Robust, tunable biological oscillations from interlinked positive and negative feedback loops

Fundamental Trade-Offs in the Robustness of Biological Systems with Feedback Regulation

Natural biological systems use feedback regulation to effectively respond and adapt to their changing environment. Even though in engineered systems we understand how accurate feedback can be depending on the electronic or mechanical parts that it is implemented with, we largely lack a similar theoretical framework to study feedback regulation in biological systems. Specifically, it is not fully understood or quantified how accurate or robust the implementation of biological feedback actually is. In this paper, we study the sensitivity of biological feedback to variations in biochemical parameters using five example circuits: positive autoregulation, negative autoregulation, double-positive feedback, positive-negative feedback, and double-negative feedback (the toggle switch). We find that some of these examples of biological feedback are subjected to fundamental performance trade-offs, and we propose multi-objective optimization as a framework to study their properties. The impact of this work is to improve robust circuit design for synthetic biology and to improve our understanding of feedback for systems biology.

Diet induced insulin resistance is due to induction of PTEN expression

Insulin resistance is a condition associated with obesity, type 2 diabetes(T2D), hyperinsulinemia, hyperglycemia and defined by reduced sensitivity to insulin signaling. Molecular causes and early signaling events underlying insulin resistance are not well understood. Here we show that insulin activation of PI3K/AKT/mTOR signaling in insulin target tissues, causes mTORC1 induction of PTEN translation, a negative regulator of PI3K signaling. We hypothesized that insulin resistance is due to insulin dependent induction of PTEN that prevents further increases in PI3K signaling. In a diet induced animal model of obesity and insulin resistance, we show that PTEN levels are increased in fat, muscle, and liver. Hyperinsulinemia and PTEN induction are followed by hyperglycemia, severe glucose intolerance, and hepatic steatosis. In response to chronic hyperinsulinemia, PTEN remains increased, while AKT activity is induced transiently before settling down to a PTEN-high and AKT-low state in the tissues, predicted by computational modeling of the PTEN-AKT feedback loop. Treatment with PTEN and mTORC1 inhibitors prevent and reverse the effect of PTEN induction, rescue insulin resistance and increase PI3K/AKT signaling. Thus, we show that PTEN induction by increased insulin levels elevates feedback inhibition of the pathway causing insulin resistance, its associated phenotypes, and is a potential therapeutic target.

DeltaC and DeltaD ligands play different roles in the segmentation clock dynamics

The vertebrate segmentation clock drives periodic somite segmentation during embryonic development. Her1 and Her7 clock proteins generate oscillatory expression of their own genes as well as that of deltaC in zebrafish. In turn, DeltaC and DeltaD ligands activate Notch signaling, which then activates transcription of clock genes in neighboring cells. While DeltaC and DeltaD proteins form homo- and heterodimers, only DeltaC-containing oscillatory dimers were expected to be functional. To investigate the contributions of DeltaC and DeltaD proteins on the transcription of her1 and her7 segmentation clock genes, we counted their transcripts by performing single molecule fluorescent in situ hybridization imaging in different genetic backgrounds of zebrafish embryos. Surprisingly, we found that DeltaD homodimers are also functional. We further found that Notch signaling promotes transcription of both deltaC and deltaD genes, thereby creating a previously unnoticed positive feedback loop. Our computational model highlighted the intriguing differential roles of DeltaC and DeltaD dimers on the clock synchronization and transcript numbers, respectively. We anticipate that a mechanistic understanding of the Notch signaling pathway will not only shed light on the mechanism driving robust somite segmentation but also inspire similar quantitative studies in other tissues and organs.

Co-evolutionary control of a class of coupled mixed-feedback systems

Oscillatory behavior is ubiquitous in many natural and engineered systems, often emerging through self-regulating mechanisms. In this paper, we address the challenge of stabilizing a desired oscillatory pattern in a networked system where neither the internal dynamics nor the interconnections can be changed. To achieve this, we propose two distinct control strategies. The first requires the full knowledge of the system generating the desired oscillatory pattern, while the second only needs local error information. In addition, the controllers are implemented as co-evolutionary, or adaptive, rules of some edges in an extended plant-controller network. We validate our approach in several insightful scenarios, including synchronization and systems with time-varying network structures.

Thermodynamic for biological development: A hypothesis

This paper proposes a thermodynamic model of biological development. Several key thoughts are presented: 1) in view of thermodynamics, biological development processes irreversibly; 2) in view of thermodynamics and molecular biology, positive autoregulation, or self-regulation, of transcription factors is the only way to ensure irreversibility of a thermodynamic process of biology; 3) change in the autoregulation of transcription factors can irreversibly result in alterations in the physiological state) a physiological state is a system of signaling networks; 5) a cell and its physiological state can be identified by the pattern of its transcription factors. 6) from points aforementioned, we can analyze some thermodynamic properties of biological development by knowledge of molecular biology and biochemistry. The possible mechanisms of plant vernalization are also proposed.

Mechanistic origins of temperature scaling in the early embryonic cell cycle

Temperature profoundly impacts organismal physiology and ecological dynamics, particularly affecting ectothermic species and making them especially vulnerable to climate changes. Although complex physiological processes usually involve dozens of enzymes, empirically it is found that the rates of these processes often obey the Arrhenius equation, which was originally proposed for individual chemical reactions. Here we have examined the temperature scaling of the early embryonic cell cycle, with the goal of understanding why the Arrhenius equation approximately holds and why it breaks down at temperature extremes. Using experimental data from Xenopus laevis, Xenopus tropicalis, and Danio rerio, plus published data from Caenorhabditis elegans, Caenorhabditis briggsae, and Drosophila melanogaster, we find that the apparent activation energies (E a values) for the early embryonic cell cycle for diverse ectotherms are all similar, 75 ± 7 kJ/mol (mean ± std.dev., n = 6), which corresponds to aQ 10 value at 20°C of 2.8 ± 0.2 (mean ± std.dev., n = 6). Using computational models, we find that the approximate Arrhenius scaling and the deviations from it at high and low temperatures can be accounted for by biphasic temperature scaling in critical individual components of the cell cycle oscillator circuit, by imbalances in theE a values for different partially rate-determining enzymes, or by a combination of both. Experimental studies of cycling Xenopus extracts indicate that both of these mechanisms contribute to the general scaling of temperature, and in vitro studies of individual cell cycle regulators confirm that there is in fact a substantial imbalance in theirE a values. These findings provide mechanistic insights into the dynamic interplay between temperature and complex biochemical processes, and into why biological systems fail at extreme temperatures.

