Modeled changes of cerebellar activity in mutant mice are predictive of their learning impairments

Abstract

Translating neuronal activity to measurable behavioral changes has been a long-standing goal of systems neuroscience. Recently, we have developed a model of phase-reversal learning of the vestibulo-ocular reflex, a well-established, cerebellar-dependent task. The model, comprising both the cerebellar cortex and vestibular nuclei, reproduces behavioral data and accounts for the changes in neural activity during learning in wild type mice. Here, we used our model to predict Purkinje cell spiking as well as behavior before and after learning of five different lines of mutant mice with distinct cell-specific alterations of the cerebellar cortical circuitry. We tested these predictions by obtaining electrophysiological data depicting changes in neuronal spiking. We show that our data is largely consistent with the model predictions for simple spike modulation of Purkinje cells and concomitant behavioral learning in four of the mutants. In addition, our model accurately predicts a shift in simple spike activity in a mutant mouse with a brainstem specific mutation. This combination of electrophysiological and computational techniques opens a possibility of predicting behavioral impairments from neural activity.

Figure 1. Cerebellar circuitry and experimental design.

(a) Organization of a basic cerebellar module of the oculomotor pathway. Vestibular input to the vestibular nucleus (VN) carries the signal about the head movement (mossy fibers, black). This signal is also relayed by mossy fibers onto granule cells (GC, green), which innervate Purkinje cells (PC, black). The inferior olive (IO) receives information about the retinal slip that is first processed by the accessory optic system (AOS). The IO neurons innervate the contralateral PCs through climbing fibers (CF; purple). Those two inputs converge on PCs, which send their output back to VN, forming a loop. This loop is modulated by an inhibitory side loop represented by molecular layer interneurons (MLIs, blue). The magenta circles and +/− signs indicate sites of plasticity incorporated in the model. (b) Schematic representation of vestibulo-ocular response (VOR) phase-reversal adaptation. During the learning, a mouse is headfixed on a turntable and phase adaptation is achieved by an in-phase table and drum rotation in the light. With each of the five training sessions there is an increase in amplitude of the drum rotation, but the oscillation frequency of the turntable remains fixed at 0.6 Hz. Note that by the end of day five the phase of eye movements of a mouse is reversed so that the eye movements are now in-phase with the rotation of the turntable.

Figure 2. Experimental and modeled phase-reversal in control mice.

(a) Experimental and modeled eye movements in control mice as a function of training time of VOR phase-reversal (training is done in the light and eye measurement is done in the dark during VOR at 0.6 Hz). Gain values (left panel) are normalized to the initial gain. Experimental data represent averages with SEM (dark area) and SD (light grey area) of all control mice used in this study. Modeled changes are displayed for both gain and phase with SD (red line). (b) Linear regression plots displaying correlation between modeled and experimental data. (c) Example cell of an in vivo extracellular recording from floccular vertical axis (VA) PCs obtained during vestibular stimulation (0.6 Hz) in the dark before and after the VOR-reversal training in wild type mice (top, grey and bottom, black panels, respectively) plotted as peri-stimulus time histograms (PSTH). Green arrows indicate the depth of the modulation in the trained animals (peak to peak, marked with a green dotted line). (d) Polar plots of SS (top) and CS (bottom) modulation before and after learning in control mice (grey and black, respectively). Phase of the modeled SS and CS are indicated with arrows. The amplitude of modulation is depicted by the radius (green asterisk; calculated by subtracting the trough of SS from the peak of the SS activity) and the phase of modulation is indicated by the angle. Each dot represents a single cell. (e) As predicted by the model (red) the SS modulation was significantly increased following learning in the control mice. There was also a small but significant increase in the SS firing frequency following the training. Error bars denote SD; *denote p < 0.05; **denote p < 0.001. (f) Modeled PC SS activity as a function of time in the cycle in wild type mice (grey, initial value before learning; black, after training). SS activity produced by the model was normalized to the mean average firing frequency of the PC in control mice. Green arrows indicate the depth of the modulation in the trained animals (peak to peak, marked with a green dotted line).

Figure 3. Predicted Purkinje cell activity before and after VOR phase-reversal is consistent with the experimental data from GC-ΔKCC2 mice.

