Models 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 Computational Model of Bidirectional Plasticity Regulation by betaCaMKII (Pinto et al. 2019)
We present a computational model that suggests how calcium-calmodulin dependent protein kinase II can act as a molecular switch in synaptic plasticity induction at an important cerebellar synapse (between parallel fibres and Purkinje cells). Our simulation results provide a potential explanation for experimental data by van Woerden et al (Van Woerden G, Hoebeek F, Gao Z, Nagaraja R, Hoogenraad C, Kushner S, et al. [beta]CaMKII controls the direction of plasticity at parallel fiber-Purkinje cell synapses. Nat Neurosci. 2009;12(7):823-825). These experiments were performed in the lab led by Professor Chris De Zeeuw.
2.  A mathematical model of evoked calcium dynamics in astrocytes (Handy et al 2017)
" ...Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. ..."
3.  A model for pituitary GH(3) lactotroph (Wu and Chang 2005)
The ATP-sensitive K(+) (K(ATP)) channels are composed of sulfonylurea receptor and inwardly rectifying K(+) channel (Kir6.2) subunit. These channels are regulated by intracellular ADP/ATP ratio and play a role in cellular metabolism. ... The objective of this study was to determine whether Diethyl pyrocarbonate (DEPC) modifies K(ATP)-channel activity in pituitary GH(3) cells. ... Simulation studies also demonstrated that the increased conductance of K(ATP)-channels used to mimic DEPC actions reduced the frequency of spontaneous action potentials and fluctuation of intracellular Ca(2+). The results indicate that chemical modification with DEPC enhances K(ATP)-channel activity and influences functional activities of pituitary GH(3) cells. See paper for more and details.
4.  A model for recurrent spreading depolarizations (Conte et al. 2017)
A detailed biophysical model for a neuron/astrocyte network is developed in order to explore mechanisms responsible for cortical spreading depolarizations. This includes a model for the Na+-glutamate transporter, which allows for a detailed description of reverse glutamate uptake. In particular, we consider the specific roles of elevated extracellular glutamate and K+ in the initiation, propagation and recurrence of spreading depolarizations.
5.  A simplified model of NMDA oscillations in lamprey locomotor neurons (Huss et al. 2008)
Using experiments in conjunction with this simplified model, we sought to understand the basic mechanisms behind NMDA-induced oscillations in lamprey locomotor neurons, specifically (a) how the oscillation frequency depends on NMDA concentration and why, and (b) what the minimal number of components for generating NMDA oscillations is (in vitro and in the model).
6.  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.
7.  Action potential of adult rat ventricle (Wang et al. 2008)
"Aconitine (ACO), a highly toxic diterpenoid alkaloid, is recognized to have effects on cardiac voltage-gated Na(+) channels. However, it remains unknown whether it has any effects on K(+) currents. The effects of ACO on ion currents in differentiated clonal cardiac (H9c2) cells and in cultured neonatal rat ventricular myocytes were investigated in this study. ..." The rat action potential in this simulation was played back into the cell for experiments reported in this paper.
8.  Action potential of striated muscle fiber (Adrian et al 1970)
1. Membrane currents during step depolarizations were determined by a method in which three electrodes were inserted near the end of a fibre in the frog's sartorius muscle. The theoretical basis and limitations of the method are discussed. 2. Measurements of the membrane capacity (CM) and resting resistance (RM) derived from the current during a step change in membrane potential are consistent with values found by other methods. 3. In fibres made mechanically inactive with hypertonic solutions (Ringer solution plus 350 mM sucrose) step depolarizations produced ionic currents which resembled those of nerve in showing (a) an early transient inward current, abolished by tetrodotoxin, which reversed when the depolarization was carried beyond an internal potential of about +20 mV, (b) a delayed outward current, with a linear instantaneous current¡Xvoltage relation, and a mean equilibrium potential with a normal potassium concentration (2¡P5 mM) of -85 mV. 4. The reversal potential for the early current appears to be consistent with the sodium equilibrium potential expected in hypertonic solutions. 5. The variation of the equilibrium potential for the delayed current (V¡¬K) with external potassium concentration suggests that the channel for delayed current has a ratio of potassium to sodium permeability of 30:1; this is less than the resting membrane where the ratio appears to be 100:1. V¡¬K corresponds well with the membrane potential at the beginning of the negative after-potential observed under similar conditions. 6. The variation of V¡¬K with the amount of current which has passed through the delayed channel suggests that potassium ions accumulate in a space of between 1/3 and 1/6 of the fibre volume. If potassium accumulates in the transverse tubular system (T system) much greater variation in V¡¬K would be expected. 7. The delayed current is not maintained but is inactivated like the early current. The inactivation is approximately exponential with a time constant of 0¡P5 to 1 sec at 20¢X C. The steady-state inactivation of the potassium current is similar to that for the sodium current, but its voltage dependence is less steep and the potential for half inactivation is 20 mV rate more positive. 8. Reconstructions of ionic currents were made in terms of the parameters (m, n, h) of the Hodgkin¡XHuxley model for the squid axon, using constants which showed a similar dependence on voltage. 9. Propagated action potentials and conduction velocities were computed for various conditions on the assumption that the T system behaves as if it were a series resistance and capacity in parallel with surface capacity and the channels for sodium, potassium and leak current. There was reasonable agreement with observed values, the main difference being that the calculated velocities and rates of rise were somewhat less than those observed experimentally.
