A model of dendritic spine Ca2+ concentration exploring possible bases for a sliding synaptic modification threshold.

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Abstract
We used a biophysical model of an isolated dendritic spine to assess quantitatively the impact of changes in spine geometry, Ca2+ buffer concentration, and channel kinetics on Ca2+ dynamics following high-frequency activation of N-methyl-D-aspartate receptors. We found that varying the buffer concentration in the postsynaptic density from 50 to 500 microM can result in an 8-fold difference in the peak Ca2+ concentration following three pulses at 100 Hz. Similarly, varying the spine neck diameter from 0.1 to 0.55 micron can result in a 15-fold difference in the peak Ca2+ concentration. The amplification of peak Ca2+ concentration also depended on temporal summation of N-methyl-D-aspartate-mediated excitatory postsynaptic currents. Variation of the current duration on the order of 100 msec can significantly affect summation at a given stimulation frequency, resulting in a 10-fold difference in the peak Ca2+ concentration at 100 Hz. It is suggested that activity-dependent modifications of these parameters may be important for the regulation of synaptic plasticity in the brain.