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.

Predicting and understanding behaviour is a primary objective of many disciplines, especially human behaviour, as it is the cause of many of the worlds most pressing problems. Although it is a fundamental concept in multiple disciplines, there is no agreed operational definition of what it is. Neither is there a generally agreed theoretical framework for predicting it. Here we propose a data-driven approach, using the "Conductome" -- the complete set of factors that both predict and explain a behaviour -- to operationalise a discipline-neutral definition of behaviour that is based on an ensemble of stimulus/response measurements of a system, showing that it must be determined through a process of statistical inference. As the prediction of behaviour can be characterised as a classification problem, we argue that Bayesian classifiers offer a promising framework in which explainable prediction models that can approximate the Conductome can be developed. We show the efficacy of the framework using a dataset of 1075 persons, with over 3000 features, constructing a model for predicting sedentariness, a behaviour that is a known risk factor for obesity and metabolic disease. We analyse the effect size, coverage, statistical significance and potential causality of a subset of 396 features associated with 58 variables.of different types.

Small molecule modifiers whence bound, allosterically, will alter the binding of a macromolecule to one- or more-cognate substrates/partners via conformational and non-conformational changes. Although allostery is inferred directly from empirical data, the mathematical basis of these models, constraints deployed and choice of parameter(s) are not clear. Here, we present and characterize a discrete-to-continuous mathematical model for ensemble distributions of a ligand-interacting macromolecular species across milieux-dependent conformational states and examine its role in the genesis and progression of cooperative binding. The premise, of our model, is a set of occupancy matrices (sparse, binary, strictly delocalized) which can be partitioned by a probability-based hyperparameter into mutually exclusive proper subsets of occupancy matrices with identical multinomial probabilities. Since each subset is canonical with a constituent occupancy matrix, it is characterized by a unique multinomial probability. The inner product of combinatorial pairs of all mutually exclusive subsets of occupancy matrices, with an expression for the summed transitional probabilities (finite differences between unique multinomial probabilities), is the differentiable matrix of strictly positive real-valued numbers for the system of ensemble distributions. Whilst the harmonic mean is presented as a generic solution for a system of ensemble distributions, the row-wise definite integral for each column is the finite union of open intervals (contiguous, strictly monotone) which in tandem with a set of interval-specific and bounded transitional probabilities constitutes a piecewise smooth curve (path-connected-, closed- and compact-set). Our discrete-to-continuous model is phenomenological and able to recapitulate the basic tenets of cooperative binding whilst offering insights into the genesis and progression of the same.

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.

Derived from previous observations on equal and cross-frequency coupling, we evaluated the proposal that equal and cross-frequency phase synchronization may characterize the integration-segregation perspective of cerebral sensory-motor processing. Using brain recordings obtained in normal conditions and in conditions of diminished sensory input (eyes closed wakefulness, sleep and coma, when there is presumably less functional segregation of sensory-motor processing in neural networks), we assessed potential differences in partitioning of the synchrony state space linked to cross-frequency synchronization. More partitions were found in conditions of decreased sensory input. In addition, there was a less complex synchrony state space in cross-frequency as compared with equal-frequency coupling, in terms of fewer connectivity configurations. These results support the idea that equal-frequency coupling favours integration from multiple brain regions occurring in a complex synchrony state space rich in possible connectivity configurations, whereas cross-frequency coupling contributes to segregation, or localized sensory-motor transformations taking place in specific brain areas. This evidence may contribute to new considerations about the much-discussed role of multi-frequency relations in neuronal activity, and how the structural and functional modular organization of the nervous system is able to generate the coordinated activity needed for conscious and appropriate cognitive behaviors in complex environments.

Numerous advances in quantum and computational chemistry over the last decades, well as the development of computer science, allowed utilisation of more precise and complex models, which can be now applied to much bigger systems than in the past. The authors used Gaussian, coupled with theoretical methods, to predict a new way of peptide bond formation, which could have taken place in prebiotic conditions. To better tackle this difficult task, the properties of substrates (glycine-derived radicals) were extensively analysed, using the aforementioned tool - Gaussian, paired with taking resonance and hybridisation into account, to better understand the stereochemistry and the very nature of processes taking place. The result is a series of reactions, which without any sophisticated catalysts and with relatively low energy thresholds ({inverted exclamation}20 kcal/mol) can lead to formation of dipeptides (and further, oligopeptides). The authors also hope, the other predicted properties of the investigated molecules can be of use to any researcher, who would like to utilise them in their experiments. Author summaryOur goal was to investigate a way first peptide bonds in prebiotic conditions could have been formed. This is an extremely important step in research into the beginning of life on Earth. We found a very promising series of reactions, which uses atomic hydrogen as its only catalyst and confirmed our expectations with theoretical calculations, using Gaussian. There are two radicals derived from glycine, which perform major roles in the process, so we investigated their properties with Gaussian and verified that the results are in agreement with our own theoretical considerations. This involved checking for possible geometric isomers and conformers and creating models which could explain their properties. We are well aware that such calculations have limitations and there is no model, which is 100% accurate, so our results should be further confirmed by empirical data in the future. However, we still to be as thorough as possible in how we approached the subject.

