Online suppl. Table 1 for all online suppl. material, see www. For all time points, negligible to low correlations were found, although overall correlations increased with higher percentiles of daily-life gait speed.

When comparing the correlations over time, similar patterns and coefficients were observed, indicating a consistent dissonant relationship between in-laboratory gait speed measures and daily-life gait speed measures over time. Table 2 shows the descriptives of in-laboratory and daily-life gait speed measures at baseline, and after 6- and month follow-ups.

Results of the 2-way mixed ANOVA are also presented in Table 2. All gait speed data in-laboratory gait speed: 4-m usual, 7-m usual, and 7-m fast, and daily-life gait speed: number of epochs, percentiles, peak 1, and peak 2 were normally distributed.

Outliers were included in further analyses. There was no significant main effect of time for any of the in-laboratory or daily-life gait speed measures, except for P90 at different time points, as shown in Table 2. For P90 only, significant differences were found between baseline and 6-month follow-up, and between 6-month and month follow-ups.

No statistically significant difference between baseline and month follow-up was present, indicating that the increase in gait speed of P90 at 6-month follow-up was not maintained. No statistically significant interactions between the intervention and time were found on any of the gait speed measures, indicating that the effect of time was independent of the allocated intervention group.

With respect to the variance components of in-laboratory and daily-life gait speed measures over time, the 2 variance components are presented in Table 3. Comparing the different variance components between types of gait speed assessment showed that all gait speed measures had 1 smaller within-subject variance than between-subject variance, and 2 variance components for both in-laboratory and daily-life gait speed in a similar order of magnitude, which was not line with our expectations.

The agreement of in-laboratory and daily-life gait speed measures over time as conducted by Bland-Altman analyses are presented in online suppl. Table 2 and visualized in Figure 2. The mean difference over time for the 4-m usual gait speed, number of epochs, P50, P90, peak 1, and peak 2 was close to zero, showing similar gait speed assessments over time.

This was independent of the baseline assessment and independent of the assigned intervention group. For 7-m usual and 7-m fast gait speed, proportional bias was present, showing a relative increase in gait speed over time for slow-walkers and a relative decrease for fast-walkers.

All gait speed measures showed wide limits of agreement as the SDs of the mean differences ranged from 0. Table 2. Bland-Altman analyses of in-laboratory and daily-life gait speed measures over time i. The present study showed that the interrelation between in-laboratory and daily-life gait speed measures showed negligible to low correlations at baseline, and after 6 months and after 12 months, underscoring that these measures are distinct constructs.

Robust results of in-laboratory as well as daily-life gait speed measures over month time in this group of high-functioning adults aged 61 to 70 years were observed, independent of the assigned intervention group.

Comparison of the variance components revealed smaller within-subject variance than between-subject variance, but in contrast to our expectations, variance components for in-laboratory gait speed measures were comparable to those of daily-life gait speed measures.

These findings suggest that both these types of gait speed measures show distinct personal features: despite the heterogeneity in absolute gait speed measures across participants, both in-laboratory and daily-life gait speed measures were not susceptible to change over 12 months.

The literature on the comparison or interrelation of in-laboratory and daily-life gait speed is limited. Recently, a study comparing multiple in-laboratory gait speed measures and daily-life gait speed was performed in slow-walking sarcopenic older adults [ 33 ].

Short bouts of daily-life gait speed were compared to the in-laboratory 4-m gait speed test, whereas longer bouts of daily-life gait speed were compared to the 6-min walking test 6MWT and m walking test MWT. However, the findings in the previous study do suggest that the assessment of gait speed using longer gait tests is more representative for daily-life gait speed [ 33 ].

In the present study, we did not show a difference between the 4- and 7-m gait speed tests and their relation with daily-life gait speed measures. This might be explained by the fact that the 7-m gait speed tests are still relatively short gait speed tests compared to the 6MWT and MWT.

Our main interest was to explore if, and how, the correlation between in-laboratory and daily-life gait speed would change over time. Despite low cross-sectional correlations, a relative change in one measure could be accompanied by a similar change in the other measure, indicating that a change in performance would affect behavior, and vice versa.

However, no relation in changes of gait speed measures over time was found, indicating an even lower correlation between the 2 constructs of gait function, and therefore, in-laboratory and daily-life gait speed measures could be considered distinct personal features.

The level of agreement for both in-laboratory and daily-life gait speed measures showed relatively wide limits of agreement. A clinically relevant change in in-laboratory gait speed usually lies between 0.

Our data revealed that the limits of agreement for all gait speed measures are well beyond these limits of a clinically relevant change as the SD of the mean differences ranged from 0.

This might indicate that intervention effects in future studies need to show a relatively large change to be able to value effect sizes on its importance, showing results beyond measurement errors. However, the reported clinically relevant changes in in-laboratory gait speed were not assessed in this specific population of healthy, high-functioning adults and could therefore not be translated without caution.

Some limitations need to be taken into account. First, we included a relatively well-functioning population of adults aged 61 to 70 years, participating in a lifestyle intervention study, which could introduce a ceiling effect due to their high level of performance.

Initially, we expected significant changes over time in the intervention groups when compared to the control group allowing us to investigate whether changes in 1 gait speed measure would be related to changes in the other measurement type.

However, the possible effect of the intervention was investigated thoroughly and showed no significant effect on both in-laboratory and daily-life gait speed measures. Moreover, the follow-up period was relatively short for such a well-functioning sample, so a decline in gait speed might not be expected.

