Conceived and designed the experiments: MK TA KTB. Performed the experiments: MK AJP RH AC LAG RFO. Analyzed the data: MK AJP RH AC LAG RFO TA KTB. Wrote the paper: MK AJP RH TA LAG KTB.
The authors have declared that no competing interests exist.
The ability of neurons to differentially respond to specific temporal and spatial input patterns underlies information storage in neural circuits. One means of achieving spatial specificity is to restrict signaling molecules to particular subcellular compartments using anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Disruption of protein kinase A (PKA) anchoring to AKAPs impairs a PKA-dependent form of long term potentiation (LTP) in the hippocampus. To investigate the role of localized PKA signaling in LTP, we developed a stochastic reaction-diffusion model of the signaling pathways leading to PKA activation in CA1 pyramidal neurons. Simulations investigated whether the role of anchoring is to locate kinases near molecules that activate them, or near their target molecules. The results show that anchoring PKA with adenylyl cyclase (which produces cAMP that activates PKA) produces significantly greater PKA activity, and phosphorylation of both inhibitor-1 and AMPA receptor GluR1 subunit on S845, than when PKA is anchored apart from adenylyl cyclase. The spatial microdomain of cAMP was smaller than that of PKA suggesting that anchoring PKA near its source of cAMP is critical because inactivation by phosphodiesterase limits diffusion of cAMP. The prediction that the role of anchoring is to colocalize PKA near adenylyl cyclase was confirmed by experimentally rescuing the deficit in LTP produced by disruption of PKA anchoring using phosphodiesterase inhibitors. Additional experiments confirm the model prediction that disruption of anchoring impairs S845 phosphorylation produced by forskolin-induced synaptic potentiation. Collectively, these results show that locating PKA near adenylyl cyclase is a critical function of anchoring.
The hippocampus is a part of the cerebral cortex involved in formation of certain types of long term memories. Activity-dependent change in the strength of neuronal connections in the hippocampus, known as synaptic plasticity, is one mechanism used to store memories. The ability to form crisp and distinguishable memories of different events implies that learning produces plasticity of specific and distinct subsets of synapses within each neuron. Synaptic activity leads to production of intracellular signaling molecules, which ultimately cause changes in the properties of the synapses. The requirement for synaptic specificity seems incompatible with the diffusibility of intracellular signaling molecules. Anchoring proteins restrict signaling molecules to particular subcellular compartments thereby combating the indiscriminate spread of intracellular signaling molecules. To investigate whether the critical function of anchoring proteins is to localize proteins near their activators or their targets, we developed a stochastic reaction-diffusion model of signaling pathways leading to synaptic plasticity in hippocampal neurons. Simulations demonstrate that colocalizing proteins with their activator molecules is more important due to inactivation mechanisms that limit the spatial extent of the activator molecules.
Synaptic plasticity, the activity-dependent change in the strength of neuronal connections, is a cellular mechanism proposed to underlie memory storage. One type of synaptic plasticity is long term potentiation (LTP), which displays physiological properties that are highly suggestive of information storage. Because of the role of the hippocampus in memory, LTP in the hippocampus is studied as a model of cellular properties underlying memory
The induction of long-lasting forms of LTP requires interaction among calcium-activated pathways and metabotropic-receptor-activated pathways, but the interactions among these pathways depend on the extent to which signals are spatially restricted to subcellular compartments. The production of diffusible second messengers facilitates interactions, but interferes with signaling specificity
Two basic mechanisms have been proposed for compartmentalization of signaling molecules: diffusional barriers and organization into multi-enzyme signaling complexes. Diffusional barriers in neurons are best exemplified by dendritic spines
Though PKA-dependent LTP requires an anchored pool of PKA
Previous experiments showed that anchoring of PKA was necessary for LTP induced with four trains of 100 Hz stimulation applied with a 300 s interval, but they did not demonstrate whether PKA needs to be anchored near its target molecules, such as the AMPA receptor GluR1 subunit, or near a source of activator molecules, such as adenylyl cyclase that produces cAMP. Thus, to evaluate which of these two possible functions of PKA anchoring in four-train LTP is more important, the signaling pathways that underlie synaptic plasticity in hippocampal CA1 pyramidal neurons (
(A) Diagram of postsynaptic signaling pathways. Each arrow is modeled with one or more bimolecular or enzyme reactions. Diffusion is not illustrated in this diagram. (B) Morphology of dendrite with attached spine and location of calcium influx in the model. Dendritic subvolumes are cuboids, whereas the spine subvolumes are either cylindrical or conical, as portrayed. Dotted lines show part of the compartmentalization. Subvolumes adjacent to the top and bottom surface of the dendrite are considered submembrane subvolumes. Other dendritic subvolumes are part of the cytosol. Calcium injection in a focal dendritic region represents influx through voltage dependent calcium channels. Calcium injection in the PSD represents influx through NMDA receptors. Diffusion is two-dimensional in the dendrite and one-dimensional in the spine, with reflective boundary conditions. (C) Morphology of dendrite with multiple spines used for evaluating spatial specificity. Stimulated spines are indicated by arrows. The different colored subvolumes serve to illustrate the boundaries.
