What is all the noise about in interval timing?

Reward positivity affects temporal interval production in a continuous timing task

The neural circuits of reward processing and interval timing (including the perception and production of temporal intervals) are functionally intertwined, suggesting that it might be possible for momentary reward processing to influence subsequent timing behavior. Previous animal and human studies have mainly focused on the effect of reward on interval perception, whereas its impact on interval production is less clear. In this study, we examined whether feedback, as an example of performance-contingent reward, biases interval production. We recorded EEG from 20 participants while they engaged in a continuous drumming task with different realistic tempos (1728 trials per participant). Participants received color-coded feedback after each beat about whether they were correct (on time) or incorrect (early or late). Regression-based EEG analysis was used to unmix the rapid occurrence of a feedback response called the reward positivity (RewP), which is traditionally observed in more slow-paced tasks. Using linear mixed modeling, we found that RewP amplitude predicted timing behavior for the upcoming beat. This performance-biasing effect of the RewP was interpreted as reflecting the impact of fluctuations in reward-related anterior cingulate cortex activity on timing, and the necessity of continuous paradigms to make such observations was highlighted.

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.

Motivated to time: Effects of reinforcer devaluation and opportunity cost on interval timing

Prior research suggests that interval timing performance is sensitive to reinforcer devaluation effects and to the rate of competing sources of reinforcement. The present study sought to replicate and account for these findings in rats. A self-paced concurrent fixed-interval (FI) random-ratio (RR) schedule of reinforcement was implemented in which the FI requirement varied across training conditions (12, 24, 48 s). The RR requirement-which imposed an opportunity cost to responding on the FI component-was adjusted so that it took about twice the FI requirement, on average, to complete it. Probe reinforcer devaluation (prefeeding) sessions were conducted at the end of each condition. To assess the effect of contextual reinforcement on timing performance, the RR requirement was removed before the end of the experiment. Consistent with prior findings, performance on the FI component tracked schedule requirement and displayed scalar invariance; the removal of the RR component yielded more premature FI responses. For some rats, prefeeding reduced the number of trials initiated without affecting timing performance; for other rats, prefeeding delayed responding on the FI component but had a weaker effect on trial initiation. These results support the notion that timing and motivational processes are separable, suggesting novel explanations for ostensible motivational effects on timing performance.

Reward Processing Alters the Time Perception Networks in Patients with Major Depressive Disorder

Behavioral studies revealed that time perception is affected by the presence of a reward. Both the experience of time and the reward processing were shown to be distorted in major depressive disorder (MDD). We aimed to investigate how neural correlates of time perception and reward anticipation interact in patients with MDD. Participants (17 healthy, seven MDD) performed a time perception task during fMRI scanning that requires estimating the speed of a moving rectangle which was briefly occluded. In the control condition, participants attended to the change in color tone of the rectangle. Half of the runs were rewarded with a monetary payment per correctly done trial to evaluate the effect of a reward. The fMRI data were acquired with a 3T scanner and analyzed with repeated-measures analysis of variance (ANOVA) using SPM12. The activations related to the integration of time with reward were different between both groups in the supplementary motor area, intraparietal sulcus, thalamus, frontal eye field and caudate nucleus. Increased coupling between supplementary motor area and caudate/putamen region during timing was found in MDD patients more than in controls. Overall, our findings suggest that functional differences related to the interaction of time perception with reward anticipation in MDD occur via dysfunction of the cortico-striatal-thalamic network.

Temporal scaling and computing time in neural circuits: Should we stop watching the clock and look for its gears?

Timing underlies a variety of functions, from walking to perceiving causality. Neural timing models typically fall into one of two categories-"ramping" and "population-clock" theories. According to ramping models, individual neurons track time by gradually increasing or decreasing their activity as an event approaches. To time different intervals, ramping neurons adjust their slopes, ramping steeply for short intervals and vice versa. In contrast, according to "population-clock" models, multiple neurons track time as a group, and each neuron can fire nonlinearly. As each neuron changes its rate at each point in time, a distinct pattern of activity emerges across the population. To time different intervals, the brain learns the population patterns that coincide with key events. Both model categories have empirical support. However, they often differ in plausibility when applied to certain behavioral effects. Specifically, behavioral data indicate that the timing system has a rich computational capacity, allowing observers to spontaneously compute novel intervals from previously learned ones. In population-clock theories, population patterns map to time arbitrarily, making it difficult to explain how different patterns can be computationally combined. Ramping models are viewed as more plausible, assuming upstream circuits can set the slope of ramping neurons according to a given computation. Critically, recent studies suggest that neurons with nonlinear firing profiles often scale to time different intervals-compressing for shorter intervals and stretching for longer ones. This "temporal scaling" effect has led to a hybrid-theory where, like a population-clock model, population patterns encode time, yet like a ramping neuron adjusting its slope, the speed of each neuron's firing adapts to different intervals. Here, we argue that these "relative" population-clock models are as computationally plausible as ramping theories, viewing population-speed and ramp-slope adjustments as equivalent. Therefore, we view identifying these "speed-control" circuits as a key direction for evaluating how the timing system performs computations. Furthermore, temporal scaling highlights that a key distinction between different neural models is whether they propose an absolute or relative time-representation. However, we note that several behavioral studies suggest the brain processes both scales, cautioning against a dichotomy.

