Time-scale invariance as an emergent property in a perceptron with realistic, noisy neurons

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.

Learning About Reward Identities and Time

We discuss three empirical findings that we think any theory attempting to integrate interval timing with associative learning concepts will need to address. These empirical phenomena all come from studies that combine peak timing procedures with reinforcer devaluation or conditional discrimination tasks commonly employed, respectively, in interval timing or associative learning research traditions. The three phenomena we discuss include: (1) the observation that disruptions in reward identity encoding have little to no impact on the encoding of reward time in the a peak procedure (Delamater., 1998), (2) the findings that organisms tend to average their time estimates when presented with a stimulus compound consisting of separately learned stimuli indicating short or long reward times but that such temporal averaging, itself, is sensitive to post-conditioning selective reward devaluation, and (3) that rats can learn a temporal patterning task in which two stimuli presented independently indicate one time to reward availability while their compound indicates another. We review our prior results and present new findings illustrating these three phenomena and we discuss the special challenges they pose for cascade theories of timing, for multiple-oscillator models, and for any approach that attempts to integrate interval timing and associative models. We close by illustrating some ways in which multi-layer connectionist network models might begin to address some of our key findings. We believe this will require an approach that includes separate mechanisms that code for reward identity and time, but that does so in a way that permits for integration between the two systems.

Oscillation/Coincidence-Detection Models of Reward-Related Timing in Corticostriatal Circuits

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.

Variation in the "coefficient of variation": Rethinking the violation of the scalar property in time-duration judgments

The coefficient of variation (CV), also known as relative standard deviation, has been used to measure the constancy of the Weber fraction, a key signature of efficient neural coding in time perception. It has long been debated whether or not duration judgments follow Weber's law, with arguments based on examinations of the CV. However, what has been largely ignored in this debate is that the observed CVs may be modulated by temporal context and decision uncertainty, thus questioning conclusions based on this measure. Here, we used a temporal reproduction paradigm to examine the variation of the CV with two types of temporal context: full-range mixed vs. sub-range blocked intervals, separately for intervals presented in the visual and auditory modalities. We found a strong contextual modulation of both interval-duration reproductions and the observed CVs. We then applied a two-stage Bayesian model to predict those variations. Without assuming a violation of the constancy of the Weber fraction, our model successfully predicted the central-tendency effect and the variation in the CV. Our findings and modeling results indicate that both the accuracy and precision of our timing behavior are highly dependent on the temporal context and decision uncertainty. And, critically, they advise caution with using variations of the CV to reject the constancy of the Weber fraction of duration estimation.

Time is body: Multimodal evidence of crosstalk between interoception and time estimation

Theoretical approaches propose a blending between interoception and time estimation. Interoception might constitute a neurophysiological mechanism for encoding duration. However, no study has assessed the convergence between interoception and time estimation using behavioral, neurophysiological, and functional anatomy signatures. We examined the multimodal convergence between interoception and time estimation using a two-fold approach. In study 1, we developed a dual design combining interoception (measuring heartbeat detection - HBD, and heartbeat evoked potential - HEP) with a time estimation paradigm (TEP, estimation of duration of a 120 s interval). In study 2, we performed a conjoint metanalysis (Multi-level Kernel Density Analysis, MKDA) of neuroimaging, including reports of interoception and time estimation. Both studies provide convergent evidence of time estimation's significant involvement in behavioral, electrophysiological (enhanced HEP), and neuroimaging (overlapping cluster in the right insula and operculum) signatures of interoception. Convergent results from both studies offer direct support for a shared mechanism of interoception and time estimation.

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.

