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

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.

Learning metabolic dynamics from irregular observations by Bidirectional Time-Series State Transfer Network

Modeling microbial metabolic dynamics is important for the rational optimization of both biosynthetic systems and industrial processes to facilitate green and efficient biomanufacturing. Classical approaches utilize explicit equation systems to represent metabolic networks, enabling the quantification of pathway fluxes to identify metabolic bottlenecks. However, these white-box models, despite their diverse applications, have limitations in simulating metabolic dynamics and are intrinsically inaccurate for industrial strains that lack information on network structures and kinetic parameters. On the other hand, black-box models do not rely on prior mechanistic knowledge of strains but are built upon observed time-series trajectories of biosynthetic systems in action. In practice, these observations are typically irregular, with discontinuously observed time points across multiple independent batches, each time point potentially containing missing measurements. Learning from such irregular data remains challenging for existing approaches. To address this issue, we present the Bidirectional Time-Series State Transfer Network (BTSTN) for modeling metabolic dynamics directly from irregular observations. Using evaluation data sets derived from both ideal dynamic systems and a real-world fermentation process, we demonstrate that BTSTN accurately reconstructs dynamic behaviors and predicts future trajectories. This approach exhibits enhanced robustness against missing measurements and noise, as compared to the state-of-the-art methods.IMPORTANCEIndustrial biosynthetic systems often involve strains with unclear genetic backgrounds, posing challenges in modeling their distinct metabolic dynamics. In such scenarios, white-box models, which commonly rely on inferred networks, are thereby of limited applicability and accuracy. In contrast, black-box models, such as statistical models and neural networks, are directly fitted or learned from observed time-series trajectories of biosynthetic systems in action. These methods typically assume regular observations without missing time points or measurements. If the observations are irregular, a pre-processing step becomes necessary to obtain a fully filled data set for subsequent model training, which, at the same time, inevitably introduces errors into the resulting models. BTSTN is a novel approach that natively learns from irregular observations. This distinctive feature makes it a unique addition to the current arsenal of technologies modeling metabolic dynamics.

A unified approach to dissecting biphasic responses in cell signaling

Biphasic responses are encountered at all levels in biological systems. At the cellular level, biphasic dose-responses are widely encountered in cell signaling and post-translational modification systems and represent safeguards against overactivation or overexpression of species. In this paper, we provide a unified theoretical synthesis of biphasic responses in cell signaling systems, by assessing signaling systems ranging from basic biochemical building blocks to canonical network structures to well-characterized exemplars on one hand, and examining different types of doses on the other. By using analytical and computational approaches applied to a range of systems across levels (described by broadly employed models), we reveal (i) design principles enabling the presence of biphasic responses, including in almost all instances, an explicit characterization of the parameter space (ii) structural factors which preclude the possibility of biphasic responses (iii) different combinations of the presence or absence of enzyme-biphasic and substrate-biphasic responses, representing safeguards against overactivation and overexpression, respectively (iv) the possibility of broadly robust biphasic responses (v) the complete alteration of signaling behavior in a network due to biphasic interactions between species (biphasic regulation) (vi) the propensity of different co-existing biphasic responses in the Erk signaling network. These results both individually and in totality have a number of important consequences for systems and synthetic biology.

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.

Enhanced DNA repair through droplet formation and p53 oscillations

Living organisms are constantly exposed to DNA damage, and optimal repair is therefore crucial. A characteristic hallmark of the response is the formation of sub-compartments around the site of damage, known as foci. Following multiple DNA breaks, the transcription factor p53 exhibits oscillations in its nuclear concentration, but how this dynamics can affect the repair remains unknown. Here, we formulate a theory for foci formation through droplet condensation and discover how oscillations in p53, with its specific periodicity and amplitude, optimize the repair process by preventing Ostwald ripening and distributing protein material in space and time. Based on the theory predictions, we reveal experimentally that the oscillatory dynamics of p53 does enhance the repair efficiency. These results connect the dynamical signaling of p53 with the microscopic repair process and create a new paradigm for the interplay of complex dynamics and phase transitions in biology.

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.

Temperature Controls Onset and Period of NF-κB Oscillations and can Lead to Chaotic Dynamics

The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

A tale of two rhythms: Locked clocks and chaos in biology

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

Cellular Responses to Platinum-Based Anticancer Drugs and UVC: Role of p53 and Implications for Cancer Therapy

Chemotherapy is intended to induce cancer cell death through apoptosis and other avenues. Unfortunately, as discussed in this article, moderate doses of genotoxic drugs such as cisplatin typical of those achieved in the clinic often invoke a cytostatic/dormancy rather than cytotoxic/apoptosis response in solid tumour-derived cell lines. This is commonly manifested by an extended apoptotic threshold, with extensive apoptosis only being seen after very high/supralethal doses of such agents. The dormancy response can be associated with senescence-like features, polyploidy and/or multinucleation, depending in part on the p53 status of the cells. In most solid tumour-derived cells, dormancy represents a long-term survival mechanism, ultimately contributing to disease recurrence. This review highlights the nonlinearity of key aspects of the molecular and cellular responses to bulky DNA lesions in human cells treated with chemotherapeutic drugs (e.g., cisplatin) or ultraviolet light-C (a widely used tool for unraveling details of the DNA damage-response) as a function of the level of genotoxic stress. Such data highlight the growing realization that targeting dormant cancer cells, which frequently emerge following conventional anticancer treatments, may represent a novel strategy to prevent or, at least, significantly suppress cancer recurrence.

A Switch in p53 Dynamics Marks Cells That Escape from DSB-Induced Cell Cycle Arrest

Cellular responses to stimuli can evolve over time, resulting in distinct early and late phases in response to a single signal. DNA damage induces a complex response that is largely orchestrated by the transcription factor p53, whose dynamics influence whether a damaged cell will arrest and repair the damage or will initiate cell death. How p53 responses and cellular outcomes evolve in the presence of continuous DNA damage remains unknown. Here, we have found that a subset of cells switches from oscillating to sustained p53 dynamics several days after undergoing damage. The switch results from cell cycle progression in the presence of damaged DNA, which activates the caspase-2-PIDDosome, a complex that stabilizes p53 by inactivating its negative regulator MDM2. This work defines a molecular pathway that is activated if the canonical checkpoints fail to halt mitosis in the presence of damaged DNA.