Cell membranes phase separate into ordered ${\rm L_o}$ and disordered ${\rm L_d}$ domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in ${\rm L_o}$ and ${\rm L_d}$ domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into ${\rm L_o}$ and ${\rm L_d}$ domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the ${\rm L_o}$ domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and mole
Provided that there is no theoretical frame for complex engineered systems (CES) as yet, this paper claims that bio-inspired engineering can help provide such a frame. Within CES bio-inspired systems play a key role. The disclosure from bio-inspired systems and biological computation has not been sufficiently worked out, however. Biological computation is to be taken as the processing of information by living systems that is carried out in polynomial time, i.e., efficiently; such processing however is grasped by current science and research as an intractable problem (for instance, the protein folding problem). A remark is needed here: P versus NP problems should be well defined and delimited but biological computation problems are not. The shift from conventional engineering to bio-inspired engineering needs bring the subject (or problem) of computability to a new level. Within the frame of computation, so far, the prevailing paradigm is still the Turing-Church thesis. In other words, conventional engineering is still ruled by the Church-Turing thesis (CTt). However, CES is ruled by CTt, too. Contrarily to the above, we shall argue here that biological computation demands a more ca
This review explores the innovative design to achieve advanced optical functions in natural materials and intricate optical systems inspired by the unique refractive index profiles found in nature. By understanding the physical principles behind biological structures, we can develop materials with tailored optical properties that mimic these natural systems. One key area discussed is biomimetic materials design, where biological systems such as apple skin and the vision system inspire new materials. Another focus is on intricate optical systems based on refractive index contrast. These principles can be extended to design devices like waveguides, photonic crystals, and metamaterials, which manipulate light in novel ways. Additionally, the review covers optical scattering engineering, which is crucial for biomedical imaging. By adjusting the real and imaginary parts of the refractive index, we can control how much light is scattered and absorbed by tissues. This is particularly important for techniques like optical coherence tomography and multiphoton microscopy, where tailored scattering properties can improve imaging depth and resolution. The review also discusses various techniqu
Examining individual components of cellular systems has been successful in uncovering molecular reactions and interactions. However, the challenge lies in integrating these components into a comprehensive system-scale map. This difficulty arises due to factors such as missing links (unknown variables), overlooked nonlinearities in high-dimensional parameter space, downplayed natural noisiness and stochasticity, and a lack of focus on causal influence and temporal dynamics. Composite static and phenomenological descriptions, while appearing complicated, lack the essence of what makes the biological systems truly "complex". The formalization of system-level problems is therefore important in constructing a meta-theory of biology. Addressing fundamental aspects of cellular regulation, adaptability, and noise management is vital for understanding the robustness and functionality of biological systems. These aspects encapsulate the challenges that cells face in maintaining stability, responding to environmental changes, and harnessing noise for functionality. This work examines these key problems that cells must solve, serving as a template for such formalization and as a step towards t
Since proteins carry out biological processes by interacting with other proteins, analyzing the structure of protein-protein interaction (PPI) networks could explain complex biological mechanisms, evolution, and disease. Similarly, studying protein structure networks, residue interaction graphs (RIGs), might provide insights into protein folding, stability, and function. The first step towards understanding these networks is finding an adequate network model that closely replicates their structure. Evaluating the fit of a model to the data requires comparing the model with real-world networks. Since network comparisons are computationally infeasible, they rely on heuristics, or "network properties." We show that it is difficult to assess the reliability of the fit of a model with any individual network property. Thus, our approach integrates a variety of network properties and further combines these with a series of probabilistic methods to predict an appropriate network model for biological networks. We find geometric random graphs, that model spatial relationships between objects, to be the best-fitting model for RIGs. This validates the correctness of our method, since RIGs have
Morphogenesis, the process of growth and shape formation in biological tissues, is driven by complex interactions between mechanical, biochemical, and genetic factors. Traditional models of biological growth often rely on the concept of homeostatic Eshelby stress, which defines an ideal target state for the growing body. Any local deviation from this state triggers growth and remodelling, aimed at restoring balance between mechanical forces and biological adaptation. Despite its relevance in the biomechanical context, the nature of homeostatic stress remains elusive, with its value and spatial distribution often chosen arbitrarily, lacking a clear biological interpretation or understanding of its connection to the lower scales of the tissue. To bring clarity on the nature of homeostatic stress, we shift the focus from Eshelby stress to growth incompatibility, a measure of geometric frustration in the tissue that is the primary source of residual stresses in the developing body. Incompatibility, measured by the Ricci tensor of the growth metric at the continuous level, can be potentially regulated at the cell level through connections with the surrounding cells, making it a more mea
Biological systems perform an astonishing array of dynamical processes -- including development and repair, regulation, behavior and motor control, sensing and signaling, and adaptation, among others. Powered by the transduction of stored energy resources, these behaviors enable biological systems to regulate functions, achieve specific outcomes, and maintain stability far from thermodynamic equilibrium. These behaviors span orders of magnitude in length and time: from nanometer-scale molecular motors driving morphogenesis to kilometer-scale seasonal migrations, and from millisecond reflexes to millennia of evolutionary adaptations. While physical laws govern the dynamics of biological systems, they alone are insufficient to fully explain how living systems sense, decide, adapt, and, ultimately, control their dynamics. In this article, we argue that control theory provides a powerful, unifying framework for understanding how biological systems regulate dynamics to maintain stability across length and time scales far from equilibrium.
