**(The model is written in the C or C++ language.)**

Models | Description |

A dynamical model of the basal ganglia (Leblois et al 2006) | |

We propose a new model for the function and dysfunction of the basal ganglia (BG). The basal ganglia are a set of cerebral structures involved in motor control which dysfunction causes high-incidence pathologies such as Parkinson's disease (PD). Their precise motor functions remain unknown. The classical model of the BG that allowed for the discovery of new treatments for PD seems today outdated in several respects. Based on experimental observations, our model proposes a simple dynamical framework for the understanding of how BG may select motor programs to be executed. Moreover, we explain how this ability is lost and how tremor-related oscillations in neuronal activity may emerge in PD. | |

A four compartmental model for ABPD complex in crustacean pyloric network (Maran et al. 2011) | |

"Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. ..." | |

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. | |

Accurate and fast simulation of channel noise in conductance-based model neurons (Linaro et al 2011) | |

We introduce and operatively present a general method to simulate channel noise in conductance-based model neurons, with modest computational overheads. Our approach may be considered as an accurate generalization of previous proposal methods, to the case of voltage-, ion-, and ligand-gated channels with arbitrary complexity. We focus on the discrete Markov process descriptions, routinely employed in experimental identification of voltage-gated channels and synaptic receptors. | |

An oscillatory neural model of multiple object tracking (Kazanovich and Borisyuk 2006) | |

An oscillatory neural network model of multiple object tracking is described. The model works with a set of identical visual objects moving around the screen. At the initial stage, the model selects into the focus of attention a subset of objects initially marked as targets. Other objects are used as distractors. The model aims to preserve the initial separation between targets and distractors while objects are moving. This is achieved by a proper interplay of synchronizing and desynchronizing interactions in a multilayer network, where each layer is responsible for tracking a single target. The results of the model simulation are presented and compared with experimental data. In agreement with experimental evidence, simulations with a larger number of targets have shown higher error rates. Also, the functioning of the model in the case of temporarily overlapping objects is presented. | |

Application of Parker-Sochacki method to Hodgkin-Huxley equations (Wilanowski 2013, in review) | |

Reproduces figures 2-3 from Wilanowski, G. Integrating Hodgkin-Huxley equations (in review) The implementation of the giant squid axon and the Booth model with the Parker-Sochacki method combined with cubic splines interpolation of the Hodgkin-Huxley equations. Contact gwilanowski@ibib.waw.pl if you have any questions about the implementation of the model. Usage: 1. Unzip wilanowski2013.zip into empty directory. 2. Run simulation.m MATLAB script 3. A menu will appear that offers a selection of models (the giant squid axon or the Booth model 4. Choose 1 or 2 to reproduce the simulations shown Fig. 1 or Fig 2 of the original article. Only the Parker-Sochacki traces can be reproduced. Curve Fitting Toolbox is required. The program runs on Windows. It bases upon Numerical Integration of Izhikevich and HH model neurons (Stewart and Bair 2009) (http://senselab.med.yale.edu/modeldb/showmodel.asp?model=117361) | |

Auditory nerve model for predicting performance limits (Heinz et al 2001) | |

A computational auditory nerve (AN) model was developed for use in modeling psychophysical experiments with normal and impaired human listeners. In this phenomenological model, many physiologically vulnerable response properties associated with the cochlear amplifier are represented by a single nonlinear control mechanism, see paper for details. Several model versions are described that can be used to evaluate the relative effects of these nonlinear properties. | |

Auditory nerve model with linear tuning (Heinz et al 2001) | |

A method for calculating psychophysical performance limits based on stochastic neural responses is introduced and compared to previous analytical methods for evaluating auditory discrimination of tone frequency and level. The method uses signal detection theory and a computational model for a population of auditory nerve (AN) fiber responses. Please see paper for details. | |

Auditory nerve response model (Tan, Carney 2003) | |

A computational model was developed to simulate the responses of auditory-nerve (AN) fibers in cat. The incorporation of both the level-independent frequency glide and the level-dependent compressive nonlinearity into a phenomenological model for the AN was the primary focus of this work. The ability of this model to process arbitrary sound inputs makes it a useful tool for studying peripheral auditory processing. | |

