Biosystems

A key scientific challenge is to develop a universal theory of life that integrates our biological knowledge with fundamental logical principles. We propose that a "five nodes" principle may govern the origin of life and consistently exist hierarchically within living systems. In our investigation, we explored autocatalytic chemical reaction networks (CRNs) as potential origins for methanotrophy and anoxygenic phototrophy, aiming to validate the "five nodes" principle in the emergence of autopoietic systems. Our research revealed the emergence of autocatalytic peptides and weakly reversible realizations within the MSA reaction network (composed of CH4, SO42-/SO32-, and NH4+) as well as in the light-Sammox (sulfurous reduction coupled to anaerobic ammonium oxidation)-driven CRN (composed of HCO3-, SO32-, and NH4+) under hydrothermal conditions. Furthermore, we identified the possible emergence of three main interdependent components essential for life within the two reaction networks: membrane compartments, peptide nucleic acids (PNA) backbones, and catalytic capacities for energy release reactions. Our findings suggest that non-equilibrium synergy of five bioessential elements (NESFBE) can facilitate proto-energy and material metabolism, thereby enabling diverse scenarios for lifes origin. Importantly, our discovery indicates linear constraints present in these CRNs that contributed to lifes inception, which is the mathematical foundation of the "five nodes" principle. Linear constraints determine both the emergence and self-disintegration of autopoietic systems. We infer a period five existence based on hierarchical structures found within autopoietic systems, and "period five indicates autopoiesis" could be one of universal theory of life.

Muscle regeneration relies on the coordinated activation of muscle stem cells, whose fate decisions are regulated by intracellular gene expression dynamics and intercellular coupling via the Notch-Dll1 signaling pathway. Central components of this regulatory network include the transcriptional repressor Hes1, its target gene Dll1, and the myogenic regulator MyoD. Experimental and theoretical studies have shown that proliferating muscle stem cells exhibit oscillatory dynamics of these molecules, whereas sustained expression is associated with differentiation. Here, we investigate the dynamics of a previously established delay differential equation model of two coupled muscle stem cells. Using linear stability analysis, we systematically characterize how model parameters affect the transition between stable and unstable steady states. In addition, numerical bifurcation analysis is employed to study the influence of intercellular coupling strength and delay on the system dynamics. Our analysis shows that continuous variation of the coupling delay induces repetitive changes in the stability of the steady state. However, this sensitivity towards the coupling delay is confined to a narrow region of parameter space and therefore requires a fine tuning of all other parameters. Beside the identification of parameter sets for in-phase and out-of-phase oscillations, we demonstrate the possibility of coexisting stable in-phase and out-of-phase oscillations, a dynamical feature that has not been reported previously. While oscillation periods are largely determined by intracellular regulatory mechanisms, oscillation amplitudes can be strongly modulated by intercellular coupling. These results provide new insight into how the intracellular network and intercellular communication interact to generate different collective dynamics.

Cell motility is powered by the bacterial flagellar motor, a rotary nanomachine whose activity is dynamically modulated by external stimuli. In Magnetospirillum gryphiswaldense, magnetic and chemical inputs are thought to converge at the level of motility control, yet the mechanisms underlying chemotactic regulation remain poorly understood. Here, we seek to establish a quantitative reference-state of a model strain of magnetotactic bacteria through bacterial flagellar motor dynamics. To achieve this goal, magnetotaxis was kept as a natural factor by keeping the earth's magnetic field as the only source of magnetism. To avoid aerotaxis bias, oxygen gradients were removed by implementing two different constant oxygen conditions: environmental oxygen exposure, and limited oxygen exposure. Together, the tethered-cell bacterial flagellar rotational assay and the free-swimming assay in the absence of external stimuli presented in this paper establish a framework for investigating motor and cellular swimming adaptation to magnetic, aerotactic, and chemical signals. Under reference-state conditions, the bacterial flagellar motor showed a tendency to exhibit log-normal distributions for the time spent in each motor state: runs in different directions (counter-clockwise and clockwise), and pause. A semi-Markov reference-state model was developed to provide a quantitative description of bacterial flagellar motor dynamics. The model revealed that cell magnetic polarity modulates the transition pathways leading to the paused state, whereas oxygen, in the absence of a gradient, primarily regulates residence in each motility state.

