during an attention distracting task. Although our findings suggest that attention is critical for numerical processing, more work is needed to shed light on how attentional manipulations impact quantity processing. Future research will be critical for understanding the unique representational formats of quantities, and additional work exploring the role of attention and arousal as cognitive mechanisms underlying quantity processing may be particularly fruitful for shedding light on the representational patterns of quantitative information.

#### ETHICS STATEMENT

This study was carried out in accordance with the recommendations of Institutional Review Board, Boston College. The protocol was approved by the Institutional Review Board, Boston College. All subjects gave written informed consent in accordance with the Declaration of Helsinki.

# REFERENCES

#### AUTHOR CONTRIBUTIONS

KH and MK completed all data collection. KH wrote the manuscript. MK, KJ, and SC provided thoughtful feedback on the manuscript. All authors contributed to the design of the study and approved of this version of the manuscript.

# FUNDING

Funding was provided by a Boston College Research Expense Grants to SC.

# ACKNOWLEDGMENTS

The authors would like to thank Kylie Gallo and Taylor Reader for their assistance with data collection and coding.

Dormal, V., Dormal, G., Joassin, F., and Pesenti, M. (2012). A common right fronto-parietal network for numerosity and duration processing: an fMRI study. Hum. Brain Mapp. 33, 1490–1501. doi: 10.1002/hbm.21300

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Hamamouche, Keefe, Jordan and Cordes. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Dilation and Constriction of Subjective Time Based on Observed Walking Speed

#### Hakan Kar ¸sılar1,2, Yagmur Deniz Kısa ˘ 1 and Fuat Balcı1,3 \*

1 Department of Psychology, Koç University, Istanbul, Turkey, 2 Department of Psychology, Özyegin University, Istanbul, ˘ Turkey, 3 Koç University Center for Translational Medicine, Istanbul, Turkey

The physical properties of events are known to modulate perceived time. This study tested the effect of different quantitative (walking speed) and qualitative (walking-forward vs. walking-backward) features of observed motion on time perception in three complementary experiments. Participants were tested in the temporal discrimination (bisection) task, in which they were asked to categorize durations of walking animations as "short" or "long." We predicted the faster observed walking to speed up temporal integration and thereby to shift the point of subjective equality leftward, and this effect to increase monotonically with increasing walking speed. To this end, we tested participants with two different ranges of walking speeds in Experiment 1 and 2 and observed a parametric effect of walking speed on perceived time irrespective of the direction of walking (forward vs. rewound forward walking). Experiment 3 contained a more plausible backward walking animation compared to the rewound walking animation used in Experiments 1 and 2 (as validated based on independent subjective ratings). The effect of walking-speed and the lack of the effect of walking direction on perceived time were replicated in Experiment 3. Our results suggest a strong link between the speed but not the direction of perceived biological motion and subjective time.

#### Edited by:

Kielan Yarrow, City, University of London, United Kingdom

#### Reviewed by:

Micha Pfeuty, Université de Bordeaux, France Hulusi Kafaligonul, Bilkent University, Turkey

> \*Correspondence: Fuat Balcı<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Perception Science, a section of the journal Frontiers in Psychology

Received: 27 August 2018 Accepted: 29 November 2018 Published: 21 December 2018

#### Citation:

Kar ¸sılar H, Kısa YD and Balcı F (2018) Dilation and Constriction of Subjective Time Based on Observed Walking Speed. Front. Psychol. 9:2565. doi: 10.3389/fpsyg.2018.02565 Keywords: biological motion, speed, psychophysics, temporal bisection, time perception

## INTRODUCTION

Given that accurate timing is essential for the preparation and execution of most motor responses (see Buhusi and Meck, 2005), it can be implicitly assumed that perception of time is highly accurate across situations irrespective of what is being timed. However, it has been shown that changes in a stimulus' properties such as its size, brightness, numerosity or loudness can also modulate time perception (e.g., Thomas and Cantor, 1976; Xuan et al., 2007; Eagleman and Pariyadath, 2009). In line with theories that assume a shared mechanism for the perception of various magnitudes by adhering to a common representational metric (e.g., time, numerosity, space; Walsh, 2003), perceived time also changes in the same direction with the changes in other stimulus properties. In other words, as one perceptual dimension is experimentally increased (e.g., loudness) so does the perceived duration of that stimulus (e.g., Berglund et al., 1969).

The relationship between motion and time perception has also been well documented (Brown, 1995; Kaneko and Murakami, 2009), where an increase in speed can lead to overestimations

of durations, and vice versa (Matthews, 2011). Since motion can inherently be defined in terms of change per unit time (Poynter, 1989), it has been theorized that the larger amount of change experienced by the timing agent whilst observing faster motion or higher temporal and spatial frequencies (i.e., events happening more frequently across time and the level of detail in a stimulus per degree of visual angle, respectively) may in fact act as a proxy for the passage of time, and therefore lead to the observed overestimation of durations (Brown, 1995; Kanai et al., 2006; Kaneko and Murakami, 2009).

A prominent information-theoretic approach to modeling these variations in timing behavior generally assumes an internal clock (Treisman, 1963; Gibbon et al., 1984) with three hypothetical components: (1) a pacemaker-accumulator unit which generates and counts pulses, (2) a reference memory unit where the total number of pulses representing the timed interval are encoded, and (3) a decision component which compares the current number of pulses in the pacemaker-accumulator unit (i.e., working memory) to a random sample drawn from the reference memory unit in order to arrive at a temporal judgment (Gibbon et al., 1984). Thus, depending on the task used, stimuli with higher speeds could, for instance, speed up the pacemaker, thereby leading to longer perceived durations as a result of a higher number of pulses being registered per unit time in the accumulator (Zakay and Block, 1997; Wearden, 1999). On the other hand, a similar stimulus may lead to inadvertent attentional lapses which may lead to some of the pulses not getting registered in the accumulator (e.g., Penney, 2003; Kars˛*ı*lar and Balc*ı*, 2016), thereby leading to shorter perceived durations (for a review see Allman et al., 2014). Examples of increases in the pacemaker rate (in addition to those mentioned above) have been shown in response to fast click-trains presented before timing a duration (Penton-Voak et al., 1996), higher body temperature (Wearden and Penton-Voak, 1995), emotional stimuli (Droit-Volet et al., 2004), auditory as opposed to visual timing stimuli (Wearden et al., 1998), physical activity/motion (Sayal*ı* et al., 2018), as well as those manifested in terms of drug effects (see Coull et al., 2011 for a review). On the other hand, variations in perceived time due to attentional modulation have generally been shown in dual-task paradigms (e.g., Thomas and Weaver, 1975) where attentional resources are directed away from timing (Fortin and Rousseau, 1987; Macar et al., 1994), as well as in the oddball paradigm, where the duration of unexpected stimuli are perceived longer than those that were expected in a given trial (e.g., Tse et al., 2004; see Brown, 2008 for a review).

The neural energy model of timing that does not contain a pacemaker-accumulator architecture also readily accounts for the stimulus-property dependent findings outlined earlier. For instance, based on the series of findings that showed reduced neural activity (known as the repetition suppression; e.g., Wark et al., 2007) and shorter duration estimates of repeated stimulus (Pariyadath and Eagleman, 2007), Pariyadath and Eagleman (2007, 2008) proposed that the strength of neural responses reflecting metabolic costs of neural information-processing (referred to as neural energy) could be the determinant of the perceived duration. In support of this claim, the manipulation of various stimulus properties that are known to lead to longer temporal judgments (e.g., flicker rate, brightness, size) are also known to lead to higher neural signals in the corresponding brain areas (for review see Eagleman and Pariyadath, 2009).

It has been suggested that disparate neural/cognitive systems might be recruited with regard to the perception of animacy vs. inanimacy as well as the biological plausibility vs. implausibility of the observed stimulus (Caramazza and Shelton, 1998; Peuskens et al., 2005; Blake and Shiffrar, 2007; Shi et al., 2010; Zago et al., 2011). As such, research on the relationship between perception of time and perception of motion has been further distinguished in relation to these variables. For instance, the presentation durations of still images of running postures are judged to have lasted longer compared to images of standing postures (Yamamoto and Miura, 2012), while timing of still images that imply human movement are more precise than those with no implied motion (Moscatelli et al., 2011). Relatedly, the presentation durations of still images which show more intense actions that imply having taken longer (and more effort) to complete (Nather and Bueno, 2011), or words implying an action with faster average speed (e.g., "gallop"; Zhang et al., 2014) are generally judged to have lasted longer compared to their counterpart experimental conditions (but see Orgs et al., 2011, for an alternate account).

On the other hand, based on the now-well-documented finding that perception of biological vs. non-biological stimuli recruits different neural structures (Downing et al., 2001; Giese and Poggio, 2003), still other researchers have shown that the modulation of perceived time induced by observing a moving stimulus is directly mediated by the biological nature/plausibility of the observed action (Watanabe, 2008; Wang and Jiang, 2012; Lacquaniti et al., 2014). Similar results have been obtained with stimuli showing animate (i.e., not implied) vs. inanimate motion in real time (e.g., Carrozzo et al., 2010; Carrozzo and Lacquaniti, 2013).

In addition to the information-processing model based "internal clock speeding up due to higher arousal" account outlined above, discussion of results demonstrating a temporal bias in response to changes in biological stimulus properties has adhered to higher-order sensory-motor processes (Yamamoto and Miura, 2012), such as an effect of cognitive embodiment of perceived stimulus properties on perceived durations (Droit-Volet et al., 2013; Zhang et al., 2014). These effects are thought to result from the simultaneous cortical "simulation" of observed actions (Nather and Bueno, 2011; Chen et al., 2013), the potential underlying structures of which employ mirror neurons (Cattaneo and Rizzolatti, 2009). In other words, the ease with which a participant can cognitively simulate the action being observed might act as a mediator in perceiving its temporal properties, where those actions with which the timing agent is more familiar (i.e., regular walking as opposed to a nonbiological action) can induce a stimulus-dependent bias in interval timing (see section "Discussion"). The mechanisms associated with "biological motion" also appear to be specific to certain brain areas. For instance, posterior superior temporal

sulcus, fusiform face area, and occipital face area (Grossman and Blake, 2002) as well as premotor frontal areas (Saygin, 2007) have been associated with the processing of biological motion. Although the middle temporal area (MT) sends input to some of these areas (e.g., superior temporal sulcus), its activity is not specifically modulated by the biological nature of motion (Grossman et al., 2000 - see also Grossman and Blake, 2002 for other differentiations).

Overall, these studies support a directional relationship between perception of motion and the perception of time. The timing mechanism appears to be susceptible to the perceived speed of actual movement, as well as the implied speed embedded within still images (i.e., no actual physical change per unit time). We hypothesized that the length of perceived durations would increase parametrically with increased observed walking speed. Consequently, smaller differences in walking speed (Experiment 1) were expected to lead to a less pronounced effect of walking speed on perceived time, as opposed to larger effects due to larger differences among levels of the same variable (Experiments 2 and 3). Moreover, we expected larger effects when participants timed forward walking as opposed to backward walking motion, in addition to observing higher precision with which durations are timed in the forward walking condition due to it being a more familiar form of motion (i.e., processed more readily) in comparison to backward walking (Moscatelli et al., 2011; Loeffler et al., 2017). While previous research has conclusively demonstrated an effect of low-level motion on time perception (e.g., Kaneko and Murakami, 2009), no study so far has utilized straightforward representations of human motion through the use of stick-figure actions to test for presumably more readily embodied effect of motion on perceived durations. Using an easily-discernible type of walking motion allows for testing the robustness and the sensitivity of the reported effect of basic motion on time perception when it is embedded in high-level (i.e., biological) motion. Additionally, perceiving biological motion might typically take place at supra-second intervals, since multiple elements are presumably patched together over longer-than-sub-second intervals to perceive various elements of the observed motion, such as its speed, agency and intentionality. Below we describe three experiments, all of which utilized the temporal bisection task, which entails categorizing experienced durations as short or long based on their subjective similarity with the short and long reference durations. As such, all three experiments tested time perception at the supra-second level with a large number of participants in order to contribute to the generalizability of earlier effects to larger samples and different procedures. Our results show that the walking speed has a parametric effect on perceived durations, irrespective of the direction of motion (i.e., forward vs. backward), supporting the first of our hypotheses, and not the second one. Importantly, direction of walking motion was chosen in this study as a variable primarily for purposes of operationalizing the qualitative familiarity and unfamiliarity to type of motion (i.e., forward vs. backward walking; see Viviani et al., 2011; Maffei et al., 2014) and not to make inferences about the possibly differential timing of biological motion per se. In essence, we use the term "biological

motion" not as a methodological term (i.e., point light displays) as originally suggested by Johansson (1973) but rather as life motion, namely the "visual motion that expresses any sort of aspect characteristic for the motion of living beings" (Troje, 2013, pg. 4).