Modeling ncRNA-Mediated Circuits in Cell Fate Decision: From Systems Biology to Synthetic Biology

Noncoding RNAs (ncRNAs) play critical roles in essential cell fate decisions. However, the exact molecular mechanisms underlying ncRNA-mediated bistable switches remain elusive and controversial. In recent years, systematic mathematical and quantitative experimental analyses have made significant contributions to elucidating the molecular mechanisms of controlling ncRNA-mediated cell fate decision processes. In this chapter, we review and summarize the general framework of mathematical modeling of ncRNA in a pedagogical way and the application of this general framework to real biological processes. We discuss the emerging properties resulting from the reciprocal regulation between mRNA, miRNA, and competing endogenous mRNA (ceRNA). We also explore the efforts within the synthetic biology approach to understand the fundamental design principles underlying cell fate decisions. Both the positive feedback loops between ncRNAs and transcription factors and the emerging properties from the miRNA-mRNA reciprocal regulation enable bistable switches to direct cell fate decisions.

Locally repulsive coupling-induced tunable oscillations

The precise amplitude and period of neuronal oscillations are crucial for the functioning of neuronal networks. We propose a chain model featuring a repulsive coupling at the first node, followed by attractive couplings at subsequent nodes. This model allows for the simultaneous regulation of both quantities. The repulsive coupling at the first neuron enables it to act as a pacemaker, generating oscillations whose amplitude and period are correlated with the coupling strength. At the same time, attractive couplings help transmit these oscillations along the chain, leading to collective oscillations of varying scales. Our study demonstrates that a three-node chain with locally repulsive coupling forms the fundamental structure for generating tunable oscillations. By using a simplified neuron model, we investigate how locally repulsive coupling affects the amplitude and period of oscillations and find results that align with numerical observations. These findings indicate that repulsive couplings play a crucial role in regulating oscillatory patterns within neuronal networks.

Emergent robust oscillatory dynamics in the interlocked feedback-feedforward loops

One of the challenges that beset modelling complex biological networks is to relate networks to function to dynamics. A further challenge is deciphering the cellular function and dynamics that can change drastically when the network edge is tinkered with by adding or removing it. To illustrate this, the authors took a well-studied three-variable Goodwin oscillatory motif with only a negative feedback loop. To this motif, an edge was added that results in an emergent structure consisting of new feedforward and feedback loops while retaining Goodwin's original negative feedback loop. To relate emergent structure to oscillatory dynamics, the authors took all the combinations of edge signs in the interlocked motif. Bifurcation analysis reveals that all the structural combinations can be grouped into two categories based on their unique dynamics. These two groups also exhibit unique amplitude-frequency (amp-freq) plots. These two categories are attributed to the emergence of interlocked motifs with specific edge signs. To support the ideas, a well-studied plant circadian model of Arabidopsis thaliana was taken to illustrate the importance of interlocked motifs in fine-tuning amplitude and frequency in circadian oscillators. The authors briefly discuss its implications for central oscillators' adaptation to different environmental cues.

Plausible, robust biological oscillations through allelic buffering

Biological oscillators can specify time- and dose-dependent functions via dedicated control of their oscillatory dynamics. However, how biological oscillators, which recurrently activate noisy biochemical processes, achieve robust oscillations remains unclear. Here, we characterize the long-term oscillations of p53 and its negative feedback regulator Mdm2 in single cells after DNA damage. Whereas p53 oscillates regularly, Mdm2 from a single MDM2 allele exhibits random unresponsiveness to ∼9% of p53 pulses. Using allelic-specific imaging of MDM2 activity, we show that MDM2 alleles buffer each other to maintain p53 pulse amplitude. Removal of MDM2 allelic buffering cripples the robustness of p53 amplitude, thereby elevating p21 levels and cell-cycle arrest. In silico simulations support that allelic buffering enhances the robustness of biological oscillators and broadens their plausible biochemical space. Our findings show how allelic buffering ensures robust p53 oscillations, highlighting the potential importance of allelic buffering for the emergence of robust biological oscillators during evolution. A record of this paper's transparent peer review process is included in the supplemental information.

Feedback driven autonomous cycles of assembly and disassembly from minimal building blocks

The construction of complex systems by simple chemicals that can display emergent network dynamics might contribute to our understanding of complex behavior from simple organic reactions. Here we design single amino acid/dipeptide-based systems that exhibit multiple periodic changes of (dis)assembly under non-equilibrium conditions in closed system, importantly in the absence of evolved biocatalysts. The two-component based building block exploits pH driven non-covalent assembly and time-delayed accelerated catalysis from self-assembled state to install orthogonal feedback loops with a single batch of reactants. Mathematical modelling of the reaction network establishes that the oscillations are transient for this network structure and helps to predict the relative contribution of the feedback loop to the ability of the system to exhibit such transient oscillation. Such autonomous systems with purely synthetic molecules are the starting point that can enable the design of active materials with emergent properties.

