Models that contain the Model Concept : Bifurcation

(A bifurcation is a sudden qualitative change in the behavior of a dynamical system caused by a change in a parameter(s).)
Re-display model names without descriptions
    Models   Description
1.  A bistable model of Spike-Wave seizure and background activity (Taylor et al. 2014)
This is a four-variable model (in the Amari formalism) of bistable Spike-Wave seizure dynamics and background activity (fixed point). The published code is the deterministic version of the model in the related publication. This model can be used to investigate seizure abatement using stimulation.
2.  A computational model of a small DRG neuron to explore pain (Verma et al. 2019, 2020)
This is a Hodgkin-Huxley type model for a small DRG neuron consisting of four voltage-gated ion channels: sodium channels 1.7 and 1.8, delayed rectifier potassium, and A-type transient potassium channels. This model was used to explore the dynamics of this neuron using bifurcation theory, with the motive to investigate pain since small DRG neuron is a pain-sensing neuron.
3.  A cortical sheet mesoscopic model for investigating focal seizure onset dynamics (Wang et al. 2014)
The model uses realistically coupled, discretised, Wilson-Cowan units to describe the spatio-temporal activity of a cortical sheet. This model has been used the investigate the dynamic onset mechanisms of focal seizures.
4.  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. ..."
5.  A Moth MGC Model-A HH network with quantitative rate reduction (Buckley & Nowotny 2011)
We provide the model used in Buckley & Nowotny (2011). It consists of a network of Hodgkin Huxley neurons coupled by slow GABA_B synapses which is run alongside a quantitative reduction described in the associated paper.
6.  Ave. neuron model for slow-wave sleep in cortex Tatsuki 2016 Yoshida 2018 Rasmussen 2017 (all et al)
Averaged neuron(AN) model is a conductance-based (Hodgkin-Huxley type) neuron model which includes a mean-field approximation of a population of neurons. You can simulate previous models (AN model: Tatsuki et al., 2016 and SAN model: Yoshida et al., 2018), and various models with 'X model' based on channel and parameter modules. Also, intracellular and extracellular ion concentration can be taken into consideration using the Nernst equation (See Ramussen et al., 2017).
7.  Bursting and oscillations in RD1 Retina driven by AII Amacrine Neuron (Choi et al. 2014)
"In many forms of retinal degeneration, photoreceptors die but inner retinal circuits remain intact. In the rd1 mouse, an established model for blinding retinal diseases, spontaneous activity in the coupled network of AII amacrine and ON cone bipolar cells leads to rhythmic bursting of ganglion cells. Since such activity could impair retinal and/or cortical responses to restored photoreceptor function, understanding its nature is important for developing treatments of retinal pathologies. Here we analyzed a compartmental model of the wild-type mouse AII amacrine cell to predict that the cell's intrinsic membrane properties, specifically, interacting fast Na and slow, M-type K conductances, would allow its membrane potential to oscillate when light-evoked excitatory synaptic inputs were withdrawn following photoreceptor degeneration. ..."
8.  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.
9.  CA1 pyramidal neuron: depolarization block (Bianchi et al. 2012)
NEURON files from the paper: On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons by D.Bianchi, A. Marasco, A.Limongiello, C.Marchetti, H.Marie,B.Tirozzi, M.Migliore (2012). J Comput. Neurosci. In press. DOI: 10.1007/s10827-012-0383-y. Experimental findings shown that under sustained input current of increasing strength neurons eventually stop firing, entering a depolarization block. We analyze the spiking dynamics of CA1 pyramidal neuron models using the same set of ionic currents on both an accurate morphological reconstruction and on its reduction to a single-compartment. The results show the specic ion channel properties and kinetics that are needed to reproduce the experimental findings, and how their interplay can drastically modulate the neuronal dynamics and the input current range leading to depolarization block.
