Dynamical Network Stability Analysis of Multiple Biological Ages Provides a Framework for Understanding the Aging Process.

Widespread interest in nondestructive biomarkers of aging has led to a multitude of biological ages that each proffers a "true" health-adjusted individual age. Although each measure provides salient information on the aging process, they are each univariate, in contrast to the "hallmark" and "pillar" theories of aging, which are explicitly multidimensional, multicausal, and multiscale. Fortunately, multiple biological ages can be systematically combined into a multidimensional network representation. The interaction network between these biological ages permits analysis of the multidimensional effects of aging, as well as quantification of causal influences during both natural aging and, potentially, after anti-aging intervention. The behavior of the system as a whole can then be explored using dynamical network stability analysis, which identifies new, efficient biomarkers that quantify long-term resilience scores on the timescale between measurements (years). We demonstrate this approach using a set of 8 biological ages from the longitudinal Swedish Adoption/Twin Study of Aging (SATSA). After extracting an interaction network between these biological ages, we observed that physiological age, a proxy for cardiometabolic health, serves as a central node in the network, implicating it as a key vulnerability for slow, age-related decline. We furthermore show that while the system as a whole is stable, there is a weakly stable direction along which recovery is slow-on the timescale of a human lifespan. This slow direction provides an aging biomarker, which correlates strongly with chronological age and predicts longitudinal decline in health-suggesting that it estimates an important driver of age-related changes.

Network dynamical stability analysis reveals key "mallostatic" natural variables that erode homeostasis and drive age-related decline of health.

Using longitudinal study data, we dynamically model how aging affects homeostasis in both mice and humans. We operationalize homeostasis as a multivariate mean-reverting stochastic process. We hypothesize that biomarkers have stable equilibrium values, but that deviations from equilibrium of each biomarker affects other biomarkers through an interaction network-this precludes univariate analysis. We therefore looked for age-related changes to homeostasis using dynamic network stability analysis, which transforms observed biomarker data into independent "natural" variables and determines their associated recovery rates. Most natural variables remained near equilibrium and were essentially constant in time. A small number of natural variables were unable to equilibrate due to a gradual drift with age in their homeostatic equilibrium, i.e. allostasis. This drift caused them to accumulate over the lifespan course and makes them natural aging variables. Their rate of accumulation was correlated with risk of adverse outcomes: death or dementia onset. We call this tendency for aging organisms to drift towards an equilibrium position of ever-worsening health "mallostasis". We demonstrate that the effects of mallostasis on observed biomarkers are spread out through the interaction network. This could provide a redundancy mechanism to preserve functioning until multi-system dysfunction emerges at advanced ages.

Network dynamical stability analysis reveals key "mallostatic" natural variables that erode homeostasis and drive age-related decline of health.

Using longitudinal study data, we dynamically model how aging affects homeostasis in both mice and humans. We operationalize homeostasis as a multivariate mean-reverting stochastic process. We hypothesize that biomarkers have stable equilibrium values, but that deviations from equilibrium of each biomarker affects other biomarkers through an interaction network - this precludes univariate analysis. We therefore looked for age-related changes to homeostasis using dynamic network stability analysis, which transforms observed biomarker data into independent "natural" variables and determines their associated recovery rates. Most natural variables remained near equilibrium and were essentially constant in time. A small number of natural variables were unable to equilibrate due to a gradual drift with age in their homeostatic equilibrium, i.e. allostasis. This drift caused them to accumulate over the lifespan course and makes them natural aging variables. Their rate of accumulation was correlated with risk of adverse outcomes: death or dementia onset. We call this tendency for aging organisms to drift towards an equilibrium position of ever-worsening health "mallostasis". We demonstrate that the effects of mallostasis on observed biomarkers are spread out through the interaction network. This could provide a redundancy mechanism to preserve functioning until multi-system dysfunction emerges at advanced ages.

Modelling lifespan reduction in an exogenous damage model of generic disease.

We model the effects of disease and other exogenous damage during human aging. Even when the exogenous damage is repaired at the end of acute disease, propagated secondary damage remains. We consider both short-term mortality effects due to (acute) exogenous damage and long-term mortality effects due to propagated damage within the context of a generic network model (GNM) of individual aging that simulates a U.S. population. Across a wide range of disease durations and severities we find that while excess short-term mortality is highest for the oldest individuals, the long-term years of life lost are highest for the youngest individuals. These appear to be universal effects of human disease. We support this conclusion with a phenomenological model coupling damage and mortality. Our results are consistent with previous lifetime mortality studies of atom bomb survivors and post-recovery health studies of COVID-19. We suggest that short-term health impact studies could complement lifetime mortality studies to better characterize the lifetime impacts of disease on both individuals and populations.

