The combination of positive and negative feedback loops confers exquisite flexibility to biochemical switches

Whole-cell modeling of E. coli confirms that in vitro tRNA aminoacylation measurements are insufficient to support cell growth and predicts a positive feedback mechanism regulating arginine biosynthesis

In Escherichia coli, inconsistencies between in vitro tRNA aminoacylation measurements and in vivo protein synthesis demands were postulated almost 40 years ago, but have proven difficult to confirm. Whole-cell modeling can test whether a cell behaves in a physiologically correct manner when parameterized with in vitro measurements by providing a holistic representation of cellular processes in vivo. Here, a mechanistic model of tRNA aminoacylation, codon-based polypeptide elongation, and N-terminal methionine cleavage was incorporated into a developing whole-cell model of E. coli. Subsequent analysis confirmed the insufficiency of aminoacyl-tRNA synthetase kinetic measurements for cellular proteome maintenance, and estimated aminoacyl-tRNA synthetase kcats that were on average 7.6-fold higher. Simulating cell growth with perturbed kcats demonstrated the global impact of these in vitro measurements on cellular phenotypes. For example, an insufficient kcat for HisRS caused protein synthesis to be less robust to the natural variability in aminoacyl-tRNA synthetase expression in single cells. More surprisingly, insufficient ArgRS activity led to catastrophic impacts on arginine biosynthesis due to underexpressed N-acetylglutamate synthase, where translation depends on repeated CGG codons. Overall, the expanded E. coli model deepens understanding of how translation operates in an in vivo context.

Computational analysis of synergism in small networks with different logic

Cell fate decision processes are regulated by networks which contain different molecules and interactions. Different network topologies may exhibit synergistic or antagonistic effects on cellular functions. Here, we analyze six most common small networks with regulatory logic AND or OR, trying to clarify the relationship between network topologies and synergism (or antagonism) related to cell fate decisions. We systematically examine the contribution of both network topologies and regulatory logic to the cell fate synergism by bifurcation and combinatorial perturbation analysis. Initially, under a single set of parameters, the synergism of three types of networks with AND and OR logic is compared. Furthermore, to consider whether these results depend on the choices of parameter values, statistics on the synergism of five hundred parameter sets is performed. It is shown that the results are not sensitive to parameter variations, indicating that the synergy or antagonism mainly depends on the network topologies rather than the choices of parameter values. The results indicate that the topology with "Dual Inhibition" shows good synergism, while the topology with "Dual Promotion" or "Hybrid" shows antagonism. The results presented here may help us to design synergistic networks based on network structure and regulation combinations, which has promising implications for cell fate decisions and drug combinations.

Network regulation meets substrate modification chemistry

Biochemical networks are at the heart of cellular information processing. These networks contain distinct facets: (i) processing of information from the environment via cascades/pathways along with network regulation and (ii) modification of substrates in different ways, to confer protein functionality, stability and processing. While many studies focus on these factors individually, how they interact and the consequences for cellular systems behaviour are poorly understood. We develop a systems framework for this purpose by examining the interplay of network regulation (canonical feedback and feed-forward circuits) and multisite modification, as an exemplar of substrate modification. Using computational, analytical and semi-analytical approaches, we reveal distinct and unexpected ways in which the substrate modification and network levels combine and the emergent behaviour arising therefrom. This has important consequences for dissecting the behaviour of specific signalling networks, tracing the origins of systems behaviour, inference of networks from data, robustness/evolvability and multi-level engineering of biomolecular networks. Overall, we repeatedly demonstrate how focusing on only one level (say network regulation) can lead to profoundly misleading conclusions about all these aspects, and reveal a number of important consequences for experimental/theoretical/data-driven interrogations of cellular signalling systems.

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.

Nonsteroidal anti-inflammatory drugs as antipyretics and modulators of a molecular clock(s) in the appendix of Sauromatum venosum inflorescence

The appendix of the Sauromatum senosum inflorescence is a striking example of thermogenesis in plants. On the day of opening, the Sauromatum appendix becomes hot, reaching up to 32 °C. Aspirin, salicylic acid and 2,6-dihydroxybenzoic acid, a subclass of NSAIDs, induce a temperature rise from three mitochondrial sources: alternative oxidase, F₁ F_O -ATP synthase and adenine nucleotide translocator. This temperature rise is synchronized and compounded under various light/dark regimes. We studied the effect of different subgroups of NSAIDs on the temperature rise. Tissue slices of appendix of Sauromatum and Arum italicum inflorescences at a pre-mature stage were treated with the three inducers in combination with one NSAID under constant light or darkness and under different photoperiods. Temperature rise generated by the three heat sources in the presence of inducers and different non-selective NSAIDs were not compounded and occurred at three different times. Under constant light, DuP-697, ibuprofen, flurbiprofen, acetaminophen and diclofenac suppressed the temperature rise induced by the three salicylates. Desynchronization and delayed temperature rise were detected with 6/42-h light/ dark and 15/33-h light/dark regimes in the presence of celecoxib and ibuprofen. With a 24/24-h light/dark regime, temperature rise was suppressed in the presence of ibuprofen. There were differences in response to individual NSAIDs between appendix tissue of A. italicum and S. venosum. Mitochondrial energy balance is affected by NSAIDs. There is an interaction between light/dark regime and temperature rise and a relationship between timing mechanism and temperature rise.

