Aging as a Decline in Purposeful Behavior: A Simulation Linking Body Repair and Physical Renewal

Aging is a system‐level, near‐ubiquitous biological process characterized by morphological and functional alterations in cellular and extracellular components, resulting in a systematic decline in biological functions.^[1^] This degenerative process is modulated by genetics, lifestyle, and environmental factors.^[2^] As cellular functionality diminishes with age, there is a corresponding decrease in physiological capacities and an enhanced vulnerability to a spectrum of diseases, including cardiovascular disorders, cancer, neurodegenerative diseases, type II diabetes, and various infections. These conditions collectively compromise the quality of human life.^[2, 3^]Figure 1 A schematically illustrates the typical life cycle of a complex organism comprising various stages from embryogenesis through maturity, decline, aging, and eventual death.

Several theories have been proposed to explain the aging process, which we can classify into damage‐based and programmatic theories,^[1, 4, 5^] with the former being more extensively studied.^[1, 3, 6, 7^] Damage‐based theories assert that aging results from the accumulation of molecular damage, impacting crucial cellular components like the genome, telomeres, mitochondria, and proteins, driven by imperfect repair mechanisms.^[6, 7, 8, 9^] Conversely, programmatic theories suggest that aging is genetically predetermined, or quasi‐programmed and encoded within the genome, not merely due to stochastic accumulation of damage.^[10, 11, 12, 13^] Here, we formulate and computationally simulate a fundamentally different hypothesis based on the nature of morphogenesis as a homeodynamic system working toward anatomical setpoints: that aging is the result of a proto‐cognitive dysfunction among the cellular collective, and does not require damage or evolved antagonistic mechanisms in order to occur. Instead, we propose that, as observed in animal behavior,^[14^] cellular living systems without goals to pursue tend to degrade. Our hypothesis is that aging is the result of intrinsic dynamics of complex cybernetic (goal‐directed) systems, and is not caused by external noise or damage. Nevertheless, it is consistent with other theories of aging^[15, 16^] which propose additional dynamics that can lead to loss of setpoints of anatomical homeostasis, and can be accelerated by various kinds of damage.

Antagonistic pleiotropy posits that certain genes have beneficial effects in early life but detrimental effects in later life. These genes confer advantages such as increased fertility and resilience in youth, which are critical for survival and reproduction. However, as an individual ages, the same genes contribute to aging and decline because their negative effects accumulate. The theory suggests that natural selection favors these genes because of their early‐life benefits, despite their harmful subsequent impacts. This results in a trade‐off between early benefits and later costs.^[17^] Another related idea is the hyperfunction theory, which suggests that aging is not primarily a result of accumulating molecular damage or genetic programming, but rather is due to a continuous and excessive operation of cellular growth processes that were beneficial during the earlier stages of life.^[15, 16^] Central to this theory is the role of the Target of Rapamycin (TOR) pathway, which is a major regulator of growth and metabolism in cells. During the growth phase of an organisms life, the TOR pathway promotes cellular and organismal growth by driving processes like protein synthesis, nutrient uptake, and cell division. These functions are vital for development and reproductive success. However, aging arises when these growth‐promoting activities are not appropriately down‐regulated after the organism has passed its reproductive prime. Instead of adjusting to a maintenance mode that would be more suitable for the non‐reproductive phase of life, the TOR pathway continues to stimulate cellular processes actively. This ongoing activity can lead to "hyperfunction", where cellular components and systems are overstimulated.^[15, 16^] It is not clear, in that scenario, why the efficient processes of morphological homeostasis^[18, 19^] do not orchestrate these active processes toward upkeep of functional anatomy (c.f., Figure 1B,C).

Our approach is consistent with the antagonistic pleiotropy and hyperfunction models in that we also propose that fundamental morphogenetic processes are involved in aging. However, we do not focus on specific genes with early versus late roles, but on the role that large‐scale morphogenetic plasticity plays in establishing and maintaining bodies and the possible disorders of such cybernetic (goal‐driven) processes. We and others have emphasized the indirect link^[21, 23, 24, 25^] between genotype and phenotype: not just complexity and pleiotropy, but the fact that the morphogenetic layer has active homeodynamic capabilities that enable collections of cells to be aligned with respect to setpoints in the space of anatomical possibilities^[18, 26, 27^] (c.f., Figure 1B,C). Living materials must navigate the space of possible organ and tissue arrangements as needed, starting from diverse initial states single cells (egg‐based development), a different body (in the case of metamorphosis), or a damaged body (in the case of regeneration). In all of these cases, drastic growth and remodeling must occur while failing or no longer needed sub‐components must be replaced on‐the‐fly. This process has been described as a collective intelligence,^[28, 29^] because of its problem‐solving capacities; like other advanced intelligences, it will be subject to specific failure modes whose origin is not organic disease or damage, but the informational dead end of completing ones mission and not having a new setpoint toward which to strive.