Torsion and bistability of double-twist elastomers.

We investigate the elastic properties of anisotropic elastomers with a double-twist director field, which is a model for collagen fibrils or blue phases. We observe a significant Poynting-like effect, coupling torsion (fibril twist) and extension. For freely-rotating boundary conditions, we identify a structural bistability at very small extensional strains which undergoes a saddle-node bifurcation at a critical strain - at approximately 1% strain for a parameterization appropriate for collagen fibrils. With clamped boundary conditions appropriate for many experimental setups, the bifurcation is not present. We expect significant helical shape effects when fixed torsion does not equal the equilibrium torsion of freely-rotating boundary conditions, due to residual torques.

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.

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 transition rates from repeated observations of binary health attributes in mice and humans to explore robustness and resilience, which respectively represent resisting or recovering from damage. We assess differences in robustness and resilience using changes in damage rates and repair rates of binary health attributes. We find a conserved decline with age in robustness and resilience in mice and humans, implying that both contribute to worsening aging health - as assessed by the frailty index (FI). A decline in robustness, however, has a greater effect than a decline in resilience on the accelerated increase of the FI 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 toward 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. We have also explored the correlations with household wealth for humans. We find that these interventions and factors affect both damage and repair rates, and hence robustness and resilience, in age and sex-dependent manners.

Interpretable machine learning for high-dimensional trajectories of aging health.

We have built a computational model for individual aging trajectories of health and survival, which contains physical, functional, and biological variables, and is conditioned on demographic, lifestyle, and medical background information. We combine techniques of modern machine learning with an interpretable interaction network, where health variables are coupled by explicit pair-wise interactions within a stochastic dynamical system. Our dynamic joint interpretable network (DJIN) model is scalable to large longitudinal data sets, is predictive of individual high-dimensional health trajectories and survival from baseline health states, and infers an interpretable network of directed interactions between the health variables. The network identifies plausible physiological connections between health variables as well as clusters of strongly connected health variables. We use English Longitudinal Study of Aging (ELSA) data to train our model and show that it performs better than multiple dedicated linear models for health outcomes and survival. We compare our model with flexible lower-dimensional latent-space models to explore the dimensionality required to accurately model aging health outcomes. Our DJIN model can be used to generate synthetic individuals that age realistically, to impute missing data, and to simulate future aging outcomes given arbitrary initial health states.

D-band strain underestimates fibril strain for twisted collagen fibrils at low strains.

Collagen fibrils are the main structural component of load-bearing tissues such as tendons, ligaments, skin, the cornea of the eye, and the heart. The D-band of collagen fibrils is an axial periodic density modulation that can be easily characterized by tissue-level X-ray scattering. During mechanical testing, D-band strain is often used as a proxy for fibril strain. However, this approach ignores the coupling between strain and molecular tilt. We examine the validity of this approximation using an elastomeric collagen fibril model that includes both the D-band and a molecular tilt field. In the low strain regime, we show that the D-band strain substantially underestimates fibril strain for strongly twisted collagen fibrils - such as fibrils from skin or corneal tissue.

Non-Fickian single-file pore transport.

Single-file diffusion exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for short porelike channels using a symmetric exclusion process with fully stochastic dynamics. We find that for shorter channels, a non-Fickian regime emerges for slow binding kinetics. In this regime the average flux 〈Φ〉∼1/L^{3}, where L is the channel length in units of the particle size. We find that a two-state model describes this behavior well for sufficiently slow binding rates, where the binding rates determine the switching time between high-flux bursts of directed transport and low-flux leaky states. Each high-flux burst is Fickian with 〈Φ〉∼1/L. Longer systems are more often in a low-flux state, leading to the non-Fickian behavior.

Chiral phase-coexistence in compressed double-twist elastomers.

We adapt the theory of anisotropic rubber elasticity to model cross-linked double-twist liquid crystal cylinders such as exhibited in biological systems. In mechanical extension we recover strain-straightening, but with an exact expression in the small twist-angle limit. In compression, we observe coexistence between high and low twist phases. Coexistence begins at small compressive strains and is robustly observed for any anisotropic cross-links and for general double-twist functions - but disappears at large twist angles. Within the coexistence region, significant compression of double-twist cylinders is allowed at constant stress. Our results are qualitatively consistent with previous observations of swollen or compressed collagen fibrils, indicating that this phenomenon may be readily accessible experimentally.

The degree of frailty as a translational measure of health in aging.