Lactate-dependent chaperone-mediated autophagy induces oscillatory HIF-1α activity promoting proliferation of hypoxic cells

Response to hypoxia is a highly regulated process, but little is known about single-cell responses to hypoxic conditions. Using fluorescent reporters of hypoxia response factor-1α (HIF-1α) activity in various cancer cell lines and patient-derived cancer cells, we show that hypoxic responses in individual cancer cells can be highly dynamic and variable. These responses fall into three classes, including oscillatory activity. We identify a molecular mechanism that can account for all three response classes, implicating reactive-oxygen-species-dependent chaperone-mediated autophagy of HIF-1α in a subset of cells. Furthermore, we show that oscillatory response is modulated by the abundance of extracellular lactate in a quorum-sensing-like mechanism. We show that oscillatory HIF-1α activity rescues hypoxia-mediated inhibition of cell division and causes broad suppression of genes downregulated in cancers and activation of genes upregulated in many cancers, suggesting a mechanism for aggressive growth in a subset of hypoxic tumor cells.

Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change

Endocrine regulation in the hypothalamic-pituitary-thyroid (HPT) axis is orchestrated by physiological circuits which integrate multiple internal and external influences. Essentially, it provides either of the two responses to overt biological challenges: to defend the homeostatic range of a target hormone or adapt it to changing environmental conditions. Under certain conditions, such flexibility may exceed the capability of a simple feedback control loop, rather requiring more intricate networks of communication between the system's components. A new minimal mathematical model, in the form of a parametrized nonlinear dynamical system, is here formulated as a proof-of-concept to elucidate the principles of the HPT axis regulation. In particular, it allows uncovering mechanisms for the homeostasis of the key biologically active hormone free triiodothyronine (FT3). One mechanism supports the preservation of FT3 homeostasis, whilst the other is responsible for the adaptation of the homeostatic state to a new level. Together these allow optimum resilience in stressful situations. Preservation of FT3 homeostasis, despite changes in FT4 and TSH levels, is found to be an achievable system goal by joining elements of top-down and bottom-up regulation in a cascade of targeted feedforward and feedback loops. Simultaneously, the model accounts for the combination of properties regarded as essential to endocrine regulation, namely sensitivity, the anticipation of an adverse event, robustness, and adaptation. The model therefore offers fundamental theoretical insights into the effective system control of the HPT axis.

Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

Living systems are products of evolution, and their present forms reflect their evolutionary history. Thus, to investigate the particularity of the evolutionary process by computer simulations, an appropriate reference system is needed for comparison with the outcomes of evolutionary simulations. In this study, we considered a model of gene regulatory networks (GRNs). Our idea was to construct a reference ensemble comprising randomly generated GRNs. To produce GRNs with high fitness values, which are rare, we employed a “rare event sampling” method developed in statistical physics. In particular, we focused on the evolution of mutational robustness. Living systems do not lose viability readily, even when some genes are mutated. This trait, called mutational robustness, has developed throughout evolution, along with functionality. Using the abovementioned method, we found that mutational robustness resulting from evolution exceeded that of the reference set. Therefore, mutational robustness is enhanced by evolution. We also found that the emergence of a new phenotype was significantly delayed in evolution. Our results suggest that this delay is a consequence of the fact that mutationally robust GRNs are favored by evolution.

Roles of mTOR in thoracic aortopathy understood by complex intracellular signaling interactions

Thoracic aortopathy–aneurysm, dissection, and rupture–is increasingly responsible for significant morbidity and mortality. Advances in medical genetics and imaging have improved diagnosis and thus enabled earlier prophylactic surgical intervention in many cases. There remains a pressing need, however, to understand better the underlying molecular and cellular mechanisms with the hope of finding robust pharmacotherapies. Diverse studies in patients and mouse models of aortopathy have revealed critical changes in multiple smooth muscle cell signaling pathways that associate with disease, yet integrating information across studies and models has remained challenging. We present a new quantitative network model that includes many of the key smooth muscle cell signaling pathways and validate the model using a detailed data set that focuses on hyperactivation of the mechanistic target of rapamycin (mTOR) pathway and its inhibition using rapamycin. We show that the model can be parameterized to capture the primary experimental findings both qualitatively and quantitatively. We further show that simulating a population of cells by varying receptor reaction weights leads to distinct proteomic clusters within the population, and that these clusters emerge due to a bistable switch driven by positive feedback in the PI3K/AKT/mTOR signaling pathway.

Cell signaling drives changes across scales, from altered transcription at the single-cell level to tissue-level growth and remodeling. Studying complex interactions within cell signaling pathways can lead to a better understanding of the progression of disease. In particular, we are interested in how vascular cells can change their phenotype in a way that exacerbates aortopathy, namely, the development of aneurysms, dissections, and rupture. In this study we built a novel cell signaling network model of a vascular smooth muscle cell using archival data and used it to capture the effects of a genetic knock-out and subsequent pharmacologic rescue. We then used the model to simulate populations of smooth muscle cells and found that small perturbations to the strength of signaling can lead to distinct clusters of cells. With further analysis of the network substructures, we found that a positive feedback loop within the network was responsible for the distinct phenotypes we saw in our clusters of simulated cells. We believe that this work not only helps us to understand changes in smooth muscle cell phenotype but also opens the possibility to study other signaling perturbations associated with aortopathy.

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.

