podcast (@ ~12:30min) likens to a "resiliency factor" or conversely, a "frailty index". So instead of changing a specific cause of aging/death (e.g. in humans, the rate of arterial plaque buildup), that you'd expect to influence infant mortality differently than late-life mortality, these interventions seem to be making the worms more resilient (or vulnerable) to all causes of aging/death simultaneously.

 

Of course the commentator in the podcast observes that these are short-lived worms, and it's unclear whether these results apply to long-lived mammals, especially humans. It brings to mind our recent discussion of intrinsic vs. damage-driven aging. I wonder if CR (or cold exposure! :)xyz) might scale the comprehensive human "frailty index" discussed in this post in a similar manner as was observed in the the mortality curves of these worms...

 

 In other words, rather than having narrowly-targeted benefits (like just cleaner arteries, or better insulin sensitivity), interventions like CR or cold exposure seem to provide wide-ranging protection against a variety of causes of aging, and so might be expected to delay the onset of the various impairments on the frailty index list.

 

--Dean

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Dean: 

Thx for the  sci-hub.io link. I didn't know about that resource. I've actually, since, acquired the full paper in PDF from Al ;)

Yes, the paper is technical, but your summary was well written, making the topic accessible to the lesser techies.

 

Lotsa info in this dense paper and its implications ... but about "underlying rate constant of aging "....

In early 2014, SENS uploaded the following presentation:

(How does the body know how old it is? - Josh Mitteldorf)

 

Also: http://www.sens.org/videos/how-does-body-know-how-old-it-josh-mitteldorf

 

Josh is actually coming out with a topical book, co-authored by Dorion Sagan, later this year:

http://mathforum.org/~josh/SuicideGenes/

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[Admin Note: Here is an interesting commentary on the study under discussion in this thread, which Al made a new thread for but which I'm moving here, where it belongs... --Dean]

 

 

Ageing: A stretch in time

Nature   530,   37–38   (04 February 2016)   doi:10.1038/nature16873 Published online   20 January 2016

 

Plots of survival against time for nematode worms in different conditions can be superimposed by rescaling the time axis. This observation has far-reaching implications for our understanding of the nature of ageing. See Letter p.103

It is a long-standing mystery why, although the rate of ageing varies greatly among species, the effects of ageing are remarkably consistent. Closely related species such as mice and naked mole rats can have average lifespans that differ by more than tenfold, yet these species (and others as distant as yeast and humans) undergo similar molecular changes throughout ageing. In this issue, Stroustrup et al.1 (page 103) rigorously demonstrate that the way in which the risk of death changes over the course of an organism's life is largely independent of the length of that life.

The nematode worm Caenorhabditis elegans is often used for studies of ageing, because it has a lifespan of about two weeks and is easy to cultivate in the laboratory. Stroustrup and colleagues used their previously developed2 'lifespan machine' to simultaneously measure the survival of tens of thousands of individual worms with 20-minute precision. The authors subjected the worms to a range of lifespan-altering conditions — different temperatures, a damaging compound, a lifespan-prolonging food source and several genetic mutations that extend or shorten lifespan. After analysing the lifespans of more than 100,000 individuals, they demonstrate that the overall shape of the survival curve (a plot of the fraction of the starting worm population alive at any given time) remains unchanged in different conditions. They find that these conditions act only to stretch or squeeze the curve along the time axis (Fig. 1a).

Figure 1: Resilience as a measure of ageing.
nature16873-f1.jpg

a, Stroustrup et al.1 measured the fraction of a population of nematode worms that remained alive over time in various conditions, constructing 'survival curves' (coloured lines) for each condition. The survival curves for many different conditions can be superimposed simply by rescaling the time axis. This observation implies that each condition alters the probability of every cause of death to the same extent. b, If this were not the case, the curves would not be superimposable. For example, if a fast-acting cause of death is made less likely, but not a slow-acting one, then the curve's shape will change in one particular region (as in the light blue compared to the dark blue curve). c, To obtain the scaling observed by Stroustrup and colleagues, there must be an organismal state, here dubbed 'resilience', that is influenced by many determinants of lifespan, and that is the sole determinant of the risk of death from any particular cause (different causes are represented by numbers).