PKA is located either in the spine head or a focal dendritic area. Similarly adenylyl cyclase (AC) is located either in the spine head or a focal dendritic area. D1R and G proteins are colocalized with AC in every case. GluR1 receptors are in the PSD compartment of the spine head for each case. Location and quantity of calcium influx (
Prior to exploring PKA location, we first investigated the effect of adenylyl cyclase location on cAMP gradients. Simulations were performed with the dopamine D1 receptor and adenylyl cyclase colocalized either to the spine head or to the dendrite submembrane region, these two locations being suggested by ultrastructual analysis of dopamine receptors
Simulations show that localization of dopamine D1 receptor and adenylyl cyclase in the spine leads to higher cAMP in response to stimulation (
(A) Calcium gradient between spine and dendrite. Stimulation consists of 100 pulses of calcium influx (with 10 ms interval) both through the spine PSD and in a focal dendrite region. The gradient of calcium from the spine to the dendrite is similar to that measured experimentally
PKA is compartmentalized to different subcellular locations through interaction with various A-kinase anchoring proteins
To explore whether anchoring PKA near its activators or near its targets is more important in the induction of four-train LTP at Schaffer collateral CA1 synapses, PKA was either localized to the spine head, or placed in a focal region of the dendrite submembrane. We simulated these two spatial variations of PKA with the two spatial variations of adenylyl cyclase (
With adenylyl cyclase located in the spine, PKA anchored in the spine produces a greater activity than PKA anchored in the dendrite (
(A) With AC in the spine, PKA activity is greater when PKA is anchored in the spine (red trace), than when PKA is anchored in the dendrite (pink trace). (B) With AC located in the dendrite (green and blue traces), the effect of PKA anchoring is not apparent. (C) Effect of colocalization is more apparent when averaging over five trials. The quantity of free PKA catalytic subunit is greater when PKA is colocalized with AC in the dendrite (green trace) than when PKA is separated from the AC (blue and pink traces). (D) Total PKA activity (calculated as area under the curve describing concentration of the free catalytic subunit of PKA), reveals that colocalization of AC and PKA produces significantly greater PKA activity than when AC and PKA are anchored apart.
Another measure of PKA activity is phosphorylation level of downstream targets, of which four (out of many) are included in the model. Three of the PKA targets, phosphodiesterase types 4B and 4D, and inhibitor-1, are distributed throughout the neuron, whereas one of the PKA targets, the AMPA receptor GluR1 subunit, is located exclusively in the post-synaptic density of the spine. Inhibitor-1 is important because its phosphorylation level increases with LTP induction
The location of PKA and adenylyl cyclase modulates the level of phospho-inhibitor 1 (
(A1) Phospho-inhibitor-1 is greatest when PKA is colocalized with adenylyl cyclase (AC) in the spine head (red trace) and second largest when PKA is colocalized with AC in the dendrite (green trace). The early decrease in phosphorylation is caused by transient, calcium activation of calcineurin. (A2) Bar graph shows mean and s.e.m. of phospho-inhibitor-1 (n = 5 for each condition). Colocalization of AC and PKA produces significantly greater phospho-inhibitor-1 than when AC and PKA are anchored apart. (B1) Phosphorylation of PDE4s by PKA is greatest when PKA is colocalized with cAMP production either in the spine or in the dendrite. Phospho-PDE4 is the sum of phospho-PDE4B and phospho-PDE4D. (B2) The mean and s.e.m. for phospho-PDE4 represents the total activity (area under the curve) of phosphodiesterase type 4B and type 4D. (C1) Fraction of GluR1 phosphorylated on Ser845 is greatest when PKA is colocalized with both cAMP production in the spine and with the GluR1 target. (C2) The mean and s.e.m. for phospho-GluR1-S845 are calculated over 5 trials.
Two additional PKA targets in the model are phosphodiesterase types 4B and 4D. Anchoring PKA produces a change in phosphorylation of phosphodiesterases (
To better assess the importance of PKA proximity to source versus target molecules, GluR1 phosphorylated on Ser845 is analyzed because it is confined to the post-synaptic density of the spine.
Black traces shows the average of 5 trials which differ only in the random seed used to start the simulations. (A) When PKA and adenylyl cyclase are colocalized in the spine, GluR1 phosphorylation increases for each trial. (B,C) When PKA is separated from adenylyl cyclase, most trials show a decrease in GluR1 phosphorylation; but some trials show an increase. (D) When PKA is colocalized with adenylyl cyclase in the dendrite, most trials show an increase in GluR1 phosphorylation; but some trials show a decrease.
These results are robust to variations in parameters. Diffusion constants
Spine morphology varies widely in hippocampal CA1 dendrites
Longer spine neck length leads to an increase in cAMP(A), which is accompanied by larger phosphorylation of inhibitor-1 (B), and greater quantity of free PKA catalytic subunit (C).