The scarecrow-like transcription factor SlSCL3 regulates volatile terpene biosynthesis and glandular trichome size in tomato (Solanum lycopersicum)

Tomato (Solanum lycopersicum L.) type VI glandular trichomes that occur on the surface of leaves, stems, young fruits and flowers produce and store a blend of volatile monoterpenes and sesquiterpenes. These compounds play important roles in the interaction with pathogens and herbivorous insects. Although the function of terpene synthases in the biosynthesis of volatile terpenes in tomato has been comprehensively investigated, the deciphering of their transcriptional regulation is only just emerging. We selected transcription factors that are over-expressed in trichomes based on existing transcriptome data and silenced them individually by virus-induced gene silencing. Of these, SlSCL3, a scarecrow-like (SCL) subfamily transcription factor, led to a significant decrease in volatile terpene content and expression of the corresponding terpene synthase genes when its transcription level was downregulated. Overexpression of SlSCL3 dramatically increased both the volatile terpene content and glandular trichome size, whereas its homozygous mutants showed reduced terpene biosynthesis. However, its heterozygous mutants also showed a significantly elevated volatile terpene content and enlarged glandular trichomes, similar to the overexpression plants. SlSCL3 modulates the expression of terpene biosynthetic pathway genes by transcriptional activation, but neither direct protein-DNA binding nor interaction with known regulators was observed. Moreover, transcript levels of the endogenous copy of SlSCL3 were decreased in the overexpression plants but increased in the heterozygous and homozygous mutants, suggesting feedback repression of its own promoter. Taken together, our results provide new insights into the role of SlSCL3 in the complex regulation of volatile terpene biosynthesis and glandular trichome development in tomato.

Bistability in cell signalling and its significance in identifying potential drug targets

MOTIVATION

Bistability is one of the salient dynamical features in various all-or-none kinds of decision-making processes. The presence of bistability in a cell signalling network plays a key role in input-output (I/O) relation. Our study is aiming to capture and emphasise the role of motif structure influencing the I/O relation between two nodes in the context of bistability. Here, a model-based analysis is made to investigate the critical conditions responsible for the emergence of different bistable protein-protein interaction (PPI) motifs and their possible applications to find the potential drug targets.

RESULTS

The global sensitivity analysis is used to identify sensitive parameters and their role in maintaining the bistability. Additionally, the bistable switching through hysteresis is explored to develop an understanding of the underlying mechanisms involved in the cell signalling processes, when significant motifs exhibiting bistability have emerged. Further, we elaborate the application of the results by the implication of the emerged PPI motifs to identify potential drug-targets in three cancer networks, which is validated with existing databases. The influence of stochastic perturbations that could hinder desired functionality of any signalling networks is also described here.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Leveraging systems biology for predicting modulators of inflammation in patients with COVID-19

Dysregulations in the inflammatory response of the body to pathogens could progress toward a hyperinflammatory condition amplified by positive feedback loops and associated with increased severity and mortality. Hence, there is a need for identifying therapeutic targets to modulate this pathological immune response. Here, we propose a single cell-based computational methodology for predicting proteins to modulate the dysregulated inflammatory response based on the reconstruction and analysis of functional cell-cell communication networks of physiological and pathological conditions. We validated the proposed method in 12 human disease datasets and performed an in-depth study of patients with mild and severe symptomatology of the coronavirus disease 2019 for predicting novel therapeutic targets. As a result, we identified the extracellular matrix protein versican and Toll-like receptor 2 as potential targets for modulating the inflammatory response. In summary, the proposed method can be of great utility in systematically identifying therapeutic targets for modulating pathological immune responses.

Toward Molecular Cybernetics - the Art of Communicating Chemical Systems

The emerging field of molecular cybernetics has the potential to widely broaden our perception of chemistry. Chemistry will develop beyond its current focus that is mainly concerned with single transformations, pure compounds, and/or defined mixtures. On this way, chemistry will become autonomous, networked and smart through communicating molecules each of which serves a control engineering purpose, like the set of wheels in the machinery of life. The present personal account describes our latest developments in this field.

Multi-stability in cellular differentiation enabled by a network of three mutually repressing master regulators

Identifying the design principles of complex regulatory networks driving cellular decision-making remains essential to decode embryonic development as well as enhance cellular reprogramming. A well-studied network motif involved in cellular decision-making is a toggle switch-a set of two opposing transcription factors A and B, each of which is a master regulator of a specific cell fate and can inhibit the activity of the other. A toggle switch can lead to two possible states-(high A, low B) and (low A, high B)-and drives the 'either-or' choice between these two cell fates for a common progenitor cell. However, the principles of coupled toggle switches remain unclear. Here, we investigate the dynamics of three master regulators A, B and C inhibiting each other, thus forming three-coupled toggle switches to form a toggle triad. Our simulations show that this toggle triad can lead to co-existence of cells into three differentiated 'single positive' phenotypes-(high A, low B, low C), (low A, high B, low C) and (low A, low B, high C). Moreover, the hybrid or 'double positive' phenotypes-(high A, high B, low C), (low A, high B, high C) and (high A, low B, high C)-can coexist together with 'single positive' phenotypes. Including self-activation loops on A, B and C can increase the frequency of 'double positive' states. Finally, we apply our results to understand cellular decision-making in terms of differentiation of naive CD4⁺ T cells into Th1, Th2 and Th17 states, where hybrid Th1/Th2 and hybrid Th1/Th17 cells have been reported in addition to the Th1, Th2 and Th17 ones. Our results offer novel insights into the design principles of a multi-stable network topology and provide a framework for synthetic biology to design tristable systems.

Emergence of cooperative bistability and robustness of gene regulatory networks

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, "on" and "off", was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between "on" and "off". This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.

