Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

Modeling different strategies towards control of lung cancer: leveraging early detection and anti-cancer cell measures

The global population has encountered significant challenges throughout history due to infectious diseases. To comprehensively study these dynamics, a novel deterministic mathematical model, TCD I L 2 Z, is developed for the early detection and treatment of lung cancer. This model incorporates I L 2 cytokine and anti-PD-L1 inhibitors, enhancing the immune system's anticancer response within five epidemiological compartments. The TCD I L 2 Z model is analyzed qualitatively and quantitatively, emphasizing local stability given the limited data-a critical component of epidemic modeling. The model is systematically validated by examining essential elements such as equilibrium points, the reproduction number (R 0 ), stability, and sensitivity analysis. Next-generation techniques based on R 0 that track disease transmission rates across the sub-compartments are fed into the system. At the same time, sensitivity analysis helps model how a particular parameter affects the dynamics of the system. The stability on the global level of such therapy agents retrogrades individuals with immunosuppression or treated with I L 2 and anti-PD-L1 inhibitors admiring the Lyapunov functions' applications. NSFD scheme based on the implicit method is used to find the exact value and is compared with Euler's method and RK4, which guarantees accuracy. Thus, the simulations were conducted in the MATLAB environment. These simulations present the general symptomatic and asymptomatic consequences of lung cancer globally when detected in the middle and early stages, and measures of anticancer cells are implemented including boosting the immune system for low immune individuals. In addition, such a result provides knowledge about real-world control dynamics with I L 2 and anti-PD-L1 inhibitors. The studies will contribute to the understanding of disease spread patterns and will provide the basis for evidence-based intervention development that will be geared toward actual outcomes.

The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms

Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.

Formal verification confirms the role of p53 protein in cell fate decision mechanism

The bio-cell cycle is controlled by a complex biochemical network of signaling pathways. Modeling such challenging networks accurately is imperative for the understanding of their detailed dynamical behavior. In this paper, we construct, analyze, and verify a hybrid Petri net (HPN) model of a complex biochemical network that captures the role of an important protein (namely p53) in deciding the fate of the cell. We model the behavior of the cell nucleus and cytoplasm as two stochastic and continuous Petri nets, respectively, combined together into a single HPN. We use simulative model checking to verify three different properties that capture the dynamical behavior of p53 protein with respect to the intensity of the ionizing radiation (IR) to which the cell is exposed. For each IR dose, 1000 simulation runs are carried out to verify each property. Our verification results showed that the fluctuations in p53, which relies on IR intensity, are compatible with the findings of the preceding simulation studies that have previously examined the role of p53 in cell fate decision.

Cytosolic p53 Inhibits Parkin-Mediated Mitophagy and Promotes Acute Liver Injury Induced by Heat Stroke

Heat stroke (HS) is a severe condition characterized by increased morbidity and high mortality. Acute liver injury (ALI) is a well-documented complication of HS. The tumor suppressor p53 plays an important role in regulation of mitochondrial integrity and mitophagy in several forms of ALI. However, the role of p53-regulated mitophagy in HS-ALI remains unclear. In our study, we discovered the dynamic changes of mitophagy in hepatocytes and demonstrated the protective effects of mitophagy activation on HS-ALI. Pretreatment with 3-MA or Mdivi-1 significantly exacerbated ALI by inhibiting mitophagy in HS-ALI mice. Consistent with the animal HS-ALI model results, silencing Parkin aggravated mitochondrial damage and apoptosis by inhibiting mitophagy in HS-treated normal human liver cell line (LO2 cells). Moreover, we described an increase in the translocation of p53 from the nucleus to the cytoplasm, and cytosolic p53 binds to Parkin in LO2 cells following HS. p53 overexpression using a specific adenovirus or Tenovin-6 exacerbated HS-ALI through Parkin-dependent mitophagy both in vivo and in vitro, whereas inhibition of p53 using siRNA or PFT-α effectively reversed this process. Our results demonstrate that cytosolic p53 binds to Parkin and inhibits mitophagy by preventing Parkin's translocation from the cytosol to the mitochondria, which decreases mitophagy activation and leads to hepatocyte apoptosis in HS-ALI. Overall, pharmacologic induction of mitophagy by inhibiting p53 may be a promising therapeutic approach for HS-ALI treatment.

Natural Products Against Renal Fibrosis via Modulation of SUMOylation

Renal fibrosis is the common and final pathological process of kidney diseases. As a dynamic and reversible post-translational modification, SUMOylation and deSUMOylation of transcriptional factors and key mediators significantly affect the development of renal fibrosis. Recent advances suggest that SUMOylation functions as the promising intervening target against renal fibrosis, and natural products prevent renal fibrosis via modulating SUMOylation. Here, we introduce the mechanism of SUMOylation in renal fibrosis and therapeutic effects of natural products. This process starts by summarizing the key mediators and enzymes during SUMOylation and deSUMOylation and its regulation role in transcriptional factors and key mediators in renal fibrosis, then linking the mechanism findings of SUMOylation and natural products to develop novel therapeutic candidates for treating renal fibrosis, and concludes by commenting on promising therapeutic targets and candidate natural products in renal fibrosis via modulating SUMOylation, which highlights modulating SUMOylation as a promising strategy for natural products against renal fibrosis.