Network dynamics and cell physiology

Adenosine Triphosphate Harnessed Transient Aggregations of Nanoparticles for Efficient Nanoreactors in Water

Living cells utilize diverse biochemical reactions occurring in microcompartments to regulate important biological functions. Although transient nanoreactors mediated by diverse fuels are achieved in discrete nanoassemblies of synthetic building blocks, the slow diffusion of substrates in and out of these solvent-dispersed nanoassemblies greatly compromises the reaction efficiency. Herein, we report adenosine triphosphate (ATP)-driven transient aggregation of nanoreactors that enable the acceleration of nucleophilic aromatic substitution (SNAr) in an aqueous solution. This system is composed of nanoparticles self-assembled from an amphiphilic molecule containing an ATP receptor, ATP, and potato apyrase (PA). The sequential addition of ATP and PA results in a reversible aggregation and disaggregation of the nanoparticles, which serve as smart nanoreactors to accelerate the SNAr reaction on demand. Notably, this reaction is temporally regulated by the autonomous aggregation and disaggregation of the nanoparticles. Furthermore, the azobenzene moiety in amphiphilic molecules allows the further modulation of the SNAr reaction in the nanoreactors using ultraviolet light.

Coarse-graining network flow through statistical physics and machine learning

Information dynamics plays a crucial role in complex systems, from cells to societies. Recent advances in statistical physics have made it possible to capture key network properties, such as flow diversity and signal speed, using entropy and free energy. However, large system sizes pose computational challenges. We use graph neural networks to identify suitable groups of components for coarse-graining a network and achieve a low computational complexity, suitable for practical application. Our approach preserves information flow even under significant compression, as shown through theoretical analysis and experiments on synthetic and empirical networks. We find that the model merges nodes with similar structural properties, suggesting they perform redundant roles in information transmission. This method enables low-complexity compression for extremely large networks, offering a multiscale perspective that preserves information flow in biological, social, and technological networks better than existing methods mostly focused on network structure.

Chemomechanical Self-Oscillatory Microgel Motility in Stratified Chemical Media

The design of chemomechanical self-oscillators, which execute oscillations in the presence of constant stimuli lacking periodicity, is a step toward the development of autonomous and interactive soft robotic systems. This work presents a simple design of prolonged chemomechanical oscillatory movement in a microgel system capable of buoyant motility within stratified chemical media containing spatially localized sinking and floating stimuli. Three design elements are developed: a stimuli-responsive membranized calcium alginate microgel, a Percoll density gradient for providing stratified antagonistic chemical media, and transduction of microgel particle size actuation into buoyant motility via membrane-mediated displacement of the Percoll media. The presence of citrate or calcium ions in different layers of the Percoll media gives rise to swelling (buoyancy) or contraction (geotaxis), respectively, which in turn mediate the shuttling of the microgels between the layers to produce prolonged or damped chemomechanical oscillatory trajectories. The concentration-dependence of the oscillatory behavior in the stratified media, the density gap between the Percoll layers, and the kinetic asymmetry of microgel swelling and deswelling are studied. The illustrated modular design allows for the development of chemomechanical self-oscillators responsive to light, pH, or temperature, which will find applications in interactive soft robotics, autonomous microbots, and intelligent materials.

Dynamics of spindle assembly and position checkpoints: Integrating molecular mechanisms with computational models

Mitotic checkpoints orchestrate cell division through intricate molecular networks that ensure genomic stability. While experimental research has uncovered key aspects of checkpoint function, the complexity of protein interactions and spatial dynamics necessitates computational modeling for a deeper, system-level understanding. This review explores mathematical frameworks-from ordinary differential equations to stochastic simulations, which reveal checkpoint dynamics across multiple scales, encompassing models ranging from simple protein interactions to whole-system simulations with thousands of parameters. These approaches have elucidated fundamental properties, including bistable switches driving spindle assembly checkpoint (SAC) activation, spatial organization principles underlying spindle position checkpoint (SPOC) signaling, and critical system-level features ensuring checkpoint robustness. This study evaluates diverse modeling approaches, from rule-based models to chemical organization theory, highlighting their successful application in predicting protein localization patterns and checkpoint response dynamics validated through live-cell imaging. Contemporary challenges persist in integrating spatial and temporal scales, refining parameter estimation, and enhancing spatial modeling fidelity. However, recent advances in single-molecule imaging, data-driven algorithms, and machine learning techniques, particularly deep learning for parameter optimization, present transformative opportunities for improving model accuracy and predictive power. By bridging molecular mechanisms with system-level behaviors through validated computational frameworks, this review offers a comprehensive perspective on the mathematical modeling of cell cycle control, with practical implications for cancer research and therapeutic development.

A new model for the inference of biological entities states: Ternary Entity State Inference System

Understanding the state transitions in biological systems and identifying critical steady states are crucial for investigating disease development and discovering key therapeutic targets. To advance the study of state transitions in specific biological entities, we proposed the Ternary Entity State Inference System (T-ESIS). T-ESIS builds upon the Entity State Inference System by providing richer information on entity states, where states can take values of 0, 1, or 1/2, representing activation, inhibition, and normal states, respectively. This method infers state transition pathways based on interaction relationships and visualizes them through the Entity State Network. Furthermore, the cyclic structures within the Entity State Network capture positive and negative feedback loops, providing a topological foundation for the formation of steady states. To demonstrate the applicability of T-ESIS, entity states were modeled, and attractor analysis was conducted in non-small cell lung cancer (NSCLC) networks. Our analysis provided valuable insights into targeted therapy for NSCLC, highlighting the potential of T-ESIS in uncovering therapeutic targets and understanding disease mechanisms. Moreover, the proposed T-ESIS framework facilitated the inference of entity state transitions and the analysis of steady states in biological systems, offering a novel approach for studying the dynamic principles of these systems. This ternary dynamic modeling approach not only deepened our understanding of biological networks but also provided a methodological reference for future research in the field.

