Genetic evidence for role of integration of fast and slow neurotransmission in schizophrenia.

The most recent genome-wide association studies (GWAS) of schizophrenia (SCZ) identified hundreds of risk variants potentially implicated in the disease. Further, novel statistical methodology designed for polygenic architecture revealed more potential risk variants. This can provide a link between individual genetic factors and the mechanistic underpinnings of SCZ. Intriguingly, a large number of genes coding for ionotropic and metabotropic receptors for various neurotransmitters-glutamate, γ-aminobutyric acid (GABA), dopamine, serotonin, acetylcholine and opioids-and numerous ion channels were associated with SCZ. Here, we review these findings from the standpoint of classical neurobiological knowledge of neuronal synaptic transmission and regulation of electrical excitability. We show that a substantial proportion of the identified genes are involved in intracellular cascades known to integrate 'slow' (G-protein-coupled receptors) and 'fast' (ionotropic receptors) neurotransmission converging on the protein DARPP-32. Inspection of the Human Brain Transcriptome Project database confirms that that these genes are indeed expressed in the brain, with the expression profile following specific developmental trajectories, underscoring their relevance to brain organization and function. These findings extend the existing pathophysiology hypothesis by suggesting a unifying role of dysregulation in neuronal excitability and synaptic integration in SCZ. This emergent model supports the concept of SCZ as an 'associative' disorder-a breakdown in the communication across different slow and fast neurotransmitter systems through intracellular signaling pathways-and may unify a number of currently competing hypotheses of SCZ pathophysiology.

Generation and annihilation of localized persistent-activity states in a two-population neural-field model.

We investigate the generation and annihilation of persistent localized activity states, so-called bumps, in response to transient spatiotemporal external input in a two-population neural-field model of the Wilson-Cowan type. Such persistent cortical states have been implicated as a biological substrate for short-term working memory, that is, the ability to store stimulus-related information for a few seconds and discard it once it is no longer relevant. In previous studies of the same model it has been established that the stability of bump states hinges on the relative inhibitory constant τ, i.e., the ratio of the time constants governing the dynamics of the inhibitory and excitatory populations: persistent bump states are typically only stable for values of τ smaller than a critical value τcr. We find here that τ is also a key parameter determining whether a transient input can generate a persistent bump state (in the regime where τ<τcr) or not. For small values of τ generation of the persistent states is found to depend only on the overall strength of the transient input, i.e., as long as the magnitude and duration of the excitatory transient input are larger and/or long enough, the persistent state will be activated. For higher values of τ we find that only specific combinations of amplitude and duration leads to persistent activation. For the corresponding annihilation process, no such delicate selectivity on the transient input is observed.

Response of the difference-of-Gaussians model to circular drifting-grating patches.

Forty years ago R.W. Rodieck introduced the Difference-of-Gaussians (DOG) model, and this model has been widely used by the visual neuroscience community to quantitatively account for spatial response properties of cells in the retina and lateral geniculate nucleus following visual stimulation. Circular patches of drifting gratings are now regularly used as visual stimuli when probing the early visual system, but for this stimulus type the mathematical evaluation of the DOG-model response is significantly more complicated than for moving bars, full-field drifting gratings, or circular flashing spots. Here we derive mathematical formulas for the DOG-model response to centered circular patch gratings. The response is found to be given as the difference between two summed series, where each term in the series involves the confluent hypergeometric function. This function is available in commonly used mathematical software, and the results should thus be readily applicable. Example results illustrate how a strong surround suppression in area-summation curves for iso-luminant circular spots may be reversed into a surround enhancement for circular patch gratings. They also show that the spatial-frequency response changes from band-pass to low-pass when going from the full-field grating situation to the situation where the patch covers only the receptive-field center.

Linear mechanistic models for the dorsal lateral geniculate nucleus of cat probed using drifting-grating stimuli.

Experiments with sinusoidal visual stimuli in the early visual pathway have traditionally been interpreted in terms of descriptive filter models. We present an alternative mechanistic approach for interpretation of this type of data recorded from X cells in the dorsal lateral geniculate nucleus (dLGN) of cat. A general, linear, rate-based mathematical expression for the geniculate transfer ratio, i.e. the ratio between the first-harmonic components of the output of a geniculate relay cell and its retinal input, is derived. In linear theory this ratio is independent of the signal processing occurring at the retinal level. Further, the ratio is straightforwardly accessible in experiments due to the presence of S-potentials, representing the retinal input, in extracellular recordings from dLGN. The expression accounts for feedforward inputs from retina and intrageniculate interneurons as well as feedback inputs from cortex and the thalamic reticular nucleus and can be used to experimentally test different mechanistic models for the geniculate circuitry. Two examples of this are considered: a purely feedforward model incorporating relay cell inputs from retinal ganglion cells and interneurons, and a model including cortical feedback inhibition of relay cells via intrageniculate interneurons.

Mathematical models for the spatial receptive-field organization of nonlagged X-cells in dorsal lateral geniculate nucleus of cat.

Spatial receptive fields of relay cells in dorsal lateral geniculate nucleus (dLGN) have commonly been modeled as a difference of two Gaussian functions. We present alternative models for dLGN cells which take known physiological couplings between retina and dLGN and within dLGN into account. The models include excitatory input from a single retinal ganglion cell and feedforward inhibition via intrageniculate interneurons. Mathematical formulas describing the receptive field and response to circular spot stimuli are found both for models with a finite and an infinite number of ganglion-cell inputs to dLGN neurons. The advantage of these models compared to the common difference-of-Gaussians model is that they, in addition to providing mathematical descriptions of the receptive fields of dLGN neurons, also make explicit contributions from the geniculate circuit. Moreover, the model parameters have direct physiological relevance and can be manipulated and measured experimentally. The discrete model is applied to recently published data (Ruksenas et al., 2000) on response versus spot-diameter curves for dLGN cells and for the retinal input to the cell (S-potentials). The models are found to account well for the results for the X-cells in these experiments. Moreover, predictions from the discrete model regarding receptive-field sizes of interneurons, the amount of center-surround antagonism for interneurons compared to relay cells, and distance between neighboring retinal ganglion cells providing input to interneurons, are all compatible with data available in the literature.