Cerebellar learning using perturbations

Desiderata for Normative Models of Synaptic Plasticity

Normative models of synaptic plasticity use computational rationales to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work in this realm, but experimental confirmation remains limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata that, when satisfied, are designed to ensure that a given model demonstrates a clear link between plasticity and adaptive behavior, is consistent with known biological evidence about neural plasticity and yields specific testable predictions. As a prototype, we include a detailed analysis of the REINFORCE algorithm. We also discuss how new models have begun to improve on the identified criteria and suggest avenues for further development. Overall, we provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

The olivary input to the cerebellum dissociates sensory events from movement plans

Neurons in the inferior olive are thought to anatomically organize the Purkinje cells (P-cells) of the cerebellum into computational modules, but what is computed by each module? Here, we designed a saccade task in marmosets that dissociated sensory events from motor events and then recorded the complex and simple spikes of hundreds of P-cells. We found that when a visual target was presented at a random location, the olive reported the direction of that sensory event to one group of P-cells, but not to a second group. However, just before movement onset, it reported the direction of the planned movement to both groups, even if that movement was not toward the target. At the end of the movement if the subject experienced an error but chose to withhold the corrective movement, only the first group received information about the sensory prediction error. We organized the P-cells based on the information content of their olivary input and found that in the group that received sensory information, the simple spikes were suppressed during fixation, then produced a burst before saccade onset in a direction consistent with assisting the movement. In the second group, the simple spikes were not suppressed during fixation but burst near saccade deceleration in a direction consistent with stopping the movement. Thus, the olive differentiated the P-cells based on whether they would receive sensory or motor information, and this defined their contributions to control of movements as well as holding still.

Emergence of syntax and word prediction in an artificial neural circuit of the cerebellum

The cerebellum, interconnected with the cerebral neocortex, plays a vital role in human-characteristic cognition such as language processing, however, knowledge about the underlying circuit computation of the cerebellum remains very limited. To gain a better understanding of the computation underlying cerebellar language processing, we developed a biologically constrained cerebellar artificial neural network (cANN) model, which implements the recently identified cerebello-cerebellar recurrent pathway. We found that while cANN acquires prediction of future words, another function of syntactic recognition emerges in the middle layer of the prediction circuit. The recurrent pathway of the cANN was essential for the two language functions, whereas cANN variants with further biological constraints preserved these functions. Considering the uniform structure of cerebellar circuitry across all functional domains, the single-circuit computation, which is the common basis of the two language functions, can be generalized to fundamental cerebellar functions of prediction and grammar-like rule extraction from sequences, that underpin a wide range of cerebellar motor and cognitive functions. This is a pioneering study to understand the circuit computation of human-characteristic cognition using biologically-constrained ANNs.

A direction-selective cortico-brainstem pathway adaptively modulates innate behaviors

Sensory cortices modulate innate behaviors through corticofugal projections targeting phylogenetically-old brainstem nuclei. However, the principles behind the functional connectivity of these projections remain poorly understood. Here, we show that in mice visual cortical neurons projecting to the optic-tract and dorsal-terminal nuclei (NOT-DTN) possess distinct response properties and anatomical connectivity, supporting the adaption of an essential innate eye movement, the optokinetic reflex (OKR). We find that these corticofugal neurons are enriched in specific visual areas, and they prefer temporo-nasal visual motion, matching the direction bias of downstream NOT-DTN neurons. Remarkably, continuous OKR stimulation selectively enhances the activity of these temporo-nasally biased cortical neurons, which can efficiently promote OKR plasticity. Lastly, we demonstrate that silencing downstream NOT-DTN neurons, which project specifically to the inferior olive-a key structure in oculomotor plasticity, impairs the cortical modulation of OKR and OKR plasticity. Our results unveil a direction-selective cortico-brainstem pathway that adaptively modulates innate behaviors.

