Bistability in the CaMKII Model

<div><p>CaMKII-thr286* indicates Thr286-phosphorylated CaMKII, and CaMKII-thr286*-thr305* indicates Thr286/Thr305-phosphorylated CaMKII.</p><p>(A) Schematic of CaMKII autophosphorylation in the PSD. Reactions (in bold) and PP1 concentrations are altered in the PSD from the basal model to achieve bistability. Block arrows indicate the CaMKII states that translocate. There are two shaded sets of molecules, indicating states that are summed to give rise to an enzyme activity. The Tot-CaM-CaMKII activity is the sum of concentrations of CaM-CaMKII and CaM–Thr286-phosphorylated CaMKII. The Aut-CaMKII activity is the sum of the calcium-autonomous states Thr286-phosphorylated and Thr286/Thr305-phosphorylated CaMKII.</p><p>(B) Bistability analysis. The Aut-CaMKII molecular species has been bifurcated into Aut-CaMKII enzyme, and Aut-CaMKII readout. The enzyme activity is buffered numerically (<i>x</i>-axis). The readout (<i>y</i>-axis) remains the sum of Thr286-phosphorylated and Thr286/Thr305-phosphorylated CaMKII. Fixed points are given by the intersection points of the amount of Aut-CaMKII with the 45° line. These fixed points indicate the number of Aut-CaMKII molecules that would exactly sustain their own activity through autophosphorylation. The upper and lower points are stable, and the middle point is the transition point.</p><p>(C) Time course of bistable response. The first arrow is a Ca²⁺ stimulus of 2.7 μM for 500 s that switches on the CaMKII bistable loop. The second arrow is a 5-fold increase in <i>k</i>_cat of PSD-localised PP1 for a period of 500 s, which switches CaMKII off.</p><p>(D) Parameter sensitivity analysis. Key parameters are scaled up and down and the model is tested for bistability. Most parameters can be varied 2-fold or more in either direction without the model losing bistability.</p><p>(E) Stochastic run showing stability in both high and low states, when PKA is buffered.</p><p>(F) Stochastic run showing spontaneous state flips in either direction, with the complete PKA model.</p><p>(G) Statistics of spontaneous state flips with the complete PKA model. Average turn on and turn off times are both over 15 h.</p></div

Simplified AMPAR Bistable Model

<div><p>IR represents internal receptor, MR represents synaptic-membrane-localised receptor and asterisks indicate phosphorylation at Ser845. PKA is protein kinase A.</p><p>(A) Complete reaction diagram.</p><p>(B) Bistability analysis for simplified model. AMPAR flux between the bulk AMPAR and the IR state from (A) is plotted against the total number of synaptic receptors (IR + IR* + IR** + MR + MR* + MR**). As seen in the complete AMPAR model in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-g005" target="_blank">Figure 5</a>B, there are two regions of receptor influx into the spine, at low and high numbers of synaptic AMPARs. The zero crossings are stable states where there is no net flux of receptor.</p><p>(C–F) Time courses of key molecules in simple model. After an initial settling period, PKA is raised to 40 molecules for 2,400 s to trigger receptor influx. After the system settles into the high state, PKA is set to zero molecules for 3,600 s, to return the system to basal levels. These stimuli are indicated by horizontal bars along the time axis.</p><p>(C) Internal receptor numbers. The number of receptors in the unphosphorylated form (IR) remains very close to the bulk receptor level except during transitions, when receptors enter or leave the system.</p><p>(D) Synaptic-membrane-bound receptor levels.</p><p>(E) Numbers of free PP1 decline sharply during the high state, because of enzyme saturation.</p><p>(F) Numbers of PP1 complexes with substrates. The high amount of PP1–MR** complex is complementary to the decline in free PP1, showing the saturation of the phosphatase.</p></div

Bistability for Tightly Coupled Switches

<div><p>(A) Schematic of PSD-localised PP1 acting on both CaMKII and AMPAR substrates in the PSD. The asterisks on CaMKII and AMPAR represent phosphate groups.</p><p>(B) Time course of response to Ca²⁺ (2.7 μM, 500-s duration), then cAMP (0.108 μM, 2,000-s duration) stimuli. The initial Ca²⁺ stimulus turns on CaMKII transiently, but it eventually returns to baseline. The subsequent cAMP stimulus turns on both switches.</p><p>(C) Time course of response to cAMP (0.108 μM, 2,000-s duration), then Ca²⁺ (2.7 μM, 500-s duration) stimuli. The initial AMPAR stimulus (cAMP elevation) is sufficient to turn both the AMPAR and the CaMKII switches on.</p><p>(D) Stochastic run in the low state. The figure illustrates a transient event that did not result in complete turn on.</p><p>(E) Stochastic run in the high state. There is a spontaneous turn off, but the average on time is over 100 h.</p></div

