Space, time, and numbers in the right posterior parietal cortex ...

NeuroImage 129 (2016) 72–79

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Space, time, and numbers in the right posterior parietal cortex: Differences between response code associations and congruency effects Martin Riemer a,⁎, Nadine Diersch a, Florian Bublatzky b, Thomas Wolbers a,c a b c

Aging & Cognition Research Group, German Center for Neurodegenerative Diseases (DZNE), Magdeburg, Germany Department of Psychology, School of Social Sciences, University of Mannheim, Mannheim, Germany Center for Behavioral Brain Sciences (CBBS), Magdeburg, Germany

a r t i c l e

i n f o

Article history: Received 3 September 2015 Accepted 12 January 2016 Available online 22 January 2016 Keywords: Posterior parietal cortex Transcranial magnetic stimulation Mental time line Mental number line Simon effect SNARC

a b s t r a c t The mental representations of space, time, and number magnitude are inherently linked. The right posterior parietal cortex (PPC) has been suggested to contain a general magnitude system that underlies the overlap between various perceptual dimensions. However, comparative studies including spatial, temporal, and numerical dimensions are missing. In a unified paradigm, we compared the impact of right PPC inhibition on associations with spatial response codes (i.e., Simon, SNARC, and STARC effects) and on congruency effects between space, time, and numbers. Prolonged cortical inhibition was induced by continuous theta-burst stimulation (cTBS), a protocol for transcranial magnetic stimulation (TMS), at the right intraparietal sulcus (IPS). Our results show that congruency effects, but not response code associations, are affected by right PPC inhibition, indicating different neuronal mechanisms underlying these effects. Furthermore, the results demonstrate that interactions between space and time perception are reflected in congruency effects, but not in an association between time and spatial response codes. Taken together, these results implicate that the congruency between purely perceptual dimensions is processed in PPC areas along the IPS, while the congruency between percepts and behavioral responses is independent of this region. © 2016 Elsevier Inc. All rights reserved.

Introduction Temporal and numerical information is strongly related to our concept of space. From a theoretical perspective, these interrelations have been pointed out by Bergson (1888), who argued ‘that the very idea of the number [...] involves the idea of a juxtaposition in space’ (p. 89) and ‘that we are compelled to borrow from space the images by which we describe what the reflective consciousness feels about time’ (p. 91). Many psychophysical studies confirmed the interactions between the perception of time, space, and numbers (Bonato et al., 2012; Bueti and Walsh, 2009; Burr et al., 2010; Dehaene and Brannon, 2011; Fabbri et al., 2012; Walsh, 2003). Thinking about large vs. small numbers increases attention to the right vs. the left side of space (Cattaneo et al., 2009; Fischer et al., 2003; Loetscher et al., 2010; Ruiz Fernandez et al., 2011), and these shifts of spatial attention in turn affect the perception of temporal intervals (Di Bono et al., 2012; Frassinetti et al., 2009; Santiago et al., 2007; Vicario et al., 2008). Finally, large vs.

⁎ Corresponding author at: Aging & Cognition Research Group, German Center for Neurodegenerative Diseases (DZNE), Leipziger Str. 44, 39120 Magdeburg, Germany. Fax: +49 391 67 24528. E-mail addresses: [email protected] (M. Riemer), [email protected] (N. Diersch), [email protected] (F. Bublatzky), [email protected] (T. Wolbers).

http://dx.doi.org/10.1016/j.neuroimage.2016.01.030 1053-8119/© 2016 Elsevier Inc. All rights reserved.