Agent-based modeling and bifurcation analysis reveal mechanisms of macrophage polarization and phenotype pattern distribution

Macrophages play a key role in tissue regeneration by polarizing to different destinies and generating various phenotypes. Recognizing the underlying mechanisms is critical in designing therapeutic procedures targeting macrophage fate determination. Here, to investigate the macrophage polarization, a nonlinear mathematical model is proposed in which the effect of IL4, IFNγ and LPS, as external stimuli, on STAT1, STAT6, and NFκB is studied using bifurcation analysis. The existence of saddle-node bifurcations in these internal key regulators allows different combinations of steady state levels which are attributable to different fates. Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization. Next, in order to investigate the polarization of a population of macrophages, bifurcation analysis is employed aligned with agent-based approach and a two-layer model is proposed in which the information from single cells is exploited to model the behavior in tissue level. Also, in this model, a partial differential equation describes the diffusion of secreted cytokines in the medium. Finally, the model was validated against a set of experimental data. Taken together, we have here developed a cell and tissue level model of macrophage polarization behavior which can be used for designing therapeutic interventions.

Interlinked GTPase cascades provide a motif for both robust switches and oscillators

GTPases regulate a wide range of cellular processes, such as intracellular vesicular transport, signal transduction and protein translation. These hydrolase enzymes operate as biochemical switches by toggling between an active guanosine triphosphate (GTP)-bound state and an inactive guanosine diphosphate (GDP)-bound state. We compare two network motifs, a single-species switch and an interlinked cascade that consists of two species coupled through positive and negative feedback loops. We find that interlinked cascades are closer to the ideal all-or-none switch and are more robust against fluctuating signals. While the single-species switch can only achieve bistability, interlinked cascades can be converted into oscillators by tuning the cofactor concentrations, which catalyse the activity of the cascade. These regimes can only be achieved with sufficient chemical driving provided by GTP hydrolysis. In this study, we present a thermodynamically consistent model that can achieve bistability and oscillations with the same feedback motif.

Scaling laws of cell-fate responses to transient stress

Analysis and modelling of dose-survival curves of cells and tissues are often used to assess therapeutic efficacy or environmental risks, much less to infer the intracellular regulatory mechanisms of cellular stress response. However, systematic measurements of how cell survival depends on the time profile of stress, such as exposure duration, provide practical means to decipher the homeostatic dynamics of stress-response regulatory networks. In this paper, we propose a dynamical framework to theoretically address the relationship between cell fate response to a transient stress and the underlying regulatory feedback mechanisms. A simple network topology that couples a homeostatic negative feedback and a death-triggering positive feedback is shown to display four response regimes for which the iso-effect relationships between duration and intensity are captured by specific power laws. These distinct response regimes define several windows of stress duration for which lethality is not merely proportional to the product of intensity and duration, and, thus, for which cells are either more tolerant or more vulnerable to a given dose. Overall, this study highlights the differential roles of feedback strength, timescale and nonlinearity in promoting survivability to particular stress profiles, providing a valuable framework for a comparative analysis of diverse stress-specific regulatory networks.

Chemical Systems Involving Two Competitive Self-Catalytic Reactions

Self-catalytic reactions are chemical phenomena, in which a product catalyzes the reactions of substrates further to yield products. A significant amplification of product concentration occurs during the reactions in a dilute solution, which exhibit notable properties such as sigmoidal kinetics, seeding effects, and thermal hysteresis. Chemical systems involving two competitive self-catalytic reactions can be considered, in which the competitive formation of two products occurs, which is affected by environmental changes, subtle perturbations, and fluctuations, and notable chemical phenomena appear such as formation of different structures in response to slow/fast temperature changes, chiral symmetry breaking, shortcut in reaction time, homogeneous-heterogeneous transitions, and mechanical responses. Studies on such chemical systems provide understanding on biological systems and can also be extended to the development of novel functional materials.

A microphysiological model of the bronchial airways reveals the interplay of mechanical and biochemical signals in bronchospasm

In asthma, airway smooth muscle (ASM) contraction and the subsequent decrease in airflow involve a poorly understood set of mechanical and biochemical events. Organ-level and molecular-scale models of the airway are frequently based on purely mechanical or biochemical considerations and do not account for physiological mechanochemical couplings. Here, we present a microphysiological model of the airway that allows for the quantitative analysis of the interactions between mechanical and biochemical signals triggered by compressive stress on epithelial cells. We show that a mechanical stimulus mimicking a bronchospastic challenge triggers the marked contraction and delayed relaxation of ASM, and that this is mediated by the discordant expression of cyclooxygenase genes in epithelial cells and regulated by the mechanosensor and transcriptional co-activator YAP (Yes-associated protein). A mathematical model of the intercellular feedback interactions recapitulates aspects of obstructive disease of the airways, including pathognomonic features of severe, difficult-to-treat asthma. The microphysiological model could be used to investigate the mechanisms of asthma pathogenesis and to develop therapeutic strategies that disrupt the positive feedback loop that leads to persistent airway constriction.