Auditory nerve response model (Zhang et al 2001) | |

A phenomenological model was developed to describe responses of high-spontaneous-rate auditory-nerve (AN) fibers, including several nonlinear response properties. The implementation of this model represents a relatively simple phenomenological description of a single mechanism that underlies several important nonlinear response properties of AN fibers. The model provides a tool for studying the roles of these nonlinearities in the encoding of simple and complex sounds in the responses of populations of AN fibers. | |

Biophysically detailed model of the mouse sino-atrial node cell (Kharche et al. 2011) | |

This model is developed to study the role of various electrophysiological mechanisms in generating cardiac pacemaking action potentials (APs).The model incorporates membrane ionic currents and intracellular mechanisms contributing to spontaneous mouse SAN APs. The model was validated by testing the functional roles of individual membrane currents in one and multiple parameter analyses.The roles of intracellular Ca2+-handling mechanisms on cardiac pacemaking were also investigated in the model. | |

Cancelling redundant input in ELL pyramidal cells (Bol et al. 2011) | |

The paper investigates the property of the electrosensory lateral line lobe (ELL) of the brain of weakly electric fish to cancel predictable stimuli. Electroreceptors on the skin encode all signals in their firing activity, but superficial pyramidal (SP) cells in the ELL that receive this feedforward input do not respond to constant sinusoidal signals. This cancellation putatively occurs using a network of feedback delay lines and burst-induced synaptic plasticity between the delay lines and the SP cell that learns to cancel the redundant input. Biologically, the delay lines are parallel fibres from cerebellar-like granule cells in the eminentia granularis posterior. A model of this network (e.g. electroreceptors, SP cells, delay lines and burst-induced plasticity) was constructed to test whether the current knowledge of how the network operates is sufficient to cancel redundant stimuli. | |

Cardiac Atrial Cell (Courtemanche et al 1998) (C++) | |

The mechanisms underlying many important properties of the human atrial action potential (AP) are poorly understood. Using specific formulations of the K+, Na+, and Ca2+ currents based on data recorded from human atrial myocytes, along with representations of pump, exchange, and background currents, we developed a mathematical model of the AP. The model AP resembles APs recorded from human atrial samples and responds to rate changes, L-type Ca2+ current blockade, Na+/Ca2+ exchanger inhibition, and variations in transient outward current amplitude in a fashion similar to experimental recordings. Rate-dependent adaptation of AP duration, an important determinant of susceptibility to atrial fibrillation, was attributable to incomplete L-type Ca2+ current recovery from inactivation and incomplete delayed rectifier current deactivation at rapid rates. Experimental observations of variable AP morphology could be accounted for by changes in transient outward current density, as suggested experimentally. We conclude that this mathematical model of the human atrial AP reproduces a variety of observed AP behaviors and provides insights into the mechanisms of clinically important AP properties. | |

Cerebellar gain and timing control model (Yamazaki & Tanaka 2007)(Yamazaki & Nagao 2012) | |

This paper proposes a hypothetical computational mechanism for unified gain and timing control in the cerebellum. The hypothesis is justified by computer simulations of a large-scale spiking network model of the cerebellum. | |

Coding of stimulus frequency by latency in thalamic networks (Golomb et al 2005) | |

The paper presents models of the rat vibrissa processing system including the posterior medial (POm) thalamus, ventroposterior medial (VPm) thalamus, and GABAB- mediated feedback inhibition from the reticular thalamic (Rt) nucleus. A clear match between the experimentally measured spike-rates and the numerically calculated rates for the full model occurs when VPm thalamus receives stronger brainstem input and weaker GABAB-mediated inhibition than POm thalamus. | |

Competition model of pheromone ratio detection (Zavada et al. 2011) | |

For some closely related sympatric moth species, recognizing a specific pheromone component concentration ratio is essential for mating success. We propose and test a minimalist competition-based feed-forward neuronal model capable of detecting a certain ratio of pheromone components independently of overall concentration. This model represents an elementary recognition unit for binary mixtures which we propose is entirely contained in the macroglomerular complex (MGC) of the male moth. A set of such units, along with projection neurons (PNs), can provide the input to higher brain centres. We found that (1) accuracy is mainly achieved by maintaining a certain ratio of connection strengths between olfactory receptor neurons (ORN) and local neurons (LN), much less by properties of the interconnections between the competing LNs proper. (2) successful ratio recognition is achieved using latency-to-first-spike in the LN populations which. (3) longer durations of the competition process between LNs did not result in higher recognition accuracy. | |