This is altogether unexpected, because it implies that the tested lifespan-altering manipulations change the probability of every possible cause of death in concert and to exactly the same extent. To explain, because each cause of death plays out along a distinct timescale, if a particular condition were to decrease the odds of a fast-acting cause of death but not a slow-acting cause (or vice versa), a particular region of the overall survival curve would be altered, and thus its overall shape changed (Fig. 1b). Even interventions such as temperature shifts might be expected to affect different causes of death differently. After all, death is a biochemical process, and changing temperatures will alter the rates of different death-promoting chemical reactions differently, depending on the activation energies of those reactions. The authors' observation of almost-perfect timescaling across different conditions thus places specific constraints on how these conditions influence survival.

How can this surprising observation be explained? One possibility is that every cause of death in the worms has the same activation energy and responds identically to changes in food source, toxic exposures and diverse genetic mutations. Another is that worms have a single mechanistic cause of death.

A more plausible interpretation is that there is some intermediate state on which all the tested interventions converge, and which determines the risk of death from each possible cause (Fig. 1c). Could this intermediate state involve, for instance, the insulin/insulin-like growth factor signalling (IIS) pathway, which is central to many aspects of ageing across species3? No — the authors found that survival curves retain their shape even when the IIS pathway is inactivated, and in response to conditions and mutations known to act independently of the IIS pathway.

The most likely explanation for this intermediate state is that the risk of death is governed not by any single pathway, but by a property that arises from interactions between the various molecular processes that influence ageing. This property, perhaps best called 'resilience', would be an intrinsic biological property of ageing C. elegans, just as temperature and pressure are intrinsic thermodynamic properties of gases that emerge from the interactions of the constituent molecules.

The temperature of water in a whistling tea kettle provides an analogy for resilience. There are many ways in which to heat the water — on a stove, in a microwave, or even by adding a strong acid. However, whether a kettle whistles depends not on the source of the heat, but on the water temperature. Similarly, alterations in the molecular processes that contribute to resilience could change the rate of ageing (the heating rate of the water) without changing its underlying nature (the relationship between temperature and whistling).

The authors use detailed simulations to demonstrate how such a property could emerge. If resilience is a measure of the fraction of biological processes in a densely interconnected network that have failed, then manipulations that alter a subset of these processes will extend or shorten lifespan without changing the shape of the survival curve. Alternatively, a single physical property, which is acted on by many molecular processes and affects the risk of death from diverse causes, could underlie an organism's resilience. Potential candidates for such physical properties include intracellular redox levels45 or global protein solubility levels and turnover rates67. Whatever the case, the current work provides a strong constraint on any proposed molecular mechanism of resilience — measurements of the levels or activity of that mechanism must correlate exactly with lifespan across temperatures and among different genetic mutants.

This study suggests that concepts such as resilience and frailty, long used in the ageing literature, might have a concrete biological meaning. In particular, the Rockwood frailty index, which calculates the fraction of measured clinical markers considered to be in a deficient state8, is a close theoretical match for the authors' interpretation of resilience. Most importantly, these results demonstrate that, although students of ageing biology have learnt much about how to manipulate the rate of ageing, the nature of organismal frailty is almost completely unknown. The few interventions the authors identify that do change the shape of the survival curve in C. elegans(such as a mutation that alters feeding ability, and another that alters function in mitochondria, the cell's energy centres) may point the way towards understanding this previously unappreciated biology.

Finally, although Stroustrup et al. consider only lifespan, increasing chronological lifespan does not necessarily increase the fraction of lifespan spent in good health9. Further work of a similar experimental and analytical rigour will be necessary to clarify the relationship between quality and quantity of life.