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision making in biological systems. We achieve this by extending previous studies that resorted to simple bifurcation normal forms, although in the present case we focus primarily on the issue of the system's sensitivity to initial conditions in the presence of two different noise distributions, Gaussian and Lévy. In addition, we also assess the impact of two-way sweeping at different rates through the critical region of a canonical Pitchfork bifurcation with a constant external asymmetry. The parallel with decision making in biocircuits is performed on this simple system since it is equivalent in its available states and dynamics to more complex genetic circuits published previously. Overall we verify that rate-dependent effects, previously reported as being important features of bifurcating systems, are specific to particular initial conditions. Processing of each starting state, which for the normal form underlying this study is akin to a classification task, is affected by the balance between sweeping speed through critical regions and the type of fluctuations added. For the heavy-tailed noise, two-way dynamic bifurcations are more efficient in processing the external signals, here understood to be jointly represented by the critical parameter profile and the external asymmetry amplitude, when compared to the system relying on escape dynamics. This is particular to the case when the system starts at an attractor not favored by the asymmetry and, in conjunction, when the sweeping amplitude is large.

Self-sustaining positive feedback loops in discrete and continuous systems

We consider a dynamic framework frequently used to model gene regulatory and signal transduction networks: monotonic ODEs that are composed of Hill functions. We derive conditions under which activity or inactivity in one system variable induces and sustains activity or inactivity in another. Cycles of such influences correspond to positive feedback loops that are self-sustaining and control-robust, in the sense that these feedback loops "trap" the system in a region of state space from which it cannot exit, even if the other system variables are externally controlled. To demonstrate the utility of this result, we consider prototypical examples of bistability and hysteresis in gene regulatory networks, and analyze a T-cell signal transduction ODE model from the literature.

Dynamics and control of the ERK signaling pathway: Sensitivity, bistability, and oscillations

Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.

Combining a Toggle Switch and a Repressilator within the AC-DC Circuit Generates Distinct Dynamical Behaviors

Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.

A compartmentalized signaling network mediates crossover control in meiosis

During meiosis, each pair of homologous chromosomes typically undergoes at least one crossover (crossover assurance), but these exchanges are strictly limited in number and widely spaced along chromosomes (crossover interference). The molecular basis for this chromosome-wide regulation remains mysterious. A family of meiotic RING finger proteins has been implicated in crossover regulation across eukaryotes. Caenorhabditis elegans expresses four such proteins, of which one (ZHP-3) is known to be required for crossovers. Here we investigate the functions of ZHP-1, ZHP-2, and ZHP-4. We find that all four ZHP proteins, like their homologs in other species, localize to the synaptonemal complex, an unusual, liquid crystalline compartment that assembles between paired homologs. Together they promote accumulation of pro-crossover factors, including ZHP-3 and ZHP-4, at a single recombination intermediate, thereby patterning exchanges along paired chromosomes. These proteins also act at the top of a hierarchical, symmetry-breaking process that enables crossovers to direct accurate chromosome segregation.

A compartmentalized signaling network mediates crossover control in meiosis

During meiosis, each pair of homologous chromosomes typically undergoes at least one crossover (crossover assurance), but these exchanges are strictly limited in number and widely spaced along chromosomes (crossover interference). The molecular basis for this chromosome-wide regulation remains mysterious. A family of meiotic RING finger proteins has been implicated in crossover regulation across eukaryotes. Caenorhabditis elegans expresses four such proteins, of which one (ZHP-3) is known to be required for crossovers. Here we investigate the functions of ZHP-1, ZHP-2, and ZHP-4. We find that all four ZHP proteins, like their homologs in other species, localize to the synaptonemal complex, an unusual, liquid crystalline compartment that assembles between paired homologs. Together they promote accumulation of pro-crossover factors, including ZHP-3 and ZHP-4, at a single recombination intermediate, thereby patterning exchanges along paired chromosomes. These proteins also act at the top of a hierarchical, symmetry-breaking process that enables crossovers to direct accurate chromosome segregation.

Parallel arrangements of positive feedback loops limit cell-to-cell variability in differentiation

Cellular differentiations are often regulated by bistable switches resulting from specific arrangements of multiple positive feedback loops (PFL) fused to one another. Although bistability generates digital responses at the cellular level, stochasticity in chemical reactions causes population heterogeneity in terms of its differentiated states. We hypothesized that the specific arrangements of PFLs may have evolved to minimize the cellular heterogeneity in differentiation. In order to test this we investigated variability in cellular differentiation controlled either by parallel or serial arrangements of multiple PFLs having similar average properties under extrinsic and intrinsic noises. We find that motifs with PFLs fused in parallel to one another around a central regulator are less susceptible to noise as compared to the motifs with PFLs arranged serially. Our calculations suggest that the increased resistance to noise in parallel motifs originate from the less sensitivity of bifurcation points to the extrinsic noise. Whereas estimation of mean residence times indicate that stable branches of bifurcations are robust to intrinsic noise in parallel motifs as compared to serial motifs. Model conclusions are consistent both in AND- and OR-gate input signal configurations and also with two different modeling strategies. Our investigations provide some insight into recent findings that differentiation of preadipocyte to mature adipocyte is controlled by network of parallel PFLs.