9.  Actions of Rotenone on ionic currents and MEPPs in Mouse Hippocampal Neurons (Huang et al 2018)
" ... With the aid of patch-clamp technology and simulation modeling, the effects of (Rotenone) Rot on membrane ion currents present in mHippoE-14 cells were investigated. Results: Addition of Rot produced an inhibitory action on the peak amplitude of INa ...; however, neither activation nor inactivation kinetics of INa was changed during cell exposure to this compound. Addition of Rot produced little or no modifications in the steady-state inactivation curve of INa. Rot increased the amplitude of Ca2+-activated Cl- current in response to membrane depolarization ... . Moreover, when these cells were exposed to 10 µM Rot, a specific population of ATP-sensitive K+ channels ... was measured, despite its inability to alter single-channel conductance. Under current clamp condition, the frequency of miniature end-plate potentials in mHippoE-14 cells was significantly raised in the presence of Rot (10 µM) with no changes in their amplitude and time course of rise and decay. In simulated model of hippocampal neurons incorporated with chemical autaptic connection, increased autaptic strength to mimic the action of Rot was noted to change the bursting pattern with emergence of subthreshold potentials. Conclusions: The Rot effects presented herein might exert a significant action on functional activities of hippocampal neurons occurring in vivo. "
10.  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.
11.  Allosteric gating of K channels (Horrigan et al 1999)
Calcium sensitive large-conductance K channel conductance is controlled by both cytoplasmic calcium and membrane potential. Experimental data obtained by the inside out patch method can be understood in terms of a gating scheme where a central transition between a closed and an open conformation is allosterically regulated by the state of four independent and identical voltage sensors. See paper for more and details.
12.  An ion-based model for swelling of neurons and astrocytes (Hubel & Ullah 2016)
The programs describe ion dynamics and osmosis-driven cellular swelling. “code_fig3.ode” shows a scenario of permanent cessation of energy supply / Na/K-pump activity, and the induced transition from normal conditions to the Donnan equilibrium for an isolated neuron and its extracellular space. “code_Fig7.ode” shows spreading depolarization induced by an interruption of energy supply in a model consisting of a neuron, a glia cell and the extracellular space. The simulations show the evolution of ion concentrations, Nernst potentials, the membrane potential, gating variables and cellular volumes.
13.  Anoxic depolarization, recovery: effect of brain regions and extracellular space (Hubel et al. 2016)
The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region-specific neuronal damage. Neurons in higher brain regions have stronger ADs and are more easily injured than neurons in lower brain region. The mechanism leading to such differences is not clear. We use a computational model based on a Hodgkin-Huxley framework which includes neural spiking dynamics, processes of ion accumulation, and homeostatic mechanisms like vascular coupling and Na/K-exchange pumps. We show that a large extracellular space (ECS) explains the recovery failure in high brain regions. A phase-space analysis shows that with a large ECS recovery from AD through potassium regulation is impossible. The code 'time_series.ode' can be used to simulate AD for a large and a small ECS and show the different behaviors. The code ‘continuations.ode’ can be used to show the fixed point structure. Depending on our choice of large or small ECS the fixed point curve implies the presence/absence of a recovery threshold that defines the potassium clearance demand.
14.  Basal ganglia-corticothalamic (BGCT) network (Chen et al., 2014)
We developed a biophysical model of the basal ganglia-corticothalamic network in this work. "... We demonstrate that the typical absence seizure activities can be controlled and modulated by the direct GABAergic projections from the substantia nigra pars reticulata (SNr) to either the thalamic reticular nucleus (TRN) or the specific relay nuclei (SRN) of thalamus, through different biophysical mechanisms. ... results highlight the bidirectional functional roles of basal ganglia in controlling and modulating absence seizures, and might provide novel insights into the therapeutic treatments of this brain disorder."
15.  Ca(2+) oscillations based on Ca-induced Ca-release (Dupont et al 1991)
We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. See paper for more and details.
16.  Ca-dependent K Channel: kinetics from rat muscle (Moczydlowski, Latorre 1983) XPP
This is an XPP version of the classic KCa channel from Moczydlowski and Latorre 1983.
17.  CA1 pyramidal cell: I_NaP and I_M contributions to somatic bursting (Golomb et al 2006)
To study the mechanisms of bursting, we have constructed a conductance-based, one-compartment model of CA1 pyramidal neurons. In this neuron model, reduced [Ca2+]o is simulated by negatively shifting the activation curve of the persistent Na+ current (INaP), as indicated by recent experimental results. The neuron model accounts, with different parameter sets, for the diversity of firing patterns observed experimentally in both zero and normal [Ca2+]o. Increasing INaP in the neuron model induces bursting and increases the number of spikes within a burst, but is neither necessary nor sufficient for bursting. We show, using fast-slow analysis and bifurcation theory, that the M-type K+ current (IM) allows bursting by shifting neuronal behavior between a silent and a tonically-active state, provided the kinetics of the spike generating currents are sufficiently, though not extremely, fast. We suggest that bursting in CA1 pyramidal cells can be explained by a single compartment *square bursting* mechanism with one slow variable, the activation of IM. See paper for more and details.
18.  CA3 pyramidal cell: rhythmogenesis in a reduced Traub model (Pinsky, Rinzel 1994)
Fig. 2A and 3 are reproduced in this simulation of Pinsky PF, Rinzel J (1994).
19.  CaMKII system exhibiting bistability with respect to calcium (Graupner and Brunel 2007)
"... We present a detailed biochemical model of the CaMKII autophosphorylation and the protein signaling cascade governing the CaMKII dephosphorylation. ... it is shown that the CaMKII system can qualitatively reproduce results of plasticity outcomes in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. This shows that the CaMKII protein network can account for both induction, through LTP/LTD-like transitions, and storage, due to its bistability, of synaptic changes."
20.  Cardiac action potential based on Luo-Rudy phase 1 model (Luo and Rudy 1991), (Wu 2004)
A mathematical model of the membrane action potential of the mammalian ventricular cell is introduced. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K]o. The fast sodium current, INa, is characterized by fast upstroke velocity (Vmax = 400 V/sec) and slow recovery from inactivation. The time-independent potassium current, IK1, includes a negative-slope phase and displays significant crossover phenomenon as [K]o is varied. The time-dependent potassium current, IK, shows only a minimal degree of crossover. A novel potassium current that activates at plateau potentials is included in the model. The simulated action potential duplicates the experimentally observed effects of changes in [K]o on action potential duration and rest potential. See papers for more and details.