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 resource allocation problem 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.

Conceptually plausible Bayesian inference in interval timing

In a world that is uncertain and noisy, perception makes use of optimization procedures that rely on the statistical properties of previous experiences. A well-known example of this phenomenon is the central tendency effect observed in many psychophysical modalities. For example, in interval timing tasks, previous experiences influence the current percept, pulling behavioural responses towards the mean. In Bayesian observer models, these previous experiences are typically modelled by unimodal statistical distributions, referred to as the prior. Here, we critically assess the validity of the assumptions underlying these models and propose a model that allows for more flexible, yet conceptually more plausible, modelling of empirical distributions. By representing previous experiences as a mixture of lognormal distributions, this model can be parametrized to mimic different unimodal distributions and thus extends previous instantiations of Bayesian observer models. We fit the mixture lognormal model to published interval timing data of healthy young adults and a clinical population of aged mild cognitive impairment patients and age-matched controls, and demonstrate that this model better explains behavioural data and provides new insights into the mechanisms that underlie the behaviour of a memory-affected clinical population.

Is the scalar property of interval timing preserved after hippocampus lesions?

Time perception is fundamental for decision-making, adaptation, and survival. In the peak-interval (PI) paradigm, one of the critical features of time perception is its scale invariance, i.e., the error in time estimation increases linearly with the to-be-timed interval. Brain lesions can profoundly alter time perception, but do they also change its scalar property? In particular, hippocampus (HPC) lesions affect the memory of the reinforced durations. Experiments found that ventral hippocampus (vHPC) lesions shift the perceived durations to longer values while dorsal hippocampus (dHPC) lesions produce opposite effects. Here we used our implementation of the Striatal Beat Frequency (SBFML) model with biophysically realistic Morris-Lecar (ML) model neurons and a topological map of HPC memory to predict analytically and verify numerically the effect of HPC lesions on scalar property. We found that scalar property still holds after both vHPC and dHPC lesions in our SBFML-HPC network simulation. Our numerical results show that PI durations are shifted in the correct direction and match the experimental results. In our simulations, the relative peak shift of the behavioral response curve is controlled by two factors: (1) the lesion size, and (2) the cellular-level memory variance of the temporal durations stored in the HPC. The coefficient of variance (CV) of the behavioral response curve remained constant over the tested durations of PI procedure, which suggests that scalar property is not affected by HPC lesions.

The specific role of the striatum in interval timing: The Huntington’s disease model

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Patients with Huntington’s Disease (HD) report a temporal deficit in daily life.

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We tested HD gene carriers and controls in spatial (cm) and temporal (s) tasks.

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Early stage HD patients, but not presymptomatic carriers, were more impaired in time.

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Striatal volume was associated with the temporal deficit in gene carriers.

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Evaluation of interval timing processing should be used as a clinical tool.

Time processing over intervals of hundreds of milliseconds to minutes, also known as interval timing, is associated with the striatum. Huntington’s disease patients (HD) with striatal degeneration have impaired interval timing, but the extent and specificity of these deficits remain unclear. Are they specific to the temporal domain, or do they extend to the spatial domain too? Do they extend to both the perception and production of interval timing? Do they appear before motor symptoms in Huntington’s disease (Pre-HD)?

We addressed these issues by assessing both temporal abilities (in the seconds range) and spatial abilities (in the cm range) in 20 Pre-HD, 25 HD patients, and 25 healthy Controls, in discrimination, bisection and production paradigms. In addition, all participants completed a questionnaire assessing temporal and spatial disorientation in daily life, and the gene carriers (i.e., HD and Pre-HD participants) underwent structural brain MRI.