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[Admin Note: For some reason Al wants to post (without comment) large sections of the study on C Elegans we're discussing in this thread. I'm not sure he realizes we've already been talking about this study. But I'm moving his post to this thread, where it belongs...  Also note most of the links in this post are broken... --Dean]

 

The temporal scaling of Caenorhabditis elegans ageing

  • Nicholas Stroustrup,
  • Winston E. Anthony,
  • Zachary M. Nash,
  • Vivek Gowda,
  • Adam Gomez
  • + et al.

A diverse range of molecular and genetic manipulations all alter lifespan distributions of Caenorhabditis elegans by an apparent stretching or shrinking of time.

See also

  • News & Views by Pincus
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  • Abstract
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  • The process of ageing makes death increasingly likely, involving a random aspect that produces a wide distribution of lifespan even in homogeneous populations12. The study of this stochastic behaviour may link molecular mechanisms to the ageing process that determines lifespan. Here, by collecting high-precision mortality statistics from large populations, we observe that interventions as diverse as changes in diet, temperature, exposure to oxidative stress, and disruption of genes including the heat shock factor hsf-1, the hypoxia-inducible factor hif-1, and the insulin/IGF-1 pathway components daf-2age-1, and daf-16 all alter lifespan distributions by an apparent stretching or shrinking of time. To produce such temporal scaling, each intervention must alter to the same extent throughout adult life all physiological determinants of the risk of death. Organismic ageing inCaenorhabditis elegans therefore appears to involve aspects of physiology that respond in concert to a diverse set of interventions. In this way, temporal scaling identifies a novel state variable, r(t), that governs the risk of death and whose average decay dynamics involves a single effective rate constant of ageing, kr. Interventions that produce temporal scaling influence lifespan exclusively by altering kr. Such interventions, when applied transiently even in early adulthood, temporarily alter kr with an attendant transient increase or decrease in the rate of change in r and a permanent effect on remaining lifespan. The existence of an organismal ageing dynamics that is invariant across genetic and environmental contexts provides the basis for a new, quantitative framework for evaluating the manner and extent to which specific molecular processes contribute to the aspect of ageing that determines lifespan.
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Body temperature is a major determinant of lifespan in poikilotherms345 that also influences mammalian ageing6. From 20 °C to 33 °C, the mean lifespan of C. elegans decreases 40-fold7. To explore the impact of temperature on the actual distribution of lifespans, we used our automated imaging technology8 to collect highly resolved mortality data in multiple replicate populations placed across this temperature range (Methods). From these data we estimated the survival curveS(t), which is the probability of being alive at time (age) t, and the hazard function h(t) = −d logS(t)/dt, which is the instantaneous risk of death at time t (Supplementary Note 1.1 and Methods).

In many invertebrates, changes in temperature alter the rate at which the risk of death increases with time459. Our lifespan data, controlled for environmental heterogeneity (see statistical methods section in Methods), confirmed this effect. However, we further observed that changes in temperature appeared to shift h(t) by an equal and opposite amount in magnitude and time when plotted on a log–log scale, suggesting that between any two temperatures T0 and T1,nature16550-m1.gif independent of any particular parametric form of h(t). This change in hazard corresponds to a simple stretching of the survival function along the time axis by a dimensionless scale factor λnature16550-m2.gif (Supplementary Note 1.2). The sole effect of changes in body temperature on lifespan therefore appeared to be a temporal rescaling of mortality statistics.

To confirm this effect, we applied an accelerated failure time (AFT) regression model10 in which lifespan distributions that only differed by temporal scaling would have identically distributed residuals (Supplementary Notes 1.3 and 1.4 and Methods). To identify any significant differences between AFT residual distributions, we applied a Kolmogorov–Smirnov test adapted to censored data (Supplementary Note 2). We identified no significant temperature-dependent deviations from temporal scaling within two thermal ranges: 19–30 °C and 30.5–33 °C (Fig. 1b–d and Extended Data Figs 123). Populations above 30.5 °C exhibited a more pronounced late-age deceleration (Fig. 1eExtended Data Fig. 3 and Supplementary Note 1.4), consistent with an increased heterogeneity11 (Supplementary Note 3). Yet, even at high temperatures, the observed hazard function appears to be dominated more by ageing (for example, a progressive increase in the hazard) than by chance events that would produce a constant hazard (that is, non-ageing).

