The detection of any of these patterns causes an NMDA spike and subsequent depolarization at the soma.
It might seem that eight to twenty synapses could not reliably recognize a pattern of activity in a large population of cells. However, robust recognition is possible if the patterns to be recognized are sparse; i.e. few neurons are active relative to the population (Olshausen and Field, 2004). For example, consider a population of 200K cells where 1% (2,000) of the cells are active at any point in time. We want a neuron to detect when a particular pattern occurs in the 200K cells. If a section of the neuron' s dendrite forms new synapses to just 10 of the 2,000 active cells, and the threshold for generating an NMDA spike is 10, then the dendrite will detect the target pattern when all 10 synapses receive activation at the same time Note that the dendrite could falsely detect many other patterns that share the same 10 active cells. However, if the patterns are sparse, the chance that the 10 synapses would become active for a different random pattern is small. In this example it is only 9.8 x 10^-21.
The probability of a false match can be calculated precisely as follows. Let n represent the size of the cell population and A the number of active cells in that population at a given point in time, for sparse patterns A ≪ n . Let s be the number of synapses on a dendritic segment and θ be the NMDA spike threshold. We say the segment recognizes a pattern if at least θ synapses become active, i.e. at least θ of the s synapses match the currently active cells.
-- If a section of the neuron' s dendrite forms new synapses to just 10 of the 2,000 active cells,and the threshold for generating an NMDA spike is 10, then the dendrite will detect the target pattern when all 10 synapses receive activation at the same time.