Operating principles of tristable circuits regulating cellular differentiation

Many cell-fate decisions during embryonic development are governed by a motif comprised of two transcription factors (TFs) A and B that mutually inhibit each other and may self-activate. This motif, called as a self-activating toggle switch (SATS), can typically have three stable states (phenotypes)-two corresponding to differentiated cell fates, each of which has a much higher level of one TF than the other-[Formula: see text] or [Formula: see text]-and the third state corresponding to an 'undecided' stem-like state with similar levels of both A and B-[Formula: see text]. Furthermore, two or more SATSes can be coupled together in various topologies in different contexts, thereby affecting the coordination between multiple cellular decisions. However, two questions remain largely unanswered: (a) what governs the co-existence and relative stability of these three stable states? (b) What orchestrates the decision-making of coupled SATSes? Here, we first demonstrate that the co-existence and relative stability of the three stable states in an individual SATS can be governed by the relative strength of self-activation, external signals activating and/or inhibiting A and B, and mutual degradation between A and B. Simultaneously, we investigate the effects of these factors on the decision-making of two coupled SATSes. Our results offer novel understanding into the operating principles of individual and coupled tristable self-activating toggle switches (SATSes) regulating cellular differentiation and can yield insights into synthesizing three-way genetic circuits and understanding of cellular reprogramming.

Pulse Generation in the Quorum Machinery of Pseudomonas aeruginosa

Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quorum sensing (QS) to coordinate gene expression, including for virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involve multiple control components, notably the las, rhl and pqs systems. In this paper, we examine the las system and, in particular, the repressive interaction of rsaL, an embedded small regulative protein, employing recent biochemical information to aid model construction. Using analytic methods, we show how this feature can give rise to excitable pulse generation in this subsystem with important downstream consequences for rhamnolipid production. We adopt a symmetric competitive inhibition to capture the binding in the lasI–rsaL intergenic region and show our results are not dependent on the exact choice of this functional form. Furthermore, we examine the coupling of lasR to the rhl system, the impact of the predicted capacity for pulse generation and the biophysical consequences of this behaviour. We hypothesize that the interaction between the las and rhl systems may provide a quorum memory to enable cells to trigger rhamnolipid production only when they are at the edge of an established aggregation.

Core-oscillator model of Caulobacter crescentus

The gram-negative bacterium Caulobacter crescentus is a powerful model organism for studies of bacterial cell cycle regulation. Although the major regulators and their connections in Caulobacter have been identified, it still is a challenge to properly understand the dynamics of its circuitry which accounts for both cell cycle progression and arrest. We show that the key decision module in Caulobacter is built from a limit cycle oscillator which controls the DNA replication program. The effect of an induced cell cycle arrest is demonstrated to be a key feature to classify the underlying dynamics.

Realization of tristability in a multiplicatively coupled dual-loop genetic network

Multistability is a crucial recurring theme in cell signaling. Multistability is attributed to the presence of positive feedback loops, but the general condition and essential mechanism for realizing multistability remain unclear. Here, we build a generic circuit model comprising two transcription factors and a microRNA, representing a kind of core architecture in gene regulatory networks. The circuit can be decomposed into two positive feedback loops (PFLs) or one PFL and one negative feedback loop (NFL), which are multiplicatively coupled. Bifurcation analyses of the model reveal that the circuit can achieve tristability through four kinds of bifurcation scenarios when parameter values are varied in a wide range. We formulate the general requirement for tristability in terms of logarithmic gain of the circuit. The parameter ranges for tristability and possible transition routes among steady states are determined by the combination of gain features of individual feedback loops. Coupling two PFLs with bistability or one NFL with a bistable PFL is most likely to generate tristability, but the underlying mechanisms are largely different. We also interpret published results and make testable predictions. This work sheds new light on interlinking feedback loops to realize tristability. The proposed theoretical framework can be of wide applicability.

Dynamic Modeling and Analysis of the Cross-Talk between Insulin/AKT and MAPK/ERK Signaling Pathways

Feedback loops play a key role in the regulation of the complex interactions in signal transduction networks. By studying the network of interactions among the biomolecules present in signaling pathways at the systems level, it is possible to understand how the biological functions are regulated and how the diseases emerge from their deregulations. This paper identifies the key feedback loops involved in the cross-talk among the insulin-AKT and MAPK/ERK signaling pathways. We developed a mathematical model that can be used to study the steady-state and dynamic behavior of the interactions among these two important signaling pathways. Modeling analysis and simulation case studies identify the key interaction parameters and the feedback loops that determine the normal and disease phenotypes.

The role of mRNA and protein stability in the function of coupled positive and negative feedback systems in eukaryotic cells

Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Here, we examine the behavior of a coupled feedback system, the Negative Autoregulated Frustrated bistability motif (NAF). This motif is a combination of two previously explored motifs, the frustrated bistability motif (FBM) and the negative auto regulation motif (NAR), which both can produce oscillations. The NAF motif was previously suggested to govern long term memory formation in animals, and was used as a synthetic oscillator in bacteria. We build a mathematical model to analyze the dynamics of the NAF motif. We show analytically that the NAF motif requires an asymmetry in the strengths of activation and repression links in order to produce oscillations. We show that the effect of time delays in eukaryotic cells, originating from mRNA export and protein import, are negligible in this system. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes.

Coupled positive and negative feedbacks produce diverse gene expression patterns in colonies

Formation of patterns is a common feature in the development of multicellular organism as well as of microbial communities. To investigate the formation of gene expression patterns in colonies, we build a mathematical model of two-dimensional colony growth, where cells carry a coupled positive-and-negative-feedback circuit. We demonstrate that the model can produce sectored, target (concentric), uniform, and scattered expression patterns of regulators, depending on gene expression dynamics and nutrient diffusion. We reconstructed the same regulatory structure in Escherichia coli cells and found gene expression patterns on the surface of colonies similar to the ones produced by the computer simulations. By comparing computer simulations and experimental results, we observed that very simple rules of gene expression can yield a spectrum of well-defined patterns in a growing colony. Our results suggest that variations of the protein content among cells lead to a high level of heterogeneity in colonies.

