This will be a tutorial style talk on mean-field models and their variations, with some analysis methods presented, and examples from different areas of neuroscience

Carmen Canavier, LSU Health Sciences Center New Orleans
Implications of Models of Dopamine Neurons at the Cellular Level for Systems Level Models

Abnormal dopaminergic signaling has been implicated in schizophrenia . Some salient hypotheses regarding midbrain dopamine neurons and explored in our cellular models are as follows: 1) In the absence of afferent input, dopamine neurons exhibit spontaneous regular pacemaker firing; this background level of tonic firing ensures that dopaminergic signaling is bidirectional so that both positive and negative signals regarding the difference between expected and actual rewards can be transmitted. 2) Dopamine neurons can fire rapid bursts only in the presence of NMDA synaptic activation. 3) In vivo, a balanced state between excitation and inhibition enables tonic single spike firing and an imbalance results in a phasic signal in the form of a burst. 4) The complex contributions of the intrinsic currents to the neural dynamics allow for rich modulatory possibilities regarding the propensity of these neurons to transmit tonic or phasic signals.

Dopamine neurons in vitro go into depolarization block at applied current levels that are not sufficient to elicit the high frequency firing observed during bursts. The role of NMDA synaptic activation in bursting and the mechanism by which the limitation on firing rate is circumvented has been hotly debated. Also, induction of depolarization block in dopamine neurons has been correlated with the efficacy of antipsychotic drugs, and antipsychotics have been shown to rapidly induce depolarization block in a developmental rat model of schizophrenia. Applied depolarization does not cause neurons to enter depolarization block by simply biasing the cell above the region in which the sodium current activates regeneratively. Instead, the spike threshold gradually increases after pulse onset causing the interspike intervals to increase until the final depolarizing prepotential fails to reach threshold. Our modeling suggests that only a second slow component of the inactivation of the sodium channel can drive a pacemaker into depolarization block in this manner, and only a regenerative inward current like the NMDA current can circumvent this limitation. Finally, since antipsychotic drugs in general block the ether-a-gogo-related (ERG) potassium current, we examine the role of this current in limiting episodes of depolarization block.

Albert Compte (IDIBAPS Spain)
Serotonin regulates working memory function non-monotonically in a computational network model: implications for schizophrenia

Independently, both serotonin and working memory (WM) have been associated with the prefrontal cortex. On the one hand, serotonergic neurons in the raphe nucleus project directly to prefrontal cortex, where serotonergic receptors are particularly enriched. On the other hand, electrophysiological and neuroimaging studies associate prefrontal cortex activations to successful WM performance. Schizophrenia provides another link between serotonin and WM: many antipsychotics target dominantly serotonin receptors, and WM impairment is considered to be a core deficit in schizophrenia. However, a direct association between serotonin and WM has proved elusive in psycho-pharmacological studies. I will present a computational network model for spatial WM in the prefrontal cortex that reveals a direct relationship between serotonin and WM. We found that serotonin modulated the network's WM performance non-monotonously, following an inverted U-shape. This could partly explain that only weak behavioral effects of serotonin treatment were found in previous WM studies. Our simulations showed that WM errors committed with low and high tonic serotonin were due to different network dynamics instabilities, suggesting that these two conditions could be distinguished experimentally based on the response confidence declared in error trials, and on prefrontal activation contrasts in neuroimaging studies. Finally, we tested the antipsychotic effects of serotonin receptor manipulations in network models with synaptic imbalances suggested by the GABAergic and glutamatergic hypotheses for schizophrenia. We found that WM deficits were attenuated by acting on serotonergic receptors, but re-emerged in high dosage treatments. This non-monotonicity was again resolved in our model by separating WM errors based on the declared response confidence. Our study underscores the relevance of identifying different types of error trials in WM tasks in order to reveal the association between neuromodulatory systems and WM, and the benefits of serotonergic treatments for cognitive deficits in schizophrenia.

Bard Ermentrout, University of Pittsburgh
Oscillations, synchrony, and disease: What can computational models tell us?

In this talk, I will survey several recent resutls related to the genesis of rhythms in the nervous system, particularly in the so-called gamma range. I will first describe some mechanisms and aspects of rhythms which depend on the interactions between excitatory and inhibitory neurons. Next I will explore what happens when there are changes in the circuitry and some ways in which the rhythms can break down. I will connect this breakdown in rhythms to symptomology in schizophrenia. Finally, if time permits, I will suggest a new role for oscillations in working memory.

Nancy Kopell, Boston University
Brain rhythms, modulation and schizophrenia

It is well known that there are changes in brain rhythms in those who have schizophrenia (SZ). However, the mechanistic causes of those changes and the functional consequences of them are far less understood. In this talk, I will discuss a few case histories to emphasize the subtlety of the changes, with potentially very large functional consequences. These will include effects on network behavior of changes in NMDA receptor function and change in cholinergic activation. The examples all concern changes in SZ to the activity of various classes of interneurons.

