Thomas A. Williams, Mallarmé and the language of mysticism, Athens, University of Georgia Press, 1970, 99 p.

<div><p>Norepinephrine, a neuromodulator that activates β-adrenergic receptors (βARs), facilitates learning and memory as well as the induction of synaptic plasticity in the hippocampus. Several forms of long-term potentiation (LTP) at the Schaffer collateral CA1 synapse require stimulation of both βARs and <i>N</i>-methyl-<i>D</i>-aspartate receptors (NMDARs). To understand the mechanisms mediating the interactions between βAR and NMDAR signaling pathways, we combined FRET imaging of cAMP in hippocampal neuron cultures with spatial mechanistic modeling of signaling pathways in the CA1 pyramidal neuron. Previous work implied that cAMP is synergistically produced in the presence of the βAR agonist isoproterenol and intracellular calcium. In contrast, we show that when application of isoproterenol precedes application of NMDA by several minutes, as is typical of βAR-facilitated LTP experiments, the average amplitude of the cAMP response to NMDA is attenuated compared with the response to NMDA alone. Models simulations suggest that, although the negative feedback loop formed by cAMP, cAMP-dependent protein kinase (PKA), and type 4 phosphodiesterase may be involved in attenuating the cAMP response to NMDA, it is insufficient to explain the range of experimental observations. Instead, attenuation of the cAMP response requires mechanisms upstream of adenylyl cyclase. Our model demonstrates that Gs-to-Gi switching due to PKA phosphorylation of βARs as well as Gi inhibition of type 1 adenylyl cyclase may underlie the experimental observations. This suggests that signaling by β-adrenergic receptors depends on temporal pattern of stimulation, and that switching may represent a novel mechanism for recruiting kinases involved in synaptic plasticity and memory.</p></div

Diffusion constants for diffusible molecules in the model.

<p>Diffusion constants for diffusible molecules in the model.</p

Effects of Gs-Gi switching and GiαGTP inhibition of AC1 in the model.

<p><b>A.</b> Traces of the cAMP responses to NMDA alone and NMDA after ISO in the presence of Gs-Gi switching and GiαGTP inhibition of AC1. In the soma, the total NMDA after ISO response of (%ΔR/R₀ = 9.6) is slightly less than the sum of the NMDA (%ΔR/R₀ = 11.4) + ISO (%ΔR/R₀ = 4.9) responses. Similarly in the dendrite, the total NMDA after ISO (%ΔR/R₀ = 12.5) is much less than the sum of the NMDA (%ΔR/R₀ = 15.6) and ISO (%ΔR/R₀ = 6.6) responses. Standard deviation of these cytosolic traces range from 0.2%ΔR/R₀ to 0.4% ΔR/R₀; standard deviation of the submembrane traces (not shown) is approximately twice that of the cytosolic traces. <b>B.</b> Amplitude of cAMP response for the conditions in A (4 PKA phosphorylation sites on βAR; mean and SEM, <i>n</i> = 3) and also in a model with only 2 PKA phosphorylation sites on the βAR. <b>C.</b> Summary of the effect of Gi binding rates on the difference between the NMDA after ISO response and the NMDA alone response (ΔISO,N-N; Solid bars). Model neurite cAMP response to NMDA after ISO is smaller than the response to NMDA alone for Gi binding rates to βARs between 0.5x and 2.0x of control. The Gi binding rate had no effect on the NMDA alone response (striped or hatched bars). <b>D.</b> Neurite cAMP response when NMDA is applied 4 min after isoproterenol exhibits attenuation of NMDA response, with smaller cAMP response decay when rate of Gi binding is lower (0,2x), but not without Gi binding (0.0x). <b>E.</b> Differential cAMP response due to various ISO concentrations in model neurites. <b>F.</b> The amplitude and time course of inhibited AC1 in model neurites in response to different ISO concentrations reveals that larger ISO produces a smaller NMDA response due to Gi inhibition of the Gs-bound AC1.</p

cAMP during experimental perturbation of the cAMP-PKA-PDE4 pathway in cultured hippocampal neurons.

