A neurocomputational model for optimal temporal processing

Humans can estimate the duration of intervals of time, and psychophysical experiments show that these estimations are subject to timing errors. According to standard theories of timing, these errors increase linearly with the interval to be estimated (Weber's law), and both at longer and shorter intervals, deviations from linearity are reported. This is not easily reconciled with the accumulation of neuronal noise, which would only lead to an increase with the square root of the interval. Here, we offer a neuronal model which explains the form of the error function as a result of a constrained optimization process. The model consists of a number of synfire chains with different transmission times, which project onto a set of readout neurons. We show that an increase in the transmission time corresponds to a superlinear increase of the timing errors. Under the assumption of a fixed chain length, the experimentally observed error function emerges from optimal selection of chains for each given interval. Furthermore, we show how this optimal selection could be implemented by competitive spike-timing dependent plasticity in the connections from the chains to the readout network, and discuss implications of our model on selective temporal learning and possible neural architectures of interval timing.     

Implicit, predictive timing draws upon the same scalar representation of time as explicit timing

It is not yet known whether the scalar properties of explicit timing are also displayed by more implicit, predictive forms of timing. We investigated whether performance in both explicit and predictive timing tasks conformed to the two psychophysical properties of scalar timing: the Psychophysical law and Weber's law. Our explicit temporal generalization task required overt estimation of the duration of an empty interval bounded by visual markers, whereas our temporal expectancy task presented visual stimuli at temporally predictable intervals, which facilitated motor preparation thus speeding target detection. The Psychophysical Law and Weber's Law were modeled, respectively, by (1) the functional dependence between mean subjective time and real time (2) the linearity of the relationship between timing variability and duration. Results showed that performance for predictive, as well as explicit, timing conformed to both psychophysical properties of interval timing. Both tasks showed the same linear relationship between subjective and real time, demonstrating that the same representational mechanism is engaged whether it is transferred into an overt estimate of duration or used to optimise sensorimotor behavior. Moreover, variability increased with increasing duration during both tasks, consistent with a scalar representation of time in both predictive and explicit timing. However, timing variability was greater during predictive timing, at least for durations greater than 200 msec, and ascribable to temporal, rather than non-temporal, mechanisms engaged by the task. These results suggest that although the same internal representation of time was used in both tasks, its external manifestation varied as a function of temporal task goals.     

Trading Speed and Accuracy by Coding Time: A Coupled-circuit Cortical Model

Our actions take place in space and time, but despite the role of time in decision theory and the growing acknowledgement that the encoding of time is crucial to behaviour, few studies have considered the interactions between neural codes for objects in space and for elapsed time during perceptual decisions. The speed-accuracy trade-off (SAT) provides a window into spatiotemporal interactions. Our hypothesis is that temporal coding determines the rate at which spatial evidence is integrated, controlling the SAT by gain modulation. Here, we propose that local cortical circuits are inherently suited to the relevant spatial and temporal coding. In simulations of an interval estimation task, we use a generic local-circuit model to encode time by ‘climbing’ activity, seen in cortex during tasks with a timing requirement. The model is a network of simulated pyramidal cells and inhibitory interneurons, connected by conductance synapses. A simple learning rule enables the network to quickly produce new interval estimates, which show signature characteristics of estimates by experimental subjects. Analysis of network dynamics formally characterizes this generic, local-circuit timing mechanism. In simulations of a perceptual decision task, we couple two such networks. Network function is determined only by spatial selectivity and NMDA receptor conductance strength; all other parameters are identical. To trade speed and accuracy, the timing network simply learns longer or shorter intervals, driving the rate of downstream decision processing by spatially non-selective input, an established form of gain modulation. Like the timing network''s interval estimates, decision times show signature characteristics of those by experimental subjects. Overall, we propose, demonstrate and analyse a generic mechanism for timing, a generic mechanism for modulation of decision processing by temporal codes, and we make predictions for experimental verification.     

