“Measurements of damage and repair in aging mice and humans reveals that robustness and resilience decrease with age, operate over broad timescales, and are affected differently by interventions”

As an organism ages, its health-state is determined by a balance between the processes of damage and repair. Measuring these processes requires longitudinal data. We extract damage and repair rates from repeated observations of health deficits in mice and humans to explore the contribution of robustness and resilience, which respectively decrease damage rates and increase repair rates, to aging health. We find a conserved decline with age in robustness and resilience in mice and humans, implying that both contribute to worsening health in aging. A decline in robustness, however, has a greater effect than a decline in resilience on accelerating damage accumulation with age, and a greater association with reduced survival. We also find that deficits are damaged and repaired over a wide range of timescales ranging from the shortest measurement scales towards organismal lifetime timescales. We explore the effect of systemic interventions that have been shown to improve health, including the angiotensin-converting enzyme inhibitor enalapril and voluntary exercise for mice, and household wealth for humans. We find that these interventions affect both damage and repair rates - but in different proportions for different interventions. These findings have implications for how health in aging, and interventions targeting health, are conceptualized and assessed.


Introduction 40
As organisms age, they can be described by a health state that evolves according to dynamical 41 processes of damage and repair. The health state is the net result of accumulated damage and 42 consequent repair (Howlett and Rockwood, 2013). Studies of aging have mostly focused on the 43 health-state rather than the underlying dynamic processes, due the difficulty of their 44 measurement. Two common approaches to measuring individual health-states, the Frailty Index 45 (FI) (Mitnitski et al., 2001) and the Frailty Phenotype (Fried et al., 2001), are assembled from 46 heath state data at a specific age and do not separate dynamic damage and repair processes. 47 Nevertheless, strong associations between frailty measures and adverse health outcomes 48 (Hoogendijk et al., 2019;Howlett et al., 2021) indicate that frailty has a strong effect on 49 underlying dynamical processes. This is supported by the increasing rate of net accumulation of 50 health deficits with worsening health (Mitnitski et al., 2007;Kojima et al., 2019). 51 Reduced resilience, or the decreasing ability to repair damage (or recover from stressors), is 53 increasingly seen as a key manifestation of organismal aging (Ukraintseva et al., 2021;Kirkland 54 et al., 2016;Hadley et al., 2017;Gijzel et al., 2017). Resilience is often assessed by the ability to 55 repair following an acute stressor, such as a heat/cold shock, viral infection, or anesthesia; or a 56 non-specific stressor such as a stochastic fluctuation of the health state, typically within a short 57 timeframe (Scheffer et al., 2018;Gijzel et al., 2019;Rector et al., 2021;Arbeev et al., 2019;58 Colón-Emeric et al., 2020;Pyrkov et al., 2021). Robustness, or an organism's resistance to 59 damage, has not been as well studiedbut there is also evidence for its decline with age (Arbeev 60 et al., 2019;Kriete, 2013). Both resilience and robustness sustain organismal health during aging, 61 but their relative importance and their timescales of action remain largely unexplored. 62

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To study resilience and robustness in aging, we have here developed a novel method of analysis 64 that uses longitudinal binarized health-deficit data from mice and humans to obtain summary 65 measures of organismal damage and repair processes over time. This approach can be adapted to 66 use any biomarker, and is not restricted to biomarkers specifically associated with resilience 67 (Ukraintseva et al., 2021). We apply our method to study how resilience and robustness evolve 68 with age and how they differ between species, between sexes, and under different health 69 interventions. 70 71 Developing interventions to extend lifespan and healthspan is the goal of geroscience (Kennedy 72 et al., 2014;Sierra, 2016;Sierra et al., 2021). While some interventions that affect aging health 73 have been identified, how they differentially affect damage and repair, and their timescales of 74 action, is less understood. We consider interventions in mice that have previously been shown to 75 have a positive impact on frailty, the angiotensin converting enzyme (ACE) inhibitor enalapril 76 (Keller et al., 2019) and voluntary exercise (Bisset et al., 2021). In humans, we stratify 77 individuals within the English Longitudinal Study of Aging by net household wealth (Phelps et 78 al., 2020). Wealth is a socioeconomic factor associated with aging health (Zimmer et al., 2021). 79 Understanding how various interventions affect aging health by affecting resilience and 80 4 robustness will better enable us to improve and combine interventions to fulfill the geroscience 81 agenda. 82 83 84

