The major tenets of beat-frequency/coincidence-detection models of reward-related timing are reviewed in light of recent behavioral and neurobiological findings. This includes the emphasis on a core timing network embedded in the motor system that is comprised of a corticothalamic-basal ganglia circuit. Therein, a central hub provides timing pulses (i.e., predictive signals) to the entire brain, including a set of distributed satellite regions in the cerebellum, cortex, amygdala, and hippocampus that are selectively engaged in timing in a manner that is more dependent upon the specific sensory, behavioral, and contextual requirements of the task. Oscillation/coincidence-detection models also emphasize the importance of a tuned ‘perception’ learning and memory system whereby target durations are detected by striatal networks of medium spiny neurons (MSNs) through the coincidental activation of different neural populations, typically utilizing patterns of oscillatory input from the cortex and thalamus or derivations thereof (e.g., population coding) as a time base. The measure of success of beat-frequency/coincidence-detection accounts, such as the Striatal Beat-Frequency model of reward-related timing (SBF), is their ability to accommodate new experimental findings while maintaining their original framework, thereby making testable experimental predictions concerning diagnosis and treatment of issues related to a variety of dopamine-dependent basal ganglia disorders, including Huntington’s and Parkinson’s disease.

Animals can learn to repeat behaviors to earn desired rewards, a process commonly known as reinforcement learning. While previous work has implicated the ascending dopaminergic projections to the basal ganglia in reinforcement learning, little is known about the role of the hippocampus. Here, we report that a specific population of hippocampal neurons and their dopaminergic innervation contribute to operant self-stimulation. These neurons are located in the dentate gyrus, receive dopaminergic projections from the locus coeruleus, and express D1 dopamine receptors. Activation of D1 + dentate neurons is sufficient for self-stimulation: mice will press a lever to earn optogenetic activation of these neurons. A similar effect is also observed with selective activation of the locus coeruleus projections to the dentate gyrus, and blocked by D1 receptor antagonism. Calcium imaging of D1 + dentate neurons revealed significant activity at the time of action selection, but not during passive reward delivery. These results reveal the role of dopaminergic innervation of the dentate gyrus in supporting operant reinforcement.

One of the major challenges for computational models of timing and time perception is to identify a neurobiological plausible implementation that predicts various behavioral properties, including the scalar property and retrospective timing. The available timing models primarily focus on the scalar property and prospective timing, while virtually ignoring the computational accessibility. Here, we first selectively review timing models based on ramping activity, oscillatory pattern, and time cells, and discuss potential challenges for the existing models. We then propose a multifrequency oscillatory model that offers computational accessibility, which could account for a much broader range of timing features, including both retrospective and prospective timing.

Durations are defined by a beginning and an end, and a major distinction is drawn between durations that start in the present and end in the future (‘prospective timing’) and durations that start in the past and end either in the past or the present (‘retrospective timing’). Different psychological processes are thought to be engaged in each of these cases. The former is thought to engage a clock-like mechanism that accurately tracks the continuing passage of time, whereas the latter is thought to engage a reconstructive process that utilizes both temporal and non-temporal information from the memory of past events. We propose that, from a biological perspective, these two forms of duration estimation are supported by computational processes that are both reliant on population state dynamics but are nevertheless distinct. Prospective timing is effectively carried out in a single step where the ongoing dynamics of population activity directly serve as the computation of duration, whereas retrospective timing is carried out in two steps: the initial generation of population state dynamics through the process of event segmentation and the subsequent computation of duration utilizing the memory of those dynamics.

Animals can learn to repeat behaviors to earn desired rewards, a process commonly known as reinforcement learning. While previous work has implicated the ascending dopaminergic projections to the basal ganglia in reinforcement learning, little is known about the role of the hippocampus. Here we report that a specific population of hippocampal neurons and their dopaminergic innervation contribute to operant self-stimulation. These neurons are located in the dentate gyrus, receive dopaminergic projections from the locus coeruleus, and express D1 dopamine receptors. Activation of D1+ dentate neurons is sufficient for self-stimulation: mice will press a lever to earn optogenetic activation of these neurons. A similar effect is also observed with selective activation of the locus coeruleus projections to the dentate gyrus, and blocked by D1 receptor antagonism. Calcium imaging of D1+ dentate neurons revealed significant activity at the time of action selection, but not during passive reward delivery. These results reveal the role of dopaminergic innervation of the hippocampus in supporting operant reinforcement. ### Competing Interest Statement The authors have declared no competing interest.

