Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The Multiscale Wisdom of the Body: Collective Intelligence as a Tractable Interface for Next-Generation Biomedicine

The dominant paradigm in biomedicine focuses on genetically-specified components of cells and their biochemical dynamics, emphasizing bottom-up emergence of complexity. Here, I explore the biomedical implications of a complementary emerging field: diverse intelligence. Using tools from behavioral science and multiscale neuroscience, we can study development, regenerative repair, and cancer suppression as behaviors of a collective intelligence of cells navigating the spaces of possible morphologies and transcriptional and physiological states. A focus on the competencies of living material-from molecular to organismal scales-reveals a new landscape for interventions. Such top-down approaches take advantage of the memories and homeodynamic goal-seeking behavior of cells and tissues, offering the same massive advantages in biomedicine and bioengineering that reprogrammable hardware has provided information technologies. The bioelectric networks that bind individual cells toward large-scale anatomical goals are an especially tractable interface to organ-level plasticity, and tools to modulate them already exist. This suggests a research program to understand and tame the software of life for therapeutic gain by understanding the many examples of basal cognition that operate throughout living bodies.

Strong and weak prediction of stochastic dynamics using reservoir computing

We propose an approach to replicate a stochastic system and forecast its dynamics using a reservoir computing (RC). We show that such machine learning models enable the prediction of the behavior of stochastic systems in a wide range of control parameters. However, the quality of forecasting depends significantly on the training approach used for the RC. Specifically, we distinguish two types of prediction-weak and strong predictions. We get what is called a strong prediction when the testing parameters are close to the training parameters, and almost a true replica of the system trajectory is obtained, which is determined by noise and initial conditions. On the contrary, we call the prediction weak if we can only predict probabilistic characteristics of a stochastic process, which happens if there exists a mismatch between training and testing parameters. The efficiency of our approach is demonstrated with the models of single and coupled stochastic FitzHugh-Nagumo oscillators and the model of an erbium-doped fiber laser with noisy diode pumping. With the help of a RC, we predict the system dynamics for a wide range of noise parameters. In addition, we find a particular regime when the model exhibits switches between strong and weak prediction types, resembling probabilistic properties of on-off intermittency.

Bistable Functions and Signaling Motifs in Systems Chemistry: Taking the Next Step Toward Synthetic Cells

A key challenge in modern chemistry research is to mimic life-like functions using simple molecular networks and the integration of such networks into the first functional artificial cell. Central to this endeavor is the development of signaling elements that can regulate the cell function in time and space by producing entities of code with specific information to induce downstream activity. Such artificial signaling motifs can emerge in nonequilibrium systems, exhibiting complex dynamic behavior like bistability, multistability, oscillations, and chaos. However, the de novo, bottom-up design of such systems remains challenging, primarily because the kinetic characteristics and energy aspects yielding bifurcation have not yet been globally defined. We herein review our recent work that focuses on the design and functional analysis of peptide-based networks, propelled by replication reactions and exhibiting bistable behavior. Furthermore, we rationalize and discuss their exploitation and implementation as variable signaling motifs in homogeneous and heterogeneous environments.The bistable reactions constitute reversible second-order autocatalysis as positive feedback to generate two distinct product distributions at steady state (SS), the low-SS and high-SS. Quantitative analyses reveal that a phase transition from simple reversible equilibration dynamics into bistability takes place when the system is continuously fueled, using a reducing agent, to keep it far from equilibrium. In addition, an extensive set of experimental, theoretical, and simulation studies highlight a defined parameter space where bistability operates.Analogous to the arrangement of protein-based bistable motifs in intracellular signaling pathways, sequential concatenation of the synthetic bistable networks is used for signal processing in homogeneous media. The cascaded network output signals are switched and erased or transduced by manipulating the order of addition of the components, allowing it to reach "on demand" either the low-SS or high-SS. The pre-encoded bistable networks are also useful as a programming tool for the downstream regulation of nanoscale materials properties, bridging together the Systems Chemistry and Nanotechnology fields. In such heterogeneous cascade pathways, the outputs of the bistable network serve as input signals for consecutive nanoparticle formation reaction and growth processes, which-depending on the applied conditions-regulate various features of (Au) nanoparticle shape and assembly.Our work enables the design and production of various signaling apparatus that feature higher complexity than previously observed in chemical networks. Future studies, briefly discussed at the end of the Account, will be directed at the design and analysis of more elaborate functionality, such as bistability under flow conditions, multistability, and oscillations. We propose that a profound understanding of the design principles facilitating the replication-based bistability and related functions bear implications for exploring the origin of protein functionality prior to the highly evolved replication-translation-transcription machinery. The integration of our peptide-based signaling motifs within future synthetic cells seems to be a straightforward development of the two alternating states as memory and switch elements for controlling cell growth and division and even communication among different cells. We furthermore suggest that such systems can be introduced into living cells for various biotechnology applications, such as switches for cell temporal and spatial manipulations.

Foraging and inertia: Understanding the developmental dynamics of overt visual attention

During early life, we develop the ability to choose what we focus on and what we ignore, allowing us to regulate perception and action in complex environments. But how does this change influence how we spontaneously allocate attention to real-world objects during free behaviour? Here, in this narrative review, we examine this question by considering the time dynamics of spontaneous overt visual attention, and how these develop through early life. Even in early childhood, visual attention shifts occur both periodically and aperiodically. These reorientations become more internally controlled as development progresses. Increasingly with age, attention states also develop self-sustaining attractor dynamics, known as attention inertia, in which the longer an attention episode lasts, the more the likelihood increases of its continuing. These self-sustaining dynamics are driven by amplificatory interactions between engagement, comprehension, and distractibility. We consider why experimental measures show decline in sustained attention over time, while real-world visual attention often demonstrates the opposite pattern. Finally, we discuss multi-stable attention states, where both hypo-arousal (mind-wandering) and hyper-arousal (fragmentary attention) may also show self-sustaining attractor dynamics driven by moment-by-moment amplificatory child-environment interactions; and we consider possible applications of this work, and future directions.

Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of bipolar disorder

Mixed affective states in bipolar disorder (BD) is a common psychiatric condition that occurs when symptoms of the two opposite poles coexist during an episode of mania or depression. A four-dimensional model by Goldbeter (Progr Biophys Mol Biol 105:119-127, 2011; Pharmacopsychiatry 46:S44-S52, 2013) rests upon the notion that manic and depressive symptoms are produced by two competing and auto-inhibited neural networks. Some of the rich dynamics that this model can produce, include complex rhythms formed by both small-amplitude (subthreshold) and large-amplitude (suprathreshold) oscillations and could correspond to mixed bipolar states. These rhythms are commonly referred to as mixed mode oscillations (MMOs) and they have already been studied in many different contexts by Bertram (Mathematical analysis of complex cellular activity, Springer, Cham, 2015), (Petrov et al. in J Chem Phys 97:6191-6198, 1992). In order to accurately explain these dynamics one has to apply a mathematical apparatus that makes full use of the timescale separation between variables. Here we apply the framework of multiple-timescale dynamics to the model of BD in order to understand the mathematical mechanisms underpinning the observed dynamics of changing mood. We show that the observed complex oscillations can be understood as MMOs due to a so-called folded-node singularity. Moreover, we explore the bifurcation structure of the system and we provide possible biological interpretations of our findings. Finally, we show the robustness of the MMOs regime to stochastic noise and we propose a minimal three-dimensional model which, with the addition of noise, exhibits similar yet purely noise-driven dynamics. The broader significance of this work is to introduce mathematical tools that could be used to analyse and potentially control future, more biologically grounded models of BD.

How do productivity gradient and diffusion shape patterns in a plant-herbivore grazing system?

Natural systems show heterogeneous patchy distributions of vegetation over large landscapes. Reaction-diffusion systems can demonstrate such heterogeneity of species distributions. Here, we analyse a reaction-diffusion model of plant-herbivore interactions in two-dimensional space to illustrate non-homogeneous distributions of plants and herbivores. The non-spatial system shows bottom-up control, where herbivore density is low under low and high primary productivity but increased at intermediate productivity. In addition, the non-spatial system provides bistability between a dense vegetation state devoid of herbivores and a coexisting state of plants and herbivores. In the spatiotemporal model, we give analytical conditions of occurring diffusion-driven (Turing) instability, where a novel point in our model is the relative dispersal of herbivores, which represents the movement of herbivores from a higher to a lower vegetation state in addition to the self-diffusion of both species. It is shown that heterogeneity in the population distribution does not occur if the relative dispersal of herbivores is low, but it appears in the opposite case. Due to bistability in the underlying non-spatial system, the spatiotemporal model produces initial value-dependent patterns. The two initial values make different patterns despite having the same primary productivity and relative dispersal rate. As productivity increases with a given relative herbivore dispersal, pattern transition occurs from a blend of stripes and spots of low vegetation state to a predominantly low-density vegetation state with smaller patches of densely vegetated states with one initial value. On the contrary, a discernible change in vegetation patterns from cold spots in the dense vegetation to hot stripes in the primarily low-vegetated state is noticed under the other initial population value. Furthermore, the population distributions of plants and herbivores in the entire domain after a long period are heterogeneous for both initial values, provided the relative herbivore dispersal is substantial. We estimated mean population densities to observe species fitness in the whole domain under variable productivity. When productivity is high, the mean population density of plants may go up or down, depending on the herbivore's relative dispersal rate. In contrast to the bottom-up control dynamics of the non-spatial system, the system exhibits a top-down control under high relative dispersal, where the herbivore regulates vegetation growth under high productivity. On the other hand, herbivores are extinct under high productivity if the relative dispersal is low.

Computation Implemented by the Interaction of Chemical Reaction, Clustering, and De-Clustering of Molecules

A chemical reaction and its reaction environment are intrinsically linked, especially within the confines of narrow cellular spaces. Traditional models of chemical reactions often use differential equations with concentration as the primary variable, neglecting the density heterogeneity in the solution and the interaction between the reaction and its environment. We model the interaction between a chemical reaction and its environment within a geometrically confined space, such as inside a cell, by representing the environment through the size of molecular clusters. In the absence of fluctuations, the interplay between cluster size changes and the activation and inactivation of molecules induces oscillations. However, in unstable environments, the system reaches a fluctuating steady state. When an enzyme is introduced to this steady state, oscillations akin to action potential spike trains emerge. We examine the behavior of these spike trains and demonstrate that they can be used to implement logic gates. We discuss the oscillations and computations that arise from the interaction between a chemical reaction and its environment, exploring their potential for contributing to chemical intelligence.

A Chemical Reaction Network Drives Complex Population Dynamics in Oscillating Self-Reproducing Vesicles

We report chemically fueled oscillations of vesicles. The population cycling of vesicles is driven by their self-reproduction and collapse within a biphasic reaction network involving the interplay of molecular and supramolecular events. We studied the oscillations on the molecular and supramolecular scales and tracked vesicle populations in time by interferometric scattering microscopy and dynamic light scattering. Complex supramolecular events were observed during oscillations─including vesicle reproduction, growth, and decomposition─and differences in the number, size, and mass of aggregates can often be observed within and between pulses. This system's dynamic behavior is reminiscent of a reproductive cycle in living cells.

Simplifications and approximations in a single-gene circuit modeling

The absence of detailed knowledge about regulatory interactions makes the use of phenomenological assumptions mandatory in cell biology modeling. Furthermore, the challenges associated with the analysis of these models compel the implementation of mathematical approximations. However, the constraints these methods introduce to biological interpretation are sometimes neglected. Consequently, understanding these restrictions is a very important task for systems biology modeling. In this article, we examine the impact of such simplifications, taking the case of a single-gene autoinhibitory circuit; however, our conclusions are not limited solely to this instance. We demonstrate that models grounded in the same biological assumptions but described at varying levels of detail can lead to different outcomes, that is, different and contradictory phenotypes or behaviors. Indeed, incorporating specific molecular processes like translation and elongation into the model can introduce instabilities and oscillations not seen when these processes are assumed to be instantaneous. Furthermore, incorporating a detailed description of promoter dynamics, usually described by a phenomenological regulatory function, can lead to instability, depending on the cooperative binding mechanism that is acting. Consequently, although the use of a regulating function facilitates model analysis, it may mask relevant aspects of the system's behavior. In particular, we observe that the two cooperative binding mechanisms, both compatible with the same sigmoidal function, can lead to different phenotypes, such as transcriptional oscillations with different oscillation frequencies.