Time compaction theory is a general framework explaining how a brain can efficiently deal with dynamic situations occurring in, e.g., sports games. It involves a geometric representation of the time dimension, which enables effective learning and strategic action planning. The theory has recently received experimental support in humans. However, its current computational model has an important limitation: it does not account for deliberate waiting and speed modulation, behaviors ubiquitous in natural environments. This work substantially extends the original model formulation by a dimensional lifting of an n-D workspace into (n + 1)-D mental space, where time remains geometrically embedded. The proposed biologically inspired computational model can generate adaptive behavior across increasingly complex situations, from navigation in everyday social environments to competitive sports. Furthermore, by actively conditioning the expected responses of other agents and stabilizing future predictions, we introduce the concept of uncertainty points in sequences of generalized cognitive maps to support the generation of adaptive strategies in interactive environments, where future prediction has a limited time horizon. Thus, we provide a mechanism for chaining short-term solutions into long-term strategies, which is illustrated by simulating the behavior of a player in a real football game. Author summaryHumans often anticipate future interactions in dynamic environments. Many behaviors, such as avoiding other pedestrians, letting someone pass through a narrow corridor, or reproducing the kind of dribbling maneuvers performed by elite football players, require deciding not only where to move but also when to move. Existing theories suggest that the brain simplifies such situations by representing future interactions as static spatial maps, making them easier to learn and recall. However, current computational models cannot naturally account for common behaviors such as waiting, slowing down, or modulating speed. Here we show that these behaviors readily emerge if the model space is extended by an additional virtual coordinate that encodes accumulated waiting rather than physical time. The proposed model simultaneously admits a wide variety of behaviors, including speed modulation, multigoal decisions, and compound actions, while preserving the principles of time compaction. We illustrate the model in everyday situations and by reproducing two real football plays, comparing the observed behaviors with model simulations. Our results suggest computational principles through which the human brain may efficiently represent, memorize, and exploit dynamic situations.

Rule-based languages have proven effective for modeling systems of interacting structured entities as typically encountered in chemistry and molecular biology. We present PyKappa, a rule-based modeling package written in Python whose interpreted nature enables interactive simulation and analysis, including by agentic AI. The package seeks to broaden the base of developers by utilizing a widely known programming language and serves as an easy-to-deploy teaching tool. Using PyKappa, we conduct a case study of phase separation.

Based on our experimental observation of activation state oscillations of different frequencies used to communicate information by the master human stress response regulator protein p38 MAPK 1, we develop a simple graphical approach for understanding and predicting the behavior of complex biological networks acting upon signals carrying information as different frequency waves of chemicals. This approach uses the same techniques used for analyzing and understanding information transmission using waves of electrical currents and fields used in electrical alternating current (AC) circuits. We show how biological components can be organized to behave as standard components found in electronic telecommunications circuits. Finally, we demonstrate how such components can be organized into complex biological signaling cascades whose behavior can be qualitatively and quantitatively understood, and whose output resembles that experimentally observed in p38.

Obesity is a major health concern worldwide and is caused by an excessive fat accumulation in the body due to adipogenesis. Recent studies suggest that excessive stress or disruption of circadian rhythms can enhance adipogenic commitment and lead to obesity. Moreover, this adipogenic commitment occurs at a specific time of day, highlighting a correlation with the circadian rhythm. However, the dynamical nature of this kind of stress-induced adipogenic differentiation remains an unresolved puzzle. Herein, we proposed a mathematical model centred on the key transcription factor PPAR{gamma}, associated with adipogenic differentiation, and demonstrated that adipogenic commitment is a bistable, irreversible differentiation process in which slow positive feedback regulation of PPAR{gamma} primarily controls the differentiation commitment threshold. The model reproduced the experimental observations regarding the extent of adipogenesis induced by constant and pulsatile stress input signals and explained the correlation between adipogenic differentiation time and circadian phase. It further predicts how to control the adipogenic commitment even under stressful conditions. Overall, our study elucidates how stress signalling dynamically governs adipogenesis.