Evelyn K. Lambe, University of Toronto
Developmental vulnerabilities in prefrontal attention circuitry: Relevance for cognitive deficits in schizophrenia

The cognitive symptoms of schizophrenia are disabling and are not well addressed by current treatments. These symptoms, which include attention deficits, arise early in the illness and suggest aberrant maturation of the prefrontal cortex. Recent work shows that corticothalamic neurons of prefrontal cortex and their cholinergic inputs are essential for normal attention under demanding conditions. I will discuss how disruptions during development result in long-lasting changes both to the structure of these neurons and to the kinetics of their excitation by acetylcholine. Given the precise timing and co-ordination of signals required for optimal performance on attention tasks, the vulnerability of corticothalamic feedback neurons to aberrant development points to a cellular mechanism relevant to the cognitive deficits of schizophrenia.

David A. Lewis, University of Pittsburgh
A Neural Substrate for Impaired Cortical Network Oscillations and Cognitive Dysfunction in Schizophrenia

Deficits in cognitive control, the ability to adjust thoughts or behaviors in order to achieve goals, are now considered to be a core feature of schizophrenia and to be the best predictor of long-term functional outcome. Cognitive control depends on the coordinated activity of a number of brain regions, including the dorsolateral prefrontal cortex (DLPFC). Subjects with schizophrenia exhibit altered activation of the DLPFC, and reduced frontal lobe gamma band (~40 Hz) oscillations, when performing tasks that require cognitive control. Because gamma oscillations require inhibition from GABA interneurons, alterations in DLPFC GABA neurotransmission have been hypothesized to contribute to impaired gamma oscillations and cognition in schizophrenia. This presentation will review the convergent lines of evidence that support this hypothesis and discuss how these findings can be integrated with other observations of altered excitatory neurotransmission. This integration suggests a mechanistic model of "re-set" excitatory-inhibitory balance in the DLPFC that both underlies the impaired gamma oscillations and accounts for the course of functional disturbances in individuals with schizophrenia.

John Lisman, Brandeis University
Network Mechanisms and Delta Frequency Oscillations that Underly the Psychotic Break in Schizophrenia

Delta oscillations in the awake state are elevated in schizophrenia (SZ) [1, 2]. In contrast to the gamma/beta oscillation abnormalities, which are a risk factor for the disease (present in unaffected relatives), the delta abnormality correlates more closely with the disease itself [3].
The thalamus is involved in delta generation, sensory gating, and sleep spindles, all of which are abnormal in SZ. Furthermore, in SZ there is a reduction in thalamic size and an increase in the volume of the adjacent third ventricle; these correlate with the delta abnormality and negative symptoms of SZ [4, 5]. Experiments in rats show that NMDAR antagonist (APV or Ketamine), when applied only to the thalamus, causes delta in the thalamus and cortex. Delta occurs because antagonist blocks NR2C channels, which contribute to resting potential because they have low Mg block and are partially activated by ambient glutamate. The resulting hyperpolarization deinactivates T-type Ca channels, which then generate delta.
The development of SZ occurs as a sudden "psychotic break". The interneuron abnormalities (and resulting gamma/beta abnormalities [3]) exist before the break and may predispose a loop of brain structures to go into positive feedback. When this occurs, delta oscillations and psychosis are generated. It was previously proposed that this loop involves the excitation of the hippocampal CA1 region (known to be selectively activated in SZ) by the thalamus (specifically the nucleus reuniens), the excitation of the VTA by the hippocampus, and the excitation of the thalamus by the VTA [6]. Further evidence for thalamic excitation of CA1 has recently been obtained [7]. The psychotic break may occur when stress (which releases dopamine) pushes the loop above the threshold for positive feedback. Consistent with a bistable system, patients normalized by antipsychotic drugs remain normal when taken off the drug, but have relapses when subsequently stressed.
In SZ, delta oscillations appear to occur in only small subregions of the thalamus, cortex and hippocampus. How might this cause "first rank" SZ symptoms, many of which involve agency, the sense of what actions are one's own? The reuniens carries "corollary discharge" about action choices from the medial PFC to the temporal lobe. The block of this information flow by delta could result in loss of "agency".
References:
1. Itoh, T., et al., LORETA analysis of three-dimensional distribution of delta band activity in schizophrenia: Relation to negative symptoms. Neuroscience research, 2011. 70(4): p. 442-8.
2. Schulman, J.J., et al., Imaging of thalamocortical dysrhythmia in neuropsychiatry. Frontiers in human neuroscience, 2011. 5: p. 69.
3. Venables, N.C., E.M. Bernat, and S.R. Sponheim, Genetic and disorder-specific aspects of resting state EEG abnormalities in schizophrenia. Schizophrenia bulletin, 2009. 35(4): p. 826-39.
4. Sponheim, S.R., et al., Clinical and biological concomitants of resting state EEG power abnormalities in schizophrenia. Biological psychiatry, 2000. 48(11): p. 1088-97.
5. Shepherd, A.M., et al., Systematic meta-review and quality assessment of the structural brain alterations in schizophrenia. Neuroscience and biobehavioral reviews, 2012. 36(4): p. 1342-56.
6. Lisman, J.E., et al., A thalamo-hippocampal-ventral tegmental area loop may produce the positive feedback that underlies the psychotic break in schizophrenia. Biological psychiatry, 2010. 68(1): p. 17-24.
7. Zhang, Y., et al., NMDAR antagonist action in thalamus imposes delta oscillations on the hippocampus. Journal of neurophysiology, 2012.