Modeling the START transition in the budding yeast cell cycle

Budding yeast, Saccharomyces cerevisiae, is widely used as a model organism to study the genetics underlying eukaryotic cellular processes and growth critical to cancer development, such as cell division and cell cycle progression. The budding yeast cell cycle is also one of the best-studied dynamical systems owing to its thoroughly resolved genetics. However, the dynamics underlying the crucial cell cycle decision point called the START transition, at which the cell commits to a new round of DNA replication and cell division, are under-studied. The START machinery involves a central cyclin-dependent kinase; cyclins responsible for starting the transition, bud formation, and initiating DNA synthesis; and their transcriptional regulators. However, evidence has shown that the mechanism is more complicated than a simple irreversible transition switch. Activating a key transcription regulator SBF requires the phosphorylation of its inhibitor, Whi5, or an SBF/MBF monomeric component, Swi6, but not necessarily both. Also, the timing and mechanism of the inhibitor Whi5's nuclear export, while important, are not critical for the timing and execution of START. Therefore, there is a need for a consolidated model for the budding yeast START transition, reconciling regulatory and spatial dynamics. We built a detailed mathematical model (START-BYCC) for the START transition in the budding yeast cell cycle based on established molecular interactions and experimental phenotypes. START-BYCC recapitulates the underlying dynamics and correctly emulates key phenotypic traits of ~150 known START mutants, including regulation of size control, localization of inhibitor/transcription factor complexes, and the nutritional effects on size control. Such a detailed mechanistic understanding of the underlying dynamics gets us closer towards deconvoluting the aberrant cellular development in cancer.

Kinetic Model for the Desensitization of G Protein-Coupled Receptor

Desensitization of G-protein-coupled receptors (GPCR) is a general regulatory mechanism adopted by biological organisms against overstimulation of G protein signaling. Although the details of the mechanism are extensively studied, it is not easy to gain an overarching understanding of the process constituted by a multitude of molecular events with vastly differing time scales. To offer a semiquantitative yet predictive understanding of the mechanism, we formulate a kinetic model for the G protein signaling and desensitization by considering essential biochemical steps from ligand binding to receptor internalization. The internalization, followed by receptor depletion from the plasma membrane, attenuates the downstream signal. Together with the kinetic model and its full numerics of the expression derived for the dose-response relation, an approximated form of the expression clarifies the role played by the individual biochemical processes and allows us to identify four distinct regimes for the downregulation that emerge from the balance between phosphorylation, dephosphorylation, and the cellular level of β-arrestin.

Programmable Entropy-Driven Circuit-Cascaded Self-Feedback DNAzyme Network for Ultra-Sensitive Fluorescence and Photoelectrochemical Dual-Mode Biosensing

Inspired by natural DNA networks, programmable artificial DNA networks have become an attractive tool for developing high-performance biosensors. However, there is still a lot of room for expansion in terms of sensitivity, atom economy, and result self-validation for current microRNA sensors. In this protocol, miRNA-122 as a target model, an ultrasensitive fluorescence (FL) and photoelectrochemical (PEC) dual-mode biosensing platform is developed using a programmable entropy-driven circuit (EDC) cascaded self-feedback DNAzyme network. The well-designed EDC realizes full utilization of the DNA strands and improves the atomic economy of the signal amplification system. The unique and rational design of the double-CdSe quantum-dot-released EDC substrate and the cascaded self-feedback DNAzyme amplification network significantly avoids high background signals and enhances sensitivity and specificity. Also, the enzyme-free, programmable EDC cascaded DNAzyme network effectively avoids the risk of signal leakage and enhances the accuracy of the sensor. Moreover, the introduction of superparamagnetic Fe3O4@SiO2-cDNA accelerates the rapid extraction of E2-CdSe QDs and E3-CdSe QDs, which greatly improves the timeliness of sensor signal reading. In addition to the strengths of linear range (6 orders of magnitude) and stability, the biosensor design with dual signal reading makes the test results self-confirming.

Transient Metallo-Lipidoid Assemblies Amplify Covalent Catalysis of Aqueous and Non-Aqueous Reactions

Dissipative supramolecular assemblies are hallmarks of living systems, contributing to their complex, dynamic structures and emerging functions. Living cells can spatiotemporally control diverse biochemical reactions in membrane compartments and condensates, regulating metabolite levels, signal transduction or remodeling of the cytoskeleton. Herein, we constructed membranous compartments using self-assembly of lipid-like amphiphiles (lipidoid) in aqueous medium. The new double-tailed lipidoid features Cu(II) coordinated with a tetravalent chelator that dictates the binding of two amphiphilic ligands in cis-orientation. Hydrophobic interactions between the lipidoids coupled with intermolecular hydrogen bonding led to a well-defined bilayer vesicle structure. Oil-soluble SNAr reaction is efficiently upregulated in the hydrophobic cavity, acting as a catalytic crucible. The modular system allows easy incorporation of exposed primary amine groups, which augments the catalysis of retro aldol and C-N bond formation reactions. Moreover, a higher-affinity chelator enables consumption of the Cu(II) template leveraging the differential thermodynamic stability, which allows a controllable lifetime of the vesicular assemblies. Concomitant temporal upregulation of the catalytic reactions could be tuned by the metal ion concentration. This work offers new possibilities for metal ion-mediated dynamic supramolecular systems, opening up a massive repertoire of functionally active dynamic "life-like" materials.

Temporal (Dis)Assembly of Peptide Nanostructures Dictated by Native Multistep Catalytic Transformations

Emergence of complex catalytic machinery via simple building blocks under non-equilibrium conditions can contribute toward the system level understanding of the extant biocatalytic reaction network that fuels metabolism. Herein, we report temporal (dis)assembly of peptide nanostructures in presence of a cofactor dictated by native multistep cascade transformations. The short peptide can form a dynamic covalent bond with the thermodynamically activated substrate and recruit cofactor hemin to access non-equilibrium catalytic nanostructures (positive feedback). The neighboring imidazole and hemin moieties in the assembled state rapidly converted the substrate to product(s) via a two-step cascade reaction (hydrolase-peroxidase like) that subsequently triggered the disassembly of the catalytic nanostructures (negative feedback). The feedback coupled reaction cycle involving intrinsic catalytic prowess of short peptides to realize the advanced trait of two-stage cascade degradation of a thermodynamically activated substrate foreshadows the complex non-equilibrium protometabolic networks that might have preceded the chemical emergence of life.