small numbers are perceived as longer in duration (Lu et al., 2009; Oliveri et al., 2008; Vicario et al., 2008; Xuan et al., 2007). A growing body of evidence suggests that the interactions between perceptual dimensions are mediated by neuronal structures in the parietal cortex (Basso et al., 1996; Bueti and Walsh, 2009; Burr et al., 2010; Coull and Nobre, 1998; Hubbard et al., 2005; Magnani et al., 2010; Oliveri et al., 2009; Oliveri et al., 2004; Walsh, 2003). The role of parietal structures for spatial, temporal, and numerical processing was also confirmed by single cell studies in non-human primates (Janssen and Shadlen, 2005; Nieder, 2004; Nieder et al., 2006; Sawamura et al., 2002; Thompson et al., 1970). Moreover, Leon and Shadlen (2003) observed that spatially tuned neurons in the right posterior parietal cortex (PPC) of rhesus monkeys were concurrently sensitive to temporal characteristics of stimuli. Together, these findings suggest that not only the processing of different magnitudes, but also their mutual interactions might be mediated by the parietal cortex (Göbel et al., 2006; Göbel et al., 2001; Hayashi et al., 2013; Rusconi et al., 2007). Imaging studies in humans similarly showed that the right PPC, especially the posterior part along the intraparietal sulcus (IPS), might contain the neural substrate of a generalized magnitude system for space, time, numbers and other magnitudes (Bueti and Walsh, 2009; Cohen Kadosh et al., 2007a; Cohen Kadosh et al., 2007b; Walsh, 2003). Interference with neuronal processes in the PPC by using transcranial magnetic stimulation (TMS) causes deficits in space (Bjoertomt et al., 2002; Fierro

M. Riemer et al. / NeuroImage 129 (2016) 72–79

et al., 2000; Muggleton et al., 2006), time (Hayashi et al., 2013; Magnani et al., 2010; Oliveri et al., 2009; Wiener, 2014), and number processing (Cattaneo et al., 2009; Göbel et al., 2006; Göbel et al., 2001). Therefore, TMS provides a promising method to investigate the interactions between these dimensions. Interactions between perceptual dimensions have often been investigated in terms of response code associations and congruency effects. For example, the spatial–numerical association of response codes (SNARC) denotes the phenomenon of faster reactions with the right hand in response to relatively large numbers, while the left hand reacts faster to relatively small numbers (Dehaene et al., 1993; Hubbard et al., 2005; Wood et al., 2008). This indicates that numbers are spatially represented along a mental number line (i.e., small numbers to the left and large numbers to the right).1 The SNARC effect represents an analog of the Simon effect, which denotes that stimuli appearing on either side of egocentric space facilitate reactions with the ipsilateral hand (Hommel, 1993; Simon and Wolf, 1963). Importantly, Simon and SNARC effects occur despite the fact that stimulus position and number magnitude are irrelevant for the task. There have been various attempts to find evidence for an analogous effect of a spatial–temporal association of response codes (STARC). Although an association between short vs. long durations and left vs. right response buttons has been confirmed (Fabbri et al., 2012; Ishihara et al., 2008; Vallesi et al., 2008), it is unknown whether this response code association applies as well for early vs. late events. As stressed by Bonato et al. (2012), however, a spatial representation of moments in time (rather than duration magnitudes) is a key aspect for the theory of spatialized time. Congruency effects denote the phenomenon that stimuli are processed faster when they possess congruent characteristics across different dimensions. For example, congruency effects between space and numbers would be reflected by shortened reaction times to large numbers, which are presented in the right hemifield (as compared to large numbers presented in the left hemifield). Thus, an important difference between response code associations and congruency effects is that the former relate to interactions between perceived dimensions and associated motor responses, whereas the latter relate to interactions between two perceived dimensions independent from response selection. There is converging evidence that cross-dimensional congruency effects are mediated by neuronal structures within the right PPC, predominantly in the IPS (Cattaneo et al., 2009; Cohen Kadosh et al., 2007a; Cohen Kadosh et al., 2007b; Oliveri et al., 2009). In contrast, evidence for a PPC involvement in response code associations is rather scarce (one example is Rusconi et al., 2007). Lesions in the right PPC often result in neglect of the left spatial hemifield (Halligan et al., 2003). While congruent neglect symptoms can extend to numerical and temporal cognition (Basso et al., 1996; Oliveri et al., 2009; Priftis et al., 2006), response code associations like the SNARC effect are not affected in the same patients (Priftis et al., 2006). Instead, prefrontal areas have been suggested to underlie the association between perceived numbers and specific motor responses (Rusconi et al., 2011). Furthermore, single cell recordings in non-human primates indicate that stimulus–response compatibility, which is assumed to underlie Simon and SNARC effects, is encoded by neurons in the premotor cortex (Kalaska and Crammond, 1995). In the present study, we investigated the relative impact of right PPC inhibition on response code associations and congruency effects within the same paradigm, enabling a direct comparison between these effects (Fig. 1). In a two-alternative forced-choice task, participants were asked for odd–even judgments on numbers, which were either small or large (numerical magnitude), appeared either on the left or the right side of a screen (spatial position), and occurred either early or late within a predefined time interval (temporal position). Inhibition of the right 1 The SNARC effect depends on relative rather than absolute number magnitude and on the culturally defined writing direction, but not on handedness or hemispheric dominance (Dehaene et al., 1993).