21.  Circadian clock model based on protein sequestration (simple version) (Kim & Forger 2012)
"… To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. …"
22.  Circadian clock model in mammals (detailed version) (Kim & Forger 2012)
"… To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. …"
23.  ClC-2 channels regulate neuronal excitability, not intracellular Cl- levels (Ratte & Prescott 2011)
"The model is for a generic, single compartment neuron with multiple ion currents. The most notable mechanisms include ClC-2 (a rectifying chloride-leak channel) and KCC2 (potassium chloride co-transporter 2). A significant feature of the model is that it tracks intracellular chloride concentration. Moreover, the GABA-A receptor is modeled as passing both chloride and bicarbonate ions, which is important for proper calculation of the GABA reversal potential. Ornstein-Unlenbeck processes to simulate synaptic inhibition and excitation are also included."
24.  Consequences of HERG mutations in the long QT syndrome (Clancy, Rudy 2001)
This study demonstrates which mutations can prolong APD sufficiently to generate early afterdepolarizations (EADs), which may trigger life-threatening arrhythmias. The severity of the phenotype is shown to depend on the specific kinetic changes and how they affect I(Kr) during the time course of the action potential. See paper for more and details.
25.  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.
26.  Control of vibrissa motoneuron firing (Harish and Golomb 2010)
We construct and analyze a single-compartment, conductance-based model of vibrissa motoneurons. Low firing rates are supported in extended regimes by adaptation currents and the minimal firing rate decreases with the persistent sodium conductance gNaP and increases with M-potassium and h-cation conductances. Suprathreshold resonance results from the locking properties of vMN firing to stimuli and from reduction of firing rates at low frequencies by slow M and afterhyperpolarization potassium conductances. h conductance only slightly affects the suprathreshold resonance. When a vMN is subjected to a small periodic CPG input, serotonergically induced gNaP elevation may transfer the system from quiescence to a firing state that is highly locked to the CPG input.
27.  Criticality,degeneracy in injury-induced changes in primary afferent excitability (Ratte et al 2014)
"Neuropathic pain remains notoriously difficult to treat despite numerous drug targets. Here, we offer a novel explanation for this intractability. Computer simulations predicted that qualitative changes in primary afferent excitability linked to neuropathic pain arise through a switch in spike initiation dynamics when molecular pathologies reach a tipping point (criticality), and that this tipping point can be reached via several different molecular pathologies (degeneracy). ..."
28.  Deterministic chaos in a mathematical model of a snail neuron (Komendantov and Kononenko 1996)
"Chaotic regimes in a mathematical model of pacemaker activity in the bursting neurons of a snail Helix pomatia, have been investigated. The model includes a slow-wave generating mechanism, a spike-generating mechanism, an inward Ca current, intracellular Ca ions, [Ca2+]in, their fast buffering and uptake by intracellular Ca stores, and a [Ca2+]in-inhibited Ca current. Chemosensitive voltage-activated conductance, gB*, responsible for termination of the spike burst, and chemosensitive sodium conductance, gNa*, responsible for the depolarization phase of the slow-wave, were used as control parameters. ... Time courses of the membrane potential and [Ca2+]in were employed to analyse different regimes in the model. ..."
29.  Dopaminergic cell bursting model (Kuznetsov et al 2006)
Dopaminergic neurons of the midbrain fire spontaneously at rates <10/s and ordinarily will not exceed this range even when driven with somatic current injection. During spontaneous bursting of dopaminergic neurons in vivo, bursts related to reward expectation in behaving animals, and bursts generated by dendritic application of N-methyl-D-aspartate (NMDA) agonists, transient firing attains rates well above this range. We suggest a way such highfrequency firing may occur in response to dendritic NMDA receptor activation. We have extended the coupled oscillator model of the dopaminergic neuron, which represents the soma and dendrites as electrically coupled compartments with different natural spiking frequencies, by addition of dendritic AMPA (voltage-independent) or NMDA (voltage-dependent) synaptic conductance. Both soma and dendrites contain a simplified version of the calcium-potassium mechanism known to be the mechanism for slow spontaneous oscillation and background firing in dopaminergic cells. We show that because of its voltage dependence, NMDA receptor activation acts to amplify the effect on the soma of the high-frequency oscillation of the dendrites, which is normally too weak to exert a large influence on the overall oscillation frequency of the neuron.
30.  Dorsal root ganglion (primary somatosensory) neurons (Rho & Prescott 2012)
In this paper, we demonstrate how dorsal root ganglion (DRG) neuron excitability can become pathologically altered, as occurs in neuropathic pain. Specifically, we reproduce pathological changes in spiking pattern (from transient to repetitive spiking) and the development of membrane potential oscillations and bursting.
31.  Double boundary value problem (A. Bose and J.E. Rubin, 2015)
For two neurons coupled with mutual inhibition, we investigate the strategies that each neuron should utilize in order to maximize the number of spikes it can fire (or equivalently the amount of time it is active) before the other neuron takes over. We derive a one-dimensional map whose fixed points correspond to periodic anti-phase bursting solutions. The model here solves a novel double boundary value problem that can be used to obtain the graph of this map. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218127415400040
32.  Drosophila 3rd instar larval aCC motoneuron (Gunay et al. 2015)
Single compartmental, ball-and-stick models implemented in XPP and full morphological model in Neuron. Paper has been submitted and correlates anatomical properties with electrophysiological recordings from these hard-to-access neurons. For instance we make predictions about location of the spike initiation zone, channel distributions, and synaptic input parameters.
33.  Dynamics of Spike Initiation (Prescott et al. 2008)
"Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin’s classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. ..."
34.  Effect of riluzole on action potential in cultured human skeletal muscle cells (Wang YJ et al. 2008)
Simulation studies also unraveled that both decreased conductance of I(Na) and increased conductance of I(K(Ca)) utilized to mimic riluzole actions in skeletal muscle cells could combine to decrease the amplitude of action potentials and increase the repolarization of action potentials.
