Circuits that contain the Modeling Application : XPP (Home Page)

(XPP (XPPAUT is another name; I (Bard Ermentrout) will use the two interchangeably) is a tool for solving differential equations, difference equations, delay equations, functional equations, boundary value problems, and stochastic equations. It evolved from a chapter written by John Rinzel and me on the qualitative theory of nerve membranes and eventually became a commercial product for MSDOS computers called PHASEPLANE. It is now available as a program running under X11 and Windows. The code brings together a number of useful algorithms and is extremely portable.)
Re-display model names without descriptions
    Models   Description
1. A theory of ongoing activity in V1 (Goldberg et al 2004)
Ongoing spontaneous activity in the cerebral cortex exhibits complex spatiotemporal patterns in the absence of sensory stimuli. To elucidate the nature of this ongoing activity, we present a theoretical treatment of two contrasting scenarios of cortical dynamics: (1) fluctuations about a single background state and (2) wandering among multiple “attractor” states, which encode a single or several stimulus features. Studying simplified network rate models of the primary visual cortex (V1), we show that the single state scenario is characterized by fast and high-dimensional Gaussian-like fluctuations, whereas in the multiple state scenario the fluctuations are slow, low dimensional, and highly non-Gaussian. Studying a more realistic model that incorporates correlations in the feedforward input, spatially restricted cortical interactions, and an experimentally derived layout of pinwheels, we show that recent optical-imaging data of ongoing activity in V1 are consistent with the presence of either a single background state or multiple attractor states encoding many features.
2. Activity patterns in a subthalamopallidal network of the basal ganglia model (Terman et al 2002)
"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. ...". Terman's XPP code and a partial implementation by Taylor Malone in NEURON and python are included.
3. Contribution of ATP-sensitive potassium channels in the neuronal network (Huang et al. 2009)
Epileptic seizures in diabetic hyperglycemia (DH) are not uncommon. This study aimed to determine the acute behavioral, pathological, and electrophysiological effects of status epilepticus (SE) on diabetic animals. ... We also used a simulation model to evaluate intracellular adenosine triphosphate (ATP) and neuroexcitability. ... In the simulation, increased intracellular ATP concentration promoted action potential firing. This finding that rats with DH had more brain damage after SE than rats without diabetes suggests the importance of intensively treating hyperglycemia and seizures in diabetic patients with epilepsy.
4. Excitatory and inhibitory interactions in populations of model neurons (Wilson and Cowan 1972)
Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.
5. Failure of Deep Brain Stimulation in a basal ganglia neuronal network model (Dovzhenok et al. 2013)
"… Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). ... This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. …" Implemented by Andrey Dovzhenok, to whom questions should be addressed.
6. High frequency stimulation of the Subthalamic Nucleus (Rubin and Terman 2004)
" ... Using a computational model, this paper considers the hypothesis that DBS works by replacing pathologically rhythmic basal ganglia output with tonic, high frequency firing. In our simulations of parkinsonian conditions, rhythmic inhibition from GPi to the thalamus compromises the ability of thalamocortical relay (TC) cells to respond to depolarizing inputs, such as sensorimotor signals. High frequency stimulation of STN regularizes GPi firing, and this restores TC responsiveness, despite the increased frequency and amplitude of GPi inhibition to thalamus that result. We provide a mathematical phase plane analysis of the mechanisms that determine TC relay capabilities in normal, parkinsonian, and DBS states in a reduced model. This analysis highlights the differences in deinactivation of the low-threshold calcium T -current that we observe in TC cells in these different conditions. ..."
7. Human sleep/wake cycle (Rempe et al. 2010)
This model simulates sleep in the human brain and is consistent with both the flip/flop concept and the two-process model of sleep regulation. The model also gives a possible mechanism for the changes in sleep timing seen in narcolepsy.
8. Inhibitory control by an integral feedback signal in prefrontal cortex (Miller and Wang 2006)
The prefrontal cortex (PFC) is known to be critical for inhibitory control of behavior, but the underlying mechanisms are unclear. Here, we propose that inhibitory control can be instantiated by an integral signal derived from working memory, another key function of the PFC. Specifically, we assume that an integrator converts excitatory input into a graded mnemonic activity that provides an inhibitory signal (integral feedback control) to upstream afferent neurons. We demonstrate this scenario in a neuronal-network model for a temporal discrimination task... See paper for details and more.
9. Modeling the effects of dopamine on network synchronization (Komek et al. 2012)
Dopamine modulates cortical circuit activity in part through its actions on GABAergic interneurons, including increasing the excitability of fast-spiking interneurons. Though such effects have been demonstrated in single cells, there are no studies that examine how such mechanisms may lead to the effects of dopamine at a neural network level. In this study, we investigated the effects of dopamine on synchronization in two simulated neural networks; one biophysical model composed of Wang-Buzsaki neurons and a reduced model with theta neurons. In both models, we show that parametrically varying the levels of dopamine, modeled through the changes in the excitability of interneurons, reveals an inverted-U shaped relationship, with low gamma band power at both low and high dopamine levels and optimal synchronization at intermediate levels. Moreover, such a relationship holds when the external input is both tonic and periodic at gamma band range. Together, our results indicate that dopamine can modulate cortical gamma band synchrony in an inverted-U fashion and that the physiologic effects of dopamine on single fast-spiking interneurons can give rise to such non-monotonic effects at the network level.