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PPC was induced by continuous theta-burst stimulation (cTBS; Chaves et al., 2012; Huang et al., 2005; Nyffeler et al., 2008). If response code associations and congruency effects are both mediated by the right PPC, they should decrease after TMS compared to sham stimulation. Furthermore, if the interrelations between space, time, and numbers are based on the PPC, TMS-induced inhibition should reduce all interactions to a similar degree. Methods Participants Twenty-two healthy participants (7 males, mean age was 25.9 years, ranging from 21 to 35) were recruited from the local community. All but one were right-handed. Exclusion criteria were metallic objects in the body, auditory impairments or previous occurrences of epileptic seizures, and advanced skills in languages that use right-to-left or top-tobottom writing directions. Participants received monetary compensation and gave written informed consent to the experimental protocol, which was approved by the local ethics committee. Stimuli and task Participants sat in front of a computer monitor (24 in. diagonal) and a centrally arranged standard German keyboard. Two buttons at the left and the right side of the keyboard were used as response buttons (button codes ‘b’ and ‘num_3’). Participants were instructed to align their body midline with monitor and keyboard and to maintain a distance of approximately 1 m between their head and the monitor. A light blue rectangular frame (47 × 8 cm; [0.6,1,1] in rgb space) was presented for 4 s in the center of the monitor (gray background) with a black fixation cross in the middle. One of four numbers (1, 2, 8, or 9) was presented for 250 ms either 13 cm to the left or to the right of the fixation cross, either 1 or 3 s after frame onset. In a reaction time task, participants had to press the right button for an even number and the left button for an odd number. Each of the possible combinations (4 numbers × 2 positions × 2 onsets) was repeated five times in randomized order, resulting in 80 trials per block. In the second block of each session, the meaning of buttons was reversed. The order of assignment was counterbalanced across participants. Previous to each block, participants performed eight practice trials to get accustomed to the specific button assignment. During the whole experiment, the frame was always presented for exactly 4 s. To familiarize participants with this duration, the frame was shown three times and participants were asked to attend to its presentation time. They were explicitly told that the frame would always appear for exactly this duration. However, the numerical value of ‘four seconds’ was not announced. In the following ten frame presentations, participants were instructed to press the space bar when half of its duration was over. No feedback was given. This method provided information on general timing abilities (no differences between experimental sessions were found) and enabled familiarization with the frame duration. Presentation of stimuli was controlled by PsychoPy (v1.80.01). Experimental sessions The experiment was performed during two experimental sessions, conducted on different days. In the TMS session, transcranial magnetic stimulation (TMS) was applied over the right PPC according to the TMS protocol described in Section 2.4. In the sham session, the coil was turned upside down and no TMS was applied. Due to this procedure, acoustic disturbance and vibrations of the coil were comparable during both sessions. Importantly, given that our aim was to test for interactions between spatial, temporal, and numerical dimensions, the left PPC was not considered as control stimulation site because of its

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Fig 1. (a) Graphical depiction of two exemplary trials where the task was to press the left button for odd and the right button for even numbers (correct buttons are indicated in green color). In each trial, a frame with a fixation cross appeared for a total duration of 4 s. Target stimuli (digits 1, 2, 8, or 9) were presented for 250 ms, starting either 1 s or 3 s after frame onset. Small vs. large digits (number) were presented at the left vs. right side of the screen (space) at an early vs. late onset (time). Parity judgments (odd vs. even) were given with the left vs. right button (response codes). (b) Schematic illustration of the utilized dimensions and their interrelations. Response code associations denote faster reactions with the right hand toward any number appearing at the right screen side (Simon), large numbers (SNARC), and late onsets (STARC). Congruency effects denote, irrespective of the responding hand, faster reactions toward large numbers appearing at the right side of the screen (space–number), large numbers appearing late in time (time–number), and any number appearing at the right side of the screen and late in time (space–time).

