Predictive neuron, extension of LSTM

Ok, so this is just a basic idea, but it seems easy to implement (I just haven't found appropriate data to train it with), but the idea is to have something like an LSTM node (http://en.wikipedia.org/wiki/LSTM) but with the extension of an external neuron that provides feedback. This would only be applicable to temporal systems, but the idea is to have a node that is part of the system that attempts to predict the next state of its governing neuron, and uses predictive error combined with backprop to contribute to weight changes in training. The prediction or the error could also be a value fed forward into the next layer. I haven't found any examples of this but am curious as to whether this could be effective/helpful/useful. There are many cognitive theories that propose the idea of pattern recognition and pattern prediction and I though this might be an effective intermediary.