Neurocomputational Models of Interval Timing: Seeing the Forest for the Trees.

Extracting temporal regularities and relations from experience/observation is critical for organisms' adaptiveness (communication, foraging, predation, prediction) in their ecological niches. Therefore, it is not surprising that the internal clock that enables the perception of seconds-to-minutes-long intervals (interval timing) is evolutionarily well-preserved across many species of animals. This comparative claim is primarily supported by the fact that the timing behavior of many vertebrates exhibits common statistical signatures (e.g., on-average accuracy, scalar variability, positive skew). These ubiquitous statistical features of timing behaviors serve as empirical benchmarks for modelers in their efforts to unravel the processing dynamics of the internal clock (namely answering how internal clock "ticks"). In this chapter, we introduce prominent (neuro)computational approaches to modeling interval timing at a level that can be understood by general audience. These models include Treisman's pacemaker accumulator model, the information processing variant of scalar expectancy theory, the striatal beat frequency model, behavioral expectancy theory, the learning to time model, the time-adaptive opponent Poisson drift-diffusion model, time cell models, and neural trajectory models. Crucially, we discuss these models within an overarching conceptual framework that categorizes different models as threshold vs. clock-adaptive models and as dedicated clock/ramping vs. emergent time/population code models.

Diverse Time Encoding Strategies Within the Medial Premotor Areas of the Primate.

The measurement of time in the subsecond scale is critical for many sophisticated behaviors, yet its neural underpinnings are largely unknown. Recent neurophysiological experiments from our laboratory have shown that the neural activity in the medial premotor areas (MPC) of macaques can represent different aspects of temporal processing. During single interval categorization, we found that preSMA encodes a subjective category limit by reaching a peak of activity at a time that divides the set of test intervals into short and long. We also observed neural signals associated with the category selected by the subjects and the reward outcomes of the perceptual decision. On the other hand, we have studied the behavioral and neurophysiological basis of rhythmic timing. First, we have shown in different tapping tasks that macaques are able to produce predictively and accurately intervals that are cued by auditory or visual metronomes or when intervals are produced internally without sensory guidance. In addition, we found that the rhythmic timing mechanism in MPC is governed by different layers of neural clocks. Next, the instantaneous activity of single cells shows ramping activity that encodes the elapsed or remaining time for a tapping movement. In addition, we found MPC neurons that build neural sequences, forming dynamic patterns of activation that flexibly cover all the produced interval depending on the tapping tempo. This rhythmic neural clock resets on every interval providing an internal representation of pulse. Furthermore, the MPC cells show mixed selectivity, encoding not only elapsed time, but also the tempo of the tapping and the serial order element in the rhythmic sequence. Hence, MPC can map different task parameters, including the passage of time, using different cell populations. Finally, the projection of the time varying activity of MPC hundreds of cells into a low dimensional state space showed circular neural trajectories whose geometry represented the internal pulse and the tapping tempo. Overall, these findings support the notion that MPC is part of the core timing mechanism for both single interval and rhythmic timing, using neural clocks with different encoding principles, probably to flexibly encode and mix the timing representation with other task parameters.

Estimating Time and Rhythm by Predicting External Stimuli.

In this chapter, we present recent findings from our group showing that elapsed time, interval timing, and rhythm maintenance might be achieved by the well-known ability of the brain to predict the future states of the world. The difference between predictions and actual sensory evidence is used to generate perceptual and behavioral adjustments that help subjects achieve desired behavioral goals. Concretely, we show that (1) accumulating prediction errors is a plausible strategy humans could use to determine whether a train of consecutive stimuli arrives at regular or irregular intervals. By analyzing the behavior of human and non-human primate subjects performing rhythm perception tasks, we demonstrate that (2) the ability to estimate elapsed time and internally maintain rhythms is shared across primates and humans. Neurophysiological recordings show that (3) the medial premotor cortex engages in rhythm entrainment and maintains oscillatory activity that reveals an internal metronome's spatial and temporal characteristics. Finally, we demonstrate that (4) the amplitude of gamma oscillations within this cortex increases proportionally to the total elapsed time. In conjunction with our most recent experiments, our results suggest that timing might be achieved by an internal simulation of the sensory stimuli and the motor commands that define the timing task that needs to be performed.

Timing Patterns in the Extended Basal Ganglia System.