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Measuring resilience and robustness 87 A well-established approach to quantify health in both humans and in animal models is to count 88 binarized health deficits in a Frailty Index (FI) (Mitnitski et al., 2001;Whitehead et al., 2014). In 89 longitudinal studies, the FI can be assessed at each follow-up. Here we use longitudinal binarized 90 FI data from mice and humans to quantify organismal damage and repair processes over time. 91 As illustrated in the schematic in Figure 1, the change in number of deficits from one follow-up 92 to the next is determined by the number of new deficits (indicating damage, with deficit values 93 transitioning from 0 to 1, red arrow) minus the number of repaired deficits that were previously 94 in a damaged state (with transitions of deficit values from 1 to 0, green arrow). These counts of 95 damaged and repaired deficits between follow-ups represent summary measures of the 96 underlying damage and repair processes. We model this process with a Bayesian Poisson model 97 for counts of damaged and repaired deficits, using age-dependent damage and repair rates. This 98 is a joint longitudinal-survival model, which couples the damage and repair rates together with 99 mortality. 100 101 In our approach, damage rates are the probability of acquiring a new deficit per unit of time, and 102 repair rates are the probability of repairing a deficit per unit time. These are measures of 103 susceptibility to damage (lack of robustness), and ability to repair (resilience). Since the FI is a 104 whole organism-level summary measure of health, these damage and repair rates are also whole 105 organism-level measures of robustness and resilience. In each of these datasets, there is a strong decrease in repair rates and increase in damage rates 118 with age (except in mouse dataset 2 for damage rates). Spearman rank correlations ρ for each 119 plot are also shown in Figure 2, highlighting the increase or decrease in rates with age, and 95% 120 posterior credible intervals of these correlations are shown in brackets. Overall, we observe 121 decreasing repair rates and increasing damage rates with age which signify decreasing resilience 122 and robustness with age in both mice and humans. Decreasing repair and increasing damage both 123 contribute to an increasing FI with age in mice and humans (shown in Figure 2-figure 124 supplement 2a-d). We also observe higher FI scores in females versus males in both mice and 125 humans, as reported previously (Kane et al., 2019;Gordon and Hubbard, 2020;Kane and 126 Howlett, 2021). 127 The acceleration of damage accumulation is determined by a decline in robustness 139 The plots of FI vs. age shown in Figure 2-figure supplement 2 (see also Mitnitski et al., 2001;140 2005;2012; 2013) has a positive curvature, accelerating upwards near death (Stolz et al., 2021). 141 This positive curvature is also seen in other summary measures such as Physiological Dysregula-142 tion (Arbeev et al., 2019). However, the origin of this curvature is unknown --whether it is due 143 to a late-life decrease in resilience or a decline in robustness. 144

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We measure the curvature of the FI with the second time-derivative, which can be computed 146 with the age-slopes of the damage and repair rates (see Methods). In Figure 3, we show the sepa-147 rate contributions to this curvature, separated into terms involving damage (pink) and terms in-148 volving repair (green). Summing these terms, we observe the typical positive curvature that indi-149 cates an acceleration of damage accumulation. 150