Figure 1: Environmental determinants rescale C. elegans lifespan distributions.
nature16550-f1.jpg

a, Populations grown at 20 °C were transferred on their second day of adulthood to a final temperature of (right to left) 20.1 °C (black), 23.7, 25.2, 29.1, 30, 30.9, 31.3, 32.5, and 32.6 (yellow). Individual lifespans were collected7 and used to estimate the hazard function of each population using numerical differentiation of the Kaplan–Meier survival estimator (solid lines). The shaded areas represent the 95% confidence bands of the true hazard (Statistical methods). d, days. b, The lifespan of individuals living at 20, 25, 27, and 33 °C.c, The data in b were fitted with an AFT model log(yi) = βxi + ϵi to remove differences in timescale (Methods and Supplementary Note 1.3). The AFT residuals exp(ϵi) corresponding to populations at 20, 25, and 27 °C are plotted using the Kaplan–Meier survival estimator. d, The AFT residuals corresponding to populations held at 25 (black) and 33 °C (red) are plotted using the Kaplan–Meier survival estimator. e, Hazard functions were estimated from the 25 and 33 °C AFT residuals. f, The survival curves of populations exposed to 0 (black), 1.5 (blue), 3 (green), and 6 mM (purple) tBuOOH. g, The AFT residuals for the data of fh, The survival curves of animals cultured on live E. coli (black) and ultraviolet-inactivated E. coli (green). i, The AFT residuals for the data of h.

We then asked whether other interventions could produce a temporal scaling. Since oxidative damage has been linked to ageing across taxa1213, we quantified the effect of the oxidant tert-butyl hydroperoxide (tBuOOH) and found that it quantitatively rescales lifespan distributions in a dose-dependent manner up to 3 mM (Kolmogorov–Smirnov P > 0.02) with significant deviations observed only at 6 mM (Kolmogorov–Smirnov P = 9 × 10−4Fig. 1f–g and Extended Data Fig. 4).

To further explore the range of interventions that might yield temporal scaling, we considered three members of the insulin/IGF-1 pathway59daf-16, a transcription factor required for lifespan extension by multiple signals14age-1, a regulatory kinase upstream of daf-16, and daf-2, the insulin/IGF receptor, all of which influence both lifespan and thermal stress resistance7. Each mutant population exhibited a lifespan distribution rescaled from the wild-type distribution, both at 20 °C (Kolmogorov–Smirnov P > 0.015; Fig. 2a–e) and at 33 °C (Kolmogorov–Smirnov P > 0.017;Extended Data Fig. 4). The insulin/IGF receptor daf-2 influences the activity of the heat shock factor hsf-1 (ref. 15), and disruption of hsf-1 also shortens lifespan by temporal rescaling (Kolmogorov–Smirnov P > 0.2; Fig. 2c, f). Elimination of the hypoxia-inducible transcription factorhif-1, known to influence lifespan through daf-16-dependent mechanisms16, behaved likewise (Kolmogorov–Smirnov P > 0.2; Extended Data Fig. 4).

Figure 2: Genetic determinants rescale C. elegans lifespan distributions.
nature16550-f2.jpg

ac, Survival curves are shown for daf-2(e1368) (red) and wild type (black) at 25 °C (a), daf-16(mu86) (red) and wild type (black) at 25 °C (b), and hsf-1(sy441) (red) and wild type (black) at 20 °C (c). df, The AFT residuals corresponding to the data in ac respectively. Survival curves are shown for eat-2(ad1116) (red) and wild type (black) at 20 °C (g), nuo-6(qm200) (red) and wild type (black) at 25 °C (h), and nuo-6(qm200) populations held at 20 °C and 25 °C (i). jl, The AFT residuals corresponding to the data in gi respectively.