Motivation: The stoichiometry (or net conversion) of a catabolic pathway is an often used principle of biochemistry. It expresses the molar yield of charged energy carriers (e.g. ATP) and catabolic products (e.g. lactate) on the energy source (e.g. glucose). Product yields are engineering targets of metabolic engineering and used in microbial ecology to assess energy metabolisms of microbial species. For a single species under a single condition, the catabolic pathway is frequently assumed fixed, while there might be multiple options encoded in its genome. To find these options, the manual (heuristic) methods that have been used for decades fall short. Results: In this paper, we explain how net conversions can be calculated from reaction stoichiometries of a metabolic network and evaluated using thermodynamic information. We start with an (old) heuristic method. Next, we explain we relate the net conversions of metabolic networks to their elementary flux modes (EFMs) and show that a single EFM gives rise to a single net conversion. EFMs are mathematical objects that are computable with existing software. We use these to illustrate how all net conversions of complex (pan-)metabolic networks can be computed. We consider examples from aerobic and anaerobic microbiology. Then, we introduce the parameter {Omega}, the driving force per unit flux, which allows for the thermodynamic comparison of pathways. To calculate {Omega}, only the standard Gibbs free energy potential, i.e., {Delta} G m' of the net conversion and its corresponding EFM are required. A generic workflow (and all underlying Python code) are provided, as well as applications to perform the workflow without coding. We also provide those software packages that automate our methods. Impact: This paper serves as an illustration of how modern computational systems biology can be used to automate the calculation of net conversions in microbial ecology and metabolic engineering. We hope that this paper inspires future metabolism research using quantitative, rigorous methods.

The circadian clock allows living systems to anticipate environmental daily variations by scheduling cellular mechanisms according to the time of the day. The reciprocal interplay between metabolism and circadian clock is essential for energy homeostasis, and the disruption of metabolic clock inputs contributes to dysfunction of clocks in peripheral tissues. However, the molecular mechanisms through which the feeding/fasting cycle entrains peripheral clocks remain incompletely understood. Here, we investigate experimentally and theoretically the role of AMP-dependent kinase (AMPK), a key fasting sensor, in metabolic regulation of the circadian clock. Using a luciferase reporter driven by the Bmal1 promoter to monitor molecular clock activity in human U2OS cells, and thanks to a signal processing method based on the Hilbert transform to retrieve the instantaneous phase and period of circadian signals, we show that pharmacological activation of AMPK by AICAR significantly elevates Bmal1 promoter activity and markedly lengthens the clock period in a dose-dependent manner. Conversely, the clock period is shortened by the pharmacological inhibition by SR18292 of Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC-1-alpha). Importantly, the action of AICAR is abolished by FK866, a nicotinamide phosphoribosyltransferase (NAMPT) inhibitor, demonstrating that AMPK-dependent modulation of Bmal1 promoter activity requires NAD+ availability. These experimental results are recapitulated by numerical simulations of our previously published mathematical model, where PGC-1-alpha plays a key role in mediating AMPK activity to the clock. Moreover, the comparison of experimentally measured and theoretically predicted phase response curves, following AMPK activation at different circadian phases, provides an additional validation of the model. By integrating biological experiments with mathematical modeling, our results identify a key mechanism through which metabolic factors can entrain and regulate the circadian clock via NAD+-dependent AMPK-mediated regulation of Bmal1 promoter activity.