Regular assessments of physical performance and gait speed are often recommended as part of follow-up measures in clinical practice, or to see whether temporal changes are associated with treatment regimen in intervention studies.

However, the present study shows that measuring both in-laboratory and daily-life gait speed measures only once in a period of 1 year seems sufficient in a high-functioning population of adults aged 61 to 70 years.

Future research should focus on investigating the interrelation between in-laboratory and daily-life gait speed measures in pre- frail populations. Furthermore, in the present analyses, a s epoch time frame was chosen to reliably estimate daily-life gait speed measures, as previously described by Rispens et al.

It may be argued that this epoch time is rather long, in comparison to the in-laboratory gait speed tests. Outdoor walking and therewith gait speed is highly dependent on behavioral and environmental factors [ 37, 38 ] which could not be taken into account in this study.

We believe our method of determining steady-state walking epochs sufficiently approximates steady-state conditions; however, it is possible that some nonsteady or nonstraight walking behavior e. Nevertheless, a systematic exploration of the effect of different epoch lengths on the interrelation between in-laboratory and daily-life gait is warranted for future implementation of the combined use of in-laboratory and daily-life gait speed measures in clinical practice.

Because daily-life gait speed is dependent on behavioral and environmental factors, the added value could be that daily-life gait speed states more about actual physical activity and physical performance behavior in everyday life.

In-laboratory and daily-life gait speed measures are distinct and robust constructs over 12 months, implying that gait speed represents a robust personal feature in a population of high-functioning adults aged 61 to 70 years. Future research should focus on the use of the combination of both measures in clinically relevant populations to investigate the potential added value in predicting health outcomes by gaining insights into actual daily-life physical behavior.

Normality of gait speed measures within the different intervention groups at different time points was not always present. Homogeneity of variances and covariances was present in all gait speed measures. The research and manuscript are in compliance with ethical standards.

All participants signed written informed consent. The funding agency had no role in the design, execution, analysis and interpretation of data, or writing of the study. Concept and design: A. Rojer, A. Coni, S. Mellone, J. Van Ancum, B. Vereijken, J. Helbostad, K.

Taraldsen, A. Mikolaizak, C. Becker, K. Aminiam, M. Trappenburg, C. Meskers, A. Maier, and M. Drafting of this manuscript: A.

Coni, M. Critical revision of the article for important intellectual content: A. Final approval of the article: A. Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy of integrity of any part of the work are appropriately investigated and resolved: A.

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Advanced Search. Skip Nav Destination Close navigation menu Article navigation. Volume 67, Issue 6. Statement of Ethics. Conflict of Interest Statement. Funding Sources. Author Contributions. Article Navigation. Research Articles March 22 Robustness of In-Laboratory and Daily-Life Gait Speed Measures over One Year in High Functioning to Year-Old Adults Subject Area: Geriatrics and Gerontology.

Rojer ; Anna G. As you indicated in Methods, "The individuals selected from ELSA with wealth data do not have mortality data available, simplifying the model from the joint model used above for mice.

Also, some narrative on the sensitivity of results to a different choice of priors would be helpful, in my view. The frailty index FI is a summary health measure that is useful to predict and correlates with many adverse outcomes. Nevertheless, we are considering transitions between these binary variables, so we use the language of damage and repair.

Since the FI is the average of the binary attributes, we use the same language for changes of the FI to distinguish increases of FI damage from decreases repair.

While the FI is a summary measure of health it is not the only one, and different summary measures will provide different natural measures of damage and repair. We have tempered our language throughout to make it more clear what we have done with binary variables and what questions this raises with the connection to non-binary approaches and conceptualizing damage.

In particular we ignore nonlinearities compensatory processes, feedback, protection and do not assess overall fitness apart from the FI. We have also added a caveat paragraph in the discussion p. See also penultimate paragraph in the introduction p. We report aggregate repair or damage rates of individual binarized attributes.

Whether these correspond to organismal repair or damage conceptualized differently is an interesting question that we do not address.

Given the proven utility of the FI to predict or associate with adverse outcomes, we do expect that aggregate repair resilience of individual binarized attributes is associated with but not the same as improved health at the population level as assessed by other health measures — and similarly with damage.

To be clear, we start with binarized variables a mechanical definition and analyze aging in that context. We obtain results that capture biological processes of aging, but through the lens of the binarized variables. We are not asserting that the biological processes are binary, but simply that binary variables can be used to study aging.

Given that much of medicine uses binary variables in diagnosis and treatment , and that much aging data is only binary from e. self-report data we feel that this is a useful and promising approach.

We have clarified these points in the text see e. In the methods p. Transitions of the binarized variables could correspond to small changes of underlying continuous processes, which also raises the question of measurement error resulting from small changes in the underlying biological state.

While we cannot avoid measurement error, we do not feel that it causes our key results. We have two reasons. The first is that we do not expect age-dependence in measurement error, so we do not feel that the age-dependence we observe for damage and repair are due to measurement error.

Second, we have performed a sensitivity analysis by removing potentially erroneous damage and repair events. For adjoining and isolated damage and repair events characterized by a sequence of variable states {0,0,1,0,0} or {1,1,0,1,1} i. With these isolated events removed, we see little change in the time-dependence of the repair and damage rates vs age and the time-scales of resilience and robustness when compared to our original results.

