Hysteresis and cell cycle transitions: how crucial is it?

Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks

The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of research. In this paper, we concentrate on two biologically relevant families of reaction networks that model multisite phosphorylation and dephosphorylation of a substrate at n sites. For small values of n, it had previously been shown that the parameter region of multistationarity is connected. Here, we extend these results and provide a proof that applies to all values of n. Our techniques are based on the study of the critical polynomial associated with these reaction networks together with polyhedral geometric conditions of the signed support of this polynomial.

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.

The allelopathy and underlying mechanism of Skeletonema costatum on Karenia mikimotoi integrating transcriptomics profiling

The roles of allelopathy for succession of marine phytoplankton communities remain controversial, especially for the development of blooms. Physiological parameters measurement (Fv/Fm value, MDA content, SOD activity, Na⁺/K⁺, Ca²⁺/ Mg²⁺-ATPase activity, cell size, chlorophyll content, apoptosis and cell cycle) and whole transcriptome profiling analysis were used to investigate allelopathy effect of Skeletonema costatum on Karenia mikimotoi. Filtrate and extracts from S. costatum culture inhibited the growth of K. mikimotoi. Allelopathic effects were dose-dependent for filtrate culture and extract culture. K. mikimotoi scavenged excessive ROS and adapted to the stress fastly and easily, so oxidative damage was not the main cause of the growth inhibition. Allelochemicals of S. costatum were found to influence the structure and function of cell membrane of K. mikimotoi by damaging membrane structure till to cell necrosis, which caused high mortality. Coupled with the sensitivity of algal cells to environmental stress and restricted cell cycle, allelopathy was suggested to be deeply detrimental to the development of competition algal population.

A minimal "push-pull" bistability model explains oscillations between quiescent and proliferative cell states

A minimal model for oscillating between quiescent and growth/proliferation states, dependent on the availability of a central metabolic resource, is presented. From the yeast metabolic cycles, metabolic oscillations in oxygen consumption are represented as transitions between quiescent and growth states. We consider metabolic resource availability, growth rates, and switching rates (between states) to model a relaxation oscillator explaining transitions between these states. This frustrated bistability model reveals a required communication between the metabolic resource that determines oscillations and the quiescent and growth state cells. Cells in each state reflect memory, or hysteresis of their current state, and “push–pull” cells from the other state. Finally, a parsimonious argument is made for a specific central metabolite as the controller of switching between quiescence and growth states. We discuss how an oscillator built around the availability of such a metabolic resource is sufficient to generally regulate oscillations between growth and quiescence through committed transitions.

Modeling-Based Investigation of the Effect of Noise in Cellular Systems

Noise is pervasive in cellular biology and inevitably affects the dynamics of cellular processes. Biological systems have developed regulatory mechanisms to ensure robustness with respect to noise or to take advantage of stochasticity. We review here, through a couple of selected examples, some insights on possible robustness factors and constructive roles of noise provided by computational modeling. In particular, we focus on (1) factors that likely contribute to the robustness of oscillatory processes such as the circadian clocks and the cell cycle, (2) how reliable coding/decoding of calcium-mediated signaling could be achieved in presence of noise and, in some cases, enhanced through stochastic resonance, and (3) how embryonic cell differentiation processes can exploit stochasticity to create heterogeneity in a population of identical cells.

MicroRNA-mediated regulation in biological systems with oscillatory behavior

As a class of small noncoding RNAs, microRNAs (miRNAs) regulate stability or translation of mRNA transcripts. Some reports bring new insights into possible roles of microRNAs in modulating cell cycle. In this paper, we focus on the mechanism and effectiveness of microRNA-mediated regulation in the cell cycle. We first describe two specific regulatory circuits that incorporate base-pairing microRNAs and show their fine-tuning roles in the modulation of periodic behavior. Furthermore, we analyze the effects of miR369-3 on the modulation of the cell cycle, confirming that miR369-3 plays a role in shortening the period of the cell cycle. These results are consistent with experimental observations.

Modeling of hysteresis in gene regulatory networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.

Computational modeling of signaling pathways mediating cell cycle checkpoint control and apoptotic responses to ionizing radiation-induced DNA damage

The shape of dose response of ionizing radiation (IR) induced cancer at low dose region, either linear non-threshold or J-shaped, has been a debate for a long time. This dose response relationship can be influenced by built-in capabilities of cells that minimize the fixation of IR-mediated DNA damage as pro-carcinogenic mutations. Key capabilities include sensing of damage, activation of cell cycle checkpoint arrests that provide time needed for repair of the damage as well as apoptosis. Here we describe computational modeling of the signaling pathways that link sensing of DNA damage and checkpoint arrest activation/apoptosis to investigate how these molecular-level interactions influence the dose response relationship for IR induced cancer. The model provides qualitatively accurate descriptions of the IR-mediated activation of cell cycle checkpoints and the apoptotic pathway, and of time-course activities and dose response of relevant regulatory proteins (e.g. p53 and p21). Linking to a two-stage clonal growth cancer model, the model described here successfully captured a monotonically increasing to a J-shaped dose response curve and identified one potential mechanism leading to the J-shape: the cell cycle checkpoint arrest time saturates with the increase of the dose.