1. Plants produce a great chemodiversity, which is the diversity of specialized metabolites (SMs). These SMs are produced in complex metabolic pathways and play an important role in inter-species interactions. There are numerous hypotheses about the evolutionary processes which brought about and maintain chemodiversity. Some have been partially tested in lab and field studies. However, some of their assumptions and predictions are better tested by quantitative modeling, and so far no quantitative model has investigated the role of metabolic pathways. 2. To close this gap, we developed an individual-based model for metabolic pathway evolution. It models enzymes creating metabolites with various modifications. Enzymes undergo inheritance and mutation. We used the model to compare the screening and interaction diversity hypotheses. 3. The screening hypothesis predicts promiscuous enzymes, genetic drift, the presence of many non-beneficial metabolites, and high metabolite richness. The interaction diversity hypothesis predicts specialized enzymes, selection, the almost exclusive presence of beneficial metabolites, and situation- dependent metabolite richness. We found that the patterns predicted by the screening hypothesis did not occur, while those predicted by the interaction diversity hypothesis did. 4. This provides reason to favor the interaction diversity hypothesis over the screening hypothesis when connecting empirical results to their evolutionary context

Predicting patterns of behavioural coordination that emerge in small interacting groups is challenging because goal-directed social action is shaped by complex reciprocal and compensatory dynamics. In this study, we examined whether formal symmetry principles derived from group theory could explain coordination patterns among children performing a triadic jumping task. We investigated how geometric symmetries of the task environment and dispositional (a)symmetries associated with leader-follower tendencies jointly constrain collective behaviour. Forty-seven children were classified into symmetric or asymmetric triads based on teacher evaluations of leadership dispositions. Each triad completed multiple trials of a synchronized jumping game requiring movement between adjacent hoops arranged in triangular or square configurations. Results showed that temporal asymmetries in inter-child movement (first, second, or last to jump) were consistent with group-theoretic predictions. In triangular configurations, observed asymmetries corresponded to the highest-order subgroup defined by task and dispositional symmetries. These findings demonstrate that environmental symmetry exerts a hierarchically dominant constraint on collective coordination, within which actor dispositional (a)symmetries further modulate emerging patterns.

Microbial growth has often been analyzed under the assumption that microorganisms have evolved to optimize phenotypic characteristics of interest, such as growth rate and growth yield. This assumption has been useful, for example, for the genome-scale modeling of metabolism and the study of the allocation of cellular resources to physiological processes. In many experimental situations of interest, however, microorganisms are found to be suboptimal with respect to phenotypic characteristics that are thought to be favorable in that situation. Whereas a strong theoretical framework exists to mathematically relate cellular resource allocation strategies to Pareto optimality of microbial growth and other biological processes, much less is known about the consequences of Pareto suboptimality. We extend the framework to the latter case and show that a given Pareto suboptimal phenotype can be explained by a range of underlying resource allocation strategies, each corresponding to a different growth physiology and biomass composition. We test the predictions with the help of a coarse-grained model of microbial growth and published experimental data, which relate Pareto suboptimal rate-yield phenotypes of Escherichia coli and the microalga Tisochrysis lutea to the macromolecular composition of the cells (storage metabolite and total protein contents). Changing the focus from Pareto optimality to suboptimality provides interesting leads to exploring the diversity of growth strategies that can support a given phenotype. This change of perspective is of practical interest, because some of the growth physiologies within this range may be important for biotechnological applications

Across metazoa, morphogen gradients differentially regulate gene expression and activate a spatially distinct program to specify body axis development. The Drosophila gap gene network, initiated by maternal morphogen Bicoid, is one of the most well-studied systems. Several regulatory interactions act synergistically to produce distinct gap gene expression patterns along the anterior-posterior (AP) axis of the blastoderm stage Drosophila embryo to ensure the proper segmentation of the larval and, eventually, adult stage fly. Several mathematical models have been proposed to summarize the interconnectivity of gap gene regulatory elements and predict expression in mutant systems. However, these models have not successfully predicted the gap gene expression profile over the entire AP axis. Here, we present an Enhancer Activity-informed Gap GEne Regulatory network (EAGER) model that incorporates enhancer activity-driven differential regulation along the AP axis, which successfully summarizes gap gene expression patterns over the entire AP axis. We validated the predictions of EAGER on Kr mutants and performed a comprehensive parametric sensitivity and identifiability analysis to evaluate the robustness of the EAGER model fits and predictions. We also propose a reduced version of the model, rEAGER, which identifies a minimal set of regulatory interactions and successfully summarizes the gap gene interactions over the entire AP axis. Our results suggest that the expression driven by individual enhancers must be accounted for in models of developmental pattern formation.

