Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus.

Determining the biological details and mechanisms that are essential for the generation of population rhythms in the mammalian brain is a challenging problem. This problem cannot be addressed either by experimental or computational studies in isolation. Here we show that computational models that are carefully linked with experiment provide insight into this problem. Using the experimental context of a whole hippocampus preparation in vitro that spontaneously expresses theta frequency (3-12 Hz) population bursts in the CA1 region, we create excitatory network models to examine whether cellular adaptation bursting mechanisms could critically contribute to the generation of this rhythm. We use biologically-based cellular models of CA1 pyramidal cells and network sizes and connectivities that correspond to the experimental context. By expanding our mean field analyses to networks with heterogeneity and non all-to-all coupling, we allow closer correspondence with experiment, and use these analyses to greatly extend the range of parameter values that are explored. We find that our model excitatory networks can produce theta frequency population bursts in a robust fashion.Thus, even though our networks are limited by not including inhibition at present, our results indicate that cellular adaptation in pyramidal cells could be an important aspect for the occurrence of theta frequency population bursting in the hippocampus. These models serve as a starting framework for the inclusion of inhibitory cells and for the consideration of additional experimental features not captured in our present network models.

Modeling oscillatory dynamics in brain microcircuits as a way to help uncover neurological disease mechanisms: a proposal.

There is an undisputed need and requirement for theoretical and computational studies in Neuroscience today. Furthermore, it is clear that oscillatory dynamical output from brain networks is representative of various behavioural states, and it is becoming clear that one could consider these outputs as measures of normal and pathological brain states. Although mathematical modeling of oscillatory dynamics in the context of neurological disease exists, it is a highly challenging endeavour because of the many levels of organization in the nervous system. This challenge is coupled with the increasing knowledge of cellular specificity and network dysfunction that is associated with disease. Recently, whole hippocampus in vitro preparations from control animals have been shown to spontaneously express oscillatory activities. In addition, when using preparations derived from animal models of disease, these activities show particular alterations. These preparations present an opportunity to address challenges involved with using models to gain insight because of easier access to simultaneous cellular and network measurements, and pharmacological modulations. We propose that by developing and using models with direct links to experiment at multiple levels, which at least include cellular and microcircuit, a cycling can be set up and used to help us determine critical mechanisms underlying neurological disease. We illustrate our proposal using our previously developed inhibitory network models in the context of these whole hippocampus preparations and show the importance of having direct links at multiple levels.

Intersegmental coordination in invertebrates and vertebrates.

How does the CNS coordinate muscle contractions between different body segments during normal locomotion? Work on several preparations has shown that this coordination relies on excitability gradients and on differences between ascending and descending intersegmental coupling. Abstract models involving chains of coupled oscillators have defined properties of coordinating circuits that would permit them to establish a constant intersegmental phase in the face of changing periods. Analyses that combine computational and experimental strategies have led to new insights into the cellular organization of intersegmental coordinating circuits and the neural control of swimming in lamprey, tadpole, crayfish and leech.

Decomposing rhythmic hippocampal data to obtain neuronal correlates.

Characterizing hippocampal electrical rhythmic activities requires a broadly applicable methodology that lends itself to physiological interpretation. In the intact hippocampal preparation, spontaneous rhythmic field potentials are exhibited in the 3--4 Hz range which evidence suggests is due to discharges in the inhibitory interneuron population. Because field rhythms arise as a network effect and models must be built from the neuron up, we focus on developing a methodology to de-construct the non-stationary rhythms into its important constituents. This study uses 50 CA1/CA3 local field potentials to determine the important constituents, and an additional field recording and two intracellular recordings are examined subsequently. We determine the suitability of several time-frequency techniques. Distinct regions in the time-frequency domain which account for the signal behaviour are then characterized in terms of duration and frequency. These characteristics are interpreted as arising from a statistical mixture distribution. The decomposition of the 50 recordings yields three components whose patterns of activity match those of the intracellular recordings. We suggest that the statistical variability of the local field data can be linked to the variability of neuronal activities seen in intracellular data.

Dynamics and diversity in interneurons: a model exploration with slowly inactivating potassium currents.