Interval timing by an invertebrate, the bumble bee Bombus impatiens

Sensitivity to temporal information and the ability to adjust behavior to the temporal structure of the environment should be phylogenetically widespread. Some timing abilities, such as sensitivity to circadian cycles, appear in a wide range of invertebrate and vertebrate taxa [1,2]. Interval timing--sensitivity to the duration of time intervals--has, however, only been shown to occur in vertebrates [3,4]. Insect pollinators make a variety of decisions that would appear to require the ability to estimate elapsed durations. We exposed bumble bees to conditions in which proboscis extension was reinforced after a fixed duration had elapsed or after either of two fixed durations had elapsed. Two groups of bees were trained with a short duration (either 6 s or 12 s) and a long duration (36 s) in separate experimental phases (independent timing groups), whereas two other groups were trained with a short duration (either 6 s or 12 s) and long duration (36 s) always intermixed unpredictably (multiple timing groups). On long intervals, independent timing groups waited longer than mixed timing groups to generate the first response and responded maximally near the end of the interval. Multiple timing groups waited the same amount of time on average before generating the first response on both long and short intervals. On individual trials, multiple timing groups appeared to time either the long duration only or both the short and long durations: most trials were characterized by a single burst of responding that began between the short and long duration values or by two bursts of responding with the first burst bracketing the short value and the second burst beginning in anticipation of the long value. These results show that bumble bees learn to time interval durations and can flexibly time multiple durations simultaneously. The results indicate no phylogenetic divide between vertebrates and invertebrates in interval timing ability.     

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.     

Representation of time by neurons in the posterior parietal cortex of the macaque

The neural basis of time perception is unknown. Here we show that neurons in the posterior parietal cortex (area LIP) represent elapsed time relative to a remembered duration. We trained rhesus monkeys to report whether the duration of a test light was longer or shorter than a remembered "standard" (316 or 800 ms) by making an eye movement to one of two choice targets. While timing the test light, the responses of LIP neurons signaled changes in the monkey's perception of elapsed time. The variability of the neural responses explained the monkey's uncertainty about its temporal judgments. Thus, in addition to their role in spatial processing and sensorimotor integration, posterior parietal neurons encode signals related to the perception of time.     

Dissociating explicit timing from temporal expectation with fMRI

Explicit timing is engaged whenever subjects make a deliberate estimate of discrete duration in order to compare it with a previously memorised standard. Conversely, implicit timing is engaged, even without a specific instruction to time, whenever sensorimotor information is temporally structured and can be used to predict the duration of future events. Both emergent timing (motor) and temporal expectation (perceptual) are forms of implicit timing. Recent fMRI studies demonstrate discrete neural substrates for explicit and implicit timing. Specifically, basal ganglia are activated almost invariably by explicit timing, with co-activation of prefrontal, premotor and cerebellar areas being more context-dependent. Conversely, implicit perceptual timing (or "temporal expectation") recruits cortical action circuits, comprising inferior parietal and premotor areas, highlighting its role in the optimisation of prospective behaviour.     

Investigations of timing during the schedule and reinforcement intervals with wheel-running reinforcement

Across two experiments, a peak procedure was used to assess the timing of the onset and offset of an opportunity to run as a reinforcer. The first experiment investigated the effect of reinforcer duration on temporal discrimination of the onset of the reinforcement interval. Three male Wistar rats were exposed to fixed-interval (FI) 30-s schedules of wheel-running reinforcement and the duration of the opportunity to run was varied across values of 15, 30, and 60s. Each session consisted of 50 reinforcers and 10 probe trials. Results showed that as reinforcer duration increased, the percentage of postreinforcement pauses longer than the 30-s schedule interval increased. On probe trials, peak response rates occurred near the time of reinforcer delivery and peak times varied with reinforcer duration. In a second experiment, seven female Long-Evans rats were exposed to FI 30-s schedules leading to 30-s opportunities to run. Timing of the onset and offset of the reinforcement period was assessed by probe trials during the schedule interval and during the reinforcement interval in separate conditions. The results provided evidence of timing of the onset, but not the offset of the wheel-running reinforcement period. Further research is required to assess if timing occurs during a wheel-running reinforcement period.     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