Importance Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

Mathematical modelling suggests a differential impact of β-transducin repeat-containing protein paralogues on Wnt/β-catenin signalling dynamics

The Wnt/β-catenin signalling pathway is involved in the regulation of a multitude of cellular processes by controlling the concentration of the transcriptional regulator β-catenin. Proteasomal degradation of β-catenin is mediated by two β-transducin repeat-containing protein paralogues, homologous to Slimb protein (HOS) and F-box/WD repeat-containing protein 1A (FWD1), which are functionally interchangeable and thereby considered to function redundantly in the pathway. HOS and FWD1 are both regulated by Wnt/β-catenin signalling, albeit in opposite directions, thus establishing interlocked negative and positive feedback loops. The functional relevance of the opposite regulation of HOS and FWD1 by Wnt/β-catenin signalling in conjunction with their redundant activities in proteasomal degradation of β-catenin remains unresolved. Using a detailed ordinary differential equation model, we investigated the specific influence of each individual feedback mechanism and their combination on Wnt/β-catenin signal transduction under wild-type and cancerous conditions. We found that, under wild-type conditions, the signalling dynamics are predominantly affected by the HOS feedback as a result of a higher concentration of HOS than FWD1. Transcriptional up-regulation of FWD1 by other signalling pathways reduced the impact of the HOS feedback. The opposite regulation of HOS and FWD1 expression by Wnt/β-catenin signalling allows the FWD1 feedback to be employed as a compensation mechanism against aberrant pathway activation as a result of a reduced HOS concentration. By contrast, the FWD1 feedback provides no protection against aberrant activation in adenomatous polyposis coli protein mutant cancer cells.

Unraveling the regulatory connections between two controllers of breast cancer cell fate

Estrogen receptor alpha (ERα) expression is critical for breast cancer classification, high ERα expression being associated with better prognosis. ERα levels strongly correlate with that of GATA binding protein 3 (GATA3), a major regulator of ERα expression. However, the mechanistic details of ERα-GATA3 regulation remain incompletely understood. Here we combine mathematical modeling with perturbation experiments to unravel the nature of regulatory connections in the ERα-GATA3 network. Through cell population-average, single-cell and single-nucleus measurements, we show that the cross-regulation between ERα and GATA3 amounts to overall negative feedback. Further, mathematical modeling reveals that GATA3 positively regulates its own expression and that ERα autoregulation is most likely absent. Lastly, we show that the two cross-regulatory connections in the ERα-GATA3 negative feedback network decrease the noise in ERα or GATA3 expression. This may ensure robust cell fate maintenance in the face of intracellular and environmental fluctuations, contributing to tissue homeostasis in normal conditions, but also to the maintenance of pathogenic states during cancer progression.

Reliable binary cell-fate decisions based on oscillations

Biological systems have often to perform binary decisions under highly dynamic and noisy environments, such as during cell-fate determination. These decisions can be implemented by two main bifurcation mechanisms based on the transitions from either monostability or oscillation to bistability. We compare these two mechanisms by using stochastic models with time-varying fields and by establishing asymptotic formulas for the choice probabilities. Different scaling laws for decision sensitivity with respect to noise strength and signal timescale are obtained, supporting a role for oscillatory dynamics in performing noise-robust and temporally tunable binary decision-making. This result provides a rationale for recent experimental evidences showing that oscillatory expression of proteins often precedes binary cell-fate decisions.

Methylation kinetics and CpG-island methylator phenotype status in colorectal cancer cell lines

Background

Hypermethylation of CpG islands is thought to contribute to carcinogenesis through the inactivation of tumor suppressor genes. Tumor cells with relatively high levels of CpG island methylation are considered CpG island methylator phenotypes (CIMP). The mechanisms that are responsible for regulating the activity of de novo methylation are not well understood.

Results

We quantify and compare de novo methylation kinetics in CIMP and non-CIMP colon cancer cell lines in the context of different loci, following 5-aza-2’deoxycytidine (5-AZA)-mediated de-methylation of cells. In non-CIMP cells, a relatively fast rate of re-methylation is observed that starts with a certain time delay after cessation of 5-AZA treatment. CIMP cells, on the other hand, start re-methylation without a time delay but at a significantly slower rate. A mathematical model can account for these counter-intuitive results by assuming negative feedback regulation of de novo methylation activity and by further assuming that this regulation is corrupted in CIMP cells. This model further suggests that when methylation levels have grown back to physiological levels, de novo methylation activity ceases in non-CIMP cells, while it continues at a constant low level in CIMP cells.

Conclusions

We propose that the faster rate of re-methylation observed in non-CIMP compared to CIMP cells in our study could be a consequence of feedback-mediated regulation of DNA methyl transferase activity. Testing this hypothesis will involve the search for specific feedback regulatory mechanisms involved in the activation of de novo methylation.

Reviewers’ report

This article was reviewed by Georg Luebeck, Tomasz Lipniacki, and Anna Marciniak-Czochra

Tuning the dials of Synthetic Biology

Synthetic Biology is the ‘Engineering of Biology’ – it aims to use a forward-engineering design cycle based on specifications, modelling, analysis, experimental implementation, testing and validation to modify natural or design new, synthetic biology systems so that they behave in a predictable fashion. Motivated by the need for truly plug-and-play synthetic biological components, we present a comprehensive review of ways in which the various parts of a biological system can be modified systematically. In particular, we review the list of ‘dials’ that are available to the designer and discuss how they can be modelled, tuned and implemented. The dials are categorized according to whether they operate at the global, transcriptional, translational or post-translational level and the resolution that they operate at. We end this review with a discussion on the relative advantages and disadvantages of some dials over others.