Experiments show that long-lasting LTP induced with four spaced trains of synaptic stimulation is impaired in the presence of Ht31 peptide, which competes for PKA anchoring
The simulation shows that the amount of free PKA catalytic subunit, phosphorylation of inhibitor-1 and GluR1 phosphorylated on Ser845 are reduced by 30–40% (
(A) Ht31 disruption of PKA anchoring decreases PKA activity and phosphorylation of downstream targets in the model. The decrease in PKA activity (PKA catalytic subunit, quantity of phospho-inhibitor-1, or fraction of phospho-GluR1-S845) is quantified as ratio of those values when PKA is diffusely distributed versus colocalized with adenylyl cyclase in the spine head. (B) Experimental test of model prediction. Long-lasting synaptic potentiation is induced using forskolin (50 µM), which is delivered for 15 minutes after 20 minute baseline recording. (B1) Forskolin-induced synaptic potentiation is impaired in mice expressing Ht31. The maintenance of synaptic potentiation is impaired 2 hours after the drug treatment in Ht31 (squares) compared with wildtype (triangles) (p = 0.012). (B2) The impairment in forskolin induced potentiation is rescued in the presence of IBMX, which inhibits phosphodiesterases. There is no difference in fEPSP between Ht31 and wildtype animals 2 hours after drug treatment (p = 0.65). (C) Forskolin-induced S845 phosphorylation is impaired in mice expressing Ht31. Representative blots for S845 and GluR1 are shown at the top. The bottom graph shows the mean quantity of phosphorylated S845 on GluR1, normalized by dividing by the total GluR1 levels. Ht31 expression did not affect basal S845 phosphorylation (p = 0.79, N = 10 per genotype). In contrast, forskolin induced S845 phosphorylation was reduced in mice expressing Ht31 (p = 0.03, N = 10 per genotype).
Collectively, the simulation results suggest that PKA needs to be near adenylyl cyclase, to be surrounded by a high concentration of cAMP, because phosphodiesterase activity lowers the cAMP concentration as it diffuses away from the adenylyl cyclase
To test the computational prediction that PKA anchoring close to the source of cAMP is critical in synaptic plasticity, we use forskolin to induce synaptic plasticity in mice expressing Ht31 peptide in the hippocampus and in wildtype controls. Previous research shows that forskolin, which elevates cAMP by direct activation of adenylyl cyclase, induces PKA-dependent LTP in wildtype mice
In a second set of slices, the quantity of phosphorylated S845 on GluR1, relative to total GluR1 levels, was measured 15 minutes after bath application with forskolin, both in wildtype and Ht31 mutant mice (
Spatial specificity of signaling and synaptic plasticity is critical for information processing, in particular for a neuron to discriminate between different patterns of input. To address whether cAMP and PKA activity exhibit spatial specificity, simulations were repeated in a 20 µm long dendrite with multiple spines (
(A) Concentration of cAMP (A1) and calcium (A2) in spines. Traces for the stimulated spines are toward the back; not all spines are illustrated. The concentration is highest in the stimulated and adjacent spines. (B) Concentration of cAMP and phospho-inhibitor versus time and space. The y-axis has been flipped, with 0 µm at the top to enhance correspondence with (A). Concentration is indicated by scale bar on the right. (B1) shows that cAMP exhibits spatial specificity. Arrows from traces in A1 to y-axis of B1 demonstrates spatial correspondence. (B2) shows that phospho-inhibitor-1 does not exhibit spatial specificity at this scale. (C) Time slices shortly after the stimulation at 10 s, 90 s and 170 s plotted against distance from the stimulated end of the dendrite. (C1) cAMP concentration exhibits spatial specificity, and does not increase with subsequent trains. (C2) Phospho-inhibitor-1 increases with subsequent trains, but does not exhibit spatial specificity.
PKA is one of the key molecules in the intracellular signaling networks mediating a long lasting form of LTP in the CA1 region of the hippocampus induced by four spaced trains of high frequency stimulation. AKAPs spatially restrict PKA signaling pathways through the organization of macromolecular complexes that effectively colocalize activators and effectors of enzymes. Compartmentalization of signaling microdomains by AKAPs may be one mechanism allowing spatial specificity of LTP.
We investigated whether the critical function of AKAPs is to localize PKA near target proteins or near the source of cAMP, using a multi-compartmental stochastic reaction-diffusion model of the signaling pathways leading to PKA activation in hippocampal CA1 pyramidal neurons. Simulations show that PKA anchoring near the source of cAMP and near specific targets both enhance PKA activity; however, anchoring near the source of cAMP dominates. PKA phosphorylation of GluR1 was greater when the PKA holoenzyme was colocalized with adenylyl cylcase in the dendrite than when the PKA holoenzyme was colocalized in the spine with GluR1, but apart from the dendritic adenylyl cyclase. Experiments confirmed this model prediction by demonstrating that forskolin-induced GluR1 phosphorylation was greater in wildtype mice than in mice which express Ht31 peptide. The ideal test of the model prediction would be imaging of cAMP concentration and PKA activity simultaneously (e.g. using both an Epac FRET probe and an AKAR FRET probe
PKA anchoring near adenylyl cyclases by AKAPs is crucial for PKA signaling due to phosphodiesterases, which produce microdomains of cAMP near the adenylyl cyclase.
