Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks

Abstract

The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.

Figure 1. Cell Shape Control of cAMP Microdomains

(A) Schematic of overall modeling approach used in this study. (B) Schematic depiction of the spatially specified signaling network used in these simulations, starting from β-adrenergic receptor to cAMP. The receptor and adenylyl cyclase are in the plasma membrane while cAMP, PDE4, and PKA are freely diffusible in the cytoplasm. (C) Simulation of cAMP microdomain formation in response to 1 μM isoproterenol activation of the signaling network depicted in (B) using a neuronal geometry. (D) Dynamics of cAMP formation in live primary hippocampal neurons (DIV 4) using the cAMP FRET sensor EPAC1. The images show the calculated nF prior to addition of isoproterenol (10 μM, left panel) and 5 min post addition (middle panel). Simulated cAMP gradient using neuronal geometry from FRET experiment (right panel). Comparison of cAMP FRET at ROI1 (dendrite) and ROI2 (cell body) with simulation results in their corresponding locations. (E) Image of a CA1 hippocampal neuron in a tissue-slice preparation, with its contours outlined, and the cell body and dendrite labeled (top panel). Simulation of the cAMP microdomains obtained using two of the idealized geometries (bottom panels). (F) Kymographs of simulation results of cAMP concentration with respect to time and space for varying dendritic diameters. (G) Concentration of cAMP at 600 s, plotted against dendritic diameter, and its corresponding surface-to-volume ratio, S/Vd.

Figure 2. Dendritic Diameter Controls PKA and P-MAPK Microdomains

(A) Schematic depiction of extended signaling network used in these simulations, starting from β-adrenergic receptor to MAPK. cAMP and all components downstream of cAMP are freely diffusible. (B) Simulation of the isoproterenol-activated PKA (PKA*, left panel) and activated MAPK (P-MAPK, right panel) microdomains obtained. (C) Kymographs of simulation of PKA* (left) and P-MAPK (right) concentration with respect to time and space for varying dendritic diameters. (D) Concentration of PKA* (left) and P-MAPK (right) at 600 s, plotted against dendritic diameter and its corresponding surface-to-volume ratio, S/Vd. (E) Table summary of the effect of varying diffusion coefficients on gradients obtained (see Figures S8–S14 for details and original kymographs). The label “component” identifies the component that the diffusion coefficient was varied, “gradient” identifies the component that was examined, “max conc” is maximal concentration, “half max conc” stands for half maximal concentration, “time half max conc” identifies the time at which the half-maximal concentration is achieved during the simulation, “distance half max conc” identifies the transverse length (0 μm is the outer edge of the cell body, 120 μm is the tip of the dendrite) at which the half-maximal concentration is achieved during the simulation.

Figure 3. Effect of the Upstream Negative Regulator PDE4 on P-MAPK Microdomains in Neurons

(A) Kymographs of simulated P-MAPK concentrations with respect to time and space for idealized geometry and with varying PDE4 concentrations at 1 μm (left panel) and 3 μm (right panel) dendritic diameter. (B) Line plots of spatial gradients (microdomain characteristics), depicting the P-MAPK gradient at 600 s in dendrites with 1 μm (left panel) and 3 μm (right panel) diameter with varying concentrations of PDE4. The concentrations of PDE4 used are color coded. (C) Comparison of P-MAPK in simulation and pseudocolored experimental images from Figure S19. For ease of visualization, the simulation and pseudocolor experimental images have similar color scales with blue (low levels) and red (high levels). Numerical scale values are different. Simulated gradient of P-MAPK in response to isoproterenol stimulation in the presence of normal phosphodiesterase concentration (0.4 μM, DMSO, Iso) or reduced phosphodiesterase concentration (0.01 μM Rol, Iso + Rol) at 10 min. (D) Comparison of the simulated and experimentally obtained mean intensity ratio of P-MAPK in cell body to dendrite. Ratios of the intensity in the cell body to the dendrite were calculated and normalized to those of the isoproterenol (iso) treatment. For each experiment, the normalization was performed independently. Data are shown from three animals.