Are biological self-organising systems more ``intelligent'' than artificial intelligence (AI)? If so, why? I address this question using a mathematical framework that defines intelligence in terms of adaptability. Systems are modelled as stacks of abstraction layers (\emph{Stack Theory}) and compared by how effectively they delegate agentic control down their stacks. I illustrate this using computational, biological, military, governmental, and economic systems. Contemporary AI typically relies on static, human-engineered stacks whose lower layers are fixed during deployment. Put provocatively, such systems resemble inflexible bureaucracies that adapt only top-down. Biological systems are more intelligent because they delegate adaptation. Formally, I prove a theorem (\emph{The Law of the Stack}) showing that adaptability at higher layers is bottlenecked by adaptability at lower layers. I further show that, under standard viability assumptions, maximising adaptability is equivalent to minimising variational free energy, implying that delegation is necessary for free-energy minimisation. Generalising bioelectric accounts of cancer as isolation from collective informational structures
Many biological functions are executed by molecular machines, which consume energy and convert it into mechanical work. Biological machines have evolved to transport cargo, facilitate folding of proteins and RNA, remodel chromatin and replicate DNA. A common aspect of these machines is that their functions are driven out of equilibrium. It is a challenge to provide a general framework for understanding the functions of biological machines, such as molecular motors, molecular chaperones, and helicases. Using these machines as prototypical examples, we describe a few general theoretical methods providing insights into their functions. Although the theories rely on coarse-graining of these complex systems they have proven useful in not only accounting for many in vitro experiments but also addressing questions such as how the trade-off between precision, energetic costs and optimal performances are balanced. However, many complexities associated with biological machines will require one to go beyond current theoretical methods. Simple point mutations in the enzyme could drastically alter functions, making the motors bi-directional or result in unexpected diseases or dramatically restr
A nonparametric learning solution framework is proposed for the global nonlinear robust output regulation problem. We first extend the assumption that the steady-state generator is linear in the exogenous signal to the more relaxed assumption that it is polynomial in the exogenous signal. Additionally, a nonparametric learning framework is proposed to eliminate the construction of an explicit regressor, as required in the adaptive method, which can potentially simplify the implementation and reduce the computational complexity of existing methods. With the help of the proposed framework, the robust nonlinear output regulation problem can be converted into a robust non-adaptive stabilization problem for the augmented system with integral input-to-state stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. Furthermore, we apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without the ne
Observable performance is commonly used to characterize biological systems. In adaptive systems, however, similar performances may arise from distinct organizations, and configurations that appear comparable at a given time may follow different longitudinal trajectories. This limitation motivates a methodological framework for moving beyond performance-based interpretation without assuming a complete mechanistic model in advance. This article proposes a bootstrap framework for latent-space representation learning in adaptive biological systems. Here, bootstrap is used in a methodological and epistemological sense: new analytical levels are introduced when the preceding representation becomes insufficient to account for observed adaptive dynamics. The framework is organized around five levels: observable performance, dynamic organization, latent organization, longitudinal viability, and internal predictive approximation. The framework is illustrated by three previously reported gait--occlusion studies, used here only as a methodological case sequence and not as new experimental evidence. The article formalizes how performance analysis led to latent organization, how static latent or
Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons in order to study the effect of their presence on the sleep-wake cycle. A quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized mode
Monocular depth estimation (MDE) aims to transform an RGB image of a scene into a pixelwise depth map from the same camera view. It is fundamentally ill-posed due to missing information: any single image can have been taken from many possible 3D scenes. Part of the MDE task is, therefore, to learn which visual cues in the image can be used for depth estimation, and how. With training data limited by cost of annotation or network capacity limited by computational power, this is challenging. In this work we demonstrate that explicitly injecting visual cue information into the model is beneficial for depth estimation. Following research into biological vision systems, we focus on semantic information and prior knowledge of object sizes and their relations, to emulate the biological cues of relative size, familiar size, and absolute size. We use state-of-the-art semantic and instance segmentation models to provide external information, and exploit language embeddings to encode relational information between classes. We also provide a prior on the average real-world size of objects. This external information overcomes the limitation in data availability, and ensures that the limited cap
Recent boom in foundation models and AI computing have raised growing concerns on the power and energy trajectories of large-scale data centers. This paper focuses on the voltage issues caused by volatile and intensity of data center power demand, which also aligns with recent observations of more frequent voltage disturbances in power grids. To address these data center integration challenges, we propose a dynamic voltage control scheme by harnessing data center's load regulation capabilities. By taking local voltage measurements and adjusting power injections at each data center buses through the dynamic voltage and frequency scaling (DVFS) scheme, we are able to maintain safe voltage magnitude in a distributed fashion with higher data center computing load. Simulations using real large language model (LLM) inference load validate the effectiveness of our proposed mechanism. Both the LLM power data and proposed control scheme are open sourced.