35.  Effect of slowly inactivating IKdr to delayed firing of action potentials (Wu et al. 2008)
"The properties of slowly inactivating delayed-rectifier K+ current (IKdr) were investigated in NG108-15 neuronal cells differentiated with long-term exposure to dibutyryl cyclic AMP. ... The computer model, in which state-dependent inactivation of IKdr was incorporated, was also implemented to predict the firing behavior present in NG108-15 cells. ... Our theoretical work and the experimental results led us to propose a pivotal role of slowly inactivating IKdr in delayed firing of APs in NG108-15 cells. The results also suggest that aconitine modulation of IKdr gating is an important molecular mechanism through which it can contribute to neuronal firing."
36.  Effect of trp-like current on APs during exposure to sinusoidal voltage (Chen et al. 2010)
"... Previous work showed that magnetic electrical field-induced antinoceptive action is mediated by activation of capsaicin-sensitive sensory afferents. In this study, a modified Hodgkin-Huxley model, in which TRP-like current (I-TRP) was incorporated, was implemented to predict the firing behavior of action potentials (APs), as the model neuron was exposed to sinusoidal changes in externally-applied voltage. ... Our simulation results suggest that modulation of TRP-like channels functionally expressed in small-diameter peripheral sensory neurons should be an important mechanism through which it can contribute to the firing pattern of APs."
37.  Effects of eugenol on the firing of action potentials in NG108-15 neurons (Huang et al. 2011)
"Rationale: Eugenol (EUG, 4-allyl-2-methoxyphenol), the main component of essential oil extracted from cloves, has various uses in medicine because of its potential to modulate neuronal excitability. However, its effects on the ionic mechanisms remains incompletely understood. Objectives: We aimed to investigate EUG`s effects on neuronal ionic currents and excitability, especially on voltage-gated ion currents, and to verify the effects on a hyperexcitability-temporal lobe seizure model. Methods: With the aid of patch-clamp technology, we first investigated the effects of EUG on ionic currents in NG108-15 neuronal cells differentiated with cyclic AMP. We then used modified Pinsky-Rinzel simulation modeling to evaluate its effects on spontaneous action potentials (APs). Finally, we investigated its effects on pilocarpine-induced seizures in rats. Results: EUG depressed the transient and late components of INa in the neurons. It not only increased the degree of INa inactivation, but specifically suppressed the non-inactivating INa (INa(NI)). ... In addition, EUG diminished L-type Ca2+ current and delayed rectifier K+ current only at higher concentrations. EUG`s effects on APs frequency reduction was verified by the simulation modeling. In pilocarpine-induced seizures, the EUG-treated rats showed no shorter seizure latency but a lower seizure severity and mortality than the control rats. ... Conclusion: The synergistic blocking effects of INa and INa(NI) contributes to the main mechanism through which EUG affects the firing of neuronal APs and modulate neuronal hyperexcitability such as pilocarpine-induced temporal lobe seizures."
38.  Efffect of propofol on potassium current in cardiac H9c2 cells (Liu et al. 2008)
"... The effects of propofol, an intravenous anesthetic agent with a distinct chemical structure, on ion currents of differentiated clonal cardiac (H9c2) cells were investigated in this study. Propofol ... suppressed the amplitude of delayed rectifier K(+) current (I(K(DR))) in a concentration-dependent manner with an IC(50) value of 36 muM. ... Propofol (30 muM) had no effect on erg-mediated K(+) current in these cells; however, it suppressed L-type Ca(2+) current (I(Ca,L)) of cardiac and skeletal types to a similar extent. ... Numerical simulations of I(K(DR)) based on a Markovian model reproduce the experimental results and show that propofol-induced blockade of I(K(DR)) is associated with an decrease in forward rate of the activation process and an increase in transitional rate into the inactivated state. ..."
39.  Excitability of DA neurons and their regulation by synaptic input (Morozova et al. 2016a, 2016b)
This code contains conductance-based models of Dopaminergic (DA) and GABAergic neurons, used in Morozova et al 2016 PLOS Computational Biology paper in order to study the type of excitability of the DA neurons and how it is influenced by the intrinsic and synaptic currents. We identified the type of excitability by calculating bifurcation diagrams and F-I curves using XPP file. This model was also used in Morozova et al 2016 J. Neurophysiology paper in order to study the effect of synchronization in GABAergic inputs on the firing dynamics of the DA neuron.
40.  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.
41.  Explaining pathological changes in axonal excitability by dynamical analysis (Coggan et al. 2011)
"... To help decipher the biophysical basis for ‘paroxysmal’ spiking, we replicated afterdischarge (i.e. continued spiking after a brief stimulus) in a minimal conductance-based axon model. ... A perturbation could abruptly switch the system between two (quasi-)stable attractor states: rest and repetitive spiking. ... Initiation of afterdischarge was explained by activation of the persistent inward current forcing the system to cross a saddle point that separates the basins of attraction associated with each attractor. Termination of afterdischarge was explained by the attractor associated with repetitive spiking being destroyed. ... The model also explains other features of paroxysmal symptoms, including temporal summation and refractoriness."
42.  External Tufted Cell Model (Ryan Viertel, Alla Borisyuk 2019)
ODE model of the Mammalian External Tufted Cell
43.  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.
44.  Fast-spiking cortical interneuron (Golomb et al. 2007)
Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. We hypothesize that this variability emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. We construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na+, delayed-rectifier K+, and slowly inactivating d-type K+ conductances. The model may display delay to firing. Stuttering (elliptic bursting) and subthreshold oscillations may be observed for small Na+ window current.
45.  Fully continuous Pinsky-Rinzel model for bifurcation analysis (Atherton et al. 2016)
The original, 2-compartment, CA3 cell, Pinsky-Rinzel model (Pinsky, Rinzel 1994) has several discontinuous functions that prevent the use of standard bifurcation analysis tools to study the model. Here we present a modified, fully continuous system that captures the behaviour of the original model, while permitting the use of available numerical continuation software to perform full-system bifurcation and fast-slow analysis in XPPAUT.