We formulate, and simulate the consequences of, the hypothesis that the aging phenotype results from morphogenetic processes ceasing their targeted navigation of anatomical morphospace, after development is completed. But adulthood, and the rigors of daily life, are precisely when these processes are needed, in the context of stress, degeneration, and cell replacement, to maintain the Ship of Theseus that is the body. What will bind the cellular components of a body toward common paths in anatomical space after their goals have been reached and the body built? Tissue renewal will continue locally, for a time, but the thing that bound individual cells into a coherent embryo a commitment to a specific navigation path in anatomical space disappears at the global scale. Damage‐based theories of aging are thus hypothesized to be secondary: they induce aging to the extent that they rob cells of clear and consistent anatomical and histological setpoints for which to aim. But the primary new proposal here is that complex goal‐driven systems can experience a kind of intrinsic disorganization after they have met their goal. In the absence of strong effort toward targets in morphospace, the cellular collective begins to disband, giving way to systemic disease states such as degeneration and cancer the inevitable outcome of a body that increasingly becomes a group of individual cells, not a unified higher‐order morphogenetic agent.^[30^]

Recent research suggests a shift in our understanding of aging, proposing that it results from changes in biological information processing rather than solely from cellular and molecular damage. This concept, linked to a malfunction in the "software of life", focuses on how aging processes are governed by the epigenetic changes, either bioelectrical or chromatin modifications.^[5, 31, 32^] The differing dynamics, capabilities, and failure modes of the molecular layer and the physiological computational layers have long been studied in neuroscience, but are only now beginning to be related to areas such as developmental biology and cancer.^[33, 34, 35^] Novel computational frameworks are needed to begin to integrate these ideas in aging and longevity research. Although substantial advancements have been made in extending lifespan in simple model organisms through genetic, dietary, and pharmacological means,^[2, 36, 37^] the fundamental mechanisms driving aging in humans remain elusive and widely debated. Current life extension strategies show limited effectiveness.^[38^] Much of the research has adopted a bottom‐up approach, focusing on the biological hardware, the cellular components such as genes, molecular pathways, and, more recently, the epigenome. However, managing aging at such a micro‐level may not be practical for complex structures like human anatomy.^[19, 39, 40^] This suggests that a broader, possibly more integrated approach may be necessary in order to fully understand and effectively intervene in the aging process.

Computational modeling has proven useful in the past to help characterize dynamics guiding complex morphogenesis.^[41, 42, 43, 44, 45, 46, 47, 48, 49^] However, to the best of our knowledge, there is currently no computational model in the literature explicating the aging process as a loss of goal‐directedness or directionality within the morphogenetic control system. The field is mostly dominated by experimental approaches and focused on the mathematical and computational modelling of a specific hallmark of aging,^[6^] network approaches to aging, or the impact of the environment on aging.^[50, 51, 52, 53^] One prior study utilized (similar to our model) an NCA to perform morphogenesis (see next section): with gradient‐based deep learning, the self‐regulatory interaction dynamics of distributed cellular agents have been optimized to grow a target morphology in a fully self‐orchestrated way. However, without explicitly stabilizing morphogenesis by additionally training the cellular agents on regenerative tasks, anatomies kept growing uncontrollably after development. Thus, the study focused on an adversarial approach to stabilize self‐orchestrated morphogenesis rather than studying aging and its causes in such a multi‐cellular tissue per se.^[54, 55^]

A key knowledge gap lies in the absence of models that explicitly simulate the evolutionary pressures shaping developmental processes while accounting for the lack of anatomical morphostasis post‐development. Existing frameworks often overlook how multi‐scale competencies – spanning molecular, cellular, and tissue levels – transition from goal‐directed morphogenesis to maintenance, leading to intrinsic disorganization and degradation without clear setpoints. This oversight limits our ability to predict aging trajectories in complex multicellular systems and to explore interventions that reactivate latent regenerative potentials.

