Model validation of eCB-iSTD/DSI characteristics.

<p><i>Panel A:</i> eCB-iSTD measure in response to the administration of CB agonist WIN55,212 (Protocol 1) with simulation results in red and experimental results with error bars in blue from [?]. Plotted with a logarithmic scale for the x axis. <i>Panel B:</i> The DSI measure in response to post-synaptic depolarisation pulses (0.5–5 sec) (Protocol 2) with simulation results in red and experimental results with error bars in blue from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058926#pone.0058926-OhnoShosaku5" target="_blank">[78]</a>. <i>Panel C:</i> The DSI time course from the experiments <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058926#pone.0058926-OhnoShosaku2" target="_blank">[18]</a> (in blue) and the model simulations (in red) in response to a 5 sec depolarising pulse (Protocol 2). The amplitude (normalised to the value before depolarisation) of the IPSPs is plotted just before, during and after the depolarising pulse. Decay time constant: 12.81 sec, Peak latency value: 5.92 sec, Peak DSI value: 89.48% (relative amplitude 10.52%). <i>Panel D:</i> The calcium concentration time course (in red) from the model simulations in response to a 5 sec depolarising step (Protocol 2). The depolarising step starts at time 1 sec. The exponential fit to the calcium concentration decay from the peak amplitude is superimposed in black (decay time constant 5.43 sec).</p

Reduced eCB signalling model at central synapses underlying eCB-iSTD.

<p>Highlighting the main factors controlling the physiology of 2-AG at post-synaptic sites of generation and release as well as pre-synaptic signalling by CB receptors in hippocampus. 2-AG is synthesised in the post-synaptic (excitatory) cell when DAG is metabolised by DGL. One of the pathways that DAG can be produced is linked to the rise of intracellular calcium concentration, which leads to the production of DAG through an as-yet-unknown pathway. The main source of intracellular calcium post-synaptically is considered to be due to depolarisation () induced entry through L-type VGCCs. A minor source of Ca is due to the leak flux from the ER. Ca exits the cytoplasm through PMCA and SERCA pumps. Once 2-AG is synthesised, it is released by a putative eCB membrane transporter and activates CB receptors, found pre-synaptically (on the inhibitory cell). This results in the splitting of the G protein heterotrimer into G and G subunits. The G subunit directly inhibits the N-type VGCCs on the pre-synaptic membrane, which puts them into a reluctant state, resulting in the inhibition of GABA neurotransmitter release. 2-AG is then returned into the cells by an as-yet-unknown eCB transporter where most of it is degraded by MGL. Post-synaptically, 2-AG undergoes oxidation by COX-2. Additional information is included in the text. 2-AG: 2-arachidonoylglycerol, COX-2: Cyclooxygenase-2, DAG: Diacylglycerol, DGL: Diacylglycerol Lipase , : Membrane Depolarisation, ER: Endoplasmic Reticulum, MGL: Monoglyceride Lipase, PLC: Phospholipase C , PMCA: plasma membrane Ca ATP-dependent pumps, VGCC: Voltage-Gated Calcium Channel, SERCA: sarco/endoplasmic reticulum Ca ATP-dependent pumps.</p

Calcium buffering and extracellular calcium.

<p><i>Panel A:</i> The effect of varying the calcium buffering parameter on DSI for various depolarisation intervals 0.1–10 sec (see Protocol 4) plotted with a logarithmic scale for the x axis. Buffering () varies from 0.01–0.1 (equivalent to 99–90%) and is colour coded accordingly. <i>Panel B:</i> The effect of varying the extracellular calcium () parameter on DSI for various depolarisation intervals 0.1–10 sec (see Protocol 4) is plotted with a logarithmic scale for the x axis. Extracellular calcium varies from 500–5000 and is colour coded accordingly. It should be noted that in both Panels A and B the blue line represents the standard set of parameters (, ).</p

DSI dependence on calcium.