YAP activation is robust to dilution

The concentration of many transcription factors exhibits high cell-to-cell variability due to differences in synthesis, degradation, and cell size. Whether the functions of these factors are robust to fluctuations in concentration, and how this may be achieved, is poorly understood. Across two independent panels of breast cancer cells, we show that the average whole cell concentration of YAP decreases as a function of cell area. However, the nuclear concentration distribution remains constant across cells grouped by size, across a 4-8 fold size range, implying unperturbed nuclear translocation despite the falling cell wide concentration. Both the whole cell and nuclear concentration was higher in cells with more DNA and CycA/PCNA expression suggesting periodic synthesis of YAP across the cell cycle offsets dilution due to cell growth and/or cell spreading. The cell area - YAP scaling relationship extended to melanoma and RPE cells. Integrative analysis of imaging and phospho-proteomic data showed the average nuclear YAP concentration across cell lines was predicted by differences in RAS/MAPK signalling, focal adhesion maturation, and nuclear transport processes. Validating the idea that RAS/MAPK and cell cycle regulate YAP translocation, chemical inhibition of MEK or CDK4/6 increased the average nuclear YAP concentration. Together, this study provides an example case, where cytoplasmic dilution of a protein, for example through cell growth, does not limit a cognate cellular function. Here, that same proteins translocation into the nucleus.

Competitive interactions shape brain dynamics and computation across species

Adaptive cognition relies on cooperation across anatomically distributed brain circuits. However, specialised neural systems are also in constant competition for limited processing resources. How does the brain's network architecture enable it to balance these cooperative and competitive tendencies? Here we use computational whole-brain modelling to examine the dynamical and computational relevance of cooperative and competitive interactions in the mammalian connectome. Across human, macaque, and mouse we show that the architecture of the models that most faithfully reproduce brain activity, consistently combines modular cooperative interactions with diffuse, long-range competitive interactions. The model with competitive interactions consistently outperforms the cooperative-only model, with excellent fit to both spatial and dynamical properties of the living brain, which were not explicitly optimised but rather emerge spontaneously. Competitive interactions in the effective connectivity produce greater levels of synergistic information and local-global hierarchy, and lead to superior computational capacity when used for neuromorphic computing. Altogether, this work provides a mechanistic link between network architecture, dynamical properties, and computation in the mammalian brain.

Physical extraction of antigen and information

To respond and adapt, cells use surface receptors to sense environmental cues. While biochemical signal processing inside the cell is studied in depth, less is known about how physical processes during cell-cell contact impact signal acquisition. New experiments found that fast-evolving immune B cells in germinal centers (GCs) apply force to acquire antigen clusters prior to internalization, suggesting adaptive benefits of physical information extraction. We present a theory of stochastic antigen transfer and show that maximizing information gain via physical extraction can explain the dramatic phenotypic transition from naive to GC B cells-attenuated receptor signaling, enhanced force usage, and decentralized contact architecture. Our model suggests that binding-lifetime measurement and physical extraction serve as complementary modes of antigen recognition, greatly extending the dynamic range of affinity discrimination when combined. This physical-information framework further predicts that the optimal size of receptor clusters decreases as affinity improves, rationalizing the use of a multifocal synaptic pattern seen in GC B cells. By linking extraction dynamics to selection fidelity via discriminatory performance, we propose that cells may physically enhance information acquisition to sustain adaptive evolution.

Study of the Synchronization and Transmission of Intracellular Signaling Oscillations in Cells Using Bispectral Analysis

The oscillation synchronization analysis in biological systems will expand our knowledge about the response of living systems to changes in environmental conditions. This knowledge can be used in medicine (diagnosis, therapy, monitoring) and agriculture (increasing productivity, resistance to adverse effects). Currently, the search is underway for an informative, accurate and sensitive method for analyzing the synchronization of oscillatory processes in cell biology. It is especially pronounced in analyzing the concentration oscillations of intracellular signaling molecules in electrically nonexcitable cells. The bispectral analysis method could be applied to assess the characteristics of synchronized oscillations of intracellular mediators. We chose endothelial cells from mouse microvessels as model cells. Concentrations of well-studied calcium and nitric oxide (NO) were selected for study in control conditions and well-described stress: heating to 40 °C and hyperglycemia. The bispectral analysis allows us to accurately evaluate the proportion of synchronized cells, their synchronization degree, and the amplitude and frequency of synchronized calcium and NO oscillations. Heating to 40 °C increased cell synchronization for calcium but decreased for NO oscillations. Hyperglycemia abolished this effect. Heating to 40 °C changed the frequencies and increased the amplitudes of synchronized oscillations of calcium concentration and the NO synthesis rate. The first part of this paper describes the principles of the bispectral analysis method and equations and modifications of the method we propose. In the second part of this paper, specific examples of the application of bispectral analysis to assess the synchronization of living cells in vitro are presented. The discussion compares the capabilities of bispectral analysis with other analytical methods in this field.

Arp2/3-dependent endocytosis ensures Cdc42 oscillations by removing Pak1-mediated negative feedback

The GTPase Cdc42 regulates polarized growth in most eukaryotes. In the bipolar yeast Schizosaccharomyces pombe, Cdc42 activation cycles periodically at sites of polarized growth. These periodic cycles are caused by alternating positive feedback and time-delayed negative feedback loops. At each polarized end, negative feedback is established when active Cdc42 recruits the Pak1 kinase to prevent further Cdc42 activation. It is unclear how Cdc42 activation returns to each end after Pak1-dependent negative feedback. We find that disrupting branched actin-mediated endocytosis disables Cdc42 reactivation at the cell ends. Using experimental and mathematical approaches, we show that endocytosis-dependent Pak1 removal from the cell ends allows the Cdc42 activator Scd1 to return to that end to enable reactivation of Cdc42. Moreover, we show that Pak1 elicits its own removal via activation of endocytosis. These findings provide a deeper insight into the self-organization of Cdc42 regulation and reveal previously unknown feedback with endocytosis in the establishment of cell polarity.

Strong delayed negative feedback

In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit.