Recent experimental and model work indicates that slowly inactivating potassium currents might play critical roles in generating population rhythms. In particular, slow (<1-4 Hz) rhythms recorded in the hippocampus correlate with oscillatory behaviors in interneurons in this frequency range. Limiting the ion channels to the traditional Hodgkin-Huxley sodium and potassium currents, a persistent sodium current, and a slowly inactivating potassium current, we explore the role of slowly inactivating conductances in a multi-compartmental interneuronal model. We find a rich repertoire of tonic and bursting behaviors depending on the distribution, density and kinetics of this conductance. Specifically, burst frequencies of appropriate frequencies could be obtained for certain distributions and kinetics of this conductance. Robust (with respect to injected currents) regimes of tonic firing and bursting behaviors are uncovered. In addition, we find a bistable tonic firing pattern that depends on the slowly inactivating potassium current. Therefore, this work shows ways in which different channel distributions and heterogeneities could produce variable signal outputs. We suggest that an understanding of the dynamical profiles of inhibitory neurons based on the density and distribution of their currents is helpful in dissecting out the complex roles played by this heterogeneous group of cells.

Artificial electrotonic coupling affects neuronal firing patterns depending upon cellular characteristics.

While there have been numerous theoretical studies indicating that electrotonic coupling via gap junctions interacts with the intrinsic characteristics of the coupled neurons to modify their electrical behaviour, little experimental evidence has been provided in coupled mammalian neurons. Using an artificial electrotonic junction, two distant uncoupled neurons were coupled through the computer, and the coupling conductance was varied. Tonically firing CA1 hippocampal pyramidal neurons reduced their spike firing frequency when coupled to thalamic or pyramidal cells, showing that the electrical coupling can be considered as a low-pass filter. The strength of coupling needed to entrain spike bursts of pyramidal neurons was considerably lower than the coupling needed to synchronize two neurons with different cellular characteristics (thalamic and pyramidal cells). Coupling promoted burst firing in a non-bursting cell if it was coupled to a spontaneously bursting neuron. These results support modelling studies that indicate a role for gap-junctional coupling in the synchronization of neuronal firing and the expression of low-frequency bursting.

Intersegmental coordination of swimmeret movements: mathematical models and neural circuits.

Swimmerets move periodically through a cycle of power-strokes and return-strokes. Swimmerets on neighboring segments differ in phase by approximately 25%, and maintain this difference even when the period of the cycle changes from < 1 to > 4 Hz. We constructed a minimal cellular model of the segmental pattern-generating circuit which incorporated its essential components, and whose dynamics were like those of the local circuit. Three different intersegmental coordinating units were known to link neighboring ganglia, but their targets are unknown. We constructed different intersegmental circuits which these units might form between neighboring cellular models, and compared their dynamics with the real system. One intersegmental circuit could maintain an approximately 25% phase difference through a range of periods. In physiological experiments, we identified three types of intersegmental interneurons that originate in each ganglion and project to its neighbors. These neurons fire bursts at certain parts of the swimmeret cycle in their home ganglion. These three neurons are necessary and sufficient to maintain normal coordination between neighboring segments. Their properties conform to the predictions of the cellular model.

Increased levels of cytosolic phospholipase A2 in dyslexics.

Research findings are increasingly reporting evidence of physiological abnormalities in dyslexia and sites for dyslexia have been identified on three chromosomes. It has been suggested that genetic inheritance may cause phospholipid abnormalities in dyslexia somewhat similar to those found in schizophrenia. A key enzyme in phospholipid metabolism, Type IV, or cytosolic, phospholipase A2 (cPLA2), releases arachidonic acid (AA), a 20-carbon fatty acid, which is the major source of production of prostaglandins and leukotrienes. An entirely new assay, which for the first time has enabled determination of the amount of the enzyme rather than its activity, was used to measure cPLA2 in dyslexic-type adults and controls and the two groups were found to differ significantly, the dyslexic-types having more of the enzyme. A report elsewhere of schizophrenics having even greater amounts of the enzyme suggests that dyslexia may be on a continuum with schizophrenia, as may be other neurodevelopmental disorders - which have also been described as phospholipid spectrum disorders.

Pump and exchanger mechanisms in a model of smooth muscle.