 

Since changes in nutrition alter lifespan across taxa17, we considered two modifications of C. elegans diet: ultraviolet inactivation of the bacterial food source18 and disruption of feeding behaviour by the eat-2(ad1116) mutation19. Ultraviolet inactivation of bacteria extended lifespan via temporal scaling (Kolmogorov–Smirnov P > 0.2; Fig. 1h, i). In contrast, eat-2(ad1116) populations exhibited a significant deviation from temporal scaling (Kolmogorov–Smirnov P = 5 × 10−5), with a disproportionate increase in the standard deviation of lifespan compared with the mean (Fig. 2g, j). We also noted that eat-2(ad1116) populations exhibited a substantially increased variation in developmental timing. While such variation does not affect lifespan statistics based on manually synchronized young adults (Methods), it is possible that the causes of this developmental variation also underlie the increased variation of lifespan. We found that disruption of the mitochondrial complex I in nuo-6(qm200) populations produced analogous effects on developmental timing with a deviation from temporal scaling of lifespan similar to eat-2(ad1116) (Kolmogorov–Smirnov P > 3 × 10−18Fig. 2h, k). Yet, populations with either allele exhibited temporally rescaled lifespan distributions in response to temperature changes (Kolmogorov–Smirnov P > 0.2; Fig. 2i, l and Extended Data Fig. 4). We conclude that while eat-2(ad1116), nuo-6(qm200), and shifts in temperatures from below to above 30 °C alter lifespan distributions outside the temporal scaling model, these interventions do not eliminate the ability ofC. elegans to respond to subsequent interventions with temporal scaling. Temporal scaling thus appears to be a pervasive response to interventions of diverse modality and intensity.

Temporal scaling would arise if all physiological determinants of the risk of death in C. elegansacted as if they were jointly governed by a single stochastic process whose rate constant alone was altered by interventions (Supplementary Note 4). If the risk of death was determined in this way, we reasoned that transient interventions early in adulthood would produce a persistent temporal shift, not a scaling, of mortality statistics (Supplementary Note 4.3). To test this, we focused on temperature, which can be quantitatively, rapidly, and reversibly switched at any age between a baseline temperature T0 and a transient temperature T1 (Fig. 3a). We confirmed that transient exposure to higher temperatures produced a permanent shortening of lifespan5 (Fig. 3b). We found that this shortening consisted of a temporal shift of the lifespan distribution (Fig. 3c, d)nature16550-m3.gif that matches the magnitude of shift ∆τ predicted if time were rescaled only for the period τ that animals were held at the transient temperature: ∆τ = τ(1 − λ−1), with λ the scale factor relating populations always held at T1 to populations always held at T0 (Fig. 3e, f,Supplementary Note 4.3Supplementary Table 2 and Extended Data Fig. 5). In a complementary experiment, we found that exposure to high temperature for different periods τ also gave shifts with the predicted magnitude (Extended Data Fig. 5). It appears, therefore, that the temporal scaling observed in Fig. 1a and the temporal shifting of Fig. 3 are compatible with a single model in which interventions alter the effective rate constant of a stochastic process governing those aspects of C. elegans physiology that determine risk of death. This process is evidently ongoing even very early in adulthood and is governed by the same rate constant as in late adulthood.

Figure 3: Transient interventions during early adulthood shift the lifespan distribution.
nature16550-f3.jpg

a, A schematic: populations were placed at 24 °C (blue), 26 °C (green), 27.5 °C (orange), and 29 °C (red). After τ = 3.2 days, sub-populations were transferred to either 24 °C or 29 °C for the remainder of their lives.b, The hazard rate was estimated using the remaining lifespan of populations transferred to the final temperature of 29 °C. c, To test for temporal scaling between the populations shown in b, death times were fitted with the regression model log(yi) = βxi + ϵi, in which exp(βi) is the best estimate for the scale factor λ. The residuals exp(ϵi) are plotted as hazard functions in the colour scheme of ad, To test for temporal shifts between the populations shown in b, death times were fitted with the regression model yi = βxi + ϵi, in which βi is the best estimate for the shift term ∆τ. The residuals ϵi are plotted as hazard functions in the colour scheme of ae, The shift term ∆τ for populations transferred from each high temperature to 24 °C was plotted against 1 − λ−1, where λ is the scale factor relating populations always held at the corresponding high temperature to those always held at 24 °C. The prediction ∆τ = τ(1 − λ−1) suggests that these points should fall along a line with a slope equal to τ in a. A linear regression on these points model estimates τ = 3.38 ± 0.17. f, As in e, but for populations transferred from lower initial temperatures to the final higher temperature of 29 °C, producing the estimate τ = 3.16 ± 0.14.

