Decoding the Architecture of Living Systems

TL;DR

The paper develops a thermodynamics-informed, network-based framework to decode how living systems organize across scales. It argues that structure, topology and dynamics intertwine within nonequilibrium constraints, best captured by multilayer, hierarchical modular networks that evolve through energy- and information-processing trade-offs. By unifying dynamical-systems theory, nonequilibrium thermodynamics and evolutionary dynamics (via replicator-mutator and maximum-caliber formalisms), it links METs, evolvability and robustness to concrete network properties like percolation, modularity and interdependence. The work proposes a practical, scalable blueprint for modeling complex biological architectures with potential implications for medicine, ecology and artificial systems, and points toward a principle of maximum evolvability as a guiding research direction.

Abstract

The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of living systems is tantalizing. However, it is often overlooked that any practical implementation of such a logic requires complementary circuitry that, in biological systems, happens through complex networks of genetic regulation, metabolic reactions, cellular signalling, communication, social and eusocial non-trivial organization. We review and discuss how circuitries are not merely passive structures, but active agents of change that, by means of hierarchical and modular organization, are able to enhance and catalyze the evolution of evolvability. Using statistical physics to analyze the role of non-trivial topologies in major evolutionary transitions, we show that biological innovations are related to deviation from trivial structures and (thermo)dynamic equilibria. We argue that sparse heterogeneous networks such as hierarchical modular, which are ubiquitously observed in nature, are favored in terms of the trade-off between energetic costs for redundancy, error-correction and maintainance. We identify three main features -- namely, interconnectivity, plasticity and interdependency -- pointing towards a unifying framework for modeling the phenomenology, discussing them in terms of dynamical systems theory, non-equilibrium thermodynamics and evolutionary dynamics. Within this unified picture, we also show that slow evolutionary dynamics is an emergent phenomenon governed by the replicator-mutator equation as the direct consequence of a constrained variational nonequilibrium process. Overall, this work highlights how dynamical systems theory and nonequilibrium thermodynamics provide powerful analytical techniques to study biological complexity.

Figures (7)