Complex spikes perturb movements and reveal the sensorimotor map of Purkinje cells

Computations that are performed by the cerebellar cortex are transmitted via simple spikes of Purkinje cells (P-cells) to downstream structures, but because P-cells are many synapses away from muscles, we do not know the relationship between modulation of simple spikes and control of behavior. Here, we recorded the spiking activities of hundreds of P-cells in the oculomotor vermis of marmosets during saccadic eye movements and found that following the presentation of a visual stimulus, the olivary input to a P-cell coarsely described the direction and amplitude of the visual stimulus as well as the upcoming movement. Occasionally, the complex spike occurred just before saccade onset, suppressing the P-cell's simple spikes and disrupting its output during that saccade. Remarkably, this brief suppression of simple spikes altered the saccade's trajectory by pulling the eyes toward the part of the visual space that was preferentially encoded by the olivary input to that P-cell. Thus, there is an alignment between the sensory space encoded by the complex spikes and the behavior conveyed by the simple spikes: a reduction in simple spikes is a signal to bias the ongoing movement toward the part of the sensory space preferentially encoded by the olivary input to that P-cell.

Recent data on the cerebellum require new models and theories

The cerebellum has been a popular topic for theoretical studies because its structure was thought to be simple. Since David Marr and James Albus related its function to motor skill learning and proposed the Marr-Albus cerebellar learning model, this theory has guided and inspired cerebellar research. In this review, we summarize the theoretical progress that has been made within this framework of error-based supervised learning. We discuss the experimental progress that demonstrates more complicated molecular and cellular mechanisms in the cerebellum as well as new cell types and recurrent connections. We also cover its involvement in diverse non-motor functions and evidence of other forms of learning. Finally, we highlight the need to explain these new experimental findings into an integrated cerebellar model that can unify its diverse computational functions.

Desiderata for normative models of synaptic plasticity

Normative models of synaptic plasticity use a combination of mathematics and computational simulations to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work on these models, but experimental confirmation is relatively limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata which, when satisfied, are designed to guarantee that a model has a clear link between plasticity and adaptive behavior, consistency with known biological evidence about neural plasticity, and specific testable predictions. We then discuss how new models have begun to improve on these criteria and suggest avenues for further development. As prototypes, we provide detailed analyses of two specific models - REINFORCE and the Wake-Sleep algorithm. We provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

Complex spikes perturb movements, revealing the sensorimotor map of Purkinje cells

The cerebellar cortex performs computations that are critical for control of our actions, and then transmits that information via simple spikes of Purkinje cells (P-cells) to downstream structures. However, because P-cells are many synapses away from muscles, we do not know how their output affects behavior. Furthermore, we do not know the level of abstraction, i.e., the coordinate system of the P-cell's output. Here, we recorded spiking activities of hundreds of P-cells in the oculomotor vermis of marmosets during saccadic eye movements and found that following the presentation of a visual stimulus, the olivary input to a P-cell encoded a probabilistic signal that coarsely described both the direction and the amplitude of that stimulus. When this input was present, the resulting complex spike briefly suppressed the P-cell's simple spikes, disrupting the P-cell's output during that saccade. Remarkably, this brief suppression altered the saccade's trajectory by pulling the eyes toward the part of the visual space that was preferentially encoded by the olivary input to that P-cell. Thus, analysis of behavior in the milliseconds following a complex spike unmasked how the P-cell's output influenced behavior: the preferred location in the coordinates of the visual system as conveyed probabilistically from the inferior olive to a P-cell defined the action in the coordinates of the motor system for which that P-cell's simple spikes directed behavior.

An emergent temporal basis set robustly supports cerebellar time-series learning

The cerebellum is considered a "learning machine" essential for time interval estimation underlying motor coordination and other behaviors. Theoretical work has proposed that the cerebellum's input recipient structure, the granule cell layer (GCL), performs pattern separation of inputs that facilitates learning in Purkinje cells (P-cells). However, the relationship between input reformatting and learning has remained debated, with roles emphasized for pattern separation features from sparsification to decorrelation. We took a novel approach by training a minimalist model of the cerebellar cortex to learn complex time-series data from time-varying inputs, typical during movements. The model robustly produced temporal basis sets from these inputs, and the resultant GCL output supported better learning of temporally complex target functions than mossy fibers alone. Learning was optimized at intermediate threshold levels, supporting relatively dense granule cell activity, yet the key statistical features in GCL population activity that drove learning differed from those seen previously for classification tasks. These findings advance testable hypotheses for mechanisms of temporal basis set formation and predict that moderately dense population activity optimizes learning.NEW & NOTEWORTHY During movement, mossy fiber inputs to the cerebellum relay time-varying information with strong intrinsic relationships to ongoing movement. Are such mossy fibers signals sufficient to support Purkinje signals and learning? In a model, we show how the GCL greatly improves Purkinje learning of complex, temporally dynamic signals relative to mossy fibers alone. Learning-optimized GCL population activity was moderately dense, which retained intrinsic input variance while also performing pattern separation.

