Excitability in the p53 network mediates robust signaling with tunable activation thresholds in single cells

p53 and p21 dynamics encode single-cell DNA damage levels, fine-tuning proliferation and shaping population heterogeneity

Cells must accurately and quickly detect DNA damage through a set of checkpoint mechanisms that enable repair and control proliferation. Heterogeneous levels of cellular stress and noisy signaling processes can lead to phenotypic variability but little is known about their role in underlying proliferation heterogeneity. Here we study two previously published single cell datasets and find that cells encode heterogeneous levels of endogenous and exogenous DNA damage to shape proliferation heterogeneity at the population level. Using a comprehensive time series analysis of short- and long-term signaling dynamics of p53 and p21, we show that DNA damage levels are quantitatively translated into p53 and p21 signal parameters in a gradual manner. Analyzing instantaneous proliferation and signaling differences among equally-radiated cells, we identify time-localized changes in the period of p53 pulses that drive cells out of a low proliferative state. Our findings suggest a novel role of the p53-p21 network in quantitatively encoding DNA damage strength and fine-tuning proliferation trajectories.

Permission to pass: on the role of p53 as a gatekeeper for aneuploidy

Aneuploidy-the karyotype state in which the number of chromosomes deviates from a multiple of the haploid chromosome set-is common in cancer, where it is thought to facilitate tumor initiation and progression. However, it is poorly tolerated in healthy cells: during development and tissue homeostasis, aneuploid cells are efficiently cleared from the population. It is still largely unknown how cancer cells become, and adapt to being, aneuploid. P53, the gatekeeper of the genome, has been proposed to guard against aneuploidy. Aneuploidy in cancer genomes strongly correlates with mutations in TP53, and p53 is thought to prevent the propagation of aneuploid cells. Whether p53 also participates in preventing the mistakes in cell division that lead to aneuploidy is still under debate. In this review, we summarize the current understanding of the role of p53 in protecting cells from aneuploidy, and we explore the consequences of functional p53 loss for the propagation of aneuploidy in cancer.

Elucidating the Implications of Diverse Dynamical Responses in p53 Protein

p53 is a well-known tumor suppressor gene that acts as a transcription factor to exhibit a variety of dynamical responses by sensing different types and extent of stress conditions causing DNA damage in Mammalian cells. Mathematical modeling has played a crucial role to correlate cell fate decision-making with some of these dynamic p53 regulations. However, it is extremely challenging to explain the various cell-type and stimulus-specific p53 protein dynamics under different stress conditions by using a single mathematical model. In this article, we propose a simple mathematical model of p53 regulation based on a generic p53 regulatory network that elucidates a range of p53 dynamical responses. By employing bifurcation analysis along with deterministic and stochastic simulations, we explain an array of p53 dynamics by correlating it with the corresponding cell fate regulations in a cell type-specific and stimulus-dependent manner. Moreover, our model makes experimentally testable predictions to fine-tune p53 dynamics under various DNA damage conditions and can be systematically used and improved to analyze complex p53 dynamics in the future.

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.

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.

Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise

The tumor suppressor protein P53 can regulate the cell cycle, thereby preventing cell abnormalities. In this paper, we study the dynamic characteristics of the P53 network under the influence of time delay and noise, including stability and bifurcation. In order to study the influence of several factors on the concentration of P53, bifurcation analysis on several important parameters is conducted; the results show that the important parameters could induce P53 oscillations within an appropriate range. Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. It is found that time delay plays a key role in inducing Hopf bifurcation and regulating the period and amplitude of system oscillation. Meanwhile, the combination of time delays can not only promote the oscillation of the system but it also provides good robustness. Changing the parameter values appropriately can change the bifurcation critical point and even the stable state of the system. In addition, due to the low copy number of the molecules and the environmental fluctuations, the influence of noise on the system is also considered. Through numerical simulation, it is found that noise not only promotes system oscillation but it also induces system state switching. The above results may help us to further understand the regulation mechanism of the P53-Mdm2-Wip1 network in the cell cycle.

A common pathway to cancer: Oncogenic mutations abolish p53 oscillations

The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, we employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby, we suggest, impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis.