# EXPERIMENT 1

## Methods

#### Participants

Thirty-four participants (11 male, Mage = 21.8) were tested in Experiment 1. Participants received 1 course credit for their participation in Experiment 1. All experiments were approved by the Institutional Review Panel for Human Subjects of Koç University and were in accordance with the Declaration of Helsinki. All participants provided written consent for their participation. Two participants in Experiment 1 were excluded from the analyses due to more than two excluded fits (see section below "Data Analysis").

#### Stimuli and Apparatus

Stimuli used in both experiments consisted of animations of a walking stick-figure (approx. height = 10 cm/9.5 visual deg. in diameter) composed of black lines for limbs and torso, as well as a black circle for the head (**Figure 1**; see **Supplementary Materials** for animations).  All stimuli and instructions were presented on a 21" LCD screen (60 Hz refresh-rate) on an Apple iMac G4 computer, generated in Matlab using the PsychToolbox extensions (Brainard, 1997). Participants sat at a distance of approximately 60 cm from the screen, in a dimly lit room with no chin-rest or other restrictions. Responses were provided by using a mechanical keyboard (Zalman ZM-K500).

One "cycle" of the walking animation consisted of two steps taken by the stick-figure, where the posture in the last frame was set so as to continue with the posture in the first frame, allowing us to perceptually wrap-around the walking motion to present it for as long as necessary. The center of the stick figure did not move on the x-axis, which gave the impression of a simultaneously moving camera at a right angle, while small movements of the body on the y-axis represented the characteristic bouncing motion as natural human walk. At 50 frames per second (fps), one cycle (i.e., two steps) lasted 1.5 s, which was considered to be the normal (baseline) speed of walking. Five distinct walking speeds were then produced by modulating the fps of the walking animation (40, 50, and 63 fps) each of which lasted for one of 6 probe durations (1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 s). Hence, lower fps values led to slower and higher fps values led to faster walking speeds. Consequently, higher fps rates for a given duration, or longer durations for a given fps rate meant that more step cycles (albeit partially) were presented in the animation. Finally, mirror animations were prepared by rewinding (i.e., reversing) the walking action in each animation where the stick-figure walked

backward, serving as the less plausible/less familiar walking condition.

#### Bisection Procedure

#### **Training**

Each session started with the presentation of two anchor durations at the offset of a space button press (short = 1 s, long = 3.5 s), represented by the presentation duration of a circular mottled texture (white, gray, black; 140, 10, 0.2 cd/m2 in brightness, respectively; approx. 8 cm/7.6 visual deg. in diameter). 10 training trials then ensued, in which the participants' task was to report if the duration of the automatically presented circular texture was the short or the long one (5 random trials each). A trial was repeated if an incorrect categorization was given by the participant. The buttons denoting a "short" or a "long" response were randomly assigned in each session. Each participant attended a single session, which lasted 50–60 min. Participants were instructed not to count or use any other chronometric methods, which has been reported to be sufficient to prevent counting (Rattat and Droit-Volet, 2012).

#### **Test**

After 10 correct responses in the training trials, the experimental block commenced, in which the participants' task was to categorize the six probe durations of walking animations as closer to the "short" or "long" anchor durations. Three walking speeds were employed: 40, 50, 63 fps. The animations started with the press of the space button. Once the animation ended, the participant was probed to respond after a stimulus-to-response interval sampled from an exponential distribution with a mean of 0.5 s and a lower bound of 0.2 s. All possible combinations of walking speeds (3 levels), probe durations (6 levels), and walking direction (2 levels) were randomly presented 12 times, leading to a total of 432 trials per session. No feedback was given after responding either for the reference or intermediate durations.

#### Data Analysis

Mean percentage of "long" responses were plotted as a function of the six probe durations for each combination of walking speed and walking direction conditions, thereby forming six sigmoidal psychometric functions per participant (see **Figure 2** – top panel for fits to average data). Standard two-parameter cumulative Weibull distribution functions were fit to these data. The parameters of fits with adjusted-R-squared values less than 0.70 (7% of the cases) were substituted by a random value that was drawn from the sample distribution. Points of subjective equality (PSE; the duration at which a short and a long response was equally likely) were calculated as the median of the Weibull fits. We were primarily interested in potential leftward or rightward shifts of the PSE values as a function of experimental conditions,

(circle) and dashed green (square) lines denote slow and fast walking speeds, respectively. Standard Error of the Mean of individually calculated Points of Subjective Equality (PSE) are marked with horizontal lines of identical colors as the walking speed condition. Weber Ratios (WR) are provided as insets.

which would typically be interpreted in terms of an increase or a decrease in clock speed (i.e., perceived time), respectively. We have also calculated the Weber Ratios (WR), which is a measure of the steepness of the psychometric function and refers to the sensitivity with which the probe durations are categorized. WR values were calculated by dividing the difference limen {[p(long) = 0.75 – p(long) = 0.25]/2} by the PSE. A higher WR value indicates that the participant had lower sensitivity (more difficult time) categorizing the durations as short or long.

A two-way repeated measures ANOVA with walking speed (3 levels; Exp 1: 40, 50, 63 fps; Exp 2: 25, 50, 100 fps) and walking direction (2 levels; forward and backward) as within subject factors, and PSE values as the dependent variable was conducted. In addition to conventional frequentist repeated-measures ANOVAs, we also report the results of these tests' Bayesian counterparts for which we report inverse Bayes Factors (BF10; the strength of evidence the data provides for the alternative hypothesis compared to the null hypothesis; e.g., Wagenmakers et al., 2018b). BF10 values between 1–10, 10–100, and 100–300 are interpreted as providing weak to moderate, moderate to strong, and strong to decisive evidence for the alternative hypothesis, respectively. Conversely, the inverse of these factors (1/BF10) provide evidence for the null hypothesis in line with the same rule-of-thumb ranges (BF01; Jeffreys, 1961; Goodman, 1999); We used the JASP <IP_ADDRESS> open-source software

with default priors for all Bayesian tests (see JASP Team, 2018; Wagenmakers et al., 2018a). In the manuscript, we indicate the model that has the highest Bayes factors with respect to the null model except for the model that contains an interaction, which is instead compared to the likelihood of the model that contains the main effects of the factors that were also included in the interaction model.

#### RESULTS

Our analysis of data from Experiment 1 showed a main effect of walking speed [F(2,62) = 47.04, p < 0.001, η 2 p = 0.60], and no main effect of walking direction [F(1,31) = 0.34, p = 0.55], or an interaction between the two variables [F(1.57,48.52) = 2.34, p = 0.11, Greenhouse-Geisser Corrected]. Post hoc analyses showed that the difference between all walking speeds reached significance (MSlow = 2.38, MNormal = 2.25, MFast = 2.02; all ps < 0.01, see **Figure 2**). The Bayesian two-way ANOVA revealed an identical pattern of results where the data provided decisive evidence for the walking speed model over the null as the best model (BF10 > 300).

Identical repeated measures ANOVAs with WR as the dependent variable and walking speed and walking direction as the independent variables were conducted. In terms of their effects on WR values, neither the main effects nor their interaction reached significance (all ps > 0.05). The same pattern of results was observed with Bayesian analyses where the Bayes factors did not yield more than anecdotal evidence for any of the main or interaction effect models (all BF10 < 1).

#### EXPERIMENT 2

We repeated Experiment 1 with a new group of participants who were tested with a larger range of walking speeds. This allowed us to replicate the first experiment as well as to observe if larger differences between walking speeds indeed lead to larger differences in subjective time compared to Experiment 1. Additionally, by using unnaturally fast and slow movement speeds as timed stimuli, Experiment 2 had the potential to reveal any effects of walking direction which may have been masked in the previous in the experiment, where fast and slow walking speeds were still within the interpretive limits of normal biological action.

#### Methods

#### Participants

Thirty-two participants were tested in Experiment 2 (10 male, Mage = 21.2) and received 12 Turkish Liras for their participation.

#### Stimuli and Apparatus

The stimuli, apparatus, and the procedure used in Experiment 2 were identical to those used in Experiment 1 except for that participants were tested with 25, 50, and 100 fps in Experiment 2 (as opposed to 40, 50, and 63 fps in Experiment 1). Data analyses were identical to Experiment 1. The parameters of fits with adjusted-R-squared values less than 0.70 (4% of the cases) were substituted by a random value that was drawn from a distribution with identical parameters as the sample distribution.

#### RESULTS

Data from Experiment 2 showed the identical pattern of results, with a larger size of the significant main effect compared to Experiment 1; namely a main effect of walking speed [F(1.34,41.64) = 105.44, p < 0.001, η 2 p = 0.77], and no main effect of walking direction [F(1,31) = 2.32, p = 0.14], or an interaction between walking speed and walking direction [F(2,62) = 0.60, p = 0.55]. Again, identical with Experiment 1, post hoc analyses in Experiment 2 showed that the difference between all walking speeds reached significance (MSlow = 2.72, MNormal = 2.24, MFast = 1.77; all ps < 0.001). Bayesian analyses affirmed these findings, where the data provided decisive evidence for walking speed as the best model over the null model (BF10 > 300).

Different from Experiment 1, a frequentist ANOVA revealed a significant main effect of walking speed on WR [F(2,62) = 7.48, p = 0.001] in Experiment 2. Post hoc analyses showed that WR values in the slow walking condition (M = 0.151) were significantly lower compared to the normal (M = 0.176) and fast (M = 0.188) walking conditions (both ps < 0.05), while the latter two conditions did not differ significantly from each other (p > 0.05). These findings were confirmed by the Bayesian ANOVA, which provided moderate evidence for the walking speed model over the null model (BF01 = 4.87) in terms of its effect on the WR values.

Finally, we aimed to see if the degree of the effects were more prominent with larger differences in walking speed as manifested by the experimental paradigm (i.e., as in Experiment 2 compared to Experiment 1). Thus, the data gathered in both experiments were subjected to a mixed ANOVA with walking speed and walking direction as two within-subjects factors, test group as the between-subjects factor (2 grouping levels; Experiment 1 and Experiment 2), and PSE as the dependent variable. Results showed a main effect of walking speed [F(1.61,99.94) = 150.93, p < 0.001, η 2 p = 0.71], in addition to an interaction between walking speed and the grouping factor [F(2,124) = 30.23, p < 0.001, η 2 p = 0.33], while there were no main effects of walking direction or the grouping variable or any other interaction effects among the factors (all ps > 0.05; **Figure 3**). Post hoc independent samples t-tests showed that, in both the forward and backward walking conditions, the PSE values in the slow and fast walking speed conditions in Experiment 2 were significantly lower and higher than those in Experiment 1, respectively (all ps < 0.05, Holm-Bonferroni corrected, see **Figure 3**), whereas there were no differences among the normal walking speed conditions in either direction (both ps > 0.05). Complementary analyses using the Bayesian method in a mixed-ANOVA setup revealed the strongest evidence for the interaction model between walking speed and the grouping variable among all models. This interaction model was decisively preferred to the walking speed and the grouping variable main effects model (both BF10 and BFinclusion > 300).

the 0.05 level. Error bars show standard error of the mean.

# EXPERIMENT 3 AND STIMULUS RATINGS

Previous research has shown that the detection of actual backward walking and digitally rewound forward walking require different types of cognitive competences (Viviani et al., 2011), and are likely perceived according to distinct perceptual factors and cognitive dynamics. This is evidenced by the fact that the simplest form of walking -in mechanistic terms-, is in fact a sequence of "falling" forward by shifting the center of the body mass, followed by a precisely timed catching of oneself before falling over or tripping, and then repeating this cycle with the contralateral limbs. As such, although walking backward utilizes the same mechanistic principle (i.e., temporarily shifting the center of mass, but this time backward), a different orchestration of a sequence of musculoskeletal coordination (and therefore a different observable movement) is utilized for relocating the body toward a backward position. Therefore, we conducted a third experiment to replicate Experiment 2 with stimuli embedded with more plausible backward walking action animations compared to those used in Experiment 1 and Experiment 2, in which backward walking animation was prepared by mimicking actual animations of forward moving profiles - see **Supplementary Materials**. We had these new animations rated by an independent group of participants in terms of how plausible they appeared.