Modeling Interval Timing by Recurrent Neural Nets

The purpose of this study was to take a new approach in showing how the central nervous system might encode time at the supra-second level using recurrent neural nets (RNNs). This approach utilizes units with a delayed feedback, whose feedback weight determines the temporal properties of specific neurons in the network architecture. When these feedback neurons are coupled, they form a multilayered dynamical system that can be used to model temporal responses to steps of input in multidimensional systems. The timing network was implemented using separate recurrent “Go” and “No-Go” neural processing units to process an individual stimulus indicating the time of reward availability. Outputs from these distinct units on each time step are converted to a pulse reflecting a weighted sum of the separate Go and No-Go signals. This output pulse then drives an integrator unit, whose feedback weight and input weights shape the pulse distribution. This system was used to model empirical data from rodents performing in an instrumental “peak interval timing” task for two stimuli, Tone and Flash. For each of these stimuli, reward availability was signaled after different times from stimulus onset during training. Rodent performance was assessed on non-rewarded trials, following training, with each stimulus tested individually and simultaneously in a stimulus compound. The associated weights in the Go/No-Go network were trained using experimental data showing the mean distribution of bar press rates across an 80 s period in which a tone stimulus signaled reward after 5 s and a flash stimulus after 30 s from stimulus onset. Different Go/No-Go systems were used for each stimulus, but the weighted output of each fed into a final recurrent integrator unit, whose weights were unmodifiable. The recurrent neural net (RNN) model was implemented using Matlab and Matlab’s machine learning tools were utilized to train the network using the data from non-rewarded trials. The neural net output accurately fit the temporal distribution of tone and flash-initiated bar press data. Furthermore, a “Temporal Averaging” effect was also obtained when the flash and tone stimuli were combined. These results indicated that the system combining tone and flash responses were not superposed as in a linear system, but that there was a non-linearity, which interacted between tone and flash. In order to achieve an accurate fit to the empirical averaging data it was necessary to implement non-linear “saliency functions” that limited the output signal of each stimulus to the final integrator when the other was co-present. The model suggests that the central nervous system encodes timing generation as a dynamical system whose timing properties are embedded in the connection weights of the system. In this way, event timing is coded similar to the way other sensory-motor systems, such as the vestibulo-ocular and optokinetic systems, which combine sensory inputs from the vestibular and visual systems to generate the temporal aspects of compensatory eye movements.

Neural Correlates of Interval Timing Deficits in Schizophrenia

Previous research has shown that schizophrenia (SZ) patients exhibit impairments in interval timing. The cause of timing impairments in SZ remains unknown but may be explained by a dysfunction in the fronto-striatal circuits. Although the current literature includes extensive behavioral data on timing impairments, there is limited focus on the neural correlates of timing in SZ. The neuroimaging literature included in the current review reports hypoactivation in the dorsal-lateral prefrontal cortex (DLPFC), supplementary motor area (SMA) and the basal ganglia (BG). Timing deficits and deficits in attention and working memory (WM) in SZ are likely due to a dysfunction of dopamine (DA) and gamma-aminobutyric acid (GABA) neurotransmission in the cortico-striatal-thalamo-cortical circuits, which are highly implicated in executive functioning and motor preparation.

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.

Neurochemical changes in basal ganglia affect time perception in parkinsonians

BACKGROUND

Parkinson's disease is described as resulting from dopaminergic cells progressive degeneration, specifically in the substantia nigra pars compacta that influence the voluntary movements control, decision making and time perception.

AIM

This review had a goal to update the relation between time perception and Parkinson's Disease.

METHODOLOGY

We used the PRISMA methodology for this investigation built guided for subjects dopaminergic dysfunction in the time judgment, pharmacological models with levodopa and new studies on the time perception in Parkinson's Disease. We researched on databases Scielo, Pubmed / Medline and ISI Web of Knowledge on August 2017 and repeated in September 2017 and February 2018 using terms and associations relevant for obtaining articles in English about the aspects neurobiology incorporated in time perception. No publication status or restriction of publication date was imposed, but we used as exclusion criteria: dissertations, book reviews, conferences or editorial work.

RESULTS/DISCUSSION

We have demonstrated that the time cognitive processes are underlying to performance in cognitive tasks and that many are the brain areas and functions involved and the modulators in the time perception performance.

CONCLUSIONS

The influence of dopaminergic on Parkinson's Disease is an important research tool in Neuroscience while allowing for the search for clarifications regarding behavioral phenotypes of Parkinson's disease patients and to study the areas of the brain that are involved in the dopaminergic circuit and their integration with the time perception mechanisms.