potential role for temporal perception (Coull and Nobre, 1998; Wiener et al., 2010). The stimulation site in the right PPC was determined on the basis of individual T1-weighted MRI scans. For each image, we identified the intersection point of Brodmann areas 39, 40, and 7 at the right intraparietal sulcus (Fig. 2). Previous studies in monkeys have identified this region as containing the highest proportion of numerosity-selective neurons (Nieder and Miller, 2004). Navigation of the coil was supported by Localite TMS Navigator (version 2.1.18).

TMS protocol TMS was controlled by a MagPro stimulator (X100 + MagOption, MagVenture), and pulses were delivered by a water-cooled figure-ofeight coil with an outer diameter of 75 mm (Cool B-65, MagVenture). We applied continuous theta-burst stimulation (cTBS) according to the protocol described in Nyffeler et al. (2008) and in Chaves et al. (2012). Bursts containing three biphasic pulses (repeated at 30 Hz) were applied over right PPC for 44 s at 6 Hz. Thus, one train of cTBS

Fig 2. Target stimulation site in the right posterior parietal cortex of one exemplary subject.


consisted of 267 bursts (801 single pulses). After an interval of 10 min, the train was repeated in order to prolong behavioral effects (Nyffeler et al., 2006). The coil was held tangentially to the scalp, with the handle pointing downwards in an angle of 45 degrees. Pulse intensity was individually set to 100% of the resting motor threshold (MT), which was defined as the lowest intensity capable to induce a motor evoked potential of 100 μV (recorded from the right abductor pollicis brevis) in at least 50% of a series of ten single pulses applied to the left motor cortex. MT was assessed for both experimental sessions separately. Mean pulse intensity for all subjects was 47.3% (ranging from 32% to 60%) of the maximal stimulator intensity. Statistical analysis Reaction times exceeding the cut-off criterion of 1 s (4.9%) were deleted as outliers, and error trials (6.7% of remaining trials) were discarded from the analysis of reaction times. For each subject, mean reaction times and arcsine transformed error rates were calculated for both sessions and subjected to a linear mixed effects model (2 × 2 × 2 × 2 × 2 factorial design), including the factors condition (cTBS vs. sham), numerical magnitude (small vs. large), spatial position (left vs. right), temporal onset (early vs. late), and response button (left vs. right). Participants were included as random factor. Response code associations are denoted by the respective interactions between response button and spatial position (Simon), numerical magnitude (SNARC), or temporal onset (STARC). Congruency effects are represented by interactions between numerical magnitude, spatial position, and temporal onset (cf. Fig. 1). To directly compare response code associations and congruency effects, we quantified all effects for each individual according to the method established by Lorch and Myers (1990). Regarding the SNARC effect, we first calculated the reaction time differences to small vs. large numbers, so that positive values indicate faster reactions toward large (compared to small) numbers. Then we calculated the linear regression coefficient predicting these values depending on the laterality of the responding hand, so that a positive regression coefficient denotes a relatively higher advantage for large numbers when using the right (compared to the left) hand, i.e., the SNARC effect. In the same vein, we calculated regression coefficients representing the other effects. As regression analyses were always computed between reaction times and a dichotomous variable coded by integers 1 (e.g., left hand) and 2 (right hand), the resulting coefficients are comparable between all effect types. A linear mixed effects model (2 × 2 factorial design) with the factors effect category (response code associations vs. congruency effects) and TMS condition (cTBS vs. sham) was performed. For a more detailed analysis, 3 × 2 factorial models were performed for each effect category separately, including the factors effect type (e.g., Simon vs. SNARC vs. STARC) and TMS condition (cTBS vs. sham). Absolute effect magnitudes (against zero) were tested by two-tailed, and relative effects (comparison between sham and cTBS) by paired one-tailed t-tests. Results The analysis of reaction time data revealed significant Simon (F1,651 = 12.5, p b .001) and SNARC effects (F1,651 = 37.8, p b .001), but no indication of an analogous STARC effect (F1,651 b 0.1, p N .5). These response code associations were not modulated by TMS application (Simon: F1,651 = 0.5, p = .5; SNARC: F1,651 = 1.1, p = .29; STARC: F1,651 b 0.1, p N .5). Response code associations are presented in Fig. 3a. When aggregated over both TMS conditions, no congruency effects were found between space and time (F1,651 b 0.1, p N .5), space and number (F1,651 = 0.1, p N .5), and time and number (F1,651 = 1.0, p = .32), but interactions indicated that the effects between space and time (F1,651 = 4.1, p = .04) and by trend between space and number (F1,651 = 2.9, p = .09) were modulated by the application of TMS

