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

Disruption of PKA anchoring, as caused by Ht31 peptide, decreases PKA phosphorylation of downstream targets.

<p>When adenylate cyclase (AC) is in the spine, disruption of PKA anchoring reduces by 30% both phosphoThr34 DARPP-32 (p = 0.0006) and phosphoSer845 GluA1 (p = 0.0036). When adenylate cyclase is in the dendrite, disruption of PKA anchoring produces a significant decrease in phosphoThr34 DARPP-32 (p = 0.0005), but not phosphoSer845 GluA1 (p = 0.16). Most of the diffusely distributed PKA is in the dendrite; thus, cAMP diffusion out of the spine (when adenylate cyclase is in the spine) to reach the PKA is more difficult than cAMP diffusion within the dendrite (when adenylate cyclase is in the dendrite). Consequently, disruption of PKA anchoring has a larger effect when adenylate cyclase is in the spine. PhosphoThr34 DARPP-32 is averaged between 50 and 350 s and phosphoSer845 GluA1 is averaged between 50 and 300 s.</p

Diffusion constants for diffusible molecules in the model.

<p>Molecules not listed do not diffuse; thus, their diffusion constants are zero. To calculate diffusion coefficients as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002383#pcbi.1002383-Oliveira1" target="_blank">[57]</a> we used a cytosolic viscosity of 4.1 for small molecules and a cytosolic viscosity of ∼8.7 for proteins . These values yielded calcium gradients similar to those measured experimentally <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002383#pcbi.1002383-Scheuss1" target="_blank">[59]</a>, and diffusion constants similar to those measured experimentally <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002383#pcbi.1002383-Schmidt1" target="_blank">[50]</a>.</p

Dopamine gradients produce intracellular gradients of cAMP, but not PKA activity.

<p>(A) cAMP concentration versus time and distance from dopamine release site. (B) cAMP concentration, averaged from 50 to 150 sec, is well fit by single exponential decay. (C) phosphoThr34 DARPP-32 concentration versus time and distance from dopamine release site exhibits minimal spatial gradient. (D) Concentration of phosphoThr34 DARPP-32, averaged between 100 and 250 sec, exhibits a spatial gradient when diffusion of all DARPP-32 forms is zero (red), or diffusion of PKA bound DARPP-32 is zero (blue). Blocking the phosphoThr75-PKA interaction does not change the gradient that appears when diffusion of all DARPP-32 forms is zero (black). All three cases overlap and have the same decay space constant; thus, they are difficult to distinguish in the figure. The inset shows the fits alone, which also overlap. (E) Percent of GluA1 phosphorylated on Ser845, averaged between 100 and 250 sec, versus distance from dopamine release site. (F) Percent of GluA1 phosphorylated on Ser845, averaged between 100 and 250 sec, exhibits a spatial gradient when diffusion of the DARPP-32 forms is zero (red), or diffusion of PKA bound DARPP-32 is zero (blue). Blocking the phosphoThr75-PKA interaction does not change the gradient that appears when diffusion of all DARPP-32 forms is zero (black).</p

Initial concentrations of anchored molecule species in the simulation.

<p>Only one of these concentrations applied, depending on whether molecules were anchored in the spine, or in the dendrite.</p><p>*Molecules initialized in the dendrite submembrane are specified in picoMoles per µm² (picoSD).</p>#<p>Molecules initialized in the spine cytosol were excluded from the PSD, except for PKA species.</p

Model of striatal medium spiny projection neuron dendrite with spines.

<p>A. Diagram of biochemical signaling pathways. Each arrow is modeled with one or more bimolecular or enzyme reactions. See text and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002383#pcbi-1002383-t001" target="_blank">Table 1</a> for details. B. Morphology of dendrite with four spines, and location of calcium influx in the model. Subvolumes of height 0.12 µm adjacent to the top and bottom surface of the dendrite are considered submembrane subvolumes. Other dendritic subvolumes are part of the cytosol. Diffusion is two-dimensional in the dendrite and one-dimensional in the spine. C. Experimental Design: The role of anchoring is evaluated using four spatial variations in the location of adenylate cyclase and PKA. The adenylate cyclase-D1R complex (AC) is located either in the spine head or a focal dendritic submembrane area. Similarly, the PKA holoenzyme is located either in the spine head or the focal dendritic submembrane area. AMPA receptors containing GluA1 subunits are in the PSD compartment of the spine head for all cases.</p

Colocalization of PKA with adenylate cyclase enhances PKA activity.

<p>(A, B) Concentration of free catalytic subunit (PKAc) is greater for the two colocalized cases. (A) Traces are averaged over 4 trials; nonetheless the stochastic fluctuations are so large that the traces overlay each other and are difficult to distinguish. (B) Mean and S.E.M. of the total PKA activity (PKAc summed between 50 and 350 s). (C,D) Concentration of phosphoThr34 DARPP-32 is greater for the two colocalized cases. (C) Traces are the average over four trials. (D) Mean and S.E.M. of the concentration of phosphoThr34 DARPP-32 averaged between 50 and 350 s. (E, F) Percent of phosphoSer845 GluA1 is greater for the two colocalized cases. (E) Traces are the average over four trials. (F) Mean and S.E.M. of the percent of phosphoSer845 GluA1 averaged between 50 and 300 s.</p

Locating dopamine receptors several microns away from the dopamine release site produces only a small change in cAMP signaling.

<p>A spatial gradient of dopamine decreases (A) cAMP and PKA activity as measured by (B) phosphoThr34 DARPP-32 and (C) phosphoSer845 GluA1, but no delay in time course. A1, B1 and C1 show the time course of a single simulation, A2 show mean and stdev (n = 4) of cAMP averaged between 50 and 200 s; B2 and C2 show mean and stdev (n = 4) of phosphoThr34 DARPP-32 averaged between 50 and 350 s, and phosphoSer845 GluA1 averaged between 50 and 300 s, respectively. The inset of B1 shows the gradient in dopamine concentration from the PSD to the dendrite. Traces are the average of four simulations.</p

The gradient in cAMP concentration depends on the location of adenylate cyclase.

<p>(A) When adenylate cyclase (AC) is in the spine head, there is a large difference (gradient) between spine cAMP and dendrite cAMP. (B) When adenylate cyclase is in the dendrite, there is a small gradient from dendrite to spine.</p

Validation of the model via simulation of agonist bath application.

<p>(A) Change in phosphoThr34 DARPP-32 is similar to that observed experimentally in response to 10 µM dopamine alone, 600 nM calcium alone (inset), and the combination of dopamine with calcium. (B) Decrease in phosphoThr75 DARPP-32 for same three conditions as (A). (C) Change in phosphoSer845 GluA1 for same three conditions as (A). All responses are similar to experimental measurements.</p