Overall, HD patients were more impaired in the temporal than in the spatial domain in the behavioral tasks, and expressed a greater disorientation in the temporal domain in the daily life questionnaire. In contrast, Pre-HD participants showed no sign of a specific temporal deficit. Furthermore, MRI analyses indicated that performances in the temporal discrimination task were associated with a larger striatal grey matter volume in the striatum in gene carriers.

Altogether, behavioral, brain imaging and questionnaire data support the hypothesis that the striatum is a specific component of interval timing processes. Evaluations of temporal disorientation and interval timing processing could be used as clinical tools for HD patients.

Reinforcement regulates timing variability in thalamus

Learning reduces variability but variability can facilitate learning. This paradoxical relationship has made it challenging to tease apart sources of variability that degrade performance from those that improve it. We tackled this question in a context-dependent timing task requiring humans and monkeys to flexibly produce different time intervals with different effectors. We identified two opposing factors contributing to timing variability: slow memory fluctuation that degrades performance and reward-dependent exploratory behavior that improves performance. Signatures of these opposing factors were evident across populations of neurons in the dorsomedial frontal cortex (DMFC), DMFC-projecting neurons in the ventrolateral thalamus, and putative target of DMFC in the caudate. However, only in the thalamus were the performance-optimizing regulation of variability aligned to the slow performance-degrading memory fluctuations. These findings reveal how variability caused by exploratory behavior might help to mitigate other undesirable sources of variability and highlight a potential role for thalamocortical projections in this process.

The Peak Interval Procedure in Rodents: A Tool for Studying the Neurobiological Basis of Interval Timing and Its Alterations in Models of Human Disease

Animals keep track of time intervals in the seconds to minutes range with, on average, high accuracy but substantial trial-to-trial variability. The ability to detect the statistical signatures of such timing behavior is an indispensable feature of a good and theoretically-tractable testing procedure. A widely used interval timing procedure is the peak interval (PI) procedure, where animals learn to anticipate rewards that become available after a fixed delay. After learning, they cluster their responses around that reward-availability time. The in-depth analysis of such timed anticipatory responses leads to the understanding of an internal timing mechanism, that is, the processing dynamics and systematic biases of the brain's clock. This protocol explains in detail how the PI procedure can be implemented in rodents, from training through testing to analysis. We showcase both trial-by-trial and trial-averaged analytical methods as a window into these internal processes. This protocol has the advantages of capturing timing behavior in its full-complexity in a fashion that allows for a theoretical treatment of the data.

Visual timing abilities of a harbour seal (Phoca vitulina) and a South African fur seal (Arctocephalus pusillus pusillus) for sub- and supra-second time intervals

Timing is an essential parameter influencing many behaviours. A previous study demonstrated a high sensitivity of a phocid, the harbour seal (Phoca vitulina), in discriminating time intervals. In the present study, we compared the harbour seal’s timing abilities with the timing abilities of an otariid, the South African fur seal (Arctocephalus pusillus pusillus). This comparison seemed essential as phocids and otariids differ in many respects and might, thus, also differ regarding their timing abilities. We determined time difference thresholds for sub- and suprasecond time intervals marked by a white circle on a black background displayed for a specific time interval on a monitor using a staircase method. Contrary to our expectation, the timing abilities of the fur seal and the harbour seal were comparable. Over a broad range of time intervals, 0.8–7 s in the fur seal and 0.8–30 s in the harbour seal, the difference thresholds followed Weber’s law. In this range, both animals could discriminate time intervals differing only by 12 % and 14 % on average. Timing might, thus be a fundamental cue for pinnipeds in general to be used in various contexts, thereby complementing information provided by classical sensory systems. Future studies will help to clarify if timing is indeed involved in foraging decisions or the estimation of travel speed or distance.

Can scalar timing explain variability in scanning patterns?

Why are scanning patterns so variable? Theory predicts that for prey species facing non-stalking predators scans to monitor predators should occur at fixed rather than unpredictable times. Yet, empirical distributions of inter-scan intervals (ISIs) are very variable. One hypothesis to explain variability is that animals initiate several of their scans in response to external disturbances that occur at random times. I propose, instead, that animals actually aim to initiate scans at fixed times, which are adjusted to perceived predation risk, but well-established cognitive processes on interval timing induce variability in ISIs. Signatures associated with scalar timing, a leading theory of interval timing in animals, include a linear increase in the standard deviation of ISIs as a function of mean ISI duration. The increase is expected to be proportional to mean ISI duration, which implies that the CV (SD*100/Mean) of ISIs is unrelated to mean ISI duration. Finally, the distribution of ISIs should be gamma-like with right skew. I tested these predictions in groups of domestic fowls (Gallus gallus domesticus) under controlled conditions and in groups of American flamingos (Phoenicopterus ruber) in the field. I found support for most but not all predictions in these two species. In particular, CV of ISIs increased with the mean, a deviation that I attribute to non-independent vigilance amongst group members. Cognitive processes associated with scanning patterns warrant further empirical testing.

