Pathological effects of cortical architecture on working memory in schizophrenia.

Neural connectivity of the prefrontal cortex is essential to working memory. Reduction of prefrontal connectivity and abnormal prefrontal dopamine modulation are common characteristics associated with schizophrenia. Two experiments separately modeled the effects of exaggerated pruning and of synaptic depression to imitate schizophrenic performance in a prefrontal neural network. In the first model, effects of cortical pruning were simulated with a set of scale-free networks of neurons and compared with empirical results from the Sternberg working memory task. The second set of simulations were based on the synaptic theory of working memory. Simulations of this model measured memory duration in relation to synaptic facilitation and depression constants and in relation to the level of neural connectivity. In the first set of simulations, modulating levels of cortical pruning resulted in a gain or loss in accuracy and speed of memory recollection. In the second set of simulations, increased facilitation time constants and decreased inhibitory time constants resulting in longer memory durations, and overly connected networks resulted in very low memory durations. In the first model, the decline in memory performance can be attributed to the emergence of pathological memory behavior brought about by the warping of the basins of attraction. Collectively, the simulations demonstrate that a reduction of prefrontal cortical hubs can lead to schizophrenia like performance in neural networks, and may account for pathological working memory in the disorder.

From systems biology to dynamical neuropharmacology: proposal for a new methodology.

The concepts and methods of systems biology are extended to neuropharmacology in order to test and design drugs for the treatment of neurological and psychiatric disorders. Computational modelling by integrating compartmental neural modelling techniques and detailed kinetic descriptions of pharmacological modulation of transmitter-receptor interaction is offered as a method to test the electrophysiological and behavioural effects of putative drugs. Even more, an inverse method is suggested as a method for controlling a neural system to realise a prescribed temporal pattern. In particular, as an application of the proposed new methodology, a computational platform is offered to analyse the generation and pharmacological modulation of theta rhythm related to anxiety.

Modulation of septo-hippocampal Theta activity by GABAA receptors: an experimental and computational approach.

Theta frequency oscillation of the septo-hippocampal system has been considered as a prominent activity associated with cognitive function and affective processes. It is well documented that anxiolytic drugs diminish septo-hippocampal oscillatory Theta activity contributing to their either therapeutic or unwanted side effects. In the present experiments we applied a combination of computational and physiological techniques to explore the functional role of GABAA receptors in Theta oscillation. In electrophysiological experiments extracellular single unit recordings were performed from medial septum/diagonal band of Broca with simultaneous hippocampal (CA1) electroencephalogram (EEG) recordings from anesthetized rats. Neurotransmission at GABAA receptors were modulated by means of pharmacological tools: the actions of the GABAA receptor positive allosteric modulator diazepam and inverse agonist/negative allosteric modulator FG-7142 were evaluated on septo-hippocampal activity. Systemic administration of diazepam inhibited, whereas FG-7142 enhanced Theta oscillation of septal neurons and hippocampal EEG Theta activity. In parallel to these experimental observations, a computational model has been constructed by implementing a septal GABA neuron model with a CA1 hippocampal model containing three types of neurons (including oriens and basket interneurons and pyramidal cells; latter modeled by multicompartmental techniques; for detailed model description with network parameters see online addendum: http://geza.kzoo.edu/theta). This connectivity made the network capable of simulating the responses of the septo-hippocampal circuitry to the modulation of GABAA transmission, and the presently described computational model proved suitable to reveal several aspects of pharmacological modulation of GABAA receptors. In addition, computational findings indicated different roles of distinctively located GABAA receptors in theta generation.

Hippocampal rhythm generation: gamma-related theta-frequency resonance in CA3 interneurons.

During different behavioral states different population activities are present in the hippocampal formation. These activities are not independent: sharp waves often occur together with high-frequency ripples, and gamma-frequency activity is usually superimposed on theta oscillations. There is both experimental and theoretical evidence supporting the notion that gamma oscillation is generated intrahippocampally, but there is no generally accepted view about the origin of theta waves. Precise timing of population bursts of pyramidal cells may be due to a synchronized external drive. Membrane potential oscillations recorded in the septum are unlikely to fulfill this purpose because they are not coherent enough. We investigated the prospects of an intrahippocampal mechanism supplying pyramidal cells with theta frequency periodic inhibition, by studying a model of a network of hippocampal inhibitory interneurons. As shown previously, interneulrons are capable of generating synchronized gamnma-requency action potential oscillations. Exciting the neurons by periodic current injection, the system could either be entrained in an oscillation with the frequency of the inducing current or exhibit in-phase periodic changes at the frequency of single cell (and network) activity. Simulations that used spatially inhomogeneous stimulus currents showed antiphase frequency changes across cells, which resulted in a periodic decrease in the synchrony of the network. As this periodic change in synchrony occurred in the theta frequency range, our network should be able to exhibit the theta-frequency weakening of inhibition of pyramidal cells, thus offering a possible mechanism for intrahippocampal theta generation.

