This model was published in E.E. Saftenku "A simplified model of
the long-term plasticity in cerebellar mossy fiber-granule cell
synapses", Neurophysiology/Neirofiziologiya, 2002, 34, N 2-3, P.216-219.
Activation of cerebellar mossy fibers using either a theta burst
stimulation mode (TBS; 100 Hz for 100 ms repeated 4 times at 250
ms intervals) or a single tetanus stimulation train (100 Hz for
1 s) results in long-term potentiation (LTP) of both AMPA and
NMDA components of EPSC in granule cells, whereas low-frequency
stimulation (2 Hz) causes long-term depression. These forms of
plasticity require Ca2+ influx through NMDA receptor channels.
When about two synapses were initially activated by TBS, the
amplitude of evoked EPSPs exceeded the control value by 70+-16%
in 1 min and then continued to slowly increase reaching in 7 min
an increment of 84+-16%. We modified a simple model for LTP/LTD
developed by Migliore and Lansky (1999) and combined it with the
model of the electrical activity in the cerebellar granule cells
developed by D'Angelo et al (Bursting and resonance in cerebellar
granule cells by D’Angelo et al., 2001 in ModelDB)with addition
of the description of AMPA and NMDA receptor kinetics. In
contrast to the model of Migliore and Lansky, an activation of
autocatalytic processes is controlled not by postsynaptic
depolarization, but by Ca2+ influx through the NMDA receptor
channels. The model completely reproduces experimental conditions
and results of LTP manifestation in the presence of bicuculline
and short-term depression of AMPA EPSPs during TBS published in
Armano S. et al. "Long-term potentiation of intrinsic
excitability at the mossy fiber-granule cell synapse of rat
cerebellum", J. Neurosci., 2000, 20, P. 5208-5216. The
observed nonlinearity in the development of long-term changes of
EPSP in granule cells was modeled by a difference in the rate
constants of two independent autocatalytic processes. The model
can be easily modified for presynaptic expression of LTP by
multiplying freqdel*(Np-Nd) by variable "u" instead of synaptic
conductances.
The transmitter concentration profile in the cleft was described by
three exponential components to reproduce the profile of glutamate
concentration from Rusakov (2001). Neurotransmitter concentration was
made proportional to release probability of glutamate on the APs.
Short-term plasticity was modeled with the use of phenomenological
model of Tsodyks and Markram, but release probability in the model
corresponds not to xu, but to x(u/U)*weight in their designations,
where "weight" can be considered as the probability to release on the
first AP. This allowed us to reproduce slower decrease of release
probability during repetitive stimulation, which occurs presumably
due to several vesicles in the ready-to-release pool under condition
of one-vesicle constraint.
Keywords: Cerebellar granule cells, Long-term plasticity.
Simulations.
Begin from start.hoc and reproduce the maintenance of LTP and
LTD as in Fig.1 from our paper. All parameters of the model
can be changed in the respective boxes.