A Population-Based Model of the Temporal Memory in the Hippocampus

Spatial and temporal dimensions are fundamental for orientation, adaptation, and survival of organisms. Hippocampus has been identified as the main neuroanatomical structure involved both in space and time perception and their internal representation. Dorsal hippocampus lesions showed a leftward shift (toward shorter durations) in peak-interval procedures, whereas ventral lesions shifted the peak time toward longer durations. We previously explained hippocampus lesion experimental findings by assuming a topological map model of the hippocampus with shorter durations memorized ventrally and longer durations more dorsal. Here we suggested a possible connection between the abstract topological maps model of the hippocampus that stored reinforcement times in a spatially ordered memory register and the "time cells" of the hippocampus. In this new model, the time cells provide a uniformly distributed time basis that covers the entire to-be-learned temporal duration. We hypothesized that the topological map of the hippocampus stores the weights that reflect the contribution of each time cell to the average temporal field that determines the behavioral response. The temporal distance between the to-be-learned criterion time and the time of the peak activity of each time cell provides the error signal that determines the corresponding weight correction. Long-term potentiation/depression could enhance/weaken the weights associated to the time cells that peak closer/farther to the criterion time. A coincidence detector mechanism, possibly under the control of the dopaminergic system, could be involved in our suggested error minimization and learning algorithm.

Inactivation of the Medial-Prefrontal Cortex Impairs Interval Timing Precision, but Not Timing Accuracy or Scalar Timing in a Peak-Interval Procedure in Rats

Motor sequence learning, planning and execution of goal-directed behaviors, and decision making rely on accurate time estimation and production of durations in the seconds-to-minutes range. The pathways involved in planning and execution of goal-directed behaviors include cortico-striato-thalamo-cortical circuitry modulated by dopaminergic inputs. A critical feature of interval timing is its scalar property, by which the precision of timing is proportional to the timed duration. We examined the role of medial prefrontal cortex (mPFC) in timing by evaluating the effect of its reversible inactivation on timing accuracy, timing precision and scalar timing. Rats were trained to time two durations in a peak-interval (PI) procedure. Reversible mPFC inactivation using GABA agonist muscimol resulted in decreased timing precision, with no effect on timing accuracy and scalar timing. These results are partly at odds with studies suggesting that ramping prefrontal activity is crucial to timing but closely match simulations with the Striatal Beat Frequency (SBF) model proposing that timing is coded by the coincidental activation of striatal neurons by cortical inputs. Computer simulations indicate that in SBF, gradual inactivation of cortical inputs results in a gradual decrease in timing precision with preservation of timing accuracy and scalar timing. Further studies are needed to differentiate between timing models based on coincidence detection and timing models based on ramping mPFC activity, and clarify whether mPFC is specifically involved in timing, or more generally involved in attention, working memory, or response selection/inhibition.

"Walking" through the sensory, cognitive, and temporal degradations of healthy aging

As we age, there is a wide range of changes in motor, sensory, cognitive, and temporal processing due to alterations in the functioning of the central nervous and musculoskeletal systems. Specifically, aging is associated with degradations in gait; altered processing of the individual sensory systems; modifications in executive control, memory, and attention; and changes in temporal processing. These age-related alterations are often inter-related and have been suggested to result from shared neural substrates. Additionally, the overlap between these brain areas and those controlling walking raises the possibility of facilitating performance in several tasks by introducing protocols that can efficiently target all four domains. Attempts to counteract these negative effects of normal aging have been focusing on research to prevent falls and/or enhance cognitive processes, while ignoring the potential multisensory benefits accompanying old age. Research shows that the aging brain tends to increasingly rely on multisensory integration to compensate for degradations in individual sensory systems and for altered neural functioning. This review covers the age-related changes in the above-mentioned domains and the potential to exploit the benefits associated with multisensory integration in aging so as to improve one's mobility and enhance sensory, cognitive, and temporal processing.