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(Fig. 3b). No interaction with TMS conditions was found for the congruency effect between time and number (F1,651 = 1.4, p = .24). The analysis of error rates revealed a strong SNARC effect (F1,651 = 54.3, p b .001), indicating more errors with the right hand in response to large numbers and more errors with the left hand to small numbers. All other response code associations and congruency effects were neither significant (all p N .21) nor modulated by TMS conditions (all p N .23). A direct comparison between response code associations and congruency effects is enabled by the analysis of regression coefficients (Lorch and Myers, 1990), providing a single value for each effect (Fig. 4). Different effect magnitudes were observed for response code associations and congruency effects (F1,239 = 19.9, p b .001) and between the TMS conditions (F1,239 = 5.3, p = .02), and a trend for an interaction was found (F1,239 = 3.3, p = .07). Separate models revealed different effect magnitudes between the three response code associations (F1,107 = 5.9, p = .02), but not between the three congruency effects (F1,107 = 1.1, p = .3). In contrast, application of TMS had no significant influence on response code associations (F1,107 = 0.1, p N .5), while congruency effects were modulated by TMS conditions (F1,107 = 12.0, p b .001). No interactions with TMS conditions were found, neither for response code associations (F1,107 = 0.3, p N .5) nor congruency effects (F1,107 = 0.5, p = .48). Absolute effects against zero were found for Simon (sham: t21 = 1.8, p = .09; TMS: t21 = 2.1, p = .05), SNARC (sham: t21 = 4.8, p b .001; TMS: t21 = 2.9, p = .009), and space–time congruency (sham: t21 = 2.1, p = .04; TMS: t21 = − 2.2, p = .04). None of the other effects were significantly different from zero (all p N 0.12). Relative effects between sham and TMS conditions were significant for space–time (t21 = − 3.2, p = .002) and space–number congruency (t21 = − 2.0, p = .03), but not for time–number congruency (t21 = −1.2, p = .12) and response code associations (Simon: t21 = 0.8, p N .5; SNARC: t21 = −1.3, p = .1; STARC: t21 = −0.3, p = .4). Finally, correlational analyses revealed that response code associations were highly correlated between sham and TMS conditions (Simon: r = 0.55, t20 = 2.9, p = .004; SNARC: r = 0.51, t20 = 2.6, p = .008; STARC: r = 0.39, t20 = 1.9, p = .035), indicating high intraindividual stability of these effects. This stands in contrast to congruency effects, which seemed to be relatively unstable at an individual level and did not correlate between sham and TMS conditions (space–time: r = 0.09, t20 = 0.4, p = .34; space-number: r = 0.03, t20 = 0.1, p = .45; time-number: r = −0.11, t20 = −0.5, p N .5). Discussion In the present study, we investigated the role of the right posterior parietal cortex (PPC) for perceptual interrelations between spatial, temporal, and numerical dimensions. We tested the impact of right PPC inhibition, as induced by cTBS (Huang et al., 2005), on associations with spatial response codes (Simon, SNARC and STARC) and on congruency effects between these dimensions within a unified paradigm, enabling direct comparison between the magnitude of these effects and their dependency on the right PPC. The results demonstrate a dissociation between response code associations and congruency effects. We found significant Simon and SNARC effects (but no STARC effect), the extent of which was independent from right PPC functioning. In contrast, spatial–temporal and spatial–numerical congruency effects (but not temporal–numerical congruency) were reversed after application of cTBS. Furthermore, correlations between effects measured after cTBS and sham stimulation were significant for response code associations, but not for congruency effects, indicating that cTBS interfered only with the latter. These results suggest different neuronal processes underlying response code associations on the one hand and congruency effects on the other hand. Involvement of parietal areas (most often in the right hemisphere) was reported for the processing of space (Bjoertomt et al., 2002; Coull