We have added Figure 5 —figure supplements 3 and 4 and Section 5 in the methods describing this approach. We have also added discussion of measurement errors in the discussion p. We also note that measurement error for mice has been assessed previously, and is small Feridooni et al.

This is a good question that we have addressed in our revised manuscript. We have considered all the deficits in the mouse frailty index to determine whether there is evidence that they can repair, either spontaneously through intrinsic repair processes or extrinsically by interventions such as drug treatment or lifestyle changes e.

exercise, caloric restriction, drug treatment etc. Interestingly, we found that virtually all the deficits in the frailty index can potentially reverse, especially in response to an intervention.

We have created Supplementary File 1 with references to support the concept that almost all deficits in the murine frailty index can repair either on their own or in response to interventions, including many interventions that are used in aging research.

We have added a new paragraph that discusses this to our revised manuscript p. We have also listed all health attributes used in this study in the methods p. Despite ubiquitous repair, not all deficits repair equally.

We have included Figure 5 —figure supplement 4 showing the repair counts for each deficit in the 3 mouse datasets.

This shows that some of these deficits that are rarely repaired may also be the result of measurement error, but as above, this small amount error does not effect the results due to the rarity of repair for these deficits.

A broader question is how our results depend on the underlying binarization thresholds of individual variables.

We have not explored that question here and cannot for the majority of our variables that are only measured as binary or ordinal values , rather we have used the binarized attributes as previously published.

While we do not expect that they will drastically change our aggregate results, we do expect that detailed transition rates of individual health attributes will depend on the binarization thresholds.

Previous work on binarization thresholds of the FI has shown weak dependence of predictive power on small changes of the thresholds Stubbings, G. and Rutenberg, A. Informative frailty indices from binarized biomarkers.

Biogerontology 21, — This is an interesting question for future study in the context of robustness and resilience. As discussed in the paper p. The mouse study was performed without replacement and studied with a joint-model to capture survivor effects.

The human study contained dropout and replacement, but without knowledge of mortality so the joint survival model was not used for humans. We did not model drop-out effects in the human study.

We have added a paragraph on potential population biases in the discussion p. All mouse deficits are demonstrably reversible see our new Supplementary File 1.

Measurement error is an understudied effect in aging research; it is not typically assessed or reported. Effects of age or intervention should not be affected by such measurement errors, and these effects make up our results.

The results are shown in Figure 5 —figure supplements 3 and 4, and do not affect our qualitative conclusions. We have improved the wording.

We were contrasting natural processes vs applied stressors. This approximation is implemented for computational convenience so that we can use Poisson statistics despite having non-zero timesteps. While this approximation is common in the modelling literature, it is uncontrolled.

Systematic effects of this approximation do not appear to be large, however, since the average model damage and repair rates lines in Figure 2 are close to the measured rates points in Figure 2 — and the individual distributions Figure 2 supplement 1 are close too.

We see no strong effects compare with Figure 4. For the mouse studies there was no replacement after mortality. Our analysis was with a joint model that modelled both health and mortality, so any survivor effect is not a bias but rather is the result of aging.

Furthermore, we did not have human mortality data so we could not treat survivor bias effects. Studying the selection effects themselves due to mortality or due to selection bias would be interesting, but beyond the scope of this study.

Modelling with respect to time to death rather than chronological age would also be interesting. Such a study would be limited to individuals who die, and so would exclude all of the human data we used — where we had no mortality information. The Github includes package information.

This has also been added to the manuscript p. A version update in pandas resulted in warnings. We have fixed these for the latest version of pandas. We have described in the text and figure captions the statistical tests done.

The first example "seen in every dataset" is addressed p. The second example "strongly reduced" is quantitatively addressed in Figure 3 —figure supplement 1. We use strongly here to summarize that the credible intervals of exercise effect in panel e exclude zero effect. We agree; we have cleared up language regarding wealth to emphasize it is not an intervention.

We have fixed this; in our results we also observe these sex effects in the FI. We have added the two references, and have listed all of the mouse and human items in the methods. All variables are now listed in the methods. All of our human variables are binary with values 0 or 1. We have clarified this section p.

To keep the FI values comparable between studies, we have used the same [0, 0. This means that for attributes with values [0, 0. For human data, all attributes are binarized and on the same [0, 1] scale with steps of size 1.

The points are binned averages, which are useful as guides to the eye. The lines are from our model. The error bars on the points and the variability of the lines indicates uncertainties. As humans enter the ELSA study at ages 50 and 70 there are large uncertainties.

As such, repair rates can be above damage rates per variable even when the total damage rate summed over all variables exceeds the total repair rate. This can occur when most variables are undamaged. We have emphasized this at the end of the first section of the results.

The second derivatives of the human age repair rate are small and are consistent with zero. The lines in Figure 2d should be compared with the lines in Figure 3e. See also detailed point 22 from reviewer 3 While we have tried to correct for interval censoring, the available methods only makes the survival curves self-consistent — it does not impose a model for short measurement intervals that are not observed.

The sharp drop of the survival curves reflect the absence of measurements at shorter measurement intervals. As such, the survival curves after the sharp drops are more reliable — but also comparisons in Figure 5 between intervention and control, between male and female, or in Figure 5 -- supplemental Figures1 and 2 between different health attributes.

We have labeled the axes with the plain language interpretation. Yes, for mice most damaged deficits approx.

See new Supplementary file 1 on repairability of mouse deficits. All deficits are evaluated with respect to standard criteria. For example, for whiskers the score is 0 if all whiskers are present, 0. We have added follow-up information in the methods p.

