Neuropsychological, neurophysiological, and neuroimaging studies suggest that right frontoparietal circuits may be necessary for the processing of mental number space, also known as the mental number line (MNL). Here we sought to specify the critical time course of three nodes that have previously been related to MNL processing: right posterior parietal cortex (rPPC), right FEF (rFEF), and right inferior frontal gyrus (rIFG). The effects of single-pulse TMS delivered at 120% distance-adjusted individual motor threshold were investigated in 21 participants, within a window of 0–400 msec (sampling interval = 33 msec) from the onset of a central digit (1–9, 5 excluded). Pulses were delivered in a random order and with equal probability at each time point, intermixed with noTMS trials. To analyze whether and when TMS interfered with MNL processing, we fitted bimodal Gaussian functions to the observed data and measured effects on changes in the Spatial–Numerical Association of Response Codes (SNARC) effect (i.e., an advantage for left- over right-key responses to small numbers and right- over left-key responses to large numbers) and in overall performance efficiency. We found that, during magnitude judgment with unimanual key-press responses, TMS reduced the SNARC effect in the earlier period of the fitted functions (∼25–60 msec) when delivered over rFEF (small and large numbers) and rIFG (small numbers); TMS further reduced the SNARC effect for small numbers in a later period when delivered to rFEF (∼200 msec). In contrast, TMS of rPPC did not interfere with the SNARC effect but generally reduced performance for small numbers and enhanced it for large numbers, thus producing a pattern reminiscent of “neglect” in mental number space. Our results confirm the causal role of an intact right frontoparietal network in the processing of mental number space. They also indicate that rPPC is specifically tied to explicit number magnitude processing and that rFEF and rIFG contribute to interfacing mental visuospatial codes with lateralized response codes. Overall, our findings suggest that both ventral and dorsal frontoparietal circuits are causally involved and functionally connected in the mapping of numbers to space.

Behavioral studies show that subjects respond more slowly to stimuli to which they previously stopped. This response slowing could be explained by “automatic inhibition” (i.e., the reinstantiation of motor suppression when a stimulus retrieves a stop association). Here we tested this using TMS. In Experiment 1, participants were trained to go or no-go to stimuli. Then, in a test phase, we compared the corticospinal excitability for go stimuli that were previously associated with stopping (no-go_then_go) with go stimuli that were previously associated with going (go_then_go). Corticospinal excitability was reduced for no-go_then_go compared with go_then_go stimuli at a mere 100 msec poststimulus. Although these results fit with automatic inhibition, there was, surprisingly, no suppression for no-go_then_no-go stimuli, although this should occur. We speculated that automatic inhibition lies within a continuum between effortful top–down response inhibition and no inhibition at all. When the need for executive control and active response suppression disappears, so does the manifestation of automatic inhibition. Therefore, it should emerge during go/no-go learning and disappear as performance asymptotes. Consistent with this idea, in Experiment 2, we demonstrated reduced corticospinal excitability for no-go versus go trials most prominently in the midphase of training but it wears off as performance asymptotes. We thus provide neurophysiological evidence for an inhibition mechanism that is automatically reinstantiated when a stimulus retrieves a learned stopping episode, but only in an executive context in which active suppression is required. This demonstrates that automatic and top–down inhibition jointly contribute to goal-directed behavior.

The right inferior frontal gyrus (rIFG) has been hypothesized to mediate response inhibition. Typically response inhibition is signaled by an external stop cue, which provides a top–down signal to initiate the process. However, recent behavioral findings suggest that response inhibition can also be triggered automatically by bottom–up processes. In the present study, we evaluated whether rIFG activity would also be observed during automatic inhibition, in which no stop cue was presented and no motor inhibition was actually required. We measured rIFG activation in response to stimuli that were previously associated with stop signals but which required a response on the current trial (reversal trials). The results revealed an increase in rIFG (pars triangularis) activity, suggesting that it can be activated by associations between stimuli and stopping. Moreover, its role in inhibition tasks is not contingent on the presence of an external stop cue. We conclude that rIFG involvement in stopping is consistent with a role in reprogramming of action plans, which may comprise inhibition, and its activity can be triggered through automatic, bottom–up processing.

An important aspect of cognitive control is the ability to respond with restraint. Here, we modeled this experimentally by measuring the degree of response slowing that occurs when people respond to an imperative stimulus in a context where they might suddenly need to stop the initiated response compared with a context in which they do not need to stop. We refer to the RT slowing that occurs as the “response delay effect.” We conjectured that this response delay effect could relate to one or more neurocognitive mechanism(s): partial response suppression (i.e., “active braking”), prolonged decision time, and slower response facilitation. These accounts make different predictions about motor system excitability and brain activation. To test which neurocognitive mechanisms underlie the response delay effect, we performed two studies with TMS and we reanalyzed fMRI data. The results suggest that the response delay effect is at least partly explained by active braking, possibly involving a mechanism that is similar to that used to stop responses completely. These results further our understanding of how people respond with restraint by pointing to proactive recruitment of a neurocognitive mechanism heretofore associated with outright stopping.