Kinetic mechanisms for overexpression insensitivity and oncogene cooperation

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.

When More Is Less: Dual Phosphorylation Protects Signaling Off State against Overexpression

Kinases in signaling pathways are commonly activated by multisite phosphorylation. For example, the mitogen-activated protein kinase Erk is activated by its kinase Mek by two consecutive phosphorylations within its activation loop. In this article, we use kinetic models to study how the activation of Erk is coupled to its abundance. Intuitively, Erk activity should rise with increasing amounts of Erk protein. However, a mathematical model shows that the signaling off state is robust to increasing amounts of Erk, and Erk activity may even decline with increasing amounts of Erk. This counterintuitive, bell-shaped response of Erk activity to increasing amounts of Erk arises from the competition of the unmodified and single phosphorylated form of Erk for access to its kinase Mek. This shows that phosphorylation cycles can contain an intrinsic robustness mechanism that protects signaling from aberrant activation e.g., by gene expression noise or kinase overexpression after gene duplication events in diseases like cancer.

A novel method for simulating insulin mediated GLUT4 translocation

Glucose transport in humans is a vital process which is tightly regulated by the endocrine system. Specifically, the insulin hormone triggers a cascade of intracellular signals in target cells mediating the uptake of glucose. Insulin signaling triggers cellular relocalization of the glucose transporter protein GLUT4 to the cell surface, which is primarily responsible for regulated glucose import. Pathology associated with the disruption of this pathway can lead to metabolic disorders, such as type II diabetes mellitus, characterized by the failure of cells to appropriately uptake glucose from the blood. We describe a novel simulation tool of the insulin intracellular response, incorporating the latest findings regarding As160 and GEF interactions. The simulation tool differs from previous computational approaches which employ algebraic or differential equations; instead, the tool incorporates statistical variations of kinetic constants and initial molecular concentrations which more accurately mimic the intracellular environment. Using this approach, we successfully recapitulate observed in vitro insulin responses, plus the effects of Wortmannin-like inhibition of the pathway. The developed tool provides insight into transient changes in molecule concentrations throughout the insulin signaling pathway, and may be employed to identify or evaluate potentially critical components of this pathway, including those associated with insulin resistance. In the future, this highly tractable platform may be useful for simulating other complex cell signaling pathways. Biotechnol. Bioeng. 2014;111: 2454-2465. © 2014 Wiley Periodicals, Inc.

Determinants of cell-to-cell variability in protein kinase signaling

Cells reliably sense environmental changes despite internal and external fluctuations, but the mechanisms underlying robustness remain unclear. We analyzed how fluctuations in signaling protein concentrations give rise to cell-to-cell variability in protein kinase signaling using analytical theory and numerical simulations. We characterized the dose-response behavior of signaling cascades by calculating the stimulus level at which a pathway responds (‘pathway sensitivity’) and the maximal activation level upon strong stimulation. Minimal kinase cascades with gradual dose-response behavior show strong variability, because the pathway sensitivity and the maximal activation level cannot be simultaneously invariant. Negative feedback regulation resolves this trade-off and coordinately reduces fluctuations in the pathway sensitivity and maximal activation. Feedbacks acting at different levels in the cascade control different aspects of the dose-response curve, thereby synergistically reducing the variability. We also investigated more complex, ultrasensitive signaling cascades capable of switch-like decision making, and found that these can be inherently robust to protein concentration fluctuations. We describe how the cell-to-cell variability of ultrasensitive signaling systems can be actively regulated, e.g., by altering the expression of phosphatase(s) or by feedback/feedforward loops. Our calculations reveal that slow transcriptional negative feedback loops allow for variability suppression while maintaining switch-like decision making. Taken together, we describe design principles of signaling cascades that promote robustness. Our results may explain why certain signaling cascades like the yeast pheromone pathway show switch-like decision making with little cell-to-cell variability.

