Mathematical Modeling and Inference of Epidermal Growth Factor-Induced Mitogen-Activated Protein Kinase Cell Signaling Pathways

The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.

High-speed parameter search of dynamic biological pathways from time-course transcriptomic profiles using high-level Petri net

Dynamic simulation promises a deeper understanding of complex molecular mechanisms of biological pathways. How to determine the reaction kinetic parameters which govern the simulation results is still an open question in the field of systems biology. (1) Background: To execute simulation experiments, it is an essential first step to search effective values of model parameters. The complexity of biological systems and the experimental measurement technology severely limit the acquirement of accurate kinetic parameters. Previously proposed genomic data assimilation (GDA) approach enables users to handle parameter estimation using time-course information. However, it highly depends on successive time points and costs massive computational resource; (2) Methods: To address this problem, we present a new high-speed parameter search method for estimating the kinetic parameters of quantitative biological pathways using time-course transcriptomic profiles. The key idea of our method is to interactively prune the search space by introducing Probabilistic Linear-time Temporal Logic (PLTL) based model checking into GDA. (3) Results and conclusion: We demonstrated the effectiveness of our method by comparing with GDA on Mus musculus transcription circuits modelled by hybrid functional Petri net with extension. As a result, our method works faster and more accurate than GDA for both time-course datasets with dense and sparse observed values.

Negative feedback-loop mechanisms regulating HOG- and pheromone-MAPK signaling in yeast

The pheromone response and the high osmolarity glycerol (HOG) pathways are considered the prototypical MAPK signaling systems. They are the best-understood pathways in eukaryotic cells, yet they continue to provide insights in how cells relate with the environment. These systems are subjected to tight regulatory circuits to prevent hyperactivation in length and intensity. Failure to do this may be a matter of life or death specially for unicellular organisms such as Saccharomyces cerevisiae. The signaling pathways are fine-tuned by positive and negative feedback loops exerted by pivotal control elements that allow precise responses to specific stimuli, despite the fact that some elements of the systems are common to different signaling pathways. Here we describe the experimentally proven negative feedback loops that modulate the pheromone response and the HOG pathways. As described in this review, MAP kinases are central mechanistic components of these feedback loops. They have the capacity to modulate basal signaling activity, a fast extranuclear response, and a longer-lasting transcriptional process.

Conceptual Evolution of Cell Signaling

During the last 100 years, cell signaling has evolved into a common mechanism for most physiological processes across systems. Although the majority of cell signaling principles were initially derived from hormonal studies, its exponential growth has been supported by interdisciplinary inputs, e.g., from physics, chemistry, mathematics, statistics, and computational fields. As a result, cell signaling has grown out of scope for any general review. Here, we review how the messages are transferred from the first messenger (the ligand) to the receptor, and then decoded with the help of cascades of second messengers (kinases, phosphatases, GTPases, ions, and small molecules such as cAMP, cGMP, diacylglycerol, etc.). The message is thus relayed from the membrane to the nucleus where gene expression ns, subsequent translations, and protein targeting to the cell membrane and other organelles are triggered. Although there are limited numbers of intracellular messengers, the specificity of the response profiles to the ligands is generated by the involvement of a combination of selected intracellular signaling intermediates. Other crucial parameters in cell signaling are its directionality and distribution of signaling strengths in different pathways that may crosstalk to adjust the amplitude and quality of the final effector output. Finally, we have reflected upon its possible developments during the coming years.

Mitogen-Activated Protein Kinase Phosphatases (MKPs) in Fungal Signaling: Conservation, Function, and Regulation

Mitogen-activated protein kinases (MAPKs) are key mediators of signaling in fungi, participating in the response to diverse stresses and in developmental processes. Since the precise regulation of MAPKs is fundamental for cell physiology, fungi bear dual specificity phosphatases (DUSPs) that act as MAP kinase phosphatases (MKPs). Whereas fungal MKPs share characteristic domains of this phosphatase subfamily, they also have specific interaction motifs and particular activation mechanisms, which, for example, allow some yeast MKPs, such as Saccharomyces cerevisiae Sdp1, to couple oxidative stress with substrate recognition. Model yeasts show that MKPs play a key role in the modulation of MAPK signaling flow. Mutants affected in S. cerevisiae Msg5 or in Schizosaccharomyces pombe Pmp1 display MAPK hyperactivation and specific phenotypes. MKPs from virulent fungi, such as Candida albicans Cpp1, Fusarium graminearum Msg5, and Pyricularia oryzae Pmp1, are relevant for pathogenicity. Apart from transcriptional regulation, MKPs can be post-transcriptionally regulated by RNA-binding proteins such as Rnc1, which stabilizes the S. pombePMP1 mRNA. P. oryzae Pmp1 activity and S. cerevisiae Msg5 stability are regulated by phosphorylation and ubiquitination, respectively. Therefore, fungi offer a platform to gain insight into the regulatory mechanisms that control MKPs.