Abstract
BackgroundCells are not mixed bags of signaling molecules. As a consequence, signals must travel from their origin to distal locations. Much is understood about the purely diffusive propagation of signals through space. Many signals, however, propagate via signaling cascades. Here, we show that, depending on their kinetics, cascades speed up or slow down the propagation of signals through space, relative to pure diffusion.Methodology/Principal FindingsWe modeled simple cascades operating under different limits of Michaelis-Menten kinetics using deterministic reaction-diffusion equations. Cascades operating far from enzyme saturation speed up signal propagation; the second mobile species moves more quickly than the first through space, on average. The enhanced speed is due to more efficient serial activation of a downstream signaling module (by the signaling molecule immediately upstream in the cascade) at points distal from the signaling origin, compared to locations closer to the source. Conversely, cascades operating under saturated kinetics, which exhibit zero-order ultrasensitivity, can slow down signals, ultimately localizing them to regions around the origin.Conclusions/SignificanceSignal speed modulation may be a fundamental function of cascades, affecting the ability of signals to penetrate within a cell, to cross-react with other signals, and to activate distant targets. In particular, enhanced speeds provide a way to increase signal penetration into a cell without needing to flood the cell with large numbers of active signaling molecules; conversely, diminished speeds in zero-order ultrasensitive cascades facilitate strong, but localized, signaling.
Highlights
Signaling cascades, series of molecules that sequentially activate each other, are ubiquitous in cellular systems [1,2,3,4]
Much of this work has focused on the long time behavior of spatially inhomogeneous systems or on the kinetics of particular pathways
The MAPK cascade has been shown to enhance signal penetration into the cell, reducing sharp signaling gradients otherwise caused by phosphatase deactivation of the signal as it travels away from the origin [8,12]. According to these studies, simple kinetic considerations do not account for how the cascade enables penetration from the membrane to the nucleus
Summary
Series of molecules that sequentially activate each other, are ubiquitous in cellular systems [1,2,3,4]. Much of this work has focused on the long time behavior of spatially inhomogeneous systems or on the kinetics of particular pathways In the latter case, for example, many studies have focused on the MAPK cascade, a ubiquitous cellular pathway. The MAPK cascade has been shown to enhance signal penetration into the cell, reducing sharp signaling gradients otherwise caused by phosphatase deactivation of the signal as it travels away from the origin [8,12]. According to these studies, simple kinetic considerations do not account for how the cascade enables penetration from the membrane to the nucleus. By extending to the spatial domain studies that productively used moment analysis in the temporal domain [6], we provide a way to summarize the complex spatiotemporal behaviors of cascades
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