Temporal encoding in nervous systems: A rigorous definition

We propose a rigorous definition for the termtemporal encoding as it is applied to schemes for the representation of information withinpatterns of neuronal action potentials, and distinguish temporal encoding schemes from those based on window-averagedmean rate encoding. The definition relies on the identification of anencoding time window, defined as the duration of a neuron's spike train assumed to correspond to a single symbol in the neural code. The duration of the encoding time window is dictated by the time scale of the information being encoded. We distinguish between the concepts of theencoding time window and theintegration time window, the latter of which is defined as the duration of a stimulus signal that affects the response of the neuron. We note that the duration of the encoding and integration windows might be significantly different. We also present objective, experimentally assessable criteria for identifying neurons and neuronal ensembles that utilize temporal encoding to any significant extent. The definitions and criteria are made rigorous within the contexts of several commonly used analytical approaches, including thestimulus reconstruction analysis technique. Several examples are presented to illustrate the distinctions between and relative capabilities of rate encoding and temporal encoding schemes. We also distinguish our usage oftemporal encoding from the termtemporal coding, which is commonly used in reference to the representation of information about thetiming of events by rate encoding schemes.     

Neurobehavioral mechanisms of temporal processing deficits in Parkinson's disease

Background

Parkinson''s disease (PD) disrupts temporal processing, but the neuronal sources of deficits and their response to dopamine (DA) therapy are not understood. Though the striatum and DA transmission are thought to be essential for timekeeping, potential working memory (WM) and executive problems could also disrupt timing.

Methodology/Findings

The present study addressed these issues by testing controls and PD volunteers ‘on’ and ‘off’ DA therapy as they underwent fMRI while performing a time-perception task. To distinguish systems associated with abnormalities in temporal and non-temporal processes, we separated brain activity during encoding and decision-making phases of a trial. Whereas both phases involved timekeeping, the encoding and decision phases emphasized WM and executive processes, respectively. The methods enabled exploration of both the amplitude and temporal dynamics of neural activity. First, we found that time-perception deficits were associated with striatal, cortical, and cerebellar dysfunction. Unlike studies of timed movement, our results could not be attributed to traditional roles of the striatum and cerebellum in movement. Second, for the first time we identified temporal and non-temporal sources of impaired time perception. Striatal dysfunction was found during both phases consistent with its role in timekeeping. Activation was also abnormal in a WM network (middle-frontal and parietal cortex, lateral cerebellum) during encoding and a network that modulates executive and memory functions (parahippocampus, posterior cingulate) during decision making. Third, hypoactivation typified neuronal dysfunction in PD, but was sometimes characterized by abnormal temporal dynamics (e.g., lagged, prolonged) that were not due to longer response times. Finally, DA therapy did not alleviate timing deficits.

Conclusions/Significance

Our findings indicate that impaired timing in PD arises from nigrostriatal and mesocortical dysfunction in systems that mediate temporal and non-temporal control-processes. However, time perception impairments were not improved by DA treatment, likely due to inadequate restoration of neuronal activity and perhaps corticostriatal effective-connectivity.     

How Long Depends on How Fast—Perceived Flicker Dilates Subjective Duration

How do humans perceive the passage of time and the duration of events without a dedicated sensory system for timing? Previous studies have demonstrated that when a stimulus changes over time, its duration is subjectively dilated, indicating that duration judgments are based on the number of changes within an interval. In this study, we tested predictions derived from three different accounts describing the relation between a changing stimulus and its subjective duration as either based on (1) the objective rate of changes of the stimulus, (2) the perceived saliency of the changes, or (3) the neural energy expended in processing the stimulus. We used visual stimuli flickering at different frequencies (4–166 Hz) to study how the number of changes affects subjective duration. To this end, we assessed the subjective duration of these stimuli and measured participants'' behavioral flicker fusion threshold (the highest frequency perceived as flicker), as well as their threshold for a frequency-specific neural response to the flicker using EEG. We found that only consciously perceived flicker dilated perceived duration, such that a 2 s long stimulus flickering at 4 Hz was perceived as lasting as long as a 2.7 s steady stimulus. This effect was most pronounced at the slowest flicker frequencies, at which participants reported the most consistent flicker perception. Flicker frequencies higher than the flicker fusion threshold did not affect perceived duration at all, even if they evoked a significant frequency-specific neural response. In sum, our findings indicate that time perception in the peri-second range is driven by the subjective saliency of the stimulus'' temporal features rather than the objective rate of stimulus changes or the neural response to the changes.     

