Synaptic integration in a model of cerebellar granule cells

1. We have developed a compartmental model of a turtle cerebellar granule cell consisting of 13 compartments that represent the soma and 4 dendrites. We used this model to investigate the synaptic integration of mossy fiber inputs in granule cells. 2. The somatic compartment contained six active ionic conductances: a sodium conductance with fast activation and inactivation kinetics, g(Na); a high-voltage-activated calcium conductance, g(Ca(HVA)); a delayed potassium conductance, g(K(DR)); a transient potassium conductance, g(K(A)); a slowly relaxing mixed Na⁺/K⁺ conductance activating at hyperpolarized membrane potentials, g(H), and a calcium- and voltage- dependent potassium conductance, g(K(Ca)). The kinetics of these conductances was derived from electrophysiological studies in a variety of preparations, including turtle and rat granule cells. 3. In the soma, dynamics of intracellular free Ca²⁺ was modeled by incorporation of a Na⁺/Ca²⁺ exchanger, radial diffusion, and binding sites for Ca²⁺. 4. The model of the turtle granule cell exhibited depolarization-induced action potential firing with properties closely resembling those seen with intracellular recordings in turtle granule cells in vitro. 5. In the most distal compartments of the dendrites, mossy fiber activity induced synaptic currents mediated by α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)- and N-methyl-D-aspartate (NMDA)-type of glutamate receptors. The strength of synaptic inputs chosen was such that the synaptic potential induced by synchronous activation of two mossy fiber synapses reached threshold for induction of a single action potential. 6. The slow time course of the NMDA synaptic current together with the slow relaxation kinetics of g(H) significantly affected the temporal summation of excitatory synaptic potentials. A priming action potential evoked by mossy fiber stimulation increased the maximal time interval between two synaptic potentials capable to reach again threshold for a subsequent action potential. This time interval then decreased in parallel with the decay of the NMDA synaptic current reached a minimum after 200 ms, and slowly recovered with reactivation of g(H). 7. Repetitive, steady activation of synaptic conductances by a single mossy fiber at different frequencies induced action potential firing with a sharp threshold at 12 Hz. Activity of a single or of several mossy fibers induced firing of the granule cell at a frequency close to that induced when the average synaptic current was directly injected into the cell. The mossy fiber activity-granule cell firing frequency curve was close to linear with a slope of about one-half for input frequencies ≤400 Hz. 8. The effects of Golgi cell inhibition on mossy fiber to granule cell transmission were studied by inserting constant Cl^- [γ-aminobutyric acid-A (GABA(A))]-conductances proximal to the mossy fiber synapses. With small values of the tonic inhibitory conductance, the temporal summation of repetitive synaptic potentials generated from two mossy fiber inputs became more dependent on their interspike interval, with maximal efficacy for coinciding inputs. Higher values of the tonic inhibitory conductance caused a shift of the output frequency versus mossy fiber frequency curve towards higher input frequency values. These two effects, taken together, suggest that Golgi cell feed forward and feed backward inhibition results in an increased sensitivity of parallel fiber output on the timing of mossy fiber inputs impinging on a single granule cell. 9. We conclude that granule cells are electrotonically very compact; the NMDA component of mossy fiber excitatory postsynaptic potentials can play an important role in synaptic integration by favoring temporal summation of excitatory inputs, and Golgi cell inhibition is a powerful regulator of the sensitivity of parallel fiber output on the timing of mossy fiber inputs. These aspects of synaptic integration are relevant to the early processing of mossy fiber input by the cerebellar cortex.