Learning what to expect and when to expect it involves dissociable neural systems

Two experiments with Long-Evans rats examined the potential independence of learning about different features of food reward, namely, "what" reward is to be expected and "when" it will occur. This was examined by investigating the effects of selective reward devaluation upon responding in an instrumental peak timing task in Experiment 1 and by exploring the effects of pre-training lesions targeting the basolateral amygdala (BLA) upon the selective reward devaluation effect and interval timing in a Pavlovian peak timing task in Experiment 2. In both tasks, two stimuli, each 60 s long, signaled that qualitatively distinct rewards (different flavored food pellets) could occur after 20 s. Responding on non-rewarded probe trials displayed the characteristic peak timing function with mean responding gradually increasing and peaking at approximately 20 s before more gradually declining thereafter. One of the rewards was then independently paired repeatedly with LiCl injections in order to devalue it whereas the other reward was unpaired with these injections. In a final set of test sessions in which both stimuli were presented without rewards, it was observed that responding was selectively reduced in the presence of the stimulus signaling the devalued reward compared to the stimulus signaling the still valued reward. Moreover, the timing function was mostly unaltered by this devaluation manipulation. Experiment 2 showed that pre-training BLA lesions abolished this selective reward devaluation effect, but it had no impact on peak timing functions shown by the two stimuli. It appears from these data that learning about "what" and "when" features of reward may entail separate underlying neural systems.

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*.

As time passes by: Observed motion-speed and psychological time during video playback

Research shows that psychological time (i.e., the subjective experience and assessment of the passage of time) is malleable and that the central nervous system re-calibrates temporal information in accordance with situational factors so that psychological time flows slower or faster. Observed motion-speed (e.g., the visual perception of a rolling ball) is an important situational factor which influences the production of time estimates. The present study examines previous findings showing that observed slow and fast motion-speed during video playback respectively results in over- and underproductions of intervals of time. Here, we investigated through three separate experiments: a) the main effect of observed motion-speed during video playback on a time production task and b) the interactive effect of the frame rate (frames per second; fps) and motion-speed during video playback on a time production task. No main effect of video playback-speed or interactive effect between video playback-speed and frame rate was found on time production.

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.

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.

Emotion and Time Perception in Children and Adults: The Effect of Task Difficulty

In the present study, adults and children aged five and eight years were given a temporal bisection task involving emotional stimuli (angry and neutral faces) and three levels of discrimination difficulty that differed as a function of the ratio used between the short and the long standard duration (very easy, easy, and difficult). In addition, their cognitive capacities in terms of working memory and attention inhibition were assessed by neuropsychological tests. In the very easy temporal task (ratio of 1:4), the results showed that the psychophysical functions were shifted toward the left in all participants for the angry faces compared to the neutral faces, with a significant lowering of the Bisection Point, suggesting that the stimulus duration was judged to last longer for the emotional stimuli. In addition, the results did not show any relationship between the magnitude of this lengthening effect and individual cognitive capacities as assessed by the neuropsychological tests. The individual differences in working memory capacities only explained differences in sensitivity to time. However, when the difficulty of the temporal task increased, the children’s performance decreased and it was no longer possible to test for the emotional effect. Unlike the children, the adults were still able to discriminate time in the emotional task. However, the emotional effect was no longer observed. In conclusion, our study on temporal task difficulty shows the influence of available cognitive resources on the emergence of an emotional effect on time perception.

