The indirect activation model of mitochondrial outer membrane permeabilisation (MOMP) initiation requires a trade-off between robustness in the absence of and sensitivity in the presence of stress

Mathematical modelling of Alzheimer's disease biomarkers: Targeting Amyloid beta, Tau protein, Apolipoprotein E and Apoptotic pathways

Introduction: The kinetics of brain cell death in Alzheimer's disease (AD) is being studied using mathematical models. These mathematical models utilize techniques like differential equations, stochastic processes, and network theory to explore crucial signalling pathways and interactions between different cell types. One crucial area of research is the intentional cell death known as apoptosis, which is crucial for the nervous system. The main purpose behind the mathematical modelling of this is for identification of which biomarkers and pathways are most influential in the progression of AD. In addition, we can also predict the natural history of the disease, by which we can make early diagnosis. Mathematical modelling of AD: Current mathematical models include the Apolipoprotein E (APOE) Gene Model, the Tau Protein Kinetics Model, and the Amyloid Beta Peptide Kinetic Model. The Bcl-2 and Bax apoptosis theories postulate that the balance of pro- and anti-apoptotic proteins in cells determines whether a cell experiences apoptosis, where the Bcl-2 model, depicts the interaction of pro- and anti-apoptotic proteins, it is also being used in research on cell death in a range of cell types, including neurons and glial cells. How peptides are produced and eliminated in the brain is explained by the Amyloid beta Peptide (Aβ) Kinetics Model. The tau protein kinetics model focuses on production, aggregation, and clearance of tau protein processes, which are hypothesized to be involved in AD. The APOE gene model investigates the connection between the risk of Alzheimer's disease and the APOE gene. These models have been used to predict how Alzheimer's disease would develop and to evaluate how different inhibitors will affect the illness's course. Conclusion: These mathematical models reflect physiological meaningful characteristics and demonstrates robust fits to training data. Incorporating biomarkers like Aβ, Tau, APOE and markers of neuronal loss and cognitive impairment can generate sound predictions of biomarker trajectories over time in Alzheimer's disease.

Mathematical model of STAT signalling pathways in cancer development and optimal control approaches

In various diseases, the STAT family display various cellular controls over various challenges faced by the immune system and cell death programs. In this study, we investigate how an intracellular signalling network (STAT1, STAT3, Bcl-2 and BAX) regulates important cellular states, either anti-apoptosis or apoptosis of cancer cells. We adapt a mathematical framework to illustrate how the signalling network can generate a bi-stability condition so that it will induce either apoptosis or anti-apoptosis status of tumour cells. Then, we use this model to develop several anti-tumour strategies including IFN-β infusion. The roles of JAK-STATs signalling in regulation of the cell death program in cancer cells and tumour growth are poorly understood. The mathematical model unveils the structure and functions of the intracellular signalling and cellular outcomes of the anti-tumour drugs in the presence of IFN-β and JAK stimuli. We identify the best injection order of IFN-β and DDP among many possible combinations, which may suggest better infusion strategies of multiple anti-cancer agents at clinics. We finally use an optimal control theory in order to maximize anti-tumour efficacy and minimize administrative costs. In particular, we minimize tumour volume and maximize the apoptotic potential by minimizing the Bcl-2 concentration and maximizing the BAX level while minimizing total injection amount of both IFN-β and JAK2 inhibitors (DDP).

The optimal regulation mode of Bcl-2 apoptotic switch revealed by bistability analysis

In most cell types, apoptosis occurs by the mitochondrial outer membrane permeability (MOMP)-mediated pathway, which is controlled by Bcl-2 family proteins (often referred to as Bcl-2 apoptotic switch). These proteins, which display a range of bioactivities, can be divided into four types: effectors, inhibitors, activators and sensitizers. Although the complex interactions among Bcl-2 family members have been studied intensively, a unifying hypothesis for the mechanism they use to regulate MOMP remains elusive. The bistable behaviors are often used to explain the all-or-none decisions of apoptosis. Here, we attempt to reveal the optimal interaction mode by comparing the bistable performances of three different modes (direct activation, indirect activation, and unified mode) proposed by biologists. Using the method that combines mathematical analysis and numerical simulation, we discover that bistability can only emerge from the unified mode when proteins synthesis and degradation are considered, which is in favor of it as an optimal regulation mode of Bcl-2 apoptotic switch. The parameter sensitivity analysis for the unified mode further consolidates this view. Moreover, two-parameter bifurcation analysis suggests that the sensitizers lower the threshold of activation of Bax, but have a negative influence on the width of the bistability region. Our study may provide mechanistic insights into the heterogeneity of tumor cells and the efficiency of BH3 mimetic-mediated killing of cancer cells, and suggest that a combination treatment might be required to overcome apoptosis resistance in the Bcl-2 family targeted therapies.

From computational modelling of the intrinsic apoptosis pathway to a systems-based analysis of chemotherapy resistance: achievements, perspectives and challenges in systems medicine

Our understanding of the mitochondrial or intrinsic apoptosis pathway and its role in chemotherapy resistance has increased significantly in recent years by a combination of experimental studies and mathematical modelling. This combined approach enhanced the quantitative and kinetic understanding of apoptosis signal transduction, but also provided new insights that systems-emanating functions (i.e., functions that cannot be attributed to individual network components but that are instead established by multi-component interplay) are crucial determinants of cell fate decisions. Among these features are molecular thresholds, cooperative protein functions, feedback loops and functional redundancies that provide systems robustness, and signalling topologies that allow ultrasensitivity or switch-like responses. The successful development of kinetic systems models that recapitulate biological signal transduction observed in living cells have now led to the first translational studies, which have exploited and validated such models in a clinical context. Bottom-up strategies that use pathway models in combination with higher-level modelling at the tissue, organ and whole body-level therefore carry great potential to eventually deliver a new generation of systems-based diagnostic tools that may contribute to the development of personalised and predictive medicine approaches. Here we review major achievements in the systems biology of intrinsic apoptosis signalling, discuss challenges for further model development, perspectives for higher-level integration of apoptosis models and finally discuss requirements for the development of systems medical solutions in the coming years.

Harnessing system models of cell death signalling for cytotoxic chemotherapy: towards personalised medicine approaches?

Most cytotoxic chemotherapeutics are believed to kill cancer cells by inducing apoptosis. Understanding the factors that contribute to impairment of apoptosis in cancer cells is therefore critical for the development of novel therapies that circumvent the widespread chemoresistance. Apoptosis, however, is a complex and tightly controlled process that can be induced by different classes of chemotherapeutics targeting different signalling nodes and pathways. Moreover, apoptosis initiation and apoptosis execution strongly depend on patient-specific, genomic and proteomic signatures. Here, we will review recent translational studies that suggest a critical link between the sensitivity of cancer cells to initiate apoptosis and clinical outcome. Next we will discuss recent advances in the field of system modelling of apoptosis pathways for the prediction of treatment responses. We propose that initiation of mitochondrial apoptosis, defined as the process of mitochondrial outer membrane permeabilisation (MOMP), is a dose-dependent decision process that allows for a prediction of individual therapy responses and therapeutic windows. We provide evidence in contrast that apoptosis execution post-MOMP may be a binary decision that dictates whether apoptosis is executed or not. We will discuss the implications of this concept for the future use of novel adjuvant therapeutics that specifically target apoptosis signalling pathways or which may be used to reduce the impact of cell-to-cell heterogeneity on therapy responses. Finally, we will discuss the technical and regulatory requirements surrounding the use and implications of system-based patient stratification tools for the future of personalised oncology.