Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Two wrongs do not make a right: the assumption that an inhibitor acts as an inverse activator

Models of biochemical networks are often large intractable sets of differential equations. To make sense of the complexity, relationships between genes/proteins are presented as connected graphs, the edges of which are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions in many cases by the identifying recurring of topological motifs, for example positive and negative feedback loops. These topological features are usually classified under the presumption that activation and inhibition are inverse relationships. For example, inhibition of an inhibitor is often classified the same as activation of an activator within a motif classification, effectively treating them as equivalent. Whilst in many contexts this may not lead to catastrophic errors, drawing conclusions about the behavior of motifs, pathways or networks from these broad classes of topological feature without adequate mathematical descriptions can lead to obverse outcomes. We investigate the extent to which a biochemical pathway/network will behave quantitatively dissimilar to pathway/ networks with similar typologies formed by swapping inhibitors as the inverse of activators. The purpose of the study is to determine under what circumstances rudimentary qualitative assessment of network structure can provide reliable conclusions as to the quantitative behaviour of the network. Whilst there are others, We focus on two main mathematical qualities which may cause a divergence in the behaviour of two pathways/networks which would otherwise be classified as similar; (i) a modelling feature we label 'bias' and (ii) the precise positioning of activators and inhibitors within simple pathways/motifs.

Mechanism of Decision Making between Autophagy and Apoptosis Induction upon Endoplasmic Reticulum Stress

Dynamic regulation of the cellular proteome is mainly controlled in the endoplasmic reticulum (ER). Accumulation of misfolded proteins due to ER stress leads to the activation of unfolded protein response (UPR). The primary role of UPR is to reduce the bulk of damages and try to drive back the system to the former or a new homeostatic state by autophagy, while an excessive level of stress results in apoptosis. It has already been proven that the proper order and characteristic features of both surviving and self-killing mechanisms are controlled by negative and positive feedback loops, respectively. The new results suggest that these feedback loops are found not only within but also between branches of the UPR, fine-tuning the response to ER stress. In this review, we summarize the recent knowledge of the dynamical characteristic of endoplasmic reticulum stress response mechanism by using both theoretical and molecular biological techniques. In addition, this review pays special attention to describing the mechanism of action of the dynamical features of the feedback loops controlling cellular life-and-death decision upon ER stress. Since ER stress appears in diseases that are common worldwide, a more detailed understanding of the behaviour of the stress response is of medical importance.

A robust ultrasensitive transcriptional switch in noisy cellular environments

Ultrasensitive transcriptional switches enable sharp transitions between transcriptional on and off states and are essential for cells to respond to environmental cues with high fidelity. However, conventional switches, which rely on direct repressor-DNA binding, are extremely noise-sensitive, leading to unintended changes in gene expression. Here, through model simulations and analysis, we discovered that an alternative design combining three indirect transcriptional repression mechanisms, sequestration, blocking, and displacement, can generate a noise-resilient ultrasensitive switch. Although sequestration alone can generate an ultrasensitive switch, it remains sensitive to noise because the unintended transcriptional state induced by noise persists for long periods. However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original transcriptional state. Because this transcriptional switch is effective in noisy cellular contexts, it goes beyond previous synthetic transcriptional switches, making it particularly valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in cells. Specifically, the concurrent use of seemingly redundant indirect repression mechanisms in diverse biological systems appears to be a strategy to achieve noise-resilience of ultrasensitive switches.

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.

In vitro cell cycle oscillations exhibit a robust and hysteretic response to changes in cytoplasmic density

Cells control the properties of the cytoplasm to ensure proper functioning of biochemical processes. Recent studies showed that cytoplasmic density varies in both physiological and pathological states of cells undergoing growth, division, differentiation, apoptosis, senescence, and metabolic starvation. Little is known about how cellular processes cope with these cytoplasmic variations. Here, we study how a cell cycle oscillator comprising cyclin-dependent kinase (Cdk1) responds to changes in cytoplasmic density by systematically diluting or concentrating cycling Xenopus egg extracts in cell-like microfluidic droplets. We found that the cell cycle maintains robust oscillations over a wide range of deviations from the endogenous density: as low as 0.2× to more than 1.22× relative cytoplasmic density (RCD). A further dilution or concentration from these values arrested the system in a low or high steady state of Cdk1 activity, respectively. Interestingly, diluting an arrested cytoplasm of 1.22× RCD recovers oscillations at lower than 1× RCD. Thus, the cell cycle switches reversibly between oscillatory and stable steady states at distinct thresholds depending on the direction of tuning, forming a hysteresis loop. We propose a mathematical model which recapitulates these observations and predicts that the Cdk1/Wee1/Cdc25 positive feedback loops do not contribute to the observed robustness, supported by experiments. Our system can be applied to study how cytoplasmic density affects other cellular processes.