Existing mathematical models have not yet captured the biological signaling dynamics in aging tissue or revealed the underlying information dynamics that drive aging and the progressive degradation of anatomy over time. Unlike previous approaches, we uniquely address this gap by developing an evolutionary framework that integrates both molecular and systemic aspects of aging within a multi‐competency architecture. Our model demonstrates how cells, trained solely through evolution to execute developmental tasks, inherently lack a regenerative goal post‐development. By simulating this dynamic, we reveal that aging arises from the absence of targeted navigation in anatomical morphospace after development, offering a novel perspective on the root cause of aging. Moreover, our approach uncovers the potential for dormant regenerative programs to be reactivated, enabling targeted restoration of anatomical structures (c.f., Figure 1).

Morphogenesis is the result of multicellular collectives acting together to achieve a specific endpoint within the space of anatomical possibilities^[23^] (see Figure 1). This process is driven by intercellular communication and information processing, where cells use different communication channels (biochemical, biomechanical or bioelectrical) to exchange information with their neighbors in a tissue^[22, 26^] and implement a process of anatomical homeostasis where deviations from the species‐specific target morphology are progressively minimized by active changes in growth and form. This enables cells to adaptively respond in a context‐sensitive manner and regulate their behavior through local signaling protocols while collectively following a system‐level agenda to grow and maintain an organism's species‐specific anatomical form in a self‐orchestrated way. Thus, the development of embryonic tissues, the growth and remodeling of adult organs, and even the suppression of cancer and aging can be understood as morphological computation.^[22^] In this sense, morphogenesis can be seen as an intermediate layer of physiological computation between genetic variation and a mature anatomical phenotype (see Figure 1C, significantly effecting the process of evolution.^[23, 46^]

Another important aspect of biology, so far neglected in the models of aging is multiscale competency^[23, 28, 56^] (see Figure 1B,C). Biological systems implement an architecture in which context‐sensitive problem‐solving operates across various levels, from molecular networks to individual cells, tissues, organs, organisms, and even collective groups such as swarms. This structure allows biological entities to solve problems within specific domains and problem spaces relevant to each scale (metabolic, physiological, anatomical, and behavioral state spaces), contributing to the overall adaptability and resilience of life.^[22, 26, 57^] At the molecular and cellular level, biological units navigate metabolic spaces to remain within adaptive regions despite changing circumstances. At higher organizational levels, these units form tissues and organs, which tackle more complex and larger‐scale physiological and morphological problems. For instance, cells can make autonomous decisions to maintain local balance while contributing to larger‐scale biological processes like tissue repair or development, and to how higher levels of organization constrain and facilitate the behavior of their parts.^[23, 58, 59, 60, 61, 62, 63^] This enables organisms to adapt to changing conditions and maintain functionality even when faced with disruptions, as observed in regulative development and regeneration where cellular activity is managed toward specific anatomical outcomes despite injury, changes of cell number and size, etc.^[27^] This is critical because resistance to both cancer and aging must involve both the upkeep of complex structures and a resistance to their progressive decline within the body.^[64^]

A key advantage of this multiscale architecture is that each level is capable of addressing its own problem‐spaces without needing constant guidance from higher organizational structures (local homeodynamic competency, see Figure 1C). This decentralized problem‐solving approach ensures that different biological processes, from cell division to behavioral adaptation, occur simultaneously and efficiently. Furthermore, this structure allows biological systems to be both robust and flexible, as failures at one level can often be compensated for by others. Additionally, the interplay between levels within this architecture enables the emergence of complex properties that cannot be explained by examining components in isolation. For example, the collective behavior of cells during processes like regeneration or morphogenesis illustrates how local interactions scale up to contribute to the organism's overall form and function.^[28^] Similarly, defects of collective behavior can lead to developmental defects or aging. These interactions are not merely a sum of their parts; rather, they represent emergent capabilities that arise from the coordinated effort of biological subunits. The relative autonomy of layers in biology must surely impact on evolutionary and physiological constraints and drivers of aging, making it essential to study their properties with respect to the lifespan of individuals and evolutionary lineages.