The Dual Role of Sulforaphane-Induced Cellular Stress-A Systems Biological Study

The endoplasmic reticulum (ER) plays a crucial role in cellular homeostasis. When ER stress is generated, an autophagic self-digestive process is activated to promote cell survival; however, cell death is induced in the case of excessive levels of ER stress. The aim of the present study was to investigate the effect of a natural compound called sulforaphane (SFN) upon ER stress. Our goal was to investigate how SFN-dependent autophagy activation affects different stages of ER stress induction. We approached our scientific analysis from a systems biological perspective using both theoretical and molecular biological techniques. We found that SFN induced the various cell-death mechanisms in a concentration- and time-dependent manner. The short SFN treatment at low concentrations promoted autophagy, whereas the longer treatment at higher concentrations activated cell death. We proved that SFN activated autophagy in a mTORC1-dependent manner and that the presence of ULK1 was required for its function. A low concentration of SFN pre- or co-treatment combined with short and long ER stress was able to promote cell survival via autophagy induction in each treatment, suggesting the potential medical importance of SFN in ER stress-related diseases.

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.

Phase Separation of DNA-Encoded Artificial Cells Boosts Signal Amplification for Biosensing

Life-like hierarchical architecture shows great potential for advancing intelligent biosensing, but modular expansion of its sensitivity and functionality remains a challenge. Drawing inspiration from intracellular liquid-liquid phase separation, we discovered that a DNA-encoded artificial cell with a liquid core (LAC) can enhance peroxidase-like activity of Hemin and its DNA G-quadruplex aptamer complex (DGAH) without substrate-selectivity, unlike its gelled core (GAC) counterpart. The LAC is easily engineered as an ultrasensitive biosensing system, benefiting from DNA's high programmability and unique signal amplification capability mediated by liquid-liquid phase separation. As proof of concept, its versatility was successfully demonstrated by coupling with two molecular recognition elements to monitor tumor-related microRNA and profile cancer cell phenotypes. This scalable design philosophy offers new insights into the design of next generation of artificial cells-based biosensors.

A Dynamic Control Center Based on a DNA Reaction Network for Programmable Building of DNA Nanostructures

DNA-based nanostructures allow for complex self-assembly with nanometer precision through the specificity of Watson-Crick base pairing, but network behavior-directed control of the kinetic process is less studied. Here we show how the DNA reaction network (DRN), which has emerged as a reliable and programmable way to implement artificial network dynamics, can be built as the control center of programmable nanostructures, allowing spatiotemporal control over the dynamic behavior of DNA nanotubes. We chose a common network motif in biological control systems, the feed-forward loop, as the model network and demonstrated that dynamic behaviors, such as self-tuning control and multilayer hierarchical assembly, could be programmed by constructing an inhibition network and an excitation network, separately, in buffer solution and inside protocells.

On quantification and maximization of information transfer in network dynamical systems

Information flow among nodes in a complex network describes the overall cause-effect relationships among the nodes and provides a better understanding of the contributions of these nodes individually or collectively towards the underlying network dynamics. Variations in network topologies result in varying information flows among nodes. We integrate theories from information science with control network theory into a framework that enables us to quantify and control the information flows among the nodes in a complex network. The framework explicates the relationships between the network topology and the functional patterns, such as the information transfers in biological networks, information rerouting in sensor nodes, and influence patterns in social networks. We show that by designing or re-configuring the network topology, we can optimize the information transfer function between two chosen nodes. As a proof of concept, we apply our proposed methods in the context of brain networks, where we reconfigure neural circuits to optimize excitation levels among the excitatory neurons.

A scalable, open-source implementation of a large-scale mechanistic model for single cell proliferation and death signaling

Mechanistic models of how single cells respond to different perturbations can help integrate disparate big data sets or predict response to varied drug combinations. However, the construction and simulation of such models have proved challenging. Here, we developed a python-based model creation and simulation pipeline that converts a few structured text files into an SBML standard and is high-performance- and cloud-computing ready. We applied this pipeline to our large-scale, mechanistic pan-cancer signaling model (named SPARCED) and demonstrate it by adding an IFNγ pathway submodel. We then investigated whether a putative crosstalk mechanism could be consistent with experimental observations from the LINCS MCF10A Data Cube that IFNγ acts as an anti-proliferative factor. The analyses suggested this observation can be explained by IFNγ-induced SOCS1 sequestering activated EGF receptors. This work forms a foundational recipe for increased mechanistic model-based data integration on a single-cell level, an important building block for clinically-predictive mechanistic models.

Transcription Factor NRF2 Participates in Cell Cycle Progression at the Level of G1/S and Mitotic Checkpoints

Transcription factor NRF2 is a master regulator of the multiple cytoprotective responses that confer growth advantages on a cell. However, its participation in the mechanisms that govern the cell division cycle has not been explored in detail. In this study, we used several standard methods of synchronization of proliferating cells together with flow cytometry and monitored the participation of NRF2 along the cell cycle by the knockdown of its gene expression. We found that the NRF2 levels were highest at S phase entry, and lowest at mitosis. NRF2 depletion promoted both G1 and M arrest. Targeted transcriptomics analysis of cell cycle regulators showed that NRF2 depletion leads to changes in key cell cycle regulators, such as CDK2, TFDP1, CDK6, CDKN1A (p21), CDKN1B (p27), CCNG1, and RAD51. This study gives a new dimension to NRF2 effects, showing their implication in cell cycle progression.

Chloroquine and COVID-19—A systems biology model uncovers the drug’s detrimental effect on autophagy and explains its failure

The COVID-19 pandemic caused by SARS-CoV-2 has resulted in an urgent need for identifying potential therapeutic drugs. In the first half of 2020 tropic antimalarial drugs, such as chloroquine (CQ) or hydroxochloroquine (HCQ) were the focus of tremendous public attention. In the initial periods of the pandemic, many scientific results pointed out that CQ/HCQ could be very effective for patients with severe COVID. While CQ and HCQ have successfully been used against several diseases (such as malaria, autoimmune disease and rheumatic illnesses); long term use of these agents are associated with serious adverse effects (i.e. inducing acute kidney injury, among many others) due to their role in blocking autophagy-dependent self-degradation. Recent experimental and clinical trial data also confirmed that there is no sufficient evidence about the efficient usage of CQ/HCQ against COVID-19. By using systems biology techniques, here we show that the cellular effect of CQ/HCQ on autophagy during endoplasmic reticulum (ER) stress or following SARS-CoV-2 infection results in upregulation of ER stress. By presenting a simple mathematical model, we claim that although CQ/HCQ might be able to ameliorate virus infection, the permanent inhibition of autophagy by CQ/HCQ has serious negative effects on the cell. Since CQ/HCQ promotes apoptotic cell death, here we confirm that addition of CQ/HCQ cannot be really effective even in severe cases. Only a transient treatment seemed to be able to avoid apoptotic cell death, but this type of therapy could not limit virus replication in the infected host. The presented theoretical analysis clearly points out the utility and applicability of systems biology modelling to test the cellular effect of a drug targeting key major processes, such as autophagy and apoptosis. Applying these approaches could decrease the cost of pre-clinical studies and facilitate the selection of promising clinical trials in a timely fashion.

