The first thing to mention is that, contrary to what I wrote previously, synaptic runaway appears to have very little to do with Alzheimer's disease, so we've lost that potential link with schizophrenia (which does have a lot to do with synaptic runaway).
EDIT: Actually, maybe synaptic runaway does have something to do with Alzheimer's: Greenstein and Ruppin (1998) mentions "Hasselmo's  hypothesis concerning ... synaptic runaway in the progression of Alzheimer's disease".
There's a whole raft of papers by Ruppin, Reggia, Horn and Levy amongst others from the mid-90s on computational modelling of both Alzheimer's disease and schizophrenia. One such paper includes a very clear description of a model of Alzheimer's disease, in which they deleted synapses at random but also caused the remaining synapses to attempt to compensate for these changes, which caused older memories to be retained long after recent (short-term) memories were destroyed by the deletion process (Ruppin and Reggia, 1995), just like in Alzheimer's disease where patients forget things like turning off the cooker long before they forget older memories such as the names of their loved ones.
They then took this model and re-spun it to model schizophrenia via synaptic runaway, such that the model retained all its memories for a long time, but interestingly also spontaneously retrieved parts of memories at random without any stimulus (Ruppin et. al., 1996), mirroring the hallucinations and delusions in schizophrenia and perhaps explaining the sensation that "someone else" (aliens, the CIA, etc.) is controlling the sufferer's thoughts.
This appears to be the last paper in this particular strand of their research, and it contains some interesting proposals for future work, which could feasibly form part of my preliminary research:
- Putting several copies of the schizophrenia model together to simulate cortical modules communicating with each other, to see if this restricts hallicinogenic symptoms (the 'biased pathological attractors' in the jargon) to individual parts of the brain, or spreads them throughout.
- Enabling the models to be reset each time they suffer a 'hallucination' so they can be repeatedly re-tested instead of forcing them to remain in the 'pathological attractor' state.
- Simply running the models with far larger neural networks, now that improved computational power is available.
Greenstein and Ruppin (1998) hypothesised that schizophrenia is due to delayed NMDA receptor maturation which leads to the neural network being "overloaded at an early stage, much before it reaches its explicit capacity limits" and therefore to synaptic runaway and schizophrenia, with no mention of unusual cell death -- so perhaps we'll have to find some other process to explain Rund (2009)'s observations of neurodegeneration in some schizophrenia patients.
Greenstein-Messica, A. and Ruppin, E. (1998), "Synaptic runaway in associative networks and the pathogenesis of schizophrenia", in Neural Computation 10:451--465.
Hasselmo, M.E. (1994), "Runaway synaptic modification in models of cortex: Implications for Alzheimer's disease", in Neural Networks 7:13--40.
Rund, B.R. (2009), "Is there a degenerativeprocess going on in the brain of people with schizophrenia?" in Frontiers in Neuroscience (3)36:1--6.
Ruppin, E. and Reggia J. (1995), "A neural model of memory impairment in diffuse cerebral atrophy", in British Journal of Psychiatry 166:19--28
Ruppin, E., Reggia, J., Horn, D. (1996), "Pathogenesis of schizophrenic delusions and hallucinations: a neural model", Schizophrenia Bulletin (22)1:105-123