Clock Speed as a Window into Dopaminergic Control of Emotion and Time Perception

Although fear-producing treatments (e.g., electric shock) and pleasure-inducing treatments (e.g., methamphetamine) have different emotional valences, they both produce physiological arousal and lead to effects on timing and time perception that have been interpreted as reflecting an increase in speed of an internal clock. In this commentary, we review the results reported by Fayolle et al. (2015):Behav. Process., 120, 135–140) and Meck (1983: J. Exp. Psychol. Anim. Behav. Process., 9, 171–201) using electric shock and by Maricq et al. (1981: J. Exp. Psychol. Anim. Behav. Process., 7, 18–30) using methamphetamine in a duration-bisection procedure across multiple duration ranges. The psychometric functions obtained from this procedure relate the proportion ‘long’ responses to signal durations spaced between a pair of ‘short’ and ‘long’ anchor durations. Horizontal shifts in these functions can be described in terms of attention or arousal processes depending upon whether they are a fixed number of seconds independent of the timed durations (additive) or proportional to the durations being timed (multiplicative). Multiplicative effects are thought to result from a change in clock speed that is regulated by dopamine activity in the medial prefrontal cortex. These dopaminergic effects are discussed within the context of the striatal beat frequency model of interval timing (Matell & Meck, 2004:Cogn. Brain Res.,21, 139–170) and clinical implications for the effects of emotional reactivity on temporal cognition (Parker et al., 2013:Front. Integr. Neurosci., 7, 75).

The Role of Dopamine in Temporal Uncertainty

The temporal preparation of motor responses to external events (temporal preparation) relies on internal representations of the accumulated elapsed time (temporal representations) before an event occurs and on estimates about its most likely time of occurrence (temporal expectations). The precision (inverse of uncertainty) of temporal preparation, however, is limited by two sources of uncertainty. One is intrinsic to the nervous system and scales with the length of elapsed time such that temporal representations are least precise for longest time durations. The other is external and arises from temporal variability of events in the outside world. The precision of temporal expectations thus decreases if events become more variable in time. It has long been recognized that the processing of time durations within the range of hundreds of milliseconds (interval timing) strongly depends on dopaminergic (DA) transmission. The role of DA for the precision of temporal preparation in humans, however, remains unclear. This study therefore directly assesses the role of DA in the precision of temporal preparation of motor responses in healthy humans. In a placebo-controlled double-blind design using a selective D2-receptor antagonist (sulpiride) and D1/D2 receptor antagonist (haloperidol), participants performed a variable foreperiod reaching task, under different conditions of internal and external temporal uncertainty. DA blockade produced a striking impairment in the ability of extracting temporal expectations across trials and on the precision of temporal representations within a trial. Large Weber fractions for interval timing, estimated by fitting subjective hazard functions, confirmed that this effect was driven by an increased uncertainty in the way participants were experiencing time. This provides novel evidence that DA regulates the precision with which we process time when preparing for an action.

Opposite Distortions in Interval Timing Perception for Visual and Auditory Stimuli with Temporal Modulations

When an object is presented visually and moves or flickers, the perception of its duration tends to be overestimated. Such an overestimation is called time dilation. Perceived time can also be distorted when a stimulus is presented aurally as an auditory flutter, but the mechanisms and their relationship to visual processing remains unclear. In the present study, we measured interval timing perception while modulating the temporal characteristics of visual and auditory stimuli, and investigated whether the interval times of visually and aurally presented objects shared a common mechanism. In these experiments, participants compared the durations of flickering or fluttering stimuli to standard stimuli, which were presented continuously. Perceived durations for auditory flutters were underestimated, while perceived durations of visual flickers were overestimated. When auditory flutters and visual flickers were presented simultaneously, these distortion effects were cancelled out. When auditory flutters were presented with a constantly presented visual stimulus, the interval timing perception of the visual stimulus was affected by the auditory flutters. These results indicate that interval timing perception is governed by independent mechanisms for visual and auditory processing, and that there are some interactions between the two processing systems.

The Developmental Emergence of the Mental Time-Line: Spatial and Numerical Distortion of Time Judgement

The perception of time is susceptible to distortion by factors such as attention, emotion, or even the physical properties of the stimulus to be timed. In adults, there is now evidence for a left-right spatial representation of time or “mental time-line”, in which short durations map to the left side of space, whereas long durations map to the right. We investigated the developmental trajectory of the mental time-line, by examining how spatial and numerical stimulus properties affect temporal bisection judgements in 3 groups of children (5, 8 or 10 year olds), as well as in adults. In contrast to previous developmental studies of the spatial representation of time, we manipulated spatial position (left-right) rather than spatial magnitude (distance) so as to pinpoint the age at which the mental time-line begins to influence the judgement of time. In addition, we manipulated spatial position symbolically, either directly, using left- or right-pointing arrows, or indirectly, using low (1) or high (9) digits. In adults and older children (10 year olds), the rightward arrow and the higher digit were judged to last longer. However, time judgements were unaffected by arrow direction and digits in the younger children. Therefore, the temporal distortions induced by symbolic representations of space (arrows) or number (digits) emerged with development, suggesting that the mental time-line is not derived from a primitive spatial representation of time but, rather, is the fruit of learning and is acquired around the age of 8-10 years old.