Collective dynamics of actin and microtubule and its crosstalk mediated by FHDC1

The coordination between actin and microtubule network is crucial, yet this remains a challenging problem to dissect and our understanding of the underlying mechanisms remains limited. In this study, we used travelling waves in the cell cortex to characterize the collective dynamics of cytoskeletal networks. Our findings show that Cdc42 and F-BAR-dependent actin waves in mast cells are mainly driven by formin-mediated actin polymerization, with the microtubule-binding formin FH2 domain-containing protein 1 (FHDC1) as an early regulator. Knocking down FHDC1 inhibits actin wave formation, and this inhibition require FHDC1's interaction with both microtubule and actin. The phase of microtubule depolymerization coincides with the nucleation of actin waves and microtubule stabilization inhibit actin waves, leading us to propose that microtubule shrinking and the concurrent release of FHDC1 locally regulate actin nucleation. Lastly, we show that FHDC1 is crucial for multiple cellular processes such as cell division and migration. Our data provided molecular insights into the nucleation mechanisms of actin waves and uncover an antagonistic interplay between microtubule and actin polymerization in their collective dynamics.

CryoEM reveals the complex self-assembly of a chemically driven disulfide hydrogel

Inspired by the adaptability of biological materials, a variety of synthetic, chemically driven self-assembly processes have been developed that result in the transient formation of supramolecular structures. These structures form through two simultaneous reactions, forward and backward, which generate and consume a molecule that undergoes self-assembly. The dynamics of these assembly processes have been shown to differ from conventional thermodynamically stable molecular assemblies. However, the evolution of nanoscale morphologies in chemically driven self-assembly and how they compare to conventional assemblies has not been resolved. Here, we use a chemically driven redox system to separately carry out the forward and backward reactions. We analyze the forward and backward reactions both sequentially and synchronously with time-resolved cryogenic transmission electron microscopy (cryoEM). Quantitative image analysis shows that the synchronous process is more complex and heterogeneous than the sequential process. Our key finding is that a thermodynamically unstable stacked nanorod phase, briefly observed in the backward reaction, is sustained for ∼6 hours in the synchronous process. Kinetic Monte Carlo modeling show that the synchronous process is driven by multiple cycles of assembly and disassembly. The collective data suggest that chemically driven self-assembly can create sustained morphologies not seen in thermodynamically stable assemblies by kinetically stabilizing transient intermediates. This finding provides plausible design principles to develop and optimize supramolecular materials with novel properties.

Irreversible Mesoscale Fluctuations Herald the Emergence of Dynamical Phases

We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios associated with parity-time symmetry breaking: oscillatory instabilities and critical exceptional points. An analytical investigation of the low-noise regime reveals a drastic increase of the mesoscopic entropy production toward the transitions. For an illustrative model of two nonreciprocally coupled Cahn-Hilliard fields, we find physical interpretations in terms of actively propelled interfaces and a coupling of eigenmodes of the linearized dynamics near the critical exceptional point.

A two-galectin network establishes mesenchymal condensation phenotype in limb development

Previous work showed that Gal-1A and Gal-8, two proteins belonging to the galactoside-binding galectin family, are the earliest determinants of the patterning of the skeletal elements of embryonic chicken limbs, and further, that their experimentally determined interactions in the embryonic limb bud can be interpreted via a reaction-diffusion-adhesion (2GL: two galectin plus ligands) model. Here, we use an ordinary differential equation-based approach to analyze the intrinsic switching modality of the 2GL network and characterize the network behavior independent of the diffusive and adhesive arms of the patterning mechanism. We identify two states: where the concentrations of both the galectins are respectively, negligible, and very high. This bistable switch-like system arises via a saddle-node bifurcation from a monostable state. For the case of mass-action production terms, we provide an explicit Lyapunov function for the system, which shows that it has no periodic solutions. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time, without any intermediate states. We test these predictions in experiments performed with high density cultures of chick limb mesenchymal cells and observe that cells inside precartilage protocondensations express Gal-1A at a much higher rate than those outside, for which it was negligible. The Gal-1A and -8-based patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell states with different developmental (chondrogenic vs. non-chondrogenic) fates. When incorporated into an adhesion and diffusion-enabled framework this system can generate a spatially patterned limb skeleton.

Whole-cell metabolic control analysis

Since its conception some fifty years ago, metabolic control analysis (MCA) aims to understand how cells control their metabolism by adjusting the activity of their enzymes. Here we extend its scope to a whole-cell context. We consider metabolism in the evolutionary context of growth-rate maximisation by optimisation of protein concentrations. This framework allows for the prediction of flux control coefficients from proteomics data or stoichiometric modelling. Since genes compete for finite biosynthetic resources, we treat all protein concentrations as interdependent. We show that elementary flux modes (EFMs) emerge naturally as the optimal metabolic networks in the whole-cell context and we derive their control properties. In the evolutionary optimum, the number of expressed EFMs is determined by the number of protein-concentration constraints that limit growth rate. We use published glucose-limited chemostat data of S. cerevisiae to illustrate that it uses only two EFMs prior to the onset of fermentation and that it uses four EFMs during fermentation. We discuss published enzyme-titration data to show that S. cerevisiae and E. coli indeed can express proteins at growth-rate maximising concentrations. Accordingly, we extend MCA to elementary flux modes operating at an optimal state. We find that the expression of growth-unassociated proteins changes results from classical metabolic control analysis. Finally, we show how flux control coefficients can be estimated from proteomics and ribosome-profiling data. We analyse published proteomics data of E. coli to provide a whole-cell perspective of the control of metabolic enzymes on growth rate. We hope that this paper stimulates a renewed interest in metabolic control analysis, so that it can serve again the purpose it once had: to identify general principles that emerge from the biochemistry of the cell and are conserved across biological species.

