Aging as a Loss of Goal-Directedness: An Evolutionary Simulation and Analysis Unifying Regeneration with Anatomical Rejuvenation

Noise influences the dynamical cell states in our NCA experiments. These states are the inputs and outputs of the virtual tissues' ANN augmented cells, and represent dynamic variables of the self‐regulatory NCA dynamics, with attractor states or instabilities. We thus interpret the effect discussed here as cellular misdifferentation‐enhanced morphological aging. Understanding such “run‐away” arguments in the “biological software” of cell state expressions, or instabilities in the context of competent tissues, seems central to understanding aging.

Next, we directly manipulate the cellular decision‐making competency ‐ the reliability with which uni‐cellular agents can regulate their own cell states within a tissue (e.g., regulative development and regenerative tissue allostasis). Here, we investigate whether degrading unicellular competencies throughout the lifetime of an organism enhances morphological aging: while young, healthy cells are highly reliable in their (re)actions to external perturbations, especially during development, the reliability of such cell decisions might be strongly affected over the lifetime of an organism, inducing morphological decline. To this end, and following,[ 46 ] we define the decision‐making as a probability P D at which proposed actions of unicellular agents are actually forwarded to the environment at a given time step. More specifically, at every instance in time t k we draw a uniform random number r i ≈ rand ∈ [0, 1] for every cell i = 1, … , N in the tissue. Only if r ⩽ P D do we consider the cell's action a i (t k ) in the NCA's update step, described by Equation (1); otherwise we omit it by setting a i (t k ) = 0. In that way, we can scale the average reliability of decision‐making of all cells in the tissue, i.e., while P D = 1 corresponds to fully reliable decision‐making of every cell at every time step, P D = 0 parameterizes fully passive cells which can't make decisions at all.

Here, we utilize P D → P D(t k ) as decreasing cellular competency by transforming P D(t k = 0) = 1 to P D(t A) = 0 in t A = 1000 time steps following the functional form PD(tk)=sin4π2(1−tktA) (see Figure 5 B). This increasingly corrupts cellular competencies by successively decreasing the reliability at which every unicellular agent in the grid can regularize, and thus “correct” their states against noise or faulty cell state configurations.

The results of Figure 5B reveal that the fitness score of NCAs whose cellular competencies are gradually affected remains similar to the baseline fitness scores of the unperturbed case (c.f., Figures 3, 4). But eventually, at t k ≈ 800, the small but finite noise of ξ c = 0.125 used in our simulations leads to accumulated damage in the NCA's states that is catastrophic for its morphological integrity, thus destroying the target morphology via diffusive processes.

Thus, decreasing cellular decision‐making competencies in a noisy collective organism necessarily lead to morphological aging effects, caused by unreliability in the “biological cell‐state reconfiguration software”. However, the rate at which these decreasing cellular competencies lead to significant aging effects is the result of an intricate interplay between the actual noise in the system and the robustness of the unicellular agents to persist against accumulating noise in their respective state configurations.

Another necessary feature of systems with decentralized collective decision‐making is reliable communication between agents. Similar to biological tissue, the cells of an NCA are integrated into a lattice of functionally homogeneous cells that only diverge in their respective cell state history. However, their neighbor coordination typically remains fixed.[ 44 , 46 , 72 ] Here, we specifically manipulate the connectivity between the unicellular agents in the NCA's grid by blocking an increasing number of communication channels between neighboring cells as time proceeds. This approach is biologically inspired by cells closing their gap junctions (GJs) to their neighbors, which is known in vivo to shift cells from cooperatively working on large morphogenetic setpoints (organ maintenance) toward individual goals appropriate to unicellular organisms such as proliferation and migration.[ 22 , 91 , 92 , 93 ] It is also related to altered cell–cell communication found during aging.[ 6 ] Indeed, aging involves deficiencies in neural, neuroendocrine, and hormonal signaling pathways[ 94 ] as well as alterations in the bidirectional communication between human genome and microbiome. Chronic inflammation is also part of this altered cellular communication.[ 6 ]

We achieve this technically by omitting the corresponding input state c ij = 0 of a blocked connection, or GJ from cell j to cell i (see Figure 2B). More specifically, we utilize a probability P GJ(t k ) which defines the fraction of GJs that should remain open for each cell in the tissue at a given time t k . In turn, if for a particular cell i, the fraction of connections to its neighbors exceeds P GJ(t k ) at time t k , we henceforth randomly block another one of its i ν = i 1, … , i N still‐connected GJs (once closed, GJs remain closed in our case); see Section 2.1 and[ 46 ] for more details on our definition of cellular neighborhoods.