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We find that the decline in robustness (indicated by the damage rate terms) has the strongest ef-152 fect on the curvature of the FI. In mice, this is seen in every dataset and is significant at the indi-153 cated ages (Figure 3b-d) and for humans at older ages ( Figure 3e). This observed effect indicates 154 that it is the increase in susceptibility to damage with age, rather than the decline of repair, that 155 causes this acceleration of damage accumulation. Credible intervals evaluating the significance 156 of these effects are shown in Figure  The effect of these interventions on the repair and damage rates is seen in Figure 4c) and d), 175 where 95% credible intervals for the age-slopes show the rate of increase or decrease of the 176 repair and damage rates as age increases. These slopes include both the change in the rate with 177 age, and the effect due to increasing FI with age. Interventions affect the rate of decrease of both 178 repair and damage rates with time, resulting in less cumulative damage. 179 180 As shown in Figure 4c, enalapril attenuates the rate of decrease of repair rates in both male and 181 female mice, resulting in age-slopes closer to zero than for controls. Significance is shown with 182 asterisks (*) at the 0.05 level. In Figure 4-figure supplement 1 we show a significant reduction in 183 damage rate (but not slope) for male and female mice with enalapril. A sex-specific effect is seen 184 for voluntary exercise. For female mice, voluntary exercise leads to stoppage of the decline in 185 repair rates (to an approximately zero slope), whereas for male mice it just attenuates the decline 186 ( Figure 4d). For damage rates, female mice exhibit an attenuation of the rise with age whereas in 187 male mice exercise stops the age-dependent rise exhibited by control mice. 188 189 For humans, we use net household wealth as a socioeconomic environmental factor that serves as 190 a proxy for medical and behavioural interventions that are not individually tracked. As such we 191 report correlations of wealth with repair and damage rates with age, rather than age-slopes after a 192 specific intervention is initiated. In Figure 4-figure supplement 2, we show rates stratified by 193 8 terciles of net household wealth, where the lowest tercile exhibits lower repair rates and higher 194 damage rates for younger ages. Correspondingly, the FI is lower for individuals with a higher net 195 household wealth. Treating the wealth variable as continuous, Figure 4e) shows that repair rates 196 are positively correlated with net household wealth, while damage rates are negatively correlated 197 with significant and stronger effects at younger ages. These results reinforce the findings in 198 mice, where interventions impact both damage and repair rates. In humans, we also see some ev-199 idence of decreasing effects of wealth with agethough these may be confounded by recruit-200 ment effects of baseline age. 201 202 203

Damage and repair have broad timescales 204
In the results above, we considered the average damage and repair transition rates vs age. Since 205 individual deficits undergo stochastic transitions between damaged and repaired states, we can 206 also measure the lifetime of these individual deficit states (see Figure 5a). These lifetimes are 207 interval censored (transitions typically occur between observation times) and can be right-208 censored (death or drop-out before transition occurs). We use an interval censored-analogue to 209 the standard Kaplan-Meier estimator for right censored data (see Methods) to estimate state-210 survival curves of individual damaged or repaired states. These state-survival curves in Figure 5, 211 considering all possible deficits, represent the probability of a deficit remaining undamaged vs 212 time since a repair transition, or remaining damaged vs time since a damage transition. 213

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We generally observe a significant drop of state-survival probability at early times, indicating 215 some rapid state transitions at or below the interval between measurements. However, all of the 216 curves also extend to very long timestowards the scale of organismal lifetimeindicating that 217 both robustness and resilience operate over a broad range of timescales. These results highlight 218 that repair can occur a long time after damage originally occurred. Note that the timescale of 219 robustness as measured here is not robustness after a specific stressor, but robustness due to the 220 continual stressors of aging. A similar form of non-specific robustness has been measured in a 221 previous study, using the onset age of disease (Arbeev et al., 2019). resilience, such that deficits were repaired faster in mice that were exercised compared to 232 controls. We expect that we would observed stronger effects of the interventions on these time-233 scales if we had sufficient data to resolve the impact of the time at which the initial damage or 234 repair event occurredhere we have grouped all times together. For humans (see Figure 5f), we 235 see strong and significant effects on resilience and robustness timescales from household wealth 236 in females, but not males. These effects are particularly strong for the damage timescales that 237 characterize robustness: states remain healthy longer at higher wealth terciles. 238 239 240