Synergistic chemomechanical dynamics of feedback-controlled microreactors

The experimental control of synergistic chemomechanical dynamics of catalytically active microgels (microreactors) is a key prerequisite for the design of adaptive and biomimetic materials. Here, we report a minimalistic model of feedback-controlled microreactors based on the coupling between the hysteretic polymer volume phase transition and a volume-controlled permeability for the internal chemical conversion. We categorize regimes of mono- and bistability, excitability, damped oscillations, as well as sustained oscillatory states with tunable amplitude, as indicated by experiments and representable by the FitzHugh-Nagumo dynamics for neurons. We summarize the features of such a "colloidal neuron" in bifurcation diagrams with respect to microgel design parameters, such as permeability and relaxation times, as a guide for experimental synthesis.

A catalytically active oscillator made from small organic molecules

Oscillatory systems regulate many biological processes, including key cellular functions such as metabolism and cell division, as well as larger-scale processes such as circadian rhythm and heartbeat1-4. Abiotic chemical oscillations, discovered originally in inorganic systems5,6, inspired the development of various synthetic oscillators for application as autonomous time-keeping systems in analytical chemistry, materials chemistry and the biomedical field7-17. Expanding their role beyond that of a pacemaker by having synthetic chemical oscillators periodically drive a secondary function would turn them into significantly more powerful tools. However, this is not trivial because the participation of components of the oscillator in the secondary function might jeopardize its time-keeping ability. We now report a small molecule oscillator that can catalyse an independent chemical reaction in situ without impairing its oscillating properties. In a flow system, the concentration of the catalytically active product of the oscillator shows sustained oscillations and the catalysed reaction is accelerated only during concentration peaks. Augmentation of synthetic oscillators with periodic catalytic action allows the construction of complex systems that, in the future, may benefit applications in automated synthesis, systems and polymerization chemistry and periodic drug delivery.

Sphingomyelin metabolism underlies Ras excitability for efficient cell migration and chemotaxis

In eukaryotic motile cells, the active Ras (Ras-GTP)-enriched domain is generated in an asymmetric manner on the cell membrane through the excitable dynamics of an intracellular signaling network. This asymmetric Ras signaling regulates pseudopod formation for both spontaneous random migration and chemoattractant-induced directional migration. While membrane lipids, such as sphingomyelin and phosphatidylserine, contribute to Ras signaling in various cell types, whether they are involved in the Ras excitability for cell motility is unknown. Here we report that functional Ras excitability requires the normal metabolism of sphingomyelin for efficient cell motility and chemotaxis. The pharmacological blockade of sphingomyelin metabolism by an acid-sphingomyelinase inhibitor, fendiline, and other inhibitors suppressed the excitable generation of the stable Ras-GTP-enriched domain. The suppressed excitability failed to invoke enough basal motility to achieve directed migration under shallow chemoattractant gradients. The fendiline-induced defects in Ras excitability, motility and stimulation-elicited directionality were due to an accumulation of sphingomyelin on the membrane, which could be recovered by exogenous sphingomyelinase or phosphatidylserine without changing the expression of Ras. These results indicate a novel regulatory mechanism of the excitable system by membrane lipids, in which sphingomyelin metabolism provides a membrane environment to ensure Ras excitation for efficient cellular motility and chemotaxis.Key words: cell polarity, cell migration, Ras, excitability, sphingomyelin.

Are physiological oscillations physiological?

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic β-cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re-thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory ('pacemaking') mechanisms at the cellular, tissue and system levels.

Feedback in the β-catenin destruction complex imparts bistability and cellular memory

Wnt ligands are considered classical morphogens, for which the strength of the cellular response is proportional to the concentration of the ligand. Herein, we show an emergent property of bistability arising from feedback among the Wnt destruction complex proteins that target the key transcriptional co-activator β-catenin for degradation. Using biochemical reconstitution, we identified positive feedback between the scaffold protein Axin and the kinase glycogen synthase kinase 3 (GSK3). Theoretical modeling of this feedback between Axin and GSK3 suggested that the activity of the destruction complex exhibits bistable behavior. We experimentally confirmed these predictions by demonstrating that cellular cytoplasmic β-catenin concentrations exhibit an "all-or-none" response with sustained memory (hysteresis) of the signaling input. This bistable behavior was transformed into a graded response and memory was lost through inhibition of GSK3. These findings provide a mechanism for establishing decisive, switch-like cellular response and memory upon Wnt pathway stimulation.

Foraging Dynamics and Entropy Production in a Simulated Proto-Cell

All organisms depend on a supply of energetic resources to power behavior and the irreversible entropy-producing processes that sustain them. Dissipative structure theory has often been a source of inspiration for better understanding the thermodynamics of biology, yet real organisms are inordinately more complex than most laboratory systems. Here we report on a simulated chemical dissipative structure that operates as a proto cell. The simulated swimmer moves through a 1D environment collecting resources that drive a nonlinear reaction network interior to the swimmer. The model minimally represents properties of a simple organism including rudimentary foraging and chemotaxis and an analog of a metabolism in the nonlinear reaction network. We evaluated how dynamical stability of the foraging dynamics (i.e., swimming and chemotaxis) relates to the rate of entropy production. Results suggested a relationship between dynamical steady states and entropy production that was tuned by the relative coordination of foraging and metabolic processes. Results include evidence in support of and contradicting one formulation of a maximum entropy production principle. We discuss the status of this principle and its relevance to biology.

Diverse coherence-resonance chimeras in coupled type-I excitable systems

Coherence-resonance chimera was discovered in [Phys. Rev. Lett. 117, 014102 (2016)10.1103/PhysRevLett.117.014102], which combines the effect of coherence-resonance and classical chimeras in the presence of noise in a network of type-II excitable systems. However, the same in a network of type-I excitable units has not been observed yet. In this paper we report the occurrence of coherence-resonance chimera in coupled type-I excitable systems. We consider a paradigmatic model of type-I excitability, namely, the saddle-node infinite period model, and show that the coherence-resonance chimera appears over an optimum range of noise intensity. Moreover, we discover a unique chimera pattern that is a mixture of classical chimera and the coherence-resonance chimera. We support our results using quantitative measures and map them in parameter space. This study reveals that the coherence-resonance chimera is a general chimera pattern and thus it deepens our understanding of role of noise in coupled excitable systems.

