Based on recent experimental data, we have developed a conductance-based computational network model of the subthalamic nucleus and the external segment of the globus pallidus in the indirect pathway of the basal ganglia. Computer simulations and analysis of this model illuminate the roles of the coupling architecture of the network, and associated synaptic conductances, in modulating the activity patterns displayed by this network. Depending on the relationships of these coupling parameters, the network can support three general classes of sustained firing patterns: clustering, propagating waves, and repetitive spiking that may show little regularity or correlation. Each activity pattern can occur continuously or in discrete episodes. We characterize the mechanisms underlying these rhythms, as well as the influence of parameters on details such as spiking frequency and wave speed. These results suggest that the subthalamopallidal circuit is capable both of correlated rhythmic activity and of irregular autonomous patterns of activity that block rhythmicity. Increased striatal input to, and weakened intrapallidal inhibition within, the indirect pathway can switch the behavior of the circuit from irregular to rhythmic. This may be sufficient to explain the emergence of correlated oscillatory activity in the subthalamopallidal circuit after destruction of dopaminergic neurons in Parkinson's disease and in animal models of parkinsonism. Key words: basal ganglia; subthalamic nucleus; globus pallidus; computational models; oscillations; synchrony; Parkinson's diseaseMost current models of the basal ganglia are static models, in that they represent the inputs and outputs of the component nuclei as firing rates. For example, the Albin et al. (1989) model, commonly used to explain the symptoms of Parkinsonism, views the interactions of the direct and indirect pathway as constant in time and explains the symptoms of Parkinson's disease in terms of changes in mean rate of the basal ganglia output (Wichmann and DeLong, 1996). In contrast, recent experimental studies have not strongly confirmed the predicted changes in mean rate in these structures under dopamine depletion, but have instead revealed prominent low-frequency periodicity (4 -30 Hz) of firing and dramatically increased correlations among neurons in the external segment of the globus pallidus (GPe) and the subthalamic nucleus (STN) (Bergman et al., 1994;Nini et al., 1995;Magnin et al., 2000;Raz et al., 2000;Brown et al., 2001). It is remarkable that the changes in firing pattern seen in those structures do not appear to be attributable to comparable changes in the firing patterns of striatal output cells, although cholinergic striatal interneurons show changes comparable with those seen in the globus pallidus (Raz et al., 1996). The authors of those studies have proposed that a rate model of the basal ganglia is inadequate to capture the dynamic interaction of the STN and GPe that may generate these pathological changes.In particular, such dynamic interactions ma...

We develop a mechanistic mathematical model of the G-protein coupled signaling pathway responsible for generating current responses in frog olfactory receptor neurons. The model incorporates descriptions of ligand-receptor interaction, intracellular transduction events involving the second messenger cAMP, effector ion-channel activity, and calcium-mediated feedback steps. We parameterized the model with respect to suction pipette current recordings from single cells stimulated with multiple odor concentrations. The proposed model accurately predicts the receptorcurrent response of the neuron to brief and prolonged odorant exposure and is able to produce the adaptation observed under repeated or sustained stimulation.mathematical model ͉ receptor neuron ͉ olfaction ͉ signal transduction ͉ cilia S ensory transduction of odors occurs in olfactory receptor neurons (ORNs) located in the olfactory epithelium of vertebrates and the antennal structures of invertebrates (1). The first step in transduction is the binding of an odorant molecule to a seven-transmembrane-domain receptor protein in the cilia of an ORN. This interaction triggers a G-protein-coupled cascade that activates the enzyme adenylyl cyclase, resulting in an increase in intraciliary adenosine-3Ј,5Ј-cyclic monophosphate (cAMP). When cAMP increases, it opens cyclic nucleotidegated (CNG) channels, allowing calcium and other extracellular cations into the cilia and generating an inward current. Elevated Ca 2ϩ levels in the cilia activate Ca 2ϩ -gated chloride [Cl(Ca)] channels, creating an outward flow of Cl Ϫ ions and producing amplification of the inward current (2-4) that results in membrane depolarization and the generation of action potentials in the cell soma (5). This increase in intracellular calcium initiates termination and adaptation of the cell's response by means of deactivation and feedback mechanisms, including interactions mediated by Ca 2ϩ -calmodulin (CaCaM) and Ca 2ϩ ͞calmodulin-kinase II (CaMK) (6-10). The Cl(Ca) channels remain open until enough calcium is extruded from the cilia via the Na͞Ca exchanger (NCX) (11).After stimulation, an ORNЈs response to subsequent stimuli becomes attenuated. Short-term adaptation is observed as a decrease in responsiveness to odor presentations that occur within a few seconds after a brief stimulus (7); it may be mediated in part by CaCaM inhibition of the CNG channel (12). Desensitization occurs when an odor is experienced for a sustained interval of at least several seconds: the ORNЈs response declines while the stimulus continues to be present (13,14). In this case, several aspects of the response to a subsequent stimulus are altered, including a decrease in the slope of the rising phase, as well as an increase in the speed of decay, of the stimulus-induced inward current (7, 13). Experiments (15) have demonstrated that the molecular mechanisms responsible for desensitization are likely to act upstream of cAMP production; inhibition of adenylyl cyclase activity by CaMK is a possible mechanism (13). L...

The capacity of coupled nonlinear Schro dinger (NLS) equations to support multipulse solutions (multibump solitary-waves) is investigated. A detailed analysis is undertaken for a system of quadratically coupled equations that describe the phenomena of second harmonic generation and parametric wave interaction in non-centrosymmetric optical materials. Utilising the framework of homoclinic bifurcation theory, and employing a Lyapunov Schmidt reduction method developed by Hale, Lin, and Sandstede, a novel mechanism for the generation of multipulses is identified, which arises from a resonant semi-simple eigenvalue configuration of the linearised steady-state equations. Conditions for the existence of multipulses, as well as a description of their geometry, are derived from the analysis. AcademicPress

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