We have added discussion in the methods p. We have chosen standard weak priors. Changing weak priors does affect the quantitative results, but weakly, and does not change the qualitative results.

Any model or analysis pipeline has many such assumptions and hyperparameters; changing any of them will have similar effects. One can think of choice of weak priors as a choice of hyperparameter.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. This article is distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use and redistribution provided that the original author and source are credited.

Article citation count generated by polling the highest count across the following sources: Crossref , PubMed Central , Scopus. Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear.

In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity.

Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive.

We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations.

Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations.

Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations.

This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

The study of protein interactions in living organisms is fundamental for understanding biological processes and central metabolic pathways.

Yet, our knowledge of the bacterial interactome remains limited. Here, we combined gene deletion mutant analysis with deep-learning protein folding using AlphaFold2 to predict the core bacterial essential interactome. We predicted and modeled interactions between essential proteins in bacteria and generated high-accuracy models.

Our analysis reveals previously unknown details about the assembly mechanisms of these complexes, highlighting the importance of specific structural features in their stability and function.

Our work provides a framework for predicting the essential interactomes of bacteria and highlight the potential of deep-learning algorithms in advancing our understanding of the complex biology of living organisms.

Also, the results presented here offer a promising approach to identify novel antibiotic targets. The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure.

Although experimental data suggest that K V 1. In female cells, which have larger K V 2. In summary, we present a new model framework to investigate the potential sex-specific impact of antihypertensive drugs.

Share this article Doi. Cite this article Spencer Farrell Alice E Kane Elise Bisset Susan E Howlett Andrew D Rutenberg Measurements of damage and repair of binary health attributes in aging mice and humans reveal that robustness and resilience decrease with age, operate over broad timescales, and are affected differently by interventions.

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Within each cell, functions are maintained by metabolic networks and cytoplasmic molecular networks, and in the nucleus, transcriptional networks are modulating cellular function Gómez-Romero et al.

Borrowing from the mathematical theory of networks, we propose that key properties determining the robustness and resilience of biological systems at any organizational level are redundancy, diversity, and connectivity see Fig. Below we provide definitions and some examples of the relationship between these network properties and robustness and resilience.

Redundancy: Multiple nodes in a network could have the same or overlapping functions. If one or more nodes lose function, others can compensate. Similarly, there could be multiple routes of communication among nodes that confer the same functionality to a network.

Redundancy is widely observed in developmental biology, where essential developmental events are often under the control of many genes that have similar or overlapping functions, and the expression of one gene compensates for the failure of another, up to a certain point.

Redundancy is often used to explain how embryos tolerate developmental errors to result in the successful development of canalized body plans and morphogenesis Lachowiec et al. Genetic knockout studies demonstrate the redundancy of many different molecular pathways Salanga and Salanga Similarly, redundancy of neuroendocrine and genetic mechanisms regulating food intake are characteristics of a system regulating energy balance homeostasis Schwarz et al.

Lastly, food webs with overlapping ecological niches at different trophic levels are considered to confer stability to the system Sanders et al.

Connectivity: We broadly define connectivity as the extent to which nodes communicate with each other, or specifically, the number and types of connections edges linking nodes in a network.

Connectivity is a universal property of networks, but the specific connectivity depends on the structure of the network and mechanisms of communication and interaction. Networks can be described as distributed, decentralized, or centralized, each having different patterns of connectivity.

Scale-free connectivity patterns are more likely to occur in biological systems than in informational or other technological systems Broido and Clauset , but the idea of universal scale-free network connectivity remains slightly contentious and requires more development Holme Connectivity plays a critical role in determining the robustness and resilience of a network.

For example, distributed networks with high levels of edges connecting nodes confer stability, as demonstrated in the stability and persistence of metapopulations linked with migration Hopf et al.

However, they are also resilient—they can bend in response to external forces, while enabling them to still maintain cohesion and function Davidson System feedback i. In the context of biological networks, feedback mechanisms are encoded in connectivity.

Feedbacks in a network allow upstream nodes to send out signals to downstream nodes in response to signals they receive from the downstream nodes. A network with feedback connections will sense the state it is in, compare the current state to a setpoint or desired state, and then adjust its output to meet the desired state.

In the scenario where the original set state cannot be met, a network with the appropriate connectivity could activate different feedbacks to break old connections, make new connections to establish a new stable state. Feedback mechanisms allow a network to correct or repair nodes and links that are perturbed or become dysfunctional under certain conditions.

Common examples include negative feedbacks in predator-prey systems that result in population oscillations Li et al. Diversity: Diversity within a network can be regarded as the number, variations, and complexity of nodes of differential identities or functions.

For example, genetic variations or differential gene expression states in microbial populations allow for the survival of resistant and persistent cells that could revive the entire population upon the termination of antibiotic treatment. High viral mutation rates create variants that escape host immune systems, resulting in robust viral infections Drake ; Fitzsimmons et al.

Genetic recombination and non-genetic memory histone modifications, DNA methylation, and prion-based inheritance mechanisms are critical for adaptation to unexpected environment changes. They provide the molecular ingredients for a heritable response, fixing these changes in phenotype within a population Payne and Wagner Animals in unpredictable or highly variable environments produce eggs of various sizes or offspring with diverse phenotypes or genotypes so that at least some of the offspring are suited for the environment bet-hedging; Olofsson et al.

