Response of schizophrenic model to 40 Hz drive. Simulated EEG traces in response to 40 Hz drive for primary schizophrenic point (left panels), and secondary schizophrenic point (right panels), as defined in text. (A, B) Power spectra of primary and secondary schizophrenic points, respectively. (C, D) Model produced EEG traces. (E, F) EEG, averaged over two consecutive cycles. (G, H) Spiking histogram and firing rates for individual neuron subtypes. Averages over sets of two consecutive cycles are shown. X-axis label applies to all three histograms. Potent = potential; spks = spikes; CR = calretinin positive cells; PV = parvalbumin positive cells; PYR = pyramidal cells. doi:10.1371/journal.pone.0058607.g005 

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... via fast Fourier transform (FFT) to determine which frequencies were present. The model reproduced, in a quantitatively similar way, frequency behaviors shown in control subjects (Fig 1A [left panels] and 1B [left panels] experimental; Fig 1C [left panels] model output). To confirm these model results, we created 20 simulated control subjects, as described in the Methods section. The results of these runs are shown in Figure 1D (blue points). It is clear that the behavior of our simulated index control subject is representative of the group of simulated controls, and that this group is similar to that of the control subjects of experimental studies. The manner in which the cellular level pathology that has been observed in schizophrenic hippocampus was instantiated as parameter changes in the model is detailed in Methods. Briefly, decreased NMDA activity was operationalized by decreasing maximum conductance (g max ) of the model NMDA receptors (in 10 increments); connectivity deficits were operationalized by decreasing pyramidal cell dendritic spine density (13 increments); and GABA system dysregulation was implemented by a joint decrease in GABA tone and increase in postsynaptic weight (7 increments). Iterations representing all possible levels of the aforementioned cellular level lesions were run: that is, we exhaustively searched the parameter space, running 10 6 13 6 7 = 910 iterations in total. Each iteration consisted of three trials; in each, the network was driven at a given frequency (20, 30, or 40 Hz), and a simulated EEG was written to file and was analyzed via fast Fourier transform (FFT) to determine which frequencies were present, and their relative power. The degree to which this matched the pattern seen in the clinical studies (i.e., the degree to which there was a specific deficit in 40 Hz response) was quantified using the illness metric, which ranged from 1 (most schizophrenic) to 0, as described in Methods. Figure 2 graphically depicts the results of these trials. Clearly, a number of points produce schizophrenia-like results. There is a prominent cluster centered at a point characterized by an NMDA decrease of 30%, a spine density decrease of 30%, and a GABA deficit of 0 (which we will call the ‘‘primary point’’). There is another point characterized by an NMDA decrease of 45%, a spine density decrease of 30%, and a GABA system defect of (–37.5, + 30%), as defined in Methods (which we will call the ‘‘secondary point’’). For the primary point, power spectra of oscillatory activity in response to 20, 30, and 40 Hz drive is shown in Fig 1C, in comparison with control behavior (Figs 1A, B). 40 Hz response is decreased to about 24% below the control case, calculated as an average of 20 simulated control patients; 20 and 30 Hz responses are roughly the same as those of controls. This again was confirmed by re-running the model with 20 simulated schizophrenic patients. To more formally test these effects, we ran a Group (control, schizophrenic) x Frequency (20 Hz, 30 Hz, 40 Hz) ANOVA. Both the main effects of Frequency (F [2, 80] = 4812.6, p , 0.001, Greenhouse-Geisser correction: e = 0.87) and Group (F [2, 80] = 289.05, p , 0.001, e = 0.87) were significant. Critically, these effects were qualified by a significant Group by Frequency interaction, driven by greatest group differences at 40 Hz (see Fig 1D). Because groups differed in all three frequencies, a set of hierarchical regression analyses was run to test the specificity of the findings. Specifically, in the first regression, we entered power at 20 and 30 Hz in the first step, and Group (dummy-coded) in the second step, in order to predict power at 40 Hz. The model was significant, indicating that Group predicted 40 Hz activity when controlling for power at 20 and 30 Hz ( D R 2 = 0.101, D F [1,38] = 77.64, p , 0.001). Critically, when entering 40 in the first step, Group predicted neither 30 Hz power ( D R 2 = 0.003, D F [1,38] = 0.81, p = 0.375) nor 20 Hz power ( D R 2 = 0.025, D F [1,38] = 0.81, p = 0.193). Thus, group differences were specific to 40 Hz. In an attempt to understand the relative contributions of each of these neural level abnormalities individually to the functioning of the system, we performed a ‘‘partial derivative’’ analysis for each. That is, we examined the overall behavior of the system in response to one lesion at a time, holding the others constant. The results are shown in Figures 3 and 4. Significantly, no single abnormality alone accounts for the findings. What neural interactions caused the primary point, with a specific