<p><b>A.</b> Effect of rolipram (1 μM) on the cAMP response to NMDA (<i>n</i> = 19) and the NMDA after isoproterenol stimulus (<i>n</i> = 13) in the neurite (<b>A1</b>) and soma (<b>A2</b>). Rolipram prevents the attenuation of the NMDA after ISO response observed in the neurite, but produces no significant effect in the soma. We used a subsaturating dose to focus on the effect of rolipram on the interaction between NMDA and ISO, and to prevent a large change in the NMDA alone or ISO alone cases. In addition, the subsaturating rolipram ensured we did not saturate the FRET sensor. <b>B.</b> Effect of PKA inhibition by H89 (10 μM) on the cAMP response to isoproterenol (<i>n</i> = 8), NMDA (<i>n</i> = 11), and the NMDA after ISO stimulus (<i>n</i> = 8). H89 prevents the attenuation of the NMDA after ISO response in the neurite (<b>B1</b>) and allows ISO pretreatment to enhance the soma response (<b>B2</b>). Note that, for ease of comparison with the averaged cAMP response to NMDA alone, the cAMP response to the NMDA after ISO stimulus is the difference between the peak response to NMDA after ISO and the response to the initial ISO application. All data represent the means and SEM.</p

Initial concentrations of molecule species in the model.

<p>Molecules not listed have initial concentrations of 0. All membrane bound molecules have zero concentration in the cytosol, and are specified as membrane densities.</p

Model simulation of cAMP dynamics controlled by mechanisms downstream of AC.

<p><b>A.</b> Traces of the cAMP responses to NMDA alone, and NMDA after ISO in the model with pPDE4 activity twice that of PDE4 activity. Arrows and dashed lines show how response amplitudes were measured, both for the model and for the experiments. Thus, the initial (ISO) part of the NMDA after ISO trace is considered ISO alone. The trace for NMDA alone has been offset 120s for ease of comparison. The NMDA alone traces and the initial (ISO) part of the NMDA after ISO traces agree with the experimentally observed cAMP response to ISO or NMDA alone, including the soma to neurite gradient. Nonetheless, the model cAMP in response to NMDA after ISO does not agree with experimental data, suggesting that some other mechanisms are operating in these cells. The darker, less noisy lines near the center of the traces show the cytosolic concentrations, which are slightly lower than the submembrane value for the soma due to a small gradient. <b>B.</b> Traces showing the dynamics of PDE4 phosphorylation in response to NMDA after ISO. The maximal phosphorylation is reached in ~3 minutes, which is slightly faster than the ~6 minutes reported for PDE4D5 in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004735#pcbi.1004735.ref019" target="_blank">19</a>]. The purpose of the slight increase in rate of phosphorylation was to enhance the operation of the negative feedback loop. Note that pPDE4 increases for both NMDA alone and NMDA after ISO. <b>C.</b> Traces showing that GsαGTP bound adenylyl cyclase increases tremendously after ISO, leading to dramatically increased cAMP production. <b>D.</b> Traces showing that PKA activity is only moderately higher after ISO than with NMDA alone, explaining the modest increase in pPDE4 with ISO compared to NMDA alone. <b>E.</b> Effect of parameter variations on dendritic cAMP response. <b>E1.</b> Increases in pPDE4 activity and GsαGTP activity were not sufficient to reproduce experimental results. Solid bars show response to NMDA after ISO, striped or hatched bars show response to NMDA alone. Similar to experiments, the cAMP response to the NMDA after ISO stimulus is the difference between the peak response to NMDA after ISO and the response to the initial ISO application measured just prior to NMDA application. Though 40x lowered the NMDA response after ISO, the NMDA response without ISO was also reduced to a value below that observed experimentally. <b>E2.</b> Increases in the rate of PKA phosphorylation of PDE4 reduces the difference between NMDA after ISO and NMDA alone, but is not sufficient to make the NMDA after ISO response smaller than the NMDA alone response. ΔISO,N-N is the difference between the NMDA after ISO response and the NMDA alone response.</p

Computational model of βAR- and NMDAR-mediated cAMP signaling pathways.

