All experimental procedures were approved by the RIKEN committee on the care and use of animals in experiments. Mice were kept in the animal facility of the RIKEN Center for Brain Science under well-controlled temperature (23–25 °C) and humidity (45%–65%) conditions. Both male and female WT mice (C57BL/6, 3–6 months) were used.

1. Preparation of Solutions Used in the Experiments

NOTE: All solutions should be made in ultrapure water free of metals (resistivity > 18.2 MΩ) and other impurities (total organic carbon (TOC) < 5.0 ppb). Working artificial cerebrospinal fluid (ACSF) for slice-cutting and recording are made freshly on the day of experiment from a 10 times (x10) stock of ACSF. Bubble the solutions with 5% CO₂/ 95% O₂ gas mixture before use. The pH of ACSF is adjusted to 7.4 ± 0.1, and osmolarity is adjusted 315 ± 5 mOsm/kg by adding ultrapure water.

1. Prepare 10x stock of ACSF containing 1250 mM NaCl, 30 mM KCl, 12.5 mM NaH₂PO₄, and 260 mM NaHCO₃. This solution can be stored at 4 °C.
2. Prepare working ACSF containing 125 mM NaCl, 3 mM KCl, 2 mM CaCl₂, 1 mM Mg₂SO₄, 1.25 mM NaH₂PO₄, 26 mM NaHCO₃ and 20 mM glucose.
   1. First, add 1 mL of 2 M CaCl₂ solution followed by 1 mL of 1 M Mg₂SO₄ solution into around 800 mL of ultrapure water, to avoid precipitation. Then add 100 mL of 10x ACSF and glucose. Finally, make up to a total volume of 1,000 mL by adding ultrapure water.
3. Prepare 3.3% agar for brain handling. Dissolve 1 g of agar in 30 mL of 0.9% NaCl solution, and heat in a microwave until just boiling. Stir to mix, then pour it into a sterile 4 cm x 10 cm plastic box and allow to solidify. Store the agar plate (~8 mm thickness) in a refrigerator.
4. Prepare the internal solution.
   1. Prepare the K⁺-based internal solution containing 60 mM KCl, 60 mM K-gluconate, 0.3 mM EGTA, 4 mM MgCl₂, 4 mM ATP, 0.4 mM GTP and 30 mM HEPES (pH 7.2).
      NOTE: Low concentration (0.3 mM) of EGTA, a slow Ca²⁺-chelator, is added to chelate possibly contaminated Ca²⁺ in pure water, but this low concentration of EGTA in the internal solution never blocks the induction of LTD (Figure 3, Figure 4, Figure 5) during whole-cell recording. Measured osmotic pressure is 285 mOsm/kg.
   2. Prepare the Cs⁺-based internal solution containing 60 mM CsCl, 46 mM D-gluconate, 27 mM tetraethylammonium chloride (TEA-Cl), 0.3 mM EGTA, 4 mM MgCl₂, 4 mM ATP, 0.4 mM GTP and 30 mM HEPES (pH 7.2, adjusted using CsOH).
      NOTE: Cs⁺ blocks voltage-dependent K-channels, and improves space-clamp conditions at remote dendrites by increasing the length-constant. Measured osmotic pressure is 285 mOsm/kg.
   3. Prepare 200 µL aliquots of the solutions and store at -30 °C.