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.

Dose-Dependent Variation of Synchronous Metabolites and Modules in a Yin/Yang Transformation Model of Appointed Ischemia Metabolic Networks

Aim

Chinese medicine Danhong injection (DHI) is an effective pharmaceutical preparation for treating cerebral infarction. Our previous study shows that DHI can remarkably reduce the ischemic stroke-induced infarct volume in a dose-dependent manner, but the pharmacological mechanism of the DHI dose-dependent relationship is not clear. Therefore, the dose-dependent efficacy of DHI on cerebral ischemia and the underlying mechanisms were further investigated in this study.

Methods

A middle cerebral artery occlusion (MCAO) model was established and the rats were randomly divided into six groups: sham, vehicle, DHI dose-1, DHI dose-2, DHI dose-3, and DHI dose-4. Forty-one metabolites in serum were selected as candidate biomarkers of efficacy phenotypes by the Agilent 1290 rapid-resolution liquid chromatography system coupled with the Agilent 6550 Q-TOF MS system. Then, the metabolic networks in each group were constructed using the Weighted Correlation Network analysis (WGCNA). Moreover, the Yang and Yin transformation of six patterns (which are defined by up- and downregulation of metabolites) and synchronous modules divided from a synchronous network were used to dynamically analyze the mechanism of the drug’s effectiveness.

Results

The neuroprotective effect of DHI has shown a dose-dependent manner, and the high-dose group (DH3 and DH4) effect is better. The entropy of the metabolic network and the Yin/Yang index both showed a consistent dose–response relationship. Seven dose-sensitive metabolites maintained constant inverse upregulation or downregulation in the four dose groups. Three synchronous modules for the DH1–DH4 full-course network were identified. Glycine, N-acetyl-L-glutamate, and tetrahydrofolate as a new emerging module appeared in DH2/DH3 and enriched in glutamine and glutamate metabolism-related pathways.

Conclusion

This study takes the DHI metabolic network as an example to provide a new method for the discovery of multiple targets related to pharmacological effects. Our results show that the three conservative allosteric module nodes, taurine, L-tyrosine, and L-leucine, may be one of the basic mechanisms of DHI in the treatment of cerebral infarction, and the other three new emerging module nodes glyoxylate, L-glutamate, and L-valine may participate in the glutamine and glutamate metabolism pathway to improve the efficacy of DHI.

The Potential of OMICs Technologies for the Treatment of Immune-Mediated Inflammatory Diseases

Immune-mediated inflammatory diseases (IMIDs), such as inflammatory bowel diseases and inflammatory arthritis (e.g., rheumatoid arthritis, psoriatic arthritis), are marked by increasing worldwide incidence rates. Apart from irreversible damage of the affected tissue, the systemic nature of these diseases heightens the incidence of cardiovascular insults and colitis-associated neoplasia. Only 40–60% of patients respond to currently used standard-of-care immunotherapies. In addition to this limited long-term effectiveness, all current therapies have to be given on a lifelong basis as they are unable to specifically reprogram the inflammatory process and thus achieve a true cure of the disease. On the other hand, the development of various OMICs technologies is considered as “the great hope” for improving the treatment of IMIDs. This review sheds light on the progressive development and the numerous approaches from basic science that gradually lead to the transfer from “bench to bedside” and the implementation into general patient care procedures.

Unsupervised logic-based mechanism inference for network-driven biological processes

Modern analytical techniques enable researchers to collect data about cellular states, before and after perturbations. These states can be characterized using analytical techniques, but the inference of regulatory interactions that explain and predict changes in these states remains a challenge. Here we present a generalizable, unsupervised approach to generate parameter-free, logic-based models of cellular processes, described by multiple discrete states. Our algorithm employs a Hamming-distance based approach to formulate, test, and identify optimized logic rules that link two states. Our approach comprises two steps. First, a model with no prior knowledge except for the mapping between initial and attractor states is built. We then employ biological constraints to improve model fidelity. Our algorithm automatically recovers the relevant dynamics for the explored models and recapitulates key aspects of the biochemical species concentration dynamics in the original model. We present the advantages and limitations of our work and discuss how our approach could be used to infer logic-based mechanisms of signaling, gene-regulatory, or other input-output processes describable by the Boolean formalism.

Therapeutic Approach of KRAS Mutant Tumours by the Combination of Pharmacologic Ascorbate and Chloroquine

The Warburg effect has been considered a potential therapeutic target to fight against cancer progression. In KRAS mutant cells, PKM2 (pyruvate kinase isozyme M2) is hyper-activated, and it induces GLUT1 expression; therefore, KRAS has been closely involved in the initiation of Warburg metabolism. Although mTOR (mammalian target of rapamycin), a well-known inhibitor of autophagy-dependent survival in physiological conditions, is also activated in KRAS mutants, many recent studies have revealed that autophagy becomes hyper-active in KRAS mutant cancer cells. In the present study, a mathematical model was built containing the main elements of the regulatory network in KRAS mutant cancer cells to explore the further possible therapeutic strategies. Our dynamical analysis suggests that the downregulation of KRAS, mTOR and autophagy are crucial in anti-cancer therapy. PKM2 has been assumed to be the key switch in the stress response mechanism. We predicted that the addition of both pharmacologic ascorbate and chloroquine is able to block both KRAS and mTOR pathways: in this case, no GLUT1 expression is observed, meanwhile autophagy, essential for KRAS mutant cancer cells, is blocked. Corresponding to our system biological analysis, this combined pharmacologic ascorbate and chloroquine treatment in KRAS mutant cancers might be a therapeutic approach in anti-cancer therapies.