Noise-induced formation of heterogeneous patterns in the Turing stability zones of diffusion systems

We study a phenomenon of stochastic generation of waveform patterns for reaction-diffusion systems in the Turing stability zone where the homogeneous equilibrium is a single attractor. In this analysis, we use a distributed variant of the Selkov glycolytic model with diffusion and random forcing. It is shown that in the Turing stability zone, random disturbances can induce a diversity of metastable spatial patterns with different waveforms. We carry out the parametric analysis of statistical characteristics of evolution of these patterns, and reveal the dominant patterns in the stochastic flow of mixed spatial structures.

Cellular sentience as the primary source of biological order and evolution

All life is cellular, starting some 4 billion years ago with the emergence of the first cells. In order to survive their early evolution in the face of an extremely challenging environment, the very first cells invented cellular sentience and cognition, allowing them to make relevant decisions to survive through creative adaptations in a continuously running evolutionary narrative. We propose that the success of cellular life has crucially depended on a biological version of Maxwell's demons which permits the extraction of relevant sensory information and energy from the cellular environment, allowing cells to sustain anti-entropic actions. These sensor-effector actions allowed for the creative construction of biological order in the form of diverse organic macromolecules, including crucial polymers such as DNA, RNA, and cytoskeleton. Ordered biopolymers store analogue (structures as templates) and digital (nucleotide sequences of DNA and RNA) information that functioned as a form memory to support the development of organisms and their evolution. Crucially, all cells are formed by the division of previous cells, and their plasma membranes are physically and informationally continuous across evolution since the beginning of cellular life. It is argued that life is supported through life-specific principles which support cellular sentience, distinguishing life from non-life. Biological order, together with cellular cognition and sentience, allow the creative evolution of all living organisms as the authentic authors of evolutionary novelty.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Oscillatory entrainment to our early social or physical environment and the emergence of volitional control

An individual's early interactions with their environment are thought to be largely passive; through the early years, the capacity for volitional control develops. Here, we consider: how is the emergence of volitional control characterised by changes in the entrainment observed between internal activity (behaviour, physiology and brain activity) and the sights and sounds in our everyday environment (physical and social)? We differentiate between contingent responsiveness (entrainment driven by evoked responses to external events) and oscillatory entrainment (driven by internal oscillators becoming temporally aligned with external oscillators). We conclude that ample evidence suggests that children show behavioural, physiological and neural entrainment to their physical and social environment, irrespective of volitional attention control; however, evidence for oscillatory entrainment beyond contingent responsiveness is currently lacking. Evidence for how oscillatory entrainment changes over developmental time is also lacking. Finally, we suggest a mechanism through which periodic environmental rhythms might facilitate both sensory processing and the development of volitional control even in the absence of oscillatory entrainment.

Gated Transient Dissipative Dimerization of DNA Tetrahedra Nanostructures for Programmed DNAzymes Catalysis

Transient dissipative dimerization and transient gated dimerization of DNA tetrahedra nanostructures are introduced as functional modules to emulate transient and gated protein-protein interactions and emergent protein-protein guided transient catalytic functions, operating in nature. Four tetrahedra are engineered to yield functional modules that, in the presence of pre-engineered auxiliary nucleic acids and the nicking enzyme Nt.BbvCI, lead to the fueled transient dimerization of two pairs of tetrahedra. The dynamic transient formation and depletion of DNA tetrahedra are followed by transient FRET signals generated by fluorophore-labeled tetrahedra. The integration of two inhibitors within the mixture of the four tetrahedra and two auxiliary modules, fueling the transient dimerization, results in selective inhibitor-guided gated transient dimerization of two different DNA tetrahedra dimers. Kinetic models for the dynamic transient dimerization and gated transient dimerization of the DNA tetrahedra are formulated and computationally simulated. The derived rate-constants allow the prediction and subsequent experimental validation of the performance of the systems under different auxiliary conditions. In addition, by appropriate modification of the four tetrahedra structures, the triggered gated emergence of selective transient catalytic functions driven by the two pairs of DNA tetrahedra dimers is demonstrated.

Slow-fast oscillatory dynamics and phantom attractors in stochastic modeling of biochemical reactions

A problem of the probabilistic analysis of stochastic phenomena in slow-fast dynamical systems modeling biochemical reactions is considered. We study how multiplicative noise induces systematic shifts of probabilistic distributions and forms "phantom" attractors in nonlinear enzymatic models. The mathematical analysis of the underlying probabilistic mechanism of such stochastic transformations is performed by the "freeze-and-average" method. Our theoretical results are supported by direct numerical simulation.

Bayesian mechanics for stationary processes

This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.

From the Belousov-Zhabotinsky reaction to biochemical clocks, traveling waves and cell cycle regulation

In the last 20 years, a growing army of systems biologists has employed quantitative experimental methods and theoretical tools of data analysis and mathematical modeling to unravel the molecular details of biological control systems with novel studies of biochemical clocks, cellular decision-making, and signaling networks in time and space. Few people know that one of the roots of this new paradigm in cell biology can be traced to a serendipitous discovery by an obscure Russian biochemist, Boris Belousov, who was studying the oxidation of citric acid. The story is told here from an historical perspective, tracing its meandering path through glycolytic oscillations, cAMP signaling, and frog egg development. The connections among these diverse themes are drawn out by simple mathematical models (nonlinear differential equations) that share common structures and properties.