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Fig 3. (a) Response code associations and (b) congruency effects for reaction times after sham stimulation (top row) and cTBS (bottom row). Error bars show standard error across participants.

and Nobre, 1998; Stein, 1989), time (Coull and Nobre, 1998; Rao et al., 2001), and numbers (Eger et al., 2009; Piazza et al., 2004; Piazza et al., 2007; Roitman et al., 2012; Sawamura et al., 2002), as well as for the mutual interactions between space and time (Magnani et al., 2010; Oliveri et al., 2009), space and numbers (Cattaneo et al., 2009; Cutini et al., 2014; Göbel et al., 2006; Göbel et al., 2001; Hubbard et al., 2005; Oliveri et al., 2004), and time and numbers (Burr et al., 2010; Hayashi et al., 2013). Furthermore, previous research has differentiated between the accumulation of sensory evidence for a behavioral decision and the integration of such evidence with specific actions (de Lafuente et al.,

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Fig 4. Relative magnitudes of (a) response code associations and (b) congruency effects for reaction times after sham stimulation (gray bars) and cTBS (white bars). Regression coefficients representing the size of effects are shown on the y-axis. A value of zero indicates that neither a positive effect (e.g., for the SNARC effect, faster right-hand reactions to large numbers), nor a negative effect (faster right-hand reactions to small numbers) is present. Error bars show standard error of the mean across participants (p b .001⁎⁎⁎, p b .01⁎⁎, p b .05⁎, p b .1t).

2015; Filimon et al., 2013; Tosoni et al., 2008). For example, Tosoni et al. (2008) reported that medial PPC areas in the precuneus and sensorimotor cortex code for sensory evidence associated with reaching movements. Here, cTBS was applied to the posterior part of the right PPC adjacent to the IPS (Cohen Kadosh et al., 2007a; Nieder and Miller, 2004). Thus, the type of interaction might explain the selective modulation of congruency effects as opposed to response code associations. Reaction time tasks with more than one response alternatives can be divided into a phase of perceptual processing and a phase of response selection (Kalaska and Crammond, 1995; Schall and Bichot, 1998). As congruency effects are based on the congruency between two purely perceptual dimensions, they should occur during perceptual processing. In contrast, response code associations are based on the congruency between a perceptual dimension and associated behavioral responses, and therefore should occur during response selection. Taking the example of space–time interrelations, the stimulus' onset (early vs. late) can be congruent to perceived space (left vs. right hemifield) or it can be congruent to spatially defined actions (left vs. right button). In non-human primates, the process of response selection is mediated by neurons in the premotor cortex (di Pellegrino and Wise, 1993; Kalaska and Crammond, 1995; Mitz et al., 1991). In line with these studies, our data suggest that inter-dimensional interference at the level of perceptual processing (i.e., congruency effects) depends on lateral parietal areas (BA 39, 40 and 7 at the right IPS; Cohen Kadosh et al., 2007a), whereas interferences at the level of response selection (i.e., response code associations) might rather depend on sensorimotor (e.g., Tosoni et al., 2008) and premotor areas (e.g., Kalaska and Crammond, 1995). The hypothesis of a spatial representation of time and numbers has been supported by many studies, and our results reveal an interesting difference between the mental time line and the mental number line: The spatial representation of early vs. late events was reflected in congruency effects, but not in response code associations (i.e., STARC), whereas the spatial representation of small vs. large numbers was significant for the association with response codes (i.e., SNARC), but not for the corresponding congruency effect between space and numbers. Together with our finding that congruency effects, but not response