In other systems, phosphodiesterases produce microdomains of elevated cAMP near the adenylyl cyclase, and prevent the widespread elevation of cAMP elsewhere in the cell
The rescue of LTP with phosphodiesterase inhibitors emphasizes the importance of inactivation mechanisms as opposed to diffusional barriers for signaling specificity. The characteristic decay length of a molecule's concentration gradient is governed by the diffusion constant of the molecule as well as the inactivation rate
Though our simulations anchored all of the PKA in a single location, these different pools of anchored PKA probably coexist in a single neuron. Diverse pools of PKA may phosphorylate different proteins in different compartments of the neuron, including the nucleus. Thus, PKA anchored in the spine may phosphorylate proteins in the spine head, of which GluR1 S845 is an example used in our simulations. Similarly, PKA anchored in the dendrite may be more important for phosphorylating molecules in the dendrite; and PKA anchored near the nucleus may be critical for control of gene transcription. The purpose of simulating the anchoring of PKA in a single location was to evaluate whether individual pools of PKA are spatially restricted. Similarly, anchoring proteins have some degree of mobility, and not all of the PKA or adenylyl cyclase is anchored to AKAPs. The mobility of the AKAP bound to both adenylyl cyclase and PKA will not alter the colocalization of PKA with adenylyl cyclase. Nonetheless, allowing for partial mobility may decrease the effect of anchoring near PKA targets in the model and may decrease the difference between colocalized and non-colocalized cases. Therefore, the rationale for completely immobilizing all of the PKA and adenylyl cyclase was to delineate which function of anchoring is most critical. One additional assumption in these simulations is that Ht31 peptide produces a uniform distribution of PKA. Imaging of PKA location in the AKAP5 knockout
The targets of PKA activity included in the model are a subset of known proteins phosphorylated by PKA. Phosphorylation of GluR1, either on S845 by PKA or on S831 by other kinases, is sufficient to support enhanced AMPA receptor conductance
Because the induction of LTP involves complex networks of intracellular signaling pathways, computational models have been developed to gain an understanding of events leading to LTP. Many of these models explain the temporal sensitivity of long term potentiation and depression, but very few have investigated spatial specificity or sensitivity to spatial pattern
Spatial, stochastic simulations were critical to the results presented. In particular, the simulations revealed that GluR1 phosphorylation on Ser845 exhibits large fluctuations, both within trials, and between trials. In general, the stochastic fluctuations were large relative to the mean when the number of molecules was low, as compared to molecules which had a high concentration. Thus, the fluctuations in GluR1 phosphorylation on Ser845 and PKA activity were greater than the fluctuations in phospho-inhibitor 1. The large within trial variation also lead to a variation between trials: in some trials GluR1 phosphorylation on Ser845 increased, and in some trials it decreased. The average over multiple trials reduced the stochastic variation, and better represented the results that would obtain when measuring hundreds of synapses using field potentials. The variability in individual trials may correspond to the variability observed in experiments when measuring few synapses
Because LTP involves spatially-restricted biochemical reactions, spatial modeling was required to investigate the effect of molecule anchoring on enzyme activation. The locally high calcium concentration in the spine was due to the diffusional barrier of the spine neck coupled with strong inactivation mechanisms. Diffusion was required for interaction between the catalytic subunit of PKA and inhibitor-1, and, in some cases, cAMP activation of PKA. Though diffusion coefficients are difficult to determine precisely (range for cAMP of 100–700 µm2/sec in vitro) due to the difficulty of measurements in vivo, we demonstrated that out simulation results are robust to variations of the diffusion coefficients.
Evidence suggests that anchoring of several other molecules is important for synaptic plasticity. Anchoring of calcineurin by AKAP5 plays a role in LTD
Additional evidence suggests that PKA is critical for synaptic tagging
All research with animals was consistent with NIH guidelines and approved by the IACUC at the University of Pennsylvania.