This hierarchical but integrated organization is essential for the evolution of complex life forms. It promotes adaptability, allowing organisms to respond to environmental changes, evolve new features, and develop intricate systems that support survival and reproduction. Moreover, this multiscale competency architecture provides a framework for innovation in fields such as synthetic biology and regenerative medicine,^[29, 39, 65^] where understanding and harnessing these principles could lead to breakthroughs in tissue engineering, organismal repair and aging.^[29, 31^] This aspect of living forms – the critical layer of computational, problem‐solving competency that lies between the genotype and the phenotype – is an essential component of any theory of aging that integrates evolutionary and physiological dynamics to understand this complex phenomenon. Thus, we focused our computational model on the role of multiscale morphogenetic competency in the aging process.

Recently,^[46^] we quantitatively investigated in silico the influence of varying levels of cellular competency of a multi‐scale competency architecture^[22, 23^] on the evolutionary process. We utilized tools from Artificial Life,^[66^] a field of research focused on developing computational and cybernetic models that exhibit life‐like behavior based on ideas derived from biology; one prominent example is Cellular Automata^[67, 68, 69, 70^] (CAs) such as Conway's Game of Life.^[71^] Specifically, we deployed NCAs^[72^] as a model for evolving morphogenesis (see Figure 2 A–C): NCAs comprise a regular spatial grid of locally interacting cellular agents which maintain a numerical state vector that is regulated by an internal, cell‐specific Artificial Neural Network (ANN). In that way, the cells of an NCA can be trained to perform a collective self‐orchestrated system‐level task, such as morphogenesis^[44, 45, 46^] or even collective navigation behavior,^[56, 73^] solely via successive perceptions of their local environment, i.e., by reading neighboring cell state information and computing corresponding actions to regulate their own states in accordance with a system‐level agenda.

Thus, NCAs exhibit striking similarities with the genome‐ and collective intelligence‐based multi‐scale competency architectures of biological life :^[21, 23, 25, 56, 74^] the instructions for how to grow an organism from the bottom up are encoded in its genome, corresponding to the NCA's (functional) ANN parameters (c.f., Figure 2A). Moreover, through subsequent localized perception‐action cycles of their ANN‐based unicellular agents (c.f., Figure 2B), NCAs model the intercellular communication pathways, intracellular memory, and integrated information processing of the adaptive and flexible internal decision‐making mechanisms of biological cells:^[75, 76, 77, 78, 79^] while biological cells regulate their gene expressions via gene regulatory networks, the cells of an NCA regulate their cell types via their internal ANN, and while biological cells utilize bioelectrical and molecular cues for intercellular signaling, cells in an NCA exchange numerical state information in a similar manner. In both cases, such communication pathways are localized between neighboring cells while the collective of cells may still follow a global agenda to self‐orchestrate the process of morphogenesis and thereby give rise to the anatomical form of a system‐level organism.

Building on our previous work,^[46^] we utilize evolutionary algorithms (EAs)^[80^] to optimize the parameters of an NCA so that its cellular agents can reliably self‐assemble a particular spatial target pattern of predefined cell states within a fixed number of developmental steps (c.f., Figure 2C). Inspired by the ability of biological organisms to sustain their physiological integrity for much longer than is necessary for reproduction, we study the long‐term behavior of NCAs by deploying the evolved virtual system for an extended period far beyond the developmental stage at which evolutionary selection occurred. In turn, this may lead to an accumulation of morphological changes that, while not necessarily lethal, can make a multiscale collective increasingly dysfunctional by altering its homeostatic setpoint (c.f., Figure 2D).

Based on such virtual organisms, we here investigate in silico the information‐dynamic implications – using Active Information Storage (AIS),^[81^] Transfer Entropy (TE),^[82^] and Spatial Entropy (SE) – of temporally affected competencies or information loss at the cellular level of a multi‐cellular collective whose parts pursue a system‐level agenda. To systematically interfere with the cellular competencies in our NCA model over time, we deploy four different strategies: We a) increase the misdifferentiation rate of cell‐state expressions; b) reduce the cellular agents' ability to self‐regulate their respective states by corrupting the reliability at which cellular actions are actually considered in the NCA's cell state updates; c) reduce the connectivity between neighboring cells, reminiscent of closing an increasing number of gap junctions (GJs) to neighbors; and d) accumulate genetic damage to the NCA's functional parameters by randomly modifying the corresponding ANN parameters with Gaussian noise successively throughout the lifetime of our virtual organisms.