Gene expression oscillations in C. elegans underlie a new developmental clock

During C. elegans larval development, thousands of genes, accounting for >20% of the transcriptome, exhibit oscillatory expression with large amplitudes. The time of peaking varies for different genes, but expression generally peaks once per larval stage, with both the oscillation period and larval stage duration varying in concert with temperature. This and other evidence support the existence of a gene expression oscillator that functions as a developmental clock. In this article, we review what is known about the biology, architecture and possible mechanisms of this clock. We compare it to other oscillators, and highlight tools and approaches suited to its study. Finally, we point out implications of these wide-spread and dynamic changes of gene expression on any type of gene expression profiling experiment in C. elegans larvae and how such experiments need to be controlled.

Nontrivial amplification below the threshold for excitable cell signaling

In many asymptotically stable fluid systems, arbitrarily small fluctuations can grow by orders of magnitude before eventually decaying, dramatically enhancing the fluctuation variance beyond the minimum predicted by linear stability theory. Here using influential quantitative models drawn from the mathematical biology literature, we establish that dramatic amplification of arbitrarily small fluctuations is found in excitable cell signaling systems as well. Our analysis highlights how positive and negative feedback, proximity to bifurcations, and strong separation of timescales can generate nontrivial fluctuations without nudging these systems across their excitation thresholds. These insights, in turn, are relevant for a broader range of related oscillatory, bistable, and pattern-forming systems that share these features. The common thread connecting all of these systems with fluid dynamical examples of noise amplification is non-normality.

A Monte Carlo method for in silico modeling and visualization of Waddington's epigenetic landscape with intermediate details

Waddington's epigenetic landscape is a classic metaphor for describing the cellular dynamics during the development modulated by gene regulation. Quantifying Waddington's epigenetic landscape by mathematical modeling would be useful for understanding the mechanisms of cell fate determination. A few computational methods have been proposed for quantitative modeling of landscape; however, to model and visualize the landscape of a high dimensional gene regulatory system with realistic details is still challenging. Here, we propose a Monte Carlo method for modeling the Waddington's epigenetic landscape of a gene regulatory network (GRN). The method estimates the probability distribution of cellular states by collecting a large number of time-course simulations with random initial conditions. By projecting all the trajectories into a 2-dimensional plane of dimensions i and j, we can approximately calculate the quasi-potential U(x_i,x_j,∗)=-ln P(x_i,x_j,∗), where P(x_i,x_j,∗) is the estimated probability of an equilibrium steady state or a non-equilibrium state. Compared to the state-of-the-art methods, our Monte Carlo method can quantify the global potential landscape (or emergence behavior) of GRN for a high dimensional system. The potential landscapes show that not only attractors represent stability, but the paths between attractors are also part of the stability or robustness of biological systems. We demonstrate the novelty and reliability of our method by plotting the potential landscapes of a few published models of GRN.

Developmental function and state transitions of a gene expression oscillator in Caenorhabditis elegans

Gene expression oscillators can structure biological events temporally and spatially. Different biological functions benefit from distinct oscillator properties. Thus, finite developmental processes rely on oscillators that start and stop at specific times, a poorly understood behavior. Here, we have characterized a massive gene expression oscillator comprising > 3,700 genes in Caenorhabditis elegans larvae. We report that oscillations initiate in embryos, arrest transiently after hatching and in response to perturbation, and cease in adults. Experimental observation of the transitions between oscillatory and non-oscillatory states at high temporal resolution reveals an oscillator operating near a Saddle Node on Invariant Cycle (SNIC) bifurcation. These findings constrain the architecture and mathematical models that can represent this oscillator. They also reveal that oscillator arrests occur reproducibly in a specific phase. Since we find oscillations to be coupled to developmental processes, including molting, this characteristic of SNIC bifurcations endows the oscillator with the potential to halt larval development at defined intervals, and thereby execute a developmental checkpoint function.

Critical slowing down and attractive manifold: A mechanism for dynamic robustness in the yeast cell-cycle process

Biological processes that execute complex multiple functions, such as the cell cycle, must ensure the order of sequential events and maintain dynamic robustness against various fluctuations. Here, we examine the mechanisms and fundamental structure that achieve these properties in the cell cycle of the budding yeast Saccharomyces cerevisiae. We show that this process behaves like an excitable system containing three well-decoupled saddle-node bifurcations to execute DNA replication and mitosis events. The yeast cell-cycle regulatory network can be divided into three modules-the G1/S phase, early M phase, and late M phase-wherein both positive feedback loops in each module and interactions among modules play important roles. Specifically, when the cell-cycle process operates near the critical points of the saddle-node bifurcations, a critical slowing down effect takes place. Such interregnum then allows for an attractive manifold and sufficient duration for cell-cycle events, within which to assess the completion of DNA replication and mitosis, e.g., spindle assembly. Moreover, such arrangement ensures that any fluctuation in an early module or event will not transmit to a later module or event. Thus, our results suggest a possible dynamical mechanism of the cell-cycle process to ensure event order and dynamic robustness and give insight into the evolution of eukaryotic cell-cycle processes.

Theory of cell fate

Cell fate decisions are controlled by complex intracellular molecular regulatory networks. Studies increasingly reveal the scale of this complexity: not only do cell fate regulatory networks contain numerous positive and negative feedback loops, they also involve a range of different kinds of nonlinear protein-protein and protein-DNA interactions. This inherent complexity and nonlinearity makes cell fate decisions hard to understand using experiment and intuition alone. In this primer, we will outline how tools from mathematics can be used to understand cell fate dynamics. We will briefly introduce some notions from dynamical systems theory, and discuss how they offer a framework within which to build a rigorous understanding of what we mean by a cell "fate", and how cells change fate. We will also outline how modern experiments, particularly high-throughput single-cell experiments, are enabling us to test and explore the limits of these ideas, and build a better understanding of cellular identities. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Biological Mechanisms > Cell Fates Models of Systems Properties and Processes > Cellular Models.

A Systems Biology Roadmap to Decode mTOR Control System in Cancer

Mechanistic target of rapamycin (mTOR) is a critical protein in the regulation of cell fate decision making, especially in cancer cells. mTOR acts as a signal integrator and is one of the main elements of interactions among the pivotal cellular processes such as cell death, autophagy, metabolic reprogramming, cell growth, and cell cycle. The temporal control of these processes is essential for the cellular homeostasis and dysregulation of mTOR signaling pathway results in different phenotypes, including aging, oncogenesis, cell survival, cell growth, senescence, quiescence, and cell death. In this paper, we have proposed a systems biology roadmap to study mTOR control system, which introduces the theoretical and experimental modalities to decode temporal and dynamical characteristics of mTOR signaling in cancer.