10.  Cardiac models of circadian rhythms in early afterdepolarizations & arrhythmias (Diekman & Wei 2021)
We fit a simplified Luo-Rudy model to voltage-clamp data showing a circadian rhythm in L-type calcium conductance. Simulations of the model (single-cell and 2-D spatial versions) suggest that circadian rhythms in early afterdepolarizations may contribute to daily rhythms in cardiac arrhythmias and sudden cardiac death.
11.  Cell signaling/ion channel variability effects on neuronal response (Anderson, Makadia, et al. 2015)
" ... We evaluated the impact of molecular variability in the expression of cell signaling components and ion channels on electrophysiological excitability and neuromodulation. We employed a computational approach that integrated neuropeptide receptor-mediated signaling with electrophysiology. We simulated a population of neurons in which expression levels of a neuropeptide receptor and multiple ion channels were simultaneously varied within a physiological range. We analyzed the effects of variation on the electrophysiological response to a neuropeptide stimulus. ..."
12.  Cerebellar stellate cells: changes in threshold, latency and frequency of firing (Mitry et al 2020)
"Cerebellar stellate cells are inhibitory molecular interneurons that regulate the firing properties of Purkinje cells, the sole output of cerebellar cortex. Recent evidence suggests that these cells exhibit temporal increase in excitability during whole-cell patch-clamp configuration in a phenomenon termed runup. They also exhibit a non-monotonic first-spike latency profile as a function of the holding potential in response to a fixed step-current. In this study, we use modeling approaches to unravel the dynamics of runup and categorize the firing behavior of cerebellar stellate cells as either type I or type II oscillators. We then extend this analysis to investigate how the non-monotonic latency profile manifests itself during runup. We employ a previously developed, but revised, Hodgkin–Huxley type model to show that stellate cells are indeed type I oscillators possessing a saddle node on an invariant cycle (SNIC) bifurcation. The SNIC in the model acts as a “threshold” for tonic firing and produces a slow region in the phase space called the ghost of the SNIC. The model reveals that (i) the SNIC gets left-shifted during runup with respect to I app = I test in the current-step protocol, and (ii) both the distance from the stable limit cycle along with the slow region produce the non-monotonic latency profile as a function of holding potential. Using the model, we elucidate how latency can be made arbitrarily large for a specific range of holding potentials close to the SNIC during pre-runup (post-runup). We also demonstrate that the model can produce transient single spikes in response to step- currents entirely below I SNIC , and that a pair of dynamic inhibitory and excitatory post- synaptic inputs can robustly evoke action potentials, provided that the magnitude of the inhibition is either low or high but not intermediate. Our results show that the topology of the SNIC is the key to explaining such behaviors."
13.  Cooling reverses pathological spontaneous firing caused by mild traumatic injury (Barlow et al 2018)
"Mild traumatic injury can modify the key sodium (Na+) current underlying the excitability of neurons. It causes the activation and inactivation properties of this current to become shifted to more negative trans-membrane voltages. This so-called coupled left shift (CLS) leads to a chronic influx of Na+ into the cell that eventually causes spontaneous or “ectopic” firing along the axon, even in the absence of stimuli. The bifurcations underlying this enhanced excitability have been worked out in full ionic models of this effect. Here, we present computational evidence that increased temperature T can exacerbate this pathological state. Conversely, and perhaps of clinical relevance, mild cooling is shown to move the naturally quiescent cell further away from the threshold of ectopic behavior. ..."
14.  Dependence of neuronal firing on astroglial membrane transport mechanisms (Oyehaug et al 2012)
"Exposed to a sufficiently high extracellular potassium concentration ([K?+?]o), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation (‘depolarisation block’). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K?+?]o causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K?+?]o conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin–Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. ..."