<p><b>A.</b> Signaling pathways leading to cAMP production, and the downstream mechanisms involving PDE4. <b>B.</b> Morphology implemented for the computational model. Reflective boundary conditions occur at the membrane as well as cut surface of the soma and dendrite. The morphology is discretized with 0.9 μm voxels for the cytosol, with one layer of 0.3 μm submembrane voxels and one layer of 0.6 μm voxels adjacent to the submembrane voxels. <b>C.</b> Signaling pathways involved in Gs-Gi switching and GRK desensitization implemented in the model. <i>p</i> indicates a phosphorylation step.</p

Reactions and rate constants for PKA-mediated desensitization and switching in the model.

<p>Reactions and rate constants for PKA-mediated desensitization and switching in the model.</p

Model response to different temporal patterns of stimulation.

<p><b>A.</b> Response to NMDA applied simultaneously with or prior to isoproterenol (ISO). Both the switching model (<b>A1</b>), and the best model without switching (<b>A2</b>: dynamic recruitment of PDE4s to the membrane, 10x activity of plasma membrane PDE4) predict a synergistic response to NMDA followed by ISO. <b>B.</b> Response of switching model to paired 30 sec pulses of NMDA (B1) or isoproterenol (B2) separated by 30, 60 or 120 sec. The switching model exhibits no decrease in the response to the second NMDA pulse compared to the first, whereas it exhibits a decrease in the response to the second isoproterenol pulse. <b><i>C</i></b>. Response of model with enhanced PDE4 to paired 30 sec pulses of NMDA (C1) or isoproterenol (C2) separated by 30, 60 or 120 sec. The enhanced PDE4 model exhibits a decrease in the response to the second pulse of both NMDA and isoproternol with longer time delays.</p

Model variations in PDE4 cannot produce a reduced cAMP response to NMDA after isoproterenol pretreatment.

<p><b>A.</b> Traces showing effect of dynamic recruitment of PDE4D on cAMP response in model neurites, with four activity rates for plasma membrane PDE4D. For the 10x case, the total NMDA after ISO (%ΔR/R₀ = 29.0) is greater than the sum of the NMDA (%ΔR/R₀ = 9.4) and ISO (%ΔR/R₀ = 5.9) responses. Standard deviation of these cytosolic trace ranged from 0.2%ΔR/R₀ to 0.6%ΔR/R₀; standard deviation of the submembrane traces (not shown) ranges from 0.4%ΔR/R₀ to 1.0%ΔR/R₀. The NMDA alone cases are shown for 1x and 40x plasma membrane PDE4D activity. The reduction in the NMDA alone case with 40x plasma membrane PDE4D prevents the enhanced PDE4D activity from reproducing the experimental results. <b>B.</b> Traces showing the concentration of total PDE4D in the membrane and cytosol during dynamic recruitment to show that stimulation by isoproterenol causes an increase of PDE4D in the membrane and a decrease in the cytosol. <b>C.</b> Difference in peak Fret between NMDA after ISO and NMDA alone (ΔISO,NMDA-NMDA) for a range of PKA phosphorylation rates and plasma membrane (pm) PDE4D activity. <b>D.</b> Neither variations in diffusion constant nor a change to Gβγ dependent recruitment of PDE4D can reproduce the experimental results. Solid bars show response to NMDA after ISO, striped or hatched bars show response to NMDA alone, which decrease as pmPDE4D activity is increased. Similar to experiments, the cAMP response to the NMDA after ISO stimulus is the difference between the peak response to NMDA after ISO and the response to the initial ISO application measured just prior to NMDA application.</p