Scalar timing in memory: A temporal map in the hippocampus

Many essential tasks, such as decision making, rate calculation and planning, require accurate timing in the second to minute range. This process, known as interval timing, involves many cortical areas such as the prefrontal cortex, the striatum, and the hippocampus. Although the neurobiological origin and the mechanisms of interval timing are largely unknown, we have developed increasingly accurate mathematical and computational models that can mimic some properties of time perception. The accepted paradigm of temporal durations storage is that the objective elapsed time from the short-term memory is transferred to the reference memory using a multiplicative "memory translation constant" K*. It is believed that K* has a Gaussian distribution due to trial-related variabilities. To understand K* genesis, we hypothesized that the storage of temporal memories follows a topological map in the hippocampus, with longer durations stored towards dorsal hippocampus and shorter durations stored toward ventral hippocampus. We found that selective removal of memory cells in this topological map model shifts the peak-response time in a manner consistent with the current experimental data on the effect of hippocampal lesions on time perception. This opens new avenues for experimental testing of our topological map hypothesis. We found numerically that the relative shift is determined both by the lesion size and its location and we suggested a theoretical estimate for the memory translation constant K*.

The Persistence of Memory: How the Brain Encodes Time in Memory

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.

Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve

We used the phase-resetting method to study a biologically relevant three-neuron network in which one neuron receives multiple inputs per cycle. For this purpose, we first generalized the concept of phase resetting to accommodate multiple inputs per cycle. We explicitly showed how analytical conditions for the existence and the stability of phase-locked modes are derived. In particular, we solved newly derived recursive maps using as an example a biologically relevant driving-driven neural network with a dynamic feedback loop. We applied the generalized phase-resetting definition to predict the relative-phase and the stability of a phase-locked mode in open loop setup. We also compared the predicted phase-locked mode against numerical simulations of the fully connected network.

A generalized phase resetting method for phase-locked modes prediction

We derived analytically and checked numerically a set of novel conditions for the existence and the stability of phase-locked modes in a biologically relevant master-slave neural network with a dynamic feedback loop. Since neural oscillators even in the three-neuron network investigated here receive multiple inputs per cycle, we generalized the concept of phase resetting to accommodate multiple inputs per cycle. We proved that the phase resetting produced by two or more stimuli per cycle can be recursively computed from the traditional, single stimulus, phase resetting. We applied the newly derived generalized phase resetting definition to predicting the relative phase and the stability of a phase-locked mode that was experimentally observed in this type of master-slave network with a dynamic loop network.

Working Memory for Sequences of Temporal Durations Reveals a Volatile Single-Item Store

When a sequence is held in working memory, different items are retained with differing fidelity. Here we ask whether a sequence of brief time intervals that must be remembered show recency effects, similar to those observed in verbal and visuospatial working memory. It has been suggested that prioritizing some items over others can be accounted for by a "focus of attention," maintaining some items in a privileged state. We therefore also investigated whether such benefits are vulnerable to disruption by attention or expectation. Participants listened to sequences of one to five tones, of varying durations (200 ms to 2 s). Subsequently, the length of one of the tones in the sequence had to be reproduced by holding a key. The discrepancy between the reproduced and actual durations quantified the fidelity of memory for auditory durations. Recall precision decreased with the number of items that had to be remembered, and was better for the first and last items of sequences, in line with set-size and serial position effects seen in other modalities. To test whether attentional filtering demands might impair performance, an irrelevant variation in pitch was introduced in some blocks of trials. In those blocks, memory precision was worse for sequences that consisted of only one item, i.e., the smallest memory set-size. Thus, when irrelevant information was present, the benefit of having only one item in memory is attenuated. Finally we examined whether expectation could interfere with memory. On half the trials, the number of items in the upcoming sequence was cued. When the number of items was known in advance, performance was paradoxically worse when the sequence consisted of only one item. Thus the benefit of having only one item to remember is stronger when it is unexpectedly the only item. Our results suggest that similar mechanisms are used to hold auditory time durations in working memory, as for visual or verbal stimuli. Further, solitary items were remembered better when more items were expected, but worse when irrelevant features were present. This suggests that the "privileged" state of one item in memory is particularly volatile and susceptible to interference.

