Figure 1: Scales of neural timing and analogy to spatial navigation.

(a) An animal is foraging for food when a predator is detected. The animal can choose to wait for a given amount of time (top) or risk continuing without waiting (bottom). (b) Diversity of timescales, brain regions, and neural circuits involved in the encoding of time from milliseconds to days. (far left) Neurons in auditory cortex tuned to msec inter-click intervals (Sadagopan & Wang 2009). (middle left) In eyeblink conditioning, a conditioned stimulus (tone) precedes an unconditioned stimulus (air puff) by a fixed interval, and animals learn to blink and cerebellar neurons respond just before the air puff (Berthier & Moore 1986; Kotani et al. 2003). (near left) Two odors are presented with a delay, and the animal licks to receive a reward only when the odors are identical. Pyramidal cells of hippocampus fire sequentially during the delay period (MacDonald et al. 2013). (near right) Animals press a lever after a delay period to receive a reward. Neurons in cortex and striatum encode the delay period with a variety of patterns including tuning to various times or ramping activity (Matell et al. 2003). (middle right) Neurons in the LEC encode the cumulative duration of traversals in alternating black and white rooms over the course of tens of minutes (Tsao et al. 2018). (far right) A transcription-translation feedback loop in neurons of the suprachiasmatic nucleus results in 24-hour rhythms (Takahashi 2017; Welsh et al. 1995). Illustrations inspired by data from the cited studies. (c) Spatial path integration in 2-D (left half). At ‘start,’ position is known exactly. As the animal moves towards target ‘end’ or goal, actual position x(t) is shown in black and internal estimate of position x’(t) in gray. Integration of a velocity signal (yellow region, inferred from self-motion cues) updates position but accumulates error until landmark or border that allows for error correction is reached (‘reset’ or ‘end’, gray arrow). Cells in spatial navigation (right half), from left to right: velocity cells and head direction cells encode speed and orientation of the animal with uncertainty indicated in yellow; grid cells encode periodic representation of position; place cells encode current position; border cells indicate proximity to borders or objects. Grid cells integrate incoming speed and orientation signals and are summed to produce single-peaked place cells. Border cells can reset or correct these position signals. (d) Interval timing through time-integration in 1-D (left half). Elapsed time is measured after a start signal. External time t shown in black while internal estimate of time t’, in gray, indicates perception that more time (gray line above black line) or less time (gray line below black line) has elapsed relative to external time. Estimate of time is informed by a moment-by-moment temporal derivative that represents the animal’s ongoing passage of time signal and runs until a ‘reset’ (correction cue) or ‘stop’ is encountered. Cells of interval timing (right half): temporal derivative cell encodes internal representation of the passage of time, represented here as a pacemaker (left) whose inter-spike-interval dt’ approximates discrete time steps dt. Continuous-time version of this process is represented by temporal derivative cell whose deviation from true time (black line) is shown by the gray trace. Output of temporal derivative cell is integrated by hypothesized periodically firing temporal cells. These are summed to produce well-tuned time cells. Border cells fire at start or stop positions and reset or correct encoding of time in temporal periodic cells and in time cells.