## Methods

#### Participants

Twenty-nine participants (11 male, Mage = 21.1) attended the Stimulus Rating experiment, and a different group of 25 participants were tested in Experiment 3 (9 male, Mage = 21.8). Participants received 1 course credit in Experiment 3 and 0.5 course credit for their participation in the Stimulus Rating experiments. All experiments were approved by the Institutional Review Panel for Human Subjects of Koç University. All participants provided written consent for their participation.

#### Stimuli and Apparatus

#### **Stimulus Rating**

Realistic backward walking animations were prepared using the same software methods used in Experiments 1 and 2 for preparing forward walking animations, this time by observing animations of humans purposefully walking backward in an upright position. Separate backward walking animations were prepared in keeping with all walking speed (3 levels) and probe duration (6 levels) conditions used in Experiment 2. Stimulus presentation and response collection methods, as well as other experimental conditions were identical to those in Experiments 1 and 2.

#### **Experiment 3**

All apparatus and response collection methods were identical to those used in Experiment 1 and 2. All "rewound backward walking" stimuli from Experiment 2 were replaced by the "realistic backward walking" animations in Experiment 3 (see section above "Stimulus Rating").

#### Procedure

#### **Stimulus Rating**

Each trial consisted of the presentation of two consecutive backward walking animations, each of which started at the onset of a space button press by the participant. On each trial, one of the animations was a backward walking animation generated by rewinding forward walking (as in Experiment 1 and 2),

and the other was the novel, more realistic backward walking animation. The order of the animations was counterbalanced across trials. The two animations matched in their fps parameters (25, 50, or 100) and presentation durations (1.0, 1.5, 2.0, 2.5, 3.0, or 3.5 s). Combined levels of both variables (fps and duration) were counterbalanced and animations depicting each combination were presented twice in a single 20–25-min-long session. Presentation of the first animation was followed by a blank screen and an inter-stimulus interval (ISI) drawn from an exponential distribution with a mean of 0.5 s and a lower bound of 0.2 s. The ISI was followed by the written instruction to "Press the space button to see the second animation." Immediately after the end of the second animation, the participant was asked to state which of the two animations (i.e., former or the latter) had the more plausible form of backward walking. The button press was followed by a response-to-stimulus interval with identical randomly distributed delays as in the ISI.

#### **Experiment 3**

All procedures, variables and parameters were identical to Experiment 2.

## RESULTS

#### Stimulus Rating

Choice (as more familiar/plausible) proportions for the rewound backward and realistic backward walking animations were calculated. A one-sample t-test comparing choice proportions for the novel stimuli (over the rewound version) to chance level (i.e., 50%) revealed that the participants were significantly more likely to choose the novel backward walking stimuli over the rewound backward walking stimuli used in Experiment 2 as more plausible [M = 58.3, SD = 19.1, t(28) = 2.34, p < 0.05] A Bayesian one sample t-test showed that the choice proportions for the novel stimuli were 2.03 times more likely than the chance level.

#### Temporal Bisection Experiment

Identical analyses as those in Experiment 2 were performed with identical inclusion/exclusion criteria and mean inoculation methods. The PSE and WR values were calculated for each participant by fitting standard two-parameter cumulative Weibull distribution functions to individual data. Identical with Experiments 1 and 2, this procedure was carried out for each combination of walking speed and walking direction conditions.

A two-way repeated measures ANOVA with walking speed (3 levels; 25, 50, 100 fps) and walking direction (2 levels; forward and backward) as within subject factors, and PSE values as the dependent variable was conducted. Results showed a main effect of walking speed [F(1.34,32.2) = 89.38, p < 0.001, η 2 p = 0.79, Greenhouse-Geisser corrected], and no main effect of walking direction [F(1,24) = 0.99, p = 0.34], or an interaction between the two variables [F(2,48) = 1.45, p = 0.26; see **Figure 4**]. Post hoc analyses showed that, identical with the results of Experiments 1 and 2, the difference between all walking speeds reached significance, where the fastest walking speed led to the lowest PSE followed by the normal and the slow walking speed conditions (MSlow = 2.74, MNormal = 2.33, MFast = 1.89; see **Figure 4**); There was a monotonic relationship between walking speed and PSE. As with Experiments 1 and 2, Bayesian ANOVAs with identical variables confirmed the results of the traditional ANOVAs such that the walking speed model was preferred against the null as the best model (BF10 > 300).

Identical repeated-measures ANOVAs with WR as the dependent variable and walking speed and walking direction as the independent variables were conducted. None of the main

effects or the interaction between the variables was found to be significant (p > 0.05). These findings were confirmed by the Bayesian ANOVA, which provided no evidence for any of the main or interaction effect models (BF10 < 1).

# GENERAL DISCUSSION

fpsyg-09-02565 December 21, 2018 Time: 17:12 # 9

We conducted three experiments in which participants' task was to categorize six durations of animations depicting a stick-figure, walking forward or backward, at three different walking speeds. The forward-backward walking direction was added to the current study as a variable in a similar vein to previous studies which assigned backward walking the unique property of representing "unfamiliarity" of a given biological motion (i.e., Viviani et al., 2011; Maffei et al., 2014), any natural form of which could be considered "familiar" unless artificially manipulated. The first two experiments differed only in the degree of difference between the faster and the slower walking speed. When data from the first two experiments were examined separately, as well as in conjunction, our results suggested that subjective time dilates with faster observed walking speed and it constricts with slower observed walking speed. On the other hand, the direction in which the stick-figure walked (forward or backward) did not have an effect on perceived time, and it did not interact with walking speed in any of the experiments. In a third experiment, we tested participants with a more naturalistic backward walking animation (as opposed to rewinding forward motion as in the first two experiments) and replicated these findings.

There are two primary mechanisms through which subjective time can be modulated within the "pacemaker-accumulator" theoretic framework; these are 1) changes in the pacemaker rate and 2) changes in the probability by which pacemaker signals are integrated in the accumulator (Penney, 2003). In relation to our experimental manipulation, faster walking speed can be assumed to either increase the pacemaker rate (e.g., due to arousal) or lead to a decrease in attention to time (e.g., due to divided attention) and vice versa for slower walking speeds. Under the first possibility (i.e., change in pacemaker rate), subjective time would be expected to dilate with faster walking speed, while the opposite predictions would be made if the effects were on attention to time. To this end, our results directly support the effect of observed walking speed on pacemaker rate. Importantly, walking speed had a parametric effect on clock speed; Compare the effect sizes in Experiment 1 with Experiments 2 and 3 with differential degrees of deviation between walking speeds (see **Figures 3**, 4).

Interval timing models which employ such a switch component also assert the possibility of stimulus effects on switch closure (timing onset) and opening (timing offset) latencies (Gibbon et al., 1984; Zakay and Block, 1995; Wearden et al., 1998). An increase in switch closing or opening latency would lead to under or over-estimation of perceived durations, respectively, whereas simultaneous action of both states would nullify each other leading to no discernible effects (e.g., Wearden et al., 2007; Bratzke et al., 2017). Our results could potentially be explained by an effect of faster motion on switch closure latency, or vica versa. Since we have used one range of durations in this study, we cannot separate the additive effects that would be induced by switch closure latency from the proportional effects that would result from clock speed effects. Comprehensively elucidating an additive switch-based effect on perceived time veiled in our data remains a fertile methodological challenge for future research.

The behavioral effects observed in this study can also be readily accounted for by the neural energy model of timing (Pariyadath and Eagleman, 2007, 2008) since based on prior work (e.g., Kaufmann et al., 2000) observing faster walking speeds would be expected to lead to stronger neural activation (i.e., more neural processing) which, in the light of the neural energy model, would lead to longer time estimates. The experimental design and tools utilized in the current study, however, cannot distinguish between these two different theoretical accounts. On the other hand, the lack of an effect of walking direction on perceived time contradicts our hypothesis that was derived from the embodied cognition perspective. According to the embodiment perspective, cognition regarding real-world objects is time-pressured and is body-oriented (Anderson, 2003). We rarely interact with backward walking motion in real life and are therefore less familiar with it compared to forward (i.e., regular) walking. Based on this rationale, we expected the effect of walking speed to be more prominent in the forward walking condition than the backward walking condition, which was not the case, even though participants were indeed able recognize a biologically plausible backward motion compared to an implausible one (see Experiment 3, Stimulus Rating). Briefly, the lack of an effect of walking direction in the light of the previous studies does not support the embodied cognition account of our findings.

On a different level, our results can be interpreted from two perspectives; one view assumes that temporal and spatial information processing are independent and the other view assumes that temporal and spatial information processing can be coupled. According to the first approach, one can think that the effect of visual stimulus (such as the flickering presentation of visual input) would be via the stimulus-dependent arousal-based modulation of the central clock mechanism as discussed above (e.g., Droit-Volet and Wearden, 2002). The second approach is supported by work that shows that time perception can be modulated by adaptation to visual properties in a spatially localized fashion, which points at the effects at the level of sensory information processing (e.g., Johnston et al., 2006).

Although our study does not allow us to differentiate between these two accounts, as part of the second theoretical framework, one can speculate regarding the possible neural mechanisms that mediate the modulation of time perception by the observed walking speed (i.e., biological motion). One of the possibilities is that these effects are mediated by the "When Pathway" containing the right parietal cortex (i.e., inferior parietal lobe-IPL) that is assumed to process event timing bilaterally in the visual field (Battelli et al., 2007). Parietal lobe has indeed been shown to be associated with event timing in both monkey (Leon and Shadlen, 2003; Morrone et al., 2005 for LIP involvement) and

human work (Husain et al., 1997). In this pathway, visual information is assumed to be relayed from V1 to the middle temporal visual area (MT), that is involved in the perception of speed and direction of motion (Krekelberg and van Wezel, 2013; Liu and Newsome, 2005- irrespective of it being biological or not). Motion-related information from MT is then relayed to multiple areas including the right inferior parietal lobe (IPL), right angular gyrus, supramarginal gyrus, and posterior superior temporal sulcus (Battelli et al., 2007). From the types of motions, the "biological motion" has been argued to be one of the most prominent signals that is processed in this high-level attention-based system that contains the IPL as well as other areas such as the posterior superior temporal sulcus (Grossman et al., 2000, 2005; Grossman and Blake, 2002; Battelli et al., 2003, 2007). It might be this very neural pathway and its functional overlaps through which the observed biological motion and time might interact so robustly as in the case of our work.

Motion-related signals (biological or not) from MT modulate the activity of neuronal populations also in the lateral intraparietal area (LIP – Mazurek et al., 2003), which in and of itself has been shown to be involved in interval timing (e.g., Leon and Shadlen, 2003; Janssen and Shadlen, 2005; Jazayeri and Shadlen, 2015). If timing mechanisms are similar to those in perceptual decision making (e.g., Simen et al., 2011; Balc*ı* and Simen, 2016), where MT neurons are associated with momentary motion whereas LIP neurons integrate those motion-related signals over time (as in the context of two alternative random dot motion discrimination), one would expect the rate of temporal integration to be closely coupled with the speed of observed motion. This constitutes another neural pathway that might mediate the effect of observed motion (biological or not) on perceived time. Note that these arguments have been typically made in relation to the timing of relatively short intervals and their extension to longer scale time such as those utilized in our study requires further work (e.g., see Coull and Nobre, 1998; Bruno and Cicchini, 2016).

Another potential mechanism for the modulation of time perception by biological motion is through the premotor frontal areas that have been implicated both in biological motion (Saygin, 2007) as well as time perception (e.g., Mita et al., 2009). Within this framework, the connections between superior temporal sulcus and premotor areas (e.g., Luppino et al., 2001; Yoshida et al., 2011) might support the modulation of perceived time by the speed of biological motion. Lastly, the temporo-occipital junction (TOJ) has been shown to be activated by unfamiliar compared to familiar walking scenes (Maffei et al., 2014). The lack of an effect of walking direction in the current study suggests that the TOJ is probably not recruited with regard to the interaction between perceived walking speed and perceived time, narrowing down the possible neuroanatomical basis of the effect. Future neuroimaging and neuromodulation studies would help differentiate between these different implementational possibilities.

Weber's ratio, in its simplest form, has been suggested to be constant when timing different durations with a constant (i.e., non-modulated) clock-speed (Gibbon, 1977; Grondin, 2001), except for very short (Getty, 1975) or very long durations (Bizo et al., 2006); a range of which does not closely bound the durations used in the current study. Simulations conducted based on the decision rules as outlined in Wearden and Ferrara (1995) and the linear modulation of Poisson clock speed by the walking speed showed that WR should remain nearly constant for all walking speeds. Consistent with this prediction, the Weber's Ratios were relatively constant across conditions in Experiments 1 and 3, however, it increased as function of walking speed in Experiment 2. Therefore, our findings regarding WRs also supported the predictions of the clock-speed modulation account of the effect of observed walking speed.