A Brief History of “The Psychology of Time Perception”

Basic mechanisms of interval timing and associative learning are shared by many animal species, and develop quickly in early life, particularly across infancy, and childhood. Indeed, John Wearden in his book “The Psychology of Time Perception”, which is based on decades of his own research with colleagues, and which our commentary serves to primarily review, has been instrumental in implementing animal models and methods in children and adults, and has revealed important similarities (and differences) between human timing (and that of animals) when considered within the context of scalar timing theory. These seminal studies provide a firm foundation upon which the contemporary multifaceted field of timing and time perception has since advanced. The contents of the book are arguably one piece of a larger puzzle, and as Wearden cautions, “The reader is warned that my own contribution to the field has been exaggerated here, but if you are not interested in your own work, why would anyone else be?” Surely there will be many interested readers, however the book is noticeably lacking in it neurobiological perspective. The mind (however it is conceived) needs a brain (even if behaviorists tend to say “the brain behaves”, and most neuroscientists currently have a tenuous grasp on the neural mechanisms of temporal cognition), and to truly understand the psychology of time, brain and behavior must go hand in hand regardless of the twists, turns, and detours along the way.

Cognitive Aging and Time Perception: Roles of Bayesian Optimization and Degeneracy

This review outlines the basic psychological and neurobiological processes associated with age-related distortions in timing and time perception in the hundredths of milliseconds-to-minutes range. The difficulty in separating indirect effects of impairments in attention and memory from direct effects on timing mechanisms is addressed. The main premise is that normal aging is commonly associated with increased noise and temporal uncertainty as a result of impairments in attention and memory as well as the possible reduction in the accuracy and precision of a central timing mechanism supported by dopamine-glutamate interactions in cortico-striatal circuits. Pertinent to these findings, potential interventions that may reduce the likelihood of observing age-related declines in timing are discussed. Bayesian optimization models are able to account for the adaptive changes observed in time perception by assuming that older adults are more likely to base their temporal judgments on statistical inferences derived from multiple trials than on a single trial's clock reading, which is more susceptible to distortion. We propose that the timing functions assigned to the age-sensitive fronto-striatal network can be subserved by other neural networks typically associated with finely-tuned perceptuo-motor adjustments, through degeneracy principles (different structures serving a common function).

Emotional modulation of interval timing and time perception

Like other senses, our perception of time is not veridical, but rather, is modulated by changes in environmental context. Anecdotal experiences suggest that emotions can be powerful modulators of time perception; nevertheless, the functional and neural mechanisms underlying emotion-induced temporal distortions remain unclear. Widely accepted pacemaker-accumulator models of time perception suggest that changes in arousal and attention have unique influences on temporal judgments and contribute to emotional distortions of time perception. However, such models conflict with current views of arousal and attention suggesting that current models of time perception do not adequately explain the variability in emotion-induced temporal distortions. Instead, findings provide support for a new perspective of emotion-induced temporal distortions that emphasizes both the unique and interactive influences of arousal and attention on time perception over time. Using this framework, we discuss plausible functional and neural mechanisms of emotion-induced temporal distortions and how these temporal distortions may have important implications for our understanding of how emotions modulate our perceptual experiences in service of adaptive responding to biologically relevant stimuli.

Clocks within Clocks: Timing by Coincidence Detection

The many existent models of timing rely on vastly different mechanisms to track temporal information. Here we examine these differences, and identify coincidence detection in its most general form as a common mechanism that many apparently different timing models share, as well as a common mechanism of biological circadian, millisecond and interval timing. This view predicts that timing by coincidence detection is a ubiquitous phenomenon at many biological levels, explains the reports of biological timing in many brain areas, explains the role of neural noise at different time scales at both biological and theoretical levels, and provides cohesion within the timing field.

A single mechanism account of duration and rate processing via the pacemaker-accumulator and beat frequency models

Time is an essential dimension of our environment that allows us to extract meaningful information about speed of movement, speech, motor actions and fine motor control. Traditionally, models of time have tried to quantify how the brain might process the duration of an event. The most commonly cited are the pacemaker-accumulator model and the beat frequency model of interval timing, which explain how duration is perceived, represented and encoded. Here we posit such models as providing a powerful tool for simultaneously extracting, representing and encoding stimulus rate information. That is, any model that can process duration has all the information needed to code stimulus rate. We explore different processing strategies which would enable rate to be read off from both the pacemaker-accumulator and beat frequency model of interval timing. Finally we explore open questions that, when answered, will shed light upon potential mechanisms for duration and rate estimation.