15.  Dopamine-modulated medium spiny neuron, reduced model (Humphries et al. 2009)
We extended Izhikevich's reduced model of the striatal medium spiny neuron (MSN) to account for dopaminergic modulation of its intrinsic ion channels and synaptic inputs. We tuned our D1 and D2 receptor MSN models using data from a recent (Moyer et al, 2007) large-scale compartmental model. Our new models capture the input-output relationships for both current injection and spiking input with remarkable accuracy, despite the order of magnitude decrease in system size. They also capture the paired pulse facilitation shown by MSNs. Our dopamine models predict that synaptic effects dominate intrinsic effects for all levels of D1 and D2 receptor activation. Our analytical work on these models predicts that the MSN is never bistable. Nonetheless, these MSN models can produce a spontaneously bimodal membrane potential similar to that recently observed in vitro following application of NMDA agonists. We demonstrate that this bimodality is created by modelling the agonist effects as slow, irregular and massive jumps in NMDA conductance and, rather than a form of bistability, is due to the voltage-dependent blockade of NMDA receptors
16.  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.
17.  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. ..."
18.  Effect of cortical D1 receptor sensitivity on working memory maintenance (Reneaux & Gupta 2018)
Alterations in cortical D1 receptor density and reactivity of dopamine-binding sites, collectively termed as D1 receptor-sensitivity in the present study, have been experimentally shown to affect the working memory maintenance during delay-period. However, computational models addressing the effect of D1 receptor-sensitivity are lacking. A quantitative neural mass model of the prefronto-mesoprefrontal system has been proposed to take into account the effect of variation in cortical D1 receptor-sensitivity on working memory maintenance during delay. The model computes the delay-associated equilibrium states/operational points of the system for different values of D1 receptor-sensitivity through the nullcline and bifurcation analysis. Further, to access the robustness of the working memory maintenance during delay in the presence of alteration in D1 receptor-sensitivity, numerical simulations of the stochastic formulation of the model are performed to obtain the global potential landscape of the dynamics.
19.  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.
20.  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.
21.  Functional impact of dendritic branch point morphology (Ferrante et al., 2013)
" ... Here, we first quantified the morphological variability of branch points from two-photon images of rat CA1 pyramidal neurons. We then investigated the geometrical features affecting spike initiation, propagation, and timing with a computational model validated by glutamate uncaging experiments. The results suggest that even subtle membrane readjustments at branch point could drastically alter the ability of synaptic input to generate, propagate, and time action potentials."
22.  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−, and B+ according to how f–I curves are modulated by input fluctuations. ..."
23.  How adaptation makes low firing rates robust (Sherman & Ha 2017)
"Low frequency firing is modeled by Type 1 neurons with a SNIC (saddle node on an invariant circle), but, because of the vertical slope of the square-root-like f–I curve, low f only occurs over a narrow range of I. When an adaptive current is added, however, the f–I curve is linearized, and low f occurs robustly over a large I range. Ermentrout (Neural Comput. 10(7):1721-1729, 1998) showed that this feature of adaptation paradoxically arises from the SNIC that is responsible for the vertical slope. We show, using a simplified Hindmarsh–Rose neuron with negative feedback acting directly on the adaptation current, that whereas a SNIC contributes to linearization, in practice linearization over a large interval may require strong adaptation strength. We also find that a type 2 neuron with threshold generated by a Hopf bifurcation can also show linearization if adaptation strength is strong. Thus, a SNIC is not necessary. More fundamental than a SNIC is stretching the steep region near threshold, which stems from sufficiently strong adaptation, though a SNIC contributes if present. In a more realistic conductance-based model, Morris–Lecar, with negative feedback acting on the adaptation conductance, an additional assumption that the driving force of the adaptation current is independent of I is needed. If this holds, strong adaptive conductance is both necessary and sufficient for linearization of f–I curves of type 2 f–I curves."