The multi-compartment, computational model (
Because calcium is crucial for activation of adenylyl cyclase, calcium dynamics were adjusted to emulate experimental observations
Molecules were either diffusible, non-diffusible that were evenly distributed, or non-diffusible that were anchored to specific regions. The diffusible molecules included cAMP, ATP, all forms of calmodulin, CaMKII, inhibitor-1 and the catalytic subunit of PKA. The anchored molecules included the dopamine D1 receptor, G protein, adenylyl cyclase, PKA, phosphodiesterases and AMPA receptors. Because G proteins have limited mobility in the membrane
A set of chemical reactions (
Reaction Equation | kf (nM−1 s−1) | kb (s−1) | kcat (s−1) |
Da+R⇌DaR | 0.0011111 | 10 | |
DaR+Gαβγ⇌DaRGαβγ→DaRGβγ+GαGTP | 6.0E-04 | 0.001 | 20 |
Gαβγ+R⇌GαβγR | 6.0E-05 | 3.00E-04 | |
GαβγR+Da⇌DaRGαβγ→DaRGβγ+GαGTP | 0.0033333 | 10 | 20 |
DaRGβγ→DaR+Gβγ | 80 | ||
GαGTP→GαGDP | 10 | ||
GαGDP+Gβγ→Gαβγ | 100 | ||
GαGTP+AC1⇌AC1GαGTP | 0.0385 | 10 | |
AC1GαGTP+CaMCa4⇌AC1GαGTP_CaMCa4 | 0.012 | 0.9 | |
AC1GαGTP_CaMCa4+ATP⇌AC1GαGTP_CaMCa4_ATP→AC1GαGTP_CaMCa4+cAMP | 0.01 | 2273 | 28.42 |
AC1+CaMCa4⇌AC1CaMCa4 | 0.006 | 0.9 | |
AC1CaMCa4+ATP⇌AC1CaMCa4_ATP→AC1CaMCa4+cAMP | 0.01 | 2273 | 2.843 |
AC8+CaMCa4⇌AC8CaMCa4 | 0.00125 | 1 | |
AC8CaMCa4+ATP⇌AC8CaMCa4_ATP→AC8CaMCa4+cAMP | 0.01 | 2273 | 2.843 |
PKA+2cAMP⇌PKAcAMP2 | 8.70E-05 | 0.02 | |
PKAcAMP2+2cAMP⇌PKAcAMP4 | 1.15E-04 | 0.2 | |
PKAcAMP4⇌R2C_cAMP4+PKAc | 0.038 | 0.016 | |
R2C_cAMP4⇌PKAr+PKAc | 0.152 | 0.004 | |
PDE1+CaMCa4⇌PDE1CaMCa4 | 0.1 | 1 | |
PDE1CaMCa4+cAMP⇌PDE1CaMCa4cAMP→PDE1CaMCa4+AMP | 0.0046 | 44 | 11 |
AMP→ATP | 1 | 0 | |
PDE4B+cAMP⇌PDE4BcAMP→PDE4B+AMP | 0.03038 | 77.78 | 19.44 |
PKAc+PDE4B⇌PKAcPDE4B→PKAc+ |
0.00428 | 5.6 | 1.25 |
0.25 | |||
0.03038 | 77.78 | 38.89 | |
PDE4BcAMP+PKAc⇌PKAcPDE4BcAMP→ |
0.00428 | 5.6 | 1.25 |
PDE4D+cAMP⇌PDE4DcAMP→PDE4D+AMP | 0.01296 | 60.14 | 15.03 |
PKAc+PDE4D⇌PKAcPDE4D→PKAc+ |
0.00428 | 5.6 | 1.25 |
0.25 | |||
0.01296 | 60.14 | 30.06 | |
PDE4DcAMP+PKAc⇌PKAcPDE4DcAMP→ |
0.00428 | 5.6 | 1.25 |
PKAcAMP4+PDE4B⇌PKAcAMP4PDE4B | 6.25E-05 | 5.44E-03 | |
PKAcAMP4+PDE4D⇌PKAcAMP4PDE4D | 6.25E-05 | 5.44E-03 | |
PKAcAMP4PDE4B⇌R2C_cAMP4+PKAcPDE4B | 0.38 | 0.016 | |
PKAcAMP4PDE4D⇌R2C_cAMP4+PKAcPDE4D | 0.38 | 0.016 |
Reaction Equation | kf (nM−1 s−1) | kb (s−1) | kcat (s−1) |
CaM+2Ca⇌CaMCa2 | 0.006 | 9.1 | |
CaMCa2+2Ca⇌CaMCa4 | 0.1 | 1000 | |
CaM+PP2B⇌PP2BCaM | 0.0046 | 0.0012 | |
PP2BCaM+2Ca⇌PP2BCaMCa2 | 0.006 | 0.91 | |
PP2BCaMCa2+2Ca⇌PP2BCaMCa4 | 0.1 | 1000 | |
CaMCa2+PP2B⇌PP2BCaMCa2 | 0.046 | 0.0012 | |
CaMCa4+PP2B⇌PP2BCaMCa4 | 0.046 | 0.0012 | |
CaMCa4+CaMKII⇌CaMKIICaMCa4 | 0.01 | 3 | |
CaMKIICaMCa4+CaMKIICaMCa4⇌Complex | 1.00E-04 | 10 | |