Communities with more diverse species composition and larger population sizes are more stable and resistant to invasive species than those with smaller sizes Hopf et al. Schematic of the properties relating to robustness and resilience of biological systems based on a network science framework.

A In this model, robustness and resilience are emergent properties blue circles of the dynamic workings of networks that have redundancy, diversity, and connectivity, which includes functional feedbacks and lines of communication among nodes. B Examples of networks that represent redundant, connected, and diverse topologies are shown.

By defining systems using this framework, biologists can use unifying experimental, mathematical, computational, and engineering approaches to understand how systems interact across levels of biological organization and respond to perturbations.

Organisms have multiple pathways to defend themselves against foreign chemicals. These multiple pathways exist in some generalized form across all domains of life. These systems are often co-regulated, forming integrated networks of genes and pathways as orchestrated defenses against toxic chemicals Goldstone et al.

Many of these defending enzymes exhibit tandem duplication—that is, rather than just one copy at a genomic locus, there are many similar copies. This property, of multiple copies of extremely similar proteins collocated at a genomic locus, with duplicated regulatory regions in the case of eukaryotes, allows an organism to be resilient to both genomic insult point mutations and to slightly changing chemical environments.

These molecular duplications are found also in other types of proteins, providing molecular resilience for a robust organism.

Prominent examples include the rise of insecticide resistance in mosquitoes due to the resilience of selected individuals with duplicated insecticide-metabolizing enzymes Milesi et al. Even at the cellular level, certain types of human cancers survive targeted chemotherapies by using an uneven distribution of extrachromosomal circular plasmids with duplicated genes critical for cellular survival Turner et al.

Each level of biological organization is conceptualized as a network consisting of nodes and edges, with the emergent collective behavior of the network as a node for the network of the next higher level of organization. With this framework, we can ask interesting questions such as how robustness and resilience are related across scales; i.

One important hypothesis that can be tested is whether resilience at lower levels of organization contributes to increasing robustness at higher spatial and biological scales.

For example, ecosystem robustness may be maintained when some populations thrive while others decline during an environment change.

Thus the output, e. While a network with appropriate levels of redundancy, diversity and connectivity could confer robustness and resilience under set conditions, these networks must also be able to adjust under fluctuating and changing environments and evolve over time.

Here, we broadly define evolvability as the ability of the system to change functions in response to significant perturbations, either by maintaining the original stable state but with enhanced stability, or by moving to a new stable state with changed properties.

This concept is commonly referred to as physiological acclimation, phenotypic plasticity, or evolutionary adaptation depending on the level of biological organization. For an example of how robustness, resilience and evolvability play out in metabolic networks in living cells, see Fig.

Cellular metabolic network of Escherichia coli illustrating the characteristics of essential and nonessential metabolites obtained from a combined gene knock-out, computational modeling, and physiological analysis adapted from Kim et al.

Evolvability can both contribute to and result from robustness and resilience under dynamic conditions. Variation in ecological niches can also promote the evolution of organismal specialization Cordeiro et al. Organismal specialization can involve a gain or loss of a response to particular environmental conditions, depending on the dynamism of the environmental stressor e.

The frequency, magnitude and type of environmental changes experienced by a lineage contribute to the evolution of robustness-supporting networks. However, ecological, physiological, or evolutionary constraints may limit a system's response during exposure to extreme conditions that are significantly different than those previously encountered Dutta et al.

Robustness, resilience, and evolvability of metabolic networks makes possible the maintenance of cellular functions in the face of different internal and environmental perturbations.

Robustness in metabolic networks emerges from at least two fundamental properties: The first derives from the kinetic properties of the individual enzymes of the network in conjunction with the steady state-pool sizes of the set of metabolites the enzymes are operating upon.

Pool sizes tend to hover at the K m value of the enzyme, which is the linear portion of the saturation behavior of the enzyme, such that the rate of the enzyme changes maximally in response to fluctuations in pool size. This even applies to metabolite pools that have extremely high rates of turnover due to high rates of metabolic flux through the pathway.

Overall, this situation results a robust maintenance of metabolic pool sizes throughout the network occurring in shorter time domains e. Resilience, likewise, has evolved though the properties contributing to robustness mentioned a moment ago, plus a myriad of homeostatic mechanisms modulating enzyme abundance and allosteric feedback mechanisms adjusting enzyme activities according to changing conditions.

These are especially valuable for adjusting to persistent stressors and perturbations, which last for hours or longer. Evolvability is apparent in metabolic networks as observed in long-term natural and laboratory experiments that are revealing adaptive genetic changes fixed in populations that have transitioned to new environmental conditions Baez and Shiloach ; La Rosa et al.

The description of these networks has been made possible by the development of computational modeling approaches and the integration of large datasets. For example, the field of metabolomics has hybridized advanced analytical biochemistry, genomics, and mathematical modeling. With advances in large-scale experimental metabolic analysis, it is possible to trace hundreds of metabolites simultaneously in a single experiment and, thus, it is now becoming possible to quantitatively evaluate fluctuations in metabolite concentrations for key metabolites across entire metabolic networks Orth et al.

Developments in genomics and computational modeling have led to a renaissance in the understanding of metabolism, leading to new understandings of metabolic system resilience and robustness.

Similar considerations apply to network models that maximize biomass production Braddrick et al. Some of the mathematical formalism for this linear programming of simultaneous reactions, network analysis shares features in common with biological networks at different scales of time and space.

