Studying “Aging clocks, entropy, and the limits of age-reversal” ….

Following what was for me a highly insightful meeting in Dublin with Peter Fedichev I did some homework to try and better understand the main motivations, concepts and foundation of his and several other experts’ work.

I refer to my previous post following Dublin at:

https://www.dhirubhai.net/posts/pasquale-di-cesare-568878_longevitysummitdublin2023-ageingresearch-activity-7100937144352845825-JuRI?utm_source=share&utm_medium=member_desktop

and one of the recent preprints:

[1] Andrei Tarkhov et al. “Aging clocks, entropy, and the limits of age-reversal” (https://doi.org/10.1101/2022.02.06.479300)

The paper is quite technical and to be understood I think it needs to be put in the context of what several of the authors already produced, in particular regarding the theoretical and mathematical foundations developed in detail e.g. in the reference [41] of the current preprint:

[2] Dmitriy Podolskiy, PhD et al. “Critical dynamics of gene networks is a mechanism behind aging and Gompertz law” (https://doi.org/10.48550/arXiv.1502.04307)), including the references therein, in particular [54] and [55].

There are several other (published) works which are very much worth to read, describing many of the main ideas developed in the preprint, such as these which are just in my own list of preferences:

[3] Konstantin Avchaciov et al. “Unsupervised learning of aging principles from longitudinal data” (https://doi.org/10.1038/s41467-022-34051-9)

[4] Tim Pyrkov et al. “Longitudinal analysis of blood markers reveals progressive loss of resilience and predicts human lifespan limit (https://doi.org/10.1038/s41467-021-23014-1)

[5] Peter Fedichev “Hacking Aging: A Strategy to Use Big Data From Medical Studies to Extend Human Life” (https://doi.org/10.3389/fgene.2018.00483)

[6] Valeria Kogan et al. "Stability analysis of a model gene network links aging, stress resistance and negligible senescence" (https://doi.org/10.1038/srep13589)

Here I focus mainly on the preprint [1], hopefully to be peer-reviewed soon.

Two sets of human data are analyzed using the well-known PCA (Principal Component Analysis) methodology to extract aging signatures, one set consisting of (cross-sectional) DNA methylation data and one of (longitudinal) electronic medical records (EMR) providing incidence of (chronic) diseases. Both the DNAm changes and incidence of disease can define state vectors and are modeled as stochastic binary variables with a specific probability distribution (Boltzmann).

In both sets of data, the PCA analysis indicates a dominant PC1 score, explaining most of the data variance, increasing linearly with age and incidence of diseases, respectively.

Moreover, in both cases the data show similar features which are typical hallmarks of stochastic processes in complex dynamical systems close to a point of criticality, providing clues to the successive model of aging, in particular:

-??????? the variance of the dominant PC1 score increases linearly with age and incident of diseases

-??????? the PC1 score of the (longitudinal data) incidence of diseases features also a linear increase in the autocorrelation function vs. time lag, hinting to a stochastic process inclusive of a drift (in our case aging)

These are very general features of processes near what is called a “critical slow-down” region alluding to the slow dynamic of whatever variable of interest one analyzes around a point of instability and the increased time (or lower resilience) to get back to stability in response to fluctuations.

The PC1 scores were correlated with Horvath’s DNAm age clock and the total number of diseases. PC2, PC3 were also analyzed as well as a gene set enrichment on the DNAm data, showing correlations to innate immunity, cancer, mental and internal organs’ health.

An important additional clue for the successive modeling was that the binary variables of DNAm and incidence of chronic diseases show infrequent transitions (called “depolarizations”) from one state to the other.

Motivated by the insight provided by these stochastic features as evidenced in the data, the authors modeled aging as a complex regulatory network “…presuming that aging is a particular case of the dynamics of a complex system unfolding near a bifurcation or a tipping point on the boundary of a dynamic stability region...” [3].

Firstly, the approach is to conceptually partition the organism into subparts (called “functional units” or FUs) which intuitively goes not without vaguely reminding to me G. Chaitin’s notion of the mutual entropy of subparts of an organism with their information content and characteristic complexity as per his algorithmic information theory (https://doi.org/10.1142/9789814434058_0011). Interestingly, I understand his approach was to progress toward a mathematical definition of life while, quite the opposite, here the authors are trying to understand aging and finally its completion to death. The approach is of course at the core of statistical physics where one finds first the statistical distribution of relevant variables of a macroscopic object considered as a small part of a larger system yet constituted itself by a large number of particles interacting stochastically (Boltzmann, Gibbs).

Each of the FUs is so treated as a macroscopic object, subpart of a larger system, yet consisting of a large number of microscopic units, acting chaotically and treated à-la-Boltzmann with a defined probability distribution and effective temperature T.