AMPAR Synaptic Membrane Localisation and Conductance in Response to Sustained Inputs

<div><p>Each panel is computed from a series of steady-state calculations where the activity of the selected input pathway was scaled with respect to its basal activity. The <i>x</i>-axis is this scaling ratio. The conductance is calculated as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-g003" target="_blank">Figure 3</a> and is expressed as the secondary <i>y</i>-axis, as a percentage of maximal conductance (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#s4" target="_blank">Materials and Methods</a>).</p><p>(A) Changing activity of CaMKII leads to small changes in synaptic membrane localisation of AMPARs, but phosphorylation of GluR1 on Ser831 gives a doubling of synaptic conductance when CaMKII activity is scaled above basal levels.</p><p>(B) Low concentrations of PKA result in reduced exocytosis of AMPAR. Basal concentrations of PKA (ratio ~ 1) are required to localise AMPAR to the synaptic membrane, and higher concentrations cause a conductance increase. This occurs because of phosphatase saturation leading indirectly to a rise in Ser831 phosphorylation due to CaMKII. The net effect is that changes in PKA activity can lead to a large change in AMPAR conductance in either direction.</p><p>(C) Changes in PP1 concentrations have little effect on AMPAR localisation. However, low PP1 leads to high phosphorylation of GluR1-Ser831 by CaMKII, and hence high conductance.</p><p>(D) Lower rates of receptor recycling to the internal pool lead to a small increase in synaptic membrane localisation. High rates bring most of the receptor to the internal pool.</p></div

Matching Models to Trafficking Time Course

<div><p>(A) AMPAR exocytosis time course; experiments from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-b10" target="_blank">10</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-b20" target="_blank">20</a>].</p><p>(B) AMPAR endocytosis time course; experiments from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-b10" target="_blank">10</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-b21" target="_blank">21</a>].</p><p>(C) CaMKII internalisation time course; experiments from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-b14" target="_blank">14</a>].</p><p>(D) CaMKII traffic to PSD; experiments from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010020#pcbi-0010020-b14" target="_blank">14</a>].</p></div

AMPAR and CaMKII Trafficking and Dependence on Steady Ca²⁺ Concentrations

<div><p>(A) Number of AMPARs in internal and synaptic membrane pools; AMPARs complexed to enzymes are not counted.</p><p>(B) Number of CaMKII molecules in the cytosol and PSD. The activity in the cytosol and PSD starts to rise at about 0.5 μM Ca²⁺, but translocation occurs around 1 μM.</p><p>(C) Conductance of membrane-inserted AMPARs. Receptor conductance is calculated by assuming that CaMKII phosphorylation of a single GluR1-Ser831 of the tetramer gives 1.5-fold basal conductance, and of two Ser831 gives 2-fold basal conductance. The conductance dips at around 300 nM Ca²⁺, when PP2B is active but CaMKII has yet to become fully active.</p></div

Nested Bistability for Weakly Coupled Switches

<div><p>(A) Schematic of independent PSD-localised PP1 enzyme activities for CaMKII and AMPAR. The two PP1 activities are labelled PP1-PSD-CaMKII and PP1-PSD-AMPAR, respectively. The asterisks represent phosphorylation.</p><p>(B) Time course of system response to Ca²⁺ (2.7 μM, 500-s duration), then cAMP (0.108 μM, 2,000-s duration) stimulus. The initial activation of CaMKII leads to a slow turn on of the AMPAR system.</p><p>(C) Time course of system response to cAMP (0.108 μM, 2,000-s duration), then Ca²⁺ (2.7 μM, 500-s duration) stimulus. First the AMPAR system turns on, then, following the Ca²⁺ stimulus, the CaMKII turns on. The conductance of the synapse has different levels in each of these states.</p><p>(D) Stochastic run for 60 h, showing resting, AMPAR only, and AMPAR + CaMKII activity states.</p></div