Postsynaptic plasticity of Purkinje cells in mice is determined by molecular identity

Cerebellar learning is expressed as upbound or downbound changes in simple spike activity of Purkinje cell subpopulations, but the underlying mechanism remains enigmatic. By visualizing murine Purkinje cells with different molecular identities, we demonstrate that the potential for induction of long-term depression is prominent in downbound and minimal in the upbound subpopulation. These differential propensities depend on the expression profile, but not on the synaptic inputs, of the individual Purkinje cell involved, highlighting the functional relevance of intrinsic properties for memory formation.

Dual STDP processes at Purkinje cells contribute to distinct improvements in accuracy and speed of saccadic eye movements

Saccadic eye-movements play a crucial role in visuo-motor control by allowing rapid foveation onto new targets. However, the neural processes governing saccades adaptation are not fully understood. Saccades, due to the short-time of execution (20-100 ms) and the absence of sensory information for online feedback control, must be controlled in a ballistic manner. Incomplete measurements of the movement trajectory, such as the visual endpoint error, are supposedly used to form internal predictions about the movement kinematics resulting in predictive control. In order to characterize the synaptic and neural circuit mechanisms underlying predictive saccadic control, we have reconstructed the saccadic system in a digital controller embedding a spiking neural network of the cerebellum with spike timing-dependent plasticity (STDP) rules driving parallel fiber-Purkinje cell long-term potentiation and depression (LTP and LTD). This model implements a control policy based on a dual plasticity mechanism, resulting in the identification of the roles of LTP and LTD in regulating the overall quality of saccade kinematics: it turns out that LTD increases the accuracy by decreasing visual error and LTP increases the peak speed. The control policy also required cerebellar PCs to be divided into two subpopulations, characterized by burst or pause responses. To our knowledge, this is the first model that explains in mechanistic terms the visual error and peak speed regulation of ballistic eye movements in forward mode exploiting spike-timing to regulate firing in different populations of the neuronal network. This elementary model of saccades could be extended and applied to other more complex cases in which single jerks are concatenated to compose articulated and coordinated movements.

Reward signals in the cerebellum: origins, targets, and functional implications

The cerebellum has long been proposed to play a role in cognitive function, although this has remained controversial. This idea has received renewed support with the recent discovery that signals associated with reward can be observed in the cerebellar circuitry, particularly in goal-directed learning tasks involving an interplay between the cerebellar cortex, basal ganglia, and cerebral cortex. Remarkably, a wide range of reward contingencies-including reward expectation, delivery, size, and omission-can be encoded by specific circuit elements in a manner that reflects the microzonal organization of the cerebellar cortex. The facts that reward signals have been observed in both the mossy fiber and climbing fiber input pathways to the cerebellar cortex and that their convergence may trigger plasticity in Purkinje cells suggest that these interactions may be crucial for the role of the cerebellar cortex in learned behavior. These findings strengthen the emerging consensus that the cerebellum plays a pivotal role in shaping cognitive processing and suggest that the cerebellum may combine both supervised learning and reinforcement learning to optimize goal-directed action. We make specific predictions about how cerebellar circuits can work in concert with the basal ganglia to guide different stages of learning.