Depolarizing/hyperpolarizing effects of the GABA(A) synapse have a beneficial role in synaptic weight resetting in the hippocampus.

To eliminate undesirable memory traces from the short-term memory system, it is a crucial question to reorganize the activity induced synaptic efficiency. Here we suggest a possible solution for this mechanism. In the first part of the paper we demonstrate, that under different physiological conditions even in the case of adult animals, the GABA(A) synapse may mediate a depolarizing effect on the membrane potential. Considering the GABA(A) receptor-mediated complex effects on the membrane potential of adult mammalian central neurons we raised the question of the properties of the network, which has elements in the synaptic weight matrix with changing signs. The second part pinpoints the beneficial learning ability of such a network.

Précis of Neural organization: structure, function, and dynamics.

NEURAL ORGANIZATION: Structure, function, and dynamics shows how theory and experiment can supplement each other in an integrated, evolving account of the brain's structure, function, and dynamics. (1) STRUCTURE: Studies of brain function and dynamics build on and contribute to an understanding of many brain regions, the neural circuits that constitute them, and their spatial relations. We emphasize Szentágothai's modular architectonics principle, but also stress the importance of the microcomplexes of cerebellar circuitry and the lamellae of hippocampus. (2) FUNCTION: Control of eye movements, reaching and grasping, cognitive maps, and the roles of vision receive a functional decomposition in terms of schemas. Hypotheses as to how each schema is implemented through the interaction of specific brain regions provide the basis for modeling the overall function by neural networks constrained by neural data. Synthetic PET integrates modeling of primate circuitry with data from human brain imaging. (3) DYNAMICS: Dynamic system theory analyzes spatiotemporal neural phenomena, such as oscillatory and chaotic activity in both single neurons and (often synchronized) neural networks, the self-organizing development and plasticity of ordered neural structures, and learning and memory phenomena associated with synaptic modification. Rhythm generation involves multiple levels of analysis, from intrinsic cellular processes to loops involving multiple brain regions. A variety of rhythms are related to memory functions. The Précis presents a multifaceted case study of the hippocampus. We conclude with the claim that language and other cognitive processes can be fruitfully studied within the framework of neural organization that the authors have charted with John Szentágothai.

Single cell and population activities in cortical-like systems.

Dynamics of single cells and large cell populations are the subject of investigation by using differently detailed models. Multicompartmental modeling techniques are used to systematically investigate the location-dependent effects of GABA-ergic inhibition on the firing patterns of hippocampal pyramidal cells. Appearance of stochastic resonance in a model of mitral and granule cells of the olfactory bulb is demonstrated by using a single-compartmental model approach. Spatial propagation of synchronized activities in hippocampal slices are studied by a model of large neural populations.

Statistical model of the hippocampal CA3 region. I. The single-cell module: bursting model of the pyramidal cell.

A model with intermediate complexity is introduced to reproduce the basic firing modes of the CA3 pyramidal cell. Our model consists of a single compartment, has two variables (membrane potential and internal calcium concentration), and involves two separate stages for interspike mechanisms and firing. Interspike dynamics is governed by voltage- and calcium-dependent ionic channels but no channel kinetics are provided. This model is suitable to be included in our statistical population model (Part II, following paper). Bifurcation analysis reveals that interspike dynamics rather than sodium firing has the dominant role in the control of bursting/nonbursting behavior.

Statistical model of the hippocampal CA3 region II. The population framework: model of rhythmic activity in the CA3 slice.

A statistical model is given to describe the electrical activity patterns of large neural populations of the hippocampal CA3 region. A continuous model has been formalized to describe the statistical processes governing the interactions within and between neural fields. The system of partial differential equations contains diffusion terms which determine the evolution of second moments of the probability distribution functions. The model is supplemented with a differential description of post-synaptic potentials. The discretization procedure has been designed so as to make the discrete equations scaling invariant. Population activities as well as underlying single-cell voltages are simulated during normal and epileptiform activities in the hippocampal CA3 slice. It is demonstrated that our model can reproduce electrophysiological phenomena characteristic to both single-cell and population activities. Specifically, fully synchronized population bursts, synchronized synaptic potentials, and low amplitude population oscillation were obtained.

Dynamic information processing in natural and artificial olfactory systems.

A new strategy for building artificial gas sensing systems is suggested based on knowledge of the dynamic response mechanism of the olfactory system. Difficulties with the processing of time-dependent inputs by neural networks are discussed.