46.  HERG K+ channels spike-frequency adaptation (Chiesa et al 1997)
Spike frequency adaptation has contributions from the IHERG current (encoded by the human eag-related gene (HERG); Warmke & Ganetzky, 1994), which develops with slow kinetics during depolarization and contributes to the repolarization of the long action potentials typically present in the heart. IHERG is one of the delayed rectifier currents (IK(r)) of the heart, and HERG mutations are associated with one of the cardiac arrhythmia LQT syndromes (LQT2). See paper for more and details.
47.  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. ..."
48.  Hippocampus CA1: Temporal sensitivity of signaling pathways underlying LTP (Kim et al. 2010)
Temporal sensitivity of signaling pathways underlying L-LTP. Single compartment, deterministic model of calcium and dopamine activated pathways, leading to CaMKII and PKA activation. Experimental verification of model prediction.
49.  Hodgkin-Huxley simplifed 2D and 3D models (Lundstrom et al. 2009)
"Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f–I curve. We introduce a novel classification of neurons into Types A, B&#8722;, and B+ according to how f–I curves are modulated by input fluctuations. ..."
50.  Hodgkin-Huxley with dynamic ion concentrations (Hubel and Dahlem, 2014)
The classical Hodgkin--Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. This model includes slow dynamics in an extended HH framework that simulates time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.
51.  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.
52.  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. Speci&#64257;cally, 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.
53.  Inhibitory control of motoneuron excitability (Venugopal et al 2011)
A two-compartment model for a motor neuron following chronic spinal cord injury with excessive dendritic persistent Ca2+ current.
54.  Inverse stochastic resonance of cerebellar Purkinje cell (Buchin et al. 2016)
This code shows the simulations of the adaptive exponential integrate-and-fire model (http://www.scholarpedia.org/article/Adaptive_exponential_integrate-and-fire_model) at different stimulus conditions. The parameters of the model were tuned to the Purkinje cell of cerebellum to reproduce the inhibiion of these cells by noisy current injections. Similar experimental protocols were also applied to the detailed biophysical model of Purkinje cells, de Shutter & Bower (1994) model. The repository also includes the XPPaut version of the model with the corresponding bifurcation analysis.
55.  Ion concentration dynamics as a mechanism for neuronal bursting (Barreto & Cressman 2011)
"We describe a simple conductance-based model neuron that includes intra and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems."
56.  Kv4.3, Kv1.4 encoded K(+) channel in heart cells (Greenstein et al 2000) (XPP)
A model of canine I:(to1) (the Ca(2+)-independent transient outward current) is formulated as the combination of Kv4.3 and Kv1.4 currents and is incorporated into an existing canine ventricular myocyte model. Simulations demonstrate strong coupling between L-type Ca(2+) current and I:(Kv4.3) and predict a bimodal relationship between I:(Kv4.3) density and APD whereby perturbations in I:(Kv4.3) density may produce either prolongation or shortening of APD, depending on baseline I:(to1) current level. The model files were submitted by: Dr. Sheng-Nan Wu, Dr. Ruey J. Sung, Ya-Jean Wang and Jiun-Shian Wu e-mail: snwu@mail.ncku.edu.tw
57.  Locational influence of dendritic PIC on input-output properties of spinal motoneurons (Kim 2017)
How does the dendritic location of calcium persistent inward current (Ca-PIC) influence dendritic excitability and firing behavior across the spinal motoneuron pool? This issue was investigated developing a model motoneuron pool where model parameters were analytically determined to reflect key motoneuron type-specific properties experimentally identified. The simulation results point out the negative relationship between the distance of Ca-PIC source from the soma and cell recruitment threshold as a basis underlying the systematic variation in input-output properties of motoneurons over the motoneuron pool.
58.  Markovian model for cardiac sodium channel (Clancy, Rudy 2002)
Complex physiological interactions determine the functional consequences of gene abnormalities and make mechanistic interpretation of phenotypes extremely difficult. A recent example is a single mutation in the C terminus of the cardiac Na(+) channel, 1795insD. The mutation causes two distinct clinical syndromes, long QT (LQT) and Brugada, leading to life-threatening cardiac arrhythmias. Coexistence of these syndromes is seemingly paradoxical; LQT is associated with enhanced Na(+) channel function, and Brugada with reduced function. Using a computational approach, we demonstrate that the 1795insD mutation exerts variable effects depending on the myocardial substrate. We develop Markov models of the wild-type and 1795insD cardiac Na(+) channels. See reference for more and details. The model files were submitted by: Dr. Jiun-Shian Wu, Dr. Sheng-Nan Wu, Dr. Ruey J. Sung, Han-Dong Chang.
59.  Markovian model for single-channel recordings of Ik_1 in ventricular cells (Matsuoka et al 2003)
The interaction between many currents in a cardiac ventricular model are examined in this paper. One of the main contributions come from a current called IK_1. An XPP version of this model was supplied by Hsieng-Jung Lai, Jiun-Shian Wu, Sheng-Nan Wu, Ruey J. Sung, Han-Dong Chang. Please see paper and model for more and details.
60.  Model of a BDNF feedback loop (Zhang et al 2016)
"Inhibitory avoidance (IA) training in rodents initiates a molecular cascade within hippocampal neurons. This cascade contributes to the transition of short- to long-term memory (i.e., consolidation). Here, a differential equation-based model was developed to describe a positive feedback loop within this molecular cascade. The feedback loop begins with an IA-induced release of brain-derived neurotrophic factor (BDNF), which in turn leads to rapid phosphorylation of the cAMP response element-binding protein (pCREB), and a subsequent increase in the level of the beta isoform of the CCAAT/enhancer binding protein (C/EBPbeta). ... " See paper for more.