Influence of various temporal recoding on pavlovian eyeblink conditioning in the cerebellum

We consider the Pavlovian eyeblink conditioning (EBC) via repeated presentation of paired conditioned stimulus (tone) and unconditioned stimulus (US; airpuff). In an effective cerebellar ring network, we change the connection probability p c from Golgi to granule (GR) cells, and make a dynamical classification of various firing patterns of the GR cells. Individual GR cells are thus found to show various well- and ill-matched firing patterns relative to the US timing signal. Then, these variously-recoded signals are fed into the Purkinje cells (PCs) through the parallel-fibers (PFs). Based on such unique dynamical classification of various firing patterns, we make intensive investigations on the influence of various temporal recoding (i.e., firing patterns) of the GR cells on the synaptic plasticity of the PF-PC synapses and the subsequent learning process for the EBC. We first note that the variously-recoded PF signals are effectively depressed by the (error-teaching) instructor climbing-fiber (CF) signals from the inferior olive neuron. In the case of well-matched PF signals, they are strongly depressed through strong long-term depression (LTD) by the instructor CF signals due to good association between the in-phase PF and the instructor CF signals. On the other hand, practically no LTD occurs for the ill-matched PF signals because most of them have no association with the instructor CF signals. This kind of "effective" depression at the PF-PC synapses coordinates firings of PCs effectively, which then makes effective inhibitory coordination on the cerebellar nucleus neuron [which elicits conditioned response (CR; eyeblink)]. When the learning trial passes a threshold, acquisition of CR begins. In this case, the timing degree T d of CR becomes good due to presence of the ill-matched firing group which plays a role of protection barrier for the timing. With further increase in the number of trials, strength S of CR (corresponding to the amplitude of eyelid closure) increases due to strong LTD in the well-matched firing group, while its timing degree T d decreases. In this way, the well- and the ill-matched firing groups play their own roles for the strength and the timing of CR, respectively. Thus, with increasing the number of learning trials, the (overall) learning efficiency degree L e (taking into consideration both timing and strength of CR) for the CR is increased, and eventually it becomes saturated. Finally, we also discuss dependence of the variety degree for firing patterns of the GR cells and the saturated learning efficiency degree L e of the CR on p c and their relations.

NMDA and AMPA receptors dysregulation in Alzheimer's disease

Alzheimer's disease (AD) is a progressive neurodegenerative condition characterized by cognitive dysfunction and synaptic failure. The current therapeutic approaches are mainly focused on symptomatic treatment and possess limited effectiveness in addressing the pathophysiology of AD. It is known that neurodegeneration is negatively correlated with synaptic plasticity. This negative correlation highlights glutamatergic neurotransmission via N-methyl-D-aspartate (NMDA) and α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid receptors and (AMPA) receptors as a critical mediator of synaptic plasticity. Despite this favorable role, extensive extracellular glutamate concentration induces excitotoxicity and neurodegeneration. NMDA receptors containing GluN2A subunits are located at synaptic sites, implicated in the protective pathways. In comparison, GluN2B containing receptors are located mainly at extrasynaptic sites and increase neuronal vulnerability. AMPA receptors are consistently endocytosed and recycled back to the membrane. An increase in the rate of endocytosis has been implicated as a part of AD pathophysiology through inducing long-term depression (LTD) and synaptic disintegration. In the present review, we focused on the mechanisms of glutamatergic system dysregulation in AD, particularly on its interaction with amyloid-beta. We concluded that assigning a specific role to an individual subtype of either NMDA receptors or AMPA receptors might be an oversimplification as they are not static receptors. Therefore, any imbalance between synaptic and extrasynaptic NMDA receptors and a reduced number of surface AMPA receptors will lead to synaptopathy.

Optimal plasticity for memory maintenance during ongoing synaptic change

Synaptic connections in many brain circuits fluctuate, exhibiting substantial turnover and remodelling over hours to days. Surprisingly, experiments show that most of this flux in connectivity persists in the absence of learning or known plasticity signals. How can neural circuits retain learned information despite a large proportion of ongoing and potentially disruptive synaptic changes? We address this question from first principles by analysing how much compensatory plasticity would be required to optimally counteract ongoing fluctuations, regardless of whether fluctuations are random or systematic. Remarkably, we find that the answer is largely independent of plasticity mechanisms and circuit architectures: compensatory plasticity should be at most equal in magnitude to fluctuations, and often less, in direct agreement with previously unexplained experimental observations. Moreover, our analysis shows that a high proportion of learning-independent synaptic change is consistent with plasticity mechanisms that accurately compute error gradients.