Frailty is a multiply determined, age-related state of increased risk for adverse health outcomes. We review how the degree of frailty conditions the development of late-life diseases and modifies their expression. The risks for frailty range from subcellular damage to social determinants. These risks are often synergistic-circumstances that favor damage also make repair less likely. We explore how age-related damage and decline in repair result in cellular and molecular deficits that scale up to tissue, organ and system levels, where they are jointly expressed as frailty. The degree of frailty can help to explain the distinction between carrying damage and expressing its usual clinical manifestations. Studying people-and animals-who live with frailty, including them in clinical trials and measuring the impact of the degree of frailty are ways to better understand the diseases of old age and to establish best practices for the care of older adults.

Non-equilibrium growth and twist of cross-linked collagen fibrils.

The lysyl oxidase (LOX) enzyme that catalyses cross-link formation during the assembly of collagen fibrils in vivo is too large to diffuse within assembled fibrils, and so is incompatible with a fully equilibrium mechanism for fibril formation. We propose that enzymatic cross-links are formed at the fibril surface during the growth of collagen fibrils; as a consequence no significant reorientation of previously cross-linked collagen molecules occurs inside collagen fibrils during fibril growth in vivo. By imposing local equilibrium only at the fibril surface, we develop a coarse-grained quantitative model of in vivo fibril structure that incorporates a double-twist orientation of collagen molecules and a periodic D-band density modulation along the fibril axis. Radial growth is controlled by the concentration of available collagen molecules outside the fibril. In contrast with earlier equilibrium models of fibril structure, we find that all fibrils can exhibit a core-shell structure that is controlled only by the fibril radius. At small radii a core is developed with a linear double-twist structure as a function of radius. Within the core the double-twist structure is largely independent of the D-band. Within the shell at larger radii, the structure approaches a constant twist configuration that is strongly coupled with the D-band. We suggest a stable radius control mechanism that corneal fibrils can exploit near the edge of the linear core regime; while larger tendon fibrils use a cruder version of growth control that does not select a preferred radius.

Bayesian counting of photobleaching steps with physical priors.

Counting fluorescence photobleaching steps is commonly used to infer the number n0 of monomeric units of individual oligomeric protein complexes or misfolded protein aggregates. We present a principled Bayesian approach for counting that incorporates the statistics of photobleaching. Our physics-based prior leads to a simple and efficient numerical scheme for maximum a posteriori probability (MAP) estimates of the initial fluorophore number n^0. Our focus here is on using a calibration to precisely estimate n^0, though our approach can also be used to calibrate the photophysics. Imaging noise increases with n^0, while bias is often introduced by temporal averaging. We examine the effects of fluorophore number n^0 of the oligomer or aggregate, lifetime photon yield µeff of an individual fluorophore, and exposure time Δt of each image frame in a time-lapse experiment. We find that, in comparison with standard ratiometric approaches or with a "change-point" step-counting algorithm, our MAP approach is both more precise and less biased.

Anomalously slow transport in single-file diffusion with slow binding kinetics.

We computationally study the effects of binding kinetics to the channel wall, leading to transient immobility, on the diffusive transport of particles within narrow channels, that exhibit single-file diffusion (SFD). We find that slow binding kinetics leads to an anomalously slow diffusive transport. Remarkably, the scaled diffusivity D[over ̂] characterizing transport exhibits scaling collapse with respect to the occupation fraction p of sites along the channel. We present a simple "cage-physics" picture that captures the characteristic occupation fraction p_{scale} and the asymptotic 1/p^{2} behavior for p/p_{scale}≳1. We confirm that subdiffusive behavior of tracer particles is controlled by the same D[over ̂] as particle transport.

Polymorphism of stable collagen fibrils.

Collagen fibrils are versatile self-assembled structures that provide mechanical integrity within mammalian tissues. The radius of collagen fibrils vary widely depending on experimental conditions in vitro or anatomical location in vivo. Here we explore the variety of thermodynamically stable fibril configurations that are available. We use a liquid crystal model of radial collagen fibril structure with a double-twist director field. Using a numerical relaxation method we show that two dimensionless parameters, the ratio of saddle-splay to twist elastic constants k24/K22 and the ratio of surface tension to chiral strength [small gamma, Greek, tilde] ≡ γ/(K22q), largely specify both the scaled fibril radius and the associated surface twist of equilibrium fibrils. We find that collagen fibrils are the stable phase with respect to the cholesteric phase only when the reduced surface tension is small, [small gamma, Greek, tilde] ⪅ 0.2. Within this stable regime, collagen fibrils can access a wide range of radii and associated surface twists. Remarkably, we find a maximal equilibrium surface twist of 0.33 rad (19°). Our results are compatible with corneal collagen fibrils, and we show how the large surface twist can explain the narrow distribution of corneal fibril radii. Conversely, we show how small surface twist is required for the thermodynamic stability of tendon fibrils in the face of considerable polydispersity of radius.