Dynamic modeling of signal transduction by mTOR complexes in cancer

Signal integration has a crucial role in the cell fate decision and dysregulation of the cellular signaling pathways is a primary characteristic of cancer. As a signal integrator, mTOR shows a complex dynamical behavior which determines the cell fate at different cellular processes levels, including cell cycle progression, cell survival, cell death, metabolic reprogramming, and aging. The dynamics of the complex responses to rapamycin in cancer cells have been attributed to its differential time-dependent inhibitory effects on mTORC1 and mTORC2, the two main complexes of mTOR. Two explanations were previously provided for this phenomenon: 1-Rapamycin does not inhibit mTORC2 directly, whereas it prevents mTORC2 formation by sequestering free mTOR protein (Le Chatelier's principle). 2-Components like Phosphatidic Acid (PA) further stabilize mTORC2 compared with mTORC1. To understand the mechanism by which rapamycin differentially inhibits the mTOR complexes in the cancer cells, we present a mathematical model of rapamycin mode of action based on the first explanation, i.e., Le Chatelier's principle. Translating the interactions among components of mTORC1 and mTORC2 into a mathematical model revealed the dynamics of rapamycin action in different doses and time-intervals of rapamycin treatment. This model shows that rapamycin has stronger effects on mTORC1 compared with mTORC2, simply due to its direct interaction with free mTOR and mTORC1, but not mTORC2, without the need to consider other components that might further stabilize mTORC2. Based on our results, even when mTORC2 is less stable compared with mTORC1, it can be less inhibited by rapamycin.

Quantitative Kinetic Models from Intravital Microscopy: A Case Study Using Hepatic Transport

The liver performs critical physiological functions, including metabolizing and removing substances, such as toxins and drugs, from the bloodstream. Hepatotoxicity itself is intimately linked to abnormal hepatic transport, and hepatotoxicity remains the primary reason drugs in development fail and approved drugs are withdrawn from the market. For this reason, we propose to analyze, across liver compartments, the transport kinetics of fluorescein-a fluorescent marker used as a proxy for drug molecules-using intravital microscopy data. To resolve the transport kinetics quantitatively from fluorescence data, we account for the effect that different liver compartments (with different chemical properties) have on fluorescein's emission rate. To do so, we develop ordinary differential equation transport models from the data where the kinetics is related to the observable fluorescence levels by "measurement parameters" that vary across different liver compartments. On account of the steep non-linearities in the kinetics and stochasticity inherent to the model, we infer kinetic and measurement parameters by generalizing the method of parameter cascades. For this application, the method of parameter cascades ensures fast and precise parameter estimates from noisy time traces.

Controlling large Boolean networks with single-step perturbations

Motivation

The control of Boolean networks has traditionally focussed on strategies where the perturbations are applied to the nodes of the network for an extended period of time. In this work, we study if and how a Boolean network can be controlled by perturbing a minimal set of nodes for a single-step and letting the system evolve afterwards according to its original dynamics. More precisely, given a Boolean network (BN), we compute a minimal subset Cmin of the nodes such that BN can be driven from any initial state in an attractor to another ‘desired’ attractor by perturbing some or all of the nodes of Cmin for a single-step. Such kind of control is attractive for biological systems because they are less time consuming than the traditional strategies for control while also being financially more viable. However, due to the phenomenon of state-space explosion, computing such a minimal subset is computationally inefficient and an approach that deals with the entire network in one-go, does not scale well for large networks.

Results

We develop a ‘divide-and-conquer’ approach by decomposing the network into smaller partitions, computing the minimal control on the projection of the attractors to these partitions and then composing the results to obtain Cmin for the whole network. We implement our method and test it on various real-life biological networks to demonstrate its applicability and efficiency.

Supplementary information

Supplementary data are available at Bioinformatics online.

Coexistence of oscillation and quenching states: Effect of low-pass active filtering in coupled oscillators

Effects of a low-pass active filter (LPAF) on the transition processes from oscillation quenching to asymmetrical oscillation are explored for diffusively coupled oscillators. The low-pass filter part and the active part of LPAF exhibit different effects on the dynamics of these coupled oscillators. With the amplifying active part only, LPAF keeps the coupled oscillators staying in a nontrivial amplitude death (NTAD) and oscillation state. However, the additional filter is beneficial to induce a transition from a symmetrical oscillation death to an asymmetrical oscillation death and then to an asymmetrical oscillation state which is oscillating with different amplitudes for two oscillators. Asymmetrical oscillation state is coexisting with a synchronous oscillation state for properly presented parameters. With the attenuating active part only, LPAF keeps the coupled oscillators in rich oscillation quenching states such as amplitude death (AD), symmetrical oscillation death (OD), and NTAD. The additional filter tends to enlarge the AD domains but to shrink the symmetrical OD domains by increasing the areas of the coexistence of the oscillation state and the symmetrical OD state. The stronger filter effects enlarge the basin of the symmetrical OD state which is coexisting with the synchronous oscillation state. Moreover, the effects of the filter are general in globally coupled oscillators. Our results are important for understanding and controlling the multistability of coupled systems.

A Boolean network control algorithm guided by forward dynamic programming

Control problem in a biological system is the problem of finding an interventional policy for changing the state of the biological system from an undesirable state, e.g. disease, into a desirable healthy state. Boolean networks are utilized as a mathematical model for gene regulatory networks. This paper provides an algorithm to solve the control problem in Boolean networks. The proposed algorithm is implemented and applied on two biological systems: T-cell receptor network and Drosophila melanogaster network. Results show that the proposed algorithm works faster in solving the control problem over these networks, while having similar accuracy, in comparison to previous exact methods. Source code and a simple web service of the proposed algorithm is available at http://goliaei.ir/net-control/www/.

Artificial Gene Regulatory Networks-A Review

In nature, gene regulatory networks are a key mediator between the information stored in the DNA of living organisms (their genotype) and the structural and behavioral expression this finds in their bodies, surviving in the world (their phenotype). They integrate environmental signals, steer development, buffer stochasticity, and allow evolution to proceed. In engineering, modeling and implementations of artificial gene regulatory networks have been an expanding field of research and development over the past few decades. This review discusses the concept of gene regulation, describes the current state of the art in gene regulatory networks, including modeling and simulation, and reviews their use in artificial evolutionary settings. We provide evidence for the benefits of this concept in natural and the engineering domains.