Thus, we relate degrading competencies and temporal information loss at the cellular level to aging at the system level. Finally, based on the hypothesis of the information‐dynamical implications of aging caused by decaying cellular competencies, we demonstrate – in a minimal in silico model – a reliable method of rejuvenation of facial features, based on targeted interventions at the cellular or organ level.

We suggest that even in the absence of accumulated cellular defects that affect information processing, communication, or genetic material, a biological system that lacks any new goal in the morphospace will begin to degrade anatomically. This is permitted by evolution, as development is typically prioritized over long‐term morphostasis, potentially leaving organisms without a clear anatomical goal after development. Using an NCA‐based in silico model of morphogenesis, we find: 1) Aging arises naturally after development due to the absence of evolved regenerative goals, rather than being caused by specific detrimental properties of developmental programs (e.g., antagonistic pleiotropy or hyperfunction); 2) While cellular misdifferenciation, affected competency and communication pathways, and genetic damage all accelerate aging, they are not its primary causes; 3) Aging correlates with increased active information storage and transfer entropy, while spatial entropy reflects structural loss and accumulated morphological noise; 4) Despite organ loss, corresponding spatial information persists in our cybernetic tissue, indicating that a pattern‐memory of lost structures can be reactivated for organ restoration through targeted regenerative information; 5) Efficient restoration and rejuvenation protocols include regenerative information of differential patterns of affected cells and their neighboring tissue. These findings provide a novel perspective on aging dynamics with significant implications for longevity research and regenerative medicine.

CAs were initially introduced by von Neumann to study self‐replicating machines.^[67^] Since then, they had become widely used as simple models for Artificial Life.^[66^] The core concept behind CAs revolved around maintaining a discrete spatial grid of cells, with each individual cell i being assigned a binary, numerical, or even vector‐valued state c_i(t_k) at every time step t_k.

The evolution of these cell states over time follows local update rules. Specifically, it was considered that ci(tk+1)=u(Ni(tk)), where u(·) is a function of the current state of cell i, i.e., ci(tk)≡ci0(tk), and of the states ciν(tk) of its i_ν = i₁, …, i_N neighboring cells, which were collected in the matrix Ni(tk)=ci0(tk),…,ciN(tk).

Despite their typically simple and predefined update rules, CAs often exhibit complex dynamics (c.f., Conway's Game of Life^[71^]) and had even been employed for universal computation tasks, as in Wolfram's rule 110.^[68, 69^]

NCAs^[72^] could be seen as extensions to "traditional" CAs. In this context, the local update rule was replaced with a more flexible ANN, u(·) → f_θ(·), where θ denotes the set of trainable parameters of the ANN, f_θ(·) (see, e.g., Appendix A in^[46^]). By employing Machine Learning (ML) techniques, NCAs had been utilized to perform tasks such as self‐orchestrated pattern formation^[44^] and the simultaneous co‐evolution of a rigid robot's morphology and controller;^[56^] and they have been proposed as a promising candidate for robust, decentralized controllers of autonomous drug delivery systems.^[73^]

An NCA was essentially a grid of interconnected cells, each equipped with an identical ANN that was capable of perceiving the numerical states of its immediate cellular neighbors, Ni(tk), and proposing actions, ai(tk)=fθ(Ni(tk)), to regulate its own cell state, following the equation (1)ci(tk+1)=ci(tk)+ai(tk)+ξcwhere possible imperfections in the cell‐specific state updates were also accounted for via a Gaussian noise term of amplitude ξ_c.

Thus, the cellular agents of an NCA perceive the numerical states of their immediate respective neighborhoods, Ni(tk), at any given time step, t_k, to update their own states (c.f., Figure 2A,B). Importantly, no explicit signature of aging was included in the model, i.e., there was no cell‐internal marker or explicit input to the cellular agents that contains temporal information, other than the self‐regulated cellular states of those agents.

However, being immersed in a dynamical multi‐cellular environment where every part had its own agenda, the cellular agents' state updates could also be utilized for active communicating with their neighbors, following a policy π(Ni(tk))≈fθ(Ni(tk)). From the perspective of Reinforcement Learning,^[84^] an NCA could thus be considered a trainable multi‐agent system that needs to utilize local communication rules to achieve a target system‐level outcome.