The human brain is a constructive organ. It generates predictions to modulate its functioning and continuously adapts to a dynamic environment. Increasingly, the temporal dimension of motor and non-motor behaviour is recognised as a key component of this predictive bias. Nevertheless, the intricate interplay of the neural mechanisms that encode, decode and evaluate temporal information to give rise to a sense of time and control over sensorimotor timing remains largely elusive. Among several brain systems, the basal ganglia have been consistently linked to interval- and beat-based timing operations. Considering the tight embedding of the basal ganglia into multiple complex neurofunctional networks, it is clear that they have to interact with other proximate and distal brain systems. While the primary target of basal ganglia output is the thalamus, many regions connect to the striatum of the basal ganglia, their main input relay. This establishes widespread connectivity, forming the basis for first- and second-order interactions with other systems implicated in timing such as the cerebellum and supplementary motor areas. However, next to this structural interconnectivity, additional functions need to be considered to better understand their contribution to temporally predictive adaptation. To this end, we develop the concept of interval-based patterning, conceived as a temporally explicit hierarchical sequencing operation that underlies motor and non-motor behaviour as a common interpretation of basal ganglia function.

Cholinergic interneurons in the dorsal striatum play an important role in the acquisition of duration memory.

The present study aimed to examine the effect of cholinergic interneuron lesions in the dorsal striatum on duration-memory formation. Cholinergic interneurons in the dorsal striatum may be involved in the formation of duration memory since they are among the main inputs to the dorsal striatal muscarinic acetylcholine-1 receptors, which play a role in the consolidation of duration memory. Rats were sufficiently trained using a peak-interval 20 s procedure and then infused with anti-choline acetyltransferase-saporin into the dorsal striatum to cause selective ablation of cholinergic interneurons. To make the rats acquire new duration-memories, we trained them with a peak interval 40 s after lesion. Before lesion, the peak times (an index of duration memory) for sham-lesioned and lesioned groups were similar at approximately 20 s. In the peak interval 40 s session, the peak times for the sham-lesioned and lesioned groups were approximately 30 and 20 s, respectively. After additional peak interval 40 s sessions, the peak times of both groups were shifted to approximately 40 s. Those results suggest that the cholinergic interneuron lesion delayed new duration-memory acquisition. Subsequent experiments showed that cholinergic interneuron lesions did not retard the shift of peak time to the original target time (20 s). Following experiment without changing the target time after lesion showed that cholinergic interneuron lesions did not change their peak times. Our findings suggest that cholinergic interneurons in the dorsal striatum are involved in new duration-memory acquisition but not in the utilization of already acquired duration memory and interval timing.

The timing database: An open-access, live repository for interval timing studies.

Interval timing refers to the ability to perceive and remember intervals in the seconds to minutes range. Our contemporary understanding of interval timing is derived from relatively small-scale, isolated studies that investigate a limited range of intervals with a small sample size, usually based on a single task. Consequently, the conclusions drawn from individual studies are not readily generalizable to other tasks, conditions, and task parameters. The current paper presents a live database that presents raw data from interval timing studies (currently composed of 68 datasets from eight different tasks incorporating various interval and temporal order judgments) with an online graphical user interface to easily select, compile, and download the data organized in a standard format. The Timing Database aims to promote and cultivate key and novel analyses of our timing ability by making published and future datasets accessible as open-source resources for the entire research community. In the current paper, we showcase the use of the database by testing various core ideas based on data compiled across studies (i.e., temporal accuracy, scalar property, location of the point of subjective equality, malleability of timing precision). The Timing Database will serve as the repository for interval timing studies through the submission of new datasets.

Temporal foundations of episodic memory.

A fundamental question in the development of animal models of episodic memory concerns the role of temporal processes in episodic memory. Gallistel, (1990) developed a framework in which animals remember specific features about an event, including the time of occurrence of the event and its location in space. Gallistel proposed that timing is based on a series of biological oscillators, spanning a wide range of periods. Accordingly, a snapshot of the phases of multiple oscillators provides a representation of the time of occurrence of the event. I review research on basic timing mechanisms that may support memory for times of occurrence. These studies suggest that animals use biological oscillators to represent time. Next, I describe recently developed animal models of episodic memory that highlight the importance of temporal representations in memory. One line of research suggests that an oscillator representation of time supports episodic memory. A second line of research highlights the flow of events in time in episodic memory. Investigations that integrate time and memory may advance the development of animal models of episodic memory.

Interval Timing as a Computational Pathway From Early Life Adversity to Affective Disorders.

