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. 2023 Dec 13;13(1):22140.
doi: 10.1038/s41598-023-49129-7.

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

Glen Pridham  1 , Andrew D Rutenberg  2
Affiliations

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

Glen Pridham et al. Sci Rep. .

Abstract

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.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Simulation example of a stable system, with λ<0. Initial conditions can differ from μ(t). A stable system is attracted to μ(t) (black line), but will be offset by -μage/|λ| in the steady-state. ODE solutions are superimposed for mean and variance (dotted lines are 95% interval). Fill density is proportional to probability density. Observing an ensemble at any time will yield Gaussian statistics.
Figure 2
Figure 2
(A) ELSA interaction network. Tile colour indicates interaction strength (saturation) and direction (colour) of the interaction from the y-axis variable to the x-axis variable. Inner dot colour indicates the limit of the 95% confidence interval (CI) closest to zero (more visible point indicates lower significance). Non-significant interactions have been whited-out. Diagonal has been suppressed for visualization (see dotted lines in B). The matrix is real and symmetric because the data were diagonalized by an orthogonal matrix (PCA). Variables are sorted by diagonal strength in both A. and B. (increasing rate). (B) Recovery rates in human-equivalent (h.e.) years i.e. negative eigenvalues (-λ). The smallest recovery rates determine system stability. A recovery rate of 0.025 implies 1-e-1=63% recovery after -λ-1=40 years (95% recovery after 120 years). The survival data all have similar minimum rates near 0.025, whereas the dementia data was faster (Paquid). The dotted lines are network diagonals (-Wjj); the solid lines are rates (-λj).
Figure 3
Figure 3
(A) Position relative to equilibrium vs recover rate. Most natural variables were homeostatic (near equilibrium at 0). Some (labeled) variables were observed to be far from equilibrium; variables are labelled by rank e.g. 01≡z01 has the fastest recovery (furthest left). (B) Characterization of natural variable deviations from equilibrium using Eq. (8). Observe that ELSA is the only dataset where memory may dominate the system behaviour (ratio ≲1=100), indicating that the followup period may have been too short to reach a steady-state. In both figures only mouse (SLAM) data points over age 80 weeks were used since biomarkers had a u-shaped curve over the lifespan.
Figure 4
Figure 4
Survival effects. (A) Allostasis drifts towards the risk direction, i.e. “mallostasis”. The relationship appears to be linear (lines), with strong correlations: − 0.96 (SLAM BL/6), − 0.71 (SLAM Het3), − 0.99 (Paquid), and − 0.53 (ELSA). The equilibrium dispersion provides a native scale for each variable. High risk natural variables for each dataset have been labelled by eigenvalue rank (e.g. z1≡01 has the smallest eigenvalue, z2≡02 the second smallest, etc). (B) Recovery rate (-eigenvalue), -λ, has an ambiguous relationship with survival. Smaller eigenvalues appear to be important survival dimensions (e.g. 01 for ELSA and Paquid), but the overall correlation is weak (ρ=-0.254, p=0.1). The C-index measures the relative risk for pairs of individuals based on the value of zj (C-index of 0.5 indicates no risk; C-index larger than 0.5 means small values are bad).
Figure 5
Figure 5
(A) Composite health measure of survival b≡(μ→ageTz→), stratified by quartile (ELSA). Separation is excellent, indicating a strong survival predictor. Fill is 95% confidence interval. See Supplemental Fig. S15 for the other datasets. (B) Natural variables can drive changes in observable biomarkers. The z1 mean is accumulating in the negative direction. This accumulation is mapped into observable variables with ⟨Pj1z1⟩ for indicated timepoints each separated by approximately 4 years. The drift direction is overwhelmingly unhealthy: increased disability measures (srh, eye, hear, FI.ADL and FI.IADL—high is bad), decreased physical ability scores (gait and grip), increased inflammation (crp), increased glucose, etc. The effect of the drift is concentrated in z1 but dilute across its covariates, which could make the effect of unhealthy z1 subclinical in the observed biomarkers. All variables are on standardized scale. Similar effects were observed for the other datasets (Supplemental Fig. S13).
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