Cells sense their surroundings and respond to soluble factors in the extracellular space. Extracellular factors frequently induce heterogeneous responses, thereby restricting the biological outcome to a fraction of the cell population. However, the question arises how such cell-to-cell variability can be controlled, because some cellular systems show a very homogenous response at a defined level of an extracellular stimulus. We derived an analytical framework to systematically characterize the cell-to-cell variability of intracellular signaling pathways which transduce external signals. We analyzed how heterogeneity arises from fluctuations in the total concentrations of signaling proteins because this is the main source of variability in eukaryotic systems. We find that signaling pathways can be highly variable or inherently invariant, depending on the kinetic parameters and the structural features of the cascade. Our results indicate that the cell-to-cell variability can be reduced by negative feedback in the cascade or by signaling crosstalk between parallel pathways. We precisely define the role of negative feedback loops in variability suppression, and show that different aspects of the dose-response curve can be controlled, depending on the feedback kinetics and site of action in the cascade. This work constitutes a first step towards a systematic understanding of cell-to-cell variability in signal transduction.

Robustness of signal transduction pathways

Signal transduction pathways transduce information about the outside of the cell to the nucleus, regulating gene expression and cell fate. To reliably inform the cell about its surroundings, information transfer has to be robust against typical perturbation that a cell experiences. Robustness of several mammalian signaling pathways has been studied recently by quantitative experimentation and using mathematical modeling. Here, we review these studies, and describe the emerging concepts of robustness and the underlying mechanisms.

Bell-shaped and ultrasensitive dose-response in phosphorylation-dephosphorylation cycles: the role of kinase-phosphatase complex formation

Background

Phosphorylation-dephosphorylation cycles (PDCs) mediated by kinases and phosphatases are common in cellular signalling. Kinetic modelling of PDCs has shown that these systems can exhibit a variety of input-output (dose-response) behaviors including graded response, ultrasensitivity and bistability. In addition to proteins, there are a class of lipids known as phosphoinositides (PIs) that can be phosphorylated. Experimental studies have revealed the formation of an antagonistic kinase-phosphatase complex in regulation of phosphorylation of PIs. However, the functional significance of this type of complex formation is not clear.

Results

We first revisit the basic PDC and show that partial asymptotic phosphorylation of substrate limits ultrasensitivity. Also, substrate levels are changed one can obtain non-monotonic bell-shaped dose-response curves over a narrow range of parameters. Then we extend the PDC to include kinase-phosphatase complex formation. We report the possibility of robust bell-shaped dose-response for a specific class of the model with complex formation. Also, we show that complex formation can produce ultrasensitivity outside the Goldbeter-Koshland zero-order ultrasensitivity regime through a mechanism similar to competitive inhibition between an enzyme and its inhibitor.

Conclusions

We conclude that the novel PDC module studied here exhibits new dose-response behaviour. In particular, we show that the bell-shaped response could result in transient phosphorylation of substrate. We discuss the relevance of this result in the context of experimental observations on PI regulation in endosomal trafficking.

Mathematical investigation of how oncogenic ras mutants promote ras signaling

We have used a mathematical model of the Ras signaling network to link observable biochemical properties with cellular levels of RasGTP. Although there is abundant data characterizing Ras biochemistry, attributing specific changes in biochemical properties to observed phenotypes has been hindered by the scope and complexity of Ras regulation. A mathematical model of the Ras signaling module, therefore, appeared to be of value for this problem. The model described the core architecture shared by pathways that signal through Ras. Mass-action kinetics and ordinary differential equations were used to describe network reactions. Needed parameters were largely available in the published literature and resulted in a model with good agreement to experimental data. Computational analysis of the model resulted in several unanticipated predictions and suggested experiments that subsequently validated some of these predictions.

Mechanistic modeling to investigate signaling by oncogenic Ras mutants

Mathematical models based on biochemical reaction mechanisms can be a powerful complement to experimental investigations of cell signaling networks. In principle, such models have the potential to find the behaviors that result from well-understood component interactions and their measurable properties, such as concentrations and rate constants. As cancer results from the acquisition of mutations that alter the expression level and/or the biochemistry of proteins encoded by mutated genes, mathematical models of cell signaling networks would also seem to have the potential to predict how these changes alter cell signaling to produce a cancer phenotype. Ras is commonly found in cancer and has been extensively characterized at the level of detail needed to develop such models. Here, we consider how biochemical mechanism-based models have been used to study mutant Ras signaling. These models demonstrate that it is clearly possible to use observable properties of individual reactions to predict how the entire system behaves to produce the high levels of signal that drive the cancer phenotype. These models also demonstrate differences in how models are developed and studied. Their evaluation suggests which approaches are most promising for future work.