Secondly, each of the FUs is pictured in a free energy landscape where it resides in a potential free energy well which, when high, “protects” the FU to transition (or “depolarize”) toward thermal equilibrium and remains in its metastable state of “youth” DNAm profile or not-diseased. Fluctuations tend to change the state with a probability of “activation” exponentially small and depending on an activation energy U_act and an effective temperature T, the latter related to the statistical proprieties of the noise.

The rarity of transitions, as evidenced in both sets of data, combines with the huge number of FUs to define an “aging drift” Z_t, proportional to the rate of transitions of the FUs at time t and the large total number N of FUs. Z_t evolves linearly with time and it also itself acquires the characteristics of a stochastic variable, evolving according to a well-known equation (Langevin) describing the evolution of stochastic variables in presence of a drift (aging) and noise. It is also this Z_t which turns to be proportional to the entropy of the system and can be considered a thermodynamical biological age (tBA). The model also explains why Z_t has precisely the same features of PC1 from the PCA analysis.

To build up the model quantitatively one can leverage a long history in physics dealing with complex dynamical systems behaving stochastically and conjectures a model equation. The idea is to introduce “regulatory fields” (e.g. in the case of DNAm data, quantifying the free energy differences between the methylation states) whose dynamics is determined by the interactions (both linear and non-linear) between the microscopic units with the addition of an external deterministic constant (or slowly changing) “force” plus a stochastic one. These “forces” terms can be interpreted in terms of known factors impacting aging such as smoking, social status, deleteriousness of the environment etc.

Moreover, a known technique (mean field approximation) allows to treat the chaotic interactions between the FUs and the rest of the system in an approximate but effective way: “…each of the FUs or large clusters of FUs operate independently and experience the average effects of the behavior of all other FUs quantified by tBA...” [1]. In physics, the mean field approximation is what can be used e.g. in the treatment of ferromagnetism in an external magnetic field (aka Ising model) with the spin states distributed as per the Boltzmann’s distribution with effective temperature T. The validity of the mean field approximation strongly depends on the spatial dimensions of the theory.

The mathematical treatment of the model equation calls upon what I think is a central idea, i.e. that life, basically a fight between order and thermal equilibrium, tends to operate near a metastable point balancing between stability and instability, the latter taking to a phase transition (aka bifurcation). Similar ideas are applied in vast and heterogeneous areas in science, engineering, economics, climate etc. And if you draw from those well-established results and mathematical treatments (an excellent read is: doi.org/10.1038/nature08227) it turns out that the model equation can be solved approximatively and the results recapitulate what found in the PCA analysis of the data: the effect of aging over long times can be quantified as the impact of a term proportional to the (slow) aging drift Z_t (~entropy, ~tBA, ~PC1) plus the effect of the external deterministic forces (the stochastics forces effect average out) both causing a shift in the mean value of the physiological states fluctuations, a reduced resilience to perturbations (higher relaxation time) and an increasing variance.

Far from equilibrium and close to the point of instability the mathematical treatment of the model equation generates the emergence of what is known as “order parameters”, a very useful concept in dealing with complex systems dynamics (in the physics of magnetic materials, for example, think of magnetization as a characteristic order parameter, details can be found in textbooks such as those by Hermann Haken). I assume in our case the order parameter role can be approximately played by the Z_t or tBA being proportional to the PC1, the latter being a general feature of these systems where one finds that the loss of stability happens along a single direction in the state vectors space.

“…The order parameter, associated with the unstable phase, is the emergent organism level property characterized by extensive relaxation time, amplified response to perturbations, and coinciding, approximately, with the first principal component score…” [5].

Also, this paragraphs in ref. [3] recapitulates well some of the findings:

“… we proposed that aging results from inherent dynamic instability of the underlying regulatory networks and manifests itself as small deviations of the organism state variables (physiological indices) get exponentially amplified and lead to the exponential acceleration of mortality. The first principal component score is then an approximation to the order parameter characterizing the unstable phase and having the meaning of the total number of regulatory errors accumulated in the course of life of the animal17. Hence, we believe that aging at criticality conjecture provides a good explanation for the success of Principal Components Analysis (PCA) as a semi-quantitative tool in aging research40–42. The idea of the order parameter associated with instability is a generalization of a concept initially introduced in the Ginzburg-Landau theory to describe phase transitions in thermodynamics. The idea was further developed for applications to open non-equilibrium systems in the form of the “enslaving-principle”13, which states that next to the critical point, the dynamics of fast-relaxing (stable) components of a system is completely determined by the ’slow’ dynamics of only a few ’order-parameters’….” [3].

I find fascinating to apply all these concepts, imported from the physics of complex systems dynamics close to instabilities, in the area of aging biology.

However, it is not only a matter of fascination: I think the methods involved are very powerful and have potential to progress the field of biology of aging research to first understand aging and then control it.