Temporal Averaging Across Stimuli Signaling the Same or Different Reinforcing Outcomes in the Peak Procedure

The present study examined factors that affect temporal averaging in rats when discriminative stimuli are compounded following separate training indicating the availability of reward after different fixed intervals (FI) on a peak procedure. One group of rats, Group Differential, learned that a flashing light stimulus signaled that one type of food pellet reward could be earned for lever pressing after an FI 5 s interval and that a second type of food pellet reward could be earned after an FI 20 s interval in the presence of a tone stimulus. A second group of rats, Group Non-Differential, was similarly trained except that both types of rewards were scheduled across flash and tone trials. When given non-reinforced flash + tone compound test trials the interval containing the maximal response rate was no different than on flash alone test trials, although some responding also appeared near the long FI time. After these FI contingencies were reversed (flash signaled FI 20 s and tone signaled FI 5 s), however, further compound test trials more clearly revealed a temporal averaging pattern in both groups. The peak interval was shifted to the right of the FI 5 stimulus. Moreover, Group Differential rats acquired the reversed discrimination somewhat more rapidly than Group Non-Differential rats, and in a final selective satiation test Group Differential rats responded less in later intervals after they had been sated on the FI 20 s reward. These data suggest that temporal averaging in stimulus compound tests occurs even when the stimuli being combined signal qualitatively different rewards, but that decreasing the value of one of those rewards can shift responding away from the relevant time interval in a selective satiation test. However, when an especially salient stimulus (e.g., flashing light) signals a short FI, rats tend to process the compound stimulus more in terms of its individual elements.

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.

What is all the noise about in interval timing?

Cognitive processes such as decision-making, rate calculation and planning require an accurate estimation of durations in the supra-second range-interval timing. In addition to being accurate, interval timing is scale invariant: the time-estimation errors are proportional to the estimated duration. The origin and mechanisms of this fundamental property are unknown. We discuss the computational properties of a circuit consisting of a large number of (input) neural oscillators projecting on a small number of (output) coincidence detector neurons, which allows time to be coded by the pattern of coincidental activation of its inputs. We showed analytically and checked numerically that time-scale invariance emerges from the neural noise. In particular, we found that errors or noise during storing or retrieving information regarding the memorized criterion time produce symmetric, Gaussian-like output whose width increases linearly with the criterion time. In contrast, frequency variability produces an asymmetric, long-tailed Gaussian-like output, that also obeys scale invariant property. In this architecture, time-scale invariance depends neither on the details of the input population, nor on the distribution probability of noise.

Comparison of interval timing behaviour in mice following dorsal or ventral hippocampal lesions with mice having δ-opioid receptor gene deletion

Mice with cytotoxic lesions of the dorsal hippocampus (DH) underestimated 15 s and 45 s target durations in a bi-peak procedure as evidenced by proportional leftward shifts of the peak functions that emerged during training as a result of decreases in both 'start' and 'stop' times. In contrast, mice with lesions of the ventral hippocampus (VH) displayed rightward shifts that were immediately present and were largely limited to increases in the 'stop' time for the 45 s target duration. Moreover, the effects of the DH lesions were congruent with the scalar property of interval timing in that the 15 s and 45 s functions superimposed when plotted on a relative timescale, whereas the effects of the VH lesions violated the scalar property. Mice with DH lesions also showed enhanced reversal learning in comparison to control and VH lesioned mice. These results are compared with the timing distortions observed in mice lacking δ-opioid receptors (Oprd1(-/-)) which were similar to mice with DH lesions. Taken together, these results suggest a balance between hippocampal-striatal interactions for interval timing and demonstrate possible functional dissociations along the septotemporal axis of the hippocampus in terms of motivation, timed response thresholds and encoding in temporal memory.