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.

Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support mammalian progenitor cells’ capacity to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species—applicable to nearly half of human protein-coding genes—can generate sustained oscillations without explicit feedback. Diverging oscillation periods synergize with noise to robustly restore cell populations’ bimodal expression on timescales of days. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism underlying development, tissue regeneration, and cancer cell heterogeneity.

Intermittent ERK oscillations downstream of FGF in mouse embryonic stem cells

Signal transduction networks generate characteristic dynamic activities to process extracellular signals and guide cell fate decisions such as to divide or differentiate. The differentiation of pluripotent cells is controlled by FGF/ERK signaling. However, only a few studies have addressed the dynamic activity of the FGF/ERK signaling network in pluripotent cells at high time resolution. Here, we use live cell sensors in wild-type and Fgf4-mutant mouse embryonic stem cells to measure dynamic ERK activity in single cells, for defined ligand concentrations and differentiation states. These sensors reveal pulses of ERK activity. Pulsing patterns are heterogeneous between individual cells. Consecutive pulse sequences occur more frequently than expected from simple stochastic models. Sequences become more prevalent with higher ligand concentration, but are rarer in more differentiated cells. Our results suggest that FGF/ERK signaling operates in the vicinity of a transition point between oscillatory and non-oscillatory dynamics in embryonic stem cells. The resulting heterogeneous dynamic signaling activities add a new dimension to cellular heterogeneity that may be linked to divergent fate decisions in stem cell cultures.

Dual roles of SIRT1 in the BAX switch through the P53 module: A mathematical modeling study

SIRT1 is a multifunctional deacetylase that participates in a variety of cellular physiological processes to cope with stress. The anticancer protein P53 is an important target of SIRT1. It has been found that SIRT1 is involved in apoptosis by regulating the activity and intracellular location of P53. Moreover, P53-dependent apoptosis is inseparable from the BCL-2 protein family. Among the members of this family, BAX’s switching dynamics may play a key role in apoptosis. Therefore, a challenging question arises: what effect does SIRT1 have on the BAX switch? To answer this question, we built a small-scale protein network model. Through computer simulation, the properties of SIRT1 that on the one hand promote and on the other inhibit apoptosis are revealed. We found that the opening time of the BAX switch will be delayed in the case of either SIRT1 excess or deficiency. Similarly, the stimulus threshold required for apoptosis will also increase in the above two scenarios. Thereby, we proposed that SIRT1 has an optimal content at which the probability of apoptosis is greatest. In addition, P53 oscillation requires the concentration of SIRT1 to be higher than the optimal value. This work may be helpful both experimentally and clinically.

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Background

Feedback loops in gene regulatory networks play pivotal roles in governing functional dynamics of cells. Systems approaches demonstrated characteristic dynamical features, including multistability and oscillation, of positive and negative feedback loops. Recent experiments and theories have implicated highly interconnected feedback loops (high-feedback loops) in additional nonintuitive functions, such as controlling cell differentiation rate and multistep cell lineage progression. However, it remains challenging to identify and visualize high-feedback loops in complex gene regulatory networks due to the myriad of ways in which the loops can be combined. Furthermore, it is unclear whether the high-feedback loop structures with these potential functions are widespread in biological systems. Finally, it remains challenging to understand diverse dynamical features, such as high-order multistability and oscillation, generated by individual networks containing high-feedback loops. To address these problems, we developed HiLoop, a toolkit that enables discovery, visualization, and analysis of several types of high-feedback loops in large biological networks.

Results

HiLoop not only extracts high-feedback structures and visualize them in intuitive ways, but also quantifies the enrichment of overrepresented structures. Through random parameterization of mathematical models derived from target networks, HiLoop presents characteristic features of the underlying systems, including complex multistability and oscillations, in a unifying framework. Using HiLoop, we were able to analyze realistic gene regulatory networks containing dozens to hundreds of genes, and to identify many small high-feedback systems. We found more than a 100 human transcription factors involved in high-feedback loops that were not studied previously. In addition, HiLoop enabled the discovery of an enrichment of high feedback in pathways related to epithelial-mesenchymal transition.