By linearly transforming P GJ(t k = 0) = 1 to P GJ(t A) = 0, we successively isolate the unicellular agents from their host tissue by blocking an increasing number of their GJs until, eventually at time t A = 1000, all cells are effectively isolated from their surroundings. In Figure 5C, we demonstrate the effects of this approach: Again, the self‐orchestrated morphogenetic program can withstand the effects of increasingly corrupted competencies for a surprisingly long time. However, at t k ≈ 500, corresponding to P GJ = 0.5 (half the GJs of every cell being closed), the effects of the removed communication channels can be observed as a resulting rapid drop in the phenotypical fitness scores caused by a rapid degradation of the target pattern.

Thus, decreasing the ability of cells to communicate with their neighbors leads to enhanced effects of morphological aging if a threshold of GJs is closed.

Another potential source for self‐induced aging is accumulating damage to the cells' genetic material via successive mutations of the functional genome x (F) → x (F)(t k ) over the lifetime of the virtual organism: To this end, we utilize the pre‐evolved NCA solution discussed above (c.f., Figures 3, 4), but at every time step t k > 0, we successively manipulate the cells' ANN parameters throughout their lifetime. This directly introduces accumulating genetic mutations to the self‐regulatory mechanisms of the NCA, causing potential dysfunctional decision‐making behavior at the uni‐cellular level, and correspondingly leading to enhanced morphological decline. More specifically, we add zero‐centered normal distributed noise N(0,σx) of standard deviation σ x = 0.01 to the functional genes of the NCA, x (F)(t k + 1) = x (F)(t k ) + δ x , where δx≈N(0,σx). The mutated functional genes x (F)(t k ) are then mapped to the ANN parameters θ → θ(t k ) of the unicellular agents' controllers at every time step t k , thus directly affecting the intracellular decision‐making machinery of the NCA.

From the results depicted in Figure 5D we can learn several things: First, the evolved NCA solutions seem incredibly resistant to accumulating genetic damage in the ANN parameters, which is reflected by the fact that most of the deployed simulations (with statistically independent mutations) retain high‐fitness target patterns for the entire simulated lifetime of the NCA of t A = 1000 timesteps. Second, and in contrast to Sections 4.2.1, 4.2.2, 4.2.3, this leads to large qualitative deviations in individual behavior of an ensemble of statistical independently mutated NCA solutions: some solutions die off early and obtain vanishing fitness scores, others degrade rather continuously with a spread‐out fitness score of ≈100, and many solutions still maintain their integrity although accumulating significant genetic damage of σmax2=tAσx2=0.1 in total.

Thus third, while many mutations appear neutral in our framework, critical mutations to specific genes might induce detrimental modifications to the behavior of the unicellular agents (if they occur at the “correct” moment), typically causing a rapid degradation of the target pattern of the affected NCA as reflected by significant drops in the fitness scores of the corresponding virtual tissue. Notably, due to technical reasons, we mutate the functional genome of every agent homogeneously, thus retaining a functionally homogeneous distributed decision‐making in the NCA, which nevertheless deviates functionally from the baseline at t k = 0. Potentially intriguing effects based on heterogeneous mutations (and thus heterogeneous agents in the NCA) are out of the scope of this work, and we leave a more thorough investigation to a future contribution.

In order to understand the information dynamics of aging and the cellular information processing in a competent tissue, we applied information‐theoretic measures such as Active Information Storage (AIS), Transfer Entropy (TE), and Spatial Entropy (SE), to the states of the organism (see Figure 6 ).

In the default behavior case, without any addition of noise or induced loss of competency, we observed that both the mean AIS and TE are decreasing during development and aging. For some organisms, we can see that TE can increase during aging, indicating episodes of regeneration in the sense that the morphology is impaired and the organisms try to recover. As we can observe it, the spatial entropy is slowly decreasing during aging, and the anatomy is slowly impaired, with the loss of organs such as eyes (see Figure 6).

Interestingly, we observe that in the cases where we increase noise, see Section 4.2.1, there is a threshold value for increasing the noise level after which a rapid decline in fitness occurs ‐ which we interpret as rapid aging/dying. Indeed, at the same moment, the SE is decreasing, showing a complete disappearance of the anatomy towards a quasi‐random distribution of the states. In this case, the AIS and TE increase around 600 steps, which is a bit past the half‐life mark. A high TE can be interpreted as a high entropy of actions, with the cells trying to act after the decline and disappearance of the anatomy.