A novel approach to modelling pump and exchanger mechanisms is presented. In this approach, new thermodynamic expressions for the calcium pump, sodium-calcium exchanger and sodium-potassium pump are developed using statistical rate theory (SRT). This theory is well-defined and is not derived empirically. This is in contrast to previous thermodynamic pump expressions which used a simple linear relationship or relied on empirical data for their functional form. The functional form of these new expressions does not require assumptions of steady state or particular forms of voltage dependencies in specific steps. Also, the explicit reaction scheme is not required. Instead, assumptions of a rate-limiting step in the scheme and a near-equilibrium ratio of intermediate substrates are required. These expressions are incorporated into an overall model of gastric smooth muscle. This model presents a novel approach whereby thermodynamic representations for calcium pumps, sodium-calcium exchangers and sodium-potassium pumps have been included together in a model of ionic transport mechanisms for smooth muscle. Variations in basal metabolic concentrations are used to explain the observed amplitude variation in the transmembrane voltage of gastric smooth muscle. The interaction of the various mechanisms are used to illustrate the large depolarization obtained in smooth muscle with ouabain as well as the forward and reverse modes of the sodium-calcium exchanger.

Spontaneous rhythmic field potentials of isolated mouse hippocampal-subicular-entorhinal cortices in vitro.

The rodent hippocampal circuit is capable of exhibiting in vitro spontaneous rhythmic field potentials (SRFPs) of 1-4 Hz that originate from the CA3 area and spread to the CA1 area. These SRFPs are largely correlated with GABA-A IPSPs in pyramidal neurons and repetitive discharges in inhibitory interneurons. As such, their generation is thought to result from cooperative network activities involving both pyramidal neurons and GABAergic interneurons. Considering that the hippocampus, subiculum and entorhinal cortex function as an integrated system crucial for memory and cognition, it is of interest to know whether similar SRFPs occur in hippocampal output structures (that is, the subiculum and entorhinal cortex), and if so, to understand the cellular basis of these subicular and entorhinal SRFPs as well as their temporal relation to hippocampal SRFPs. We explored these issues in the present study using thick hippocampal-subicular-entorhinal cortical slices prepared from adult mice. SRFPs were found to spread from the CA1 area to the subicular and entorhinal cortical areas. Subicular and entorhinal cortical SRFPs were correlated with mixed IPSPs/EPSPs in local pyramidal neurons, and their generation was dependent upon the activities of GABA-A and AMPA glutamate receptors. In addition, the isolated subicular circuit could elicit SRFPs independent of CA3 inputs. We hypothesize that the SRFPs represent a basal oscillatory activity of the hippocampal-subicular-entorhinal cortices and that the subiculum functions as both a relay and an amplifier, spreading the SRFPs from the hippocampus to the entorhinal cortex.

Two-cell to N-cell heterogeneous, inhibitory networks: precise linking of multistable and coherent properties.

Inhibitory networks are now recognized as being the controllers of several brain rhythms. However, experimental work with inhibitory cells is technically difficult not only because of their smaller percentage of the neuronal population, but also because of their diverse properties. As such, inhibitory network models with tight links to the experimental data are needed to understand their contributions to population rhythms. However, mathematical analyses of network models with more than two cells is challenging when the cellular models involve biophysical details. We use bifurcation analyses and simulations to show that two-cell analyses can quantitatively predict N-cell (N = 20, 50, 100) network dynamics for heterogeneous, inhibitory networks. Interestingly, multistable states in the two-cell system are manifest as different and distinct coherent network patterns in the N-cell networks for the same parameter sets.

Using heterogeneity to predict inhibitory network model characteristics.

From modeling studies it has been known for >10 years that purely inhibitory networks can produce synchronous output given appropriate balances of intrinsic and synaptic parameters. Several experimental studies indicate that synchronous activity produced by inhibitory networks is critical to the production of population rhythms associated with various behavioral states. Heterogeneity of inputs to inhibitory networks strongly affect their ability to synchronize. In this paper, we explore how the amount of input heterogeneity to two-cell inhibitory networks affects their dynamics. Using numerical simulations and bifurcation analyses, we find that the ability of inhibitory networks to synchronize in the face of heterogeneity depends nonmonotonically on each of the synaptic time constant, synaptic conductance and external drive parameters. Because of this, an optimal set of parameters for a given cellular model with various biophysical characteristics can be determined. We suggest that this could be a helpful approach to use in determining the importance of different, underlying biophysical details. We further find that two-cell coherence properties are maintained in larger 10-cell networks. As such, we think that a strategy of "embedding" small network dynamics in larger networks is a useful way to understand the contribution of biophysically derived parameters to population dynamics in large networks.