On the role of self-excitation in the development of topographic order in the visual system of the frog.

A two-level model is presented for explaining the development of the topographically ordered retinotectal connections of the visual system of the frog. The columnar structure of the tectum were taken into account explicitly. Simulations suggest that the self-excitatory intracolumnar connections play an important role in the formation of the topography. In the case of self-excitation the system is able to recognize the topology of the visual field by the continuity of the object's movement.

Rhythmogenesis in single cells and population models: olfactory bulb and hippocampus.

Dynamics of single cells, small networks and large cell populations are the subject of investigation. The generation and propagation of action potentials in the two major cell types of the olfactory bulb, i.e. in the mitral and granule cells, are simulated by multi-compartmental modeling techniques. The specific effects of the individual ionic currents, the propagation of the signals through the compartments, and dynamic phenomena occurring in small networks (such as synchronized oscillation due to excitatory and inhibitory coupling) have been demonstrated. A statistical model is given to describe the electrical activity patterns of large neural populations. The model is applied for describing the CA3 region of the hippocampus by incorporating some basic electrophysiological properties of hippocampal pyramidal and inhibitory neurons. Population activities as well as underlying single cell voltages are simulated during population bursts in the model of disinhibited hippocampal CA3 slice.

Multicompartmental modeling of neural circuits in the olfactory bulb.

The generation and propagation of action potentials in the excitatory and inhibitory cell types of the olfactory bulb are simulated by applying multi-compartmental modeling technique. Detailed models of the main cell types of the olfactory bulb have been presented previously. Further simulations on granule and periglomerular cells have been done to find proper parameters matching to the physiological recordings. Elementary synaptic interactions and dynamic behaviour of small networks of excitatory and inhibitory neurons have been studied. To investigate the relationship between the anatomical structure of the neural circuits of whole olfactory bulb and the generated firing patterns, further series of simulations have been done.

The brain as a hermeneutic device.

An attempt has been made to reconcile the 'device approach' and the 'philosophical approach' to the brain. Systems exhibiting high structural and dynamic complexity may be candidates of being hermeneutic devices. The human brain, which is a structurally and dynamically complex device, not only perceives but also creates new reality: it is a hermeneutic device.

Neurodynamic system theory: scope and limits.

This paper proposes that neurodynamic system theory may be used to connect structural and functional aspects of neural organization. The paper claims that generalized causal dynamic models are proper tools for describing the self-organizing mechanism of the nervous system. In particular, it is pointed out that ontogeny, development, normal performance, learning, and plasticity, can be treated by coherent concepts and formalism. Taking into account the self-referential character of the brain, autopoiesis, endophysics and hermeneutics are offered as elements of a poststructuralist brain (-mind-computer) theory.

Mathematical description and computer simulation of retinal cometlike afterimages: a modified neural equation with stability analysis.

A mathematical model for the spatiotemporal description of a well-known psychophysical phenomenon, the cometlike afterimage effect (CLAIE), is presented. The CLAIE occurs when a bright circular light spot moves slowly in the peripheral human retina. Under these conditions, the leading edge of the dot looks circular, but the trailing edge becomes elongated like a comet's tail whose length increases with speed and luminance, and the illusion is more prominent for photopic backgrounds. This cometlike motion smear is described on the basis of the temporal responsiveness and adaptation of rods. The model is an extension of an existing neural model of M. N. Oguztöreli et al., with an additional term that allows prolonged saturation and long decay time following exposure to intense stimuli, and these effects are held responsible for the cometlike smear. The model predicts the response of photoreceptors through a nonlinear ordinary integrodifferential equation, which includes known biophysical terms for response dynamics, adaptation, saturation, and kinetics of intermediate components of the phototransduction process. The introduction of a saturation coefficient into the neural equation makes it possible to distinguish the different saturation thresholds of the rod-and-cone system. Numerical determination of the stationary solutions and complete linear stability analysis of the improved neural equation are given for a neuron of second order, and some computational results are presented for phase flows around different singular points in the phase field. A computer simulation based on the improved neural equation is presented for modeling the development and features of the CLAIE as a function of the speed and luminance of the stimulus and the background intensity. The computational results agree well with the psychophysical findings relating to the CLAIE.

Dynamics of the olfactory bulb: bifurcations, learning, and memory.

A mathematical model for describing dynamic phenomena in the olfactory bulb is presented. The nature of attractors and the bifurcation sequences in terms of the lateral connection strength in the mitral layer are studied numerically. Chaotic activity has only been found in the case of strong excitatory coupling. Synaptic modification-induced transition from oscillation to chaos is demonstrated. A model for a simple associative memory is also presented.