Accurate and precise timing is crucial for complex and purposeful behaviors, such as foraging for food or playing a musical instrument. The brain is capable of processing temporal information in a coordinated manner, as if it contains an 'internal clock'. Similar to the need for the brain to orient itself in space in order to understand its surroundings, temporal orientation and tracking is an essential component of cognition as well. While there have been multiple models explaining the neural correlates of timing, independent lines of research appear to converge on the conclusion that populations of neurons in the dorsal striatum encode information relating to where a subject is in time relative to an anticipated goal. Similar to other learning processes, acquisition and maintenance of this temporal information is dependent on synaptic plasticity. Microtubules are cytoskeletal proteins that have been implicated in synaptic plasticity mechanisms and therefore are considered key elements in learning and memory. In this study, we investigated the role of microtubule dynamics in temporal learning by local infusions of microtubule stabilizing and destabilizing agents into the dorsolateral striatum. Our results suggested a bidirectional role for microtubules in timing, such that microtubule stabilization improves the maintenance of learned target durations, but impairs the acquisition of a novel duration. On the other hand, microtubule destabilization enhances the acquisition of novel target durations, while compromising the maintenance of previously learned durations. These findings suggest that microtubule dynamics plays an important role in synaptic plasticity mechanisms in the dorsolateral striatum, which in turn modulates temporal learning and time perception.

The perception of time is critical to adaptive behavior. While prefrontal cortex and basal ganglia have been implicated in interval timing in the seconds to minutes range, little is known about the role of the mediodorsal thalamus (MD), which is a key component of the limbic cortico-basal ganglia-thalamocortical loop. In this study, we tested the role of the MD in timing, using an operant temporal production task in male mice. In this task, that the expected timing of available rewards is indicated by lever pressing. Inactivation of the MD with muscimol produced rightward shifts in peak pressing on probe trials as well as increases in peak spread, thus significantly altering both temporal accuracy and precision. Optogenetic inhibition of glutamatergic projection neurons in the MD also resulted in similar changes in timing. The observed effects were found to be independent of significant changes in movement. Our findings suggest that the MD is a critical component of the neural circuit for interval timing, without playing a direct role in regulating ongoing performance.SIGNIFICANCE STATEMENT The mediodorsal nucleus (MD) of the thalamus is strongly connected with the prefrontal cortex and basal ganglia, areas which have been implicated in interval timing. Previous work has shown that the MD contributes to working memory and learning of action-outcome contingencies, but its role in behavioral timing is poorly understood. Using an operant temporal production task, we showed that inactivation of the MD significantly impaired timing behavior.

A robust adaptation to environmental changes is vital for survival. Almost all living organisms have a circadian timing system that allows adjusting their physiology to cyclic variations in the surrounding environment. Among vertebrates, many birds are also seasonal species, adapting their physiology to annual changes in photoperiod (amplitude, length and duration). Tawny Owls (Strix aluco) are nocturnal birds of prey that use vocalization as their principal mechanism of communication. Diurnal and seasonal changes in vocalization have been described for several vocal species, including songbirds. Comparable studies are lacking for owls. In the present work, we show that male Tawny Owls present a periodic vocalization pattern in the seconds-to-minutes range that is subject to both daily (early vs. late night) and seasonal (spring vs. summer) rhythmicity. These novel theory-generating findings appear to extend the role of the circadian system in regulating temporal events in the seconds-to-minutes range to other species.

The majority of studies in the field of timing and time perception have generally focused on sub- and supra-second time scales, specific behavioral processes, and/or discrete neuronal circuits. In an attempt to find common elements of interval timing from a broader perspective, we review the literature and highlight the need for cell and molecular studies that can delineate the neural mechanisms underlying temporal processing. Moreover, given the recent attention to the function of microtubule proteins and their potential contributions to learning and memory consolidation/re-consolidation, we propose that these proteins play key roles in coding temporal information in cerebellar Purkinje cells (PCs) and striatal medium spiny neurons (MSNs). The presence of microtubules at relevant neuronal sites, as well as their adaptability, dynamic structure, and longevity, makes them a suitable candidate for neural plasticity at both intra- and inter-cellular levels. As a consequence, microtubules appear capable of maintaining a temporal code or engram and thereby regulate the firing patterns of PCs and MSNs known to be involved in interval timing. This proposed mechanism would control the storage of temporal information triggered by postsynaptic activation of mGluR7. This, in turn, leads to alterations in microtubule dynamics through a “read-write” memory process involving alterations in microtubule dynamics and their hexagonal lattice structures involved in the molecular basis of temporal memory.