61.  Model of DARPP-32 phosphorylation in striatal medium spiny neurons (Lindskog et al. 2006)
The work describes a model of how transient calcium and dopamine inputs might affect phosphorylation of DARPP-32 in the medium spiny neurons in the striatum. The model is relevant for understanding both the "three-factor rule" for synaptic plasticity in corticostriatal synapses, and also for relating reinforcement learning theories to biology.
62.  Modeling interactions in Aplysia neuron R15 (Yu et al 2004)
"The biophysical properties of neuron R15 in Aplysia endow it with the ability to express multiple modes of oscillatory electrical activity, such as beating and bursting. Previous modeling studies examined the ways in which membrane conductances contribute to the electrical activity of R15 and the ways in which extrinsic modulatory inputs alter the membrane conductances by biochemical cascades and influence the electrical activity. The goals of the present study were to examine the ways in which electrical activity influences the biochemical cascades and what dynamical properties emerge from the ongoing interactions between electrical activity and these cascades." See paper for more and details.
63.  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.
64.  Motoneuron model of self-sustained firing after spinal cord injury (Kurian et al. 2011)
" ... During the acute-stage of spinal cord injury (SCI), the endogenous ability to generate plateaus is lost; however, during the chronic-stage of SCI, plateau potentials reappear with prolonged self-sustained firing that has been implicated in the development of spasticity. In this work, we extend previous modeling studies to systematically investigate the mechanisms underlying the generation of plateau potentials in motoneurons, including the influences of specific ionic currents, the morphological characteristics of the soma and dendrite, and the interactions between persistent inward currents and synaptic input. ..."
65.  Multiscale model of olfactory receptor neuron in mouse (Dougherty 2009)
Collection of XPP (.ode) files simulating the signal transduction (slow) and action potential (fast) currents in the olfactory receptor neuron of mouse. Collection contains model configured for dual odorant pulse delivery and model configured for prolonged odorant delivery. For those interested more in transduction processes, each whole cell recording model comes with a counter part file configured to show just the slow transduction current for ease of use and convenience. These transduction-only models typically run faster than the full multi-scale models but do not demonstrate action potentials.
66.  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).
67.  Nicotinic control of dopamine release in nucleus accumbens (Maex et al. 2014)
Minimal model of the VTA (ventral segmental area) representing two (GABA versus dopamine) neuron populations and two subtypes of nicotinic receptors (alpha4beta2 versus alpha7). The model is used to tell apart circuit from receptor mechanisms in the nicotinic control of dopamine release and its pharmacological manipulation.
68.  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.
69.  Persistent Spiking in ACC Neurons (Ratte et al 2018)
"Neurons use action potentials, or spikes, to encode information. Some neurons can store information for short periods (seconds to minutes) by continuing to spike after a stimulus ends, thus enabling working memory. This so-called “persistent” spiking occurs in many brain areas and has been linked to activation of canonical transient receptor potential (TRPC) channels. However, TRPC activation alone is insufficient to explain many aspects of persistent spiking such as resumption of spiking after periods of imposed quiescence. Using experiments and simulations, we show that calcium influx caused by spiking is necessary and sufficient to activate TRPC channels and that the ensuing positive feedback interaction between intracellular calcium and TRPC channel activation can account for many hitherto unexplained aspects of persistent spiking."
70.  PreBotzinger Complex inspiratory neuron with NaP and CAN currents (Park and Rubin 2013)
We have built on earlier models to develop a single-compartment Hodgkin-Huxley type model incorporating NaP and CAN currents, both of which can play important roles in bursting of inspiratory neurons in the PreBotzinger Complex of the mammalian respiratory brain stem. The model tracks the evolution of membrane potential, related (in)activation variables, calcium concentration, and available fraction of IP3 channels. The model can produce several types of bursting, presented and analyzed from a dynamical systems perspective in our paper.
71.  Prediction for the presence of voltage-gated Ca2+ channels in myelinated central axons (Brown 2003)
"The objective of this current study was to investigate whether voltage gated Ca(2+) channels are present on axons of the adult rat optic nerve (RON). Simulations of axonal excitability using a Hodgkin-Huxley based one-compartment model incorporating I(Na), I(K) and leak currents were used to predict conditions under which the potential contribution of a Ca(2+) current to an evoked action potential could be measured. ... , as predicted by the simulation, reducing the repolarizing effect of I(K) by adding the K(+) channel blocker 4-AP revealed a Ca(2+) component on the repolarizing phase of the action potential that was blocked by the Ca(2+) channel inhibitor nifedipine."
72.  Properties of aconitine-induced block of KDR current in NG108-15 neurons (Lin et al. 2008)
"The effects of aconitine (ACO), a highly toxic alkaloid, on ion currents in differentiated NG108-15 neuronal cells were investigated in this study. ACO (0.3-30 microM) suppressed the amplitude of delayed rectifier K+ current (IK(DR)) in a concentration-dependent manner with an IC50 value of 3.1 microM. The presence of ACO enhanced the rate and extent of IK(DR) inactivation, although it had no effect on the initial activation phase of IK(DR). ... A modeled cell was designed to duplicate its inhibitory effect on spontaneous pacemaking. ... Taken together, the experimental data and simulations show that ACO can block delayed rectifier K+ channels of neurons in a concentration- and state-dependent manner. Changes in action potentials induced by ACO in neurons in vivo can be explained mainly by its blocking actions on IK(DR) and INa."
73.  Pyramidal neurons switch from integrators to resonators (Prescott et al. 2008)
During wakefulness, pyramidal neurons in the intact brain are bombarded by synaptic input that causes tonic depolarization, increased membrane conductance (i.e. shunting), and noisy fluctuations in membrane potential; by comparison, pyramidal neurons in acute slices typically experience little background input. Such differences in operating conditions can compromise extrapolation of in vitro data to explain neuronal operation in vivo. ... in slice experiments, we show that CA1 hippocampal pyramidal cells switch from integrators to resonators, i.e. from class 1 to class 2 excitability. The switch is explained by increased outward current contributed by the M-type potassium current IM ... Thus, even so-called “intrinsic” properties may differ qualitatively between in vitro and in vivo conditions.