So far, the approach was agnostic to the particular ANN architecture of the update function, f_θ(·). Closely following,^[46^] here, the genuine ANN architecture deployed in our cellular agents was briefly described, which was schematically depicted in Figure 2B: Inspired by,^[85^] the NCA's cells' ANN was partitioned into i) a sensory part, εiν=fθ(s)(ciν(tk))∈Rs, preprocessing each neighborhood cell state separately into a respective sensor embedding, which were collected in the matrix E(Ni(tk))=εi0(tk),…,εiN(tk). These sensor embeddings are then ii) averaged across all neighbor embeddings into a single context vector si(tk)=1N+1∑ν=0Nεiν(tk)∈Rs. A subsequent iii) controller ANN, fθ(c)(·), potentially with recurrent feedback connections, eventually outputs the cell's action, ai(tk)=fθ(Ni(tk))=fθ(c)(si(tk)) based on the cell‐specific context vector s_i(t_k). Notably, for the controller module, so‐called RGRN architectures were utilized^[46^] that were inspired by a combination of Recurrent ANNs (RNNs)^[86^] and Gene Regulatory Networks^[87^] (see Appendix A in^[46^] for details).

Analogous to,^[46^] morphogenesis was modeled by employing NCAs on a 2D N_x × N_y square grid with the objective that all cells of the grid assume a cell‐specific predefined target cell type, g^i, after a fixed number of t_D developmental time steps, starting from an initial cell state configuration c_i(0), The first N_G elements, gi(tk)=ci1(tk),…,ciNG(tk), of an NCA's NC‐dimensional cell state ci(tk)=ci1(tk),…,ciNC(tk) were assigned as indicators for expressing one of 1,…,NG discrete cell types, while the remaining NH=(NC−NG) elements of the cell state represent its hidden states, hi(tk)=ci(NC−NH)(tk),…,ciNC(tk). While the full NC‐dimensional cell state vectors c_i(t_k) could be utilized for intercellular communication by the NCA, a cell's "type", g_i(t_k), is now defined as the index, 1,…,NG, of the maximum element of its indicator vector g_i(t_k): (2)gi(tk)=argmaxg∈RNGgi(tk)

For an NCA to assemble a predefined target pattern of N_j = N_x × N_y target cell types g^={g^1,…,g^Nj}, a suitable set of NCA parameters must thus be found that minimizes the deviation of all actual cell types gi(tD) and the desired ones g^i after tD developmental time steps. Below, an evolutionary algorithm was introduced to evolve suitable sets of NCA parameters that maximize a fitness score based on comparing the "final" cell types of the NCA, gi(tD), after the developmental stage to the predefined target cell types g^i. In this context, the NCA parameters thus correspond to the virtual organism's genotype, while the grid of final cell types represent the system‐level phenotype that was seen by the selection mechanism of the evolutionary process (c.f., Figure 2C).

Evolutionary Algorithms (EAs) were heuristic optimization techniques designed to maintain and optimize a set, or population, X={x1,…,xNP}, comprising parameters or individuals, xj∈RX, over successive generations in order to maximize an objective function or fitness score, r(xj):RX→R. Drawing inspiration from the principles of natural selection and biological life's DNA‐based reproduction mechanisms, EAs predominantly select high‐fitness individuals for reproduction, and utilize crossover and mutation operations to generate new offspring by merging the genomic material of two high‐quality individuals from the current population, xo=xj⨁xk, and occasionally mutating offspring genomes, x_o → x_o + ξ_x, by adding typically Gaussian noise to the parameters; the ⨁ symbol signifies a genuine merging operation of two genomes, which may vary according to the specific EA implementation. Thus, populations of individuals were directed toward high‐fitness regions within the parameter space RX, typically across numerous generations of successive selection and reproduction cycles.^[46^]