In all of our experiments, we modulated fps values in order to increase/decrease the speed at which the stick-figure seemed to move. Importantly, a higher fps stimulus (our fast walking condition) by definition employs more frames that are presented to the participant per unit time. In relation to theories of timing that emphasize "perceived change per unit time" as the fundamental index of perceived duration (Poynter, 1989), it can be argued that it wasn't the high speed of movement per se that altered perceived durations in our paradigm, but rather the number of frames perceived by the participant per unit time. However, given that all of the simulation videos used in our study were presented with upward of 24 frames per second, beyond which most participants perceive continuous motion (e.g., Condon and Ogston, 1966; Haggard and Isaacs, 1966), such an argument seems implausible. Nonetheless, this possibility could be tested for by keeping the frame rate constant (e.g., 50 fps) among speed conditions in a future study.

Our experimental manipulation of walking speed was implemented in a fashion isolated from other visual correlates at the background scene (i.e., the rate of change in the background visual scene). This limited the ecological validity of the stimulus manipulation since natural visual processing of objects typically occurs in the presence of complex backgrounds. An experimental design that contains conditions with (a) a constant walking speed coupled with different rates of change in the background visual scene, (b) the rate of change in the background visual scene congruent with the change in walking speed, and (c) the rate of change in the background visual scene incongruent with the change in walking speed would allow future research to capture the differential effect of rate of change in the visual scene on time perception. In such experimental settings, we would expect the observed effects on time perception to be enhanced in visually congruent conditions and diminished in incongruent conditions provided that the participants process the scene (e.g., visual flow) together with the figure. Under this rationale, for a constant walking speed the rate of change in the background visual scene could also be an independent determinant of alterations in time perception. However, given the object-based visual attentional processing and the fact that various brain regions are differentially involved in the processing of biological and non-biological motion (e.g., Grossman et al., 2000), we would also expect the walking speed of the attended agent to have the dominant modulatory effect on time perception. Lastly, the current study employed no eye-tracking-based visual

restrictions throughout the trials so as not to prevent voluntary exploration of the stimuli during the timing of presented intervals. Saccadic eye movements are known to affect perceived time (Yarrow et al., 2001; Morrone et al., 2005; Burr et al., 2010; Suzuki and Yamazaki, 2010; Kars˛*ı*lar and Balc*ı*, 2016; Penney et al., 2016) and therefore future studies could test similar effects to ours by forcing some type of foveal fixation either at the center of the stimulus, or allow for fixations only within the area encompassed by the size of the presented videos. Future studies with such experimental designs are needed to complement our understanding of the effect of observed motion on time perception.

Relatedly, all of our experiments employed stimuli depicting a simple walking motion performed by an animated human-like agent, none of which showed an effect of walking direction on perceived time. As mentioned above, biological plausibility is possibly linked to the mechanism by which an object is timed. Therefore, a future study that tests how self-governing, non-biological motion stimuli (as opposed to backward movement used in the current study) are timed in contrast to stimuli depicting biological motion (i.e., walking), could further elucidate the mechanism by which this modulation of time perception was achieved in the current study. As such, it is possible that the backward walking motion used in our experiments failed to tap into the mechanism by which non-biological/unnaturally moving stimuli are processed (Maffei et al., 2014), which is why it might have exerted no discernible effect on perceived time, as opposed to what was hypothesized. We find such an investigation particularly relevant to our overarching research question since the motor system would be more likely to imitate the biological motion due to higher structural overlap between the human motor system and the observed stimulus (for detailed discussion see Wilson, 2001; Shiffrar and Heinen, 2011) and thereby better extract information regarding the motion-related state of the observed stimulus as a result of its stronger embodiment (Loula et al., 2005). Neuroscientific evidence in related fields further bolsters the relevance of addressing this issue as the brain areas (e.g., premotor areas and cerebellum) that have been implicated in the processing of human movement (Stevens et al., 2000; Saygin et al., 2004; Saygin, 2007) are also known to be involved in interval timing (Merchant et al., 2013).

As a final note, most types of biological motion used in experimental settings, -including many different forms of walking- are typically represented either by video recordings of actual actors, or by point-light animations (Johansson, 1973) which present the action in terms of coherently moving nodes/joints (see Grosbras et al., 2012 for a comprehensive review). While stimuli composed of video recordings benefit from high fidelity in terms of biological plausibility of the observed motion, these types of stimuli suffer from potential embodiment-related confounds depending on the (dis)similarity between the actor and the timing agent. On the other hand, point-light animations (e.g., Saygin et al., 2004; Watanabe, 2008) sidestep this problem by utilizing a more "symbolic" and flexible expression of biological motion with an otherwise invisible actor projected over a static background, which effectively omits all potential confounds such as color, shape, preconceived biases etc. However, point-light stimuli arguably lack some ecological validity, since timing of motion stimuli entails perception of almost all aspects of the observed organism and not just a sub-component of implied coherent motion vectorized in terms of moving dots. The stimuli used in the current study were, in principle, closer to point-light walker animations compared to video recordings; yet unlike their counterpart, they concretely and visibly represented the human motion in its entirety, including the action of the limbs, torso and the head (see **Supplementary Materials** for animations). To the best of our knowledge, these types of stick-figure stimuli have never been utilized in the context of timing. This methodological novelty, compounded by the relatively prominent effects, which parametrically increase with the experimental manipulation of observed walking speed, put forth the possibility for future studies to employ other similar forms of animation, (including 3-dimensional stimuli embedded within virtual or augmented reality environments), which in turn could more accurately elucidate the mechanism by which observing (or interacting with) some form of biological or non-biological motion could exert its effects on how humans perceive the "flow" of time.

## DATA AVAILABILITY STATEMENT

The datasets analyzed for this study can be found in the Drive Folder URL: https://tinyurl.com/ycc8cgkr.

## AUTHOR CONTRIBUTIONS

HK, YK, and FB contributed equally to the conception and design of the study. HK and YK prepared the stimuli and collected the data. HK organized the database. HK and FB performed the statistical analyses. All authors contributed to the first and revised draft of the manuscript, read, and approved the submitted version.

# FUNDING

This study was supported by a New Agendas for the Study of Time and TÜBA (Turkish Academy of Sciences) GEB˙IP 2015 grant to FB.

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyg. 2018.02565/full#supplementary-material

DATA SHEET S1 | The model comparison tables for all Bayesian analyses conducted.

PRESENTATION S1 | The stimuli used in all experiments.

## REFERENCES

fpsyg-09-02565 December 21, 2018 Time: 17:12 # 12

Jeffreys, H. (1961). Theory of Probability, 3rd Edn. Oxford: Oxford University Press.

Johansson, G. (1973). Visual perception of biological motion and a model for its analysis. Percept. Psychophys. 14, 201–211. doi: 10.3758/BF03212378

Johnston, A., Arnold, D. H., and Nishida, S. (2006). Spatially localized distortions of event time. Curr. Biol. 16, 472–479. doi: 10.1016/j.cub.2006.01.032

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Kar¸sılar, Kısa and Balcı. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# 1-s Productions: A Validation of an Efficient Measure of Clock Variability

Sarah C. Maaß1,2\* and Hedderik van Rijn1

1Department of Experimental Psychology, University of Groningen, Groningen, Netherlands, 2Behavioral and Cognitive Neurosciences, University of Groningen, Groningen, Netherlands

Objective: Clock variance is an important statistic in many clinical and developmental studies. Existing methods require a large number of trials for accurate clock variability assessment, which is problematic in studies using clinical or either young or aged participants. Furthermore, these existing methods often implicitly convolute clock and memory processes, making it difficult to disentangle whether the clock or memory system are driving the observed deviations. Here we assessed whether 20 repeated productions of a well-engrained interval (1 s), a task that does not incorporate memory updating nor the processing of feedback, could provide an accurate assessment of clock variability.

#### Edited by:

Trevor B. Penney, The Chinese University of Hong Kong, China

#### Reviewed by:

Sven Thoenes, Leibniz-Institut für Arbeitsforschung an der TU Dortmund (IfADo), Germany Darren Rhodes, Nottingham Trent University, United Kingdom

> \*Correspondence: Sarah C. Maaß<EMAIL_ADDRESS>
Received: 30 September 2018 Accepted: 10 December 2018 Published: 21 December 2018

#### Citation:

Maaß SC and van Rijn H (2018) 1-s Productions: A Validation of an Efficient Measure of Clock Variability. Front. Hum. Neurosci. 12:519. doi: 10.3389/fnhum.2018.00519 Method: Sixty-eight undergraduate students completed two tasks: a 1-s production task in which they were asked to produce a 1-s duration by ending a tone by a keypress, and a multi-duration reproduction task. Durations presented in the reproduction task were tones lasting 1.17, 1.4 and 1.68 s. No feedback was presented in either task, and the order of presentation was counterbalanced between participants.

Results: The observed central tendency in the reproduction task was better explained by models including the measures of clock variability derived from the 1-s production task than by models without it. Three clock variability measures were calculated for each participant [standard deviation, root mean squared residuals (RMSRs) from an estimated linear slope, and RMSR scaled by mean production duration]. The model including the scaled RMSR was preferred over the alternative models, and no notable effects of the order of task presentation were observed. These results suggest that: (1) measures of variability should account for drift; (2) the presentation of another timing task before a 1-s production task did not influence the assessment of the clock variability; and (3) the observed variability adheres to the scalar property and predicts temporal performance, and is thus a usable index of clock variability.

Conclusion: This study shows that just 20 repeated productions of 1 s provide a reliable index of clock variability. As administering this task is fast and easy, it could prove to be useful in a large variety of developmental and clinical populations.

Keywords: interval timing, precision, clock variance, individual differences, clinical populations

# INTRODUCTION

Estimating and reproducing short intervals in the hundreds of milliseconds to seconds range is central to a wide range of behaviors. Irrespective of the theoretical framework, this type of timing is assumed to be driven by an internal time source, or clock, and memory traces of previously experienced intervals. Because of this dyad, variations in interval timing proficiency can either be driven by changes in the accuracy of the clock, or by variations in the efficacy of the memory mechanisms. Interestingly, deviations in timing performance observed in clinical populations are often attributed to variations in clock precision and accuracy (for a review see Allman and Meck, 2011). For example, Alzheimer diseased patients demonstrate increased timing variability in a bisection task using sub-second intervals (Caselli et al., 2009), and similar observations are associated with the performance of patients with bipolar disorder (Bolbecker et al., 2014) and Parkinson's disease (Pastor et al., 1992; Harrington et al., 1998; Malapani et al., 1998). Furthermore, performance of autistic children is poorer in temporal discrimination tasks when compared with healthy, age-matched controls (Karaminis et al., 2016). Changes in temporal accuracy are, however, not limited to clinical conditions. Even during normal, healthy aging, temporal precision declines, observable by more variable timing estimations and a general decrease in accuracy (for a review see Paraskevoudi et al., 2018).

Even though these phenomena are often explained in terms of deviations in clock variance, the impairment of temporal precision may also be clock-unspecific. For example, individuals with schizophrenia display greater variability in a rhythmic tapping task, potentially caused by larger timing variability (Carroll et al., 2009). Yet, these effects have also been attributed to procedural learning (Da Silva et al., 2012), or the inability to synchronize to external events (Wilquin et al., 2018). Thoenes and Oberfeld (2017) propose general cognitive deficiencies as a potential explanation for the impaired temporal performance in individuals with schizophrenia.

Distinguishing between clock-based and more general deficiencies is difficult as most tasks that are used to assess the precision of the clock implicitly rely on a convolution of clock and memory processes. Typically, the precision of interval timing is indexed by a rhythmic tapping task or by calculating a Weber fraction (e.g., Harrington et al., 1998; Karaminis et al., 2016), a measure indicating the minimal proportional chance for a changed stimulus to be discernible from the original (''just noticeable difference''). The Weber fraction is typically calculated from a psychometric function derived from a bisection or discrimination task. In both tasks, participants have to learn either one or two comparison durations or ''anchors'' during the scope of the experiment. Performance in both tasks thus depends on generating the correct memory representations during the experiment itself. Moreover, calculating an accurate psychometric function requires a relatively large number of trials making it unsuitable for populations with shorter attention spans or for those that are more easily fatigued. The rhythmic tapping task on the other hand is closely linked to motor performance, a process that undergoes a separate decline in aging and certain clinical conditions (Paraskevoudi et al., 2018; PD: Jankovic, 2008). Based on similar considerations, Paraskevoudi et al. (2018) proposed that ''more appropriate methods for detecting the accuracy and imprecision signatures of a slower clock are verbal estimation tasks, production tasks, and unpaced finger tapping tasks, which presumably reflect the internal tempo in its pure form'' (page 11). Here, we present a first validation of a pure clock variability measure that does not incorporate memory updating during the experiment, nor the processing of feedback, and can be quickly administered.