pCaMKIICaMCa4+CaMKIICaMCa4⇌pComplex | 1.00E-04 | 10 | |
pCaMKIICaMCa4+Complex⇌pCaMKIICaMCa4+pComplex | 1.00E-04 | ||
CaMKIICaMCa4+Complex⇌CaMKIICaMCa4+pComplex | 1.00E-04 | ||
Complex+Complex⇌Complex+pComplex | 0.01 | ||
Complex+pComplex⇌pComplex+pComplex | 0.03 | ||
pCaMKIICaMCa4⇌CaMCa4+pCaMKII | 8.00E-04 | 0.01 | |
pCaMKII+PP1⇌pCaMKIIPP1→PP1+CaMKII | 6.00E-07 | 0.34 | 0.086 |
pCaMKIICaMCa4+PP1⇌pCaMKIICaMCa4PP1→PP1+CaMKIICaMCa4 | 6.00E-07 | 0.34 | 0.086 |
I1+PKAc⇌I1PKAc→Ip35+PKAc | 0.0014 | 5.6 | 1.4 |
I1+PKAcAMP4⇌I1PKA cAMP4 | 1.40E-04 | 5.6 | |
I1PKA cAMP4⇌R2C_ cAMP4+PKAcI1 | 0.38 | 0.016 | |
Ip35+PP1⇌Ip35PP1 | 0.001 | 0.0011 | |
Ip35+PP2B⇌Ip35PP2B→I1+PP2B | 0.00233 | 11.2 | 2.8 |
Ip35PP1+PP2B⇌Ip35PP1PP2B→I1+PP1PP2B | 0.00233 | 11.2 | 2.8 |
PP1PP2B→PP1+PP2B | 1.5 |
Reaction Equation | kf (nM−1 s−1) | kb (s−1) | kcat (s−1) |
GluR1+PKAc⇌GluR1−PKAc .→pS845GluR1+PKAc | 0.00402 | 24 | 6 |
PKAcAMP4+GluR1⇌GluR1−PKAcAMP4 | 4.02E-04 | 24 | |
GluR1−PKAcAMP4⇌R2C_cAMP4+GluR1−PKAc | 0.38 | 0.016 | |
GluR1+CaMKIICaMCa4⇌GluR1−CaMKIICaMCa4→pS831GluR1+CaMKIICaMCa4 | 2.224E-05 | 1.6 | 0.4 |
GluR1+pCaMKIICaMCa4⇌GluR1−pCaMKIICaMCa4→pS831GluR1+pCaMKIICaMCa4 | 2.780E-05 | 2 | 0.5 |
GluR1+pCaMKII⇌GluR1−pCaMKII→pS831GluR1+pCaMKII | 2.224E-05 | 1.6 | 0.4 |
pS845GluR1+CaMKIICaMCa4⇌pS845GluR1−CaMKIICaMCa4→pS845pS831GluR1+CaMKIICaMCa4 | 2.224E-05 | 1.6 | 0.4 |
pS845GluR1+pCaMKIICaMCa4⇌pS845GluR1−pCaMKIICaMCa4→pS845pS831GluR1+pCaMKIICaMCa4 | 2.780E-05 | 2 | 0.5 |
pS845GluR1+pCaMKII⇌pS845GluR1−pCaMKII→pS845pS831GluR1+pCaMKII | 2.224E-05 | 1.6 | 0.4 |
pS831GluR1+PKAc⇌pS831GluR1−PKAc→pS845pS831GluR1+PKAc | 0.004 | 24 | 6 |
PKAcAMP4+pS831GluR1⇌pS831GluR1−PKAcAMP4 | 4.02E-04 | 24 | |
pS831GluR1−PKAcAMP4⇌R2C_cAMP4+pS831GluR1-PKAc | 0.38 | 0.016 | |
pS845GluR1+PP1⇌pS845GluR1−PP1→GluR1+PP1 | 8.700E-04 | 0.68 | 0.17 |
pS845pS831GluR1+PP1⇌pS845pS831GluR1−PP1→pS831GluR1+PP1 | 8.750E-04 | 1.4 | 0.35 |
pS831GluR1+PP1⇌pS831GluR1−PP1→GluR1+PP1 | 8.750E-04 | 1.4 | 0.35 |
pS845GluR1+PP2BCaMCa4⇌pS845GluR1−PP2B→GluR1+PP2BCaMCa4 | 0.00201 | 8 | 2 |
Reaction Equation | kf (nM−1 s−1) | kb (s−1) | kcat (s−1) |
Ca+pmca⇌pmcaCa→pmca+Ca_ext | 0.05 | 7 | 3.5 |
Ca+ncx⇌ncxCa→ncx+Ca_ext | 0.0168 | 11.2 | 5.6 |
Ca_ext⇌Ca | 0.0017 | ||
Ca+Calbindin⇌CalbindinCa | 0.028 | 19.6 | |
Ca+CaB→CaBCa | 0.028 | ||
L⇌L_ext | 2 | 0.000020 |
To compensate for the inability to implement the known voltage dependent control of calcium dynamics that was beyond the scope of the present research, an irreversible calcium buffer (CaB) was injected after calcium influx ceased for the sole purpose of returning calcium concentration to resting level with a time course similar to experiments.
