A kinetic model of multiple phenotypic states for breast cancer cells

Enhancing search efficiency through diffusive echo

Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We obtain analytic expressions for the joint distribution of the hitting time and the hitting angle in two and three dimensions. For certain configurations we observe a ``diffusive echo", i.e. two well-defined maxima in the first passage time distribution to a targeted position on the absorbing boundary. This effect, which results from the interplay between the starting location and the environmental constraints, may help to significantly increase the efficiency of the random search by generating a high, sustained flux to the targeted position over a short period. Finally, we examine the corresponding one-dimensional system for which there is no well-defined echo. In a confined system, the flux integrated over all target positions always displays a shoulder. This does not, however, guarantee the presence of an echo in the joint distribution.

Network modeling-based identification of the switching targets between pyroptosis and secondary pyroptosis

The newly identified cell death type, pyroptosis plays crucial roles in various diseases. Most recently, mounting evidence accumulates that pyroptotic signaling is highly correlated with coronavirus disease 2019 (COVID-19). Thus, understanding the induction of the pyroptotic signaling and dissecting the detail molecular control mechanisms are urgently needed. Based on recent experimental studies, a core regulatory model of the pyroptotic signaling is constructed to investigate the intricate crosstalk dynamics between the two cell death types, i.e., pyroptosis and secondary pyroptosis. The model well reproduces the experimental observations under different conditions. Sensitivity analysis determines that only the expression level of caspase-1 or GSDMD has the potential to individually change death modes. The decrease of caspase-1 or GSDMD level switches cell death from pyroptosis to secondary pyroptosis. Besides, eight biochemical reactions are identified that can efficiently switch death modes. While from the viewpoint of bifurcation analysis, the expression level of caspase-3 is further identified and twelve biochemical reactions are obtained. The coexistence of pyroptosis and secondary pyroptosis is predicted to be observed not only within the bistable range, but also within proper monostable range, presenting two potential different control mechanisms. Combined with the landscape theory, we further explore the stochastic dynamic and global stability of the pyroptotic system, accurately quantifying how each component mediates the individual occurrence probability of pyroptosis and secondary pyroptosis. Overall, this study sheds new light on the intricate crosstalk of the pyroptotic signaling and uncovers the regulatory mechanisms of various stable state transitions, providing potential clues to guide the development for prevention and treatment of pyroptosis-related diseases.

Tristability in mitochondrial permeability transition pore opening

Mitochondrial permeability transition pore (PTP), a key regulator of cell life and death processes, is triggered by calcium ions (Ca²⁺) and potentiated by reactive oxygen species (ROS). Although the two modes of PTP opening, i.e., transient and persistent, have been identified for a long time, its dynamical mechanism is still not fully understood. To test a proposed hypothesis that PTP opening acts as a tristable switch, which is characterized by low, medium, and high open probability, we develop a three-variable model that focused on PTP opening caused by Ca²⁺ and ROS. For the system reduced to two differential equations for Ca²⁺ and ROS, both the stability analysis and the potential landscape feature that it exhibits tristability under standard parameters. For the full system, the bifurcation analysis suggests that it can achieve tristability over a wide range of input parameters. Furthermore, parameter sensitivity analysis demonstrates that the existence of tristability is a robust property. In addition, we show how the deterministic tristable property can be understood within a stochastic framework, which also explains the PTP dynamics at the level of a single channel. Overall, this study may yield valuable insights into the intricate regulatory mechanism of PTP opening.

Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons

Potassium ion and sodium ion channels play important roles in the propagation of action potentials along a myelinated axon. The random opening and closing of ion channels can cause the fluctuation of action potentials. In this paper, an improved Hodgkin-Huxley chain network model is proposed to study the effects of ion channel blocks, temperature, and ion channel noise on the propagation of action potentials along the myelinated axon. It is found that the chain network has minimum coupling intensity threshold and maximum tolerance temperature threshold that allow the action potentials to pass along the whole axon, and the blockage of ion channels can change these two thresholds. A striking result is that the simulated value of the optimum membrane size (inversely proportional to noise intensity) coincides with the area range of feline thalamocortical relay cells in biological experiments.