Establishing a conceptual framework for holistic cell states and state transitions

Cell states were traditionally defined by how they looked, where they were located, and what functions they performed. In this post-genomic era, the field is largely focused on a molecular view of cell state. Moving forward, we anticipate that the observables used to define cell states will evolve again as single-cell imaging and analytics are advancing at a breakneck pace via the collection of large-scale, systematic cell image datasets and the application of quantitative image-based data science methods. This is, therefore, a key moment in the arc of cell biological research to develop approaches that integrate the spatiotemporal observables of the physical structure and organization of the cell with molecular observables toward the concept of a holistic cell state. In this perspective, we propose a conceptual framework for holistic cell states and state transitions that is data-driven, practical, and useful to enable integrative analyses and modeling across many data types.

Quantifying Landscape-Flux via Single-Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle

Recent developments in single-cell sequencing technology enable the acquisition of entire transcriptome data. Understanding the underlying mechanism and identifying the driving force of transcriptional regulation governing cell function directly from these data remains challenging. This study reconstructs a continuous vector field of the cell cycle based on discrete single-cell RNA velocity to quantify the single-cell global nonequilibrium dynamic landscape-flux. It reveals that large fluctuations disrupt the global landscape and genetic perturbations alter landscape-flux, thus identifying key genes in maintaining cell cycle dynamics and predicting associated functional effects. Additionally, it quantifies the fundamental energy cost of the cell cycle initiation and unveils that sustaining the cell cycle requires curl flux and dissipation to maintain the oscillatory phase coherence. This study enables the inference of the cell cycle gene regulatory networks directly from the single-cell transcriptomic data, including the feedback mechanisms and interaction intensity. This provides a golden opportunity to experimentally verify the landscape-flux theory and also obtain its associated quantifications. It also offers a unique framework for combining the landscape-flux theory and single-cell high-through sequencing experiments for understanding the underlying mechanisms of the cell cycle and can be extended to other nonequilibrium biological processes, such as differentiation development and disease pathogenesis.

Comprehensive Parameter Space Mapping of Cell Cycle Dynamics under Network Perturbations

Studies of quantitative systems and synthetic biology have extensively utilized models to interpret data, make predictions, and guide experimental designs. However, models often simplify complex biological systems and lack experimentally validated parameters, making their reliability in perturbed systems unclear. Here, we developed a droplet-based synthetic cell system to continuously tune parameters at the single-cell level in multiple dimensions with full dynamic ranges, providing an experimental framework for global parameter space scans. We systematically perturbed a cell-cycle oscillator centered on cyclin-dependent kinase (Cdk1), enabling comprehensive mapping of period landscapes in response to network perturbations. The data allowed us to challenge existing models and refine a new model that matches the observed response. Our analysis demonstrated that Cdk1 positive feedback inhibition restricts the cell cycle frequency range, confirming model predictions; furthermore, it revealed new cellular responses to the inhibition of the Cdk1-counteracting phosphatase PP2A: monomodal or bimodal distributions across varying inhibition levels, underscoring the complex nature of cell cycle regulation that can be explained by our model. This comprehensive perturbation platform may be generalizable to exploring other complex dynamic systems.

Orthogonal inducible control of Cas13 circuits enables programmable RNA regulation in mammalian cells

RNA plays an indispensable role in mammalian cell functions. Cas13, a class of RNA-guided ribonuclease, is a flexible tool for modifying and regulating coding and non-coding RNAs, with enormous potential for creating new cell functions. However, the lack of control over Cas13 activity has limited its cell engineering capability. Here, we present the CRISTAL (Control of RNA with Inducible SpliT CAs13 Orthologs and Exogenous Ligands) platform. CRISTAL is powered by a collection (10 total) of orthogonal split inducible Cas13 effectors that can be turned ON or OFF via small molecules in multiple cell types, providing precise temporal control. Also, we engineer Cas13 logic circuits that can respond to endogenous signaling and exogenous small molecule inputs. Furthermore, the orthogonality, low leakiness, and high dynamic range of our inducible Cas13d and Cas13b enable the design and construction of a robust incoherent feedforward loop, leading to near-perfect and tunable adaptation response. Finally, using our inducible Cas13 effectors, we achieve simultaneous multiplexed control of multiple genes in vitro and in mice. Together, our CRISTAL design represents a powerful platform for precisely regulating RNA dynamics to advance cell engineering and elucidate RNA biology.

Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition

In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Ramos et al., Phys. Rev. E 83, 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate.

Coupling allows robust mammalian redox circadian rhythms despite heterogeneity and noise

Circadian clocks are endogenous oscillators present in almost all cells that drive daily rhythms in physiology and behavior. There are two mechanisms that have been proposed to explain how circadian rhythms are generated in mammalian cells: through a transcription-translation feedback loop (TTFL) and based on oxidation/reduction reactions, both of which are intrinsically stochastic and heterogeneous at the single cell level. In order to explore the emerging properties of stochastic and heterogeneous redox oscillators, we simplify a recently developed kinetic model of redox oscillations to an amplitude-phase oscillator with 'twist' (period-amplitude correlation) and subject to Gaussian noise. We show that noise and heterogeneity alone lead to fast desynchronization, and that coupling between noisy oscillators can establish robust and synchronized rhythms with amplitude expansions and tuning of the period due to twist. Coupling a network of redox oscillators to a simple model of the TTFL also contributes to synchronization, large amplitudes and fine-tuning of the period for appropriate interaction strengths. These results provide insights into how the circadian clock compensates randomness from intracellular sources and highlight the importance of noise, heterogeneity and coupling in the context of circadian oscillators.

Design of oscillatory dynamics in numerical simulations of compartment-based enzyme systems

Enzymatic reactions that yield non-neutral products are known to involve feedback due to the bell-shaped pH-rate curve of the enzyme. Compartmentalizing the reaction has been shown to lead to transport-driven oscillations in theory; however, there have been few reproducible experimental examples. Our objective was to determine how the conditions could be optimized to achieve pH oscillations. We employed numerical simulations to investigate the hydrolysis of ethyl acetate in a confined esterase enzyme system, examining the influence of key factors on its behavior. Specific parameter ranges that lead to bistability and self-sustained pH oscillations and the importance of fast base transport for oscillations in this acid-producing system are highlighted. Suggestions are made to expand the parameter space for the occurrence of oscillations, including modifying the maximum of the enzyme pH-rate curve and increasing the negative feedback rate. This research not only sheds light on the programmable nature of enzyme-driven pH regulation but also furthers knowledge on the optimal design of such feedback systems for experimentalists.