Adverse early life experiences can have remarkably enduring negative consequences on mental health, with numerous, varied psychiatric conditions sharing this developmental origin. Yet, the mechanisms linking adverse experiences to these conditions remain poorly understood. Here, we draw on a principled model of interval timing to propose that statistically optimal adaptation of temporal representations to an unpredictable early life environment can produce key characteristics of anhedonia, a transdiagnostic symptom associated with affective disorders like depression and anxiety. The core observation is that early temporal unpredictability produces broader, more imprecise temporal expectations. As a result, reward anticipation is diminished, and associative learning is slowed. When agents with such representations are later introduced to more stable environments, they demonstrate a negativity bias, responding more to the omission of reward than its receipt. Increased encoding of negative events has been proposed to contribute to disorders with anhedonia as a symptom. We then examined how unpredictability interacts with another form of adversity, low reward availability. We found that unpredictability's effect was most strongly felt in richer environments, potentially leading to categorically different phenotypic expressions. In sum, our formalization suggests a single mechanism can help to link early life adversity to a range of behaviors associated with anhedonia, and offers novel insights into the interactive impacts of multiple adversities.

Core clock gene, Bmal1, is required for optimal second-level interval production.

Perception and production of second-level temporal intervals are critical in several behavioral and cognitive processes, including adaptive anticipation, motor control, and social communication. These processes are impaired in several neurological and psychological disorders, such as Parkinson's disease and attention-deficit hyperactivity disorder. Although evidence indicates that second-level interval timing exhibit circadian patterns, it remains unclear whether the core clock machinery controls the circadian pattern of interval timing. To investigate the role of core clock molecules in interval timing capacity, we devised a behavioral assay called the interval timing task to examine prospective motor interval timing ability. In this task, the mouse produces two separate nose pokes in a pretrained second-level interval to obtain a sucrose solution as a reward. We discovered that interval perception in wild-type mice displayed a circadian pattern, with the best performance observed during the late active phase. To investigate whether the core molecular clock is involved in the circadian control of interval timing, we employed Bmal1 knockout mice (BKO) in the interval timing task. The interval production of BKO did not display any difference between early and late active phase, without reaching the optimal interval production level observed in wild-type. In summary, we report that the core clock gene Bmal1 is required for the optimal performance of prospective motor timing typically observed during the late part of the active period.

Context-specific and context-invariant computations of interval timing.

Introduction: An accurate sense of time is crucial in flexible sensorimotor control and other cognitive functions. However, it remains unknown how multiple timing computations in different contexts interact to shape our behavior. Methods: We asked 41 healthy human subjects to perform timing tasks that differed in the sensorimotor domain (sensory timing vs. motor timing) and effector (hand vs. saccadic eye movement). To understand how these different behavioral contexts contribute to timing behavior, we applied a three-stage Bayesian model to behavioral data. Results: Our results demonstrate that the Bayesian model for each effector could not describe bias in the other effector. Similarly, in each task the model-predicted data could not describe bias in the other task. These findings suggest that the measurement stage of interval timing is context-specific in the sensorimotor and effector domains. We also showed that temporal precision is context-invariant in the effector domain, unlike temporal accuracy. Discussion: This combination of context-specific and context-invariant computations across sensorimotor and effector domains suggests overlapping and distributed computations as the underlying mechanism of timing in different contexts.

Keep your finger on the pulse: Better rate perception and gap detection with vibrotactile compared to visual stimuli.

Important characteristics of the environment can be represented in the temporal pattern of sensory stimulation. In two experiments, we compared accuracy of temporal processing by different modalities. Experiment 1 examined binary categorization of rate for visual (V) or vibrotactile (T) stimulus pulses presented at either 4 or 6 Hz. Inter-pulse intervals were either constant or variable, perturbed by random Gaussian variates. Subjects categorized the rate of T pulse sequences more accurately than V sequences. In V conditions only, subjects disproportionately tended to mis-categorize 4-Hz pulse rates, for all but the most variable sequences. In Experiment 2, we compared gap detection thresholds across modalities, using the same V and T pulses from Experiment 1, as well as with bimodal (VT) pulses. Visual gap detection thresholds were larger (3[Formula: see text]) than tactile thresholds. Additionally, performance with VT stimuli seemed to be nearly completely dominated by their T components. Together, these results suggest (i) that vibrotactile temporal acuity surpasses visual temporal acuity, and (ii) that vibrotactile stimulation has considerable, untapped potential to convey temporal information like that needed for eyes-free alerting signals.

An open-source behavior controller for associative learning and memory (B-CALM).