code associations, are modulated by cortical inhibition of the right IPS, this suggests that the interaction between time and space on the one hand and between number and space on the other hand might not be driven by the same neuronal mechanism, as it is proposed by a theory of magnitude (ATOM; Bueti and Walsh, 2009; Walsh, 2003). The IPS in the right PPC seems to be especially relevant for the interrelations between spatial and temporal aspects of physical stimuli. The general validity of our design is confirmed by the replication of Simon and SNARC effects. Thus, the absence of any indication of an analogous STARC effect (Figs. 3a and 4a) strongly suggests that there indeed is no association between early vs. late events and left vs. right response buttons, as it has frequently been reported for events appearing in the left vs. right hemifield (Hommel, 1993; Simon and Wolf, 1963) and for small vs. large numbers (Dehaene et al., 1993; Hubbard et al., 2005). Ishihara et al. (2008) also investigated a left-to-right representation of early vs. late events. In their study, a series of seven acoustic clicks was presented in regular intervals and an eighth click was slightly advanced or delayed. Participants indicated whether the eighth click occurred earlier or later than expected. Indeed, Ishihara et al. (2008) found a right-hand advantage for late and a left-hand advantage for early onsets. However, a critical point in this and other studies on the presumed STARC effect refers to the distinction between judgments on the temporal duration and on the temporal position of stimuli. This distinction is important, because evidence for a spatial representation of time would rather be provided by an association between response codes and the stimuli's position in time, while an association between response codes and duration magnitude can also be understood as a special case of the SNARC effect (Bonato et al., 2012). In the study by Ishihara et al. (2008), participants might have responded to the ‘position in time’ of the eighth click, but, alternatively, they might as well have compared the duration between the seventh and eighth click with the preceding durations. Given the dominance of rhythm perception (Grahn, 2012; Grahn and Rowe, 2013), the latter seems likely. Thus, while many studies reported that short durations are associated with the left and long durations with the right side of space (Di Bono et al., 2012; Fabbri et al., 2012; Ishihara et al., 2008; Vallesi et al., 2008), the present study shows that this spatial representation of short vs. long durations does not generalize to early vs. late events. However, the correlations of Simon, SNARC, and STARC effects between both days of testing indicate a high intra-individual stability of response code associations. In the Simon effect, it is plausible to associate left stimuli with the left button and right stimuli with the right button. This intuitiveness of associations is also given for the SNARC effect (although to a lesser degree). Small numbers should be more easily associated with the left side and large numbers with the right side because in Western cultures, we are extremely familiar with writing and reading numbers from left to right. However, the flow of time might not exclusively be represented along the left/right axis. There are many examples that people associate time with the up/down axis or the proximal/distal axis, with early events being located above or proximal and late events below or distal (Eikmeier et al., 2013; Hartmann et al., 2014; Torralbo et al., 2006). Together with the high stability of STARC effects, these considerations raise the possibility that the absence of a STARC effect might be due to a considerable proportion of participants exhibiting a reliable up/down or proximal/distal association with time, which is orthogonal to the left/right direction tested here. Finally, independent of TMS conditions, we observed reliable Simon and SNARC effects, signifying shorter reaction times with the left vs. right hand in response to small vs. large numbers (SNARC) presented in the left vs. right hemifield (Simon). Regarding the Simon effect, shorter reaction times were accompanied by less errors (though not significant), indicating an improved processing of stimuli. In contrast, for the SNARC effect, shorter reaction times coincided with higher error rates, indicating that faster reactions were not based on improved perceptual processing, but rather on automatic reflexes, triggered by task-irrelevant numerical magnitude. This observation alludes to a

