Theoretical considerations for understanding a Purkinje cell timing mechanism

A computational passage-of-time model of the cerebellar Purkinje cell in eyeblink conditioning

The cerebellar Purkinje cell controlling eyeblinks can learn, remember, and reproduce the interstimulus interval in a classical conditioning paradigm. Given temporally separated inputs, the cerebellar Purkinje cell learns to pause its tonic inhibition of a motor pathway with high temporal precision so that an overt blink occurs at the right time. Most models place the passage-of-time representation in upstream network effects. Yet, bypassing the upstream network and directly stimulating the Purkinje cell's pre-synaptic fibers during conditioning still causes acquisition of a well-timed response. Additionally, while network models are sensitive to variance in the temporal structure of probe stimulation, in vivo findings suggest that the acquired Purkinje cell response is not. Such findings motivate alternative approaches to modeling neural function. Here, we present a proof-of-principle model of the passage-of-time which is internal to the Purkinje cell and is invariant to probe structure. The model is consistent with puzzling findings, accurately recapitulates Purkinje cell firing during classical conditioning and makes testable electrophysiological predictions.

A biochemical mechanism for time-encoding memory formation within individual synapses of Purkinje cells

Within the classical eye-blink conditioning, Purkinje cells within the cerebellum are known to suppress their tonic firing rates for a well defined time period in response to the conditional stimulus after training. The temporal profile of the drop in tonic firing rate, i.e., the onset and the duration, depend upon the time interval between the onsets of the conditional and unconditional training stimuli. Direct stimulation of parallel fibers and climbing fiber by electrodes was found to be sufficient to reproduce the same characteristic drop in the firing rate of the Purkinje cell. In addition, the specific metabotropic glutamate-based receptor type 7 (mGluR₇) was found responsible for the initiation of the response, suggesting an intrinsic mechanism within the Purkinje cell for the temporal learning. In an attempt to look for a mechanism for time-encoding memory formation within individual Purkinje cells, we propose a biochemical mechanism based on recent experimental findings. The proposed mechanism tries to answer key aspects of the “Coding problem” of Neuroscience by focusing on the Purkinje cell’s ability to encode time intervals through training. According to the proposed mechanism, the time memory is encoded within the dynamics of a set of proteins—mGluR₇, G-protein, G-protein coupled Inward Rectifier Potassium ion channel, Protein Kinase A, Protein Phosphatase 1 and other associated biomolecules—which self-organize themselves into a protein complex. The intrinsic dynamics of these protein complexes can differ and thus can encode different time durations. Based on their amount and their collective dynamics within individual synapses, the Purkinje cell is able to suppress its own tonic firing rate for a specific time interval. The time memory is encoded within the effective dynamics of the biochemical reactions and altering these dynamics means storing a different time memory. The proposed mechanism is verified by both a minimal and a more comprehensive mathematical model of the conditional response behavior of the Purkinje cell and corresponding dynamical simulations of the involved biomolecules, yielding testable experimental predictions.

Kir3 channel blockade in the cerebellar cortex suppresses performance of classically conditioned Purkinje cell responses

In the eyeblink conditioning paradigm, cerebellar Purkinje cells learn to respond to the conditional stimulus with an adaptively timed pause in its spontaneous firing. Evidence suggests that the pause is elicited by glutamate released from parallel fibers and acting on metabotropic receptors (mGluR7) which initiates a delayed-onset suppression of firing. We suggested that G protein activation of hyperpolarizing K_ir3 channels (or ‘GIRK’, G protein-coupled inwardly-rectifying K⁺ channels) could be part of such a mechanism. Application of the K_ir3 antagonist Tertiapin-LQ locally in the superficial layers of the cerebellar cortex in decerebrate ferrets suppressed normal performance of Purkinje cell pause responses to the conditional stimulus. Importantly, there was no detectable effect on spontaneous firing. These findings suggest that intact functioning of K_ir3 channels in the cerebellar cortex is required for normal conditioned Purkinje cell responses.

A model for time interval learning in the Purkinje cell

Recent experimental findings indicate that Purkinje cells in the cerebellum represent time intervals by mechanisms other than conventional synaptic weights. These findings add to the theoretical and experimental observations suggesting the presence of intra-cellular mechanisms for adaptation and processing. To account for these experimental results we propose a new biophysical model for time interval learning in a Purkinje cell. The numerical model focuses on a classical delay conditioning task (e.g. eyeblink conditioning) and relies on a few computational steps. In particular, the model posits the activation by the parallel fiber input of a local intra-cellular calcium store which can be modulated by intra-cellular pathways. The reciprocal interaction of the calcium signal with several proteins forming negative and positive feedback loops ensures that the timing of inhibition in the Purkinje cell anticipates the interval between parallel and climbing fiber inputs during training. We systematically test the model ability to learn time intervals at the 150-1000 ms time scale, while observing that learning can also extend to the multiple seconds scale. In agreement with experimental observations we also show that the number of pairings required to learn increases with inter-stimulus interval. Finally, we discuss how this model would allow the cerebellum to detect and generate specific spatio-temporal patterns, a classical theory for cerebellar function.