Discussion 241
We have presented a new approach for the assessment of damage (robustness) and repair (resili-242 ence) rates in longitudinal aging studies with binarized health deficits. With this approach, we 243 have shown that both humans and mice exhibit increasing damage and decreasing repair rates 244 with age, corresponding to decreasing robustness and resilience respectively. We also demon-245 strate that decreasing robustness and resilience with age contribute to the acceleration of aging 246 for organisms. Decreasing robustness has approximately twice as large an effect when compared 247 to declining resilience; decreasing robustness also has a stronger and significant effect on surviv-248 al. While much of the focus in previous work has been on the decline of resilience in aging 249 (Ukraintseva et al., 2021), our results indicate that both decreasing robustness and decreasing 250 10 resilience are important processes underlying the increasing accumulation of health-related defi-251 cits with age, and the increasing rate of accumulation at older ages. 252

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In the current study, the observed damage is thought to occur due to natural stochastic transitions, 254 rather than a specific identified stressor (Kirkland et al., 2016;Colon-Emeric et al., 2020). 255 Resilience measured by the observed repair also occurs without interventions (certainly in mice, 256 due to their absence of health-care), and so is likely to represent intrinsic resilience with respect 257 to spontaneous damage. This natural resilience can be thought of as resilience to the natural 258 stressors of life, which continually occur during aging. While errors in deficit assessment could 259 contribute to the damage or repair assessment, we would expect such errors to be constant with 260 age. In contrast, we observe decreasing repair rates and increasing damage rates with age. 261 Therefore, these age dependent rates signify decreasing resilience and robustness with age in 262 both mice and humans. Previous work has modeled the change in count of deficits from baseline to a follow-up 268 (Mitnitski et al., 2006;2007;2012;2014), however that work only modeled the mean number of 269 deficitsso that damage and repair rates were not directly assessed. Conversely, some approaches measure resilience by the recovery after an acute stressor such hip 279 11 fracture or viral respiratory infection (Colon-Emeric et al., 2021). An advantage to our approach 280 is that we observe both resilience and robustness using similar methods on the same data, so we 281 can compare their relative effects. 282 283 One caveat with our approach is that we may miss fast damage and repair dynamics that occur 284 on time-scales shorter than the separation between observed time-points, e.g., we cannot observe 285 daily or weekly changes in deficit states. Therefore, our measurements of damage and repair 286 should only be interpreted as the net damage and net repair between observed time-points. Our 287 approach therefore results in summary measures of damage and repair rates. Nevertheless, we 288 assess these summary measures against both age and interventions. 289

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We find that damage and repair processes are targeted by interventions in mice. As a result, de-291 veloping interventions to target either damage or repair separately is conceivable. While target-292 ing either would affect net deficit accumulation, we found that the damage rate has a stronger 293 effect on both mortality and the acceleration of damage accumulation than the repair rate. We 294 predict that interventions that facilitate robustness (resistance to damage) may be more important 295 at older ages, where damage accumulation normally accelerates. More broadly, rather than just 296 targeting deficit accumulation or FI (Howlett et al., 2021), our results indicate that interventions 297 could be improved by targeting an appropriate balance of damage and repair processesin an 298 age and sex dependent manner. Since both damage and repair occur on long timescales, this rais-299 es the possibility that these rates could be manipulated by interventions over a similarly broad 300 range of timescales from the shortest times to organismal lifetimes. How to optimally deploy 301 available interventions is not yet clear. 302