Whole-brain functional ultrasound imaging in awake head-fixed mice

Most brain functions engage a network of distributed regions. Full investigation of these functions thus requires assessment of whole brains; however, whole-brain functional imaging of behaving animals remains challenging. This protocol describes how to follow brain-wide activity in awake head-fixed mice using functional ultrasound imaging, a method that tracks cerebral blood volume dynamics. We describe how to set up a functional ultrasound imaging system with a provided acquisition software (miniScan), establish a chronic cranial window (timing surgery: ~3-4 h) and image brain-wide activity associated with a stimulus at high resolution (100 × 110 × 300 µm and 10 Hz per brain slice, which takes ~45 min per imaging session). We include codes that enable data to be registered to a reference atlas, production of 3D activity maps, extraction of the activity traces of ~250 brain regions and, finally, combination of data from multiple sessions (timing analysis averages ~2 h). This protocol enables neuroscientists to observe global brain processes in mice.

Frozen algorithms: how the brain's wiring facilitates learning

Synapses and neural connectivity are plastic and shaped by experience. But to what extent does connectivity itself influence the ability of a neural circuit to learn? Insights from optimization theory and AI shed light on how learning can be implemented in neural circuits. Though abstract in their nature, learning algorithms provide a principled set of hypotheses on the necessary ingredients for learning in neural circuits. These include the kinds of signals and circuit motifs that enable learning from experience, as well as an appreciation of the constraints that make learning challenging in a biological setting. Remarkably, some simple connectivity patterns can boost the efficiency of relatively crude learning rules, showing how the brain can use anatomy to compensate for the biological constraints of known synaptic plasticity mechanisms. Modern connectomics provides rich data for exploring this principle, and may reveal how brain connectivity is constrained by the requirement to learn efficiently.

Synaptic plasticity rules with physiological calcium levels

Spike-timing-dependent plasticity (STDP) is considered as a primary mechanism underlying formation of new memories during learning. Despite the growing interest in activity-dependent plasticity, it is still unclear whether synaptic plasticity rules inferred from in vitro experiments are correct in physiological conditions. The abnormally high calcium concentration used in in vitro studies of STDP suggests that in vivo plasticity rules may differ significantly from in vitro experiments, especially since STDP depends strongly on calcium for induction. We therefore studied here the influence of extracellular calcium on synaptic plasticity. Using a combination of experimental (patch-clamp recording and Ca²⁺ imaging at CA3-CA1 synapses) and theoretical approaches, we show here that the classic STDP rule in which pairs of single pre- and postsynaptic action potentials induce synaptic modifications is not valid in the physiological Ca²⁺ range. Rather, we found that these pairs of single stimuli are unable to induce any synaptic modification in 1.3 and 1.5 mM calcium and lead to depression in 1.8 mM. Plasticity can only be recovered when bursts of postsynaptic spikes are used, or when neurons fire at sufficiently high frequency. In conclusion, the STDP rule is profoundly altered in physiological Ca²⁺, but specific activity regimes restore a classical STDP profile.

Effect of diverse recoding of granule cells on optokinetic response in a cerebellar ring network with synaptic plasticity

We consider a cerebellar ring network for the optokinetic response (OKR), and investigate the effect of diverse recoding of granule (GR) cells on OKR by varying the connection probability p_c from Golgi to GR cells. For an optimal value of p_c^∗(=0.06), individual GR cells exhibit diverse spiking patterns which are in-phase, anti-phase, or complex out-of-phase with respect to their population-averaged firing activity. Then, these diversely-recoded signals via parallel fibers (PFs) from GR cells are effectively depressed by the error-teaching signals via climbing fibers from the inferior olive which are also in-phase ones. Synaptic weights at in-phase PF-Purkinje cell (PC) synapses of active GR cells are strongly depressed via strong long-term depression (LTD), while those at anti-phase and complex out-of-phase PF-PC synapses are weakly depressed through weak LTD. This kind of "effective" depression (i.e., strong/weak LTD) at the PF-PC synapses causes a big modulation in firings of PCs, which then exert effective inhibitory coordination on the vestibular nucleus (VN) neuron (which evokes OKR). For the firing of the VN neuron, the learning gain degree L_g, corresponding to the modulation gain ratio, increases with increasing the learning cycle, and it saturates at about the 300th cycle. By varying p_c from p_c^∗, we find that a plot of saturated learning gain degree L_g^∗ versus p_c forms a bell-shaped curve with a peak at p_c^∗ (where the diversity degree in spiking patterns of GR cells is also maximum). Consequently, the more diverse in recoding of GR cells, the more effective in motor learning for the OKR adaptation.