For example, mathematical descriptions of low apparent HIV viral titers with high viral turnover rates are described in the same form as findings that metabolites present in cells at very low concentrations often correspond to pathways that have the highest flux traffic through them Xiong et al.

In both cases, low steady state levels reflect high turnover due to high rates of production matched by high rates of consumption. No doubt ecological and population dynamic process have parallel dynamical features.

This illustrates how entirely different biological processes, studied using very different experimental techniques, and by scientists in different disciplines can find common ground in describing and integrating different phenomena.

Linking the changes that promote robustness or resilience in a particular environment to a single gene or small set of genes or a small set of organisms may artificially limit our understanding of the nature of these emerging properties.

Evolutionary history shapes responses to environmental conditions; understanding these changes in broader terms that incorporate network changes or community changes is important.

It is also important to note that phenotypic plasticity within a generation that can be transmitted to the next generation via epigenetic or non-genetic changes contribute to gain or loss of robustness in an organism Payne and Wagner Regardless of whether its origin is genetic or epigenetic, study of flexible networks that occur at different levels of organization is needed to understand generalizable strategies.

These strategies can then be modeled across scales to show how robustness or resilience at one level relates to those at another. Evolutionary biologists can help us understand how stability and resilience of systems change in response to selection different pressures or how diverse mechanisms create systems that confer stability and control.

Now is an opportune time to establish a framework that enables the modeling of complex systems across scales to understand biological robustness and resilience. Population-wide and individual behaviors at the large can be recorded remotely and analyzed in near real-time, through large-scale phenomics systems or satellite images.

Most importantly, we are developing better tools for data acquisition, analysis, and transfer that will allow us to bridge data from atomic to stellar scales. We now possess technologies to manipulate, observe, analyze and synthesize our understanding of model and non-model systems in controlled lab environments as well as in the field, even up to the global scale.

Much is now known about the mechanisms of life, including the biochemical reactions of information and energy processing within microbial cells, programs that define the development and evolution of multicellular organisms from plants to humans, and interactions among diverse life forms that contribute to ecosystem emergence and dynamics.

At the molecular scale, we can access large quantities of genomic and transcriptomic information in near real time across phenotypes, populations, species, and lineages through NGS, single-cell sequencing and RNA-seq approaches Iacono et al.

Advanced mass spectroscopic techniques provide quantitative proteomic and metabolomic analyses to address a wide range of biological questions. Cryo-electron microscopy and tomography can visualize structures of macromolecular complexes in native or near native environments with atomic resolutions.

Super-resolution and single-molecule imaging push the detection of molecules and cellular structures in live cells beyond the diffraction limit of light microscopy. We also possess incredible powers in manipulating organisms through genome editing and targeted perturbations.

At the organismal level, it is feasible to build synthetic cells and grow organoids that recapitulate essential features of life, and now even sustain mammalian development in vitro Aguilera-Castrejon et al.

At the population level, the most advanced tracking technologies are able to monitor the dynamics of large populations of animals and changes in ecosystems Barnas et al. Various social media outlets offer new platforms to gather and disseminate information at the societal level.

Growing computational and mathematical power, coupled with mechanistic modeling, machine learning, and artificial intelligence algorithms, have the potential to describe systems and predicate outcomes at different scales, across different levels of biological organization molecules to ecosystems , spanning broad time scales nanoseconds, seconds, minutes, and hours , or by some metric of complexity e.

We have an abundance of in-depth data not only from model systems, but also from diverse, non-lab adapted systems.

io , these data can be used to systems and examine strategies universal to different scales. The substantial amount of historical genetic and ecological data can be integrated with current data to develop algorithms of hindcasts to forecast robustness and resilience of systems.

While there are many advances that make this paradigm shift possible at this time, there are also many barriers that need to be overcome before a wide range of scientists are able to embrace applying network theory for robustness and resilience across all biological scales. As described in more detail below, engineers, computer scientists, and biologists in different research communities lack a common language for describing the meaning of robustness or resilience across different levels of biological organization, although the field of systems biology has adapted many of the ideas of network theory for some biological systems, typically focused at the molecular, cellular, and tissue levels e.

In addition, there are many institutional and structural barriers to be overcome. For a unified theory of robustness and resilience to emerge, meaningful incentives to promote collaborative research must be implemented, and traditional divisional barriers must be bridged.

There is a lack of a common language for describing robustness or resilience across different levels of biological organization see Table 1. Developing a common language across fields provides an opportunity to identify unifying threads across biological levels and across scientific fields e.

Common terms will allow scientists to find relevant concepts and empirical data in other fields through literature searches and increase opportunities to collaborate across fields. We propose that the language of network theory see above could take a first step toward unifying how researchers from diverse fields conceptualize and communicate information about complex systems.

Another general problem when integrating information across subdisciplines in the biological sciences is the use of jargon, such that the same phenomena are studied independently, preventing the integration of these disciplines.

For example, we have amazing tools for searching primary literature that combine sources of information across diverse scientific disciplines e. As shown in Table 1 , there are terms of similar meaning related to the concepts of robustness and resilience across fields, although in each case there are specific nuances, connotations or usages that differ among terms.

Creating interdisciplinary educational programming will enhance this merging of language and terminology so that discipline-specific jargon will be eased. A process that is altered and returns to a previous state resilient may exhibit a robust response at a higher level of temporal, spatial, or organismal integration.

Measures need to be relevant both to the physical and temporal scale of perturbation and must subsequently transmit a signal associated with this perturbation to adjacent levels.