Closely following the previous work^[46^] and in contrast to many "traditional" EA use‐cases, a distinguish was explicitly made between the genotypic parameters, x_j, and the corresponding phenotypic realizations, p_j. More specifically, we utilize NCAs (c.f., Section 2.1) to model the biologically inspired developmental layer^[23^] in between genotypes and phenotypes, x_j → p_j, akin to the process of morphogenesis: Here, a genotype, x_j, corresponds to a particular realization j of an NCA's parameters, comprising the set of initial cell states xj(S)={ci=(1,…,Nj)(0)}j and the corresponding ANN parameters xj(F)=θj, such that (3)xj=xj(S)∪xj(F)={ci(0)}j,θj,where a distinguish was explicitly made between structural (S) and functional (F) genes. Equation (1) was then employed for t_D developmental steps to successively transform the NCA's cell states from an initial state into a "final" set of cell types {g_i(t_D)}_j on the NCA's grid. This mature phenotype,(4)pj={gi(tD)}jrepresents a 2D tissue of cells, and is the input to the fitness score based on which the EA selects: As illustrated in Figure 2C, optimization was performed for a fitness score in the phenotype space rather than the genotype space, r(x_j) → r(p_j), while still performing genetic recombination and mutation in the genotype space.

Let's recall: the goal was to achieve morphogenesis of a 2D spatial tissue of cell types, p_j, that optimally resembles a predefined target pattern, {g^1,…,g^Nj}, of a total of N_j cells on an N_x × N_y square grid of an NCA. Moreover, the aim was to derive a virtual organism with this capability by modeling a biologically inspired evolutionary process with EAs to evolve a suitable set of NCA parameters (c.f., Figure 2 (C)). Thus, the phenotype‐based fitness score was introduced, r(p_j), as^[46^](5)r(pj)=(2nj(G)−Nj)+rTnj(T)−rSnj(S)where nj(G) counts the number of correctly assumed cell types after t_D developmental steps (where gi(tD)=g^i), nj(T) counts the number of developmental steps at which the target pattern is realized entirely (whenever gi(tk≤tD)=g^i for all i), and nj(S) counts pairs of successive time steps, (t_s, t_{s + 1}) ⩽ t_D, without cell type updates in the entire tissue (where g_i(t_{s + 1}) = g_i(t_s) for all i).

Thus, an evolutionary process was designed that primarily selects for NCAs that assume the correct cell type pattern after (precisely) t_D developmental steps and reinforces NCAs (by a factor of r_T in the fitness score) that prematurely achieve and maintain the target pattern. To avoid developmental stagnation and increase the EA's performance, the fitness score of NCAs was specifically discounted with static behavior by r_S. A fitness score of N_j = N_x × N_y indicated that the problem is solved.

Although the above framework^[46^] could be utilized in conjunction with any black‐box evolutionary or genetic algorithm, the well‐established Covariance Matrix Adaptation Evolutionary Strategy (CMA‐ES)^[80^] to be a viable choice for our purposes.

Information theory^[88^] offers valuable insights into the dynamics of complex systems. In order to understand the NCA's information dynamics during aging, three key information‐theoretic metrics were used to examine the information dynamics: active information storage,^[81^] transfer entropy,^[82^] and the spatial entropy.

Active Information Storage (AIS) quantified the amount of information from an agent's past that was pertinent to predicting its future state. Specifically, AIS refers to the portion of stored information currently utilized for determining the agent's next state.^[81^] Mathematically, the AIS of an agent Q was expressed as the local mutual information between its semi‐infinite past qn(k) as k → ∞ and its next state q_{n + 1} at time step n + 1: (6)aQ(n+1)=limk→∞log2p(qn(k),qn+1)p(qn(k))p(qn+1)

Here, a_Q(n, k) is an approximation with history length k. The time‐averaged value, weighted by the distribution of (qn(k),qn+1), is denoted as A_Q(k) = 〈a_Q(n, k)〉. In this study, the local was calculated AIS across the states of the cells.

Transfer Entropy (TE) measures the information transferred from a source agent to a destination agent that was not contained in the past of the destination agent. The local TE concept introduced by Lizier was employed.^[81^] The local TE from a source agent Z to a destination agent Q was defined as the local mutual information between the previous state of the source z_n and the next state of the destination agent q_{n + 1}, conditioned on the semi‐infinite past of the destination qn(k) (as k → ∞): (7)tZ→Q(n+1)=limk→∞log2p(qn+1|qn(k),zn)p(qn+1|qn(k)).

The transfer entropy T_Q(n, k) was the local TE averaged over time, denoted as T_Q(k) = 〈t_Q(n, k)〉, where t_Q(n, k) was an approximation with history length k. Unlike mutual information, which measures static correlation, transfer entropy captures the dynamic, directional flow of information within the agent network.