Intrinsic memory of temporal intervals in cerebellar Purkinje cells

The general consensus for learning and memory, including in the cerebellum, is that modification of synaptic strength via long-term potentiation (LTP) or long-term depression (LTD) are the primary mechanisms for the formation of memories. Recent findings suggest additional cellular mechanisms - referred to as 'intrinsic plasticity' - where a neuron's membrane excitability intrinsically changes. These mechanisms act like a dimmer and alter neuronal responsiveness by adjusting response amplitudes and spike thresholds. Here, I argue that classical conditioning of cerebellar Purkinje cell responses reveals yet another cell-intrinsic learning mechanism which significantly differs from both changes in synaptic strength and changes in membrane excitability. When the conditional (CS) and unconditional stimuli (US) are delivered directly to the Purkinje cell's immediate pre-synaptic afferents, the parallel fibres and the climbing fibre, the cell learns to respond to the CS with a pause in its spontaneous firing that reflects the interval between the two stimuli. The pause response has a delayed onset and adaptively timed maximum, offset and duration, determined by the previously experienced CS-US interval. The timing is not dependent on any network-generated time-varying input. This implies the existence of a timing mechanism and a memory substrate that encodes the duration of the CS-US interval inside the Purkinje cell. Such temporal interval learning is not simply a change that causes more or less firing in response to an input. Here, I review these findings in relation to the standard theory of synaptic strength changes and the network interactions believed to be necessary for generating time codes.

Storage and erasure of behavioural experiences at the single neuron level

Although predictions from the past about the future have been of major interest to current neuroscience, how past and present behavioral experience interacts at the level of a single neuron remains largely unknown. Using the pond snail Lymnaea stagnalis we found that recent experience of terrestrial locomotion (exercise) results in a long-term increase in the firing rate of serotonergic pedal (PeA) neurons. Isolation from the CNS preserved the "memory" about previous motor activity in the neurons even after the animals rested for two hours in deep water after the exercise. In contrast, in the CNS, no difference in the firing rate between the control and "exercise-rested" (ER) neurons was seen. ER snails, when placed again on a surface to exercise, nevertheless showed faster locomotor arousal. The difference in the firing rate between the control and ER isolated neurons disappeared when the neurons were placed in the microenvironment of their home ganglia. It is likely that an increased content of dopamine in the CNS masks an increased excitation of PeA neurons after rest: the dopamine receptor antagonist sulpiride produced sustained excitation in PeA neurons from ER snails but not in the control. Therefore, our data suggest the involvement of two mechanisms in the interplay of past and present experiences at the cellular level: intrinsic neuronal changes in the biophysical properties of the cell membrane and extrinsic modulatory environment of the ganglia.

Double dissociation of single-interval and rhythmic temporal prediction in cerebellar degeneration and Parkinson's disease

Predicting the timing of upcoming events is critical for successful interaction in a dynamic world, and is recognized as a key computation for attentional orienting. Temporal predictions can be formed when recent events define a rhythmic structure, as well as in aperiodic streams or even in isolation, when a specified interval is known from previous exposure. However, whether predictions in these two contexts are mediated by a common mechanism, or by distinct, context-dependent mechanisms, is highly controversial. Moreover, although the basal ganglia and cerebellum have been linked to temporal processing, the role of these subcortical structures in temporal orienting of attention is unclear. To address these issues, we tested individuals with cerebellar degeneration or Parkinson's disease, with the latter serving as a model of basal ganglia dysfunction, on temporal prediction tasks in the subsecond range. The participants performed a visual detection task in which the onset of the target was predictable, based on either a rhythmic stream of stimuli, or a single interval, specified by two events that occurred within an aperiodic stream. Patients with cerebellar degeneration showed no benefit from single-interval cuing but preserved benefit from rhythm cuing, whereas patients with Parkinson's disease showed no benefit from rhythm cuing but preserved benefit from single-interval cuing. This double dissociation provides causal evidence for functionally nonoverlapping mechanisms of rhythm- and interval-based temporal prediction for attentional orienting, and establishes the separable contributions of the cerebellum and basal ganglia to these functions, suggesting a mechanistic specialization across timing domains.