1.Partial Rank Correlation Coefficient (PRCC), usually performed following Latin Hyper-cube Sampling (LHS), is a global sensitivity analysis that quantifies the monotonic relationship between model parameters and the desired output. To carry out this analysis, a range of acceptable parameter values must be known or estimated. However, within a biological context, approximating these values may be difficult. Parameter values and ranges can be taken from different organisms or systems or be estimated to produce qualitative phenomena in the model. Using a mathematical model of the epithelial mesenchymal transition (EMT) as a test case, this work examines how the parameter ranges chosen prior to analysis can influence LHS-PRCC results and shape subsequent analysis interpretations. Previous LHS-PRCC analysis of this model restricted parameters to {+/-}10% of their original value, which limits the scope and interpretability of parameter influence. Such a small range assumes, in the biological sense, that parameters are well-measured with little variability. Here, this work extends the previous analysis and explores several parameter ranges ({+/-}25%, {+/-}50% of the original value). This work also tests whether, within the {+/-}10%, {+/-}25% and {+/-}50% parameter ranges, the bistable switch present in the original model are maintained. Ultimately, this work showcases how a choice made prior to analysis, such as the accepted parameter ranges for biological rates and values in complex dynamical systems can influence sensitivity analysis results and interpretability. Additionally, these choices can have hidden consequences, such as the loss of phenomenological behavior. Thus, explicit prior knowledge about the appropriate parameter values is needed before using analysis to guide future experiments and model development.

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.

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.

Although the "RNA world" hypothesis suggests that RNA played a crucial role in the origin of life [7], the functional framework of RNA in prebiotic protein synthesis and the mechanisms of genetic code formation during the prebiotic period remain poorly understood. Here, using the prebiotic "primordial soup" as a model, we reconstructed the detailed steps that would yield a protein with a stable ordered amino-acid sequence in the "primordial soup" at the prebiotic period. In the "primordial soup", a large number of medium- to large-sized biomolecule-like substances--such as RNA-like and protein-like molecules of various sizes and shapes, as well as related polymers like amino-acid-RNA-like etc.--did generate and accumulate. Moreover, protein-like and RNA-like molecules formed even more intricate complexes. These complexes bound free mRNA-like molecules through complementary base pairing. Subsequently, with an extremely low probability, two adjacent amino-acid-RNA-like molecules became bound to this free mRNA-like molecule, and their amino acids underwent a condensation reaction by the complexes, producing peptides and eventually proteins or polypeptides. This free mRNA-like molecule exhibits a certain flexible structure, whereas the super-large complexes formed by protein-like and RNA-like molecules (which possess certain activities) and the amino-acid-RNA molecules exhibit relatively rigid structures. Long-term evolution and mutual selection led to the emergence of proteins with stable amino acid sequences and moderate catalytic activity. In this way, the nucleotide information embedded in such mRNA-like molecules indirectly express through protein synthesis--a process we term the "A Co-Adaptation Flexible-Rigid Docking Model", where flexible mRNA-like molecules dock onto rigid complexes to enable ordered peptide formation. Finally, we show how trinucleotide codons emerge naturally from the flexible-rigid docking constraints.

Single cells display a range of complex behaviors normally associated with a nervous system, including basic forms of learning like habituation. The giant ciliate Stentor coeruleus habituates to mechanical stimuli and shows many of the hallmark features characteristic of habituation in animal cells. When Stentor cells are mechanically stimulated by a predator or other stimuli, an action potential fires and leads to calcium-dependent contraction. When the same cell is repeatedly stimulated, it becomes less likely to respond, thus showing habituation. While the molecular basis of habituation in Stentor is not yet known, it has been shown to involve CaMKII, which also plays a key role in learning in neurons. The presence of an action potential, the role of calcium in the response, and the involvement of CaMKII in habituation, all suggest a potential deep conservation of learning mechanisms between single-celled protists and the neurons of animals. A number of different models have been proposed to explain habituation in a single cell but existing data in Stentor are unable to clearly rule out any of these models or favor others. Here we report a frequency domain analysis of habituation in which we measure the response probability of Stentor cells to pulsatile stimuli delivered at a range of frequencies. We find that the Bode plot of the frequency response resembles a classic low pass filter, with a flat passband at low frequencies, a clear corner frequency, and a linear roll-off. However, unlike standard low pass filter, the roll-off occurs with a slope of -30dB/decade, thus showing a fractional-order behavior. None of the existing models for habituation in Stentor, at least in their current form, predict this form of the frequency response, leading us to look for other explanations. We tested, and ruled out, a model based on a refractory period associated with the re-extension of cells following contraction. Inspired by methods used in analog circuit design to approximate fractional order systems using conventional lumped devices, we developed a model in which a series of distinct molecular species, such as different multimeric complexes of CaMKII, acting in parallel to inhibit the response, produce a fractional-order effect. The fractional order behavior of habituation in Stentor resembles the fractional-order behavior of adaptation in neurons, further supporting the idea that neurons may employ similar mechanisms for learning as were already present in unicellular eukaryotes prior to the evolution of metazoa.