Biphasic amplitude oscillator characterized by distinct dynamics of trough and crest

Biphasic amplitude dynamics (BAD) of oscillation have been observed in many biological systems. However, the specific topology structure and regulatory mechanisms underlying these biphasic amplitude dynamics remain elusive. Here, we searched all possible two-node circuit topologies and identified the core oscillator that enables robust oscillation. This core oscillator consists of a negative feedback loop between two nodes and a self-positive feedback loop of the input node, which result in the fast and slow dynamics of the two nodes, thereby achieving relaxation oscillation. Landscape theory was employed to study the stochastic dynamics and global stability of the system, allowing us to quantitatively describe the diverse positions and sizes of the Mexican hat. With increasing input strength, the size of the Mexican hat exhibits a gradual increase followed by a subsequent decrease. The self-activation of input node and the negative feedback on input node, which dominate the fast dynamics of the input node, were observed to regulate BAD in a bell-shaped manner. Both deterministic and statistical analysis results reveal that BAD is characterized by the linear and nonlinear dependence of the oscillation trough and crest on the input strength. In addition, combining with computational and theoretical analysis, we addressed that the linear response of trough to input is predominantly governed by the negative feedback, while the nonlinear response of crest is jointly regulated by the negative feedback loop and the self-positive feedback loop within the oscillator. Overall, this study provides a natural and physical basis for comprehending the occurrence of BAD in oscillatory systems, yielding guidance for the design of BAD in synthetic biology applications.

The Arp2/3 complex promotes periodic removal of Pak1-mediated negative feedback to facilitate anticorrelated Cdc42 oscillations

The conserved GTPase Cdc42 is a major regulator of polarized growth in most eukaryotes. Cdc42 periodically cycles between active and inactive states at sites of polarized growth. These periodic cycles are caused by positive feedback and time-delayed negative feedback loops. In the bipolar yeast S. pombe, both growing ends must regulate Cdc42 activity. At each cell end, Cdc42 activity recruits the Pak1 kinase which prevents further Cdc42 activation thus establishing negative feedback. It is unclear how Cdc42 activation returns to the end after Pak1-dependent negative feedback. Using genetic and chemical perturbations, we find that disrupting branched actin-mediated endocytosis disables Cdc42 reactivation at the cell ends. With our experimental data and mathematical models, we show that endocytosis-dependent Pak1 removal from the cell ends allows the Cdc42 activator Scd1 to return to that end to enable reactivation of Cdc42. Moreover, we show that Pak1 elicits its own removal via activation of endocytosis. In agreement with these observations, our model and experimental data show that in each oscillatory cycle, Cdc42 activation increases followed by an increase in Pak1 recruitment at that end. These findings provide a deeper insight into the self-organization of Cdc42 regulation and reveal previously unknown feedback with endocytosis in the establishment of cell polarity.

A synthetic biology approach to engineering circuits in immune cells

A synthetic circuit in a biological system involves the designed assembly of genetic elements, biomolecules, or cells to create a defined function. These circuits are central in synthetic biology, enabling the reprogramming of cellular behavior and the engineering of cells with customized responses. In cancer therapeutics, engineering T cells with circuits have the potential to overcome the challenges of current approaches, for example, by allowing specific recognition and killing of cancer cells. Recent advances also facilitate engineering integrated circuits for the controlled release of therapeutic molecules at specified locations, for example, in a solid tumor. In this review, we discuss recent strategies and applications of synthetic receptor circuits aimed at enhancing immune cell functions for cancer immunotherapy. We begin by introducing the concept of circuits in networks at the molecular and cellular scales and provide an analysis of the development and implementation of several synthetic circuits in T cells that have the goal to overcome current challenges in cancer immunotherapy. These include specific targeting of cancer cells, increased T-cell proliferation, and persistence in the tumor microenvironment. By harnessing the power of synthetic biology, and the characteristics of certain circuit architectures, it is now possible to engineer a new generation of immune cells that recognize cancer cells, while minimizing off-target toxicities. We specifically discuss T-cell circuits for antigen density sensing. These circuits allow targeting of solid tumors that share antigens with normal tissues. Additionally, we explore designs for synthetic circuits that could control T-cell differentiation or T-cell fate as well as the concept of synthetic multicellular circuits that leverage cellular communication and division of labor to achieve improved therapeutic efficacy. As our understanding of cell biology expands and novel tools for genome, protein, and cell engineering are developed, we anticipate further innovative approaches to emerge in the design and engineering of circuits in immune cells.

Configured quantum reservoir computing for multi-task machine learning

Amidst the rapid advancements in experimental technology, noise-intermediate-scale quantum (NISQ) devices have become increasingly programmable, offering versatile opportunities to leverage quantum computational advantage. Here we explore the intricate dynamics of programmable NISQ devices for quantum reservoir computing. Using a genetic algorithm to configure the quantum reservoir dynamics, we systematically enhance the learning performance. Remarkably, a single configured quantum reservoir can simultaneously learn multiple tasks, including a synthetic oscillatory network of transcriptional regulators, chaotic motifs in gene regulatory networks, and the fractional-order Chua's circuit. Our configured quantum reservoir computing yields highly precise predictions for these learning tasks, outperforming classical reservoir computing. We also test the configured quantum reservoir computing in foreign exchange (FX) market applications and demonstrate its capability to capture the stochastic evolution of the exchange rates with significantly greater accuracy than classical reservoir computing approaches. Through comparison with classical reservoir computing, we highlight the unique role of quantum coherence in the quantum reservoir, which underpins its exceptional learning performance. Our findings suggest the exciting potential of configured quantum reservoir computing for exploiting the quantum computation power of NISQ devices in developing artificial general intelligence.

