Fig 1.
Schematic of the control loop.
a) The target displacement information (desired target) is sent to the internal feedback loop (IFL) and to the cerebellum. In the cerebellum, the target displacement is encoded by the gaussian receptive field of the Mossy fibers (MF), MF are connected to the granule cells (GrC), which, through their axonal endings (namely the parallel fibers (PFs)) excite both the Purkinje cells (PC), and the molecular layer interneurons (MLI), composed of basket and stellate cells. The connection between PF and PC is the only plastic one in the model (represented by the green arrows). The MLI are connected to the PCs. The PCs are split in two subpopulations: pause PC and burst PC (light blue). PCs are connected to the deep cerebellar nuclei (DCN), which are the output of the cerebellum and project to the IFL. The IFL is composed by the Displacement integrator (DI) and the Burst generator (BG), and sends signals to the neural integrator (NI). The IFL generates speed command (u(t)) to be followed by the eye, while the NI transforms this speed command into motor torques by means of pulse-step integration. If the resulting movement is erroneous, then the error information is encoded by the firing rate of the inferior olive (IO), which projects onto to the PCs. b) Relation between the foveal error (e) and the IO firing probability (PIO spikes). The effect of different PIO spike on the PF-PC weight changes are shown for 3 scenarios for the foveal error: error < = 0, error = 0.5 and error > = 1. For each error range, the effect of the related IO’s firing probability (producing an LTD in PF-PC synapses), and the error-independent LTP on the two PC subpopulations is showed. If the arrow points down the overall PF-PC weight decreases due to dominant LTD process, decreasing the firing rate of the PCs on subsequent trials, if the arrow points up then the resulting weight change is positive due to dominant LTP process, increasing the PC firing rate on subsequent trials.
Fig 2.
Effect of cerebellar learning by dual PF-PC plasticity mechanisms on the behavioral and neural variables.
Simple spike firing rate: a) burst PC subpopulation. b) pause PC subpopulation, c) all PCs together. In these panels, the simple spike activity before training is shown in blue while the one after training is shown in orange. t = 0 ms corresponds to the onset of the eye movement. Eye movement kinematics: d) saccade speed and e) displacement of the eye model before training, after training and without cerebellum in blue, orange, and dashed-black. The pink rectangle represents the target within accuracy limits of +-0.5 degree. t = 0 ms corresponds to the onset of the eye movement. Movement properties across trials: f) Peak speed, g) end foveal error. h) Raster plot of the spiking activity of all cerebellar neuron populations in the model. The dots correspond to a single spike of the given cell, where the cell type is denoted in the right column. The eye movement starts at t = 0 ms and the gray box highlights the extent of movement after training. While all the pause PCs and burst PCs are shown, for the other populations only the cells that spike the most during the trial are shown.
Fig 3.
Exemplary saccade kinematics across different target amplitudes.
a) Peak speed against target amplitude. b) saccade duration against target amplitude, tested at four different target amplitudes at 10, 15, 20, 25 degrees using cerebellum models with dual plasticity and only LTD.
Fig 4.
Predictive encoding of saccade eye speed in PC activity.
Modulation of simple spike firing rate caused by decreased input on the cerebellar MFs (1, 0.83, 0.67 and 0.5 of the input used for training) for a) the burst PC subpopulation, b) the pause PC subpopulation, and c) for all PCs together (t = 0 ms is the onset of the eye movement). d) Comparison of PC population activity and saccade eye speed (dashed lines) for different MF input levels. e) Relationship between the peak of PC SSpike firing rate in the anticipatory period and the corresponding peak eye speed. Pearson correlation = 0.99, p value < 0.01. f) The foveal error occurring at the different input levels to the cerebellar network. The dashed black line corresponds to the foveal error without the cerebellum.
Fig 5.
Effect of selective switch-off of plasticity (LTP or LTD) on PC population activity and saccade kinematics.
Simple spike activity before and after training when switching-off LTP or LTD. in a,e) the burst PC subpopulation and in b, f) the pause PC subpopulation. c, g) Peak eye speed across learning trials when switching-off LTP or LTD. d, h) Foveal error across training trials by switching-off LTP or LTD.
Fig 6.
Effect of selectively switching-off of dual plasticity process in each PC subpopulation on the PC population activity and saccade kinematics.
Simple spike activity before and after training in a, e) the burst PC subpopulation when switching-off burst or pause PC plasticity and in b, f) the pause PC subpopulation when switching-off burst or pause PC plasticity. c, g) Peak eye speed across learning trials when switching-off burst or pause PC plasticity d, h) Foveal error across training trials by switching-off burst or pause PC plasticity.
Table 1.
List of abbreviations.
Table 2.
Plasticity parameters of LTP and LTD for different PC subpopulations.
Note that these parameters are not the sole measure of the amount of learning per unit error, but are in fact the constants used to scale and adjust the direction of PF-PC synaptic weight update.