Initial concentrations.

<p>Initial concentrations.</p

Fractional activation of enzymes for different stimulations.

<p>All curves correspond to spine 559. A, 8 Hz; B, 20 Hz; C, 40 Hz; D, 40 Hz long stimulation. The long intervals between successive entries of calcium in the 8 Hz and 20 Hz stimulations allow CaMKII and PP1 to get activated (after calcium binds calmodulin). The number of phosphorylated AMPARs increases because CaMKII concentration is higher than PP1 concentration. The situation is different with the 40 Hz stimulation, where the first train is too short to activate CaMKII significantly, causing only a small increase. However, when the second train arrives, CaMKII is activated quicker than PP1, causing an increase of phosphorylated AMPARs.</p

Comparison of the event driven algorithm with while loops and different sparseness.

<p>A, comparison of the event driven algorithm with while cycles. B, comparison of the event driven algorithm with while loops under different sparseness. The event driven algorithm offers a significant improvement over the usage of a while loop with a small . The slight improvement of the while loop with and for the highest number of events is due to a different load on the cluster at the time the simulations were ran. B, scalability of the event algorithm with the increase of sparseness, compared to the while loop approach which cannot cope with it.</p

Synchronization principle.

<p>The dashed arrows refer to the variable exchanges from one simulator to the other. The solid arrows represent the time progression of the simulators. A, one synchronization loop. 1,2,3,4 represent the successive phases which are taking place at every synchronization cycle. B, repetition of the synchronization through several events. The brown boxes represent the synchronizations happening during one synchronization cycle. The duration of a synchronization is decided by the parameter. is the slow timescales simulator, is the fast timescales simulator.</p

Effect of stimulation frequency on AMPARs phosphorylation in the stimulated spine.

<p>The same amount of inputs are delivered for all the frequencies but <i>40 Hz long</i>. The lower frequencies are able to trigger a higher phosphorylation, and therefore a higher conductance of the AMPARs in response to the first train. However, in response to the second train the high frequencies can still trigger a comparable phosphorylation of the AMPARs, even if the inputs are delivered after a large amount of time due to the stiffness of the biochemical pathways.</p

Spines stimulated by the first and second trains of input.

<p>Upper left, the “500” series; bottom right the “1400” series. The red spines are the ones receiving the double trains, the green ones are the ones receiving only one train. The axes are in m.</p

Different responses of spines differentially located.

<p>d1 is the average for the spines of the “500” series, closer to the soma, in dendrite dend1_1_2, while d4 is the average for the spines of “1400”, farther from the soma, in dendrite dend4_1_2.</p

Additional parameters for the biochemical model.

<p>Additional parameters for the biochemical model.</p

Interaction between ion channels and biochemical signaling.

<p>DARPP-32 forms a complex with PP1 after having been phosphorylated by PKA (grey line). Two possible pathways can be activated according to the concentration of calcium: at low calcium concentration Calmodulin forms a complex with Calcineurin, dephosphorylating DARPP-32, releasing PP1 inhibition, with subsequent dephosphorylation of AMPARs (orange line). At high calcium concentration, the complex CaMKII/Calmodulin is able to phosphorylate AMPARs (yellow line). The calcium flux incoming from the ionic channels AMPARs, NMDARs and VGCCs is represented in light blue.</p

Parameters for the calcium channels.

<p>Parameters for the calcium channels.</p