Role of Fast and Slow Inhibitors in Oscillatory Rhythm Design

In biological or abiotic systems, rhythms occur, owing to the coupling between positive and negative feedback loops in a reaction network. Using the Semenov-Whitesides oscillatory network for thioester hydrolysis as a prototype, we experimentally and theoretically analyzed the role of fast and slow inhibitors in oscillatory reaction networks. In the presence of positive feedback, a single fast inhibitor generates a time delay, resulting in two saddle-node bifurcations and bistability in a continuously stirred tank reactor. A slow inhibitor produces a node-focus bifurcation, resulting in damped oscillations. With both fast and slow inhibitors present, the node-focus bifurcation repeatedly modulates the saddle-node bifurcations, producing stable periodic oscillations. These fast and slow inhibitions result in a pair of time delays between steeply ascending and descending dynamics, which originate from the positive and negative feedbacks, respectively. This pattern can be identified in many chemical relaxation oscillators and oscillatory models, e.g., the bromate-sulfite pH oscillatory system, the Belousov-Zhabotinsky reaction, the trypsin oscillatory system, and the Boissonade-De Kepper model. This study provides a novel understanding of chemical and biochemical rhythms and suggests an approach to designing such behavior.

Modulating Biological Rhythms: A Noncomputational Strategy Harnessing Nonlinearity and Decoupling Frequency and Amplitude

Understanding and achieving concurrent modulation of amplitude and frequency, particularly adjusting one quantity and simultaneously sustaining the other at an invariant level, are of paramount importance for complex biophysical systems, including the signal pathway where different frequency indicates different upstream signal yielding a certain downstream physiological function while different amplitude further determines different efficacy of a downstream output. However, such modulators with clearly described and universally valid mechanisms are still lacking. Here, we rigorously propose an easy-to-use control strategy containing only one or two steps, leveraging the nonlinearity in the modulated systems to decouple frequency and amplitude in a noncomputational manner. The strategy's efficacy is demonstrated using representative biochemical systems and, thus, it could be potentially applicable to modulating rhythms in experiments of biochemistry and synthetic biology.

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics

A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.

The Intrinsic Similarity of Topological Structure in Biological Neural Networks

Most previous studies mainly have focused on the analysis of structural properties of individual neuronal networks from C. elegans. In recent years, an increasing number of synapse-level neural maps, also known as biological neural networks, have been reconstructed. However, it is not clear whether there are intrinsic similarities of structural properties of biological neural networks from different brain compartments or species. To explore this issue, we collected nine connectomes at synaptic resolution including C. elegans, and analyzed their structural properties. We found that these biological neural networks possess small-world properties and modules. Excluding the Drosophila larval visual system, these networks have rich clubs. The distributions of synaptic connection strength for these networks can be fitted by the truncated pow-law distributions. Additionally, compared with the power-law model, a log-normal distribution is a better model to fit the complementary cumulative distribution function (CCDF) of degree for these neuronal networks. Moreover, we also observed that these neural networks belong to the same superfamily based on the significance profile (SP) of small subgraphs in the network. Taken together, these findings suggest that biological neural networks share intrinsic similarities in their topological structure, revealing some principles underlying the formation of biological neural networks within and across species.

MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division

Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division. Single-cell time-lapse experiments can measure both fluctuations by simultaneously recording protein levels inside a cell and its stochastic division. These information-rich noisy trajectory data sets can be harnessed to learn about the underlying molecular and cellular details that are often not known a priori. A critical question is: How can we infer a model given data where fluctuations at two levels-gene expression and cell division-are intricately convoluted? We show the principle of maximum caliber (MaxCal)-integrated within a Bayesian framework-can be used to infer several cellular and molecular details (division rates, protein production, and degradation rates) from these coupled stochastic trajectories (CSTs). We demonstrate this proof of concept using synthetic data generated from a known model. An additional challenge in data analysis is that trajectories are often not in protein numbers, but in noisy fluorescence that depends on protein number in a probabilistic manner. We again show that MaxCal can infer important molecular and cellular rates even when data are in fluorescence, another example of CST with three confounding factors-gene expression noise, cell division noise, and fluorescence distortion-all coupled. Our approach will provide guidance to build models in synthetic biology experiments as well as general biological systems where examples of CSTs are abundant.

The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms

Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.

Cell cycle oscillations driven by two interlinked bistable switches

Regular transitions between interphase and mitosis during the cell cycle are driven by changes in the activity of the enzymatic protein complex cyclin B with cyclin-dependent kinase 1 (Cdk1). At the most basic level, this cell cycle oscillator is driven by negative feedback: active cyclin B-Cdk1 activates the anaphase-promoting complex/cyclosome, which triggers the degradation of cyclin B. Such cell cycle oscillations occur fast and periodically in the early embryos of the frog Xenopus laevis, where several positive-feedback loops leading to bistable switches in parts of the regulatory network have been experimentally identified. Here, we build cell cycle oscillator models to show how single and multiple bistable switches in parts of the underlying regulatory network change the properties of the oscillations and how they can confer robustness to the oscillator. We present a detailed bifurcation analysis of these models.

A synthetic population-level oscillator in non-microfluidic environments

Synthetic oscillators have become a research hotspot because of their complexity and importance. The construction and stable operation of oscillators in large-scale environments are important and challenging. Here, we introduce a synthetic population-level oscillator in Escherichia coli that operates stably during continuous culture in non-microfluidic environments without the addition of inducers or frequent dilution. Specifically, quorum-sensing components and protease regulating elements are employed, which form delayed negative feedback to trigger oscillation and accomplish the reset of signals through transcriptional and post-translational regulation. We test the circuit in devices with 1 mL, 50 mL, 400 mL of medium, and demonstrate that the circuit could maintain stable population-level oscillations. Finally, we explore potential applications of the circuit in regulating cellular morphology and metabolism. Our work contributes to the design and testing of synthetic biological clocks that function in large populations.