However, the loss of cell competency does not impact the AIS and TE immediately as in the noise case. Instead, the effect on AIS and TE is delayed; we observe the onset of a lot of random states in the anatomy, with an increase in AIS and TE at the end of the organism's lifespan. And when both increases in noise and loss of cell competency are present, the increases in AIS and TE are higher than when noise alone is present. Maybe the loss of competency alters the capacity of the cells to understand the decline of the anatomy and their potentials to counteract it. On the other hand, noise clearly creates a lot of cellular actions during the organism's lifespan.

When the connectivity of the cells is altered, after 500 steps we can observe an increase in AIS and more variability in TE (decrease and increase during aging). With the closing of the gap junctions, the cells are not able to receive a steady flow of information; this increases the uncertainty about their actions. We can see with the SE that the cells can counteract the loss of connectivity up to about 500 steps, after which they experience a significant decrease in spatial entropy and a complete inversion of the states of the anatomy.

The case that is creating the highest variability in anatomical outcome is the one where we altered the ANN parameters. AIS decreases and then increases slightly over time, TE is close to zero after development, and SE shows three different types of aging: a loss of structure (organs), proliferation of a specific states in the tissue (cancer), and random activation of cell states.

We can conclude that if the states of the organisms do not change over time – if the anatomy reached a steady state – the AIS and TE are low. AIS is low because there is no new information to be gained from observing past states – future states are always the same and known, independent of the past. Essentially, the predictability is absolute, but since the system does not utilize past information to determine this (because the state is intrinsically static), the AIS has low values. This indicates that in a non‐changing system there is no information flow necessary between past and future states. The future state is always known (its the same as the current state), and thus the storage of information from past states is irrelevant for future predictions. However, when AIS increases, it is also associated with an increase in TE. It happens in the cases of catastrophic changes in the morphology, as related to changes in spatial entropy. Important morphological change implies an important information flow between cells, possibly representing the cellular attempts to recover from the high morphological changes. The absence of information flow in the default behavior can indicate that the system considers its goal as reached, i.e., since neither development nor morphostasis are among the goals of the organism at this point, we see a steady degradation of the anatomy, which we can equate to aging. SE measures the entropy of the grid states. When SE is very high it corresponds to a random distribution of the states over the tissue. This random distribution can be found mainly in the cases with competency loss alone, noise alone, or both noise and competency loss.

SE reveals also a different kind of aging corresponding to a loss of structure, with the loss of specific organs or the proliferation of a specific states in the tissue, as in the loss of connectivity and ANN parameters cases, meaning that the different perturbations lead to different kind of morphological degradation.

In biological systems, certain cells or tissues retain “memories” of past states, influencing future behaviors. For instance, epigenetic memory in cells allows them to “remember” previous environmental exposures or developmental cues. Even if the external trigger is removed, cells can maintain certain gene expression patterns or epigenetic marks.[ 95 ] Similarly, tissues may retain information about past structural organization. For example, some amphibians can regenerate limbs or eyes after they are entirely removed.[ 96 , 97 , 98 ] Planarian flatworms exhibit a kind of holographic memory where, upon being cut into many pieces, each fragment of the animal regenerates everything that is missing to create a perfect and complete copy.[ 99 , 100 ] This persistence of information about the systems target morphology, which serves as the setpoint for the process of anatomical homeostasis, can be implemented in a variety of biochemical, bioelectrical, and biomechanical information; thus it is important to study this important question.

In order to analyze the information dynamics during loss of organs, we computed the spatial AIS and TE (see Figure 7 ). We observed that the loss of the eyes during aging does not imply the loss of the AIS at the location of the eye, as we can see at step 800 of Figure 7. The AIS is high and located at the position of the eyes in 100% of the cases. This suggests a memory retention in the system. For example, high AIS values at the “eye” locations in our system parallels the prepattern of the developing amphibian face consisting of regions of specialized cellular resting potential that determine the organs.[ 101 ] Even after visible features are lost, underlying patterns (like bioelectric signals or AIS) can persist, reflecting the system's inherent memory of structure. AIS measures how much information about the past states is retained in a system over time. This retention can create a lingering effect, wherein regions that previously had distinct structures (like the eyes) continue to show high AIS values. Even if the explicit structure is no longer present (e.g., the “eyes” disappear in the smiley face), the underlying system dynamics may still carry information related to those past configurations. This residual AIS indicates that the system “remembers” these regions as important parts of its past structure, maintaining high information storage due to the prior role they played.