Associative learning and memory, i.e., learning and remembering the associations between environmental stimuli, self-generated actions, and outcomes such as rewards or punishments, are critical for the well-being of animals. Hence, the neural mechanisms underlying these processes are extensively studied using behavioral tasks in laboratory animals. Traditionally, these tasks have been controlled using commercial hardware and software, which limits scalability and accessibility due to their cost. More recently, due to the revolution in microcontrollers or microcomputers, several general-purpose and open-source solutions have been advanced for controlling neuroscientific behavioral tasks. While these solutions have great strength due to their flexibility and general-purpose nature, for the same reasons, they suffer from some disadvantages including the need for considerable programming expertise, limited online visualization, or slower than optimal response latencies for any specific task. Here, to mitigate these concerns, we present an open-source behavior controller for associative learning and memory (B-CALM). B-CALM provides an integrated suite that can control a host of associative learning and memory behaviors. As proof of principle for its applicability, we show data from head-fixed mice learning Pavlovian conditioning, operant conditioning, discrimination learning, as well as a timing task and a choice task. These can be run directly from a user-friendly graphical user interface (GUI) written in MATLAB that controls many independently running Arduino Mega microcontrollers in parallel (one per behavior box). In sum, B-CALM will enable researchers to execute a wide variety of associative learning and memory tasks in a scalable, accurate, and user-friendly manner.

Lost in time: Relocating the perception of duration outside the brain.

It is well-accepted in neuroscience that animals process time internally to estimate the duration of intervals lasting between one and several seconds. More than 100 years ago, Henri Bergson nevertheless remarked that, because animals have memory, their inner experience of time is ever-changing, making duration impossible to measure internally and time a source of change. Bergson proposed that quantifying the inner experience of time requires its externalization in movements (observed or self-generated), as their unfolding leaves measurable traces in space. Here, studies across species are reviewed and collectively suggest that, in line with Bergson's ideas, animals spontaneously solve time estimation tasks through a movement-based spatialization of time. Moreover, the well-known scalable anticipatory responses of animals to regularly spaced rewards can be explained by the variable pressure of time on reward-oriented actions. Finally, the brain regions linked with time perception overlap with those implicated in motor control, spatial navigation and motivation. Thus, instead of considering time as static information processed by the brain, it might be fruitful to conceptualize it as a kind of force to which animals are more or less sensitive depending on their internal state and environment.

Effects of Hallucination Proneness and Sensory Resolution on Prior Biases in Human Perceptual Inference of Time Intervals.

Bayesian models of perception posit that percepts result from the optimal integration of new sensory information and prior expectations. In turn, prominent models of perceptual disturbances in psychosis frame hallucination-like phenomena as percepts excessively biased toward perceptual prior expectations. Despite mounting support for this notion, whether this hallucination-related prior bias results secondarily from imprecise sensory representations at early processing stages or directly from alterations in perceptual priors-both suggested candidates potentially consistent with Bayesian models-remains to be tested. Using modified interval timing paradigms designed to arbitrate between these alternative hypotheses, we show in human participants (16 females and 24 males) from a nonclinical population that hallucination proneness correlates with a circumscribed form of prior bias that reflects selective differences in weighting of contextual prior variance, a prior bias that is unrelated to the effect of sensory noise and to a separate index of sensory resolution. Our results thus suggest distinct mechanisms underlying prior biases in perceptual inference and favor the notion that hallucination proneness could reflect direct alterations in the representation or use of perceptual priors independent of sensory noise.SIGNIFICANCE STATEMENT Current theories of psychosis posit that hallucination proneness results from excessive influence of prior expectations on perception. It is not clear whether this prior bias represents a primary top-down process related to the representation or use of prior beliefs or instead a secondary bottom-up process stemming from imprecise sensory representations at early processing stages. To address this question, we examined interval timing behaviors captured by Bayesian perceptual-inference models. Our data support the notion that excessive influence of prior expectations associated with hallucination propensity is not directly secondary to sensory imprecision and is instead more consistent with a primary top-down process. These results help refine computational theories of psychosis and may contribute to the development of improved intervention targets.

Working memory for time intervals: Another manifestation of the central tendency effect.

The relationship between working memory and time perception has been typically investigated using dual-task paradigms (e.g., testing timing performance during a concurrent task). To our knowledge, none of these studies used time intervals as the target stimulus to be remembered. The current study investigated the working memory for time intervals by asking participants to reproduce durations they experienced at different orders in a series of experienced intervals (n-back task). One of the experiments was conducted online and the other one in the lab setting. Results showed a central tendency bias and additive elongation of time reproductions with increasing working memory load. Our results also showed that participants assigned different weights to experienced intervals based on their order of presentation (higher weight to the target interval). We conclude that the recall of intervals from working memory under high cognitive load leads to a central tendency effect, which is known to be induced by the temporal context and present particularly in aging and in those with Parkinson's disease.

