Inclusion of noise in iterated firing time maps based on the PRC
© Sieling et al; licensee BioMed Central Ltd. 2009
Published: 13 July 2009
Methods using the phase response curves (PRCs) of component neurons to predict network activity suffer from biological variability intrinsic to the studied neural oscillators, often described as noise. To make analytical predictions, researchers minimize this noise either by averaging the measured PRC or by controlling the period of oscillation. Here, we present an alternate method that incorporates measured noise into PRCs. In a hybrid network of two bursting neural oscillators coupled via synaptic excitation (tsyn ≈ 10 ms), we found that this method could accurately predict phase locking in the presence of variability in the intrinsic period of 10%.
where P0 is the intrinsic period, fj, k [n] is the phase at which neuron j receives the kth input in the current cycle, and fj, l [n-1] is the phase at which the lth input was received by neuron j in the previous cycle. We defined time of input as the start of a burst in the presynaptic neuron. To simulate a reduction in the overall amount of noise in the system, we scaled the noise envelope by a factor less than 1. The inclusion of noise in the PRC-based iterative map is similar to those of ; the major difference is the use of F2 in addition to F1 in our method.
We compared experimental observations to predictions made using a noiseless model of pulsatile coupling  and to the predictions of our iterated map. Out of 86 networks tested , the noiseless model was incorrect 16 times and the iterative map was able to make the correct prediction for 12 of those networks. Further, the success of the iterative map method was predictable by inspection of the PRCs and noise envelopes.
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