In our study, participants were asked to produce 20 1-s intervals by ending a machine-started tone by a key-press, without feedback or prior presentation of the defined interval. As 1-s intervals are likely to be highly familiar or trained to the participants, we assumed a stable internal representation and thus attributed the variability observed in the repeated production of this interval to clock variability. The most straightforward way of determining the precision of the repeated 1-s duration is by calculating a standard deviation. This way of determining precision assumes that the accuracy of the 1-s estimation remains the same over the 20 repeated productions. However, human performance on simple tasks such as continuation tapping (e.g., Lemoine et al., 2006) is known to be subject to drifts, especially over the shorter sequences used in this study (Wagenmakers et al., 2004). These drifts are defined as slow changes of the running mean, for example, participants might speed up or slow down during the course of the experiment. Even though there is disagreement in literature about the patterns best describing long-term dependencies, it is clear that an accurate measurement of precision in the 1-s production task should account for potential drifts.

Noise is ubiquitous in human information processing (Faisal et al., 2008), and earlier work has demonstrated that humans use knowledge of their sensory variability to produce estimates that are optimal in the context of the task (e.g., Körding and Wolpert, 2004; Murai and Yotsumoto, 2018): the noisier the incoming information on a particular trial, the stronger the influence of the expectation that was built up during previous trials. Thus, the temporal precision measures derived from the 1-s task should determine how much a learnt temporal context influences the performance on a specific trial. We therefore asked participants to also complete a reproduction task of three different durations. A typical phenomenon observed in these tasks is a central-tendency effect (Hollingworth, 1910, often referred to as Vierordt's law; see Lejeune and Wearden, 2009, for a discussion). This tendency of judgments of quantities to gravitate towards their mean, irrespective of whether it is in terms of spatial distances, durations, or any other perceptual quantity, is a highly robust perceptual effect (Jazayeri and Shadlen, 2010; Petzschner and Glasauer, 2011; Wiener et al., 2016). This effect is typically explained by assuming that the internal representation of a currently observed quantity is a mixture of the actually perceived quantity and a memory representation of all previous quantities. In the context of this study, the consequence of this ''central tendency'' driven by previously experienced durations is that durations shorter than this central tendency are overestimated, whereas those longer than it are underestimated.

This highly robust phenomenon that demonstrates the influence of memory on perception (see for reviews on memory influences on timing Shi and Burr, 2016 or van Rijn, 2016) can be captured in terms of Bayesian Inference (Jazayeri and Shadlen, 2010; Shi et al., 2013; see also Taatgen and van Rijn, 2011), in which the perceived duration (sensory likelihood) is integrated with previously perceived intervals that are stored in the reference memory (prior). The key feature of this process for the purpose of this work is that a narrower (or less noisy) likelihood will yield a smaller regression to the mean, and, vice versa, a stronger prior will result in more central tendency, and that the likelihood is driven by the precision of the interval timing processes. For example, in highly trained professional musicians, such as percussionists, reproduced auditory durations are reproduced to perfection, indicative of an extremely peaked likelihood, and resulting in a relatively small influence of the prior (Cicchini et al., 2012). Inversely, as aged participants exhibit more uncertainty, indicative of a wide likelihood, the influence of the prior increases, causing a stronger reliance on prior memories (Turgeon et al., 2016). In other words, the individual differences observed in the 1-s task should correlate with the central tendency observed in the reproduction task. However, both tasks rely on the production or reproduction of intervals in a similar time range. It is therefore possible that sequential effects can be observed (note that these are at a more global level than the trial-by-trial sequential effects discussed in, for example, Taatgen and van Rijn, 2011; Dyjas et al., 2012; Di Luca and Rhodes, 2016). We tested for this possibility by counterbalancing the order in which the production and reproduction task were administered.

Summarizing, we set out to test whether clock variability can be assessed with a short production task, consisting of 20 repeated productions of a 1-s interval and hypothesize that a measure of variability derived from this task should predict the amount of central tendency observed in a multi-duration reproduction task.

# MATERIALS AND METHODS

### Participants

Sixty-eight undergraduate students from the University of Groningen completed the experiment in exchange for course credit. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Psychology Ethical Committee of the University of Groningen. We excluded a total of five participants based on their performance in either the production or reproduction task. One participant was excluded based on failing to follow task instructions (98% of trials failing to meet the inclusion criteria for the Reproduction task discussed below; average response time during the reproduction task was 288 ms). For the production task, four participants were excluded due to large deviations in produced durations, even after excluding the first two startup trials (i.e., out of the 67 remaining participants, 63 did not produce any intervals longer than 3 s, whereas two participants produced intervals of over 3 s on five trials, one participant on 10 trials, and one on 15 trials). In total, 63 participants remained for further analyses (mean age: 21.4, range: 17–54, SD: 5.8, 43 female).

## Apparatus

A MacBook Pro 13'' (2011) controlled all experimental events. Auditory stimuli were presented through headphones (Sennheiser, HD280 Pro), with volume adjusted to comfortable levels. The experiment was programmed using Psychtoolbox-3 (Brainard, 1997; Pelli, 1997; Kleiner et al., 2007) in Matlab R2014b.

## Procedure

The production task consisted of 20 trials. To prevent a rhythmic sequence, each trial commenced with an intertrial interval (ITI) with the presentation of a fixation cross ''+'' for a random duration between 2 s and 3 s sampled from a uniform distribution. Then a ''?'' appeared on the screen and simultaneously a 440 Hz pure tone started. Participants were asked to indicate when they thought 1 s since the onset of the tone had passed by pressing the spacebar (see **Figure 1**). As counting has been shown to increase the precision of duration judgments (Thönes and Hecht, 2017), participants were instructed to refrain from counting or keep track of time in any other way (e.g., tapping). This instruction has been shown to prevent influences of chronometric timing (Rattat and Droit-Volet, 2012).

The reproduction task consisted of two blocks of 120 trials each. Each trial consisted of the presentation of a duration, and the reproduction of that duration (see **Figure 2**). The durations presented were 1.17, 1.4 or 1.68 s long. Each trial commenced with an ITI of a random duration between 2 s and 3 s sampled from a uniform distribution during which a fixation cross (''+'') was presented in the center of the screen. Then a ''!'' appeared on the screen for 700 ms to prepare the

subjects for the presentation of the duration. Following this, the duration was presented by means of a 440 Hz pure tone that lasted for the duration associated with the current trial. Within each block of 120 trials, all three durations were presented 40 times, in random order. After completion of the tone, an inter stimulus interval (ISI) of 1.5 s was presented with a ''?'' displayed on screen. Then another 440 Hz pure tone was started. The task was to press the spacebar when the earlier presented duration had passed. To test for order effects, 31 participants performed the task in ''production—reproduction'' order, and 32 in reversed order (based on parity of their sequential participant number).

#### Statistical Analysis

For the reproduction task, we marked trials on which response times were lower than 500 ms or greater than 2.5 s as outliers, and removed them from analyses. Of the resulting dataset, 1.4% of all data points in the reproduction task were marked as outliers.

All analyses were performed in R, with the full script and data available at the OSF1 . The Bayesian analyses were performed with the R package BayesFactor (version 0.9.12-4.2; Morey et al., 2015) using the default prior settings, and are interpreted based on the guidelines provided by Jeffreys (1961), as adapted by Lee and Wagenmakers (2014). The reported Bayes factors summarize the extent to which an observer's opinion of the tested variable should change based on the data. A Bayes factor of 1 indicates that both hypotheses are equally likely under the data and therefore is inconclusive. Bayes factors larger than 1 represent evidence for the alternative hypothesis of an influence of the tested independent variable on the dependent variable, and Bayes factors less than 1 represent evidence for the null hypothesis of no effect of the tested variable. For the Bayesian linear mixed effect models, we built models predicting centered estimated duration by the entered effects including participant as random factor. We then assessed the variable of interest by comparing the

1https://osf.io/bhe97/?view\_only=9c3ea605d482416691b43588fecf92f5

Bayes factor of the model including this variable with the Bayes factor associated with a model omitting this variable. To facilitate interpretation, we invert Bayes factors below 1 and describe in the text whether the Bayes factor is evidence for inclusion or exclusion of the factor. This way, all reported Bayes factors express the evidence for presence or absence of an effect as values progressively greater than 1.

# RESULTS

#### Production Task: Accuracy

As no feedback was given during the production task, the average reproduced durations provide an index of the accuracy of the internal representation of 1-s veridical time. The first two trials were excluded, as discussed in the next section. **Figure 3** depicts the average produced durations per participant and the resulting distributions as violin plots. The bar graphs depict the mean produced durations for both order conditions (0.98 s, SE = 0.08, when the production task preceded the reproduction task, and 0.76 s, SE = 0.07, for the inverse order). A Bayesian linear effect model indicated that there was no conclusive evidence either in favor or against an effect of order (BF = 1.46 ± 0.01%). However, the accuracy of the internal representation of a 1-s interval is of secondary relevance in the context of this study, as the purpose of the 1-s production task was to assess clock variability instead of (veridical) accuracy.

#### Production Task: Precision

Assuming that the internal representation of a 1-s interval is firmly encoded in long-term memory, and thus not likely to be affected by a small number of production trials without feedback, the variance observed in the 1-s productions reflects the trial-by-trial clock variability. The mean trial-by-trial estimates are depicted in **Figure 4**, plotted separately for the two order conditions. As can be seen in this figure, the first trial is associated

FIGURE 3 | Violin plots depicting the distributions of the 1-s productions and the individual participant means, separately for the order conditions (Pr: Production, Repr: Reproduction). The inset depicts the average duration of the 1-s productions, including error bars representing standard errors of the mean with the within-participants Cousineau-Morey correction applied (Morey, 2008).

Reproduction). Error bars represent standard errors of the mean with the within-participants Cousineau-Morey correction applied.

with very long average responses, and both the first and second trial have noticeably bigger error bars than the following trials. In all subsequent analyses (and the analyses reported in the previous section), we have therefore considered these two initial trials to be ''start-up trials,'' and excluded them from further analysis.

The most straightforward measure of this variability is the variance or standard deviation. **Figure 5** shows, again for both order conditions, the standard deviation of the final 18 trials of the sequence of 20 trials. A Bayesian linear model provided anecdotal evidence against order having an influence on the deviation expressed in SD (BF = 2.23 ± 0%).

The standard deviation is an appropriate measure if the noise can be assumed to be centered around a fixed mean. However, if the repeated samples are drawn from a distribution of which the mean changes over time, the standard deviation calculated assuming a fixed mean will overestimate the true variance as the shift in mean will increase the standard deviation. In the context of this task, if the internal representation of a 1-s interval shifts, the standard deviation will overestimate the clock's noisiness. **Figure 6** depicts the 1-s production data of a single participant. As can be seen, this participant shows a slow drift from productions of around 2 s to productions of 1 s, but actually shows relatively little variance around this estimated trend. Assuming slow drifts in performance, calculating a standard deviance would overestimate this participant's clock

FIGURE 5 | Violin plots depicting observed standard deviation per participant, and the resulting continuous distributions, separately for the order conditions (Pr: Production, Repr: Reproduction). Inset depicts mean deviation with error bars representing standard errors of the mean with the within-participants Cousineau-Morey correction applied.

noise. Even though **Figure 4** might suggest an overall slope close to 0 (the mean of individual slopes is −0.0055), the range is relatively large (−0.08 to 0.04, reflecting a drift of −1,440 to 720 ms between trial 3 and 20). As there is decisive evidence for a drift (one sample Bayesian t-test on the absolute slopes as depicted in **Figure 6**, BF = 4.83 × 104 ± 0%), a reliable measure should account for drift when estimating clock

FIGURE 7 | Violin plots depicting observed deviation expressed in root mean squared residual (RMSR) from a linear fit estimated per participant, and the resulting continuous distribution, separately for the order conditions (Pr: Production, Repr: Reproduction). Inset depicts mean deviation with error bars representing standard errors of the mean with the within-participants Cousineau-Morey correction applied.

variance. We therefore also calculated the root mean squared residuals (RMSRs) based on a linear regression predicting produced duration as a function of trial number (coded as 1–18, after removing the first two trials) fitted separately for each participant.

**Figure 7** depicts the RMSR for the two order conditions, analogous to the way the SD was plotted in **Figure 5**. As with the SD measures, a Bayesian linear model provided anecdotal evidence against order having an influence on the deviation expressed in RMSR (BF = 2.26 ± 0%).