Composite spiking network/neural field model of Parkinsons (Kerr et al 2013) | |

This code implements a composite model of Parkinson's disease (PD). The composite model consists of a leaky integrate-and-fire spiking neuronal network model being driven by output from a neural field model (instead of the more usual white noise drive). Three different sets of parameters were used for the field model: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. The aim of this model is to explore how the different dynamical patterns in each each of these field models affects the activity in the network model. | |

Connection-set Algebra (CSA) for the representation of connectivity in NN models (Djurfeldt 2012) | |

"The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. ... The expressiveness of CSA makes prototyping of network structure easy. A C++ version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31–42, 2008b) and an implementation in Python has been publicly released." | |

Constructed Tessellated Neuronal Geometries (CTNG) (McDougal et al. 2013) | |

We present an algorithm to form watertight 3D surfaces consistent with the point-and-diameter based neuronal morphology descriptions widely used with spatial electrophysiology simulators. ... This (point-and-diameter) representation is well-suited for electrophysiology simulations, where the space constants are larger than geometric ambiguities. However, the simple interpretations used for pure electrophysiological simulation produce geometries unsuitable for multi-scale models that also involve three-dimensional reaction–diffusion, as such models have smaller space constants. ... Although one cannot exactly reproduce an original neuron's full shape from point-and-diameter data, our new constructive tessellated neuronal geometry (CTNG) algorithm uses constructive solid geometry to define a plausible reconstruction without gaps or cul-de-sacs. CTNG then uses “constructive cubes” to produce a watertight triangular mesh of the neuron surface, suitable for use in reaction–diffusion simulations. ..." | |

Continuous time stochastic model for neurite branching (van Elburg 2011) | |

"In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. ..." | |

Cortex learning models (Weber at al. 2006, Weber and Triesch, 2006, Weber and Wermter 2006/7) | |

A simulator and the configuration files for three publications are provided. First, "A hybrid generative and predictive model of the motor cortex" (Weber at al. 2006) which uses reinforcement learning to set up a toy action scheme, then uses unsupervised learning to "copy" the learnt action, and an attractor network to predict the hidden code of the unsupervised network. Second, "A Self-Organizing Map of Sigma-Pi Units" (Weber and Wermter 2006/7) learns frame of reference transformations on population codes in an unsupervised manner. Third, "A possible representation of reward in the learning of saccades" (Weber and Triesch, 2006) implements saccade learning with two possible learning schemes for horizontal and vertical saccades, respectively. | |

Data-driven, HH-type model of the lateral pyloric (LP) cell in the STG (Nowotny et al. 2008) | |

This model was developed using voltage clamp data and existing LP models to assemble an initial set of currents which were then adjusted by extensive fitting to a long data set of an isolated LP neuron. The main points of the work are a) automatic fitting is difficult but works when the method is carefully adjusted to the problem (and the initial guess is good enough). b) The resulting model (in this case) made reasonable predictions for manipulations not included in the original data set, e.g., blocking some of the ionic currents. c) The model is reasonably robust against changes in parameters but the different parameters vary a lot in this respect. d) The model is suitable for use in a network and has been used for this purpose (Ivanchenko et al. 2008) | |

Democratic population decisions result in robust policy-gradient learning (Richmond et al. 2011) | |

This model demonstrates the use of GPU programming (with CUDA)to simulate a two-layer network of Integrate-and-Fire neurons with varying degrees of recurrent connectivity and to investigate its ability to learn a simplified navigation task using a learning rule stemming from Reinforcement Learning, a policy-gradient rule. | |

Development of orientation-selective simple cell receptive fields (Rishikesh and Venkatesh, 2003) | |

Implementation of a computational model for the development of simple-cell receptive fields spanning the regimes before and after eye-opening. The before eye-opening period is governed by a correlation-based rule from Miller (Miller, J. Neurosci., 1994), and the post eye-opening period is governed by a self-organizing, experience-dependent dynamics derived in the reference below. | |

Distributed cerebellar plasticity implements adaptable gain control (Garrido et al., 2013) | |