2. Brain Dissection and Trimming

1. Chill and oxygenate two 50 mL beakers of ACSF on ice until the temperature is lower than 4 °C. Add 50 µL of tetrodotoxin (TTX, 1 mM) into one of the ice-cold beakers of ACSF and reserve it for slices cutting. To obtain mouse cerebellar slice reserving LTD-inducing ability, the addition of TTX to the normal ACSF is necessary.
2. Cool down the metal specimen tray by filling an ice-bath area of the slicing chamber with ice.
3. Pour 1 mL of isoflurane into an anesthetizing jar (~1000 mL) then place a mouse in it for 30–45 s. Ensure that the mouse is deeply anesthetized by confirming its inability to respond to mechanical stimulation.
4. Decapitate the mouse using surgical scissors. Hold the head and cut the superficial skin along the midline using an ophthalmological scissor. Pull the skin by holding with fingers to widely expose the skull’s surface.
5. Cut the skull horizontally along a line from the major spinocerebellar hole just above the ear and eye using an ophthalmological scissor. Cut the skull along a line above both eyes and remove to isolate the skull.
6. Cut the brain at the middle of cerebrum by using a scalpel, then isolate the caudal part of the brain including the cerebellum from the skull. Immerse it into an ice-cold beaker of ACSF. Usually, the total time from decapitation to immersion of the brain block into the pre-chilled beaker of ACSF should be less than 60 s.
7. Position of bubbling tubing should be adjusted so as not to stir the brain block in the beaker. Mechanical damage might cause swelling of the slice during recording. Leave it for at least 7 min and allow the brain to cool down.
8. To trim the brain block, cut a rectangular agar piece (2 cm x 2 cm) from a large agar plate (4 cm x 10 cm, stored at 4 °C) and put it on a filter paper to absorb the excess liquid.
9. Turn the agar piece upside-down on the filter paper, then place the agar piece on a filter paper on a pre-chilled metal specimen tray (16 cm x 20 cm). Pick up the brain block using a spatula and absorb excessive liquid around it with a piece of filter paper.
10. Mount the brain block onto the agar block using glue (medical cyanoacrylate instant adhesive). Make sure to attach the bottom (ventral side) of the brain block to the agar.
11. Cut out the right hemisphere with a blade. Be sure that the side of the cutting plane is as parallel as possible to the dendritic plane of the PC because this side is attached to the surface of the specimen tray. Cut and remove the other side of the hemisphere. Then, cut the brain between the superior and inferior colliculi, and cut off the spinal cord.
12. Glue the right side of trimmed cerebellum with the agar block onto the pre-chilled specimen tray. Spread excess glue around the cerebellum with the flat part of a spatula, to prevent excess glue from attaching to the cerebellar surface. Tilt the metal tray and pour ACSF in order to fix the glue and wash away the excess glue.

3. Brain Slicing

1. Orient the sample such that the dorsal side of the cerebellum is on the front side. Pour ice-cold cutting ACSF, containing 1 µM TTX, sufficient to immerse the cerebellum completely. Place a gas tube into the ACSF and start bubbling with O₂/CO₂ gas mixture.
2. Remove the arachnoid mater using a fine tweezer under binoculars. Cut the cerebellar peduncle with a blade, and remove the brainstem and agar block. Rotate the tray 180°, so that the dorsal surface of the cerebellum faces a razorblade.
3. Set the blade, and adjust the first cutting location. Set the vibratome slicing parameters to the following: amplitude to 5.5, frequency to 85 Hz, speed to 3–4, and slice thickness to 300 µm.
4. Transfer the cerebellar slice on a nylon-net into an acrylic incubator and immerse the slice completely into the oxygenated ACSF. The incubator should be placed in a water-bath that maintains a temperature at 26 °C.
5. Store the slices for at least 1 h to allow recovery from the damage during slicing.

4. Whole-cell Patch-clamp Recording

NOTE: A patch-clamp recording requires following equipment: an upright microscope with infrared differential interference contrast (IR-DIC) optics, a patch-clamp amplifier, data digitizer, digital stimulator, isolator, computer, software for data-acquisition and analysis, motorized manipulator, microscope platform, vibration isolation table, Faraday cage, solution heating system, peristaltic pumps and electrode puller.