Conclusions

HiLoop makes the study of complex networks accessible without significant computational demands. It can serve as a hypothesis generator through identification and modeling of high-feedback subnetworks, or as a quantification method for motif enrichment analysis. As an example of discovery, we found that multistep cell lineage progression may be driven by either specific instances of high-feedback loops with sparse appearances, or generally enriched topologies in gene regulatory networks. We expect HiLoop’s usefulness to increase as experimental data of regulatory networks accumulate. Code is freely available for use or extension at https://github.com/BenNordick/HiLoop.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04405-z.

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 guardian's choice: how p53 enables context-specific decision-making in individual cells

p53 plays a central role in defending the genomic integrity of our cells. In response to genotoxic stress, this tumour suppressor orchestrates the expression of hundreds of target genes, which induce a variety of cellular outcomes ranging from damage repair to induction of apoptosis. In this review, we examine how the p53 response is regulated on several levels in individual cells to allow precise and context-specific fate decisions. We discuss that the p53 response is not only controlled by its canonical regulators but also controlled by interconnected signalling pathways that influence the dynamics of p53 accumulation upon damage and modulate its transcriptional activity at target gene promoters. Additionally, we consider how the p53 response is diversified through a variety of mechanisms at the promoter level and beyond to induce context-specific outcomes in individual cells. These layers of regulation allow p53 to react in a stimulus-specific manner and fine-tune its signalling according to the individual needs of a given cell, enabling it to take the right decision on survival or death.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Cell-cycle-gated feedback control mediates desensitization to interferon stimulation

Cells use molecular circuits to interpret and respond to extracellular cues, such as hormones and cytokines, which are often released in a temporally varying fashion. In this study, we combine microfluidics, time-lapse microscopy, and computational modeling to investigate how the type I interferon (IFN)-responsive regulatory network operates in single human cells to process repetitive IFN stimulation. We found that IFN-α pretreatments lead to opposite effects, priming versus desensitization, depending on input durations. These effects are governed by a regulatory network composed of a fast-acting positive feedback loop and a delayed negative feedback loop, mediated by upregulation of ubiquitin-specific peptidase 18 (USP18). We further revealed that USP18 upregulation can only be initiated at the G1/early S phases of cell cycle upon the treatment onset, resulting in heterogeneous and delayed induction kinetics in single cells. This cell cycle gating provides a temporal compartmentalization of feedback loops, enabling duration-dependent desensitization to repetitive stimulations.

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

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

Inferring Leading Interactions in the p53/Mdm2/Mdmx Circuit through Live-Cell Imaging and Modeling

The tumor-suppressive transcription factor p53 is a master regulator of stress responses. In non-stressed conditions, p53 is maintained at low levels by the ubiquitin ligase Mdm2 and its binding partner Mdmx. Mdmx depletion leads to a biphasic p53 response, with an initial post-mitotic pulse followed by oscillations. The mechanism underlying this dynamical behavior is unknown. Two different roles for Mdmx have been proposed: enhancing p53 ubiquitination by Mdm2 and inhibiting p53 activity. Here, we developed a mathematical model of the p53/Mdm2/Mdmx network to investigate which Mdmx functions quantitatively affect specific features of p53 dynamics under various conditions. We found that enhancement of Mdm2 activity was the most critical role of Mdmx under unstressed conditions. The model also accurately predicted p53 dynamics in Mdmx-depleted cells following DNA damage. This work outlines a strategy for rapidly testing possible network interactions to reveal those most impactful in regulating the dynamics of key proteins.