We tested the role of plasticity distributed over multiple synaptic sites (Hansel et al., 2001; Gao et al., 2012) by generating an analog cerebellar model embedded into a control loop connected to a robotic simulator. The robot used a three-joint arm and performed repetitive fast manipulations with different masses along an 8-shape trajectory. In accordance with biological evidence, the cerebellum model was endowed with both LTD and LTP at the PF-PC, MF-DCN and PC-DCN synapses. This resulted in a network scheme whose effectiveness was extended considerably compared to one including just PF-PC synaptic plasticity. Indeed, the system including distributed plasticity reliably self-adapted to manipulate different masses and to learn the arm-object dynamics over a time course that included fast learning and consolidation, along the lines of what has been observed in behavioral tests. In particular, PF-PC plasticity operated as a time correlator between the actual input state and the system error, while MF-DCN and PC-DCN plasticity played a key role in generating the gain controller. This model suggests that distributed synaptic plasticity allows generation of the complex learning properties of the cerebellum. | |

Duration-tuned neurons from the inferior colliculus of the big brown bat (Aubie et al. 2009) | |

dtnet is a generalized neural network simulator written in C++ with an easy to use XML description language to generate arbitrary neural networks and then run simulations covering many different parameter values. For example, you can specify ranges of parameter values for several different connection weights and then automatically run simulations over all possible parameters. Graphing ability is built in as long as the free, open-source, graphing application GLE (http://glx.sourceforge.net/) is installed. Included in the examples folder are simulation descriptions that were used to generate the results in Aubie et al. (2009). Refer to the README file for instructions on compiling and running these examples. The most recent source code can be obtained from GitHub: https://github.com/baubie/dtnet | |

Emergence of Connectivity Motifs in Networks of Model Neurons | |

Recent evidence suggests that short-term dynamics of excitatory synaptic transmission is correlated to stereotypical connectivity motifs. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). | |

ERG current in repolarizing plateau potentials in dopamine neurons (Canavier et al 2007) | |

"Blocking the small-conductance (SK) calcium-activated potassium channel promotes burst firing in dopamine neurons both in vivo and in vitro. ... We focus on the underlying plateau potential oscillation generated in the presence of both apamin and TTX, so that action potentials are not considered. We find that although the plateau potentials are mediated by a voltage-gated Ca2+ current, they do not depend on the accumulation of cytosolic Ca2+, then use a computational model to test the hypothesis that the slowly voltage-activated ether-a-go-go–related gene (ERG) potassium current repolarizes the plateaus. The model, which includes a material balance on calcium, is able to reproduce the time course of both membrane potential and somatic calcium concentration, and can also mimic the induction of plateau potentials by the calcium chelator BAPTA." See paper for more. | |

Excitation-contraction coupling/mitochondrial energetics (ECME) model (Cortassa et al. 2006) | |

"An intricate network of reactions is involved in matching energy supply with demand in the heart. This complexity arises because energy production both modulates and is modulated by the electrophysiological and contractile activity of the cardiac myocyte. Here, we present an integrated mathematical model of the cardiac cell that links excitation-contraction coupling with mitochondrial energy generation. The dynamics of the model are described by a system of 50 ordinary differential equations. The formulation explicitly incorporates cytoplasmic ATP-consuming processes associated with force generation and ion transport, as well as the creatine kinase reaction. Changes in the electrical and contractile activity of the myocyte are coupled to mitochondrial energetics through the ATP, Ca21, and Na1 concentrations in the myoplasmic and mitochondrial matrix compartments. ..." | |

Formation of synfire chains (Jun and Jin 2007) | |

"Temporally precise sequences of neuronal spikes that span hundreds of milliseconds are observed in many brain areas, including songbird premotor nucleus, cat visual cortex, and primary motor cortex. Synfire chains—networks in which groups of neurons are connected via excitatory synapses into a unidirectional chain—are thought to underlie the generation of such sequences. It is unknown, however, how synfire chains can form in local neural circuits, especially for long chains. Here, we show through computer simulation that long synfire chains can develop through spike-time dependent synaptic plasticity and axon remodeling—the pruning of prolific weak connections that follows the emergence of a finite number of strong connections. ..." | |

Generating oscillatory bursts from a network of regular spiking neurons (Shao et al. 2009) | |

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the tectal layer 10 (L10) neurons and respond with oscillatory bursts to visual stimulation. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. | |