NRF2-regulated cell cycle arrest at early stage of oxidative stress response mechanism

Oxidative stress results in activation of several signal transduction pathways controlled by the PERK-substrate NRF2 (nuclear factor erythroid 2-related factor 2); meanwhile the ongoing cell division cycle has to be blocked. It has been recently shown that Cyclin D1 got immediately down-regulated via PERK pathway in response to oxidative stress leading to cell cycle arrest. However, the effect of NRF2 on cell cycle regulation has not been explored yet. We aimed to reveal a crosstalk between PERK-substrate NRF2 and the key elements of cell cycle regulatory network upon oxidative stress using molecular biological techniques- Although Cyclin D1 level remained constant, its activity was blocked by various stoichiometric inhibitors (such as p15, p21 and p27) even at low level of oxidative stress. The activity of these CDK inhibitors completely disappeared, when the addition of oxidative agent was combined with silencing of either PERK or NRF2.This further confirms the important role of NRF2 in blocking Cyclin D1 with stoichiometric inhibitors at early stage of oxidative stress.

Modeling the Bistable Dynamics of the Innate Immune System

The size of primary challenge with lipopolysaccharide induces changes in the innate immune cells phenotype between pro-inflammatory and pro-tolerant states when facing a secondary lipopolysaccharide challenge. To determine the molecular mechanisms governing this differential response, we propose a mathematical model for the interaction between three proteins involved in the immune cell decision making: IRAK-1, PI3K, and RelB. The mutual inhibition of IRAK-1 and PI3K in the model leads to bistable dynamics. By using the levels of RelB as indicative of strength of the immune responses, we connect the size of different primary lipopolysaccharide doses to the differential phenotypical outcomes following a secondary challenge. We further predict under what circumstances the primary LPS dose does not influence the response to a secondary challenge. Our results can be used to guide treatments for patients with either autoimmune disease or compromised immune system.

Systems biology primer: the basic methods and approaches

Systems biology is an integrative discipline connecting the molecular components within a single biological scale and also among different scales (e.g. cells, tissues and organ systems) to physiological functions and organismal phenotypes through quantitative reasoning, computational models and high-throughput experimental technologies. Systems biology uses a wide range of quantitative experimental and computational methodologies to decode information flow from genes, proteins and other subcellular components of signaling, regulatory and functional pathways to control cell, tissue, organ and organismal level functions. The computational methods used in systems biology provide systems-level insights to understand interactions and dynamics at various scales, within cells, tissues, organs and organisms. In recent years, the systems biology framework has enabled research in quantitative and systems pharmacology and precision medicine for complex diseases. Here, we present a brief overview of current experimental and computational methods used in systems biology.

General method to find the attractors of discrete dynamic models of biological systems

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

Analysis of Critical and Redundant Vertices in Controlling Directed Complex Networks Using Feedback Vertex Sets

Controlling complex networks through a small number of controller vertices is of great importance in wide-ranging research fields. Recently, a new approach based on the minimum feedback vertex set (MFVS) has been proposed to find such vertices in directed networks in which the target states are restricted to steady states. However, multiple MFVS configurations may exist and thus the selection of vertices may depend on algorithms and input data representations. Our attempts to address this ambiguity led us to adopt an existing approach that classifies vertices into three categories. This approach has been successfully applied to maximum matching-based and minimum dominating set-based controllability analysis frameworks. In this article, we present an algorithm as well as its implementation to compute and evaluate the critical, intermittent, and redundant vertices under the MFVS-based framework, where these three categories include vertices belonging to all MFVSs, some (but not all) MFVSs, and none of the MFVSs, respectively. The results of computational experiments using artificially generated networks and real-world biological networks suggest that the proposed algorithm is useful for identifying these three kinds of vertices for relatively large-scale networks, and that the fraction of critical and intermittent vertices is considerably small. Moreover, an analysis of the signal pathways indicates that critical and intermittent MFVSs tend to be enriched by essential genes.

Transition from homogeneous to inhomogeneous limit cycles: Effect of local filtering in coupled oscillators

We report an interesting symmetry-breaking transition in coupled identical oscillators, namely, the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the Turing-type symmetry-breaking transition from amplitude death (i.e., stable homogeneous steady state) to oscillation death (i.e., stable inhomogeneous steady state). This novel transition occurs in the parametric zone of occurrence of rhythmogenesis and oscillation death as a consequence of the presence of local filtering in the coupling path. We consider paradigmatic oscillators, such as Stuart-Landau and van der Pol oscillators, under mean-field coupling with low-pass or all-pass filtered self-feedback and through a rigorous bifurcation analysis we explore the genesis of this transition. Further, we experimentally demonstrate the observed transition, which establishes its robustness in the presence of parameter fluctuations and noise.

Endocytosis as a stabilizing mechanism for tissue homeostasis

Cells in tissues communicate by secreted growth factors (GF) and other signals. An important function of cell circuits is tissue homeostasis: maintaining proper balance between the amounts of different cell types. Homeostasis requires negative feedback on the GFs, to avoid a runaway situation in which cells stimulate each other and grow without control. Feedback can be obtained in at least two ways: endocytosis in which a cell removes its cognate GF by internalization and cross-inhibition in which a GF down-regulates the production of another GF. Here we ask whether there are design principles for cell circuits to achieve tissue homeostasis. We develop an analytically solvable framework for circuits with multiple cell types and find that feedback by endocytosis is far more robust to parameter variation and has faster responses than cross-inhibition. Endocytosis, which is found ubiquitously across tissues, can even provide homeostasis to three and four communicating cell types. These design principles form a conceptual basis for how tissues maintain a healthy balance of cell types and how balance may be disrupted in diseases such as degeneration and fibrosis.

A toolbox for discrete modelling of cell signalling dynamics

We present a library of network motifs for the development of complex and realistic biological network models using the BioModelAnalyzer, and demonstrate their wider value by using them to construct a model of the cell cycle.