Robust stability analysis of genetic regulatory network with time delays

The robust asymptotic stability problem of genetic regulatory networks with time delays is investigated by Lyapunov functional approach and linear matrix inequality techniques (LMIs). Stability criteria for the delayed genetic regulatory networks are expressed as a set of LMIs, yielding much less conservative analytic results. New criteria with reduced conservatism are obtained and they involve less matrix parameters than the existing ones. Finally, three numerical examples are presented to illustrate effectiveness and less conservative results.

A bistable hysteretic switch in an activator-repressor regulated restriction-modification system

Restriction–modification (RM) systems are extremely widespread among bacteria and archaea, and are often specified by mobile genetic elements. In type II RM systems, where the restriction endonuclease (REase) and protective DNA methyltransferase (MTase) are separate proteins, a major regulatory challenge is delaying expression of the REase relative to the MTase after RM genes enter a new host cell. Basic understanding of this regulation is available for few RM systems, and detailed understanding for none. The PvuII RM system is one of a large subset in which the central regulatory role is played by an activator–repressor protein (called C, for controller). REase expression depends upon activation by C, whereas expression of the MTase does not. Thus delay of REase expression depends on the rate of C-protein accumulation. This is a nonlinear process, as C also activates transcription of its own gene. Mathematical modeling of the PvuII system led to the unexpected predictions of responsiveness to a factor not previously studied in RM system control—gene copy number—and of a hysteretic response. In this study, those predictions have been confirmed experimentally. The results may apply to many other C-regulated RM systems, and help explain their ability to spread so widely.

Minimal models for cell-cycle control based on competitive inhibition and multisite phosphorylations of Cdk substrates

The eukaryotic cell cycle is characterized by alternating oscillations in the activities of cyclin-dependent kinase (Cdk) and the anaphase-promoting complex (APC). Successful completion of the cell cycle is dependent on the precise, temporally ordered appearance of these activities. A modest level of Cdk activity is sufficient to initiate DNA replication, but mitosis and APC activation require an elevated Cdk activity. In present-day eukaryotes, this temporal order is provided by a complex network of regulatory proteins that control both Cdk and APC activities via sharp thresholds, bistability, and time delays. Using simple computational models, we show here that these dynamical features of cell-cycle organization could emerge in a control system driven by a single Cdk/cyclin complex and APC wired in a negative-feedback loop. We show that ordered phosphorylation of cellular proteins could be explained by multisite phosphorylation/dephosphorylation and competition of substrates for interconverting kinase (Cdk) and phosphatase. In addition, the competition of APC substrates for ubiquitylation can create and maintain sustained oscillations in cyclin levels. We propose a sequence of models that gets closer and closer to a realistic model of cell-cycle control in yeast. Since these models lack the elaborate control mechanisms characteristic of modern eukaryotes, they suggest that bistability and time delay may have characterized eukaryotic cell divisions before the current cell-cycle control network evolved in all its complexity.

Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.

Coupling between feedback loops in autoregulatory networks affects bistability range, open-loop gain and switching times

Biochemical regulatory networks governing diverse cellular processes such as stress-response, differentiation and cell cycle often contain coupled feedback loops. We aim at understanding how features of feedback architecture, such as the number of loops, the sign of the loops and the type of their coupling, affect network dynamical performance. Specifically, we investigate how bistability range, maximum open-loop gain and switching times of a network with transcriptional positive feedback are affected by additive or multiplicative coupling with another positive- or negative-feedback loop. We show that a network's bistability range is positively correlated with its maximum open-loop gain and that both quantities depend on the sign of the feedback loops and the type of feedback coupling. Moreover, we find that the addition of positive feedback could decrease the bistability range if we control the basal level in the signal-response curves of the two systems. Furthermore, the addition of negative feedback has the capacity to increase the bistability range if its dissociation constant is much lower than that of the positive feedback. We also find that the addition of a positive feedback to a bistable network increases the robustness of its bistability range, whereas the addition of a negative feedback decreases it. Finally, we show that the switching time for a transition from a high to a low steady state increases with the effective fold change in gene regulation. In summary, we show that the effect of coupled feedback loops on the bistability range and switching times depends on the underlying mechanistic details.

Dynamical principles of cell-cycle arrest: reversible, irreversible, and mixed strategies

Living cells often alternate between proliferating and nonproliferating states as part of individual or collective strategies to adapt to complex and changing environments. To this aim, they have evolved a biochemical regulatory network enabling them to switch between cell-division cycles (i.e., oscillatory state) and cell-cycle arrests (i.e., steady state) in response to extracellular cues. This can be achieved by means of a variety of bifurcation mechanisms that potentially give rise to qualitatively distinct cell-cycle arrest properties. In this paper, we study the dynamics of a minimal biochemical network model in which a cell-division oscillator and a differentiation switch mutually antagonize. We identify the existence of three biologically plausible bifurcation scenarios organized around a codimension-four swallowtail-homoclinic singularity. As a result, the model exhibits a broad repertoire of cell-cycle arrest properties in terms of reversibility of these arrests, tunability of interdivision time, and ability to track time-varying signals. This dynamic versatility would explain the diversity of cell-cycle arrest strategies developed in different living species and functional contexts.