Generic Bi-directional Real-time Neural Interface (Zrenner et al. 2010) | |

Matlab/Simulink toolkit for generic multi-channel short-latency bi-directional neural-computer interactions. High-bandwidth (> 10 megabit per second) neural recording data can be analyzed in real-time while simultaneously generating specific complex electrical stimulation feedback with deterministically timed responses at sub-millisecond resolution. The commercially available 60-channel extracellular multi-electrode recording and stimulation set-up (Multichannelsystems GmbH MEA60) is used as an example hardware implementation. | |

Global structure, robustness, and modulation of neuronal models (Goldman et al. 2001) | |

"The electrical characteristics of many neurons are remarkably robust in the face of changing internal and external conditions. At the same time, neurons can be highly sensitive to neuromodulators. We find correlates of this dual robustness and sensitivity in a global analysis of the structure of a conductance-based model neuron. ..." | |

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. ..." | |

Huntington`s disease model (Gambazzi et al. 2010) | |

"Although previous studies of Huntington’s disease (HD) have addressed many potential mechanisms of striatal neuron dysfunction and death, it is also known based on clinical findings that cortical function is dramatically disrupted in HD. With respect to disease etiology, however, the specific molecular and neuronal circuit bases for the cortical effects of mutant huntingtin (htt) have remained largely unknown. In the present work we studied the relation between the molecular effects of mutant htt fragments in cortical cells and the corresponding behavior of cortical neuron microcircuits using a novel cellular model of HD. We observed that a transcript-selective diminution in activity-dependent BDNF expression preceded the onset of a synaptic connectivity deficit in ex vivo cortical networks, which manifested as decreased spontaneous collective burst-firing behavior measured by multi-electrode array substrates. Decreased BDNF expression was determined to be a significant contributor to network-level dysfunction, as shown by the ability of exogenous BDNF to ameliorate cortical microcircuit burst firing. The molecular determinants of the dysregulation of activity-dependent BDNF expression by mutant htt appear to be distinct from previously elucidated mechanisms, as they do not involve known NRSF/REST-regulated promoter sequences, but instead result from dysregulation of BDNF exon IV and VI transcription. These data elucidate a novel HD-related deficit in BDNF gene regulation as a plausible mechanism of cortical neuron hypoconnectivity and cortical function deficits in HD. Moreover, the novel model paradigm established here is well-suited to further mechanistic and drug screening research applications. A simple mathematical model is proposed to interpret the observations and to explore the impact of specific synaptic dysfunctions on network activity. Interestingly, the model predicts a decrease in synaptic connectivity to be an early effect of mutant huntingtin in cortical neurons, supporting the hypothesis of decreased, rather than increased, synchronized cortical firing in HD." | |

Hypocretin and Locus Coeruleus model neurons (Carter et al 2012) | |

Conductance based model of the hypocretin neurons (HCRT) and another one of the Locus Coeruleus one (LC). The HCRT drive the LCs via the HCRT receptor on the LCs. The LCs lead to the awakening of the mice if the number of spikes raises over 10 spikes in 10 seconds window. | |

Increased computational accuracy in multi-compartmental cable models (Lindsay et al. 2005) | |

Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional models assign a single potential to a compartment. This potential is associated with the membrane potential at the centre of the segment represented by the compartment. All input to that segment, independent of its location on the segment, is assumed to act at the centre of the segment with the potential of the compartment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the location of input to a segment on the model solution by partitioning the effect of this input between the axial currents at the proximal and distal boundaries of segments. For a given neuron, the new and traditional approaches to compartmental modelling use the same number of locations at which the membrane potential is to be determined, and lead to ordinary differential equations that are structurally identical. However, the solution achieved by the new approach gives an order of magnitude better accuracy and precision than that achieved by the latter in the presence of point process input. | |

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." | |

Ionic basis of alternans and Timothy Syndrome (Fox et al. 2002), (Zhu and Clancy 2007) | |

From Zhu and Clancy: "... Here we employ theoretical simulations to examine the effects of a Timothy Syndrome (TS) mutation in the L-type Ca2+ channel on cardiac dynamics over multiple scales, from a gene mutation to protein, cell, tissue, and finally the ECG, to connect a defective Ca2+ channel to arrhythmia susceptibility. ..." | |