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fundamental difference between Simon and SNARC effects, the former resulting from enhanced perceptual processing, and the latter from automatically triggered motor reactions (e.g., Eriksen and Eriksen, 1974). Differences between Simon and SNARC effects have been reported previously (Mapelli et al., 2003; Rusconi et al., 2007). In these studies, the SNARC effect increased for longer reaction times, while the Simon effect vanished (Hommel, 1994; Rusconi et al., 2007) or even was reversed (Mapelli et al., 2003). Based on these observations, Rusconi et al. (2007) suggested that Simon and SNARC effects are based on different neuronal mechanisms (but see Gevers et al., 2005; Gevers and Notebaert, 2008). Our study revealed different modulations of error rates between Simon and SNARC effects, which reinforces the assumption of different mechanisms, though it does neither imply nor eliminate the possibility of different underlying neuronal systems (Gevers and Notebaert, 2008). Conclusions In the present study, we report a dissociation between response code associations and congruency effects. We found causal evidence that congruency effects are mediated by neuronal structures along the IPS in the right PPC, which is in line with previous studies. In contrast, response code associations seem to be processed in different areas. Despite the fact that Simon and SNARC effects could be replicated in our design, we did not find evidence for an analogous STARC effect. This result disclaims the proposed existence of such a phenomenon, at least in terms of an association between early/late events and left/right response buttons. Declaration The study was approved by the local ethical committee and conducted according to the ethical standards laid down in the 6th Revision of the Declaration of Helsinki (Version Seoul 2008). The authors have no conflict of interest. References Basso, G., Nichelli, P., Frassinetti, F., di Pellegrino, G., 1996. Time perception in a neglected space. Neuroreport 7 (13), 2111–2114. Bergson, H., 1888. Sur les données immédiates de la conscience. Paris [Time and free will (transl. Pogson FL). George Allen and Unwin (1910), London]. Presses Universitaires de France. Bjoertomt, O., Cowey, A., Walsh, V., 2002. Spatial neglect in near and far space investigated by repetitive transcranial magnetic stimulation. Brain 125 (Pt 9), 2012–2022. Bonato, M., Zorzi, M., Umilta, C., 2012. When time is space: evidence for a mental time line. Neurosci. Biobehav. Rev. 36 (10), 2257–2273. http://dx.doi.org/10.1016/j. neubiorev.2012.08.007. Bueti, D., Walsh, V., 2009. The parietal cortex and the representation of time, space, number and other magnitudes. Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 364 (1525), 1831–1840. http://dx.doi.org/10.1098/rstb.2009.0028. Burr, D.C., Ross, J., Binda, P., Morrone, M.C., 2010. Saccades compress space, time and number. Trends Cogn. Sci. 14 (12), 528–533. http://dx.doi.org/10.1016/j.tics.2010. 09.005. Cattaneo, Z., Silvanto, J., Pascual-Leone, A., Battelli, L., 2009. The role of the angular gyrus in the modulation of visuospatial attention by the mental number line. NeuroImage 44 (2), 563–568. http://dx.doi.org/10.1016/j.neuroimage.2008.09.003. Chaves, S., Vannini, P., Jann, K., Wurtz, P., Federspiel, A., Nyffeler, T., ... Müri, R.M., 2012. The link between visual exploration and neuronal activity: a multi-modal study combining eye tracking, functional magnetic resonance imaging and transcranial magnetic stimulation. NeuroImage 59 (4), 3652–3661. http://dx.doi.org/10.1016/j. neuroimage.2011.10.094. Cohen Kadosh, R., Cohen Kadosh, K., Linden, D.E., Gevers, W., Berger, A., Henik, A., 2007a. The brain locus of interaction between number and size: a combined functional magnetic resonance imaging and event-related potential study. J. Cogn. Neurosci. 19 (6), 957–970. http://dx.doi.org/10.1162/jocn.2007.19.6.957. Cohen Kadosh, R., Cohen Kadosh, K., Schuhmann, T., Kaas, A., Goebel, R., Henik, A., Sack, A.T., 2007b. Virtual dyscalculia induced by parietal-lobe TMS impairs automatic magnitude processing. Curr. Biol. 17 (8), 689–693. http://dx.doi.org/10.1016/j.cub. 2007.02.056. Coull, J.T., Nobre, A.C., 1998. Where and when to pay attention: the neural systems for directing attention to spatial locations and to time intervals as revealed by both PET and fMRI. J. Neurosci. 18 (18), 7426–7435. Cutini, S., Scarpa, F., Scatturin, P., Dell'Acqua, R., Zorzi, M., 2014. Number-space interactions in the human parietal cortex: enlightening the SNARC effect with functional

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