Modeling Time Cell Neuron-Level Dynamics

The timing of intervals in both humans and nonhuman animals is susceptible to imprecision, leading to trial-to-trial variations in timed behaviors. A notable statistical characteristic of this timing behavior is the linear increase in the standard deviation of timed responses as the intervals become longer, known as time-scale invariance. Although the exact mechanism responsible for this property is not yet fully understood, "time cells" have emerged as a potential mechanism, particularly in relation to interval timing within the episodic memory system. These specialized networks of neurons exhibit sequential firing, with each neuron becoming active during a specific phase of the timed experiment. Notably, the resulting "ramping wave" decelerates during later phases of the timed event, and the duration of cell activity increases over time. In this paper, we propose a new model of a biological neural network composed of time cells, utilizing integrate-and-fire neurons with slow after-hyperpolarization currents and varying resting membrane potentials. This proposed network does not rely on any specific network architecture apart from self-excitation. Remarkably, the network successfully reproduces the experimentally observed ramping activity, with the standard deviation of spike times among the participating neurons increasing linearly with the average spike time. Furthermore, the results of the model are consistent with the experimental findings, providing additional evidence for its accuracy and validity.