Cell fate decisions are tightly regulated by complex signalling networks. Disturbed signalling through these networks is prominent in disease development. To elucidate pathway contributions and effects of alterations to the regulation of proliferation, quiescence, senescence, and apoptosis, computational modelling has been essential. Modelling heterogeneity on different scales was shown to be important for cell fate prediction. In recent years, personalised models capturing signalling and cell fate decisions have been developed. Of special interest is the application of these models to predict the response to drugs. In this review, we highlight examples of mathematical models of signalling pathways that regulate disease-relevant cell fate decisions on the path to develop individualised patient models for optimal treatment prediction.
Metabolism, whose reprogramming is an established cancer hallmark, promotes growth and proliferation in cancer cells. Genome-wide metabolic models are becoming increasingly capable of describing cancer growth. Multiscale models may allow the capture of other relevant features of cancer cells and their relationship with the tumor microenvironment. The merging of multiscale metabolic modeling and artificial intelligence can lead to a paradigm shift in oncology, possibly leading to patient-specific personalized digital twins.
Metabolic diseases (MD) are amenable to network-based modeling frameworks, given the systemic perturbations induced by disrupted molecular mechanisms. We present here a brief overview of network modeling methods applied to inborn errors of metabolism (IEM), systemic metabolic conditions (mainly diabetes), and metabolism-related inflammation and autoimmune disorders. Clinical diagnosis and identification of causal agents in IEMs and uncovering the multifactorial mechanisms underlying the development of diabetes and other systemic metabolic diseases are the main challenges being addressed. The review also highlights some of the studies undertaken to investigate the role of the gut microbiome in MD, especially in diabetes. While the network frameworks employed in different modeling approaches have provided novel insights, some technique-specific limitations and overall gaps in general research trends need further attention.
The human immune system is determined by the functionality of the human lymph node. With the use of high-throughput techniques in clinical diagnostics, a large number of data is currently collected. The new data on the spatiotemporal organization of cells offer new possibilities to build a mathematical model of the human lymph node - a virtual lymph node. The virtual lymph node can be applied to simulate drug responses and may be used in clinical diagnosis. Here, we review mathematical models of the human lymph node from the viewpoint of cellular processes. Starting with classical methods, such as systems of differential equations, we discuss the values of different levels of abstraction and methods in the range of artificial intelligence techniques formalism.
Aberrant metabolism and nutrient processing are hallmarks of cancer. Autophagy is a catabolic process, clearing macromolecules and providing metabolite intermediates for anabolism. Autophagy safeguards healthy cells from tumorigenesis while mobilizing metabolites promoting tumor growth. Autophagy is controlled by the mTOR signaling network in conjunction with AMPK and ULK1. This kinase triad features highly intertwined feedback and feedforward mechanisms, complicating predictions on nutrient and drug response. ODE-based models offer a deterministic approach frequently used for the exploration of signaling dynamics. Recent ODE models of the mTOR-AMPK-ULK1 network revealed non-linear behaviors, bistable switches, and oscillatory patterns, shedding light on the robustness and adaptability of autophagy control. We highlight emerging perspectives on AMPK in mTORC1-ULK1 crosstalk and mechanisms for integration into future models.
Periodic segmentation of vertebrate embryos or somitogenesis is regulated by a dynamic network of signalling pathways. Signalling gradients determine the spacing of the forming segments, while signalling oscillations, collectively termed the segmentation clock, ensure their regular timing. Since the segmentation clock is a paradigm of signalling dynamics at tissue level, its mechanism and function have been the topic of many studies. Recently, researchers have been able to analyse and quantify these signalling dynamics with unprecedented precision, revealing the complexity of interlinked oscillations and tissue-wide dynamics throughout development. Initial studies have shown how the interplay between signalling dynamics and cellular mechanics drive the periodic formation of segments. Looking ahead, new techniques such as in vitro stem cell-based models of (human) embryonic development will enable detailed investigations into the mechanisms of somitogenesis.