deficit in response to 40 Hz drive, to arise, and how did this differ from the secondary point? To answer this, we examined simulated EEG traces and histograms of spiking activity from both cases. Of note, for 40 Hz drive, the EEG traces of the primary point shows a depression of every other peak, effectively creating a mix of 20 and 40 Hz activity, and a decrease in the 40 Hz response (Fig 5). The spiking probability histograms for the primary and secondary points show averages over two cycles at a time, in an attempt to reveal differential contributions from inhibitory interneurons in alternating cycles. Notably, while both points produce a schizophrenic pattern of oscillatory activity when analyzed at the power spectrum level, there are clear differences in underlying neurophysiologic dynamics, as shown in Figure 5C and D. Panel C clearly shows alternating pyramidal cell activity across cycles; it also reveals a somewhat less marked alternation of PV + cell activity, as well as modest cycle-to-cycle CR + activity imbalance. Panel D (secondary point) shows a general damping down of pyramidal cell activity that is roughly constant across cycles, and little cycle-to-cycle variation in PV + or CR + activity. Negative controls: An important goal of this work is to develop a model that can identify novel pharmacologic agents that can potentially treat the symptoms of schizophrenia. Such a model should also be capable of rejecting current medications known to have no known antipsychotic efficacy. Therefore, when applied to the schizophrenic model they should not produce normalization of oscillatory powers. These then serve as ‘‘negative controls’’. We chose the test agents described below based on the following considerations: (a) Their neurophysiologic effects are well-characterized, and they can therefore be included in the model in a rigorous manner. (b) There is a published literature documenting their non-effectiveness in the illness. (c) There is a history of clinical use, and their effects on (control) subject EEG activity are known. For these trials, the primary point schizophrenic model, as defined above, is used as our test system. In separate trials, we apply the effects of phenytoin, an antiepileptic drug that has a specific effect at the Na + channel (Fig 6); nifedipine, an antihypertensive that acts by blocking calcium channels (Fig 7); and ampakines, medications that allosterically bind to AMPA receptors and increase their activity [42–44], both by increasing maximum conductance and by increasing the decay time constant (Fig 8). In no case does the agent correct the 40 Hz deficit. Moreover, when applied to our unaffected model, they produce EEG changes comparable to those seen in the clinical literature. This serves as additional confirmation of the validity of the computational model. Virtual medication trials: Many experimental medications for schizophrenia act through one particular mechanism of action. However, it is possible that adjustment of a number of cellular level ‘‘levers’’ would be necessary to return the system to a healthy equilibrium state. We examined five such effects, applying each to the model individually, and in combinations with others. Broadly, these mechanisms fall into two categories: those that can be effected with currently known medications (discussed under AMPA g max , alpha2, and NMDA sections below); and those that, to the knowledge of these authors, cannot be implemented with any currently known agent (discussed under AMPA t 2 and CR + projection below)—if effective, these would then represent potential targets for drug development efforts. The manner in which these were modeled is briefly described below, and are summarized in Table 1. AMPA g max . The effect of drugs that boost AMPA current were modeled by increasing the maximum conductance (g max ) of the AMPA synaptic current. We did this in increments of 20%, increasing g max from 0% to 80%. Alpha 2 . The experimental drug MK-0777 (also known as TPA- 023) has partial agonist activity at GABA A receptors, specifically acting at the a 2 and a 3 subtypes [45], and has shown partial effectiveness in treating some of the cognitive symptoms of schizophrenia [46]. These receptor subtypes are located on the initial segment of pyramidal cells, and are thought to be associated with the inhibitory projections of chandelier cells. While dissociation constants have been quantified [45], to our knowledge, MK-0777’s quantitative effect on GABA channel conductance has not been. Electrophysiological studies with mutant mice (knock-in mice selectively expressing GABA A a 2 , a 3 , etc subtypes), has indicated that benzodiazepines can increase a 2 and a 3 conductance by as much as 50% [47]. Thus, to capture a plausible range of drug- induced conductance changes, we selectively increased the g max of the GABA channels that synapse on the initial segment of pyramidal cells in increments of 15%, increasing g max from 0 to 60%, in five gradations. MK-0777 is one of the few cases in which a drug was tested in an experimental paradigm that involved schizophrenic patients and measurement of gamma band oscillations [46]. In this work, schizophrenic patients taking this drug showed a trend toward greater gamma band activity, which did not reach statistical significance at the p = 0.05 level (their Figure 1, p. ...