Asynchrony adaptation reveals neural population code for audio-visual timing

The relative timing of auditory and visual stimuli is a critical cue for determining whether sensory signals relate to a common source and for making inferences about causality. However, the way in which the brain represents temporal relationships remains poorly understood. Recent studies indicate that our perception of multisensory timing is flexible--adaptation to a regular inter-modal delay alters the point at which subsequent stimuli are judged to be simultaneous. Here, we measure the effect of audio-visual asynchrony adaptation on the perception of a wide range of sub-second temporal relationships. We find distinctive patterns of induced biases that are inconsistent with the previous explanations based on changes in perceptual latency. Instead, our results can be well accounted for by a neural population coding model in which: (i) relative audio-visual timing is represented by the distributed activity across a relatively small number of neurons tuned to different delays; (ii) the algorithm for reading out this population code is efficient, but subject to biases owing to under-sampling; and (iii) the effect of adaptation is to modify neuronal response gain. These results suggest that multisensory timing information is represented by a dedicated population code and that shifts in perceived simultaneity following asynchrony adaptation arise from analogous neural processes to well-known perceptual after-effects.     

Timing Rhythms: Perceived Duration Increases with a Predictable Temporal Structure of Short Interval Fillers

Variations in the temporal structure of an interval can lead to remarkable differences in perceived duration. For example, it has previously been shown that isochronous intervals, that is, intervals filled with temporally regular stimuli, are perceived to last longer than intervals left empty or filled with randomly timed stimuli. Characterizing the extent of such distortions is crucial to understanding how duration perception works. One account to explain effects of temporal structure is a non-linear accumulator-counter mechanism reset at the beginning of every subinterval. An alternative explanation based on entrainment to regular stimulation posits that the neural response to each filler stimulus in an isochronous sequence is amplified and a higher neural response may lead to an overestimation of duration. If entrainment is the key that generates response amplification and the distortions in perceived duration, then any form of predictability in the temporal structure of interval fillers should lead to the perception of an interval that lasts longer than a randomly filled one. The present experiments confirm that intervals filled with fully predictable rhythmically grouped stimuli lead to longer perceived duration than anisochronous intervals. No general over- or underestimation is registered for rhythmically grouped compared to isochronous intervals. However, we find that the number of stimuli in each group composing the rhythm also influences perceived duration. Implications of these findings for a non-linear clock model as well as a neural response magnitude account of perceived duration are discussed.     

Neuropsychological mechanisms of interval timing behavior

Interval timing in the seconds-to-minutes range is believed to underlie a variety of complex behaviors in humans and other animals. One of the more interesting problems in interval timing is trying to understand how the brain times events lasting for minutes with millisecond-based neural processes. Timing models proposing the use of coincidence-detection mechanisms (e.g., the detection of simultaneous activity across multiple neural inputs) appear to be the most compatible with known neural mechanisms. From an evolutionary perspective, coincidence detection of neuronal activity may be a fundamental mechanism of timing that is expressed across a wide variety of species. BioEssays 22:94-103, 2000.     

Do rats time filled and empty intervals of equal duration differently?

The goal was to determine whether rats time filled and empty intervals of equal duration differently. Each of five rats was trained for 50 sessions on an instrumental appetitive head entry procedure in which food was available (primed) every 120 s. On "empty" cycles, 30s prior to the next food prime, a 0.5-s pulse of white noise was presented. On "filled" cycles, 30s prior to the next food prime, white noise came on and stayed on until food was delivered. The two types of cycles were presented with equal probability. The results showed that the rats timed both the food-to-food interval and the stimulus-to-food interval. A comparison of the response gradients on filled and empty cycles following stimulus presentation showed better temporal discrimination on filled cycles. The results were modeled using a Packet theory of timing, with a linear averaging rule to combine the temporal information provided by the stimulus and food. The model fits to the individual response gradients were evaluated with a Turing test.     

Time representing cortical activities: two models inspired by prefrontal persistent activity

 Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors. Received: 12 March 2002 / Accepted in revised form: 26 November 2002 / Published online: 28 March 2003 Correspondence to: T. Fukai (e-mail: tfukai@eng.tamagawa.ac.jp, Tel.: +81-42-7398434, Fax: +81-42-7397135) Acknowledgements. K. Kitano was supported by Japan Society for the Promotion of Science.