Signaling cascades as cellular devices for spatial computations

Abstract

Signaling networks usually include protein-modification cycles. Cascades of such cycles are the backbones of multiple signaling pathways. Protein gradients emerge from the spatial separation of opposing enzymes, such as kinases and phosphatases, or guanine nucleotide exchange factors (GEFs) and GTPase activating proteins (GAPs) for GTPase cycles. We show that different diffusivities of an active protein form and an inactive form leads to spatial gradients of protein abundance in the cytoplasm. For a cascade of cycles, using a discrete approximation of the space, we derive an analytical expression for the spatial gradients and show that it converges to an exact solution with decreasing the size of the quantization. Our results facilitate quantitative analysis of the dependence of spatial gradients on the network topology and reaction kinetics. We demonstrate how different cascade designs filter and process the input information to generate precise, complex spatial guidance for multiple GTPase effector processes. Thus, protein-modification cascades may serve as devices to compute complex spatial distributions of target proteins within intracellular space.

Signaling gradients in cascades of two-state reaction-diffusion systems

“…Among the numerous examples of cascades are proteolytic cascades in blood clotting, phoshorylation cascades in intracellular signal transduction systems, and gene expression cascades that control cell differentiation. Biophysical studies of lumped cascades have shown that they can serve as noise filters, time-delay, or thresholding elements, but the operation and functional capabilities of spatially distributed cascades are much less understood (1)(2)(3)(4)(5)(6). One class of problems where this understanding is necessary arises in studies of embryonic pattern formation.…”

Spatial organization of the Ran pathway by microtubules in mitosis

“…Although mechanics and chemistry are individually sufficient to give rise to structure at micrometer-length scales, increasing evidence suggests that the joint contribution of both of them leads to novel phenomena that might be important for subcellular organization: The interactions of diffusible molecules with the cytoskeleton can alter their mobility and localization, greatly modifying reaction-diffusion processes (4)(5)(6)(7)(8); large-scale patterns can arise if signaling molecules are advected by the motors they regulate (9) or if they recruit factors that further activate them (10); and a shallow reaction-diffusion signaling gradient can produce a sharp concentration gradient in a downstream factor if the signaling molecule regulates the cooperative association of the downstream factor (11). Thus, there is a plethora of mechanisms capable of generating subcellular organization from mechanics, chemistry, or a combination of the two, but it is unclear how prevalent these different possibilities are in cells.…”

The topology design principles that determine the spatiotemporal dynamics of G-protein cascades

“…7, the reaction-diffusion equations that govern the spatiotemporal dynamics of active GTPase fractions, g 1 p(x,t), g 2 p(x,t) and g 3 p(x,t), are presented as follows (see Eqs. 8 and 9), 6 …”

“…This spatial heterogeneity facilitates the generation of positional information 21,22 . Even if a GTPase cascade displays only a single, stable steady state, the spatial segregation of GEFs and opposing GAPs on different cellular structures can result in complex spatial patterns of GTPase activities 6,[23][24][25] . Such complex activity profiles were observed for a chromosome-dependent RanGTPase-importin cascade 26,27 .…”

“…The cycling of GTPases between inactive and active states is catalyzed by guanine nucleotide exchange factors (GEFs), which facilitate GDP/GTP exchange and the transition to the active, GTP-bound state, and GTPase activating proteins (GAPs), which stimulate GTP hydrolysis and the transition to the inactive, GDP-bound state. Crosstalk between functional cycles of different GTPases generates signaling cascades where each GTPase may positively or negatively control GEFs or GAPs at its level and other cascade levels [4][5][6] . Experimentally observed examples of such cascades include a cascade of interacting Rab GTPases that control the conversion of early endosomes into late endosomes 7 and cascades of the Rho family GTPases that regulate cytoskeleton dynamics and cell motility 8,9 .…”