Orthogonal inducible control of Cas13 circuits enables programmable RNA regulation in mammalian cells

RNA plays an indispensable role in mammalian cell functions. Cas13, a class of RNA-guided ribonuclease, is a flexible tool for modifying and regulating coding and non-coding RNAs, with enormous potential for creating new cell functions. However, the lack of control over Cas13 activity has limited its cell engineering capability. Here, we present the CRISTAL ( C ontrol of R NA with Inducible S pli T C A s13 Orthologs and Exogenous L igands) platform. CRISTAL is powered by a collection (10 total) of orthogonal split inducible Cas13s that can be turned ON or OFF via small molecules in multiple cell types, providing precise temporal control. Also, we engineered Cas13 logic circuits that can respond to endogenous signaling and exogenous small molecule inputs. Furthermore, the orthogonality, low leakiness, and high dynamic range of our inducible Cas13d and Cas13b enable the design and construction of a robust incoherent feedforward loop, leading to near-perfect and tunable adaptation response. Finally, using our inducible Cas13s, we achieve simultaneous multiplexed control of multiple genes in vitro and in mice. Together, our CRISTAL design represents a powerful platform for precisely regulating RNA dynamics to advance cell engineering and elucidate RNA biology.

Systematic analysis of negative and positive feedback loops for robustness and temperature compensation in circadian rhythms

Temperature compensation and robustness to biological noise are two key characteristics of the circadian clock. These features allow the circadian pacemaker to maintain a steady oscillation in a wide range of environmental conditions. The presence of a time-delayed negative feedback loop in the regulatory network generates autonomous circadian oscillations in eukaryotic systems. In comparison, the circadian clock of cyanobacteria is controlled by a strong positive feedback loop. Positive feedback loops with substrate depletion can also generate oscillations, inspiring other circadian clock models. What makes a circadian oscillatory network robust to extrinsic noise is unclear. We investigated four basic circadian oscillators with negative, positive, and combinations of positive and negative feedback loops to explore network features necessary for circadian clock resilience. We discovered that the negative feedback loop system performs the best in compensating temperature changes. We also show that a positive feedback loop can reduce extrinsic noise in periods of circadian oscillators, while intrinsic noise is reduced by negative feedback loops.

Encoding and Decoding of p53 Dynamics in Cellular Response to Stresses

In the cellular response to stresses, the tumor suppressor p53 is activated to maintain genomic integrity and fidelity. As a transcription factor, p53 exhibits rich dynamics to allow for discrimination of the type and intensity of stresses and to direct the selective activation of target genes involved in different processes including cell cycle arrest and apoptosis. In this review, we focused on how stresses are encoded into p53 dynamics and how the dynamics are decoded into cellular outcomes. Theoretical modeling may provide a global view of signaling in the p53 network by coupling the encoding and decoding processes. We discussed the significance of modeling in revealing the mechanisms of the transition between p53 dynamic modes. Moreover, we shed light on the crosstalk between the p53 network and other signaling networks. This review may advance the understanding of operating principles of the p53 signaling network comprehensively and provide insights into p53 dynamics-based cancer therapy.

Differential roles of transcriptional and translational negative autoregulations in protein dynamics

Cells continuously respond to stimuli to function properly by employing a wide variety of regulatory mechanisms that often involve protein up or down regulations. This study focuses on dynamics of a protein with negative autoregulations in E. coli, and assumes that the input signal up-regulates the protein, and then the protein down-regulates its own production via 2 distinct types of mechanisms. The mathematical models describe the dynamics of mRNA and protein for 3 scenarios: (i) a simplistic model with no regulation, (ii) a model with transcriptional negative autoregulation, and (iii) a model with translational negative autoregulation. Our analysis shows that the negative autoregulation models produce faster responses and quicker return times to the input signals compared to the model with no regulation, while the transcriptional autoregulation model is the only model capable of producing oscillatory dynamics. The stochastic simulations predict that the transcriptional autoregulation model is the noisiest followed by the simplistic model, and the translational autoregulation model has the least noise. The noise level depends on the strength of inhibition. Furthermore, the transcriptional autoregulation model filters out the noise in the input signal for longer periods of time, and this time increases as the strength of the feedback gets stronger.

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.

Nuclear-cytoplasmic compartmentalization of cyclin B1-Cdk1 promotes robust timing of mitotic events

The cyclin-dependent kinase (Cdk1) oscillator is widely characterized in homogenized cytosolic extracts, leaving unclear the impact of nucleocytoplasmic compartmentalization. Here, by developing a Förster resonance energy transfer (FRET) biosensor, we track Cdk1 spatiotemporal dynamics in reconstituted cells with or without side by side and find compartmentalization significantly modulates clock properties previously found in bulk studies. Although nucleus-absent cells display highly tunable frequency, the nucleus-present cells maintain constant frequency against cyclin B1 variations. Despite high expression variability, cyclin degraded within the same duration, enabling a robust mitotic phase. Moreover, Cdk1 and cyclin B1 cycle rigorously out-of-phase, ensuring wide phase-plane orbits, essential for oscillation robustness. Although Cdk1 in homogeneous extracts is well known for delayed switch-like activation, we find active cyclin B1-Cdk1 accumulates in nuclei, without delay, until the nuclear envelope breakdown (NEB) when another abrupt activation triggers anaphase. Cdk1 biphasic activation and spatial compartmentalization may together coordinate the accurate ordering of different downstream events.

Heterogeneity induced splay state of amplitude envelope in globally coupled oscillators

Splay states of the amplitude envelope are stably observed as a heterogenous node is introduced into the globally coupled identical oscillators with repulsive coupling. With the increment of the frequency mismatches between the heterogenous nodes and the rest identical globally coupled oscillators, the formal stable splay state based on the time series becomes unstable, while a splay state based on the new-born amplitude envelopes of time series is stably observed among the rest identical oscillators. The characteristics of the splay state based on the amplitude envelope are numerically and theoretically presented for different parameters of the coupling strength ϵ and the frequency mismatches Δω for small coupling strength and large frequency mismatches. We expect that all these results could reveal the generality of splay states in coupled nonidentical oscillators and help to understand the rich dynamics of amplitude envelopes in multidisciplinary fields.

Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock

Living systems exhibit an unmatched complexity, due to countless, entangled interactions across scales. Here, we aim to understand a complex system, that is, segmentation timing in mouse embryos, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach, in which theory guides the experimental identification of the segmentation clock entrainment responses. We demonstrate period- and phase-locking of the segmentation clock across a wide range of entrainment parameters, including higher-order coupling. These quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the segmentation clock, revealing its essential dynamical properties. Our results indicate that the somite segmentation clock has characteristics reminiscent of a highly non-linear oscillator close to an infinite period bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system, providing precise experimental control over the pace and rhythm of the somite segmentation clock.

Rhythmic transcription of Bmal1 stabilizes the circadian timekeeping system in mammals

In mammals, the circadian clock consists of transcriptional and translational feedback loops through DNA cis-elements such as E-box and RRE. The E-box-mediated core feedback loop is interlocked with the RRE-mediated feedback loop, but biological significance of the RRE-mediated loop has been elusive. In this study, we established mutant cells and mice deficient for rhythmic transcription of Bmal1 gene by deleting its upstream RRE elements and hence disrupted the RRE-mediated feedback loop. We observed apparently normal circadian rhythms in the mutant cells and mice, but a combination of mathematical modeling and experiments revealed that the circadian period and amplitude of the mutants were more susceptible to disturbance of CRY1 protein rhythm. Our findings demonstrate that the RRE-mediated feedback regulation of Bmal1 underpins the E-box-mediated rhythm in cooperation with CRY1-dependent posttranslational regulation of BMAL1 protein, thereby conferring the perturbation-resistant oscillation and chronologically-organized output of the circadian clock.

Electrifying rhythms in plant cells

Physiological oscillations (or rhythms) pervade all spatiotemporal scales of biological organization, either because they perform critical functions or simply because they can arise spontaneously and may be difficult to prevent. Regardless of the case, they reflect regulatory relationships between control points of a given system and offer insights as read-outs of the concerted regulation of a myriad of biological processes. Here we review recent advances in understanding ultradian oscillations (period < 24h) in plant cells, with a special focus on single-cell oscillations. Ion channels are at the center stage due to their involvement in electrical/excitabile phenomena associated with oscillations and cell-cell communication. We highlight the importance of quantitative approaches to measure oscillations in appropriate physiological conditions, which are essential strategies to deal with the complexity of biological rhythms. Future development of optogenetics techniques in plants will further boost research on the role of membrane potential in oscillations and waves across multiple cell types.

Reconstructing distant interactions of multiple paths between perceptible nodes in dark networks

Quantitative research of interdisciplinary fields, including biological and social systems, has attracted great attention in recent years. Complex networks are popular and important tools for the investigations. Explosively increasing data are created by practical networks, from which useful information about dynamic networks can be extracted. From data to network structure, i.e., network reconstruction, is a crucial task. There are many difficulties in fulfilling network reconstruction, including data shortage (existence of hidden nodes) and time delay for signal propagation between adjacent nodes. In this paper a deep network reconstruction method is proposed, which can work in the conditions that even only two nodes (say A and B) are perceptible and all other network nodes are hidden. With a well-designed stochastic driving on node A, this method can reconstruct multiple interaction paths from A to B based on measured data. The distance, effective intensity, and transmission time delay of each path can be inferred accurately.

The nonequilibrium mechanism of noise-enhanced drug synergy in HIV latency reactivation

Noise-modulating chemicals can synergize with transcriptional activators in reactivating latent HIV to eliminate latent HIV reservoirs. To understand the underlying biomolecular mechanism, we investigate a previous two-gene-state model and identify two necessary conditions for the synergy: an assumption of the inhibition effect of transcription activators on noise enhancers; and frequent transitions to the gene non-transcription-permissive state. We then develop a loop-four-gene-state model with Tat transcription/translation and find that drug synergy is mainly determined by the magnitude and direction of energy input into the genetic regulatory kinetics of the HIV promoter. The inhibition effect of transcription activators is actually a phenomenon of energy dissipation in the nonequilibrium gene transition system. Overall, the loop-four-state model demonstrates that energy dissipation plays a crucial role in HIV latency reactivation, which might be useful for improving drug effects and identifying other synergies on lentivirus latency reactivation.

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The inhibition of Activator on Noise enhancer is necessary for their synergy in reactivating HIV

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The drug synergy is a nonequilibrium phenomenon in the gene regulatory system

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The magnitude and direction of energy input determine the drug synergy

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This nonequilibrium mechanism is general without regarding molecular details

Combined multiple transcriptional repression mechanisms generate ultrasensitivity and oscillations

Transcriptional repression can occur via various mechanisms, such as blocking, sequestration and displacement. For instance, the repressors can hold the activators to prevent binding with DNA or can bind to the DNA-bound activators to block their transcriptional activity. Although the transcription can be completely suppressed with a single mechanism, multiple repression mechanisms are used together to inhibit transcriptional activators in many systems, such as circadian clocks and NF-κB oscillators. This raises the question of what advantages arise if seemingly redundant repression mechanisms are combined. Here, by deriving equations describing the multiple repression mechanisms, we find that their combination can synergistically generate a sharply ultrasensitive transcription response and thus strong oscillations. This rationalizes why the multiple repression mechanisms are used together in various biological oscillators. The critical role of such combined transcriptional repression for strong oscillations is further supported by our analysis of formerly identified mutations disrupting the transcriptional repression of the mammalian circadian clock. The hitherto unrecognized source of the ultrasensitivity, the combined transcriptional repressions, can lead to robust synthetic oscillators with a previously unachievable simple design.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.