1. Add picrotoxin (0.1 mM) to ACSF and resolve it using ultra-sonication for 3 min.
2. Perfuse a recording chamber with picrotoxin-containing, O₂-CO₂-saturated ACSF at rate of 2 mL/min. Maintain the temperature of the recording chamber at around 30 °C.
3. Make a recording electrode by pulling a borosilicate glass capillary with filament (outer diameter = 1.5 mm) using a puller with 4 steps. The tip-diameter should be around 1 µm.
4. Make a stimulating electrode by pulling the same capillary using the puller with 2 steps, then break to produce a fine tip by striking the tip against an iron block under a binocular microscope. The final diameter should be 3–5 µm.
5. Transfer the cerebellar slice to the recording chamber and fix it with a Pt-weight with nylon threads. Fill a stimulating electrode with ACSF.
6. For stimulation of the PFs, place the stimulating electrode on the surface of the molecular layer, around 50 µm away from the Purkinje cell layer.
7. For stimulation of the CF, place the stimulating electrode at the bottom of the Purkinje cell layer (steps 5.3, 5.4).
8. Filter K⁺-based or Cs⁺-based internal solution with a 0.45 µm filter. Use a micro-loader to fill a recording electrode with 8 µL of internal solution.
9. Apply a weak positive pressure to the recording electrode before immersing it into the ACSF. Its resistance should be 2–4 MΩ and the liquid junctional potential should be corrected.
10. Approach the healthy, bright cell body of the PC with the recording electrode. Push the surface of Purkinje cell slightly, stop applying positive pressure, next apply negative pressure until forming a giga-ohm seal. Then establish the whole-cell configuration using negative pressure.
11. Hold the membrane potential at -70 mV, and apply -2 mV pulse (duration, 100 ms) at 0.1 Hz to monitor input resistance, series resistance and input capacitance, continuously. Do not use the series resistance compensation. Discard data when the series resistance varies by more than 15%.

5. Induction of LTD

1. Stimulate the molecular layer with a pulse (duration, 0.1 ms). Identify the PF-excitatory postsynaptic currents (EPSC) by applying a double pulse stimulus (interspike interval (ISI) of 50 ms). The PF-EPSC should show paired-pulse facilitation and gradual increase in amplitude relative to increase in stimulation intensity.
2. Record the test response of the PF-EPSC by applying a single pulse at 0.1 Hz. Adjust the intensity of the stimulus so that the evoked EPSC amplitude is around 200 pA. Avoid contamination of current through the voltage-dependent ionic channel.
3. Stimulate the CF at the bottom of the Purkinje cell layer, and identify the EPSC elicited by the CF activation (by applying a double pulse stimulus). The CF-EPSC should show paired-pulse depression and an all-or-none manner according to the increase in stimulation intensity. For LTD induction, a single stimulus should be used.
4. LTD-inducing protocol 1
   1. Using an electrode containing K⁺-based internal solution under current-clamp conditions, apply a single PF-stimulus and a single CF-stimulus simultaneously at 1 Hz for 5 min (300 pulses) (Figure 1A).
5. LTD-inducing protocol 2
   1. Using an electrode-containing K⁺-based internal solution under current-clamp conditions, apply double PF-stimuli (ISI of 50 ms) and single CF-stimulus as the second PF-stimulus is coincident with CF-stimuli at 1 Hz for 5 min (Figure 1B).
6. LTD-inducing protocol 3
   1. Using an electrode containing Cs⁺-based internal solution under voltage-clamp conditions, apply a double PF-stimulus (ISI of 50 ms) and a single depolarizing voltage-step (-70 to 0 mV, 50 ms) to the soma at 1 Hz for 3 min, so that the second PF-stimulus is equivalent to the beginning of the depolarizing voltage step (Figure 1C).
7. LTD-inducing protocol-4
   1. Using an electrode containing Cs⁺-based internal solution under voltage-clamp conditions, apply the PF-stimuli (5x at 100 Hz) and a single depolarizing voltage-step (-70 to 0 mV, 50 ms) to the soma at 0.5 Hz for 3 min, simultaneously (Figure 1D).