Abrogation of FBW7α-dependent p53 degradation enhances p53's function as a tumor suppressor

The gene encoding the tumor suppressor p53 is mutated in most cancers. p53 expression is known to be tightly controlled by several E3 ligases. Here, we show that F-box and WD repeat domain-containing 7α (FBW7α), the substrate-recognition component of the SCF^FBW7 multiprotein E3 ligase complex, targets both WT and tumor-derived mutants of p53 for proteasomal degradation in multiple human cancer cell lines (HCT116 and U2OS). We found that lack of FBW7α stabilizes p53 levels, thereby increasing its half-life. p53 ubiquitylation and subsequent degradation require the F-box and the C-terminal WD40 repeats in FBW7α. The polyubiquitylation of p53 occurred via Lys-48 linkage and involved phosphorylation on p53 at Ser-33 and Ser-37 by glycogen synthase kinase 3β (GSK3β) and DNA-dependent protein kinase (DNA-PK), respectively. These phosphorylation events created a phosphodegron that enhanced p53 binding to FBW7α, allowing for the attachment of polyubiquitin moieties at Lys-132 in p53. FBW7α-dependent p53 polyubiquitylation apparently occurred during and immediately after DNA double-strand breaks induced by either doxorubicin or ionizing radiation. Accordingly, in cells lacking FBW7α, p53 induction was enhanced after DNA damage. Phosphodegron-mediated polyubiquitylation of p53 on Lys-132 had functional consequences, with cells in which FBW7α-mediated p53 degradation was abrogated exhibiting enhancement of their tumorigenic potential. We conclude that p53, which previously has been reported to transactivate FBW7, is also targeted by the same E3 ligase for degradation, suggesting the presence of a regulatory feedback loop that controls p53 levels and functions during DNA damage.

Excitable dynamics of Ras triggers spontaneous symmetry breaking of PIP3 signaling in motile cells

Spontaneous cell movement is underpinned by an asymmetric distribution of signaling molecules including small G proteins and phosphoinositides on the cell membrane. However, the molecular network necessary for spontaneous symmetry breaking has not been fully elucidated. Here, we report that, in Dictyostelium discoideum, the spatiotemporal dynamics of GTP bound Ras (Ras-GTP) breaks the symmetry due its intrinsic excitability even in the absence of extracellular spatial cues and downstream signaling activities. A stochastic excitation of local and transient Ras activation induced phosphatidylinositol (3,4,5)-trisphosphate (PIP3) accumulation via direct interaction with Phosphoinositide 3-kinase (PI3K), causing tightly coupled traveling waves that propagated along the membrane. Comprehensive phase analysis of the waves of Ras-GTP and PIP3 metabolism-related molecules revealed the network structure of the excitable system including positive-feedback regulation of Ras-GTP by the downstream PIP3. A mathematical model reconstituted a series of the observed symmetry-breaking phenomena, illustrating the essential involvement of Ras excitability in the cellular decision-making process.

Self-Amplifying Pulsatile Protein Dynamics without Positive Feedback

Many proteins exhibit dynamic activation patterns in the form of irregular pulses. Such behavior is typically attributed to a combination of positive and negative feedback loops in the underlying regulatory network. However, the presence of positive feedbacks is difficult to demonstrate unequivocally, raising the question of whether stochastic pulses can arise from negative feedback only. Here, we use the protein kinase A (PKA) system, a key regulator of the yeast pulsatile transcription factor Msn2, as a case example to show that irregular pulses of protein activity can arise from a negative feedback loop alone. Simplification to two variables reveals that a combination of zero-order ultrasensitivity, timescale separation between the activator and the repressor, and an effective delay in the feedback are sufficient to amplify a perturbation into a pulse. The same circuit topology can account for both activation and inactivation pulses, pointing toward a general mechanism of stochastic pulse generation.

The stretch to stray on time: Resonant length of random walks in a transient

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent ν depends on the chain length N like ν=-N/(N+1) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.

Recent progress and open challenges in modeling p53 dynamics in single cells

In mammalian cells, the tumor suppressor p53 is activated upon a variety of cellular stresses and ensures an appropriate response ranging from arrest and repair to the induction of senescence and apoptosis. Quantitative measurements in individual living cells showed stimulus-dependent dynamics of p53 accumulation upon stress induction. Due to the complexity of the underlying biochemical interactions, mathematical models were indispensable for understanding the topology of the network regulating p53 dynamics. Recent work provides furhter insights into the causes of heterogeneous responses in individual cells, the rewiring of the network in response to different inputs and the role of the downstream processes in determining the cellular fate upon stress.