Multistability in Macrophage Activation Pathways and Metabolic Implications

Macrophages are innate immune cells with a dynamic range of reversible activation states including the classical pro-inflammatory (M1) and alternative anti-inflammatory (M2) states. Deciphering how macrophages regulate their transition from one state to the other is key for a deeper understanding of inflammatory diseases and relevant therapies. Common regulatory motifs reported for macrophage transitions, such as positive or double-negative feedback loops, exhibit a switchlike behavior, suggesting the bistability of the system. In this review, we explore the evidence for multistability (including bistability) in macrophage activation pathways at four molecular levels. First, a decision-making module in signal transduction includes mutual inhibitory interactions between M1 (STAT1, NF-KB/p50-p65) and M2 (STAT3, NF-KB/p50-p50) signaling pathways. Second, a switchlike behavior at the gene expression level includes complex network motifs of transcription factors and miRNAs. Third, these changes impact metabolic gene expression, leading to switches in energy production, NADPH and ROS production, TCA cycle functionality, biosynthesis, and nitrogen metabolism. Fourth, metabolic changes are monitored by metabolic sensors coupled to AMPK and mTOR activity to provide stability by maintaining signals promoting M1 or M2 activation. In conclusion, we identify bistability hubs as promising therapeutic targets for reverting or blocking macrophage transitions through modulation of the metabolic environment.

Predictable topological sensitivity of Turing patterns on graphs

Reaction-diffusion systems implemented as dynamical processes on networks have recently renewed the interest in their self-organized collective patterns known as Turing patterns. We investigate the influence of network topology on the emerging patterns and their diversity, defined as the variety of stationary states observed with random initial conditions and the same dynamics. We show that a seemingly minor change, the removal or rewiring of a single link, can prompt dramatic changes in pattern diversity. The determinants of such critical occurrences are explored through an extensive and systematic set of numerical experiments. We identify situations where the topological sensitivity of the attractor landscape can be predicted without a full simulation of the dynamical equations, from the spectrum of the graph Laplacian and the linearized dynamics. Unexpectedly, the main determinant appears to be the degeneracy of the eigenvalues or the growth rate and not the number of unstable modes.

Bioinspired Artificial Photosynthetic Systems

Mimicking photosynthesis using artificial systems, as a means for solar energy conversion and green fuel generation, is one of the holy grails of modern science. This perspective presents recent advances towards developing artificial photosynthetic systems. In one approach, native photosystems are interfaced with electrodes to yield photobioelectrochemical cells that transform light energy into electrical power. This is exemplified by interfacing photosystem I (PSI) and photosystem II (PSII) as an electrically contacted assembly mimicking the native Z-scheme, and by the assembly of an electrically wired PSI/glucose oxidase biocatalytic conjugate on an electrode support. Illumination of the functionalized electrodes led to light-induced generation of electrical power, or to the generation of photocurrents using glucose as the fuel. The second approach introduces supramolecular photosensitizer nucleic acid/electron acceptor complexes as functional modules for effective photoinduced electron transfer stimulating the subsequent biocatalyzed generation of NADPH or the Pt-nanoparticle-catalyzed evolution of molecular hydrogen. Application of the DNA machineries for scaling-up the photosystems is demonstrated. A third approach presents the integration of artificial photosynthetic modules into dynamic nucleic acid networks undergoing reversible reconfiguration or dissipative transient operation in the presence of auxiliary triggers. Control over photoinduced electron transfer reactions and photosynthetic transformations by means of the dynamic networks is demonstrated.

Natural Selection beyond Life? A Workshop Report

Natural selection is commonly seen not just as an explanation for adaptive evolution, but as the inevitable consequence of “heritable variation in fitness among individuals”. Although it remains embedded in biological concepts, such a formalisation makes it tempting to explore whether this precondition may be met not only in life as we know it, but also in other physical systems. This would imply that these systems are subject to natural selection and may perhaps be investigated in a biological framework, where properties are typically examined in light of their putative functions. Here we relate the major questions that were debated during a three-day workshop devoted to discussing whether natural selection may take place in non-living physical systems. We start this report with a brief overview of research fields dealing with “life-like” or “proto-biotic” systems, where mimicking evolution by natural selection in test tubes stands as a major objective. We contend the challenge may be as much conceptual as technical. Taking the problem from a physical angle, we then discuss the framework of dissipative structures. Although life is viewed in this context as a particular case within a larger ensemble of physical phenomena, this approach does not provide general principles from which natural selection can be derived. Turning back to evolutionary biology, we ask to what extent the most general formulations of the necessary conditions or signatures of natural selection may be applicable beyond biology. In our view, such a cross-disciplinary jump is impeded by reliance on individuality as a central yet implicit and loosely defined concept. Overall, these discussions thus lead us to conjecture that understanding, in physico-chemical terms, how individuality emerges and how it can be recognised, will be essential in the search for instances of evolution by natural selection outside of living systems.

DNAzyme- and light-induced dissipative and gated DNA networks

Nucleic acid-based dissipative, out-of-equilibrium systems are introduced as functional assemblies emulating transient dissipative biological transformations. One system involves a Pb²⁺-ion-dependent DNAzyme fuel strand-driven network leading to the transient cleavage of the fuel strand to “waste” products. Applying the Pb²⁺-ion-dependent DNAzyme to two competitive fuel strand-driven systems yields two parallel operating networks. Blocking the competitively operating networks with selective inhibitors leads, however, to gated transient operation of dictated networks, yielding gated catalytic operations. A second system introduces a “non-waste” generating out-of-equilibrium, dissipative network driven by light. The system consists of a trans-azobenzene-functionalized photoactive module that is reconfigured by light to an intermediary state consisting of cis-azobenzene units that are thermally recovered to the original trans-azobenzene-modified module. The cyclic transient photoinduced operation of the device is demonstrated. The kinetic simulation of the systems allows the prediction of the transient behavior of the networks under different auxiliary conditions.

Functional DNA modules are triggered in the presence of appropriate inhibitors to yield transient gated catalytic functions, and a photoresponsive DNA module leads to “waste-free” operation of transient, dissipative dynamic transitions.