Feed-forward recruitment of electrical synapses enhances synchronous spiking in the mouse cerebellar cortex

In the cerebellar cortex, molecular layer interneurons use chemical and electrical synapses to form subnetworks that fine-tune the spiking output of the cerebellum. Although electrical synapses can entrain activity within neuronal assemblies, their role in feed-forward circuits is less well explored. By combining whole-cell patch-clamp and 2-photon laser scanning microscopy of basket cells (BCs), we found that classical excitatory postsynaptic currents (EPSCs) are followed by GABA_A receptor-independent outward currents, reflecting the hyperpolarization component of spikelets (a synapse-evoked action potential passively propagating from electrically coupled neighbors). FF recruitment of the spikelet-mediated inhibition curtails the integration time window of concomitant excitatory postsynaptic potentials (EPSPs) and dampens their temporal integration. In contrast with GABAergic-mediated feed-forward inhibition, the depolarizing component of spikelets transiently increases the peak amplitude of EPSPs, and thus postsynaptic spiking probability. Therefore, spikelet transmission can propagate within the BC network to generate synchronous inhibition of Purkinje cells, which can entrain cerebellar output for driving temporally precise behaviors.

Is Purkinje Neuron Hyperpolarisation Important for Cerebellar Synaptic Plasticity? A Retrospective and Prospective Analysis

Two recent studies have demonstrated that the dendritic Ca²⁺ signal associated with a climbing fibre (CF) input to the cerebellar Purkinje neuron (PN) depends on the membrane potential (V_m). Specifically, when the cell is hyperpolarised, this signal is mediated by T-type voltage-gated Ca²⁺ channels; in contrast, when the cell is firing, the CF-PN signal is mediated by P/Q-type voltage-gated Ca²⁺ channels. When the CF input is paired with parallel fibre (PF) activity, the signal is locally amplified at the sites of PF-activated synapses according to the V_m at the time of the CF input, suggesting that the standing V_m is a critical parameter for the induction of PF synaptic plasticity. In this review, I analyse how the V_m can potentially play a role in cerebellar learning focussing, in particular, on the hyperpolarised state that appears to occur episodically, since PNs are mostly firing under physiological conditions. By revisiting the recent literature reporting in vivo recordings and synaptic plasticity studies, I speculate on how a putative role of the PN V_m can provide an interpretation for the results of these studies.

The Origin of Physiological Local mGluR1 Supralinear Ca2+ Signals in Cerebellar Purkinje Neurons