When and How-Long: A Unified Approach for Time Perception

The representation of the environment assumes the encoding of four basic dimensions in the brain, that is the 3D space and time. The vital role of time for cognition is a topic that recently attracted increasing research interest. Surprisingly, the scientific community investigating mind-time interactions has mainly focused on interval timing, paying less attention on the encoding and processing of distant moments. The present work highlights two basic capacities that are necessary for developing temporal cognition in artificial systems. In particular, the seamless integration of agents in the environment assumes they are able to consider when events have occurred and how-long they have lasted. This information, although rather standard in humans, is largely missing from artificial cognitive systems. In this work we consider how a time perception model that is based on neural networks and the Striatal Beat Frequency (SBF) theory is extended in a way that besides the duration of events, facilitates the encoding of the time of occurrence in memory. The extended model is capable to support skills assumed in temporal cognition and answer time-related questions about the unfolded events.

During Running in Place, Grid Cells Integrate Elapsed Time and Distance Run

The spatial scale of grid cells may be provided by self-generated motion information or by external sensory information from environmental cues. To determine whether grid cell activity reflects distance traveled or elapsed time independent of external information, we recorded grid cells as animals ran in place on a treadmill. Grid cell activity was only weakly influenced by location, but most grid cells and other neurons recorded from the same electrodes strongly signaled a combination of distance and time, with some signaling only distance or time. Grid cells were more sharply tuned to time and distance than non-grid cells. Many grid cells exhibited multiple firing fields during treadmill running, parallel to the periodic firing fields observed in open fields, suggesting a common mode of information processing. These observations indicate that, in the absence of external dynamic cues, grid cells integrate self-generated distance and time information to encode a representation of experience.

Contribution of Cerebellar Loops to Action Timing

Recent studies of sensorimotor processing have benefited from decision-making paradigms that emphasize the selection of appropriate movements. Selecting when to make those responses, or action timing, is important as well. Although the cerebellum is commonly viewed as a controller of movement dynamics, its role in action timing is also firmly supported. Several lines of research have now extended this idea. Anatomical findings have revealed connections between the cerebellum and broader timing circuits, neurophysiological results have suggested mechanisms for timing within its microcircuitry, and theoretical work has indicated how temporal signals are processed through it and decoded by its targets. These developments are inspiring renewed studies of the role of the cerebellar loops in action timing.

Low-dimensional attractor for neural activity from local field potentials in optogenetic mice

We used optogenetic mice to investigate possible nonlinear responses of the medial prefrontal cortex (mPFC) local network to light stimuli delivered by a 473 nm laser through a fiber optics. Every 2 s, a brief 10 ms light pulse was applied and the local field potentials (LFPs) were recorded with a 10 kHz sampling rate. The experiment was repeated 100 times and we only retained and analyzed data from six animals that showed stable and repeatable response to optical stimulations. The presence of nonlinearity in our data was checked using the null hypothesis that the data were linearly correlated in the temporal domain, but were random otherwise. For each trail, 100 surrogate data sets were generated and both time reversal asymmetry and false nearest neighbor (FNN) were used as discriminating statistics for the null hypothesis. We found that nonlinearity is present in all LFP data. The first 0.5 s of each 2 s LFP recording were dominated by the transient response of the networks. For each trial, we used the last 1.5 s of steady activity to measure the phase resetting induced by the brief 10 ms light stimulus. After correcting the LFPs for the effect of phase resetting, additional preprocessing was carried out using dendrograms to identify “similar” groups among LFP trials. We found that the steady dynamics of mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar “8”-shaped attractors across different animals. Our results also open the possibility of designing a low-dimensional model for optical stimulation of the mPFC local network.

Complex sensorimotor transformation processes required for response selection are facilitated by the striatum

Both fronto-parietal networks and the basal ganglia play an important role in action cascading. It is well-known that cortical structures mediate sensorimotor transformation for this purpose. The striatum receives extensive input from those cortical structures and has been shown to be modulated by the predictability of cortical input. Until today, it has however remained unclear whether the processing of spatial codes or even sensorimotor transformation processes for the purpose of action cascading involve the striatum. We therefore examined this question by means of fMRI using a stop-change task that varied the predictability as well as the complexity of sensorimotor transformations required for correct responding in the context of action cascading. On the behavioral level, we found that the complexity of sensorimotor transformation processes only prolonged reaction times when the requirement for this transformation was predictable. fMRI results matched this effect showing enhanced activity of the caudate in case a complex sensorimotor transformation could be anticipated. Irrespective of the complexity of the required transformations, the putamen was furthermore involved in the prediction of imminent action cascading demands. Taken together, our findings give rise to a conceptual advance regarding basal ganglia function by showing that the anticipation and, more importantly, processing of complex sensorimotor transformation processes involves the striatum.