Phase resetting and its implications for interval timing with intruders

Time perception in the second-to-minutes range is crucial for fundamental cognitive processes like decision making, rate calculation, and planning. We used a striatal beat frequency (SBF) computational model to predict the response of an interval timing network to intruders, such as gaps in conditioning stimulus (CS), or distracters presented during the uninterrupted CS. We found that, depending on the strength of the input provided to neural oscillators by the intruder, the SBF model can either ignore it or reset timing. The significant delays in timing produced by emotionally charged distracters were numerically simulated by a strong phase resetting of all neural oscillators involved in the SBF network for the entire duration of the evoked response. The combined effect of emotional distracter and pharmacological manipulations was modeled in our SBF model by modulating the firing frequencies of neural oscillators after they are released from inhibition due to emotional distracters. This article is part of a Special Issue entitled: SI: Associative and Temporal Learning.

Associative and temporal processes: a dual process approach

Approaches to the study of associative learning and interval timing have traditionally diverged on methodological and theoretical levels of analysis. However, more recent attempts have been made to explain one class of phenomena in terms of the other using various single-process approaches. In this paper we suggest that an interactive dual-process approach might more accurately reflect underlying behavioral and neural processes. We will argue that timing in Pavlovian conditioning is best understood in terms of an abstract temporal code that is not a feature of the predictive stimulus (i.e., the conditioned stimulus, CS), per se. Rather, we assume that the time between the CS and the unconditioned stimulus (US) is encoded in the form of an abstract representation of this temporal interval produced as an output of a central multiple-oscillator interval timing system. As such, associations can then develop between the CS and this abstract temporal code in much the same way that the CS develops associations with different features of the US. To support the dual-process approach, we first show that exposure to a Pavlovian zero contingency procedure results in a failure to acquire new associations, not a failure to express learning due to some temporally defined performance mask. We also consider evidence that supports the abstract temporal coding idea in a US preexposure task, and, finally, present some evidence to encourage the dissociation between basic associative and temporal learning processes by exploring reward devaluation effects in a peak timing task.

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".

Executive dysfunction in Parkinson's disease and timing deficits

Patients with Parkinson’s disease (PD) have deficits in perceptual timing, or the perception and estimation of time. PD patients can also have cognitive symptoms, including deficits in executive functions such as working memory, planning, and visuospatial attention. Here, we discuss how PD-related cognitive symptoms contribute to timing deficits. Timing is influenced by signaling of the neurotransmitter dopamine in the striatum. Timing also involves the frontal cortex, which is dysfunctional in PD. Frontal cortex impairments in PD may influence memory subsystems as well as decision processes during timing tasks. These data suggest that timing may be a type of executive function. As such, timing can be used to study the neural circuitry of cognitive symptoms of PD as they can be studied in animal models. Performance of timing tasks also maybe a useful clinical biomarker of frontal as well as striatal dysfunction in PD.

Hippocampus, time, and memory--a retrospective analysis

In 1984, there was considerable evidence that the hippocampus was important for spatial learning and some evidence that it was also involved in duration discrimination. The article "Hippocampus, Time, and Memory" (Meck, Church, & Olton, 1984), however, was the first to isolate the effects of hippocampal damage on specific stages of temporal processing. In this review, to celebrate the 30th anniversary of Behavioral Neuroscience, we look back on factors that contributed to the long-lasting influence of this article. The major results were that a fimbria-fornix lesion (a) interferes with the ability to retain information in temporal working memory, and (b) distorts the content of temporal reference memory, but (c) did not decrease sensitivity to signal duration. This was the first lesion experiment in which the results were interpreted by a well-developed theory of behavior (scalar timing theory). It has led to extensive research on the role of the hippocampus in temporal processing by many investigators. The most important ones are the development of computational models with plausible neural mechanisms (such as the striatal beat-frequency model of interval timing), the use of multiple behavioral measures of timing, and empirical research on the neural mechanisms of timing and temporal memory using ensemble recording of neurons in prefrontal-striatal-hippocampal circuits.

Why noise is useful in functional and neural mechanisms of interval timing?