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The effects of age on both damage and repair, in mice and humans, are qualitatively similar in 304 male and female populations. Nevertheless, we have found that systemic interventions can have 305 qualitatively distinct sex effects in mice. The ACE inhibitor enalapril has stronger effects in fe-306 male mice. Voluntary exercise stopped the decline in repair rate with age for female mice, but 307 not male mice, and stopped the increase in damage rate with age for male mice, but not female 12 mice. These differences suggest that assessing both damage and repair rates, together with accu-309 mulated damage as a FI, in interventional aging studies can provide a clearer assessment of sex 310 differences. Further studies are needed to tease out the sex-dependent effects of other aging in-311 terventions, and to provide quantitative insight into the mortality-morbidity paradox, where fe-312 males live longer but have higher FI scores than males (Kane and Howlett, 2021;Oksuzyan et 313 al., 2008). 314 315 Summary measures of health such as the FI exhibit an accelerating accumulation of health defi-316 cits with age (Mitnitski et al., 2001;2005;2012;2013). This universally observed behavior must 317 be reflected in either increasing damage rates with age, or decreasing repair rates (Pyrkov et al.,   ). For each plot, the mean Spearman's rank correlation ρ between the rate and age is indicated by the median of the posterior and a 95% posterior credible interval in parenthesis. e)-f ) Posterior distributions of log hazard ratios of death for damage and repair rates are shown as violin plots for the mouse datasets. These hazard ratios correspond to a 1 standard deviation increase in the damage or repair rates. The black interval shows a 95% credible interval around the median point.   The effect of enalapril and exercise on Frailty Index curvature for mice for mouse datasets 1 and 2. 95% credible intervals for these curvatures are shown by errorbars around the median (point). Asterisks (*) indicate credible intervals for the difference between intervention and control fully exclude zero. c),d) Repair rates and damage rates time-slopes vs time since intervention for the effect of enalapril and exercise for mouse datasets 1 and 2. 95% credible intervals for these curvatures are shown by errorbars around the median (point). Asterisks (*) indicate credible intervals for the difference between intervention and control fully exclude zero. e) Spearman rank correlation ρ between wealth and repair rate (green) and damage rate (pink), vs age for ELSA humans. Individuals are separated by decades of baseline age, and 95% credible intervals for these correlations are shown as coloured regions around the median (thick line). We restrict this plot to ages with at least 3 individuals.       Testing the effect of robustness, resilience, and interventions on curvature. We compute the posterior distribution mean difference between the curvature terms involving damage rates and repair rates for the control. Here we show the median of the posterior (points) with 95% credible intervals for the control groups for mouse datasets a) 1, b) 2, and c) 3. For credible intervals above zero, the effect of the damage rate on the curvature is considered significant at the 95% level. In d) and e), we show test the effect of enalapril and exercise on the curvature, showing that exercise strongly reduces curvature. f ) We compute the posterior distribution mean difference between the curvature terms involving damage rates and repair rates for humans.   Humans stratified by terciles of household wealth. Repair rate, damage rate and Frailty Index vs age for ELSA humans (Phelps et al. 2020) are shown, stratified by terciles of net household wealth. These plots show binned averages of the rates of Frailty Index as the points with standard errors, overlayed with posterior samples from the models. The lowest tercile exhibits lower repair rates and higher damage rates for younger ages.  Exponential time-scales for damaged state survival curves. Exponential survival models are fit for the survival of the damaged state for each binary health variable. Time-scales are computed as the inverse of the exponential rate, and the posterior median is shown as a point, with a 95% credible interval. This is shown for mouse datasets 1, 2, and 3, and the ELSA human data. Variables are sorted by the ascending mean-timescale over all datasets. We see that there is a broad range of time-scales.  Exponential time-scales for undamaged state survival curves. Exponential time-scales for undamaged state survival curves. Exponential survival models are fit for the survival of the undamaged state for each binary health variable. Time-scales are computed as the inverse of the exponential rate, and the posterior median is shown as a point, with a 95% credible interval. This is shown for mouse datasets 1, 2, and 3, and the ELSA human data. Variables are sorted by the ascending mean-timescale over all datasets. We see that there is a broad range of time-scales.