#### Clock Variability

To assess which of the proposed measures is a better estimate of the clock variance, we assessed whether a participant's standard deviation or RMSR was a better predictor of the central tendency observed in a reproduction task. The data of the multi-duration reproduction task is graphically depicted in **Figure 8**.

For the analyses of this data, we centered both presented and reproduced duration by subtracting 1.4 s from the presented and reproduced durations. For the presented durations, this ensures that the predictors have mean 0, making it easier to interpret the effects of additional predictors. Moreover, and this holds for both presented and reproduced durations, it allows for easier interpretation of resulting coefficients. As a baseline model, we fitted a Bayesian linear mixed effect model, with participant as random factor, predicting centered estimated duration by centered presented duration. Evidence in favor of the more complex model that included presented duration was decisive when compared to a model just including

FIGURE 8 | Reproduced durations as a function of presented duration, plotted staggered on the horizontal axis, separately for the order conditions (Pr: Production, Repr: Reproduction). Error bars are standard errors of the mean with the within-participants Cousineau-Morey correction applied. The dotted line represents veridical time.

an intercept (BF = 9.17 × 101244 ± 7.99%). Comparing this model to a model that also included experimental order provided decisive evidence against the more complex model (BF = 407.24 ± 14.59%). Based on the rationale that clock variability should influence the width of the likelihood, and as such the relative contribution of the prior, the best estimate of the veridical clock variability should best predict reproduced duration. Decisive evidence was obtained for the inclusion of each of the clock variance measures when compared to the simpler model that did not include any estimate of clock variance (BF = 4.48 × 1010 ± 9.74% for the SD-based measure, and BF = 2.47 × 1013 ± 9.75%, for the RMSR-based measure), demonstrating that clock variability as estimated by a 1-s production task does indeed predict the amount of central tendency in a multi-duration reproduction task. This is depicted in **Figure 9**, where participants with higher clock variance also demonstrate a stronger central tendency effect. More importantly, a Bayesian model including RMSR is a decisively better predictor of the estimated durations than a model including the SD-based measure (BF = 5514.79 ± 7.9), demonstrating the superiority of the new RMSR measure.

One of the central findings in interval timing is that temporal precision is relative to the duration of the interval being estimated, a phenomenon called the scalar property of variance. As **Figure 3** demonstrates, the average produced durations range from a couple of hundred milliseconds to approximately 2 s. Scaling the observed variances by the mean produced duration would result in a less biased estimate of the internal noisiness of the clock. To test this assumption,

we fitted another Bayesian model that included the RMSR variance divided by the mean produced duration. This scaled model is a decisively better predictor of the estimated durations than a model including the non-scaled RMSR measure (BF = 4.15 × 107 ± 13.39%).

To assess the influence of the scaled RMSR measure on the regression towards the mean, we have plotted the estimated slope of the regression line as shown in, for example, **Figure 8**, against the scaled RMSR (see **Figure 10**). A slope of 1 would indicate a participant, whose reproductions are not at all influenced by context, whereas a slope of 0 would indicate a participant who always reproduces the exact same duration, irrespective of the duration of the presented interval. Or, in Bayesian inference terms, a slope of 1 indicates complete reliance on the likelihood, whereas a slope of 0 indicates complete reliance on the prior. As expected, increased clock variance is associated with smaller slopes, and vice versa: results of the Bayesian correlation indicate extreme evidence (BF = 325.58 ± 0%) in favor of a large or moderate negative association between the scaled RSMR measure and the slope, expressing the regression towards the mean [r = −0.45, MAD = 0.11, 90% CI (−0.63, −0.25)].

#### DISCUSSION

The goal of this article was to assess whether clock variability could be reliably measured in a span of a couple of minutes so that it can be applied in both prototypical experimental populations (i.e., young adults) and clinical or developmental studies in which complex or lengthy experiments are often problematic. We determined clock variability in a simple production task, and demonstrate that this variability predicts the central tendency observed in a multi-duration reproduction task. Following the rationale of Bayesian inference, this indicates that the measured variance in the production task is related to the width of the likelihood distribution in the multi-duration reproduction task, which has been associated with the noise in the clock parts of the temporal system (e.g., Shi et al., 2013). Thus, we can assume that the assessed variance in the production task, which takes less than 3 min to administer, is a reliable index of clock variance. Here, we will first discuss a number of methodological issues related to this paradigm and experiment, and then discuss a number of more theoretical considerations.

We asked the participants to produce 1-s durations by ending a tone 1 s after onset by a keypress. We explicitly opted for this duration as we assumed that typical participants will have a reasonably stable and well encoded representation of a second duration, due to the prevalence of this duration in everyday life. Because of this well ingrained duration, participants will hopefully be able to produce this duration without too much effort, and at the same time, it is unlikely that 20 repeated productions of this duration, without any external feedback, would cause noticeable changes in the internal representation.

Before conducting this experiment, we did not not have specific information on whether it would be necessary to exclude a number of initial trials as ''start-up trials,'' but as the first two trials were clearly associated with longer and more variable (between participants) produced durations, we categorized these first two 1-s productions as start-up trials. However, the population tested in this experiment are young adults who were well trained in participating in psychophysiological experiments, making it likely that more start-up trials might be needed when this paradigm is administered in other populations. Also, we considered the possibility that order effects might influence performance in either the production, or reproduction task. For example, after performing two blocks of the reproduction task, which contained durations between 1 s and 2 s, the 1-s estimates could be affected. However, **Figure 3** does not show any hints of the reproduction task influencing the 1-s production task (the numerical effects are in opposite direction as what we be expected), and the Bayesian analyses did not provide any reliable evidence for a difference between the two order conditions. This indicates that the 1-s estimations are immune to perturbations from the multi-duration reproduction task used in this study.

To quantify the clock variability, we assessed the predictive power of different measures of variance. As the produced durations show clear drifts during the 20 trials even though no feedback was provided, standard measures of variance that assume a fixed mean would overestimate clock variability. We therefore fitted a linear model to the produced duration of each individual, and calculated a deviation measure by taking the RMSRs of this linear model. Obviously, it is not unlikely that the drift in produced durations follows a more complex pattern than is captured by a simple linear regression (see, for example, the discussions on short range dependencies in Wagenmakers et al., 2004). However, fitting more complicated patterns would quickly result in overfitting given the limited number of trials acquired in this task. We therefore refrained from estimating more complex patterns. When the different variability measures were contrasted, the linear-model-based RMSR measure provided the best prediction of the central tendency observed in a multi-duration production task. As variance is known to be linearly related to the length of the durations produced (scalar property see e.g., Gibbon et al., 1984), we also tested the predictive power of a model in which we divided the RMSR by the produced durations. This scaled RMSR measure outperformed the non-scaled RMSR variance measure, indicating that the measured variance adhered to the scalar property. Bayesian models of time estimations (e.g., Jazayeri and Shadlen, 2010) have demonstrated that the perception of longer durations are reflected in wider likelihoods than those associated with shorter intervals. Here, we demonstrate that a similar effect can be observed between participants: the higher the variance of participants' performance during the 20 repeated 1-s productions, the more their reproduced durations will be affected by the prior.

One potential caveat of this method is that the observed variance in the 1-s production task may be driven by motor noise, which would also result in a stronger reliance on the prior in the reproduction task. This potential convolution of motor and clock noise is a challenge in studies assessing clock variability (see, for example, Cicchini et al., 2012; Turgeon et al., 2016, for discussion). If motor noise would be the driving factor, noise should be independent of produced durations, as all durations have the same motor action (i.e., the keypress indicating the end of the interval). Conversely, if the observed variability is driven by a noisy clock, the amount of variability should be directly related to the length of the produced duration. As the variance measure that accounts for produced length, the scaled RMSR, resulted in the best fit, we do not find support for the notion that motor noise is driving the observed phenomena. Yet, a future study could independently measure a participant's motor noise to separately assess its contribution to the central tendency effect.

In this manuscript, we assess whether we can measure clock variance in a short, 20-trial production task. This observed statistic predicts central tendency in a multi-duration task, a phenomenon known to be dependent on clock variability. Another way to assess the reliability of the measured clock variability is to compare the scaled RMSR measure with the Weber fraction, a measure typically used when clock variability is estimated. However, as Weber fractions are derived from paradigms that rely on memory representations learned during the experimental session, the Weber fraction is indicative of the noisiness of the whole temporal system (but note that experimental or pharmacological manipulations might allow separating both influences, e.g., Meck, 1983). Therefore, it would be useful to determine Weber fractions based on paradigms that vary in their reliance on memory processes to determine the consistency of estimated clock variance statistics. At the same time, additional research is needed to relate the here presented 1-s production method to other established measured of clock variability.

To conclude, we have shown that just 20 trials of a 1-s production task result in a reliable measure of clock variance. The observed variability adheres to the scalar property and predicts temporal performance observed in a reproduction task. As no feedback is required, and memory processes are unlikely to play an important role in this paradigm, this clock variance measure can be used to disentangle the extent to which temporal behavior in a task is driven by memory processes or clock deviations. With its fast and easy application, this task is suitable to be implemented in clinical and various developmental populations, even in attention-span limited participants. Hopefully, this task can be a useful addition to the toolkit of researchers interested in unraveling the locus of deviations found in temporal performance.

#### DATA AVAILABILITY

The datasets analyzed for this study can be found in the Open Science Framework (https://osf.io/bhe97/?view\_only=9c3ea6 05d482416691b43588fecf92f5).

#### REFERENCES

# AUTHOR CONTRIBUTIONS

SM and HR conceived the experiment, analyzed the data, and wrote the manuscript. SM collected all data.

#### FUNDING

This work is part of the NWO VICI research program ''Interval Timing in the Real World: a functional, computational and neuroscience approach'' with project number 453-16-005, awarded to HR, financed by the Netherlands Organization for Scientific Research (Nederlandse Organisatie voor Wetenschappelijk Onderzoek). HR's work was partially funded by EU Horizon 2020 FET Proactive grant ''TimeStorm'' #641100.

## ACKNOWLEDGMENTS

We would like to thank Thomas Wolbers and Martin Riemer for fruitful discussions regarding the setup of this study.

**Conflict of Interest Statement**: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Maaß and van Rijn. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Neural Correlates of Interval Timing Deficits in Schizophrenia

Ariel W. Snowden and Catalin V. Buhusi\*

Interdisciplinary Program in Neuroscience, Department of Psychology, Utah State University, Logan, UT, United States

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-striatalthalamo-cortical circuits, which are highly implicated in executive functioning and motor preparation.

Keywords: schizophrenia, interval timing, attention, cognitive dysfunction, working memory, neural correlates

#### Edited by:

Fuat Balcı, Koç University, Turkey

#### Reviewed by:

Anne Giersch, Institut National de la Santé et de la Recherche Médicale (INSERM), France Martin Wiener, George Mason University, United States

#### \*Correspondence:

Catalin V. Buhusi<EMAIL_ADDRESS>
Received: 30 September 2018 Accepted: 09 January 2019 Published: 29 January 2019

#### Citation:

Snowden AW and Buhusi CV (2019) Neural Correlates of Interval Timing Deficits in Schizophrenia. Front. Hum. Neurosci. 13:9. doi: 10.3389/fnhum.2019.00009

## INTRODUCTION

Schizophrenia (SZ) is a complex, heterogeneous psychiatric disorder characterized by a broad range of symptoms including delusions, hallucinations, impaired cognitive functioning, disorganized speech and behavior (Patel et al., 2014). SZ patients show deficits in interval timing, perceiving durations in the seconds-to-minutes range (Densen, 1977; Lee et al., 2009). **Table 1** shows the inconsistent pattern of time perception (TP) in SZ, possibly due to population heterogeneity and variability in illness duration (often not reported), symptom severity, and differential effects of typical vs. atypical antipsychotics. As temporal production tasks (Buhusi and Meck, 2010) often report less precision (greater variability) in time estimation (Carroll et al., 2009a,b; Roy et al., 2012; see also recent meta-analyses Ciullo et al., 2016; Thoenes and Oberfeld, 2017) and temporal estimation tasks often report overestimating durations (Densen, 1977; Wahl and Sieg, 1980; Tysk, 1983) differences in task demands may also account for inconsistent findings in SZ.

**Figure 1A** shows a schematic of a cognitive model of TP, the Information-Processing model (Gibbon et al., 1984). Regular pulses emitted by an internal clock are collected by an accumulator, stored in working memory (WM), and encoded for later use in the reference memory. At test, the current duration stored in WM and the duration encoded in reference memory are compared, and a response is made at the appropriate time. In this model, duration overestimation in SZ is explained by a faster clock resulting in greater accumulation of pulses at the time of the response, whereas variability in time estimation in SZ may be due to variability at clock, memory, and decision making levels (Gibbon et al., 1984).