Understanding breast cancer heterogeneity through non-genetic heterogeneity

Intricacy in treatment and diagnosis of breast cancer has been an obstacle due to genotype and phenotype heterogeneity. Understanding of non-genetic heterogeneity mechanisms along with considering role of genetic heterogeneity may fill the gaps in landscape painting of heterogeneity. The main factors contribute to non-genetic heterogeneity including: transcriptional pulsing/bursting or discontinuous transcriptions, stochastic partitioning of components at cell division and various signal transduction from tumor ecosystem. Throughout this review, we desired to provide a conceptual framework focused on non-genetic heterogeneity, which has been intended to offer insight into prediction, diagnosis and treatment of breast cancer.

Kinetic Modeling of DUSP Regulation in Herceptin-Resistant HER2-Positive Breast Cancer

BACKGROUND

HER2 (human epidermal growth factor 2)-positive breast cancer is an aggressive type of breast cancer characterized by the overexpression of the receptor-type protein tyrosine kinase HER2 or amplification of the HER2 gene. It is commonly treated by the drug trastuzumab (Herceptin), but resistance to its action frequently develops and limits its therapeutic benefit. Dual-specificity phosphatases (DUSPs) were previously highlighted as central regulators of HER2 signaling; therefore, understanding their role is crucial to designing new strategies to improve the efficacy of Herceptin treatment. We investigated whether inhibiting certain DUSPs re-sensitized Herceptin-resistant breast cancer cells to the drug. We built a series of kinetic models incorporating the key players of HER2 signaling pathways and simulating a range of inhibition intensities. The simulation results were compared to live tumor cells in culture, and showed good agreement with the experimental analyses. In particular, we observed that Herceptin-resistant DUSP16-silenced breast cancer cells became more responsive to the drug when treated for 72 h with Herceptin, showing a decrease in resistance, in agreement with the model predictions. Overall, we showed that the kinetic modeling of signaling pathways is able to generate predictions that assist experimental research in the identification of potential targets for cancer treatment.

Modeling of mesenchymal hybrid epithelial state and phenotypic transitions in EMT and MET processes of cancer cells

Based on the transcriptional regulatory mechanisms between microRNA-200 and transcription factor ZEB in an individual cancer cell, a minimal dynamic model is proposed to study the epithelial-mesenchymal transition (EMT) and mesenchymal-epithelial transition (MET) processes of cancer cells. It is shown that each cancer cell can exit in any of three phenotypic states: the epithelial (E) state, the mesenchymal (M) state, and the epithelial/mesenchymal (E/M) hybrid state, and the state of cancer cell can interconvert between different states. The phase diagram shows that there are monostable, bistable, and tristable phenotypic states regions in a parameters plane. It is found that different pathway in the phase diagram can correspond to the EMT or the MET process of cancer cells, and there are two possible EMT processes. It is important that the experimental phenomenon of E/M hybrid state appearing in the EMT process but rather in the MET process can be understood through different pathways in the phase diagram. Our numerical simulations show that the effects of noise are opposite to these of time delay on the expression of transcription factor ZEB, and there is competition between noise and time delay in phenotypic transitions process of cancer cells.

Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing

An improved Hindmarsh-Rose (HR) neuron model, where the memristor is a bridge between membrane potential and magnetic flux, can be used to investigate the effect of periodic signals on autaptic regulation of neurons under electromagnetic radiation. Based on the improved HR model driven by periodic high-low-frequency current and electromagnetic radiation, the responses of electrical autaptic regulation with diverse high-low-frequency signals are investigated using bifurcation analysis. It is found that the electrical modes of neurons are determined by the selecting parameters of both periodic high and low-frequency current and electromagnetic radiation, and the Hamiltonian energy depends on the neuronal firing modes. The effects of Gaussian white noise on the membrane potential are discussed using numerical simulations. It is demonstrated that external high-low-frequency stimulus plays a significant role in the autaptic regulation of neural firing mode, and the electrical mode of neurons can be affected by the angular frequency of both high-low-frequency forcing current and electromagnetic radiation. The mechanism of neuronal firing regulated by high-low-frequency signal and electromagnetic radiation discussed here could be applied to research neuronal networks and synchronisation modes.