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Abstract:
The MAPK cascades are principal kinase transduction pathways in eukaryotic cells. This family includes RAF/ERK, JNK, and p38 pathways. In the MAPK cascade, the signal is transmitted through three layers of sequentially activated kinases, MAP3K, MAP2K, and MAPK. The latter two kinases require dual phosphorylation for activation. The dual phosphorylation requirement has been implicated in bringing about bistability and switch-like responses in the cascade. MAPK signaling has been known to involve scaffolds—multidomain proteins that can assemble protein complexes; in this case the three MAPK components. Scaffolds are thought to increase the specificity of signaling by pairing enzymes and substrates. Scaffolds have been shown to biphasically control the response (the level of activated MAPK) and amplify it at a certain scaffold concentration range. In order to understand the interplay of scaffolding and multisite phosphorylation, in this study we analyze simplified MAPK signaling models in which we assume that either mono- or double phosphorylation of MAP2K and MAPK is required for activation. We demonstrate that the requirement for double phosphorylation directs signaling through scaffolds. In the hypothetical scenario in which mono-phosphorylation suffices for kinase activity, the presence of scaffolds has little effect on the response. This suggests that double phosphorylation in MAPK pathways, although not as efficient as mono-phosphorylation, evolved together with scaffolds to assure the tighter control and higher specificity in signaling, by enabling scaffolds to function as response amplifiers.

Keywords:
Kinase cascades, Rule based modeling, Molecular pathways evolution

Abstract:
Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme–substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FceRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.

Abstract:
The stochastic dynamics of T cell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligand–receptor binding kinetics) and negative and positive feedback regulation mediated, respectively, by the phosphatase SHP1 and the MAP kinase ERK. The model incorporates protein–protein interactions involved in initiating TCR-mediated cellular responses and reproduces several experimental observations about the behavior of TCR signaling, including robust responses to as few as a handful of ligands (agonist peptide–MHC complexes on an antigen-presenting cell), distinct responses to ligands that bind TCR with different lifetimes, and antagonism. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability, which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that single-cell trajectories differ qualitatively from the trajectory predicted in the deterministic approximation of the dynamics. Because of bistability, the average of single-cell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switch-like responses to signals, which may aid T cells in making committed cell-fate decisions.

Keywords:
T cell activation, Mathematical model, Kinetic proofreading, Hysteresis, Ordinary differential equations, Stochastic simulations