Scalar timing in memory: A temporal map in the hippocampus.

Many essential tasks, such as decision making, rate calculation and planning, require accurate timing in the second to minute range. This process, known as interval timing, involves many cortical areas such as the prefrontal cortex, the striatum, and the hippocampus. Although the neurobiological origin and the mechanisms of interval timing are largely unknown, we have developed increasingly accurate mathematical and computational models that can mimic some properties of time perception. The accepted paradigm of temporal durations storage is that the objective elapsed time from the short-term memory is transferred to the reference memory using a multiplicative "memory translation constant" K*. It is believed that K* has a Gaussian distribution due to trial-related variabilities. To understand K* genesis, we hypothesized that the storage of temporal memories follows a topological map in the hippocampus, with longer durations stored towards dorsal hippocampus and shorter durations stored toward ventral hippocampus. We found that selective removal of memory cells in this topological map model shifts the peak-response time in a manner consistent with the current experimental data on the effect of hippocampal lesions on time perception. This opens new avenues for experimental testing of our topological map hypothesis. We found numerically that the relative shift is determined both by the lesion size and its location and we suggested a theoretical estimate for the memory translation constant K*.