Incoherent modulation of bi-stable dynamics orchestrates the Mushroom and Isola bifurcations

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington's landscape theory and bifurcation analysis, we demonstrate that Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining a positive feedback motif with various incoherent feed-forward loops. Our study reveals that the intrinsic bi-stable dynamics originating from the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these minimal networks to produce these complex bifurcations. These modeling insights will be useful in identifying the possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

A new class of chimeras in locally coupled oscillators with small-amplitude, high-frequency asynchrony and large-amplitude, low-frequency synchrony

Chimeras are surprising yet important states in which domains of decoherent (asynchronous) and coherent (synchronous) oscillations co-exist. In this article, we report on the discovery of a new class of chimeras, called mixed-amplitude chimera states, in which the structures, amplitudes, and frequencies of the oscillations differ substantially in the decoherent and coherent regions. These mixed-amplitude chimeras exhibit domains of decoherent small-amplitude oscillations (phase waves) coexisting with domains of stable and coherent large-amplitude or mixed-mode oscillations (MMOs). They are observed in a prototypical bistable partial differential equation with oscillatory dynamics, spatially homogeneous kinetics, and purely local, isotropic diffusion. They are observed in parameter regimes immediately adjacent to regimes in which common large-amplitude solutions exist, such as trigger waves, spatially homogeneous MMOs, and sharp-interface solutions. Also, key singularities, folded nodes, and folded saddles arising commonly in multi-scale, bistable systems play important roles, and these have not previously been studied in systems with chimeras. The discovery of these mixed-amplitude chimeras is an important advance for understanding some processes in neuroscience, pattern formation, and physics, which involve both small-amplitude and large-amplitude oscillations. It may also be of use for understanding some aspects of electroencephalogram recordings from animals that exhibit unihemispheric slow-wave sleep.

The miR-200 Family of microRNAs: Fine Tuners of Epithelial-Mesenchymal Transition and Circulating Cancer Biomarkers

The miR-200 family of microRNAs (miRNAs) includes miR-200a, miR-200b, miR-200c, miR-141 and miR-429, five evolutionarily conserved miRNAs that are encoded in two clusters of hairpin precursors located on human chromosome 1 (miR-200b, miR-200a and miR-429) and chromosome 12 (miR-200c and miR-141). The mature -3p products of the precursors are abundantly expressed in epithelial cells, where they contribute to maintaining the epithelial phenotype by repressing expression of factors that favor the process of epithelial-to-mesenchymal transition (EMT), a key hallmark of oncogenic transformation. Extensive studies of the expression and interactions of these miRNAs with cell signaling pathways indicate that they can exert both tumor suppressor- and pro-metastatic functions, and may serve as biomarkers of epithelial cancers. This review provides a summary of the role of miR-200 family members in EMT, factors that regulate their expression, and important targets for miR-200-mediated repression that are involved in EMT. The second part of the review discusses the potential utility of circulating miR-200 family members as diagnostic/prognostic biomarkers for breast, colorectal, lung, ovarian, prostate and bladder cancers.

A modular approach for modeling the cell cycle based on functional response curves

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

Bistability plays an important role in many biochemical processes and typically emerges from complex interaction patterns such as positive and double negative feedback loops. Here, we propose to theoretically study the effect of bistability in a larger interaction network. We explicitly incorporate a functional expression describing an S-shaped input-output curve in the model equations, without the need for considering the underlying biochemical events. This expression can be converted into a functional module for an ultrasensitive response, and a time delay is easily included as well. Exploiting the fact that several of these modules can easily be combined in larger networks, we construct a cell cycle model consisting of multiple bistable switches and show how this approach can account for a number of known properties of the cell cycle.

Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm

Nuclei import and export proteins, including cell cycle regulators. These import-export processes are modulated periodically by the cell cycle, for example due to the periodic assembly and breakdown of the nuclear envelope. As such, replicated DNA can be segregated between the two daughter cells and the proteins that were localized in the nucleus are free to diffuse throughout the cytoplasm. Here, we study a mathematical import-diffusion model to show how proteins, i.e. cell cycle regulators, could be redistributed in the cytoplasm by nuclei that periodically toggle between interphase and mitosis. We show that when the cell cycle period depends on the local concentration of regulators, the model exhibits mitotic waves. We discuss how the velocity and spatial origin of these mitotic waves depend on the different model parameters. This work is motivated by recent in vitro experiments reporting on mitotic waves in cycling cell-free extracts made with Xenopus laevis frog eggs, where multiple nuclei share the same cytoplasm. Such experiments have shown that nuclei act as pacemakers for the cell cycle and thus play an important role in collectively defining the spatial origin of mitotic waves.