Associative and temporal learning: new directions

Associative and temporal learning are fundamental properties of behavior. Despite the temporal dynamics of behavior, traditional associative (trial based) approaches have often ignored (within trial) timing properties of behavior. Therefore, associative and temporal learning are considered different, parallel strategies, whose mechanisms and rules are domain-specific. The rift between the two fields is not surprising considering the difference in questions, measures, and approaches. Some questions explored in this mini-review are as follows: Are the behavioral phenomena appropriately described, measured or quantified? How do animals integrate associative and temporal information? What are the behavioral processes that bridge the associative and temporal fields? How are associative and temporal information instantiated and processed in the brain? A resolution involves finding a more adept way (e.g., computational or biological) to describe the associative and temporal phenomena, for example by transforming them in a more abstract dimension, such as information (e.g., entropy calculation) or frequency (e.g., neural firing). When seen from this neural-computation vantage point, the distinctions between associative and temporal learning vanish, and the question becomes: What are the mechanisms that coexist, cooperate and compete in a brain that processes associative and temporal information in real time? This article is part of a Special Issue entitled: Associative and Temporal Learning.

Oscillatory multiplexing of neural population codes for interval timing and working memory

Interval timing and working memory are critical components of cognition that are supported by neural oscillations in prefrontal-striatal-hippocampal circuits. In this review, the properties of interval timing and working memory are explored in terms of behavioral, anatomical, pharmacological, and neurophysiological findings. We then describe the various neurobiological theories that have been developed to explain these cognitive processes - largely independent of each other. Following this, a coupled excitatory - inhibitory oscillation (EIO) model of temporal processing is proposed to address the shared oscillatory properties of interval timing and working memory. Using this integrative approach, we describe a hybrid model explaining how interval timing and working memory can originate from the same oscillatory processes, but differ in terms of which dimension of the neural oscillation is utilized for the extraction of item, temporal order, and duration information. This extension of the striatal beat-frequency (SBF) model of interval timing (Matell and Meck, 2000, 2004) is based on prefrontal-striatal-hippocampal circuit dynamics and has direct relevance to the pathophysiological distortions observed in time perception and working memory in a variety of psychiatric and neurological conditions.

Time perception: the bad news and the good

Time perception is fundamental and heavily researched, but the field faces a number of obstacles to theoretical progress. In this advanced review, we focus on three pieces of 'bad news' for time perception research: temporal perception is highly labile across changes in experimental context and task; there are pronounced individual differences not just in overall performance but in the use of different timing strategies and the effect of key variables; and laboratory studies typically bear little relation to timing in the 'real world'. We describe recent examples of these issues and in each case offer some 'good news' by showing how new research is addressing these challenges to provide rich insights into the neural and information-processing bases of timing and time perception. WIREs Cogn Sci 2014, 5:429-446. doi: 10.1002/wcs.1298 This article is categorized under: Psychology > Perception and Psychophysics Neuroscience > Cognition.

What does scalar timing tell us about neural dynamics?

The “Scalar Timing Law,” which is a temporal domain generalization of the well known Weber Law, states that the errors estimating temporal intervals scale linearly with the durations of the intervals. Linear scaling has been studied extensively in human and animal models and holds over several orders of magnitude, though to date there is no agreed upon explanation for its physiological basis. Starting from the assumption that behavioral variability stems from neural variability, this work shows how to derive firing rate functions that are consistent with scalar timing. We show that firing rate functions with a log-power form, and a set of parameters that depend on spike count statistics, can account for scalar timing. Our derivation depends on a linear approximation, but we use simulations to validate the theory and show that log-power firing rate functions result in scalar timing over a large range of times and parameters. Simulation results match the predictions of our model, though our initial formulation results in a slight bias toward overestimation that can be corrected using a simple iterative approach to learn a decision threshold.

Dedicated clock/timing-circuit theories of time perception and timed performance

Scalar Timing Theory (an information-processing version of Scalar Expectancy Theory) and its evolution into the neurobiologically plausible Striatal Beat-Frequency (SBF) theory of interval timing are reviewed. These pacemaker/accumulator or oscillation/coincidence detection models are then integrated with the Adaptive Control of Thought-Rational (ACT-R) cognitive architecture as dedicated timing modules that are able to make use of the memory and decision-making mechanisms contained in ACT-R. The different predictions made by the incorporation of these timing modules into ACT-R are discussed as well as the potential limitations. Novel implementations of the original SBF model that allow it to be incorporated into ACT-R in a more fundamental fashion than the earlier simulations of Scalar Timing Theory are also considered in conjunction with the proposed properties and neural correlates of the "internal clock".