The dominant paradigm for temperature robustness in biomolecular circuits is for the parameters to be tuned to have matching temperature dependencies so that their overall effect cancels out. This contrasts with the robustness due to circuit structure, typically operative in circuits where robustness to a single input parameter is desired. The importance of the circuit structure in temperature robustness is generally unclear. We addressed this issue in a benchmark negative feedback circuit using a combination of theoretical modelling and experimental measurements. We found that the response to a temperature perturbation in a model of negative feedback was qualitatively different from the response in a model without feedback. We experimentally measured the response of the negative feedback circuit to a temperature perturbation and found that it was smaller than that of the circuit without feedback, in line with the theoretical finding. We confirmed this theoretical prediction experimentally. The initial response of the negative feedback circuit, paradoxically, was larger than the circuit without feedback. The resolution of this paradox was in accounting for the faster dynamics in the negative feedback circuit. These results show a simple design principle of temperature robustness that can operate in a widespread circuit motif and may also apply to other perturbations which, like temperature, affect multiple parameters simultaneously.

We show that the p53-Mdm2 gene interaction can be understood as a form of antithetic feedback, but with mixed feedback loops. In particular, we show that this viewpoint sheds light on the emergence and robustness properties of p53's oscillatory behaviour, as observed experimentally.

Understanding noise propagation in gene regulatory circuits requires accounting for both model and resource constraints. In this work, we investigated the role of model order in influencing stochastic behaviour by deriving and analytically comparing reduced protein-only models with higher-order models that include mRNA and molecular complexes, and found that protein-based models can exhibit higher noise levels in the gene expression. Through frequency-response analysis, we explained that the higher-order models provide additional noise-filtering effects. We also analyzed a one-dimensional constrained model and showed that the Fano factor decreases as the strength of resource constraint increases. Finally, we considered larger circuit motifs, such as toggle switches and incoherent feed-forward loops, and found that resource limitations can minimise stochastic switching in a bistable circuit, whereas in an incoherent feed-forward loop, resource constraints can make the adaptation faster. Our results highlight that both mechanistic detail and shared resource constraints play a central role in determining fluctuation levels in biomolecular circuits.

This paper presents and critically reviews the results of original and some literature based experimental studies conducted by the authors last years on the structural organization of DNA in dormant (starvation stress), anabiotic dormant (4 HR treatment) E. coli cells, as well as the K12 {Delta}dps strain, which lacks the Dps protein (Dps null E. coli). The experimental data includes small-angle synchrotron radiation diffraction (SAXS) and transmission electron microscopy (TEM) data. Synchrotron radiation diffraction experiments on K12{Delta}dps cells allowed us to conclude that peaks at 44.3, 22.1, and 14.8 angstrom resolutions are associated exclusively with ordered DNA organization. Peaks at 44.3, 22.1, and 14.8 angstrom resolutions are also observed for samples of dormant (starvation stress) cells and anabiotically dormant cells. Therefore, this ordered DNA organization also applies to samples of dormant and anabiotically dormant cells. A model is proposed that considers the ordered DNA organization in the cell as a cholesteric liquid crystal. The powder diffraction pattern calculated based on this model is compared with experimental small angle X ray scattering (SAXS) data obtained on Dps-null cell samples. The model completely reproduces the key features of the experimental diffraction pattern from Dps-null cell samples. Accordingly, the cholesteric liquid crystal model corresponds to DNA packaging in dormant and anabiotically dormant cells. Cholesteric liquid crystal ordering should be further considered in all models of cellular DNA packaging. To address the question of which structural organization of DNA predominates in the cell: the cholesteric liquid crystal or nanocrystalline or whether they coexist and fully manifest themselves under different external conditions, it is necessary to utilize the latest methodological advances in structural analysis.