A framework to find the logic backbone of a biological network

Background

Cellular behaviors are governed by interaction networks among biomolecules, for example gene regulatory and signal transduction networks. An often used dynamic modeling framework for these networks, Boolean modeling, can obtain their attractors (which correspond to cell types and behaviors) and their trajectories from an initial state (e.g. a resting state) to the attractors, for example in response to an external signal. The existing methods however do not elucidate the causal relationships between distant nodes in the network.

Results

In this work, we propose a simple logic framework, based on categorizing causal relationships as sufficient or necessary, as a complement to Boolean networks. We identify and explore the properties of complex subnetworks that are distillable into a single logic relationship. We also identify cyclic subnetworks that ensure the stabilization of the state of participating nodes regardless of the rest of the network. We identify the logic backbone of biomolecular networks, consisting of external signals, self-sustaining cyclic subnetworks (stable motifs), and output nodes. Furthermore, we use the logic framework to identify crucial nodes whose override can drive the system from one steady state to another. We apply these techniques to two biological networks: the epithelial-to-mesenchymal transition network corresponding to a developmental process exploited in tumor invasion, and the network of abscisic acid induced stomatal closure in plants. We find interesting subnetworks with logical implications in these networks. Using these subgraphs and motifs, we efficiently reduce both networks to succinct backbone structures.

Conclusions

The logic representation identifies the causal relationships between distant nodes and subnetworks. This knowledge can form the basis of network control or used in the reverse engineering of networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0482-5) contains supplementary material, which is available to authorized users.

Notch transactivates Rheb to maintain the multipotency of TSC-null cells

Differentiation abnormalities are a hallmark of tuberous sclerosis complex (TSC) manifestations; however, the genesis of these abnormalities remains unclear. Here we report on mechanisms controlling the multi-lineage, early neuronal progenitor and neural stem-like cell characteristics of lymphangioleiomyomatosis (LAM) and angiomyolipoma cells. These mechanisms include the activation of a previously unreported Rheb-Notch-Rheb regulatory loop, in which the cyclic binding of Notch1 to the Notch-responsive elements (NREs) on the Rheb promoter is a key event. This binding induces the transactivation of Rheb. The identified NRE2 and NRE3 on the Rheb promoter are important to Notch-dependent promoter activity. Notch cooperates with Rheb to block cell differentiation via similar mechanisms in mouse models of TSC. Cell-specific loss of Tsc1 within nestin-expressing cells in adult mice leads to the formation of kidney cysts, renal intraepithelial neoplasia, and invasive papillary renal carcinoma.

Tuberous sclerosis complex (TSC) is a rare genetic condition causing tumours with differentiation abnormalities; however the molecular mechanisms causing these defects are unclear. Here the authors show that Notch cooperates with Rheb to block cell differentiation forming a regulatory loop that could underlie TSC tumorigenesis.

Fundamental limitations of network reconstruction from temporal data

Inferring properties of the interaction matrix that characterizes how nodes in a networked system directly interact with each other is a well-known network reconstruction problem. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations governing which properties of the interaction matrix (e.g. adjacency pattern, sign pattern or degree sequence) can be inferred from given temporal data of individual nodes remain unknown. Here, we rigorously derive the necessary conditions to reconstruct any property of the interaction matrix. Counterintuitively, we find that reconstructing any property of the interaction matrix is generically as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. Revealing these fundamental limitations sheds light on the design of better network reconstruction algorithms that offer practical improvements over existing methods.

The E3 ubiquitin ligase SCFFBXL14 complex stimulates neuronal differentiation by targeting the Notch signaling factor HES1 for proteolysis

Molecular oscillators are important cellular regulators of, for example, circadian clocks, oscillations of immune regulators, and short-period (ultradian) rhythms during embryonic development. The Notch signaling factor HES1 (hairy and enhancer of split 1) is a well-known repressor of proneural genes, and HES1 ultradian oscillation is essential for keeping cells in an efficiently proliferating progenitor state. HES1 oscillation is driven by both transcriptional self-repression and ubiquitin-dependent proteolysis. However, the E3 ubiquitin ligase targeting HES1 for proteolysis remains unclear. Based on siRNA-mediated gene silencing screening, co-immunoprecipitation, and ubiquitination assays, we discovered that the E3 ubiquitin ligase SCF^FBXL14 complex regulates HES1 ubiquitination and proteolysis. siRNA-mediated knockdown of the Cullin-RING E3 ubiquitin ligases RBX1 or CUL1 increased HES1 protein levels, prolonged its half-life, and dampened its oscillation. FBXL14, an F-box protein for SCF ubiquitin ligase, associates with HES1. FBXL14 silencing stabilized HES1, whereas FBXL14 overexpression decreased HES1 protein levels. Of note, the SCF^FBXL14 complex promoted the ubiquitination of HES1 in vivo, and a conserved WRPW motif in HES1 was essential for HES1 binding to FBXL14 and for ubiquitin-dependent HES1 degradation. HES1 knockdown promoted neuronal differentiation, but FBXL14 silencing inhibited neuronal differentiation induced by HES1 ablation in mES and F9 cells. Our results suggest that SCF^FBXL14 promotes neuronal differentiation by targeting HES1 for ubiquitin-dependent proteolysis and that the C-terminal WRPW motif in HES1 is required for this process.

Core signalling motif displaying multistability through multi-state enzymes

Bistability, and more generally multistability, is a key system dynamics feature enabling decision-making and memory in cells. Deciphering the molecular determinants of multistability is thus crucial for a better understanding of cellular pathways and their (re)engineering in synthetic biology. Here, we show that a key motif found predominantly in eukaryotic signalling systems, namely a futile signalling cycle, can display bistability when featuring a two-state kinase. We provide necessary and sufficient mathematical conditions on the kinetic parameters of this motif that guarantee the existence of multiple steady states. These conditions foster the intuition that bistability arises as a consequence of competition between the two states of the kinase. Extending from this result, we find that increasing the number of kinase states linearly translates into an increase in the number of steady states in the system. These findings reveal, to our knowledge, a new mechanism for the generation of bistability and multistability in cellular signalling systems. Further the futile cycle featuring a two-state kinase is among the smallest bistable signalling motifs. We show that multi-state kinases and the described competition-based motif are part of several natural signalling systems and thereby could enable them to implement complex information processing through multistability. These results indicate that multi-state kinases in signalling systems are readily exploited by natural evolution and could equally be used by synthetic approaches for the generation of multistable information processing systems at the cellular level.