(a) Part of cerebellar circuitry shown in Fig. 1a; Red lightning bolts indicate loss of KCC2 from GCs. (b) Experimental and modeled eye movements in GC-ΔKCC2 mice as a function of training time of VOR phase-reversal training. Gain values (top panel) are normalized to the initial gain. Experimental data represent averages with SEM (green shaded area) and SD (grey shaded area) of the GC-ΔKCC2 mice. Grey dotted line indicates the values of the littermate controls. Modeled changes are displayed for both gain and phase with SD (red line). (c) Linear regression plots displaying correlation between modeled and experimental data. (d) Representative PSTHs of floccular VA PC cells depict SS and CS modulation in GC-ΔKCC2 mice before and after the VOR-reversal training during vestibular stimulation (0.6 Hz) (top and bottom panels, respectively). (e) Polar plots of SS (left) and CS (right) modulation before and after learning in GC-ΔKCC2 mice (lighter and darker color, respectively) reveal increase in the modulation amplitude following learning. Each dot represents a single cell. Phase of the modeled SS and CS are indicated with the arrows. (f) As predicted by the model SS modulation in GC-ΔKCC2 mice was much lower than that of the wild type before learning and increased after learning. Error bars denote SD; *denote p < 0.05; **denote p < 0.001. (g) SS activity displayed as a function of time in the cycle in the model with increased GC excitability (light green, initial value before learning; dark green, after training) and in controls (grey, initial value before learning; black, after training). The model predicts both the lowered modulation in naïve GC-ΔKCC2 mice and an increase in the modulation following the training.

Figure 4. Experimental and modeled Purkinje cell modulation is disrupted in the PC-Δγ2 mice.

(a) Part of cerebellar circuitry shown in Fig. 1a; Red “X” depicts severed connectivity between MLIs and PCs in the PC-Δγ2 mice. (b) Experimental and modeled eye movements in PC-Δγ2 mice as a function of training time of VOR phase-reversal training. Gain values (top panel) are normalized to the initial gain. Experimental data represent averages with SEM (blue shaded area) and SD (grey shaded area) of the PC-Δγ2 mice. Grey dotted line indicates the values of the littermate controls. Modeled changes are displayed for both gain and phase with SD (red line). (c) Linear regression plots displaying correlation between modeled and experimental data. (d) Representative PSTHs from in vivo recording in PC-Δγ2 during vestibular stimulation (0.6 Hz). (e) Polar plots of SS and CS modulation before and after learning (lighter and darker blue, respectively). The plots reveal much lower modulation amplitude than that of the controls. Note that some PCs did not modulate their SS activity (indicated with black arrows). Each dot represents a single cell. Phase of the modeled SS and CS are indicated with the arrows. (f) Modeled and experimentally measured modulation was initially lower than that of the controls and increased significantly following learning in the PC-Δγ2. The firing frequency was also significantly higher following learning both in experimental and modeled data. Error bars denote SD; *denote p < 0.05; **denote p < 0.001. (g) SS activity as a function of time in the cycle in a control (grey, initial value before learning; black, after training) and in the model with blocked MLI to PC inhibition (light blue, initial value before learning; dark blue, after training).

Figure 5. Experimental and modeled phase-reversal in the PC-ΔKCC2 mice.

(a) Part of cerebellar circuitry shown in Fig. 1a; Red “X” depicts severed connectivity between MLIs and PCs in the PC-ΔKCC2 mice. (b) Experimental and modeled eye movements in PC-ΔKCC2 mice as a function of training time of VOR phase-reversal training. Gain values (top panel) are normalized to the initial gain. Experimental data represent averages with SEM (purple shaded area) and SD (grey shaded area) the PC -ΔKCC2 mice. Grey dotted line indicates the values of the littermate controls. Modeled changes are displayed for both gain and phase with SD (red line). (c) Linear regression plots displaying correlation between modeled and experimental data. (d) Representative PSTHs from in vivo recording in PC -ΔKCC2 during vestibular stimulation (0.6 Hz). (e) Polar plots of SS and CS modulation before and after learning (lighter and darker purple, respectively). The plots reveal much lower modulation amplitude than that of the controls. Note that some PCs did not modulate their SS activity (indicated with black arrows). Each dot represents a single cell. Phase of the modeled SS and CS are indicated with the arrows. (f) Modeled and experimentally measured modulation was initially lower than that of the controls and increased significantly following learning in the PC -ΔKCC2. In contrast to the model, there was no significant increase to the firing frequency after training in PC -ΔKCC2 mice. Error bars denote SD; *denote p < 0.05; **denote p < 0.001. (g) SS activity as a function of time in the cycle in a control (grey, initial value before learning; black, after training) and in the model with blocked MLI to PC inhibition (light purple, initial value before learning; dark blue, after training).