Spatial Entropy (SE) measured the randomness or disorder within a spatial distribution of states. It provided insight into the complexity of spatial patterns in a system, such as an NCA with multiple states. In this study, SE was computed by evaluating the entropy of the distribution of cell states across the grid at each time step. Formally, the spatial entropy H at time step n is defined as: (8)H(n)=−∑s∈Sp(s)log2p(s)where S is the set of possible states, and p(s) is the probability of state s occurring in the grid at time step n. This measure provided an indication of the level of unpredictability or complexity in the spatial arrangement of cell states. In this article, the spatial entropy for the states of the NCA was calculated across different time steps.

We aimed to assess whether the self‐regulatory behavior of biological systems that drive morphogenesis induces aging‐like phenomena at long time‐frames. To this end, we use NCAs evolved in silico to model the process of morphogenesis and then deploy their self‐regulatory dynamics for much longer times compared to the reproduction stage during evolution (i.e., when selected for reproduction). We monitor and analyze the NCAs morphological integrity throughout their lifetimes and compare such long‐term morphological trajectories with biological aging. The evolutionary process described in Sections 2.2, 3 explicitly selects for optimal fitness scores after t_D developmental steps, which corresponds to the fertility age of real‐world organisms. However, this implies that the behavior of an NCA with a potentially much longer lifetime of t_A > t_D, and particularly t_A ≫ t_D, is not subject to selection and may fundamentally be considered ill‐defined or ambiguous.

To demonstrate this, we deploy the NCA solution that has been evolved to self‐assemble a 16 × 16 smiley‐face pattern during a morphogenesis phase of t_D = 35 developmental steps (c.f., Figure 3) for a much longer lifetime of up to t_A = 1500 time steps, notably without any further optimization considering the extended lifetime. From the results presented in Figure 4, we learn that after an initial rapid rise in the fitness score during the developmental phase, the NCA's long‐term fitness score gradually declines, primarily due to the loss of different internal organs such as one or both eyes and, occasionally, the mouth. Moreover, this is not only a feature of the particular NCA demonstrated here, but is a systematic phenomenon of the presented framework.

Thus, we argue that the biologically‐ubiquitous self‐regulatory behavior of a substrates agential parts may induce system‐level dynamics that resemble the process of biological aging if applied on timescales that exceed development. The organisms learned during evolution with development as the primary goal; once they reached that goal, we observed that they don't regenerate by themselves and slowly show signs of morphological deterioration, e.g., aging. In this sense, aging can be seen primarily as a loss of goal‐directedness, the goal of development being different from the goal of maintenance of the anatomy over timescales exceeding development. This view on aging is related to programmatic theories of aging like antagonistic pleiotropy or hyperfunction theory^[11, 16, 17^] that state that what is good for development could ultimately cause aging. In our framework, the lack of goal‐directedness after development may give rise to informational antagonistic pleiotropy (or hyperfunction) as cells may lose some developmental policies after reaching the target morphology. However, our framework goes beyond antagonistic pleiotropy by enabling the deliberate re‐targeting of the morphogenetic setpoint in an aging tissue toward new anatomical goals. In turn, a continually regenerative setpoint – e.g., by reactivating developmental pathways – may reverse aging, as we demonstrate in silico in Section 4.4.

To determine how the perception‐action cycles of the unicellular agents of a collective multi‐cellular organism influence, at least in part, the rate of morphological decline, we here investigate the effects of an NCA's system parameters on its long‐term morphological integrity. Based on the NCA system defined in Section , we identify four key mechanisms involved in the corresponding uni‐cellular perception‐action cycles affecting morphological integrity: a) cell‐specific differentiation reliablility, b) reliable state updates, c) reliable communication between neighbors, and d) persistent genetic encoding. Our framework allows us to selectively control these corresponding processes (a–d) and explicitly corrupt them independently over the lifetime of the virtual organism. Thereby we demonstrate the severe effects of these processes on the rate of morphological aging. 3

In the following sections, we therefore study the factors accelerating aging, not the cause of aging per se that we see primarily as a loss of goal‐directedness. We introduce these known aging mechanisms (a–d), respectively, based on and deployed to the biologically motivated unicellular competencies in our NCA system. We then demonstrate and discuss the corresponding implications on enhanced rates of morphological aging in long‐term simulations of such virtual organisms. We illustrate the respective results in a compact form in Figure 5A–D, and continue below with an information‐theoretic analysis of these processes.

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 , 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. 4.2.1

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.