74.  Reliability of Morris-Lecar neurons with added T, h, and AHP currents (Zeldenrust et al. 2013)
We investigated the reliability of the timing of spikes in a spike train in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected. The neuron responded with spike trains that showed trial-to-trial variability. The reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates.
75.  Rescue of plasticity by a computationally predicted protocol (Liu et al. 2013)
" ... A computational model, which simulated molecular processes underlying long-term synaptic facilitation (LTF) induction, predicted a rescue protocol of five pulses of 5-HT at non-uniform interstimulus intervals that overcame the consequences of reduced CREB-binding protein (CBP) and restored LTF. ..."
76.  Respiratory central pattern generator (mammalian brainstem) (Rubin & Smith 2019)
This model includes a conditional respiratory pacemaker unit (representing the pre-Botzinger Complex), which can be tuned across oscillatory and non-oscillatory dynamic regimes in isolation, embedded into a full respiratory network. The work shows that under this embedding, the pacemaker unit's dynamics become masked: the network exhibits similar dynamical properties regardless of the conditional pacemaker node's tuning, and that node's outputs are dominated by network influences.
77.  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.
78.  Respiratory control model with brainstem CPG and sensory feedback (Diekman, Thomas, and Wilson 2017)
This is a closed-loop respiratory control model incorporating a central pattern generator (CPG), the Butera-Rinzel-Smith (BRS) model, together with lung mechanics, oxygen handling, and chemosensory components. The closed-loop system exhibits bistability of bursting and tonic spiking. Bursting corresponds to coexistence of eupnea-like breathing, with normal minute ventilation and blood oxygen level. Tonic spiking corresponds to a tachypnea-like state, with pathologically reduced minute ventilation and critically low blood oxygen. In our paper, we use the closed-loop system to demonstrate robustness to changes in metabolic demand, spontaneous autoresuscitation in response to hypoxia, and the distinct mechanisms that underlie rhythmogenesis in the intact control circuit vs. the isolated, open-loop CPG.
79.  Role of active dendrites in rhythmically-firing neurons (Goldberg et al 2006)
"The responsiveness of rhythmically-firing neurons to synaptic inputs is characterized by their phase response curve (PRC), which relates how weak somatic perturbations affect the timing of the next action potential. The shape of the somatic PRC is an important determinant of collective network dynamics. Here we study theoretically and experimentally the impact of distally-located synapses and dendritic nonlinearities on the synchronization properties of rhythmically firing neurons. Combining the theories of quasi-active cables and phase-coupled oscillators we derive an approximation for the dendritic responsiveness, captured by the neuron's dendritic PRC (dPRC). This closed-form expression indicates that the dPRCs are linearly-filtered versions of the somatic PRC, and that the filter characteristics are determined by the passive and active properties of the dendrite. ... collective dynamics can be qualitatively different depending on the location of the synapse, the neuronal firing rates and the dendritic nonlinearities." See paper for more and details.
80.  Role of KCNQ1 and IKs in cardiac repolarization (Silva, Rudy 2005) (XPP)
Detailed Markov model of IKs (the slow delayed rectifier K+ current) is supplied here in XPP. The model is compared to experiment in the paper. The role of IKs in disease and drug treatments is elucidated (the prevention of excessive action potential prolongation and development of arrhythmogenic early afterdepolarizations). See also modeldb accession number 55748 code and reference for more and details. This XPP version of the model reproduces Figure 3C in the paper by default. These model files were submitted by: Dr. Sheng-Nan Wu, Han-Dong Chang, Jiun-Shian Wu Department of Physiology National Cheng Kung University Medical College
81.  Roles of I(A) and morphology in AP prop. in CA1 pyramidal cell dendrites (Acker and White 2007)
" ...Using conductance-based models of CA1 pyramidal cells, we show that underlying “traveling wave attractors” control action potential propagation in the apical dendrites. By computing these attractors, we dissect and quantify the effects of IA channels and dendritic morphology on bAP amplitudes. We find that non-uniform activation properties of IA can lead to backpropagation failure similar to that observed experimentally in these cells. ... "
82.  Simulation of calcium signaling in fine astrocytic processes (Denizot et al 2019)
This model corresponds to the model presented in Denizot et al, 2019. The model indicates that the frequency of calcium signals crucially depends on the spatial organization of the IP3R channels, including their clustering and co-localization with the other sources of calcium influx to the cytosol. Spontaneous calcium signals generated by the model with realistic PAPs volume and calcium concentration successfully reproduce spontaneous calcium transients that we measured in calcium micro-domains with confocal microscopy. To our knowledge, this model is the first model suited to the investigation of spontaneous calcium dynamics in fine astrocytic processes, a crucial step towards a better understanding of the spatio-temporal integration of astrocyte signals in response to neuronal activity.
83.  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.
84.  Single neuron with dynamic ion concentrations (Cressman et al. 2009)
These are the full and reduced models of a generic single neuron with dynamic ion concentrations as described in Cressman et al., Journal of Computational Neuroscience (2009) 26:159–170.
85.  Spike trains in Hodgkin–Huxley model and ISIs of acupuncture manipulations (Wang et al. 2008)
The Hodgkin-Huxley equations (HH) are parameterized by a number of parameters and shows a variety of qualitatively different behaviors depending on the parameter values. Under stimulation of an external periodic voltage, the ISIs (interspike intervals) of a HH model are investigated in this work, while the frequency of the voltage is taken as the controlling parameter. As well-known, the science of acupuncture and moxibustion is an important component of Traditional Chinese Medicine with a long history. Although there are a number of different acupuncture manipulations, the method for distinguishing them is rarely investigated. With the idea of ISI, we study the electrical signal time series at the spinal dorsal horn produced by three different acupuncture manipulations in Zusanli point and present an effective way to distinguish them.