Figure 6. The model can reproduce neither behavioral nor electrophysiological changes during VOR phase-reversal in PC-ΔPP2B mice.

(a) Simplified view of molecular pathways involved in PF to PC plasticity and role of protein phosphatase 2B (PP2B, orange frame). LTD is induced by simultaneous CF and PF activation (purple and green). A large Ca²⁺ transient resulting from Ca²⁺ influx together with release of Ca²⁺ from intracellular stores mediated by IP₃, promotes protein kinase C (PKC) activation, which phosphorylates AMPA receptors leading to their internalization. PF activation also causes presynaptic release of nitric oxide (NO) and results in activation of protein kinase G (PKG), which inhibits PP2B and thus inhibits dephosphorylation of AMPA receptors. Stimulation of PFs alone leads to a much smaller Ca²⁺ influx, promoting activation of PP2B and regulating AMPA receptor insertion leading to LTP. (b) Experimental and modeled eye movements in PC-ΔPP2B mice as a function of training time of VOR phase-reversal training. Gain values (top panel) are normalized to the initial gain. Experimental data represent averages with SEM (orange shaded area) and SD (grey shaded area) of the PC-ΔPP2B mice. Grey dotted line indicates the values of the littermate controls. Note that the modeled values (red) are locked at the gain of 1 and phase of 0 due to the blockage of the potentiation at the PF-PC synapse. (c) Representative PSTHs from in vivo recording in PC-ΔPP2B during vestibular stimulation (0.6 Hz). (d) Polar plots of SS and CS modulation before and after learning (lighter and darker orange, respectively). Note that some PCs did not modulate their SS activity (indicated with black arrows). Each dot represents a single cell. Phase of the modeled SS and CS are indicated with the arrows. (e) Our model predicted low modulation of the SS modulation but failed to reproduce initial and trained firing frequencies. Error bars denote SD; *denote p < 0.05; **denote p < 0.001. (f) PC SS activity as a function of time in the cycle in a model with no PF-PC LTP. Note that the model cannot reproduce the experimental data due to the limitations explained in the discussion and methods.

Figure 7. Silencing majority of granule cells prevents the model from learning the VOR phase-reversal.

(a) Part of cerebellar circuitry shown in Fig. 1a; Red “X” symbols indicate loss of signal transmission from GCs. (b) Experimental and modeled eye movements in GC-ΔCACNA1A mice as a function of training time of VOR phase-reversal training. Gain values (top panel) are normalized to the initial gain. Experimental data represent averages with SEM (green shaded area) and SD (grey shaded area) of the GC-ΔCACNA1A mice. Grey dotted line indicates the values of the littermate controls. Note that the modeled values (red) are locked at the gain of 1 and phase of 0 due to the blockage of the potentiation at the PF-PC synapse. (c) Representative PSTHs from in vivo recording from naive GC-ΔCACNA1A mice, in which GC output is reduced by ~75% during VOR stimulation (0.6 Hz). (d) Polar plot of SS and CS responses to VOR stimulation in naïve GC-ΔCACNA1A mice. Each dot represents one cell. Phase of the modeled SS and CS are indicated with the arrows. (e) Modulation of SS, is attenuated in GC-ΔCACNA1A mice. Error bars denote SD. (f) In our model the effect of reducing GC output by 75% and blocking PF-PC long–term plasticity is in line with the experimental data, in that the modulation depth of simple-spikes in Purkinje cells of GC-ΔCACNA1A mice is also significantly reduced during VOR.

Figure 8. The model can account for 180 degree shift in the PC activity and eye movement impairment in IO-ΔRobo3 mice during VOR.

(a) Schematic illustration of the altered olivocerebellar circuitry in IO-ΔRobo3 mice. For the wildtype schematics and abbreviations see Fig. 1a. Note that the climbing fibers (CF, purple) project to the PCs on the ipsilateral side. (b, top) Representative PSTHs of SS and CS activity from in vivo recording during VOR stimulation as a function of time in the cycle in IO-ΔRobo3 (purple) and littermate controls (black). (b, bottom) SS and CS activity predicted by the model with ipsilateral projecting CFs (purple) and controls (black dashed line). Note that the peak of the modulation is reversed with respect to the wild type mice, which is consistent with experimental data (raw experimental data obtained from: Badura et al.22). (c) Gain and phase values of the eye movements during VOR (0.6 Hz) in naïve wild type (black) and IO-ΔRobo3 (purple) mice. Error bars denote SD; *denote p < 0.05; **denote p < 0.001.