Despite access to huge sets of molecular, behavior, and population data, the current state-of-the-art techniques generally lack the ability to integrate information across length scales and time scales; how networks are defined and interactions quantified requires more development, including new technologies to measure how networks respond to perturbations across scales.

It is also unclear which experimental systems best serve as case studies in which this technology can be tested and optimized. Even when there is a desire to collaborate across fields, finding potential colleagues with similar interests and willingness to collaborate can be challenging.

Most scientific conferences are field-specific; thus, it is challenging for scientists to find opportunities to meet and discuss ideas with others in different fields. Even after finding a collaborator, there are logistical hurdles in carrying out a project such as grant administration and international access to sensitive data.

In addition, there are institutional barriers that prevent scientists from gaining access to the physical infrastructure and tools needed to study transdisciplinary robustness and resilience across scales.

Often funding opportunities and financial incentives that promote the formation of novel transdisciplinary collaborations are limited. When inter- or transdisciplinary proposals are submitted to traditional funding mechanisms, the small pool of reviewers who have discipline-specific expertise but also appreciate the novelty of transdisciplinary collaborations could limit the funding of such proposals.

Robustness is a concept that crosses many levels of biological organization; a fuller understanding of this characteristic requires the integration of many different disciplines so that a common language emerges. A multidisciplinary team approach would eliminate the inherent scale and model bias, allowing for broader perspectives into the rules of life.

We therefore need platforms for researchers who are interested in understanding robustness and resilience from biophysics, mathematics, molecular biology, physiology, population genetics, and ecosystem biology, etc. who do not otherwise interact to brainstorm ideas.

This could be done in workshops resulting in new collaborations and possible research coordination networks. Funding mechanisms that promote the formation of new multidisciplinary research teams will also broaden participation of researchers from different backgrounds and institutional types e.

Funding agencies such as the National Science Foundation have acknowledged that they can play a major role in promoting cross-disciplinary training of a new generation of scientists by changing funding schemes, paradigms and training programs.

These changes will promote cross-disciplinary training of a new generation of scientists who have the skills to discover and describe the important overarching questions of life on Earth.

For example, we might harness existing big data and integrate insights from available models of community and population dynamics that are successfully used for metabolism, viruses, microbiomes, and ecosystems Cantor et al.

We can also leverage our understanding of the evolution to advance our understanding of robust and resilient systems. With large-scale, multidimensional networks, comparative analysis of network interactions over time will allow the role of evolutionary pressure to be examined in biological robustness.

This analysis would move beyond our current reliance on gene or protein networks, to incorporate communications between nearest neighbors intra- and inter-habitat and entire communities over time. Then specific nodes or network strategies to overcome challenges and promote robustness that recur over time could then be used to re-engineer robust and scalable networks from gene to community levels.

To overcome technological barriers, we need to develop suitable metrics and tools to measure robustness and resilience or lack thereof across space and time scales. Ideally such a tool would measure or provide a measure of the response of a system at one scale and seamlessly measure the propagation of the response across multiple scales.

For example, noise in the production of RNA during the activation of gene expression can contribute to cellular heterogeneity, resulting in a robust response to perturbations across a population of cells.

It is unclear how heterogeneity that is generated at the cellular level affects higher-order processes. Real-time readouts would enable us to capture events that happen throughout the life of the organism.

One method of obtaining this type of data would be using optical methods, requiring the development of stable reporters that are not susceptible to bleaching or degradation biases. Optical or other readouts of behavior, neural status, and molecular reporters could then be integrated across scales to provide networks in context.

Eventually, to support the development of full molecular networks in context, real-time molecular sampling of a freely-responding super -organism will be necessary. At the most ambitious level, advanced technologies would be deployed to generate and analyze network data in real time.

These technologies might include real-time analysis of transcriptomes, proteomes, metabolomes, neural readouts, and behavior in an environmental context.

Not all of these technologies are ready, but many are very close, enhanced by the current growth in computational power data analytics , real-time sequencing, and computer vision. Assuming no limitations, we could have all the experimental data possible to build dynamic networks.

This will require integrated hypotheses that probe networks and additional strategies to address evolutionary selection, particularly the survival of an individual and a population. To move toward this integrative network-based analysis of robustness, in the next few years we would need to implement model test systems across multiple life scales with scientific teams to develop testable hypotheses that validated network development.

understand In addition to the development of new sensing and measurement technologies, we need to develop new data analytics and computational methods to transform current data streams into multidimensional networks. With these developments, we could not only test network robustness but analyze redundancy.

Exploring redundancy and determining essential nodes for stability and robustness of networks at multiple levels would provide essential insight into robustness that has been inaccessible due to the lack of global monitoring systems capable of collecting data at sufficient scales.

Infrastructure will also need to be created to host these databases, enable user contributions and make databases searchable and available to the public, much like NCBI databases. In order to realize a reintegration of biology and generate the workforce needed to create the technologies needed to advance network-level study of biological systems, we need to reform science and math education.

Critically, science education from K through the post-doctoral level should be designed to foster problem-based scientific thinking not siloed by discipline. Integration of knowledge from different scientific disciplines needs to become a common way of thinking for the next generation of scientists and innovators.

In addition, curricula should include requirements that emphasize analytical reasoning and quantitative skills. Network theory and computer science courses could be included as standard biological science curricula in addition to algebra, calculus, and statistics.