Resource Allocation in the Noise-Free Striatal Beat Frequency Model of Interval Timing.

The Striatal Beat Frequency (SBF) model of interval timing uses many neural oscillators, presumably located in the frontal cortex (FC), to produce beats at a specific criterion time Tc. The coincidence detection produces the beats in the basal ganglia spiny neurons by comparing the current state of the FC neural oscillators against the long-term memory values stored at reinforcement time Tc. The neurobiologically realistic SBF model has been previously used for producing precise and scalar timing in the presence of noise. Here we simplified the SBF model to gain insight into the problem of resource allocation in interval timing networks. Specifically, we used a noise-free SBF model to explore the lower limits of the number of neural oscillators required for producing accurate timing. Using abstract sine-wave neural oscillators in the SBF-sin model, we found that the lower limit of the number of oscillators needed is proportional to the criterion time Tc and the frequency span (fmax - fmin) of the FC neural oscillators. Using biophysically realistic Morris-Lecar model neurons in the SBF-ML model, the lower bound increased by one to two orders of magnitude compared to the SBF-sin model.

Not All Mice Are Created Equal: Interval Timing Accuracy and Scalar Timing in 129, Swiss-Webster, and C57Bl/6 Mice.

Many species, including humans, show both accurate timing-appropriate time estimation in the seconds to minutes range-and scalar timing-time estimation error varies linearly with estimated duration. Behavioral paradigms aimed at investigating interval timing are expected to evaluate these dissociable characteristics of timing. However, when evaluating interval timing in models of neuropsychiatric disease, researchers are confronted with a lack of adequate studies about the parent (background) strains, since accuracy and scalar timing have only been demonstrated for the C57Bl/6 strain of mice (Buhusi et al., 2009). We used a peak-interval procedure with three intervals-a protocol in which other species, including humans, demonstrate accurate, scalar timing-to evaluate timing accuracy and scalar timing in three strains of mice frequently used in genetic and behavioral studies: 129, Swiss-Webster, and C57Bl/6. C57Bl/6 mice showed accurate, scalar timing, while 129 and Swiss-Webster mice showed departures from accuracy and/or scalar timing. Results suggest that the genetic background / strain of the mouse is a critical variable for studies investigating interval timing in genetically-engineered mice. Our study validates the PI procedure with multiple intervals as a proper technique, and the C57Bl/6 strain as the most suitable genetic background to date for behavioral investigations of interval timing in genetically engineered mice modeling human disorders. In contrast, studies using mice in 129, Swiss-Webster, or mixed-background strains should be interpreted with caution, and thorough investigations of accuracy and scalar timing should be conducted before a less studied strain of mouse is considered for use in timing studies.

Filling your time: Auditory flutter alters perceived duration via stimulus-locked responses.

In the current article, we examined the flutter-duration illusion; the extension of perceived duration when an interval is filled with auditory flutter. Participants reproduced flutter-filled and empty durations while electrophysiological activity was recorded. As expected, participants over-produced durations when they were filled with auditory flutter rather than unfilled. Using multivariate pattern analysis, we found several differentiating patterns of neural activity while participants listened to either flutter-filled or empty intervals. However, in subsequent single trial analysis, only two of these clusters predicted perceived duration in the flutter condition; one occurring in line with the second click of the flutter, and one in line with the fourth click. We relate this finding to the N1P2 component and P3a component to timing initiation and arousal, respectively.

Mechanisms of impulsive choice: Experiments to explore and models to map the empirical terrain.

Impulsive choice is preference for a smaller-sooner (SS) outcome over a larger-later (LL) outcome when LL choices result in greater reinforcement maximization. Delay discounting is a model of impulsive choice that describes the decaying value of a reinforcer over time, with impulsive choice evident when the empirical choice-delay function is steep. Steep discounting is correlated with multiple diseases and disorders. Thus, understanding the processes underlying impulsive choice is a popular topic for investigation. Experimental research has explored the conditions that moderate impulsive choice, and quantitative models of impulsive choice have been developed that elegantly represent the underlying processes. This review spotlights experimental research in impulsive choice covering human and nonhuman animals across the domains of learning, motivation, and cognition. Contemporary models of delay discounting designed to explain the underlying mechanisms of impulsive choice are discussed. These models focus on potential candidate mechanisms, which include perception, delay and/or reinforcer sensitivity, reinforcement maximization, motivation, and cognitive systems. Although the models collectively explain multiple mechanistic phenomena, there are several cognitive processes, such as attention and working memory, that are overlooked. Future research and model development should focus on bridging the gap between quantitative models and empirical phenomena.