Abstract
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.
Highlights
External stimuli typically induce cellular responses by binding to cell surface receptors
Our results indicate that the cellto-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
Summary
External stimuli typically induce cellular responses by binding to cell surface receptors. The basic building blocks of eukaryotic signaling networks are protein kinase cascades (Figure 1A): The signaling proteins in the cascade act as enzymes (‘‘kinases’’) that catalyze the activation of downstream kinases by phosphorylation. The proto-typical example for such a signaling cascade is the conserved mitogen-activated protein kinase (MAPK) pathway which consists of three kinases (Raf, Mek, Erk) [1]. The cascade may act as an ultrasensitive switch that responds in a digital (‘‘all-or-none’’) manner: low background signals are strongly dampened and rejected, while amplification and cellular commitment occur once a threshold stimulus is reached. Ultrasensitive signaling cascades act as cellular decision making devices. Ultrasensitive decision making requires additional regulation mechanisms which increase the steepness of the dose-response curve, e.g., strong enzyme saturation in the (de)phosphorylation reactions (‘‘zero-order ultrasensitivity’’), multisite phosphorylation, competitive inhibition, or positive feedback [3,5]
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