<p><i>Panel A:</i> Simulated peak calcium concentrations in response to various depolarisation durations (0.5–5 sec) with Protocol 2, plotted against the respective DSI measure for each depolarisation. <i>Panel B:</i> Experimental results from slices <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058926#pone.0058926-Wang1" target="_blank">[40]</a> showing the fitted Hill function (in blue) of the relation between calcium concentration and DSI. The light blue area indicates the range of maximum and minimum values for the fitted Hill function. The results from the model simulations obtained with Protocol 3 - case 1 are shown in black circles and for Protocol 3 - case 2 in red circles.</p

Dynamic Variables.

<p>The table describes all the dynamic variables of the model.</p

Post-synaptic Cell Parameters.

<p>The table describes the parameters for the post-synaptic cell model regarding the dynamics of the intracellular calcium, L-type VGCC, 2-AG synthesis and synapses.</p

Pre-synaptic Cell Parameters.

<p>The table describes the parameters for the pre-synaptic cell model regarding the CB receptor model.</p

DSI induction with various stimulation protocols.

<p><i>Panel A:</i> DSI is induced for various durations of stimulation (0.5–5 sec) with three different protocols; a depolarising voltage step to 0 mV, a 30 Hz train of current pulses (5 msec duration) and a 30 Hz train of action potentials on the excitatory synapse. <i>Panel B:</i> The DSI for all three protocols (depolarising voltage step to 0 mV in red, 30 current pulses in green and synaptic input in black) is superimposed on the experimental results from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058926#pone.0058926-OhnoShosaku1" target="_blank">[16]</a>, obtained for depolarising voltage steps of varying duration (in blue). <i>Panel C and D:</i> DSI is induced for various durations of stimulation (0.5–5 sec) with a train of current pulses, 5 msec duration, (Panel C) and a train of synaptic events (Panel D). The frequency of the stimulatory trains in both cases is varied from 5–100 Hz generating almost identical results (see Protocol 5).</p

DSI modulation by the timing of pre- and post- synaptic cells' activity.

<p><i>Panel A:</i> The illustration of the <i>in silico</i> experimental Protocol 8. A signal (1 sec long) arrives at both the inhibitory pre-synaptic cell (indicated by the cell I) and excitatory post-synaptic cell (indicated by cell E) and, thus, evoking a train of action potentials (black spikes). The signal arrives at the two cells with a time difference . As in experiments with pair recordings, a test current pulse of 0.2 Hz is also applied on the pre-synaptic cell, for assessment of DSI (indicated by the blue spikes). The pre-synaptic cell inhibits the post-synaptic cell whereas the post-synaptic cell under certain conditions mobilises eCBs, activates the CB receptor and as a result reduces the inhibition it receives. <i>Panel B:</i> The post-synaptic cell receives input always at sec and the pre-synaptic cell receives input at different times indicated by . The DSI magnitude is plotted (indicated by the open circles) versus the centre ( sec) of the time window within which the pre-synaptic cell receives input. The same protocol is applied to the two cells for different frequencies in the range of 30–50 Hz. Depending on the arrival time of the signal at the pre-synaptic cell, the modulation of DSI magnitude differs. When the two bursts coincide they cancel out and, hence, DSI is completely abolished. The maximal effect of DSI, other than this case, occurs with certain latency for the frequencies 30–50 Hz. The horizontal lines indicate the basal value on DSI in each frequency case (i.e. the DSI due to 1 sec firing of the post-synaptic cell with a given frequency, in the absence of input to the pre-synaptic cell). See the text for more information.</p

DSI modulation by the timing of pre- and post- synaptic cells' activity - Spotlight on 50 Hz case.

<p><i>Panel D</i>: Re-plotting the results from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058926#pone-0058926-g008" target="_blank">Figure 8</a> - Panel B for the case in which the 1 sec input to the two cells is 50 Hz. Roman numbers I-XV mark each different sub-case of pre-synaptic input at a different time relative to the input at the post-synaptic cell. The horizontal line indicates the basal value on DSI for the 50 Hz Case. <i>Panels A-C and E-H</i>: Plots of the fraction of willing Ca channels () in blue, the CB receptor activation () in purple and the amplitude of the IPSPs () in black dots, for a few of the sub-cases indicated by roman numbers I-XV on Panel D. The red circles indicate the average pre-stimulation IPSP and the minimum post-stimulus IPSP. See the text for more information.</p