Molecule Name | General Cytosol (nM) |
Ca | 51 |
Ca_ext | 2015100 |
Calbindin | 149590 |
CalbindinCa | 11348 |
L | 10.379 |
L_ext | 1019100 |
ATP | 1997200 |
cAMP | 60 |
PDE1 | 3371 |
PDE1CaMCa4 | 574 |
PDE1CaMCa4cAMP | 3 |
AMP | 839 |
CaM | 9126 |
CaMCa2 | 315 |
CaMCa4 | 2 |
PP2BCaM | 2960 |
PP2BCaMCa2 | 1020 |
PP2BCaMCa4 | 6 |
CaMKII | 19266 |
CaMKII CaMCa4 | 112 |
pCaMKII CaMCa4 | 598 |
pCaMKII | 26 |
I1 | 530 |
I1PKAc | 2 |
Ip35 | 6 |
PP1 | 587 |
Ip35PP1 | 884 |
PDE4B | 902 |
PDE4BcAMP | 24 |
PKAcPDE4B | 9 |
pPDE4B | 48 |
PDE4D | 915 |
PDE4DcAMP | 13 |
PKAcPDE4D | 9 |
pPDE4D | 45 |
Molecule Name | PSD (nM) |
pmca | 65.86 |
pmcaCa | 17.79 |
ncx | 2996 |
ncxCa | 157 |
|
|
pmca | 329.28 |
pmcaCa | 88.94 |
ncx | 0 |
ncxCa | 0 |
|
|
GluR1 | 9756 |
pS845GluR | 1580 |
pS831GluR1 | 279 |
pS845GluR -PP1 | 836 |
pS831GluR1-PP1 | 93 |
Anchored Molecules |
Spine Cytosol |
Focal Dendrite Submembrane (picoSD) |
R | 1012 | 110 |
G | 38427 | 4192 |
GR | 6523 | 712 |
GaGTP | 15 | 2 |
Gbg | 483 | 53 |
AC1 | 34078 | 3717 |
AC1GaGTP | 151 | 16 |
AC1GaGTPCaMCa4ATP | 60 | 3 |
AC1CaMCa4 | 377 | 41 |
AC1CaMCa4ATP | 3397 | 371 |
AC8 | 37098 | 4047 |
AC8CaMCa4 | 60 | 7 |
AC8CaMCa4ATP | 649 | 71 |
PKA | 18666 | 2698 |
PKAcAMP2 | 7225 | 1044 |
PKAcAMP4 | 319 | 46 |
PKAr | 387 | 56 |
PKAc | 365 | 53 |
R2C_cAMP4 | 205 | 30 |
PKAcAMP4_PDE4B | 160 | 23 |
PKAcAMP4_PDE4D | 205 | 20 |
Molecules not listed have initial concentrations of 0. A single molecule produces a concentration of 28 nM in the dendrite subvolumes of the single spine morphology; thus molecule concentrations less than 28 nM indicate that some subvolumes contained a single molecule and some did not, to produce the indicated concentration averaged over the entire morphology. General cytosol means that molecules populated the entire morphology.
*Molecules initialized in the dendrite submembrane are specified in picoMoles per µm2 (picoSD).
#Molecules initialized in the spine cytosol were excluded from the PSD, except for PKA species.
&Only one of these concentrations applied, depending on whether molecules were anchored in the spine, or in the dendrite.
Molecule Name | Diffusion Constant ( |
Calbindin | 9.3 |
Calbindin·Ca | 9.3 |
CaB·Ca | 10 |
CaB | 10 |
Da | 111.3 |
ATP | 74.7 |
AMP | 85.5 |
cAMP | 86.4 |
CaM | 11 |
CaMCa2 | 11 |
CaMCa4 | 11 |
CaMKII·CaMCa4 | 3.6 |
pCaMKII·CaMCa4 | 3.6 |
pCaMKII | 3.6 |
PKAC | 8.1 |
Inhibitor-1 | 10.6 |
Inhibitor-1· PKAC | 10.6 |
Phospho-Inhibitor-1 | 10.6 |
Note: Molecules not listed above do not diffuse; their diffusion constants are zero.