Absence of associative motor learning and impaired time perception in a rare case of complete cerebellar agenesis

Primary cerebellar agenesis (PCA), a brain disease where the cerebellum does not develop, is an extremely rare congenital disease with only eleven living cases reported thus far. Studies of the PCA case will thus provide valuable insights into the necessity of cerebellar development for controlling and modulating cognitive functions of the brain. In this follow-up study, we further investigated the performance of associative learning and time perception of a 26-year-old female complete PCA case. We assessed whether delayed eyeblink conditioning (EBC), which represents prototypical associative motor learning function of the cerebellum, could be partially compensated by the extracerebellar brain regions in complete absence of the cerebellum. We also assessed whether the cerebellum, a critical brain region for millisecond-range interval timing, is essential for perception of the second-range time interval. Twelve neurotypical age-matched individuals were used as controls. We found that although the complete PCA patient had only mild to moderate motor deficits, she was unable to perform the delayed EBC even after 1-week of extensive training. Additionally, the PCA patient also performed poorly during time reproduction experiments in which she overproduced the millisecond-range time intervals, while underproduced the second-range time intervals. The PCA patient also failed to perform the temporal eyeblink conditioning with a 5 s fixed interval as the conditioned stimulus. These results indicate that the cerebellum is indispensable for associative motor learning and involved in timing of sub-second intervals, as well as in the perception of second-range intervals.

Learned response sequences in cerebellar Purkinje cells

Associative learning in the cerebellum has previously focused on single movements. In eyeblink conditioning, for instance, a subject learns to blink at the right time in response to a conditional stimulus (CS), such as a tone that is repeatedly followed by an unconditional corneal stimulus (US). During conditioning, the CS and US are transmitted by mossy/parallel fibers and climbing fibers to cerebellar Purkinje cells that acquire a precisely timed pause response that drives the overt blink response. The timing of this conditional Purkinje cell response is determined by the CS-US interval and is independent of temporal patterns in the input signal. In addition to single movements, the cerebellum is also believed to be important for learning complex motor programs that require multiple precisely timed muscle contractions, such as, for example, playing the piano. In the present work, we studied Purkinje cells in decerebrate ferrets that were conditioned using electrical stimulation of mossy fiber and climbing fiber afferents as CS and US, while alternating between short and long interstimulus intervals. We found that Purkinje cells can learn double pause responses, separated by an intermediate excitation, where each pause corresponds to one interstimulus interval. The results show that individual cells can not only learn to time a single response but that they also learn an accurately timed sequential response pattern.

Nonspecific synaptic plasticity improves the recognition of sparse patterns degraded by local noise

Many forms of synaptic plasticity require the local production of volatile or rapidly diffusing substances such as nitric oxide. The nonspecific plasticity these neuromodulators may induce at neighboring non-active synapses is thought to be detrimental for the specificity of memory storage. We show here that memory retrieval may benefit from this non-specific plasticity when the applied sparse binary input patterns are degraded by local noise. Simulations of a biophysically realistic model of a cerebellar Purkinje cell in a pattern recognition task show that, in the absence of noise, leakage of plasticity to adjacent synapses degrades the recognition of sparse static patterns. However, above a local noise level of 20%, the model with nonspecific plasticity outperforms the standard, specific model. The gain in performance is greatest when the spatial distribution of noise in the input matches the range of diffusion-induced plasticity. Hence non-specific plasticity may offer a benefit in noisy environments or when the pressure to generalize is strong.

Are Purkinje Cell Pauses Drivers of Classically Conditioned Blink Responses?

Several lines of evidence show that classical or Pavlovian conditioning of blink responses depends on the cerebellum. Recordings from cerebellar Purkinje cells that control the eyelid and the conditioned blink show that during training with a conditioning protocol, a Purkinje cell develops a pause response to the conditional stimulus. This conditioned cellular response has many of the properties that characterise the overt blink. The present paper argues that the learned Purkinje cell pause response is the memory trace and main driver of the overt conditioned blink and that it explains many well-known behavioural phenomena.

Mechanisms for motor timing in the cerebellar cortex

In classical eyeblink conditioning a subject learns to blink to a previously neutral stimulus. This conditional response is timed to occur just before an air puff to the eye. The learning is known to depend on the cerebellar cortex where Purkinje cells respond with adaptively timed pauses in their spontaneous firing. The pauses in the inhibitory Purkinje cells cause disinhibition of the cerebellar nuclei, which elicit the overt blinks. The timing of a Purkinje cell response was previously thought to require a temporal code in the input signal but recent work suggests that the Purkinje cells can learn to time their responses through an intrinsic mechanism that is activated by metabotropic glutamate receptors (mGluR7).