Ionic mechanisms of bursting in CA3 pyramidal neurons (Xu and Clancy 2008) | |

"... We present a single-compartment model of a CA3 hippocampal pyramidal neuron based on recent experimental data. We then use the model to determine the roles of primary depolarizing currents in burst generation. The single compartment model incorporates accurate representations of sodium (Na+) channels (NaV1.1) and T-type calcium (Ca2+) channel subtypes (CaV3.1, CaV3.2, and CaV3.3). Our simulations predict the importance of Na+ and T-type Ca2+ channels in hippocampal pyramidal cell bursting and reveal the distinct contribution of each subtype to burst morphology. We also performed fastslow analysis in a reduced comparable model, which shows that our model burst is generated as a result of the interaction of two slow variables, the T-type Ca2+ channel activation gate and the Ca2+-dependent potassium (K+) channel activation gate. The model reproduces a range of experimentally observed phenomena including afterdepolarizing potentials, spike widening at the end of the burst, and rebound. Finally, we use the model to simulate the effects of two epilepsy-linked mutations: R1648H in NaV1.1 and C456S in CaV3.2, both of which result in increased cellular excitability." | |

Large cortex model with map-based neurons (Rulkov et al 2004) | |

We develop a new computationally efficient approach for the analysis of complex large-scale neurobiological networks. Its key element is the use of a new phenomenological model of a neuron capable of replicating important spike pattern characteristics and designed in the form of a system of difference equations (a map). ... Interconnected with synaptic currents these model neurons demonstrated responses very similar to those found with Hodgkin-Huxley models and in experiments. We illustrate the efficacy of this approach in simulations of one- and two-dimensional cortical network models consisting of regular spiking neurons and fast spiking interneurons to model sleep and activated states of the thalamocortical system. See paper for more. | |

Markov models of SCN1A (NaV1.1) applied to abnormal gating and epilepsy (Clancy and Kass 2004) | |

"Recently, some forms of idiopathic epilepsy have been causally related to genetic mutations in neuronal ion channels. To understand disease mechanisms, it is crucial to understand how a gene defect can disrupt channel gating, which in turn can affect complex cellular dynamic processes. We develop a theoretical Markovian model of the neuronal Na+ channel NaV1.1 to explore and explain gating mechanisms underlying cellular excitability and physiological and pathophysiological mechanisms of abnormal neuronal excitability in the context of epilepsy. ..." | |

Measuring neuronal identification quality in ensemble recordings (isoitools) (Neymotin et al. 2011) | |

"... Here we describe information theoretic measures of action potential waveform isolation applicable to any dataset, that have an intuitive, universal interpretation, and that are not dependent on the methods or choice of parameters for single unit isolation, and that have been validated using a dataset." | |

Mechanisms of very fast oscillations in axon networks coupled by gap junctions (Munro, Borgers 2010) | |

Axons connected by gap junctions can produce very fast oscillations (VFOs, > 80 Hz) when stimulated randomly at a low rate. The models here explore the mechanisms of VFOs that can be seen in an axonal plexus, (Munro & Borgers, 2009): a large network model of an axonal plexus, small network models of axons connected by gap junctions, and an implementation of the model underlying figure 12 in Traub et al. (1999) . The large network model consists of 3,072 5-compartment axons connected in a random network. The 5-compartment axons are the 5 axonal compartments from the CA3 pyramidal cell model in Traub et al. (1994) with a fixed somatic voltage. The random network has the same parameters as the random network in Traub et al. (1999), and axons are stimulated randomly via a Poisson process with a rate of 2/s/axon. The small network models simulate waves propagating through small networks of axons connected by gap junctions to study how local connectivity affects the refractory period. | |

Modified Traub model (Wilanowski and Piotrkiewicz, in review) | |

This is the README for the model associated with the paper Wilanowski G. and Piotrkiewicz M. How to assess synaptic noise in human motoneurons?. Front. Cell. Neurosci.(in review). These files were contributed by Grzegorz Wilanowski. This is a five compartment motoneuron model based on the Traub model. It is adjusted to mimic human motoneurons observed during EMG studies. To obtain AHP of the depth equal to 8 mV and lasting 170 ms, calcium-dependent potassium conductance was increased 5 times. However, such a great increase in potassium conductance resulted in blocking spikes. To correct this we changed the potassium ions reversal potential from +5 mV to +10 mV. The resulting model produced more physiological interspike intervals variability. This variability is represented by plotting the standard deviation of interspike intervals as a function of their mean value for a given level of stimulation (so called sd-mean curve). To obtain this sd-mean curve compile the provided files in a C++ compiler of your choice (gcc 4.4 was used by the author). | |

