Integration of biochemical and electrical signaling-multiscale model of the medium spiny neuron of the striatum

Abstract

Neuron behavior results from the interplay between networks of biochemical processes and electrical signaling. Synaptic plasticity is one of the neuronal properties emerging from such an interaction. One of the current approaches to study plasticity is to model either its electrical aspects or its biochemical components. Among the chief reasons are the different time scales involved, electrical events happening in milliseconds while biochemical cascades respond in minutes or hours. In order to create multiscale models taking in consideration both aspects simultaneously, one needs to synchronize the two models, and exchange relevant variable values. We present a new event-driven algorithm to synchronize different neuronal models, which decreases computational time and avoids superfluous synchronizations. The algorithm is implemented in the TimeScales framework. We demonstrate its use by simulating a new multiscale model of the Medium Spiny Neuron of the Neostriatum. The model comprises over a thousand dendritic spines, where the electrical model interacts with the respective instances of a biochemical model. Our results show that a multiscale model is able to exhibit changes of synaptic plasticity as a result of the interaction between electrical and biochemical signaling. Our synchronization strategy is general enough to be used in simulations of other models with similar synchronization issues, such as networks of neurons. Moreover, the integration between the electrical and the biochemical models opens up the possibility to investigate multiscale process, like synaptic plasticity, in a more global manner, while taking into account a more realistic description of the underlying mechanisms.

Figure 1. Synchronization principle.

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.

Figure 2. Schematic representation of the Hybrid Model.

The electric model is shown in blue and the biochemical model is shown in red. Each spine’s biochemical model is connected with the spine’s electrical counterpart, all of which are integrated with the main electrical model of the neuron.

Figure 3. Event-driven algorithm applied to the Hybrid Model.

Algorithm applied using E-CELL3 as the biochemical simulator () and NEURON as electrical simulator ().

Figure 4. Comparison of the event driven algorithm with while loops and different sparseness.

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.

Figure 5. Spines stimulated by the first and second trains of input.

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.

Figure 6. Response of the spine to the first and second trains.

Spine 559 is stimulated with both trains, spine 560 only with the first one.

Figure 7. Different responses of spines differentially located.

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.

Figure 8. Depolarization and variation of phosphorylated AMPARs triggered by two trains of input.

Spine 559 receives two trains of stimuli, while spine 560 receives only one train. A, spine 559. B, spine 560.

Figure 9. Effect of stimulation frequency on AMPARs phosphorylation in the stimulated spine.

The same amount of inputs are delivered for all the frequencies but 40 Hz long. 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.

Figure 10. Fractional activation of enzymes for different stimulations.

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.

Figure 11. Response of non stimulated spines.

Influence of stimulation of spine 97 on depolarization and number of AMPARs of distant spine 75 (panel A) and neighbor spine 96 (panel B). The amount of biochemical calcium in the two spines is plotted on panel C.

Figure 12. Spine dimensions and equivalent circuit.

The dimensions are expressed in , the post-synaptic density is in green, the head in red and the neck in blue.

Figure 13. Fit of the spine membrane surface and spine distribution per branch.

Panel A shows the polynomial fit (17^th order) of the spine membrane surface using digitized data from . In panel B, the histogram of the spine distribution calculated with the equivalent spine surface is shown in blue. The final number of spines used (371 per branch, 1504 total), after removal of the noise due to spines positioned over the soma and the proximal dendrites, is shown in green.

Figure 14. Interaction between ion channels and biochemical signaling.

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.

Figure 15. Feedback loop between calcium concentration and synaptic weight.