BACKGROUND

The ability to estimate durations in the seconds-to-minutes range - interval timing - is essential for survival, adaptation and its impairment leads to severe cognitive and/or motor dysfunctions. The response rate near a memorized duration has a Gaussian shape centered on the to-be-timed interval (criterion time). The width of the Gaussian-like distribution of responses increases linearly with the criterion time, i.e., interval timing obeys the scalar property.

RESULTS

We presented analytical and numerical results based on the striatal beat frequency (SBF) model showing that parameter variability (noise) mimics behavioral data. A key functional block of the SBF model is the set of oscillators that provide the time base for the entire timing network. The implementation of the oscillators block as simplified phase (cosine) oscillators has the additional advantage that is analytically tractable. We also checked numerically that the scalar property emerges in the presence of memory variability by using biophysically realistic Morris-Lecar oscillators. First, we predicted analytically and tested numerically that in a noise-free SBF model the output function could be approximated by a Gaussian. However, in a noise-free SBF model the width of the Gaussian envelope is independent of the criterion time, which violates the scalar property. We showed analytically and verified numerically that small fluctuations of the memorized criterion time leads to scalar property of interval timing.

CONCLUSIONS

Noise is ubiquitous in the form of small fluctuations of intrinsic frequencies of the neural oscillators, the errors in recording/retrieving stored information related to criterion time, fluctuation in neurotransmitters' concentration, etc. Our model suggests that the biological noise plays an essential functional role in the SBF interval timing.

Individual differences in motor timing and its relation to cognitive and fine motor skills

The present study investigated the relationship between individual differences in timing movements at the level of milliseconds and performance on selected cognitive and fine motor skills. For this purpose, young adult participants (N = 100) performed a repetitive movement task paced by an auditory metronome at different rates. Psychometric measures included the digit-span and symbol search subtasks from the Wechsler battery as well as the Raven SPM. Fine motor skills were assessed with the Purdue Pegboard test. Motor timing performance was significantly related (mean r = .3) to cognitive measures, and explained both unique and shared variance with information-processing speed of Raven's scores. No significant relations were found between motor timing measures and fine motor skills. These results show that individual differences in cognitive and motor timing performance is to some extent dependent upon shared processing not associated with individual differences in manual dexterity.

Impaired interval timing and spatial-temporal integration in mice deficient in CHL1, a gene associated with schizophrenia

Interval timing is crucial for decision-making and motor control and is impaired in many neuropsychiatric disorders, including schizophrenia - a neurodevelopmental disorder with a strong genetic component. Several gene mutations, polymorphisms or rare copy number variants have been associated with schizophrenia. L1 cell adhesion molecules (L1CAMs) are involved in neurodevelopmental processes, and in synaptic function and plasticity in the adult brain. Mice deficient in the Close Homolog to L1 (CHL1) adhesion molecule show alterations of hippocampal and thalamo-cortical neuroanatomy as well as deficits in sensorimotor gating and exploratory behavior. We analyzed interval timing and attentional control of temporal and spatial information in male CHL1 deficient (KO) mice and wild type (WT) controls. In a 20-s peak-interval timing procedure (standard and reversed), KO mice showed a maintained leftward shift of the response function relative to WT, indicative of a deficit in memory encoding/decoding. In trials with 2, 5, or 10-s gaps, KO mice shifted their peak times less than WT controls at longer gap durations, suggesting a decreased (attentional) effect of interruptions. In the spatial-temporal task, KO mice made more working and reference memory errors than controls, suggestive of impaired use of spatial and/or temporal information. When the duration spent on the central platform of the maze was manipulated, WT mice showed fewer spatial errors at the trained duration than at shorter or longer durations, indicative of discrimination based upon spatial-temporal integration. In contrast, performance was similar at all tested durations in KO mice, indicative of control by spatial cues, but not by temporal cues. These results suggest that CHL1 KO mice selectively attend to the more relevant cues of the task, and fail to integrate more complex spatial-temporal information, possibly as a result of reduced memory capacity related to hippocampal impairment, and altered temporal-integration mechanisms possibly due to thalamo-cortical anomalies.