Figure 4. Transmission of Spatial Information within Signaling Networks

(A) Neuronal geometry used in the simulations in (B). (B) The cAMP microdomain is conserved during signal propagation. A line scan was done on the dendrite highlighted (white line) in the neuronal geometry used (A). Kymographs along that dendrite depict the activation profile of components downstream of cAMP, after isoproterenol stimulation. Information flow for conservation of microdomain from cAMP to MAPK appears to occur through modulation of PTP by PKA. (C) Comparison of P-MEK in simulation and pseudocolored experimental confocal images from Figure S23. Both have similar color scales. P-MEK levels were measured in control (ct) and iso neurons. (D) Comparison of the simulated and experimentally obtained mean intensity ratio of P-MEK in cell body to dendrite. Ratios of the intensity in the cell body to the dendrite were calculated and normalized to those of the ct. For each experiment, the normalization was performed independently.

Figure 5. Effect of the Negative Regulator PTP on P-MAPK Microdomains in Neurons

(A) Simulations analyzing the contribution of PKA-PTP link to P-MAPK gradient in geometries with varying dendritic diameters using idealized neuronal geometry. (B) Comparison of P-MAPK in simulations and pseudocolored experimental images from Figure S27. Simulated microdomain P-MAPK in response to isoproterenol activation, in the presence (top) and absence of PTP (bottom). (C) Quantification mean intensity ratio of P-MAPK in cell body to dendrites as described in Figures 3 and 4. Experimental data represent two to three slices per condition from two animals in separate experiments, each injected with antisense or scrambled oligonucleotides.

Figure 6. Comparison of the Effects of the Kinetic Parameters for PKA, PP2A, and PP1 Reactions with B-Raf and PTP on Microdomains of Activated B-Raf, MEK, and P-PTP

For all of these simulations, the idealized neuronal geometry was used. Dendritic diameter was either 1 or 3 μm. The standard kinetic parameters used are noted under the reaction. (A) Simulation of the P-B-Raf microdomain with kinetic parameter variation for the reaction of PKA phosphorylating B-Raf in a neuron with a dendritic diameter of 1 μm (top) or 3 μm (bottom). White asterisk marks the standard kinetics parameter combination used in all the simulations in this study. Simulation of the P-MEK microdomain with kinetic parameter variation for the reaction of PKA phosphorylating B-Raf in neuron with a dendritic diameter of 1 μm (top) or 3 μm (bottom). White asterisk marks the standard kinetics parameter combination used in all the simulations used in this study. (B) Simulation of the P-PTP microdomain with kinetic parameter variation for the reaction of PKA phosphorylating PTP in a geometry with a dendritic diameter of 1 μm (top) or 3 μm (bottom). Black asterisk marks the standard kinetics parameter combination used in all the simulations used in this study. (C) Simulation of the P-B-Raf microdomain with kinetic parameter variation for the reaction of PP2A dephosphorylating P-B-Raf in a geometry with a dendritic diameter of 1 μm (top) or 3 μm (bottom). Black asterisk marks the standard kinetics parameter combination used in all the simulations used in this study. (D) Simulation of the P-PTP microdomain with kinetic parameter variation for the reaction of PP1 dephosphorylating P-PTP in a geometry with a dendritic diameter of 1 μm (top) or 3 μm (bottom). White asterisk marks the standard kinetics parameter combination used in all the simulations used in this study.

Figure 7. Integration of the Physical Determinants and the Biochemical Characteristics Required for the Transmittal of Spatial Information through Signaling Networks

The flowchart depicts the origins of spatially restricted signal generation and how the integration of physical constraints (physical domains: cell shape and membrane-delimited reactions) and biochemical reactions, kinetic parameters, and network topology (chemical domain) allows for the flow of spatial information from upstream to downstream components in signaling networks.