In mouse cerebellar Purkinje neurons (PNs), the climbing fiber (CF) input provides a signal to parallel fiber (PF) synapses, triggering PF synaptic plasticity. This signal is given by supralinear Ca²⁺ transients, associated with the CF synaptic potential and colocalized with the PF Ca²⁺ influx, occurring only when PF activity precedes the CF input. Here, we unravel the biophysical determinants of supralinear Ca²⁺ signals associated with paired PF-CF synaptic activity. We used membrane potential (V _m) and Ca²⁺ imaging to investigate the local CF-associated Ca²⁺ influx following a train of PF synaptic potentials in two cases: (1) when the dendritic V _m is hyperpolarized below the resting V _m, and (2) when the dendritic V _m is at rest. We found that supralinear Ca²⁺ signals are mediated by type-1 metabotropic glutamate receptors (mGluR1s) when the CF input is delayed by 100-150 ms from the first PF input in both cases. When the dendrite is hyperpolarized only, however, mGluR1s boost neighboring T-type channels, providing a mechanism for local coincident detection of PF-CF activity. The resulting Ca²⁺ elevation is locally amplified by saturation of endogenous Ca²⁺ buffers produced by the PF-associated Ca²⁺ influx via the mGluR1-mediated nonselective cation conductance. In contrast, when the dendritic V _m is at rest, mGluR1s increase dendritic excitability by inactivating A-type K⁺ channels, but this phenomenon is not restricted to the activated PF synapses. Thus, V _m is likely a crucial parameter in determining PF synaptic plasticity, and the occurrence of hyperpolarization episodes is expected to play an important role in motor learning.SIGNIFICANCE STATEMENT In Purkinje neurons, parallel fiber synaptic plasticity, determined by coincident activation of the climbing fiber input, underlies cerebellar learning. We unravel the biophysical mechanisms allowing the CF input to produce a local Ca²⁺ signal exclusively at the sites of activated parallel fibers. We show that when the membrane potential is hyperpolarized with respect to the resting membrane potential, type-1 metabotropic glutamate receptors locally enhance Ca²⁺ influx mediated by T-type Ca²⁺ channels, and that this signal is amplified by saturation of endogenous buffer also mediated by the same receptors. The combination of these two mechanisms is therefore capable of producing a Ca²⁺ signal at the activated parallel fiber sites, suggesting a role of Purkinje neuron membrane potential in cerebellar learning.

Climbing Fibers Provide Graded Error Signals in Cerebellar Learning

The cerebellum plays a critical role in coordinating and learning complex movements. Although its importance has been well recognized, the mechanisms of learning remain hotly debated. According to the classical cerebellar learning theory, depression of parallel fiber synapses instructed by error signals from climbing fibers, drives cerebellar learning. The uniqueness of long-term depression (LTD) in cerebellar learning has been challenged by evidence showing multi-site synaptic plasticity. In Purkinje cells, long-term potentiation (LTP) of parallel fiber synapses is now well established and it can be achieved with or without climbing fiber signals, making the role of climbing fiber input more puzzling. The central question is how individual Purkinje cells extract global errors based on climbing fiber input. Previous data seemed to demonstrate that climbing fibers are inefficient instructors, because they were thought to carry “binary” error signals to individual Purkinje cells, which significantly constrains the efficiency of cerebellar learning in several regards. In recent years, new evidence has challenged the traditional view of “binary” climbing fiber responses, suggesting that climbing fibers can provide graded information to efficiently instruct individual Purkinje cells to learn. Here we review recent experimental and theoretical progress regarding modulated climbing fiber responses in Purkinje cells. Analog error signals are generated by the interaction of varying climbing fibers inputs with simultaneous other synaptic input and with firing states of targeted Purkinje cells. Accordingly, the calcium signals which trigger synaptic plasticity can be graded in both amplitude and spatial range to affect the learning rate and even learning direction. We briefly discuss how these new findings complement the learning theory and help to further our understanding of how the cerebellum works.

Complex spike clusters and false-positive rejection in a cerebellar supervised learning rule

KEY POINTS

Spike doublets comprise ∼10% of in vivo complex spike events under spontaneous conditions and ∼20% (up to 50%) under evoked conditions. Under near-physiological slice conditions, single complex spikes do not induce parallel fibre long-term depression. Doublet stimulation is required to induce long-term depression with an optimal parallel-fibre to first-complex-spike timing interval of 150 ms.

ABSTRACT

The classic example of biological supervised learning occurs at cerebellar parallel fibre (PF) to Purkinje cell synapses, comprising the most abundant synapse in the mammalian brain. Long-term depression (LTD) at these synapses is driven by climbing fibres (CFs), which fire continuously about once per second and therefore generate potential false-positive events. We show that pairs of complex spikes are required to induce LTD. In vivo, sensory stimuli evoked complex-spike doublets with intervals ≤150 ms in up to 50% of events. Using realistic [Ca2+ ]o and [Mg2+ ]o concentrations in slices, we determined that complex-spike doublets delivered 100-150 ms after PF stimulus onset were required to trigger PF-LTD, which is consistent with the requirements for eyeblink conditioning. Inter-complex spike intervals of 50-150 ms provided optimal decoding. This stimulus pattern prolonged evoked spine calcium signals and promoted CaMKII activation. Doublet activity may provide a means for CF instructive signals to stand out from background firing.