It is important to impress upon students how mathematical tools applied in modeling and engineering fields can be employed to derive potential solutions to important societal problems NRC ; see Box 3.

Stepping quantitatively toward robustness and resilience through mathematical modeling. These equations provide a foundation to start thinking quantitatively about mechanisms of robustness or resilience, where systems with potentially multiple changing inputs achieve states or outputs that are stable over time.

Stability over time implies a balance of positive and negative terms, deposit and withdrawn in the case of our bank account, or growth and stasis for living cells. To overcome logistical barriers to advancing research on robustness and resilience, it is important for both funding agencies and research institutions to facilitate and incentivize interdisciplinary interactions among scientists.

This can be best accomplished with specialized funding mechanisms that call for such interdisciplinary teams, such as the joint National Institutes of Health and National Science Foundation Ecology and Evolution of Infectious Disease mechanism, and the newly established NSF Integrative Research in Biology IntBIO and the Biology Integration Institutes mechanisms.

However, it is still a challenge for researchers to establish relationships with collaborators, especially biomathematicians and bioinformaticians with allied interests and expertise.

Within research institutions, increasing internal funding opportunities to encourage interdisciplinary collaborations, cluster hiring around interdisciplinary research themes, and encouraging young investigators to engage in collaborative research through established or new institutional interdisciplinary or transdisciplinary centers could increase research in robustness and resilience.

Studying biological systems within a unifying framework as living and interacting networks will allow us to address some of the most important biological and social questions of our time see Table 2. Understanding the underlying principles of biological robustness and resilience will allow us to model and anticipate consequences of environmental changes across scales and enable controlling of biological systems for most beneficial outcomes.

For example, it is desirable to destabilize the state of persistent neural seizures resulting from epilepsy or neurotoxin exposure, in which neural signals are persistently entrained. Similarly, we may want to model or forecast consequences of anthropogenic effects such as an oil spill and develop ways to return ecosystems to its healthy state.

Models of robustness and resilience can inform methods to stabilize or destabilize agri- and aquaculture, improving sustainability or reducing the impact of invasive species. They could also provide insight into disease development and progression, either in natural or modified systems. In a world with a rapidly changing climate, such interventions may be essential for organismal survival and to prevent a sixth extinction but will require significant ethical restraint in their applications.

Important biological and societal questions that could be addressed with a unifying understanding of the rules of robustness and resilience across scales.

Collaboration among researchers from experimental, mathematical, computational, and engineering fields will allow the application of developed models to improve the health of the ecosystem and human lives. For example, useful experimental datasets, mathematical models, and computational tools for validating and understanding behaviors of complex systems may be generated.

New software incorporating improved parameter definitions and modeling techniques could facilitate the investigation and understanding of intra- and inter-level connections of complex biological systems. Synthetic datasets with standardized format could also result from this research to allow downstream applications for other multiscale studies.

A greater understanding of the theoretical mechanisms of robust or resilient networks will also help develop better computation tools and more reliable artificial intelligence AI algorithms. By identifying essential networks and nodes that promote robustness, we can implement them to perform complex AI-driven tasks such as self-driving vehicles, rover navigation undersea, or on Mars, or exploration of oceans and moons.

Robustness and resilience theory will provide new algorithms for implementing complex tasks in constantly changing environments. Understanding the role of robustness in evolution will also enable artificial systems to learn how to rapidly navigate new and complex environmental contexts.

Finding common rules of robustness and resilience across scales in natural systems will accelerate new discoveries and progress on elucidating the rules of life on Earth, transform the way we understand biological systems and revolutionize synthetic biology.

We will begin elucidating design and engineering principles of living systems and use them to deploy stable and viable synthetic systems. As biological systems of different organization levels are interconnected across scales, we may be able to forecast how changes at one organization level affect the other levels, contributing to a holistic understanding of all biological systems.

The property of a network that describes the existence of multiple independent routes of communication among nodes or diverse nodes with unique connections and feedbacks. The ability of the system to change in response to perturbations, either maintaining the original stable state but with better stability or moving to a new stable state with changed properties.

Networks can evolve by altering routes of communication and utilization of nodes. Networks may autonomously configure, monitor, and maintain structure, depending on data acquisition and communication path use.

A circuit or loop in which the output of the system is routed back as input to become part of a chain of cause-and-effect. Often employed in systems that control network behaviors. Connections between the nodes of a network.

Also called links in graph theory. Connection points of a network. The specific character of a node depends on the nature of the network, but it is generally capable of creating, receiving, transmitting, or blocking information.

Also called vertices in graph theory. The structure and makeup of the network as a whole, a collection of interconnected nodes and edges.

The study of complex interacting systems that can be represented mathematically as sets of equations or visually as graphs. The property of a network of having multiple independent means of connecting nodes or the existence of alternative nodes that have similar connections.

The greater the redundancy of nodes and edges, the greater the availability of the network, and the less the risk of failure of the network. The ability to recover to a previous state or a new establish a new baseline after some time following an environmental perturbation.

The stability of biological outputs given diverse internal and external environmental states. This vision paper resulted from participation in the National Science Foundation Reintegration of Biology initiative.

We thank the anonymous reviewers for helpful comments. This work was supported by funding to EJC in part by NSF-DEB ; JVG in part by the Boston University Superfund Center NIH P42ES , and the NHGRI U24HG Based on a Jumpstart-Reintegrating Biology Vision Paper, developed during Town Hall meetings funded by The National Science Foundation in Adger WN.

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