86.  Spontaneous calcium oscillations in astrocytes (Lavrentovich and Hemkin 2008)
" ... We propose here a mathematical model of how spontaneous Ca2+ oscillations arise in astrocytes. This model uses the calcium-induced calcium release and inositol cross-coupling mechanisms coupled with a receptor-independent method for producing inositol (1,4,5)-trisphosphate as the heart of the model. By computationally mimicking experimental constraints we have found that this model provides results that are qualitatively similar to experiment."
87.  Spreading depression model for FHM3 with Nav1.1 mutation (Dahlem et al. 2014)
Familial hemiplegic migraine (FHM) is a rare subtype of migraine with aura. A mutation causing FHM type 3 (FHM3) has been identified in SCN1A encoding the Nav1.1 Na+ channel. This genetic defect affects the inactivation gate. The code describes an extended Hodgkin-Huxley framework with dynamic ion concentrations in a wilde-type and mutant form.
88.  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."
89.  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.
90.  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. ..."
91.  Synergistic inhibitory action of oxcarbazepine on INa and IK (Huang et al. 2008)
"Oxcarbazepine (OXC), one of the newer anti-epileptic drugs, has been demonstrating its efficacy on wide-spectrum neuropsychiatric disorders. ... With the aid of patch-clamp technology, we first investigated the effects of OXC on ion currents in NG108-15 neuronal cells differentiated with cyclic AMP. We found OXC ... caused a reversible reduction in the amplitude of voltage-gated Na+ current (INa) ... and produce(d) a significant prolongation in the recovery of INa inactivation. ... Moreover, OXC could suppress the amplitude of delayed rectifier K+ current (IK(DR)), with no effect on M-type K+ current (IK(M)). ... Furthermore, the simulations, based on hippocampal pyramidal neurons (Pinsky-Rinzel model) and a network of the Hodgkin-Huxley model, were analysed to investigate the effect of OXC on action potentials. Taken together, our results suggest that the synergistic blocking effects on INa and IK(DR) may contribute to the underlying mechanisms through which OXC affects neuronal function in vivo."
92.  Tapered whiskers are required for active tactile sensation (Hires et al. 2013)
" ... The diverse shapes of facial whiskers reflect distinct ecological niches. Rodent whiskers are conical, often with a remarkably linear taper. Here we use theoretical and experimental methods to analyze interactions of mouse whiskers with objects. ... " This is a quasi-static solution of the bending of an isolated whisker. For Fig. 2, stable solution, use: theta=-0.174533 rad. Use "Bndryval -> Show" in XPPAUT.
93.  Thalamocortical loop with delay for investigation of absence epilepsy (Liu et al 2019)
Conductance based network model of one thalamic reticular neuron, one thalamic pyramidal neuron and one cortical pyramidal neuron. Used to show that large delay in the corticothalamic connection can lead to multistability.
94.  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.
95.  The role of ATP-sensitive potassium channels in a hippocampal neuron (Huang et al. 2007)
"Hyperglycemia-related neuronal excitability and epileptic seizures are not uncommon in clinical practice. However, their underlying mechanism remains elusive. ATP-sensitive K(+) (K(ATP)) channels are found in many excitable cells, including cardiac myocytes, pancreatic beta cells, and neurons. These channels provide a link between the electrical activity of cell membranes and cellular metabolism. We investigated the effects of higher extracellular glucose on hippocampal K(ATP) channel activities and neuronal excitability. The cell-attached patch-clamp configuration on cultured hippocampal cells and a novel multielectrode recording system on hippocampal slices were employed. In addition, a simulation modeling hippocampal CA3 pyramidal neurons (Pinsky-Rinzel model) was analyzed to investigate the role of K(ATP) channels in the firing of simulated action potentials. ..."
96.  The role of glutamate in neuronal ion homeostasis: spreading depolarization (Hubel et al 2017)
This model includes ion concentration dynamics (sodium, potassium, chloride) inside and outside the neuron, the exchange of ions with glia and blood vessels, volume dynamics of neuron, glia, and extracellular space, glutamate homeostasis involving release by neuron and uptake by both neuron and glia. Spreading depolarization is used as a case study.
97.  Ventricular cell model (Luo Rudy dynamic model) (Luo Rudy 1994) used in (Wang et al 2006) (XPP)
A mathematical model of the membrane action potential of the mammalian ventricular cell introduced in Luo, Rudy 1991 and used in Wang et al 2006 is made available here in XPP. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K]o. ... The results are consistent with recent experimental observations, and the model simulations relate these phenomena to the underlying ionic channel kinetics. See papers for more and details.
98.  Zonisamide-induced inhibition of the firing of APs in hippocampal neurons (Huang et al. 2007)
Zonisamide (ZNS), a synthetic benzisoxazole derivative, has been used as an alternative choice in the treatment of epilepsy with a better efficacy and safety profile. However, little is known regarding the mechanism of ZNS actions on ion currents in neurons. We thus investigated its effect on ion currents in differentiated hippocampal 19-7 cells. The ZNS (30 uM) reversibly increased the amplitude of K+ outward currents and paxilline (1 uM) was effective in suppressing ZNS-induced increase of K+ outward currents. In inside-out configuration, ZNS (30 uM) applied to the intracellular face of the membrane did not alter single-channel conductance; however, it did enhance the activity of large-conductance Ca2+-activated K+ (BKCa) channels primarily by decreasing mean closed time. The EC50 value for ZNS-stimulated BKCa channels was 34 uM. This drug caused a left shift in the activation curve of BKCa channels with no change in the gating charge of these channels. ZNS at a concentration greater than 100 uM also reduced the amplitude of A-type K+ current in these cells. A simulation modeling based on hippocampal CA3 pyramidal neurons (Pinsky-Rinzel model) was also analyzed to investigate the inhibitory effect of ZNS on the firing of simulated action potentials. Taken together, this study suggests that in hippocampal neurons, during the exposure to ZNS, the ZNS-mediated effects on BKCa channels and IA could be one of the ionic mechanisms through which it affects neuronal excitability.

Re-display model names without descriptions