• Figure 1: Complex adaptive networks. (A) The dynamic interplay between structure and function in complex adaptive networks, governed by a fitness landscape, highlights how network topology influences dynamics and vice versa, shaping the network's plasticity and its evolutionary trajectory. Each possible network configuration corresponds to a point in the fitness landscape, whose elevation reflects functional performance -- e.g., efficiency, robustness or information throughput -- under given constraints. Adaptive dynamics describe how mutations or rewiring events modify topology, enabling the system to explore and climb this landscape toward locally or globally optimal architectures. (panel readapted from berner2023adaptive) (B) Intercellular interactions unfold through different mechanisms. Contact-based exchange includes signaling via cell surfaces, connecting through structures like gap junctions to directly transfer signals, or exerting direct mechanical stress. Mechanisms based on soluble factors involve cells releasing neurotransmitters across synapses, influencing themselves or nearby cells (autocrine and paracrine signaling), or sending hormones through the bloodstream to distant cells (endocrine signaling), along with creating changes in their environment that indirectly apply mechanical stress to nearby cells (panel readapted from yang2021engineered). (C) In eusocial systems like ant and termite colonies, indirect communication occurs through stigmergy, a phenomenon where each insect's secretion of chemicals onto a physical substrate leads to environmental changes that allow for self-coordinating the collective activity of the colony theraulaz1999briefholland1999stigmergy. (D) Visual signals are encoded in the waggle dance of bees, for social learning and signaling information about food sources dong2023social. Auditory communication is observed in sperm whales, who use codas to maintain social interactions sharma2024contextual. In humans, direct communication is facilitated through spoken language (see fedorenko2024language and refs. therein), as well as visual cues and possibly chemical signals, while indirect and asynchronous communication occurs through various art forms, enabling the expression and transmission of complex cultural and emotional information across individuals and generations.
• Figure 2: Formation of a hierarchical structure. (A) Illustration of a toy model where $N$ elementary units, initially disconnected, interact to form assemblies of size $n < N$. The resulting groups, now $N/n$, in turn aggregate into new assemblies of size $n$, and so on, until the process ends for some value $\ell = \log_{n} N$ that sets the depth of the hierarchy. The transition between two consecutive levels of the hierarchy is denoted by $T_{n}^{(i)}$. (B) Schematic representation of the resulting network model: connections within the same module occur with probability $p_{\text{in}}$, connections between different modules at the same level with $p_{\text{out}}$, and connections across different hierarchical levels with $p_{\text{hier}}$. (C) Probability matrix corresponding to a three-level hierarchy, where the off-diagonal blocks encode cross-level links. Depending on the mechanism, $p_{\text{hier}}$ can be a constant value or decay exponentially (e.g., $p_{\text{hier}} \propto e^{-\Delta \ell}$).
• Figure 3: Generalized thermodynamics of a synthetic benchmark. (A) Sketch of the von Neumann entropy of complex networks as a function of diffusion time. The networks have the same average degree while being characterized by distinct connectivity patterns corresponding to distinct statistical ensembles. The configurational ensemble is not characterized by topological correlations, while the modular and hierarchical-modular ensembles provide different types of mesoscale organization. Hierarchical network ensembles have the highest information entropy ghavasieh2020statistical. (B) The network model described in Fig. \ref{['fig:hierarchy']} is used to generate synthetic benchmarks (size $N=1024$, levels $L=4$) with distinct hierarchical modular structure. Top: network von Neumann entropy versus time de2016spectral (solid lines) and corresponding generalized thermodynamic susceptibility (dashed lines) whose peak identifies the points of entropic phase transitions villegas2022laplacian. Bottom: network generalized efficiency ghavasieh2024diversity Left: modular structure is fixed, while hierarchy is varied by tuning the probability ($p_{\text{hier}}$) to connect nodes on distinct levels; Right: hierarchy is fixed, while modularity is varied by tuning the ratio between the probability to connect within ($p_{\text{in}}$) and across ($p_{\text{out}}$) community.
• Figure 4: Structural percolation in complex networks. Emergence of a giant connected component (GCC) as a function of the probability $p$ of connecting any pair of nodes in the Erdős-Rényi model. The order parameter is the fraction of nodes belonging to the GCC, while $p$ acts as control parameter. The dashed lines correspond to three distinctive regions related to the percolation threshold $p_{\text{c}}$: (i) sub-critical, for $p < p_{\text{c}}$ the system is disconnected; critical, at $p=p_{\text{c}}$ the system undergoes a phase transition where a giant connected component appears; super-critical, for $p > p_{\text{c}}$ the system is connected. 100 independent random simulations of networks with size $N=1000$ have been performed.
• Figure 5: Emergent circuitry in living systems. (A) Gene regulatory network of Escherichia coli, where red colored nodes indicates transcription factor encoding genes; figure from martin2016graphlet. (B) The physical interactome of Saccharomyces cerevisiae; figure readapted from collins2007toward. (C) Metabolic network of Escherichia coli and its functional organization into modules, which are represented as pie charts with colors indicating the involved metabolic pathways; figure from guimera2005functional. (D) Hierarchical organization of modules in Escherichia coli; figure from ravasz2002hierarchical. (E) Multicellular yeast called snowflake yeast, obtained through many generations of directed evolution from unicellular yeast in the lab, captured using spinning disk confocal microscopy. Cells are connected to one another by their cell walls, shown in blue. Stained cytoplasm (green) and membranes (magenta) show that the individual cells remain separate. (F) Connectome of Caenorhabditis elegans, where node size encodes neuron's degree and color codes cell type (sensory neuron, interneuron, motor neuron, muscle); figure from yan2017network. (G) Social network of an ant colony (no. 5, day 3), where the number of interactions and their average duration is encoded by edge width and darkness, respectively. Node color codes different ant roles, while node size is proportional to ant size. Figure from mersch2013tracking. (H) Cambrian food web (Burgess Shale), where nodes represent taxa, vertically organized by their trophic level, and links indicate feeding: figure from dunne2008compilation. Panel (A) is licensed under CC-BY 4.0. Panels (D,G) reprinted with permission from AAAS. Panels (C,F) Reprinted with permission from Nature. Panel (E) Source: William Ratcliff, Georgia Institute of Technology; Credits: Anthony Burnetti, Ozan Bozdağ, and William Ratcliff, Georgia Institute of Technology. Panel (H) is licensed under CC-BY 4.0. Icon for panel (H) Source: Wikimedia; Credits: Zingone A, D'Alelio D, Mazzocchi MG, Montresor M, Sarno D, LTER-MC team (2019), licensed under the CC BY 4.0 Icons from Freepik.