An alternative, neurobiological model of TP, the Striatal Beat Frequency (SBF) model (Matell and Meck, 2004; Buhusi and Meck, 2005; Buhusi and Oprisan, 2013), is shown in **Figure 1E**.

 classification

 motor area; BG, basal ganglia.

 of diseases; yr, year; ↓,

decrease/slower/under;

 ↑,

increase/faster/over;

ns, non-significant

 differences;

 N/A, not available/not

 provided; PFC, prefrontal cortex; DLPFC, dorsal-lateral

 prefrontal cortex; SMA, supplementary

healthy controls; m, mean; SD, standard deviation; M, male; F, female; DSM, Diagnostic and statistical manual of mental disorders; ICD, International

glutamate; orange arrows, abnormal brain activation.

The model proposes that the cortico-striatal-thalamo-cortical system mediates cognitive processes involved in TP such as attention and WM (Buhusi and Meck, 2005). Cortical oscillations produce oscillatory beat patterns detected and encoded by striatal medium spiny neurons. The onset of a temporal duration initiates a phasic release of dopamine (DA), whereby DA neurons in the ventral tegmental area (VTA)/substantia nigra (SN) synchronize both cortical oscillations and the membrane levels of striatal medium spiny neurons (Matell and Meck, 2004; Buhusi et al., 2016). Indeed, DA is thought to be a neurotransmitter system crucial for both TP and attention to time (Buhusi and Meck, 2002; Buhusi, 2003). The SBF model is supported by data implicating dorsal-lateral prefrontal cortex (DLPFC), the supplementary motor area (SMA), the posterior parietal cortex, basal ganglia (BG), and the thalamus (Buhusi and Meck, 2005; Ivry and Schlerf, 2008) in TP. In this model, duration overestimation in SZ is explained by an increase in DA activation (equivalent to a faster clock, see Oprisan and Buhusi, 2011), whereas variability in time estimation in SZ may be due to abnormalities in neurotransmission/activation along the corticostriato-thalamo-cortical loop, as discussed in this review article.

As SZ patients exhibit both impairments in cognitive functioning and TP, it is unclear whether cognitive deficits in attention and WM are responsible for timing deficits in SZ, or disruption of TP is responsible for greater cognitive dysfunction. The current review will address this issue by examining the neural network involved in TP and highlighting abnormalities in these regions in SZ patients and proposes that both TP and cognitive deficits in SZ patients are a result of a malfunction of neurotransmission in the cortico-striatal-thalamo-cortical network.

# DORSAL-LATERAL PREFRONTAL CORTEX (DLPFC) AND WORKING MEMORY FOR TIME

The DLPFC is responsible for attending to presented stimuli and maintaining a representation of a given duration in WM in timing tasks (Curtis and D'Esposito, 2003; Coull et al., 2004). Neuroimaging and repetitive transcranial magnetic stimulation (rTMS) studies support a role for the DLPFC in TP. Healthy participants underestimate the to-be-timed duration when rTMS is delivered to the right DLPFC (Koch et al., 2003; Jones et al., 2004), while rTMS delivered to the DLPFC has been shown to improve timing accuracy in Parkinson's disease (PD) patients (Koch et al., 2004). The effects of rTMS on timing in PD patients may be due to decreases in DLPFC activation due to lower DA levels in comparison to healthy participants. Functional magnetic resonance imaging (fMRI) studies indicate greater activation in the DLPFC in healthy participants during timing tasks (Rao et al., 2001; Hinton and Meck, 2004; Üstün et al., 2017). Additionally, the PFC is implicated in TP in animals, both in lesion studies (Buhusi et al., 2018), pharmacological studies (Matthews et al., 2012), and in animal models of SZ (Buhusi et al., 2013).

Very few studies have investigated the neural correlates of TP in SZ patients. Volz et al. (2001) reported DLPFC hypoactivation in SZ patients relative to controls during temporal discrimination (**Table 1**). **Figure 1B** shows a contrast in activation between the control and SZ groups after subtraction of resting activation (bright yellow = greater contrast, dark red = smaller contrast). **Figure 1B** shows that SZ patients exhibited less DLPFC activation than controls, primarily due to DA imbalances in the BG, and secondarily due to abnormalities in the cortico-striatal-thalamo-cortical circuitry which may be responsible for attention and WM deficits (Volz et al., 2001). These findings are consistent with previous research reporting DLPFC hypoactivation in SZ patients in tasks involving sustained attention, such as the Continuous Performance Test (CPT), and tasks requiring WM, such as the Wisconsin Card Sorting Task (WCST, Weinberger et al., 1986; Barch et al., 2001). Decreased DLPFC activation during these tasks typically correlate with worse performance in patients.

One explanation for hypofrontality in SZ is a dysfunction in gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter. Studies in primates indicate an increase in the firing rate of GABAergic DLPFC neurons during a delay in WM tasks (Lewis et al., 2005). Similarly, in the CPT task, decreases in DLPFC activation were observed in SZ patients during a delay presented between a cue stimulus and target stimulus (Barch et al., 2001). These findings indicate that recruitment of the DLPFC, mediated by GABA neurons, is necessary for WM and is disrupted in SZ. Lower GABA levels in the DLPFC in patients may explain hypoactivation in SZ: GABA increases synchronization of pyramidal cell neurons, facilitating task performance and resulting in increased DLPFC activation during WM tasks in healthy participants (Lewis et al., 2005).

# SUPPLEMENTARY MOTOR AREA (SMA) AND TEMPORAL ATTENTION

The SMA is involved in the generation of voluntary movements and storage of learned motor actions (Eccles, 1982). Although the SMA is primarily responsible for generating movement, many timing tasks have shown SMA activation when no motor output is required (e.g., Schubotz et al., 2000). Current research suggests that the role of the SMA in TP is to select populations of neurons to mediate temporal attention. Single-cell recording studies in primates have indicated neuronal coding of interval timing in the pre-SMA (Mita et al., 2009) and many studies have reported increased SMA activation during interval timing (Coull et al., 2004; Macar et al., 2004). In the Information-Processing model (**Figure 1A**), the SMA may act as an accumulator, recording the number of pulses in a given period (Coull et al., 2004). The SMA is also active during tasks involving the processing of rhythms and beat perception (Grahn and Brett, 2007), supporting the SBF model, which proposes that SMA, together with other cortical areas, generates oscillatory input which is detected and encoded in BG medium spiny neurons (**Figure 1E**).

SZ patients exhibit abnormal SMA activation during timing tasks. Ortuño et al. (2005) used positron emission tomography (PET) to examine cerebral blood flow in healthy controls (HCs) and SZ patients during a temporal reproduction task (**Table 1**). Although Ortuño et al. (2005) reported no statistically significant differences in temporal reproduction relative to controls, less SMA activation was reported for SZ patients relative to controls during the timing condition. **Figure 1C** shows SMA activation (yellow) in the control group (left panel) and SZ group (right panel; Ortuño et al., 2005), indicating that SZ patients exhibit less SMA activation relative to controls, and suggesting dysfunction of the right SMA and prefrontal areas in SZ patients, which may reflect a failure in early time processing related to attentional deficits.

A decrease in SMA activation has been previously reported in SZ patients in both fMRI (Schröder et al., 1995) and electroencephalography (EEG) studies (Dreher et al., 1999). For example, SZ patients exhibit an attenuated readiness potential (Dreher et al., 1999). The readiness potential is observed during the planning of motor actions, and source-localization techniques suggest that it is generated in the SMA (Praamstra et al., 1996). SMA recruitment is necessary for facilitating temporal attention, and SZ patients do not actively recruit the SMA during timing tasks, indicated by SMA hypoactivation. As the SMA is responsible for sending information to the BG for motor preparation (DeLong and Wichmann, 2007), it is possible that the SMA encodes a distorted duration before sending it to the BG to be stored in reference memory.

# BASAL GANGLIA (BG) AND REFERENCE MEMORY FOR TIME

The role of the BG in TP is well-established (Buhusi and Meck, 2005; Buhusi and Cordes, 2011). PD patients show both interval timing and motor timing deficits (e.g., reproducing rhythms by finger-tapping), indicating that BG is necessary for TP (Harrington et al., 1998). Similarly, Huntington's disease patients, in which BG degeneration occurs, perform worse than HCs on timing tasks (Cope et al., 2014). Increased BG activation during interval timing tasks has also been observed in fMRI scans of healthy participants (Ferrandez et al., 2003; Nenadic et al., 2003). Further, Rao et al. (2001) used event-related fMRI in a temporal discrimination task designed to activate regions in the fronto-striatal network during the encoding of a standard duration and a comparison of a new duration to the standard duration. An early BOLD signal (2.5–5 s after trial onset) associated with encoding a representation of the standard duration was observed in the BG, whereas a late BOLD signal (7.5–10 s after trial onset) associated with the retrieval and comparison of the two durations was observed in the right DLPFC (Rao et al., 2001).

As DA mediates BG functioning (Rammsayer and Classen, 1997), studies have examined the effects of altering DA levels on TP. In the framework of the Information-Processing model (**Figure 1A**, Gibbon et al., 1984), pacemaker pulses have been described as the firing of DA neurons (Gibbon et al., 1997). Indeed, administration of DA agonists results in a faster clock speed, whereas administration of DA antagonists results in a slower clock speed (Meck, 1996; Buhusi and Meck, 2002).

In the SBF model of TP, DA is assumed to mediate the encoding of temporal durations in the BG, suggesting that a dysfunction in the neuromodulation of DA may be responsible for both timing and other cognitive (e.g., attention, WM) deficits in SZ patients. Indeed, Buhusi (2003) showed that DA has a role both in timing and attention to time. Meyer-Lindenberg et al. (2002) found that PFC hypoactivation in SZ is associated with increased DA levels in the striatum. Relative cerebral blood flow was measured in the DLPFC during the WCST using PET and tracer-6 FDOPA to measure presynaptic DA activity in the striatum (Meyer-Lindenberg et al., 2002). Patients exhibited activity in the DLPFC that was negatively correlated with presynaptic DA activity; the less activation observed in the DLPFC, the greater the striatal DA uptake. This finding is compatible with the finding that increases in striatal DA are associated with a faster internal clock speed, which is often exhibited in SZ patients. This research suggests that timing deficits in SZ may be due to an interaction of increased DA activity in the BG and dysfunction of the DLPFC.

In addition to the DLPFC hypoactivation discussed above, Volz et al. (2001) reported hypoactivation of the caudate nucleus in SZ patients when compared to HCs, and concluded that the cortico-striatal-thalamo-cortical network is disrupted in SZ. If DA hyperactivity of the BG is associated with hypoactivation of the DLPFC in SZ, as observed in Meyer-Lindenberg et al.'s (2002) study, one should expect increases in activation in the BG to be correlated with decreases in DLPFC activation, which is contradictory to Volz et al.'s (2001) findings of hypoactivation in the caudate nucleus. Additional studies report hypoactivation of the caudate nucleus in SZ during WM tasks (e.g., Koch et al., 2008; Yoon et al., 2013). During the response phase of a WM task (**Table 1**), Yoon et al. (2013) found hypoactivation of the caudate nucleus and reduced functional connectivity between the PFC and the striatum in SZ. **Figure 1D** shows an fMRI contrast of activation between the control and SZ groups, showing brain regions where activation was greater in controls compared to SZ group (light blue = greater contrast). A large contrast is shown in the caudate nucleus, where patients exhibited hypofunction relative to controls. Functional connectivity between the PFC and striatum was also reduced.

The BG receive input primarily from the PFC and send output to the frontal regions via the thalamus (Alexander et al., 1986; Alexander and Crutcher, 1990; **Figure 1E**). It is therefore unclear whether abnormalities in the corticostriatal-thalamo-cortical circuits are primarily due to DLPFC dysfunction, or rather dysfunction of the BG. Many studies report that symptoms caused by PFC dysfunction in SZ (e.g., cognitive deficits) occur before positive symptoms (e.g., hallucinations and delusions; Lesh et al., 2011), resulting from hyperactivity in the mesolimbic DA pathway. DA activity is typically increased in the striatum in SZ and decreased in the frontal regions, which suggests less DA is released to the DLPFC during tasks involving WM and attention, reflecting an inability to actively recruit these regions during task performance.