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.

In mammalian cells, under normal circumstances, the p53 protein exhibits oscillatory dynamics in response to DNA damage and maintains the cells in a cell-cycle-arrested state. Intriguingly, some cells can escape this cell-cycle-arrested state even after prolonged DNA damage, and often undergo mitotic catastrophe. In this context, the precise role of p53 dynamics and its complex interplay with cell-cycle regulation remain poorly understood. Herein, by constructing a comprehensive network model, we have identified crucial crosstalk regulations between the p53 protein and key cell-cycle regulators that enable some cells to escape cell-cycle arrest during prolonged DNA damage. The model further illustrates a probable cellular mechanism underlying mitotic catastrophe and predicts ways to induce it in a therapeutically relevant manner.

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.

Dung beetles can use a variety of orientation cues to maintain a consistent bearing during ball-rolling. Where several cues are available, they appear to learn the spatial relationship between them, providing redundancy if some cues are removed. Mounting evidence indicates that such a learning process is implemented in the insect head direction circuit; specifically, in the plastic substrate between sensory input neurons and compass neurons in the central complex. This plasticity appears to be driven by rotational movements, providing a clear link with observed beetle 'dance' behaviour. Here, we extend our functional model of this circuit and use it on a robot platform, to test it in the same behavioural assay as was used for the beetles. The robot was able to replicate the beetle's ability to substitute a directional wind cue for a point source light cue in guiding straight-line movement. However, it also revealed significant biasing coupled to dance direction. This biasing appears to be caused by inherent conflict between recurrent and instantaneous inputs to the compass circuit. We predict that the real insect should experience similar issues unless it has evolved a neural mechanism to compensate.

The classical model of bacterial flagellar motility posits a rotary engine driven by proton motive force (pmf), with torque generated by stator-rotor interactions and transmitted through a flexible hook to a helical filament. Despite decades of acceptance, this model faces fundamental challenges in thermodynamics, structural mechanics, evolutionary parsimony, and direct observational evidence. We develop and quantitatively test the murburn model, a new paradigm for bacterial motility in which water, produced as an inevitable byproduct of metabolic redox activity, is ejected via the basal secretory module and channelled along the spiral grooves of the flagellar filament. The ejected flow creates a local shear field that induces a transverse bending wave; the precession of this wave is observed as apparent rotation and generates thrust through anisotropic viscous drag, without any rotary motor, ion gradient, or axial rotation. The principal contribution of this work is a self-contained, first-principles treatment of this mechanism: for a unipolar flagellated cell we derive the governing low-Reynolds-number elastohydrodynamic relations from slender-body theory and show that physiologically realistic rates of metabolic water production reproduce the observed swimming speeds and apparent-rotation frequencies at a small fraction of the cellular energy budget, while direct jet propulsion is quantitatively excluded. Building on this derivation, we provide a force-balance comparison of the competing propulsion mechanisms, obtain a set of falsifiable predictions that distinguish the murburn model from the rotary motor, and report a structural analysis of cryo-EM flagellar-hook architectures that reveals solvent-accessible radial canals consistent with lateral water transport. The same single principle accounts for swimming, tumbling, gliding, spirochete undulation, and archaeal motility, without requiring rotating shafts, ion-gradient coupling, or complex switching mechanisms.

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.

The reliable operation of biomolecular circuits depends on the availability of shared cellular resources such as ribosomes, whose levels can vary substantially across growth conditions and cellular contexts. Although resource competition among co-expressed genes is well recognized, the relationship between resource variation and the robustness of circuit dynamics has not been characterized quantitatively. This paper integrates a resource-aware gene expression model, contraction theory-based analytical bounds, and experimental validation to study the effect of translational resource variation on constitutive gene expression and its mitigation through feedback. We show that the constitutive circuit exhibits sensitivity to resource perturbations, and that redesigning it with negative autoregulatory feedback enhances the contraction rate and reduces the steady-state deviation bound, though at lower expression levels. Experiments in E. coli using both plasmid copy number variation and a ribosome sequestration module are consistent with these predictions, confirming that the feedback circuit maintains relatively stable expression under conditions where the constitutive circuit shows large changes. These findings offer a systematic approach for analyzing and improving the robustness of biomolecular circuits operating under variable resource conditions.