Unifying aging and frailty through complex dynamical networks.

To explore the mechanistic relationships between aging, frailty and mortality, we developed a computational model in which possible health attributes are represented by the nodes of a complex network, with the connections showing a scale-free distribution. Each node can be either damaged (i.e. a deficit) or undamaged. Damage of connected nodes facilitates local damage and makes local recovery more difficult. Our model demonstrates the known patterns of frailty and mortality without any assumption of programmed aging. It helps us to understand how the observed maximum of the frailty index (FI) might arise. The model facilitates an initial understanding of how local damage caused by random perturbations propagates through a dynamic network of interconnected nodes. Very large model populations (here, 10 million individuals followed continuously) allow us to exploit new analytic tools, including information theory, showing, for example that highly connected nodes are more informative than less connected nodes. This model permits a better understanding of factors that influence the health trajectories of individuals.

Photobleaching of randomly rotating fluorescently decorated particles.

Randomly rotating particles that have been isotropically labeled with rigidly linked fluorophores will undergo non-isotropic (patchy) photobleaching under illumination due to the dipole coupling of fluorophores with light. For a rotational diffusion rate D of the particle and a photobleaching time scale τ of the fluorophores, the dynamics of this process are characterized by the dimensionless combination Dτ. We find significant interparticle fluctuations at intermediate Dτ. These fluctuations vanish at both large and small Dτ or at small or large elapsed times t. Associated with these fluctuations between particles, we also observe transient non-monotonicities of the brightness of individual particles. These non-monotonicities can be as much as 20% of the original brightness. We show that these novel photobleach-fluctuations dominate over variability of single-fluorophore orientation when there are at least 103 fluorophores on individual particles.

Network model of human aging: Frailty limits and information measures.

Aging is associated with the accumulation of damage throughout a persons life. Individual health can be assessed by the Frailty Index (FI). The FI is calculated simply as the proportion f of accumulated age-related deficits relative to the total, leading to a theoretical maximum of f≤1. Observational studies have generally reported a much more stringent bound, with f≤f_{max}<1. The value of f_{max} in observational studies appears to be nonuniversal, but f_{max}≈0.7 is often reported. A previously developed network model of individual aging was unable to recover f_{max}<1 while retaining the other observed phenomenology of increasing f and mortality rates with age. We have developed a computationally accelerated network model that also allows us to tune the scale-free network exponent α. The network exponent α significantly affects the growth of mortality rates with age. However, we are only able to recover f_{max} by also introducing a deficit sensitivity parameter 1-q, which is equivalent to a false-negative rate q. Our value of q=0.3 is comparable to finite sensitivities of age-related deficits with respect to mortality that are often reported in the literature. In light of nonzero q, we use mutual information I to provide a nonparametric measure of the predictive value of the FI with respect to individual mortality. We find that I is only modestly degraded by q<1, and this degradation is mitigated when increasing number of deficits are included in the FI. We also find that the information spectrum, i.e., the mutual information of individual deficits versus connectivity, has an approximately power-law dependence that depends on the network exponent α. Mutual information I is therefore a useful tool for characterizing the network topology of aging populations.

αTAT1 controls longitudinal spreading of acetylation marks from open microtubules extremities.

Acetylation of the lysine 40 of α-tubulin (K40) is a post-translational modification occurring in the lumen of microtubules (MTs) and is controlled by the α-tubulin acetyl-transferase αTAT1. How αTAT1 accesses the lumen and acetylates α-tubulin there has been an open question. Here, we report that acetylation starts at open ends of MTs and progressively spreads longitudinally from there. We observed acetylation marks at the open ends of in vivo MTs re-growing after a Nocodazole block, and acetylated segments growing in length with time. Bias for MTs extremities was even more pronounced when using non-dynamic MTs extracted from HeLa cells. In contrast, K40 acetylation was mostly uniform along the length of MTs reconstituted from purified tubulin in vitro. Quantitative modelling of luminal diffusion of αTAT1 suggested that the uniform acetylation pattern observed in vitro is consistent with defects in the MT lattice providing lateral access to the lumen. Indeed, we observed that in vitro MTs are permeable to macromolecules along their shaft while cellular MTs are not. Our results demonstrate αTAT1 enters the lumen from open extremities and spreads K40 acetylation marks longitudinally along cellular MTs. This mode of tip-directed microtubule acetylation may allow for selective acetylation of subsets of microtubules.