Gated Dissipative Dynamic Artificial Photosynthetic Model Systems

Gated dissipative artificial photosynthetic systems modeling dynamically modulated environmental effects on the photosynthetic apparatus are presented. Two photochemical systems composed of a supramolecular duplex scaffold, a photosensitizer-functionalized strand (photosensitizer is Zn(II)protoporphyrin IX, Zn(II)PPIX, or pyrene), an electron acceptor bipyridinium (V²⁺)-modified strand, and a nicking enzyme (Nt.BbvCI) act as functional assemblies driving transient photosynthetic-like processes. In the presence of a fuel strand, the transient electron transfer quenching of the photosensitizers, in each of the photochemical systems, is activated. In the presence of a sacrificial electron donor (mercaptoethanol) and continuous irradiation, the resulting electron transfer process in the Zn(II)PPIX/V²⁺ photochemical module leads to the transient accumulation and depletion of the bipyridinium radical-cation (V·⁺) product, and in the presence of ferredoxin-NADP⁺ reductase and NADP⁺, to the kinetically modulated photosynthesis of NADPH. By subjecting the mixture of two photochemical modules to one of two inhibitors, the gated transient photoinduced electron transfer in the two modules is demonstrated. Such gated dissipative process highlights its potential as an important pathway to protect artificial photosynthetic module against overdose of irradiance and to minimize photodamage.

Thermodynamic Optimality of Glycolytic Oscillations

Temporal order in living matters reflects the self-organizing nature of dynamical processes driven out of thermodynamic equilibrium. Because of functional reasons, the period of a biochemical oscillation must be tuned to a specific value with precision; however, according to the thermodynamic uncertainty relation (TUR), the precision of the oscillatory period is constrained by the thermodynamic cost of generating it. After reviewing the basics of chemical oscillations using the Brusselator as a model system, we study the glycolytic oscillation generated by octameric phosphofructokinase (PFK), which is known to display a period of several minutes. By exploring the phase space of glycolytic oscillations, we find that the glycolytic oscillation under the cellular condition is realized in a cost-effective manner. Specifically, over the biologically relevant range of parameter values of glycolysis and octameric PFK, the entropy production from the glycolytic oscillation is minimal when the oscillation period is (5-10) min. Furthermore, the glycolytic oscillation is found at work near the phase boundary of limit cycles, suggesting that a moderate increase of glucose injection rate leads to the loss of oscillatory dynamics, which is reminiscent of the loss of pulsatile insulin release resulting from elevated blood glucose level.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

From embryos to embryoids: How external signals and self-organization drive embryonic development

Embryonic development has been traditionally seen as an inductive process directed by exogenous maternal inputs and extra-embryonic signals. Increasing evidence, however, is showing that, in addition to exogenous signals, the development of the embryo involves endogenous self-organization. Recently, this self-organizing potential has been highlighted by a number of stem cell models known as embryoids that can recapitulate different aspects of embryogenesis in vitro. Here, we review the self-organizing behaviors observed in different embryoid models and seek to reconcile this new evidence with classical knowledge of developmental biology. This analysis leads to reexamine embryonic development as a guided self-organizing process, where patterning and morphogenesis are controlled by a combination of exogenous signals and endogenous self-organization. Finally, we discuss the multidisciplinary approach required to investigate the genetic and cellular basis of self-organization.

MicroRNA governs bistable cell differentiation and lineage segregation via a noncanonical feedback

Positive feedback driven by transcriptional regulation has long been considered a key mechanism underlying cell lineage segregation during embryogenesis. Using the developing spinal cord as a paradigm, we found that canonical, transcription-driven feedback cannot explain robust lineage segregation of motor neuron subtypes marked by two cardinal factors, Hoxa5 and Hoxc8. We propose a feedback mechanism involving elementary microRNA-mRNA reaction circuits that differ from known feedback loop-like structures. Strikingly, we show that a wide range of biologically plausible post-transcriptional regulatory parameters are sufficient to generate bistable switches, a hallmark of positive feedback. Through mathematical analysis, we explain intuitively the hidden source of this feedback. Using embryonic stem cell differentiation and mouse genetics, we corroborate that microRNA-mRNA circuits govern tissue boundaries and hysteresis upon motor neuron differentiation with respect to transient morphogen signals. Our findings reveal a previously underappreciated feedback mechanism that may have widespread functions in cell fate decisions and tissue patterning.

Brain Entropy During Aging Through a Free Energy Principle Approach

Neural complexity and brain entropy (BEN) have gained greater interest in recent years. The dynamics of neural signals and their relations with information processing continue to be investigated through different measures in a variety of noteworthy studies. The BEN of spontaneous neural activity decreases during states of reduced consciousness. This evidence has been showed in primary consciousness states, such as psychedelic states, under the name of "the entropic brain hypothesis." In this manuscript we propose an extension of this hypothesis to physiological and pathological aging. We review this particular facet of the complexity of the brain, mentioning studies that have investigated BEN in primary consciousness states, and extending this view to the field of neuroaging with a focus on resting-state functional Magnetic Resonance Imaging. We first introduce historic and conceptual ideas about entropy and neural complexity, treating the mindbrain as a complex nonlinear dynamic adaptive system, in light of the free energy principle. Then, we review the studies in this field, analyzing the idea that the aim of the neurocognitive system is to maintain a dynamic state of balance between order and chaos, both in terms of dynamics of neural signals and functional connectivity. In our exploration we will review studies both on acute psychedelic states and more chronic psychotic states and traits, such as those in schizophrenia, in order to show the increase of entropy in those states. Then we extend our exploration to physiological and pathological aging, where BEN is reduced. Finally, we propose an interpretation of these results, defining a general trend of BEN in primary states and cognitive aging.

Molecules, Information and the Origin of Life: What Is Next?