Modeling Dose-response at Low Dose: A Systems Biology Approach for Ionization Radiation

For ionization radiation (IR) induced cancer, a linear non-threshold (LNT) model at very low doses is the default used by a number of national and international organizations and in regulatory law. This default denies any positive benefit from any level of exposure. However, experimental observations and theoretical biology have found that both linear and J-shaped IR dose-response curves can exist at those very low doses. We develop low dose J-shaped dose-response, based on systems biology, and thus justify its use regarding exposure to IR. This approach incorporates detailed, molecular and cellular descriptions of biological/toxicological mechanisms to develop a dose-response model through a set of nonlinear, differential equations describing the signaling pathways and biochemical mechanisms of cell cycle checkpoint, apoptosis, and tumor incidence due to IR. This approach yields a J-shaped dose response curve while showing where LNT behaviors are likely to occur. The results confirm the hypothesis of the J-shaped dose response curve: the main reason is that, at low-doses of IR, cells stimulate protective systems through a longer cell arrest time per unit of IR dose. We suggest that the policy implications of this approach are an increasingly correct way to deal with precautionary measures in public health.

Coevolutionary cycling of host sociality and pathogen virulence in contact networks

Infectious diseases may place strong selection on the social organization of animals. Conversely, the structure of social systems can influence the evolutionary trajectories of pathogens. While much attention has focused on the evolution of host sociality or pathogen virulence separately, few studies have looked at their coevolution. Here we use an agent-based simulation to explore host-pathogen coevolution in social contact networks. Our results indicate that under certain conditions, both host sociality and pathogen virulence exhibit continuous cycling. The way pathogens move through the network (e.g., their interhost transmission and probability of superinfection) and the structure of the network can influence the existence and form of cycling.

Deducing topology of protein-protein interaction networks from experimentally measured sub-networks

Background

Protein-protein interaction networks are commonly sampled using yeast two hybrid approaches. However, whether topological information reaped from these experimentally-measured sub-networks can be extrapolated to complete protein-protein interaction networks is unclear.

Results

By analyzing various experimental protein-protein interaction datasets, we found that they are not random samples of the parent networks. Based on the experimental bait-prey behaviors, our computer simulations show that these non-random sampling features may affect the topological information. We tested the hypothesis that a core sub-network exists within the experimentally sampled network that better maintains the topological characteristics of the parent protein-protein interaction network. We developed a method to filter the experimentally sampled network to result in a core sub-network that more accurately reflects the topology of the parent network. These findings have fundamental implications for large-scale protein interaction studies and for our understanding of the behavior of cellular networks.

Conclusion

The topological information from experimental measured networks network as is may not be the correct source for topological information about the parent protein-protein interaction network. We define a core sub-network that more accurately reflects the topology of the parent network.

Evolutionary design principles of modules that control cellular differentiation: consequences for hysteresis and multistationarity

MOTIVATION

Gene regulatory networks (GRNs) govern cellular differentiation processes and enable construction of multicellular organisms from single cells. Although such networks are complex, there must be evolutionary design principles that shape the network to its present form, gaining complexity from simple modules.

RESULTS

To isolate particular design principles, we have computationally evolved random regulatory networks with a preference to result either in hysteresis (switching threshold depending on current state), or in multistationarity (having multiple steady states), two commonly observed dynamical features of GRNs related to differentiation processes. We have analyzed the resulting evolved networks and compared their structures and characteristics with real GRNs reported from experiments.

CONCLUSION

We found that the artificially evolved networks have particular topologies and it was notable that these topologies share important features and similarities with the real GRNs, particularly in contrasting properties of positive and negative feedback loops. We conclude that the structures of real GRNs are consistent with selection to favor one or other of the dynamical features of multistationarity or hysteresis.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Deactivation of Src family kinases: hypothesis testing using a Monte Carlo sensitivity analysis of systems-level properties

Src family tyrosine kinases play a key role in many cellular signalling networks, but due to the high complexity of these networks their precise function remains elusive. Many factors involved in Src regulation, such as specific kinases and phosphatases, are still unknown. Mathematical models have been constructed to improve the understanding of the system and its dynamic behavior. Using a computational random parameter search, we characterized and compared the dynamics of three alternative models in order to assess their likelihoods. For this, we investigated how systems-level properties such as bistability and excitable behavior relate to kinetic and physiological parameters and how robust these properties were. Our results suggest the existence of a putative negative feedback loop in the Src system. A previously suggested role for PTPalpha in the deactivation of Src was not supported by the model.

Coupled feedback loops form dynamic motifs of cellular networks

Cellular networks are composed of complicated interconnections among components, and some subnetworks of particular functioning are often identified as network motifs. Among such network motifs, feedback loops are thought to play important dynamical roles. Intriguingly, such feedback loops are very often found as a coupled structure in cellular circuits. Therefore, we integrated all the scattered information regarding the coupled feedbacks in various cellular circuits and investigated the dynamical role of each coupled structure. Finally, we discovered that coupled positive feedbacks enhance signal amplification and bistable characteristics; coupled negative feedbacks realize enhanced homeostasis; coupled positive and negative feedbacks enable reliable decision-making by properly modulating signal responses and effectively dealing with noise.