Motor context dominates output from purkinje cell functional regions during reflexive visuomotor behaviours

The cerebellum integrates sensory stimuli and motor actions to enable smooth coordination and motor learning. Here we harness the innate behavioral repertoire of the larval zebrafish to characterize the spatiotemporal dynamics of feature coding across the entire Purkinje cell population during visual stimuli and the reflexive behaviors that they elicit. Population imaging reveals three spatially-clustered regions of Purkinje cell activity along the rostrocaudal axis. Complementary single-cell electrophysiological recordings assign these Purkinje cells to one of three functional phenotypes that encode a specific visual, and not motor, signal via complex spikes. In contrast, simple spike output of most Purkinje cells is strongly driven by motor-related tail and eye signals. Interactions between complex and simple spikes show heterogeneous modulation patterns across different Purkinje cells, which become temporally restricted during swimming episodes. Our findings reveal how sensorimotor information is encoded by individual Purkinje cells and organized into behavioral modules across the entire cerebellum.

Cerebellar learning using perturbations

The cerebellum aids the learning of fast, coordinated movements. According to current consensus, erroneously active parallel fibre synapses are depressed by complex spikes signalling movement errors. However, this theory cannot solve the credit assignment problem of processing a global movement evaluation into multiple cell-specific error signals. We identify a possible implementation of an algorithm solving this problem, whereby spontaneous complex spikes perturb ongoing movements, create eligibility traces and signal error changes guiding plasticity. Error changes are extracted by adaptively cancelling the average error. This framework, stochastic gradient descent with estimated global errors (SGDEGE), predicts synaptic plasticity rules that apparently contradict the current consensus but were supported by plasticity experiments in slices from mice under conditions designed to be physiological, highlighting the sensitivity of plasticity studies to experimental conditions. We analyse the algorithm's convergence and capacity. Finally, we suggest SGDEGE may also operate in the basal ganglia.

Climbing Fibers Control Purkinje Cell Representations of Behavior

A crucial issue in understanding cerebellar function is the interaction between simple spike (SS) and complex spike (CS) discharge, the two fundamentally different activity modalities of Purkinje cells. Although several hypotheses have provided insights into the interaction, none fully explains or is completely consistent with the spectrum of experimental observations. Here, we show that during a pseudo-random manual tracking task in the monkey (Macaca mulatta), climbing fiber discharge dynamically controls the information present in the SS firing, triggering robust and rapid changes in the SS encoding of motor signals in 67% of Purkinje cells. The changes in encoding, tightly coupled to CS occurrences, consist of either increases or decreases in the SS sensitivity to kinematics or position errors and are not due to differences in SS firing rates or variability. Nor are the changes in sensitivity due to CS rhythmicity. In addition, the CS-coupled changes in encoding are not evoked by changes in kinematics or position errors. Instead, CS discharge most often leads alterations in behavior. Increases in SS encoding of a kinematic parameter are associated with larger changes in that parameter than are decreases in SS encoding. Increases in SS encoding of position error are followed by and scale with decreases in error. The results suggest a novel function of CSs, in which climbing fiber input dynamically controls the state of Purkinje cell SS encoding in advance of changes in behavior.SIGNIFICANCE STATEMENT Purkinje cells, the sole output of the cerebellar cortex, manifest two fundamentally different activity modalities, complex spike (CS) discharge and simple spike (SS) firing. Elucidating cerebellar function will require an understanding of the interactions, both short- and long-term, between CS and SS firing. This study shows that CSs dynamically control the information encoded in a Purkinje cell's SS activity by rapidly increasing or decreasing the SS sensitivity to kinematics and/or performance errors independent of firing rate. In many cases, the CS-coupled shift in SS encoding leads a change in behavior. These novel findings on the interaction between CS and SS firing provide for a new hypothesis in which climbing fiber input adjusts the encoding of SS information in advance of a change in behavior.