How life did originate and what is life, in its deepest foundation? The texture of life is known to be held by molecules and their chemical-physical laws, yet a thorough elucidation of the aforementioned questions still stands as a puzzling challenge for science. Focusing solely on molecules and their laws has indirectly consolidated, in the scientific knowledge, a mechanistic (reductionist) perspective of biology and medicine. This occurred throughout the long historical path of experimental science, affecting subsequently the onset of the many theses and speculations about the origin of life and its maintenance. Actually, defining what is life, asks for a novel epistemology, a ground on which living systems’ organization, whose origin is still questioned via chemistry, physics and even philosophy, may provide a new key to focus onto the complex nature of the human being. In this scenario, many issues, such as the role of information and water structure, have been long time neglected from the theoretical basis on the origin of life and marginalized as a kind of scenic backstage. On the contrary, applied science and technology went ahead on considering molecules as the sole leading components in the scenery. Water physics and information dynamics may have a role in living systems much more fundamental than ever expected. Can an organism be simply explained by a mechanistic view of its nature or we need “something else”? Probably, we can earn sound foundations about life by simply changing our prejudicial view about living systems simply as complex, highly ordered machines. In this manuscript we would like to reappraise many fundamental aspects of molecular and chemical biology and reading them through a new paradigm, which includes Prigogine’s dissipative structures and informational dissipation (Shannon dissipation). This would provide readers with insightful clues about how biology and chemistry may be thoroughly revised, referring to new models, such as informational dissipation. We trust they are enabled to address a straightforward contribution in elucidating what life is for science. This overview is not simply a philosophical speculation, but it would like to affect deeply our way to conceive and describe the foundations of organisms’ life, providing intriguing suggestions for readers in the field.

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.

Many systems in nature show bistability, which means they can evolve to one of two stable steady states under exactly the same conditions. Which state they evolve to depends on where the system comes from. Such bistability underlies the switching behavior that is essential for cells to progress in the cell division cycle. A quick switch happens when the cell jumps from one steady state to another steady state. Typical of this switching behavior is its robustness and irreversibility. In this paper, we expand this viewpoint of the dynamics of the cell cycle by considering bistable switches which themselves are changing in time. This gives the cell an extra layer of control over transitions both in time and in space, and can make those transitions more robust. Such dynamically changing bistability can appear very naturally. We show this in a model of mitotic entry, in which we include a nuclear and cytoplasmic compartment. The activity of a crucial cell cycle protein follows a bistable switch in each compartment, but the shape of its response is changing in time as proteins are imported into and exported from the nucleus.

Activation of Functional Brain Networks in Children With Psychogenic Non-epileptic Seizures

Objectives

Psychogenic non-epileptic seizures (PNES) have been hypothesized to emerge in the context of neural networks instability. To explore this hypothesis in children, we applied a graph theory approach to examine connectivity in neural networks in the resting-state EEG in 35 children with PNES, 31 children with other functional neurological symptoms (but no PNES), and 75 healthy controls.

Methods

The networks were extracted from Laplacian-transformed time series by a coherence connectivity estimation method.

Results

Children with PNES (vs. controls) showed widespread changes in network metrics: increased global efficiency (gamma and beta bands), increased local efficiency (gamma band), and increased modularity (gamma and alpha bands). Compared to controls, they also had higher levels of autonomic arousal (e.g., lower heart variability); more anxiety, depression, and stress on the Depression Anxiety and Stress Scales; and more adverse childhood experiences on the Early Life Stress Questionnaire. Increases in network metrics correlated with arousal. Children with other functional neurological symptoms (but no PNES) showed scattered and less pronounced changes in network metrics.

Conclusion

The results indicate that children with PNES present with increased activation of neural networks coupled with increased physiological arousal. While this shift in functional organization may confer a short-term adaptive advantage-one that facilitates neural communication and the child's capacity to respond self-protectively in the face of stressful life events-it may also have a significant biological cost. It may predispose the child's neural networks to periods of instability-presenting clinically as PNES-when the neural networks are faced with perturbations in energy flow or with additional demands.

Robust synchronization of the cell cycle and the circadian clock through bidirectional coupling

The cell cycle and the circadian clock represent major cellular rhythms, which appear to be coupled. Thus the circadian factor BMAL1 controls the level of cell cycle proteins such as Cyclin E and WEE1, the latter of which inhibits the kinase CDK1 that governs the G2/M transition. In reverse the cell cycle impinges on the circadian clock through direct control by CDK1 of REV-ERBα, which negatively regulates BMAL1. These observations provide evidence for bidirectional coupling of the cell cycle and the circadian clock. By merging detailed models for the two networks in mammalian cells, we previously showed that unidirectional coupling to the circadian clock can entrain the cell cycle to 24 or 48 h, depending on the cell cycle autonomous period, while complex oscillations occur when entrainment fails. Here we show that the reverse unidirectional coupling via phosphorylation of REV-ERBα or via mitotic inhibition of transcription, both controlled by CDK1, can elicit entrainment of the circadian clock by the cell cycle. We then determine the effect of bidirectional coupling of the cell cycle and circadian clock as a function of their relative coupling strengths. In contrast to unidirectional coupling, bidirectional coupling markedly reduces the likelihood of complex oscillations. While the two rhythms oscillate independently as long as both couplings are weak, one rhythm entrains the other if one of the couplings dominates. If the couplings in both directions become stronger and of comparable magnitude, the two rhythms synchronize, generally at an intermediate period within the range defined by the two autonomous periods prior to coupling. More surprisingly, synchronization may also occur at a period slightly below or above this range, while in some conditions the synchronization period can even be much longer. Two or even three modes of synchronization may sometimes coexist, yielding examples of birhythmicity or trirhythmicity. Because synchronization readily occurs in the form of simple periodic oscillations over a wide range of coupling strengths and in the presence of multiple connections between the two oscillatory networks, the results indicate that bidirectional coupling favours the robust synchronization of the cell cycle and the circadian clock.

Effect of filtered feedback on birhythmicity: Suppression of birhythmic oscillation

The birhythmic oscillation, generally known as birhythmicity, arises in a plethora of physical, chemical, and biological systems. In this paper we investigate the effect of filtered feedback on birhythmicity as both are relevant in many living and engineering systems. We show that the presence of a low-pass filter in the feedback path of a birhythmic system suppresses birhythmicity and supports monorhythmic oscillations depending on the filtering parameter. Using harmonic decomposition and energy balance methods we determine the conditions for which birhythmicity is removed. We carry out a detailed bifurcation analysis to unveil the mechanism behind the quenching of birhythmic oscillations. Finally, we demonstrate our theoretical findings in analog simulation with electronic circuit. This study may have practical applications in quenching birhythmicity in several biochemical and physical systems.