The multi-compartment morphology (as default) included a 5 µm long segment of dendrite (0.6 µm wide by 0.4 µm depth) with a single spine. The spine consisted of spine head (0.6 µm diameter), neck (0.2 µm diameter and 0.3 µm long) and post-synaptic density (PSD;
The morphology was subdivided into multiple compartments in order to simulate the reactions and diffusion mesoscopially. The dendrite was subdivided into 200 subvolumes of dimension 0.12×0.125×0.4 µm3, allowing 2-dimensional diffusion The spine was subdivided into 0.1 µm cylindrical or conical slices, yielding 3 spine neck subvolumes, 2 spine head subvolumes and 1 PSD subvolume, permitting 1-dimensional diffusion. One layer of dendritic subvolumes on either edge of the dendrite was considered to be the submembrane region. The 0.12 µm width submembrane region with 0.36 µm width cytosol gave the same ratio of submembrane to cytosol volume as a cylinder with 0.07 µm width submembrane region. For simulations of the 20 µm long dendrite with 11 spines, all molecules were anchored in the spine head; thus the dendrite was subdivided into 300 subvolumes of dimension 0.2×0.2×0.4 µm3 and two spines located at one end of the dendrite were stimulated. Empirically, these subvolume sizes were both large enough to meet the well-stirred criterion
Stimulation for long-lasting LTP induction consisted of four 1 sec trains of 100 Hz stimulation. Each stimulation pulse consisted of a 0.7 msec influx of calcium (62.5 molecules/msec) which accumulated during the train to approach a plateau
We used a computationally efficient, Monte Carlo (stochastic) reaction-diffusion algorithm, called NeuroRD
We used 3–5 months old Ht31(1) mice which express Ht31 peptide in the hippocampus
For measurements of GluR1 phosphorylation, directly after forskolin or vehicle treatment, mouse hippocampal slices were flash frozen and stored at −80°C. Slices were lysed in buffer containing 50 mM Tris, pH 9; 1% Sodium deoxycholate, 50 mM sodium fluoride, 20 mM EDTA, 40 µM β-glycerophosphate, and 1∶100 dilutions of protease and phosphatase inhibitors. After adding NuPAGE LDS Sample Buffer (Invitrogen), 20 µg of protein was resolved using NuPAGE 4–12% Bis-Tris gels and NuPAGE MOPS Running Buffer (Invitrogen) for 2 hrs at 120 V. The separated proteins were transferred to PVDF membranes (Invitrogen) at 30 mA over night at 4°C. After blocking with 5% milk in Tris-buffered saline containing 0.1% (v/v) Tween-20 (TBST) for 1 hr with gentle shaking, membranes were incubated with antibodies directed specifically against beta-tubulin (Sigma, 1∶10,000, mouse) and phospho-S845 (Millipore, 1∶1,000, rabbit) over night at 4°C. The membranes were washed 3 times for 10 minutes in TBST. Horseradish peroxidase (HRP)-conjugated anti-rabbit or anti-mouse (Santa Cruz Biotechnology) were added 1∶1,000 in 5% milk in TBST and incubated for 2 hrs at 4°C. The membranes were washed as previously described, then incubated with Amersham ECL Western Blotting Detection Regents (GE Healthcare) for one minute. Excess ECL substrate was blotted away and the signal was detected on film (Kodak BioMax) for several time points ranging from 5 seconds to 15 minutes. Afterwards, the membranes were stripped using 10 mL Restore Western Blot Stripping Buffer (Thermo Scientific) for 20 minutes at room temperature. The membranes were washed 3 times for 10 minutes in TBST and blocked with 5% milk in TBST for 1 hr. The membranes were then incubated with total GluR1 antibody (Millipore, 1∶1000, mouse) over night at 4°C. Membranes were incubated with HRP-conjugated anti-mouse, incubated with ECL and developed following the procedure as described above. Densitometry was performed using mean gray values on ImageJ software.
The model simulations and the role of anchoring were evaluated from the total quantity (representing both amplitude and duration of the elevation) of the enzymes PKA catalytic subunit, phosphodiesterase type 4B, and phosphodiesterase type 4D, and the mean quantity of phosphorylated inhibitor-1, and GluR1 phosphorylated on Ser845. Simulations were repeated due to stochastic variability, and the procedure General Linear Models (SAS) was employed for statistical analysis of the simulation results. In order to protect against an elevated type I error due to multiple comparisons, post-hoc tests used planned comparisons only. The effect of PKA anchoring disruption by Ht31 peptide in FSK induced chemical LTP was analyzed using the last 20 minutes of the experimental recordings. The two-sided t-test procedure was used, including tests for equality of variance, separately for the IBMX condition and for the no IBMX condition. Western blots were analyzed by first calculating the quantity of GluR1 phoshorylation on S845 relative to total GluR1, and then using the procedure General Linear Models (SAS) followed by planned contrasts. For both experiments and model simulations, data were first tested for normality using the procedure univariate (SAS), and P>0.05 was considered not significant. Both the bar graphs summarizing model simulations and the fEPSP versus time traces display mean and S.E.M.
Robustness of results to parameters (A) Variations in diffusion constant. (A1) cAMP concentration is greater when adenylyl cyclase is anchored in the spine (red and pink traces), than when it is anchored in the dendrite (blue and green traces). DcAMP = 172.8 µm2/sec. (A2) PKA activity is greater when adenylyl cyclase and PKA are colocalized in the spine, similar to default cases. (B) Robustness to rate for dephosphorylation of GluR1 Ser845 by PP1. Colocalization of adenylyl cyclase with PKA still produces the greatest PKA activity (B1) and GluR1 phosphorylation on Ser845 (B2).
(JPG)