Primates exhibit a robust deviation from canonical allometric scaling: at fixed body mass, their lifespans exceed those of non-primate mammals by factors of two to three. A rhesus macaque (8 kg) lives 25-40 years, whereas a cat of similar mass rarely exceeds 18 years. This statistically significant clade-level excess cannot be explained by standard metabolic or ecological models. We provide a thermodynamic explanation within the Principle of Biological Time Equivalence (PBTE), where lifespan is determined by a finite cycle budget governed by entropy production. We show that primates reduce entropy production per physiological cycle through increased neural energy allocation. The neural power fraction acts as a control parameter, extending the effective lifetime cycle count. Three mechanisms, predictive regulation, enhanced repair, and behavioral buffering, jointly suppress dissipation. This yields a quantitative neuro-metabolic multiplier that explains primate longevity and provides testable predictions linking brain energetics, entropy production, and lifespan.
Droplet formation has emerged as an essential concept for the spatiotemporal organisation of biomolecules in cells. However, classical descriptions of droplet dynamics based on passive liquid-liquid phase separation cannot capture the complex situation inside cells. This review discusses three distinct aspects that are crucial in cells: (i) biomolecules are diverse and individually complex, implying that cellular droplets possess complex internal behaviour, e.g., in terms of their material properties; (ii) the cellular environment contains many solid-like structures that droplets can wet; (iii) cells are alive and use fuel to drive processes out of equilibrium. We illustrate how these principles control droplet nucleation, growth, position, and count to unveil possible regulatory mechanisms in biological cells and other applications of phase separation.
There are innumerable 'biological complexity measure's. While some patterns emerge from these attempts to represent biological complexity, a single measure to encompass the seemingly countless features of biological systems, still eludes the students of Biology. It is the pursuit of this paper to discuss the feasibility of finding one complete and objective measure for biological complexity. A theoretical construct (the 'Thread-Mesh model') is proposed here to describe biological reality. It segments the entire biological space-time in a series of different biological organizations before modeling the property space of each of these organizations with computational and topological constructs. Acknowledging emergence as a key biological property, it has been proved here that the quest for an objective and all-encompassing biological complexity measure would necessarily end up in failure. Since any study of biological complexity is rooted in the knowledge of biological reality, an expression for possible limit of human knowledge about ontological biological reality, in the form of an uncertainty principle, is proposed here. Two theorems are proposed to model the fundamental limitatio
Effective collaboration requires Socially Shared Regulation (SSRL), but students often lack these skills. This study introduces the MIRACLE (Multi-Agent Intelligent Regulation to Advance Collaborative Learning Environment) system, which supports SSRL by orchestrating metacognitive regulation and proactively providing emotional and motivational support. We conducted a quasi-experimental study with 90 fifth-grade students. The experimental group (n=42) used a collaborative platform CocoNote equipped with MIRACLE, while the control group (n=48) used the same platform with a general GPT assistant. Quantitative results show the MIRACLE group achieved significant gains across SSRL phases (Planning, Monitoring, Reflection) and produced higher-quality collaborative artifacts compared to the control group. Qualitative findings indicate students perceived MIRACLE as an effective facilitator for cognitive, regulatory, and emotional support. This study demonstrates that specialized, orchestrated AI systems are more effective than generic AI in enhancing SSRL.
In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for fast variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed.
This book discusses the necessity and perhaps urgency for the regulation of algorithms on which new technologies rely; technologies that have the potential to re-shape human societies. From commerce and farming to medical care and education, it is difficult to find any aspect of our lives that will not be affected by these emerging technologies. At the same time, artificial intelligence, deep learning, machine learning, cognitive computing, blockchain, virtual reality and augmented reality, belong to the fields most likely to affect law and, in particular, administrative law. The book examines universally applicable patterns in administrative decisions and judicial rulings. First, similarities and divergence in behavior among the different cases are identified by analyzing parameters ranging from geographical location and administrative decisions to judicial reasoning and legal basis. As it turns out, in several of the cases presented, sources of general law, such as competition or labor law, are invoked as a legal basis, due to the lack of current specialized legislation. This book also investigates the role and significance of national and indeed supranational regulatory bodies f