10. Networks of spiking neurons: a review of tools and strategies (Brette et al. 2007)
This package provides a series of codes that simulate networks of spiking neurons (excitatory and inhibitory, integrate-and-fire or Hodgkin-Huxley type, current-based or conductance-based synapses; some of them are event-based). The same networks are implemented in different simulators (NEURON, GENESIS, NEST, NCS, CSIM, XPP, SPLIT, MVAspike; there is also a couple of implementations in SciLab and C++). The codes included in this package are benchmark simulations; see the associated review paper (Brette et al. 2007). The main goal is to provide a series of benchmark simulations of networks of spiking neurons, and demonstrate how these are implemented in the different simulators overviewed in the paper. See also details in the enclosed file Appendix2.pdf, which describes these different benchmarks. Some of these benchmarks were based on the Vogels-Abbott model (Vogels TP and Abbott LF 2005).
11. Pallidostriatal projections promote beta oscillations (Corbit, Whalen, et al 2016)
This model consists of an inhibitory loop combining the projections from GPe neurons back to the striatum (shown experimentally to predominantly affect fast spiking interneurons, FSIs), together with the coupling from FSIs to medium spiny neurons (MSNs) in the striatum, along with the projections from MSNs to GPe. All models are in the Hodgkin-Huxley formalism, adapted from previously published models for each cell type. The connected circuit produces irregular activity under control conditions, but increasing FSI-to-MSN connectivity as observed experimentally under dopamine depletion yields exaggerated beta oscillations and synchrony. Additional mechanistic aspects are also explored.
12. Respiratory central pattern generator including Kolliker-Fuse nucleus (Wittman et al 2019)
We present three highly reduced conductance-based models for the core of the respiratory CPG. All successfully simulate respiratory outputs across eupnoeic and vagotomized conditions and show that loss of inhibition to the pontine Kolliker-Fuse nucleus reproduces the key respiratory alterations associated with Rett syndrome.
13. Respiratory central pattern generator network in mammalian brainstem (Rubin et al. 2009)
This model is a reduced version of a spatially organized respiratory central pattern generation network consisting of four neuronal populations (pre-I, early-I, post-I, and aug-E). In this reduction, each population is represented by a single neuron, in an activity-based framework (which includes the persistent sodium current for the pre-I population). The model includes three sources of external drive and can produce several experimentally observed rhythms.
14. Simulation studies on mechanisms of levetiracetam-mediated inhibition of IK(DR) (Huang et al. 2009)
Levetiracetam (LEV) is an S-enantiomer pyrrolidone derivative with established antiepileptic efficacy in generalized epilepsy and partial epilepsy. However, its effects on ion currents and membrane potential remain largely unclear. In this study, we investigated the effect of LEV on differentiated NG108-15 neurons. ... Simulation studies in a modified Hodgkin-Huxley neuron and network unraveled that the reduction of slowly inactivating IK(DR) resulted in membrane depolarization accompanied by termination of the firing of action potentials in a stochastic manner. Therefore, the inhibitory effects on slowly inactivating IK(DR) (Kv3.1-encoded current) may constitute one of the underlying mechanisms through which LEV affects neuronal activity in vivo.
15. Study of augmented Rubin and Terman 2004 deep brain stim. model in Parkinsons (Pascual et al. 2006)
" ... The model by Rubin and Terman [31] represents one of the most comprehensive and biologically plausible models of DBS published recently. We examined the validity of the model, replicated its simulations and tested its robustness. While our simulations partially reproduced the results presented by Rubin and Terman [31], several issues were raised including the high complexity of the model in its non simplified form, the lack of robustness of the model with respect to small perturbations, the nonrealistic representation of the thalamus and the absence of time delays. Computational models are indeed necessary, but they may not be sufficient in their current forms to explain the effect of chronic electrical stimulation on the activity of the basal ganglia (BG) network in PD."
16. Subiculum network model with dynamic chloride/potassium homeostasis (Buchin et al 2016)
This is the code implementing the single neuron and spiking neural network dynamics. The network has the dynamic ion concentrations of extracellular potassium and intracellular chloride. The code contains multiple parameter variations to study various mechanisms of the neural excitability in the context of chloride homeostasis.
17. Synchronization by D4 dopamine receptor-mediated phospholipid methylation (Kuznetsova, Deth 2008)
"We describe a new molecular mechanism of dopamine-induced membrane protein modulation that can tune neuronal oscillation frequency to attention related gamma rhythm. This mechanism is based on the unique ability of D4 dopamine receptors (D4R) to carry out phospholipid methylation (PLM) that may affect the kinetics of ion channels. We show that by deceasing the inertia of the delayed rectifier potassium channel, a transition to 40 Hz oscillations can be achieved. ..."
18. The activity phase of postsynaptic neurons (Bose et al 2004)
We show, in a simplified network consisting of an oscillator inhibiting a follower neuron, how the interaction between synaptic depression and a transient potassium current in the follower neuron determines the activity phase of this neuron. We derive a mathematical expression to determine at what phase of the oscillation the follower neuron becomes active. This expression can be used to understand which parameters determine the phase of activity of the follower as the frequency of the oscillator is changed. See paper for more.

Re-display model names without descriptions