# IMPLICATIONS FOR SCHIZOPHRENIA

Frith (1987) proposed that positive symptoms in SZ are a result of abnormalities in the intentions of actions. Patients are unaware of the sources of their actions which results in misattributions of the causes of consequences (e.g., delusions and false beliefs), and a disturbed sense of agency and self (Martin et al., 2017). Patients show a stronger binding of actions and consequences (Haggard et al., 2003), and a stronger binding of separate events in the absence of actions (Franck et al., 2005), judging events as synchronous over larger temporal disparities (Noel et al., 2018). These results suggest that temporal integration of events may lead to misrepresentations of events that are lost (e.g., inability to identify the beginning or end of an action sequence), therefore leading to misattributions. However, there are limitations to these findings, as explicit timing tasks were not employed in all studies.

Voss et al. (2017) identified the angular gyrus and DLPFC as being implicated in matching outcomes to actions and observed decreased connectivity between these regions in SZ. As hypoactivation of the inferior parietal gyri has been observed in SZ patients in TP (Alustiza et al., 2016), future studies should employ binding paradigms (e.g., Haggard et al., 2003) to examine neural activation during TP in SZ. Interestingly, Lošák et al. (2016) found decreased activation of the cerebellar vermis in SZ patients correlated with a faster clock during a time prediction task, suggesting that this region is critical for time prediction during salient events. As many studies report a correlation between a faster clock and positive symptoms in SZ patients, the nature of the relationship between TP and positive symptoms in SZ should be further investigated.

Here, we propose that both timing deficits and cognitive deficits in SZ are a result of neurotransmitter dysfunction in the cortico-striatal-thalamo-cortical loop. As information is transmitted in a loop, dysfunction in one region may cause impairments in another along the loop, rather than disruption occurring in a unidirectional manner. For example, correlations between TP performance and cognitive functioning measures have been observed in SZ (Lee et al., 2009; Roy et al., 2012). Roy et al. (2012) reported greater variability that was negatively correlated with WM performance during a reproduction task; patients with better WM exhibited less variability in the time reproduction task. Neuroimaging may be used to further examine dysfunction in the cortico-striatal-thalamo-cortical circuit and correlations between cognitive functioning and timing. As timing deficits have also been observed in individuals at high risk for SZ (Penney et al., 2005), neuroimaging studies may be used to assess dysfunction in this circuit correlated with TP in first-degree relatives of SZ patients, to assess timing deficits as a potential biomarker for SZ.

#### CONCLUSIONS

Current research examining the neural correlates of TP in SZ patients is limited. Previous research suggests a disrupted cortico-striatal-thalamo-cortical network which may be responsible for timing deficits observed in SZ. The DLPFC, SMA, and BG play distinct roles in TP, and abnormal activation in these regions is reported in timing tasks as well as additional tasks involving attention and WM in SZ. Timing deficits in SZ may be primarily due to increased DA levels in the BG and less DA and GABA in the DLPFC, which are necessary to mediate WM and attention during TP. Rather than timing deficits in SZ occurring as a result of cognitive dysfunction or vice versa, a malfunction in the neurotransmission of DA and GABA in the cortico-striatal-thalamo-cortical network may be responsible for disruption in the internal clock and cognitive functioning in SZ. As there are very few studies which examine neural activation during TP tasks in SZ, further research is needed to corroborate current findings. Future research should consider potential differences in TP performance due to duration of the illness and the extent to which abnormalities in neural

#### REFERENCES

activation during timing tasks are correlated with positive symptom severity, as disruptions in the internal clock rate may be linked to positive symptoms exhibited in SZ. Lastly, future research including neuroleptic-naive patients is necessary to rule out the potential confounds of antipsychotic medication effects on TP (**Table 1**).

#### AUTHOR CONTRIBUTIONS

Authors contributed equally to all aspects of developing and writing this manuscript.

#### FUNDING

This work was supported by a National Institutes of Health (NIH) grant MH073057 and an Independent Investigator Award from the Brain & Behavior Research Foundation (formerly National Alliance for Research on Schizophrenia and Depression, NARSAD) to CB.

#### ACKNOWLEDGMENTS

We would like to thank Dr. Christopher M. Warren and Mr. Michael Williams for helpful discussions.

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Yoon, J. H., Minzenberg, M. J., Raouf, S., D'Esposito, M., and Carter, C. S. (2013). Impaired prefrontal-basal ganglia functional connectivity and substantia nigra hyperactivity in schizophrenia. Biol. Psychiatry 74, 122–129. doi: 10.1016/j.biopsych.2012.11.018

**Conflict of Interest Statement**: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Snowden and Buhusi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# A Simplified Model of Communication Between Time Cells: Accounting for the Linearly Increasing Timing Imprecision

#### Mustafa Zeki 1 \* and Fuat Balcı 2

1 Department of Mathematics, College of Engineering and Technology, American University of the Middle East, Egaila, Kuwait, 2 Department of Psychology, Koç University, Istanbul, Turkey

Many organisms can time intervals flexibly on average with high accuracy but substantial variability between the trials. One of the core psychophysical features of interval timing functions relates to the signatures of this timing variability; for a given individual, the standard deviation of timed responses/time estimates is nearly proportional to their central tendency (scalar property). Many studies have aimed at elucidating the neural basis of interval timing based on the neurocomputational principles in a fashion that would explain the scalar property. Recent experimental evidence shows that there is indeed a specialized neural system for timekeeping. This system, referred to as the "time cells," is composed of a group of neurons that fire sequentially as a function of elapsed time. Importantly, the time interval between consecutively firing time cell ensembles has been shown to increase with more elapsed time. However, when the subjective time is calculated by adding the distributions of time intervals between these sequentially firing time cell ensembles, the standard deviation would be compressed by the square root function. In light of this information the question becomes, "How should the signaling between the sequentially firing time cell ensembles be for the resulting variability to increase linearly with time as required by the scalar property?" We developed a simplified model of time cells that offers a mechanism for the synaptic communication of the sequentially firing neurons to address this ubiquitous property of interval timing. The model is composed of a single layer of time cells formulated in the form of integrate-and-fire neurons with feed-forward excitatory connections. The resulting behavior is simple neural wave activity. When this model is simulated with noisy conductances, the standard deviation of the time cell spike times increases proportionally to the mean of the spike-times. We demonstrate that this statistical property of the model outcomes is robustly observed even when the values of the key model parameters are varied.

Keywords: interval timing, scalar variability, time cells, chain models, hippocampus, Weber's law

#### Edited by:

Matjaž Perc, University of Maribor, Slovenia

#### Reviewed by:

Jun Ma, Lanzhou University of Technology, China Daqing Guo, University of Electronic Science and Technology of China, China

> \*Correspondence: Mustafa Zeki<EMAIL_ADDRESS>
Received: 22 October 2018 Accepted: 31 December 2018 Published: 29 January 2019

#### Citation:

Zeki M and Balcı F (2019) A Simplified Model of Communication Between Time Cells: Accounting for the Linearly Increasing Timing Imprecision. Front. Comput. Neurosci. 12:111. doi: 10.3389/fncom.2018.00111

# 1. INTRODUCTION

Time is a fundamental quantity that cannot be derived from other dimensions. Thus, keeping track of time requires its measurement by a neural "clock" mechanism. To that end, evolution has favored at least two timing mechanisms that operate at different time-scales. One of these timekeeping mechanisms, namely the circadian clock, captures periods with 24-h long cycles based on well-regulated molecular machinery (e.g., Partch et al., 2014). Many events in nature, on the other hand, are rarely periodic and/or too short to be captured based on the time-scales of the molecular events implicated for the circadian clock. Thus, capturing the temporal features of such events requires a rather flexible timekeeping apparatus that can be started and stopped arbitrarily, namely a neural mechanism with stopwatch-like properties (Buhusi and Meck, 2005). Accordingly, a mechanism of the latter type indeed enables many animals ranging from fish (Drew et al., 2005), to mice (Balci et al., 2009), to humans (Rakitin et al., 1998; Çavdaroglu ˘ et al., 2014) to flexibly keep track of time intervals in the range of seconds to minutes. This very ability is referred to as "interval timing."

There are a number of core features of this ubiquitous cognitive timekeeping function. For instance, for a given target time interval, the timed anticipatory responses of animals are approximately Gaussian distributed, which is typically centered at around the target interval, pointing at on-average high timing accuracy. However, the flexibility of this mechanism exerts a non-negligible cost in the form of imprecision: predictions/productions of a given target interval exhibit substantial variability between trials, which is reflected in the spread of the response time distributions. Thus, when it comes to precision, the operation of the internal stopwatch is far from perfect (i.e., outputs are not Dirac delta distributed). Importantly, within an individual, the resultant timing imprecision has a welldefined relationship to the target intervals; the standard deviation of the timed responses is proportional to their mean, namely the coefficient of variation of timed responses is virtually constant. This statistical property leads to the timescale invariance of interval timing and accounts for Weber's Law in the timing domain (Gibbon, 1977).

A line of empirical and theoretical research in the timing field has focused on the neurocomputational principles that would explain interval timing with its psychophysical features outlined above (for review see Karmarkar and Buonomano, 2007; Simen et al., 2011; Merchant et al., 2013; Hass and Durstewitz, 2014; Balcı and Simen, 2016). A recent line of neuroscientific evidence has introduced novel empirical ground for these approaches by demonstrating the existence of a specialized neural mechanism for timekeeping, namely the time cell ensembles that fire sequentially during different episodes of a temporally structured task (Kraus et al., 2013; Salz et al., 2016; Tiganj et al., 2016). Importantly, as a feature of information processing in the time cell architecture, the time interval from the activation of one ensemble to the next ensemble (inter-spike interval, ISI) has been shown to lengthen with progressing neuronal activity (MacDonald et al., 2011). In a very simple network of a neural chain architecture with feedforward excitatory connections, we aimed to address how the communication between the consecutive cell ensembles can be set to achieve scalar variability of interval timing behavior.

Even in very simplified cell and network settings, one needs to address several neurocomputational challenges to explain the statistical features of experimentally observed activity/behavior as a function of time. One of these features is the scalar property of interval timing. The challenge faced here is that when the distributions are added together, the standard deviation of the resulting distribution is compressed by the square root function. For example, when N identical normal distributions with mean = 1, 000 and the standard deviation = 100 are summed, the mean of the resulting distribution would be 1, 000N and its standard deviation would be 100N. Thus, the standard deviation would not increase linearly with the mean, contrary to what would be required by the scalar property. The important question that arises at this point is whether it is possible to compensate for the compression in variability (i.e., CV) due to the square root function via some inherent property of neural networks and thereby explain the scalar property as an emergent property of the network.

The second challenge faced in accounting for the experimentally observed activity with realistic neurons is the limiting timescale of the neuronal currents. Whether intrinsic or synaptic, many known neuronal currents operate in a timescale ranging from milliseconds to a few seconds. But the increase of ISIs in time cells (TC) is observed for as long as tens of seconds (Ermentrout and Terman, 2010). This motivated us to ask how neuronal currents with very short lifetimes can be used to generate effects that last much longer than their individual timescales.

In order to address such neurocomputational issues in signal transmission between the time cells, we constructed a simple time cell model in such a way that the delay from the firing of the ith time cell ensemble to the firing of the i + 1th ensemble increases with the inhibition. This is due to the hyperpolarizing intrinsic current that is activated with inhibition and inactivated with excitation. In other words, in this model, the time cells undergo a temporal integration that depends on the level of inhibitory current. In the chain architecture, when the time cells are connected with feedforward excitatory current, the way the time cells are modeled leads to experimentally observed increasing ISIs with propagating activity in the chain. We simulated the outlined network with noisy conductances multiple times to generate the distribution of spike times of various time cells. We observed that the standard deviation of the time cell spike times indeed increased linearly with the mean spike times and the mean-normalized distributions of different time cell activity superposed as often observed in the empirical data (i.e., timescale invariance). We finally showed that the observed results are the robust features of the model outputs that are preserved even after changing the values of the key parameters of the model.

# 2. METHODS: THE MODEL

In the current model, we use a network with feedforward connections among excitatory time cells to simulate the transmission of activity between time cells (see **Figure 1**). Importantly, the model focuses on the time it takes to transmit the excitatory signal from one time cell to the next time cell in the chain, namely, the inter-spike intervals (ISIs). Our assumptions regarding the role of inhibition in the model are explained below. The time cells are modeled using the spikeless integrate-andfire type neuron model (see Ermentrout and Terman, 2010) with currents that are modeled using the Hodgkin-Huxley type formalism as follows:

$$C\_m \frac{d\nu}{dt} = -\left(I\_L + I\_D + I\_{\text{Exc}} + I\_{Inh}\right) + I\_{input} + I\_{noise}$$