Intersegmental coordination of limb movements during locomotion: mathematical models predict circuits that drive swimmeret beating.

Normal locomotion in arthropods and vertebrates is a complex behavior, and the neural mechanisms that coordinate their limbs during locomotion at different speeds are unknown. The neural modules that drive cyclic movements of swimmerets respond to changes in excitation by changing the period of the motor pattern. As period changes, however, both intersegmental phase differences and the relative durations of bursts of impulses in different sets of motor neurons are preserved. To investigate these phenomena, we constructed a cellular model of the local pattern-generating circuit that drives each swimmeret. We then constructed alternative intersegmental circuits that might coordinate these local circuits. The structures of both the model of the local circuit and the alternative models of the coordinating circuit were based on and constrained by previous experimental results on pattern-generating neurons and coordinating interneurons. To evaluate the relative merits of these alternatives, we compared their dynamics with the performance of the real circuit when the level of excitation was changed. Many of the alternative coordinating circuits failed. One coordinating circuit, however, did effectively match the performance of the real system as period changed from 1 to 3.2 Hz. With this coordinating circuit, both the intersegmental phase differences and the relative durations of activity within each of the local modules fell within the ranges characteristic of the normal motor pattern and did not change significantly as period changed. These results predict a mechanism of coordination and a pattern of intersegmental connections in the CNS that is amenable to experimental test.

The use of two automated neuropsychological tests, Cogfun and the Perceptual Maze Test, with alcoholics.

Forty-eight male detoxified alcoholics completed the automated neuropsychological tests, Cogfun II and the Perceptual Maze Test. On both tests, the younger group of patients performed better than the older group. No differences were found between short- and long-term drinkers, although there was some indication that older long-term drinkers performed less well than younger long-term drinkers. Control subjects performed significantly better than alcoholic subjects. Thus characteristics found by others using conventional psychometric tests were also apparent when using new, automated tests, and baselines were established from which to measure change over the passage of time.

Phase-coupled oscillator models can predict hippocampal inhibitory synaptic connections.

What factors are responsible for propagating electrical activity in the hippocampus? Using an intact, isolated hippocampus preparation, it is possible to observe spontaneous delta (< or = 4 Hz) waves of rhythmic field potentials. These rhythmic potentials are inhibitory in nature, mediated by GABAergic inhibitory potentials originating from a population of principal neurons. They start in the ventro-temporal region and move longitudinally towards the dorso-septal region with a phase lag of approximately 10% between the extracellular recordings. We use the mathematical framework of phase-coupled oscillators (PCO) to gain some insight into the underlying network system. A chain of 15 nearest-neighbour bidirectionally coupled PCOs is used where each oscillator refers to a segment of the CA1 region of the hippocampus that can generate these slow field potentials. We find that ventro-dorsal delta waves exist if there is a dominance in coupling strength in one direction. Without a one-way coupling dominance, ventro-dorsal waves can still exist, but then the coupling strengths need to be much larger. The relationship between entrained and intrinsic frequencies and the variation of propagation speeds along the longitudinal axis can be used to determine which case applies. Currently available experimental data supports one of the cases, predicting that there is a stronger ventral to dorsal inhibitory effect.

How does the crayfish swimmeret system work? Insights from nearest-neighbor coupled oscillator models.

Rhythmic movements of crayfish swimmerets are coordinated by a neural circuit that links their four abdominal ganglia. Each swimmeret is driven by its own small local circuit, or pattern-generating module. We modeled this network as a chain of four oscillators, bidirectionally coupled to their nearest neighbors, and tested the model's ability to reproduce experimentally observed changes in intersegmental phases and in period caused by differential excitation of selected abdominal ganglia. The choices needed to match the experimental data lead to the following predictions: coupling between ganglia is asymmetric; the ascending and descending coupling have approximately equal strengths; intersegmental coupling does not significantly affect the frequency of the system; and excitation affects the intrinsic frequencies of the oscillators and might also change properties of intersegmental coupling.