William W Lytton, SUNY Downstate Medical Center
Schizophrenia: a failure of homeostasis?

Mental health reflects homeostatic balances of multiple dynamical processes at diverse time constants where imbalance will disrupt emotional or cognitive competence. One of these homeostatic influences balances the spectral power of oscillations that are thought to underlie binding: binding of percepts, binding of percept with memory, and binding of the binder itself (i.e. theta organizing gamma). Homeostatic failure fits with the hypothesis that schizophrenia involves a failure of cognitive coordination, manifesting in the core cognitive deficits of this disease. Failures of neural coordination would produce these failures of cognitive coordination, as ensembles either fragment (fragmentation of experience, dissociation, disorganized thought) or bind too tightly (delusions, autistic thought). We have utilized moderately detailed models of neocortex (event-driven, laminar model) and archicortex (CA3, multicompartmental model with 3 cell types). Both models demonstrate frequency homeostasis, where alterations in network drive changes the power in characteristic frequencies without substantially shifting these frequencies. Given a failure of homeostasis, we hypothesize that secondary homeostatic mechanisms will tend to overshoot the set point in both directions, yielding alternation of too much gamma coordination and too little. We then measured the relation of gamma power with information transfer. In simulations of ketamine effect on CA3, high gamma arose from strong excitatory synaptic connections and resulted in reduced information flow-through with augmented information provided by the network itself. This would be a gamma rut that would provide cognitive processing with excessive internal information, reducing reactivity to the external world. By contrast, reduction in gamma coordination, associated with increased information flow-through, would be associated with a disorganization due to external stimuli
being unconnected with prior experience. This might also be associated with internal stimuli that float free of their efference copy so as to be falsely attributed to external source (hallucination) or external control (delusion of control).

Edmund T Rolls, Oxford Centre for Computational Neuroscience, University of Oxford
Instability in attractor neural network dynamics and schizophrenia

Building on a theory of hippocampal function in episodic memory, and on a stochastic dynamics approach to integrate-and-fire neuronal attractor networks that can implement short and long term memory, implications for understanding the stability of such systems in schizophrenia are described. A decrease in the NMDA receptor conductances, consistent with hypofunction of the NMDA receptor system in schizophrenia, reduces the depth of the attractor basins, decreases the stability of short term memory states and increases distractibility. The cognitive symptoms of schizophrenia such as distractibility, working memory deficits or poor attention could be caused by this instability of attractor states in prefrontal cortical networks. Lower firing rates are also produced, and in the orbitofrontal and anterior cingulate cortex could account for the negative symptoms including a reduction of emotion. Decreasing the GABA as well as the NMDA conductances produces not only switches between the attractor states, but also jumps from spontaneous activity into one of the attractors. This is related to the positive symptoms of schizophrenia including delusions, paranoia, and hallucinations, which may arise because the basins of attraction are shallow and there is instability in temporal lobe memory networks, leading thoughts to move too freely round the attractor energy landscape.
Loh,M., Rolls,E.T. and Deco,G. (2007) A dynamical systems hypothesis of schizophrenia. PLoS Computational Biology 3 (11): e228.
Loh,M., Rolls,E.T. and Deco,G. (2007) Statistical fluctuations in attractor networks related to schizophrenia. Pharmacopsychiatry 40: S78-84.
Rolls,E.T., Loh,M., Deco,G. and Winterer,G. (2008) Computational models of schizophrenia and dopamine modulation in the prefrontal cortex. Nature Reviews Neuroscience 9: 696-709.
Rolls,E.T. and Deco,G. (2010) The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function. Oxford University Press: Oxford.
Rolls,E.T. and Deco,G. (2011) A computational neuroscience approach to schizophrenia and its onset.
Neuroscience and Biobehavioral Reviews 35: 1644-1653.
Rolls,E.T. (2012) Glutamate, obsessive-compulsive disorder, schizophrenia, and the stability of cortical attractor neuronal networks. Pharmacology, Biochemistry and Behavior 100: 736-751.