A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms.

The neurons of the deep cerebellar nuclei (DCNn) represent the main functional link between the cerebellar cortex and the rest of the central nervous system. Therefore, understanding the electrophysiological properties of DCNn is of fundamental importance to understand the overall functioning of the cerebellum. Experimental data suggest that DCNn can reversibly switch between two states: the firing of spikes (F state) and a stable depolarized state (SD state). We introduce a new biophysical model of the DCNn membrane electro-responsiveness to investigate how the interplay between the documented conductances identified in DCNn give rise to these states. In the model, the F state emerges as an isola of limit cycles, i.e. a closed loop of periodic solutions disconnected from the branch of SD fixed points. This bifurcation structure endows the model with the ability to reproduce the [Formula: see text] transition triggered by hyperpolarizing current pulses. The model also reproduces the [Formula: see text] transition induced by blocking Ca currents and ascribes this transition to the blocking of the high-threshold Ca current. The model suggests that intracellular current injections can trigger fully reversible [Formula: see text] transitions. Investigation of low-dimension reduced models suggests that the voltage-dependent Na current is prominent for these dynamical features. Finally, simulations of the model suggest that physiological synaptic inputs may trigger [Formula: see text] transitions. These transitions could explain the puzzling observation of positively correlated activities of connected Purkinje cells and DCNn despite the former inhibit the latter.

Endocannabinoid dynamics gate spike-timing dependent depression and potentiation.

Synaptic plasticity is a cardinal cellular mechanism for learning and memory. The endocannabinoid (eCB) system has emerged as a pivotal pathway for synaptic plasticity because of its widely characterized ability to depress synaptic transmission on short- and long-term scales. Recent reports indicate that eCBs also mediate potentiation of the synapse. However, it is not known how eCB signaling may support bidirectionality. Here, we combined electrophysiology experiments with mathematical modeling to question the mechanisms of eCB bidirectionality in spike-timing dependent plasticity (STDP) at corticostriatal synapses. We demonstrate that STDP outcome is controlled by eCB levels and dynamics: prolonged and moderate levels of eCB lead to eCB-mediated long-term depression (eCB-tLTD) while short and large eCB transients produce eCB-mediated long-term potentiation (eCB-tLTP). Moreover, we show that eCB-tLTD requires active calcineurin whereas eCB-tLTP necessitates the activity of presynaptic PKA. Therefore, just like glutamate or GABA, eCB form a bidirectional system to encode learning and memory.

Endocannabinoids mediate bidirectional striatal spike-timing-dependent plasticity.

KEY POINTS: Although learning can arise from few or even a single trial, synaptic plasticity is commonly assessed under prolonged activation. Here, we explored the existence of rapid responsiveness of synaptic plasticity at corticostriatal synapses in a major synaptic learning rule, spike-timing-dependent plasticity (STDP). We found that spike-timing-dependent depression (tLTD) progressively disappears when the number of paired stimulations (below 50 pairings) is decreased whereas spike-timing-dependent potentiation (tLTP) displays a biphasic profile: tLTP is observed for 75-100 pairings, is absent for 25-50 pairings and re-emerges for 5-10 pairings. This tLTP induced by low numbers of pairings (5-10) depends on activation of the endocannabinoid system, type-1 cannabinoid receptor and the transient receptor potential vanilloid type-1. Endocannabinoid-tLTP may represent a physiological mechanism operating during the rapid learning of new associative memories and behavioural rules characterizing the flexible behaviour of mammals or during the initial stages of habit learning. ABSTRACT: Synaptic plasticity, a main substrate for learning and memory, is commonly assessed with prolonged stimulations. Since learning can arise from few or even a single trial, synaptic strength is expected to adapt rapidly. However, whether synaptic plasticity occurs in response to limited event occurrences remains elusive. To answer this question, we investigated whether a low number of paired stimulations can induce plasticity in a major synaptic learning rule, spike-timing-dependent plasticity (STDP). It is known that 100 pairings induce bidirectional STDP, i.e. spike-timing-dependent potentiation (tLTP) and depression (tLTD) at most central synapses. In rodent striatum, we found that tLTD progressively disappears when the number of paired stimulations is decreased (below 50 pairings) whereas tLTP displays a biphasic profile: tLTP is observed for 75-100 pairings, absent for 25-50 pairings and re-emerges for 5-10 pairings. This tLTP, induced by very few pairings (∼5-10) depends on the endocannabinoid (eCB) system. This eCB-dependent tLTP (eCB-tLTP) involves postsynaptic endocannabinoid synthesis, requires paired activity (post- and presynaptic) and the activation of type-1 cannabinoid receptor (CB1R) and transient receptor potential vanilloid type-1 (TRPV1). eCB-tLTP occurs in both striatopallidal and striatonigral medium-sized spiny neurons (MSNs) and is dopamine dependent. Lastly, we show that eCB-LTP and eCB-LTD can be induced sequentially in the same neuron, depending on the cellular conditioning protocol. Thus, while endocannabinoids are usually thought simply to depress synaptic function, they also constitute a versatile system underlying bidirectional plasticity. Our results reveal a novel form of synaptic plasticity, eCB-tLTP, which may underlie rapid learning capabilities characterizing behavioural flexibility.