Ecological interactions play a crucial role in driving speciation and adaptive radiation. According to the adaptive dynamics theory of evolution in one-dimensional trait spaces, such evolutionary diversifications can occur when evolutionary branching points (convergence stable and evolutionarily unstable singular points) exist in the trait spaces. However, these evolutionary diversifications may occur across multiple traits at once, as exemplified by various within-species ecotypic diversifications involving multiple traits or genes. This paper attempt to extend this branching point condition to evolution in multi-dimensional trait spaces. Two criteria, termed branching possibility and branching inevitability, are developed to evaluate the likelihood of evolutionary branching in multi-dimensional trait spaces. Branching possibility guarantees the existence of evolutionary pathways that lead to branching (where deterministic parts of these pathways are described with the canonical equation of adaptive dynamics theory). Branching inevitability guarantees a steady progression of evolutionary branching (where the progression degree is described with a time-increasing function related to the local Lyapunov function, the potential function in an evolutionary potential game, and Fisher's fundamental theorem). Numerically simulated evolution in multi-dimensional trait spaces show that points having branching possibility or inevitability can induce evolutionary branching not only under asexual reproduction but also under sexual reproduction.

Dysfunctions in transcription cause severe human diseases. In eukaryotes, transcription initiation by RNA polymerase (Pol) II requires the formation of the pre-initiation complex (PIC) composed of general transcription factors (GTFs), Pol II, and an essential multiprotein coactivator, Mediator. In vitro experiments with GTFs and Pol II have depicted a linear sequence of PIC assembly. However, PIC assembly paths in vivo at the genomic scale and Mediator's role in these paths remain poorly understood. One strategy characterizes ChIP-seq occupancy alterations in Mediator mutants, but analysis of these data still lacks a formalized interpretation framework. In this study, we address this need by developing a quantitative framework that scores candidate assembly paths according to their ability to explain these alterations. This framework combines a model of PIC assembly based on a system of differential equations with parameter optimization based on a penalized criterion. We applied this new framework to datasets from two yeast Mediator mutants, in the Med17 and Med10 subunits. Our results show that the best-supported PIC assembly paths differ from those inferred in vitro. In particular, we show that it is important to distinguish the core TFIIH module from the TFIIK kinase module, and that similar paths starting with Mediator or TBP receive different levels of support. Furthermore, although multiple paths fit the data equally well, they differ markedly for specific gene groups. Taken together, the results show that the path can depend on the gene, and are also compatible with more than one path being operational in vivo for a single gene. This work improves our understanding of PIC assembly paths and transcription initiation, and opens perspectives for future modeling and experimental studies.

Organisms must adapt to environmental changes occurring across multiple time scales, with endogenous multiscale clocks coordinating physiology and behavior with recurring environmental rhythms, including the dominant 24-hour cycle and faster ultradian rhythms. The Madeira cockroach (Rhyparobia maderae) provides a suitable model for investigating such multiscale temporal organization. Here, locomotor activity was recorded in running-wheel experiments under constant darkness. While the endogenous circadian clock produces a clearly visible 24-hour rhythm, it remains unknown whether locomotor behavior also exhibits temporal patterns at additional time scales. These temporal patterns cannot be found by classical frequency analysis, as they are veiled by higher harmonics of the circadian rhythm which are in the same frequency range. Unsupervised machine learning methods such as K-Means clustering, self-organizing maps and Gaussian mixture are used in search for fast ultradian rhythms possibly linked to circadian cycles in locomotor activity. Prior to applying these methods, data metrics are defined which characterize bouts of activity (called activity impulses) compared to periods of reduced activity. A stochastic pattern was found in these activity metrics which characterizes the time distance between activity impulses. Across all approaches, a consistent ultradian rhythm of approximately one hour was identified in the timing of the activity maxima. This rhythm was mainly detected during the subjective night, suggesting circadian control, and appears to consist of two components with periods of approximately 40 minutes and 1.5 hours. The method proposed in this paper is applied to two cockroach groups with different levels of activity, and is generalizable to diverse datasets occurring in the form of a time series with a dominant rhythm.