24.  Irregular spiking in NMDA-driven prefrontal cortex neurons (Durstewitz and Gabriel 2006)
Slow N-Methyl-D-aspartic acid (NMDA) synaptic currents are assumed to strongly contribute to the persistently elevated firing rates observed in prefrontal cortex (PFC) during working memory. During persistent activity, spiking of many neurons is highly irregular. ... The highest interspike-interval (ISI) variability occurred in a transition regime where the subthreshold membrane potential distribution shifts from mono- to bimodality, ... Predictability within irregular ISI series was significantly higher than expected from a noise-driven linear process, indicating that it might best be described through complex (potentially chaotic) nonlinear deterministic processes. Accordingly, the phenomena observed in vitro could be reproduced in purely deterministic biophysical model neurons. High spiking irregularity in these models emerged within a chaotic, close-to-bifurcation regime characterized by a shift of the membrane potential distribution from mono- to bimodality and by similar ISI return maps as observed in vitro. ... NMDA-induced irregular dynamics may have important implications for computational processes during working memory and neural coding.
25.  Leech Heart Interneuron model (Sharma et al 2020)
Fractional order Leech heart interneuron model is investigated. Different firing properties are explored. In this article, we investigate the alternation of spiking and bursting phenomena of an uncoupled and coupled fractional Leech-Heart (L-H) neurons. We show that a complete graph of heterogeneous de-synchronized neurons in the backdrop of diverse memory settings (a mixture of integer and fractional exponents) can eventually lead to bursting with the formation of cluster synchronization over a certain threshold of coupling strength, however, the uncoupled L-H neurons cannot reveal bursting dynamics. Using the stability analysis in fractional domain, we demarcate the parameter space where the quiescent or steady-state emerges in uncoupled L-H neuron. Finally, a reduced-order model is introduced to capture the activities of the large network of fractional-order model neurons.
26.  Mean-field models of neural populations under electrical stimulation (Cakan & Obermayer 2020)
Weak electrical inputs to the brain in vivo using transcranial electrical stimulation or in isolated cortex in vitro can affect the dynamics of the underlying neural populations. However, it is poorly understood what the exact mechanisms are that modulate the activity of neural populations as a whole and why the responses are so diverse in stimulation experiments. Despite this, electrical stimulation techniques are being developed for the treatment of neurological diseases in humans. To better understand these interactions, it is often necessary to simulate and analyze very large networks of neurons, which can be computationally demanding. In this theoretical paper, we present a reduced model of coupled neural populations that represents a piece of cortical tissue. This efficient model retains the dynamical properties of the large network of neurons it is based on while being several orders of magnitude faster to simulate. Due to the biophysical properties of the neuron model, an electric field can be coupled to the population. We show that weak electric fields often used in stimulation experiments can lead to entrainment of neural oscillations on the population level, and argue that the responses critically depend on the dynamical state of the neural system.
27.  Minimal model of interictal and ictal discharges “Epileptor-2” (Chizhov et al 2018)
"Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. ..."
28.  Mixed mode oscillations as a mechanism for pseudo-plateau bursting (Vo et al. 2010)
"We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. ..."
29.  Morphological determinants of dendritic arborization neurons in Drosophila larva (Nanda et al 2018)
"Pairing in vivo imaging and computational modeling of dendritic arborization (da) neurons from the fruit fly larva provides a unique window into neuronal growth and underlying molecular processes. We image, reconstruct, and analyze the morphology of wild-type, RNAi-silenced, and mutant da neurons. We then use local and global rule-based stochastic simulations to generate artificial arbors, and identify the parameters that statistically best approximate the real data. We observe structural homeostasis in all da classes, where an increase in size of one dendritic stem is compensated by a reduction in the other stems of the same neuron. Local rule models show that bifurcation probability is determined by branch order, while branch length depends on path distance from the soma. Global rule simulations suggest that most complex morphologies tend to be constrained by resource optimization, while simpler neuron classes privilege path distance conservation. Genetic manipulations affect both the local and global optimal parameters, demonstrating functional perturbations in growth mechanisms."
30.  Multiple dynamical modes of thalamic relay neurons (Wang XJ 1994)
The (Wang 1994) papers model was replicated in python by (Detorakis 2016). "The model is conductance-based and takes advantage of the interplay between a T-type calcium current and a non-specific cation sag current and thus, it is able to generate spindle and delta rhythms." The model also generates intermittent phase locking, non periodic firing, bursts, and tonic spike patterns.