Time perception is an essential element of conscious and subconscious experience, coordinating our perception and interaction with the surrounding environment. In recent years, major technological advances in the field of neuroscience have helped foster new insights into the processing of temporal information, including extending our knowledge of the role of the cerebellum as one of the key nodes in the brain for this function. This consensus paper provides a state-of-the-art picture from the experts in the field of the cerebellar research on a variety of crucial issues related to temporal processing, drawing on recent anatomical, neurophysiological, behavioral, and clinical research.The cerebellar granular layer appears especially well-suited for timing operations required to confer millisecond precision for cerebellar computations. This may be most evident in the manner the cerebellum controls the duration of the timing of agonist-antagonist EMG bursts associated with fast goal-directed voluntary movements. In concert with adaptive processes, interactions within the cerebellar cortex are sufficient to support sub-second timing. However, supra-second timing seems to require cortical and basal ganglia networks, perhaps operating in concert with cerebellum. Additionally, sensory information such as an unexpected stimulus can be forwarded to the cerebellum via the climbing fiber system, providing a temporally constrained mechanism to adjust ongoing behavior and modify future processing. Patients with cerebellar disorders exhibit impairments on a range of tasks that require precise timing, and recent evidence suggest that timing problems observed in other neurological conditions such as Parkinson's disease, essential tremor, and dystonia may reflect disrupted interactions between the basal ganglia and cerebellum.The complex concepts emerging from this consensus paper should provide a foundation for further discussion, helping identify basic research questions required to understand how the brain represents and utilizes time, as well as delineating ways in which this knowledge can help improve the lives of those with neurological conditions that disrupt this most elemental sense. The panel of experts agrees that timing control in the brain is a complex concept in whom cerebellar circuitry is deeply involved. The concept of a timing machine has now expanded to clinical disorders.

An integral component to the validity of timing models is their ability to accurately fit behavioral data from detection and discrimination tasks such as the temporal bisection procedure. Two of the most prominent timing models are the Sample Known Exactly (SKE), based on scalar timing theory, and the pseudo-logistic model (PLM). Recently, evidence accumulation models based on drift–diffusionprocesses (DDM) have been utilized for modeling temporal bisection data. Currently, there is no standard by which timing behavioral data are fit, resulting in the implementation of both theoretical and atheoretical models, such as generalized logistic functions (L4P). As differences in timing behavior have been shown across sub- and supra-second durations, a comparative evaluation of these 4 different types of models (SKE, PLM, L4P, and DDM) was conducted to assess each model’s ability to capture these differences using timing data from the temporal bisection procedure. Psychometric functions from rats, trained on a bisection task using sub-sec (200 ms vs. 800 ms.) and supra-sec (2 s vs. 8 s) conditions, were fit with each of the four models. Using Akaike Information Criterion (AIC) we demonstrate that theoretical models vastly outperformed the L4P across both duration ranges, Furthermore, significant differences existed in key parameters between L4P and PLM. Three DDM models were analyzed with varying degrees of freedom, which showed that allowing for non-decision time, drift rate, and starting point to vary across signal durations outperform simpler models (Δi ≥ 10) that only allowed for variation in drift rate or drift rate and starting point. These models explained variance in both choice and reaction time data. While we were unable to directly compare timing and temporal decision models the results from both demonstrate the need for a shift toward theoretically based models such as the SKE, PLM, or DDM which provide greater parsimony as well as provide for greater qualitative analysis and interpretation of the data.

We present an integrated view of interval timing and reinforcement learning (RL) in the brain. The computational goal of RL is to maximize future rewards, and this depends crucially on a representation of time. Different RL systems in the brain process time in distinct ways. A model-based system learns 'what happens when', employing this internal model to generate action plans, while a model-free system learns to predict reward directly from a set of temporal basis functions. We describe how these systems are subserved by a computational division of labor between several brain regions, with a focus on the basal ganglia and the hippocampus, as well as how these regions are influenced by the neuromodulator dopamine.

Ordinal comparison of successively presented signal durations requires (a) the encoding of the first signal duration (standard), (b) maintenance of temporal information specific to the standard duration in memory, and (c) timing of the second signal duration (comparison) during which a comparison is made of the first and second durations. Rats were first trained to make ordinal comparisons of signal durations within three time ranges using 0.5, 1.0, and 3.0-s standard durations. Local field potentials were then recorded from the dorsal striatum and sensorimotor cortex in order to investigate the pattern of neural oscillations during each phase of the ordinal-comparison process. Increased power in delta and theta frequency ranges was observed during both the encoding and comparison stages. Active maintenance of a selected response, "shorter" or "longer" (counter-balanced across left and right levers), was represented by an increase of theta and delta oscillations in the contralateral striatum and cortex. Taken together, these data suggest that neural oscillations in the delta-theta range play an important role in the encoding, maintenance, and comparison of signal durations.

Time and memory are inextricably linked, but it is far from clear how event durations and temporal sequences are encoded in memory. In this review, we focus on resource allocation models of working memory which suggest that memory resources can be flexibly distributed amongst several items such that the precision of working memory decreases with the number of items to be encoded. This type of model is consistent with human performance in working memory tasks based on visual, auditory as well as temporal stimulus patterns. At the neural-network level, we focus on excitatory-inhibitory oscillatary processes that are able to encode both interval timing and working memory in a coupled excitatory-inhibitory network. This modification of the striatal beat-frequency model of interval timing shows how memories for multiple time intervals are represented by neural oscillations and can also be used to explain the mechanisms of resource allocation in working memory.