Dendritic signals command firing dynamics in a mathematical model of cerebellar Purkinje cells.

Dendrites of cerebellar Purkinje cells (PCs) respond to brief excitations from parallel fibers with lasting plateau depolarizations. It is unknown whether these plateaus are local events that boost the synaptic signals or they propagate to the soma and directly take part in setting the cell firing dynamics. To address this issue, we analyzed a likely mechanism underlying plateaus in three representations of a reconstructed PC with increasing complexity. Analysis in an infinite cable suggests that Ca plateaus triggered by direct excitatory inputs from parallel fibers and their mirror signals, valleys (putatively triggered by the local feed forward inhibitory network), cannot propagate. However, simulations of the model in electrotonic equivalent cables prove that Ca plateaus (resp. valleys) are conducted over the entire cell with velocities typical of passive events once they are triggered by threshold synaptic inputs that turn the membrane current inward (resp. outward) over the whole cell surface. Bifurcation analysis of the model in equivalent cables, and simulations in a fully reconstructed PC both indicate that dendritic Ca plateaus and valleys, respectively, command epochs of firing and silencing of PCs.

Multiple forms of activity-dependent intrinsic plasticity in layer V cortical neurones in vivo.

Synaptic plasticity is classically considered as the neuronal substrate for learning and memory. However, activity-dependent changes in neuronal intrinsic excitability have been reported in several learning-related brain regions, suggesting that intrinsic plasticity could also participate to information storage. Compared to synaptic plasticity, there has been little exploration of the properties of induction and expression of intrinsic plasticity in an intact brain. Here, by the means of in vivo intracellular recordings in the rat we have examined how the intrinsic excitability of layer V motor cortex pyramidal neurones is altered following brief periods of repeated firing. Changes in membrane excitability were assessed by modifications in the discharge frequency versus injected current (F-I) curves. Most (approximately 64%) conditioned neurones exhibited a long-lasting intrinsic plasticity, which was expressed either by selective changes in the current threshold or in the slope of the F-I curve, or by concomitant changes in both parameters. These modifications in the neuronal input-output relationship led to a global increase or decrease in intrinsic excitability. Passive electrical membrane properties were unaffected by the intracellular conditioning, indicating that intrinsic plasticity resulted from modifications of voltage-gated ion channels. These results demonstrate that neocortical pyramidal neurones can express in vivo a bidirectional use-dependent intrinsic plasticity, modifying their sensitivity to weak inputs and/or the gain of their input-output function. These multiple forms of experience-dependent intrinsic changes, which expand the computational abilities of individual neurones, could shape new network dynamics and thus might participate in the formation of mnemonic motor engrams.

A new principle for information storage in an enzymatic pathway model.

Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activity-dependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans.

A biophysical model of nonlinear dynamics underlying plateau potentials and calcium spikes in purkinje cell dendrites.

Computational capabilities of Purkinje cells (PCs) are central to the cerebellum function. Information originating from the whole nervous system converges on their dendrites, and their axon is the sole output of the cerebellar cortex. PC dendrites respond to weak synaptic activation with long-lasting, low-amplitude plateau potentials, but stronger synaptic activation can generate fast, large amplitude calcium spikes. Pharmacological data have suggested the involvement of only the P-type of Ca channels in both of these electric responses. However, the mechanism allowing this Ca current to underlie responses with such different dynamics is still unclear. This mechanism was explored by constraining a biophysical model with electrophysiological, Ca-imaging, and single ion channel data. A model is presented here incorporating a simplified description of [Ca](i) regulation and three ionic currents: 1) the P-type Ca current, 2) a delayed-rectifier K current, and 3) a generic class of K channels activating sharply in the sub-threshold voltage range. This model sustains fast spikes and long-lasting plateaus terminating spontaneously with recovery of the resting potential. Small depolarizing, tonic inputs turn plateaus into a stable membrane state and endow the dendrite with bistability properties. With larger tonic inputs, the plateau remains the unique equilibrium state, showing long traces of transient inhibitory inputs that are called "valley potentials" because their dynamics mirrors that of inverted, finite-duration plateaus. Analyzing the slow subsystem obtained by assuming instantaneous activation of the delayed-rectifier reveals that the time course of plateaus and valleys is controlled by the slow [Ca](i) dynamics, which arises from the high Ca-buffering capacity of PCs. A bifurcation analysis shows that tonic currents modulate sub-threshold dynamics by displacing the resting state along a hysteresis region edged by two saddle-node bifurcations; these bifurcations mark transitions from finite-duration plateaus to bistability and from bistability to valley potentials, respectively. This low-dimensionality model may be introduced into large-scale models to explore the role of PC dendrite computations in the functional capabilities of the cerebellum.