Novel bursting patterns emerging from model inhibitory networks with synaptic depression.

Studies show that short-term synaptic plasticity plays important roles in neural coding and the normal operation of the synapse. Basket cells in the hippocampus demonstrate this plasticity in the form of synaptic depression, and recent in vivo work indicates that basket cell activities contribute significantly to hippocampal output associated with different behavioural states. Thus it is essential to understand the generation and synchronization of patterns produced by basket cell networks with depression. We study two-cell model inhibitory networks with depression and obtain alternating bursting patterns and synchronous activity occurring between bursts. We describe mechanisms for how these patterns emerge by performing several simulations in the plane of different depression time constants, tauD. Such patterns might contribute significantly to various population activities observed in the hippocampus.

Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks.

We describe four different mechanisms that lead to oscillations in a network of two reciprocally inhibitory cells. In two cases (intrinsic release and intrinsic escape) the frequency of the network oscillation is insensitive to the threshold voltage of the synaptic potentials. In the other two cases (synaptic release and synaptic escape) the network frequency is strongly determined by the threshold voltage of the synaptic connections. The distinction between the different mechanisms blurs as the function describing synaptic activation becomes less steep and as the model neurons are removed from the relaxation regime. These mechanisms provide insight into the parameters that control network frequency in motor systems that depend on reciprocal inhibition.

Mechanisms of oscillation in dynamic clamp constructed two-cell half-center circuits.

1. The dynamic clamp was used to create reciprocally inhibitory two-cell circuits from pairs of pharmacologically isolated gastric mill neurons of the stomatogastric ganglion of the crab, Cancer borealis. 2. We used this system to study how systematic alterations in intrinsic and synaptic parameters affected the network behavior. This has previously only been possible in purely computational systems. 3. In the absence of additional hyperpolarization-activated inward current (IH), stable half-center oscillatory behavior was not observed. In the presence of additional IH, a variety of circuit dynamics, including stable half-center oscillatory activity, was produced. 4. Stable half-center behavior requires that the synaptic threshold lie within the voltage envelope of the slow wave oscillation. 5. Changes in the synaptic threshold produce dramatic changes in half-center period. As predicted by previous theoretical work, when the synaptic threshold is depolarized, the period first increases and then decreases in a characteristic inverted U-shaped relationship. Analysis of the currents responsible for the transition between the active and inhibited neurons shows that the mechanism of oscillation changes as the synaptic threshold is varied. 6. Increasing the time constant and the conductance of the inhibitory synaptic current increased the period of the half-center oscillator. 7. Increasing the conductance of IH or changing the voltage dependence of IH can either increase or decrease network period, depending on the initial mode of network oscillation. A depolarization of the activation curve causes the network to respond in a similar fashion as increasing the conductance of IH. 8. Many neuromodulatory substances are known to alter synaptic strength and the conductance and voltage dependence of IH, parameters we studied with the dynamic clamp. To understand the response of the network to modulation of a single parameter, it is necessary to understand the nature of the altered conductance and how it interacts with the other conductances in the system.

Frequency and burst duration in oscillating neurons and two-cell networks.

We study the relationship of injected current to oscillator period in single neurons and two-cell model networks formed by reciprocal inhibitory synapses. Using a Morris-Lecar-like model, we identify two qualitative types of oscillatory behavior for single model neurons. The "classical" oscillator behavior is defined as type A. Here the burst duration is relatively constant and the frequency increases with depolarization. For oscillator type B, the frequency first increases and then decreases when depolarized, due to the variable burst duration. Our simulations show that relatively modest changes in the maximal inward and outward conductances can move the oscillator from one type to another. Cultured stomatogastric ganglion neurons exhibit both A and B type behaviors and can switch between the two types with pharmacological manipulation. Our simulations indicate that the stability of a two-cell network with injected current can be extended with inhibitory coupling. In addition, two-cell networks formed from type A or type B oscillators behave differently from each other at lower synaptic strengths.