31.  Neural mass model of spindle generation in the isolated thalamus (Schellenberger Costa et al. 2016)
The model generates different oscillatory patterns in the thalamus, including delta and spindle band oscillations.
32.  Neural mass model of the neocortex under sleep regulation (Costa et al 2016)
This model generates typical human EEG patterns of sleep stages N2/N3 as well as wakefulness and REM. It further contains a sleep regulatory component, that lets the model transition between those stages independently
33.  Neural mass model of the sleeping cortex (Weigenand et al 2014)
Generates typical EEG data of sleeping Humans for sleep stages N2/N3 as well as wakefulness
34.  Neural mass model of the sleeping thalamocortical system (Schellenberger Costa et al 2016)
This paper generates typical human EEG data of sleep stages N2/N3 as well as wakefulness and REM sleep.
35.  Origin of heterogeneous spiking patterns in spinal dorsal horn neurons (Balachandar & Prescott 2018)
"Neurons are often classified by spiking pattern. Yet, some neurons exhibit distinct patterns under subtly different test conditions, which suggests that they operate near an abrupt transition, or bifurcation. A set of such neurons may exhibit heterogeneous spiking patterns not because of qualitative differences in which ion channels they express, but rather because quantitative differences in expression levels cause neurons to operate on opposite sides of a bifurcation. Neurons in the spinal dorsal horn, for example, respond to somatic current injection with patterns that include tonic, single, gap, delayed and reluctant spiking. It is unclear whether these patterns reflect five cell populations (defined by distinct ion channel expression patterns), heterogeneity within a single population, or some combination thereof. We reproduced all five spiking patterns in a computational model by varying the densities of a low-threshold (KV1-type) potassium conductance and an inactivating (A-type) potassium conductance and found that single, gap, delayed and reluctant spiking arise when the joint probability distribution of those channel densities spans two intersecting bifurcations that divide the parameter space into quadrants, each associated with a different spiking pattern. ... "
36.  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.
37.  Reduction of nonlinear ODE systems possessing multiple scales (Clewley et al. 2005)
" ... We introduce a combined numerical and analytical technique that aids the identification of structure in a class of systems of nonlinear ordinary differential equations (ODEs) that are commonly applied in dynamical models of physical processes. ... These methods have been incorporated into a new software tool named Dssrt, which we demonstrate on a limit cycle of a synaptically driven Hodgkin–Huxley neuron model."
38.  Robust and tunable bursting requires slow positive feedback (Franci et al 2018)
"We highlight that the robustness and tunability of a bursting model critically rely on currents that provide slow positive feedback to the membrane potential. Such currents have the ability to make the total conductance of the circuit negative in a timescale that is termed “slow” because it is intermediate between the fast timescale of the spike upstroke and the ultraslow timescale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale."
39.  Robust modulation of integrate-and-fire models (Van Pottelbergh et al 2018)
"By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks."
40.  Simulating ion channel noise in an auditory brainstem neuron model (Schmerl & McDonnell 2013)
" ... Here we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burstlike dynamics. ..." Preprint available at
41.  The relationship between two fast/slow analysis techniques for bursting oscill. (Teka et al. 2012)
"Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical manifold. … We find that the z-curve and Hopf bifurcation of the twofast/ one-slow decomposition are closely related to the voltage nullcline and folded node singularity of the one-fast/two-slow decomposition, respectively. They become identical in the double singular limit in which voltage is infinitely fast and calcium is infinitely slow."
42.  Understanding how fast activating K+ channels promote bursting in pituitary cells (Vo et al 2014)
"... Experimental observations have shown ... that fast-activating voltage- and calcium-dependent potassium (BK) current tends to promote bursting in pituitary cells. This burst promoting effect requires fast activation of the BK current, otherwise it is inhibitory to bursting. In this work, we analyze a pituitary cell model in order to answer the question of why the BK activation must be fast to promote bursting. ..."

Re-display model names without descriptions