As in my previous post and references, the aging network model has the potential to explain and possibly integrate prevailing theories of aging, explaining trends as the Gompertz’s mortality curve and the occurring damage driving the mortality acceleration, the phenomenon of mortality deceleration, the intriguing cross-impact of interventions on the aging hallmarks implied intuitively by the intrinsic nature of a central regulatory network and more, as discussed in [1] and [2] , and the very peculiar characteristics of PCA data in humans, when compared to other model animals, depending on the time the organism reaches its metastable state.

While the explication power of the theory developed in the paper is impressive, an interest I would have relates to the robustness of the model and its equations and how hard-to-vary it is without jeopardizing the results.

I also think we need to wait as more experimental verifications cumulate: as stated by the authors: “…it is important to understand, that all the relevant vectors and constants cannot be derived and could only be measured experimentally...” [1]. What I understood from the meeting in Dublin is the need for more fundamental research specifically using longitudinal human data for verification. I do also have some minor technical points regarding the mathematics in the paper, not impacting the results though.

In the community the preprint has been taken under a somewhat negative connotation as it points to an immutable max life span given by a critical point at 100-150 yo, as in particular shown by the PC3 score, in the DNAm data set, when the inverse variance data extrapolation hits zero (the variance becoming infinite). This limit also confirms the findings in ref. [4].

However, as the authors state: “…The fact that the process of aging is entropic does not necessarily mean that one cannot reset some of the organismal subsystems closer to a younger state. The entropic character of aging implies that age-reversal would be limited to a specific organismal subsystem without a full rejuvenation of the whole organism…” [1].

It is very interesting and encouraging that some of the authors are already working on these aspects of resetting, e.g. in Andrei Tarkhov et al preprint “Nature of epigenetic aging from a single-cell perspective” (https://doi.org/10.1101/2022.09.26.509592) where they state: “…It is important to note that our analyses are limited to the process of functional aging, and do not consider the effects of rejuvenation therapies on the epigenome48–50. Stochasticity of age-related epigenetic changes does not imply the impossibility of reversal, as is the case for epigenetic reprogramming protocols resetting the DNAm patterns. At the same time, stochasticity behind the process of accumulation of epigenetic changes with age does not preclude programmatic behavior, a quasi-program of aging, defined by the developmental biology predisposing species to follow a particular aging trajectory…”.

Next to the epigenetic reset, other hallmarks of aging might be acted upon, e.g. maintaining the DNA repair or protein homeostasis efficiency, as discussed in [5].

Also, the effective temperature T mentioned above seems to play a crucial role as it is related to the deleteriousness of the environment and hints to some actionability: “…Our model, however, suggests that there must be a practical way to intercept aging, that is to reduce the rate of aging dramatically. The rates controlling configuration transitions between any two states depend exponentially on the effective temperature. Hence, even minor alterations of the parameter may cause a dramatic drop in the rate of aging. In condensed matter physics, this situation is known as glass transition, where the viscosity and relaxation times may grow by ten to fifteen orders of magnitude in a relatively small temperature range [46-53]. We note, of course, that living organisms are non-equilibrium open systems, and hence the effective temperature must not coincide with body or environment temperatures. Rather, the effective temperature is a measure of deleteriousness of the environment …” [1]. The speculation here is that negligible senescence animals might have evolved to somehow reduce the effective temperature T (related to noise), becoming a little more “glassy” than “liquid”, meaning increasing their “viscosity” which itself is related to the entropy production.

Also on actionability, the ref. [6] (of which [2] is a generalization) is particularly interesting, providing a formal justification to many possible “handles” to stabilize the described regulatory network and thus extend lifespan (see Table 1).

In conclusion, while there is a non-reversibility in aging, thermodynamic in nature and confirming the views of many experts e.g. Hayflick (who “…distinguishes the genetic determinism of longevity from the stochasticity of the aging process...” [1]), one interpretation of the study is the practical possibility to at least slow down the aging process and maybe stop it.

I think we are living exciting times in the area of aging research and I look forward to the future progresses!

(Update Oct 2024)

The preprint paper in ref [1] has been finally published in Aging Biology:

Tarkhov A.E., Denisov K.A., & Fedichev P.O. (2024). Aging Clocks, Entropy, and the Challenge of Age Reversal, AgingBio, 2, e20240031. doi: 10.59368/agingbio.20240031

Since the initial publication as a preprint, the paper now ends with an interesting and important supportive update:

“… P.S. Since our first publication of a preprint of this article, it inspired a number of follow-up works by other groups. For example, three papers investigated the stochastic nature of aging by extensive simulations and analyses of gene expression and DNAm data and supported our original proposal that the dominant component of aging changes was stochastic: on a single-cell level72, for DNAm-based clocks73, and gene expression74. The studies of dynamical properties of stochastic changes in DNAm75 and other longitudinal signals in mice50 in the course of aging and in response to antiaging interventions also corroborated our analyses and predictions regarding the distinction between entropic/irreversible and dynamic/reversible components of aging signatures…”

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