 

To clarify how molecular pathways contribute to temporal scaling, we quantified the magnitude of scaling produced by different intensities of intervention: that is, the scaling function. In the case of temperature, we applied an Arrhenius analysis2021 to interpret the change of λ (which in our framework rescales the rate constant of ageing) across the range 20–35 °C (Fig. 4a). We identified three distinct thermal regimes: I, 20–29.4 °C; II, 29.4–32.1 °C; III, 32.1–35 °C (Fig. 4b, Methods and Extended Data Figs 6 and 7) with regime I being further subdivided into Ia and Ib by a reproducible transition point at 24.4 °C.

Figure 4: Scaling functions.
nature16550-f4.jpg

a, The magnitude of temporal scaling was estimated for wild-type populations held at fractional degree intervals across the range 20–35 °C. The scale factor λ of each population was estimated relative to a reference population at 25 °C. Grey lines mark the average lifespan of the reference population scaled by λ. Each replicate is shown as a separate colour, with each point corresponding to an aggregate population consisting of on average 130 individuals at the outset. b, The scale factor λ was determined for populations across the temperature range of a. The data points were fitted with a segmented Arrhenius model λ(T)–1 = p0 exp(–p1/RT) (red). c, The magnitude of scaling produced by daf-16(mu86) (red), daf-2(e1368) (green), and age-1(hx546) (blue) alleles relative to wild type was estimated at each temperature considered (points). Solid curves represent trends across temperature as fitted by a Loess regression. d, The combined magnitude of scaling produced by each allele and change of temperature was estimated relative to a single wild-type population 24 °C; colours as in c. Regimes II and III are shown in Extended Data Fig. 7.e, Wild-type populations at 20 °C were exposed to a series of tBuOOH concentrations ranging from 0 to 10 mM. For each population, λ was calculated relative to an unexposed population (0 mM). Data for concentrations above 0.75 mM were fitted by the model nature16550-m12.gif (red), yielding p2 = 0.47 ± 0.02 and p3 = −1.86 ± 0.15. f, As in c, but for the tBuOOH dosage series.

 

Each scaling regime appears to correspond to a distinct molecular mechanism and barrier process dominating the timescale of ageing (Supplementary Table 1). Sharp decreases in lifespan have been observed to occur around 30 °C in Drosophila melanogaster21, hinting at a more general phenomenon in poikilotherms. Notably, this transition coincided with a deviation from temporal scaling of lifespan distributions (Fig. 1e and Extended Data Fig. 3). Intriguingly, the scaling across the breakpoint between regimes Ia and Ib suggested that temporal scaling need not be disrupted by a change in the molecular mechanisms dominating the timescale of ageing.

Quantifying the effects of temperature on mutant strains, we found that the elimination of DAF-16 shorted lifespan by a rescaling of 28% in regime Ia and 25% in Ib (Fig. 4c, d). The daf-16(mu86) population exhibited the same slope in scaling function as wild type in Ia, and differed only by about 5% across regime Ib, suggesting that the mechanisms mediating the temperature dependence of lifespan in regime I were not altered by elimination of DAF-16. In contrast, the hypomorphic alleles daf-2(e1368) and age-1(hx546) exhibit clear temperature-dependent effects across regime I (Fig. 4c, d). Both genes influence lifespan at 20 °C and 35 °C primarily by suppressing daf-16 activity22, which itself appears independent of temperature. Thus, daf-2(e1368) and age-1(hx546) alleles appear to be neomorphic in respect of the temperature dependence of their regulation of DAF-16.

