Switching On Depression and Potentiation in the Cerebellum

Abstract

Long-term depression (LTD) and long-term potentiation (LTP) in the cerebellum are important for motor learning. However, the signaling mechanisms controlling whether LTD or LTP is induced in response to synaptic stimulation remain obscure. Using a unified model of LTD and LTP at the cerebellar parallel fiber-Purkinje cell (PF-PC) synapse, we delineate the coordinated pre- and postsynaptic signaling that determines the direction of plasticity. We show that LTP is the default response to PF stimulation above a well-defined frequency threshold. However, if the calcium signal surpasses the threshold for CaMKII activation, then an ultrasensitive "on switch" activates an extracellular signal-regulated kinase (ERK)-based positive feedback loop that triggers LTD instead. This postsynaptic feedback loop is sustained by another, trans-synaptic, feedback loop that maintains nitric oxide production throughout LTD induction. When full depression is achieved, an automatic "off switch" inactivates the feedback loops, returning the network to its basal state and demarcating the end of the early phase of LTD.

A unified computational model for cortical post-synaptic plasticity

“…We started by using the model of [Jedrzejewska-Szmek et al, 2017] for GluR1 phosphorylation at sites S831 and S845, which are phosphorylated by protein kinase A (PKA) and Ca 2+ /calmodulin-dependent kinase II (CaMKII), respectively, as a basis for our unified model. We added the metabotropic glutamate receptor (mGluR) and muscarinic acetylcholine M1 receptor-dependent pathways leading to protein kinase C (PKC) activation from [Kim et al, 2013] and [Blackwell et al, 2018], respectively, and adopted the PKC-dependent endocytosis of GluR2 and reinsertion to the membrane from [Gallimore et al, 2018] as these pathways are critical for neocortical plasticity [Seol et al, 2007]. As we included molecular species from different models and as we omitted certain molecular species that affected the dynamics of the underlying species but were not imperative for the pathways we wanted to describe, calibration of the model reactions was necessary.…”

“…1A), following experimental data according to which 45% of GluR2s were membrane-inserted at resting conditions [Ashby et al, 2004]. We also adopted the three-step calmodulin (CaM) activation of [Gallimore et al, 2018] instead of the two-step activation of [Jedrzejewska-Szmek et al, 2017] where the reaction rates of CaM binding two Ca 2+ ions were linearly dependent on the number of Ca 2+ ions.…”

“…1E, 1F, and 1G, respectively. GluR2 in 4xHFS when the forward rate of the membrane insertion of non-phosphorylated GluR2 was 0.0055 1/ms [Gallimore et al, 2018] (grey) or 0.00025 1/ms (black). The rate 0.00025 1/ms caused a resting-state concentration of 121 nM for the membrane-bound GluR2 subunits, which is 45% of the total GluR2 concentration (270 nM).…”

“…The full model along with the fitting and data-analysis algorithms (Python scripts) that were used in this study are publicly available in ModelDB at http://modeldb.yale.edu/260971 (password "plasticity" required during peer review). Iyengar, 1999, Jedrzejewska-Szmek et al, 2017], generic [Hayer and Bhalla, 2005], cerebellar Purkinje cells [Gallimore et al, 2018], striatal spiny projection neuron [Blackwell et al, 2018]…”

“…Hippocampal CA1 [Bhalla and Iyengar, 1999], striatal spiny projection neuron [Kim et al, 2013, Blackwell et al, 2018 cerebellar Purkinje cells [Hellgren Kotaleski et al, 2002, Gallimore et al, 2018…”