We conclude that the loss of organs does not imply the loss of information about the organ (see example Figure 7). Following this result we decided to explore the implications for rejuvenation by inducing the regeneration of the organs in the system in the next section.

The main reason for the long‐term fitness degradation in our experiments ‐ as discussed in Section 4.1 (i.e., even without artificially affected cellular competencies), is the loss of specific internal organs, such as the eyes or the mouth. Thus, we here aim to correspondingly counteract the loss of detrimentally affected organs by replacing either the entire organ or specifically reconfiguring the affected cells of the NCA with “regenerative” state information (also erasing their internal working memory by resetting their RNN state information; see Appendix A in[ 46 ] for details).

To achieve this, we define an organ‐specific score function, ro(tk)=Ng^(tk)/N^o, that quantifies for every time‐step t k the fraction of correctly expressed target cells Ng^(tk) out of the total number of target cells N^o of a specific organ, o∈{LeftEye,RightEye,Mouth} (c.f., blue, green, and red cells in the snapshot of the 16 × 16 smiley‐face pattern NCA in Figure 8, respectively). Whenever an organ's score falls below a predefined threshold value of r o(t k ) < r th, we perform an intervention to the affected organ, aiming at restoring its morphology locally. To interfere as little as possible with the NCA's inherent developmental program, we propose utilizing the initial cell states as the regenerative state information of affected cells, ci∗(tk)→ci(0) (c.f., Section 2.1). This corresponds to reconfiguring the affected cells to their initial (primordial) state at the onset of the developmental program of the NCA.

We thus deploy the NCA solution discussed in Section 4.1 (c.f., Figure 4) for an extended life‐span of t A = 1000 time steps and apply the here discussed rejuvenation interventions whenever an organ's score r o(t k ) falls below a threshold value of r th = 0.6. In Figure 8A,B, we respectively present the results of this procedure by either (A) resetting all cells of an affected organ with their initial configuration or (B) only resetting the particular cells of an affected organ that express different cell states than their target types. We present for both (A) and (B) the long‐term fitness scores of 10 statistically independent simulations, contrast their mean behavior with the baseline case without interventions (see Figure 4), and visualize the organ‐specific scores and the corresponding intervention events for selected individuals.

We see that method (A) is not very sustainable: Although we generally measure significant short‐term improvements in a respective organs' scores after such intervention events, the intervened organs dissolve again quickly so that after ≈25 time steps (which we set as the lower limit of two consecutive interventions, allowing for unperturbed development during this period) the organ needs to be reset again, and again. This periodic need for interventions ‐ also reflected in correspondingly oscillating fitness scores of the entire organism ‐ seems fundamental in our system and is not significantly affected by the delay between two interventions. The resulting fitness scores of the intervened individuals are only slightly improved compared to the baseline case.

Strikingly, if only the wrongly expressed cells of an affected organ are reconfigured to their initial state, as in case (B), very few of such targeted interventions (on the order of ≈5 − 15, c.f., bar plots in Figure 8B) are sufficient to sustainably restore degrading organs and allow the corresponding virtual organism to maintain its morphological integrity over an extended lifespan. The corresponding long‐term fitness scores of the rejuvenated individuals show significant improvement compared to the baseline case and can even be stabilized into a steady state of a constant value of, here, r A ≈ 200; notably, the difference to the maximum fitness score of r max = 256 right after the developmental stage at t D = 35 arises due to the accumulative stagnation loss term r S in Equation (5).

Although the above approach is already promising, we further investigate how including the cells at the boundary to adjacent tissue surrounding the respective organs affects regeneration in our procedure. Thus, we additionally consider the respective boundary cells for the left and right eyes in the evaluation of the respective organs' scores, but we intentionally omit the boundaries of the mouth (c.f., emphasized color‐coded cells in Figure 9 , similar to Figure 8); notably, the mouth is much more stable than the eyes, and its cells already occupy a substantial fraction of the face.

Deploying the same experiments as above in Section 4.4.3, we see in Figure 9 that (A) interventions reconfiguring all the cells of affected organs (now also including their respective surrounding tissue) show similar performance to the corresponding case shown in Figure 9A. However, the more targeted cell‐specific interventions depicted in Figure 9B – manipulating not only the wrongly expressed cells of an affected organ, but also the wrongly expressed cells of their respective boundaries – greatly improve the performance of restoration interventions as compared to the cases shown in Figures 8, 9 and Figure 9B. Here, an average number of as few as 5 − 6 interventions (in some cases even 1 or 2) suffice to stabilize the morphology of the here investigated 16 × 16 smiley‐face pattern organism in long lifespan experiments.