We found that tBuOOH decreased lifespan at concentrations above 750 μM, with λ decreasing as a power law (Fig. 4e and Methods). This suggests an overall mass-action kinetics for the chain of events linking the direct targets of tBuOOH to the rescaling of the lifespan distribution. The distinct scaling functions of tBuOOH (power law) and temperature (multiple Arrhenius regimes) further suggest distinct molecular targets and mechanisms through which each type of intervention rescales the lifespan distribution.

As with temperature, the elimination of DAF-16 in the presence of tBuOOH reduced lifespan by a constant amount (Fig. 4f), 19.5 ± 8.8%, across all concentrations tested. Taken together with our temperature data in Fig. 4c, these results suggest that DAF-16 acts antagonistically but in parallel to the mechanisms through which tBuOOH and temperature shorten lifespan. DAF-16, tBuOOH, and temperature appear to affect ageing through their influence on risk determinants downstream of all three. For example, DAF-16 might attenuate or mitigate certain types of error or damage regardless of how the errors are created. The magnitude of temporal scaling produced both bydaf-2(e1368) and by age-1(hx546) alleles varied across tBuOOH concentrations (Fig. 4g), which seems yet another aspect of a quantitative stress-dependent regulation of DAF-16 present in these strains but absent in wild type.

Disruption of daf-2daf-16hif-1 or hsf-1 produces distinct metabolic, cell-biological, and behavioural effects1523, as do changes in diet24, temperature25, and exposure to tBuOOH26. Yet, temporal scaling arises independently of the molecular targets specific to each intervention and requires that all risk determinants be affected to the same extent. This suggests that ageing inC. elegans can be described in terms of a whole-organism state variable r that completely determines all-cause mortality (Extended Data Fig. 9). State variables familiar from other contexts include temperature, pressure, and entropy, all of which describe the behaviour of a system resulting from the collective action of its many constituent elements without reference to their nature. In the same way, the change of the state over time, r(t), describes the ageing process of C. elegans in terms of a collective action of all physiological determinants of risk. Where multiple risk determinants independently influence lifespan, temporal scaling requires that interventions simultaneously rescale, to an identical extent throughout life, the risk functions associated with each determinant (Supplementary Note 5.1). In models including dependencies among risk determinants, temporal scaling can emerge even when interventions act differentially across risk determinants (Supplementary Notes 5.2 and 5.3): dependencies can propagate the influence of interventions from one to all risk determinants, in effect producing a system-wide property that we call r(t).

The temporal scaling of lifespan distributions constrains the dynamics of the state variable r(t): the single stochastic process determining C. elegans lifespan must be invariant to timescale transformations and follow an average dynamics governed by an effective rate constant: dr/dt = −krF(r), where F(r) is an unknown function of r that does not depend on kr. In this formulation, temporal scaling arises when interventions change kr into kr/λ. These dynamics place constraints on any stochastic process proposed to describe organismal ageing, as its parameters must change in a coordinated fashion. For example, if r(t) were described by a biased random walk27, the drift coefficient and the square of the diffusion coefficient must remain in a fixed proportion under intervention (Supplementary Note 6).

The idea that ageing is driven by changes in an organismal physiological state has been variously framed in terms of notions such as organization, vitality, organ reserve or resilience32829. The temporal scaling across interventions justifies this notion, allowing an initial formalization. We note that any aspects of C. elegans physiology that change over time but do not influence lifespan, influencing ‘quality’ rather than ‘quantity’ of life, need not change in concert with r(t).

We know neither the physiological basis of the state r(t) nor the specific dynamics by which it changes with age. Yet, we can expect a broad set of lifespan determinants to affect only kr, including minimally all determinants that influence lifespan exclusively through DAF-16 (refs 14and 30), HSF-1 or HIF-1, or through the mechanisms that mediate the effects of temperature and tBuOOH on lifespan. If most ageing mechanisms currently studied influence only kr, then future studies directed at clarifying the physiological origins of r and its dynamics should identify novel ageing mechanisms F(r).

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