Network model with neocortical architecture (Anderson et al. 2011 plus under review paper) | |

Architecturally realistic neocortical model using seven classes of excitatory and inhibitory single compartment Hodgkin-Huxley cells. This is an addendum to ModelDB Accession # 98902, Studies of stimulus parameters for seizure disruption (Anderson et al. 2007). Wiring is adapted from the minicolumn hypothesis and incorporates visual and neocortical wiring data. Simulation demonstrates spontaneous bursting onset and cessation. This activity can be induced by random fluctuations in the surrounding background input (Manuscript in preparation). | |

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) available at this link http://arxiv.org/abs/q-bio.NC/0611089 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). | |

Neural mass model based on single cell dynamics to model pathophysiology (Zandt et al 2014) | |

The model code as described in "A neural mass model based on single cell dynamics to model pathophysiology, Zandt et al. 2014, Journal of Computational Neuroscience" A Neural mass model (NMM) derived from single cell dynamics in a bottom up approach. Mean and standard deviation of the firing rates in the populations are calculated. The sigmoid is derived from the single cell FI-curve, allowing for easy implementation of pathological conditions. NMM is compared with a detailed spiking network model consisting of HH neurons. NMM code in Matlab. The network model is simulated using Norns (ModelDB # 154739) | |

Neural modeling of an internal clock (Yamazaki and Tanaka 2008) | |

"We studied a simple random recurrent inhibitory network. Despite its simplicity, the dynamics was so rich that activity patterns of neurons evolved with time without recurrence due to random recurrent connections among neurons. The sequence of activity patterns was generated by the trigger of an external signal, and the generation was stable against noise.... Therefore, a time passage from the trigger of an external signal could be represented by the sequence of activity patterns, suggesting that this model could work as an internal clock. ..." | |

Norns - Neural Network Studio (Visser & Van Gils 2014) | |

The Norns - Neural Network Studio is a software package for designing, simulation and analyzing networks of spiking neurons. It consists of three parts: 1. "Urd": a Matlab frontend with high-level functions for quickly defining networks 2. "Verdandi": an optimized C++ simulation environment which runs the simulation defined by Urd 3. "Skuld": an advanced Matlab graphical user interface (GUI) for visual inspection of simulated data. | |

Numerical Integration of Izhikevich and HH model neurons (Stewart and Bair 2009) | |

The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing the integration timestep. We apply the Parker-Sochacki method to the Izhikevich ‘simple’ model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods. | |

Olfactory bulb network model of gamma oscillations (Bathellier et al. 2006; Lagier et al. 2007) | |

This model implements a network of 100 mitral cells connected with asynchronous inhibitory "synapses" that is meant to reproduce the GABAergic transmission of ensembles of connected granule cells. For appropriate parameters of this special synapse the model generates gamma oscillations with properties very similar to what is observed in olfactory bulb slices (See Bathellier et al. 2006, Lagier et al. 2007). Mitral cells are modeled as single compartment neurons with a small number of different voltage gated channels. Parameters were tuned to reproduce the fast subthreshold oscillation of the membrane potential observed experimentally (see Desmaisons et al. 1999). | |

Optimal deep brain stimulation of the subthalamic nucleus-a computational study (Feng et al. 2007) | |

Here, we use a biophysically-based model of spiking cells in the basal ganglia (Terman et al., Journal of Neuroscience, 22, 2963-2976, 2002; Rubin and Terman, Journal of Computational Neuroscience, 16, 211-235, 2004) to provide computational evidence that alternative temporal patterns of DBS inputs might be equally effective as the standard high-frequency waveforms, but require lower amplitudes. Within this model, DBS performance is assessed in two ways. First, we determine the extent to which DBS causes Gpi (globus pallidus pars interna) synaptic outputs, which are burstlike and synchronized in the unstimulated Parkinsonian state, to cease their pathological modulation of simulated thalamocortical cells. Second, we evaluate how DBS affects the GPi cells' auto- and cross-correlograms. | |

Paradoxical GABA-mediated excitation (Lewin et al. 2012) | |

"GABA is the key inhibitory neurotransmitter in the adult central nervous system, but in some circumstances can lead to a paradoxical excitation that has been causally implicated in diverse pathologies from endocrine stress responses to diseases of excitability including neuropathic pain and temporal lobe epilepsy. We undertook a computational modeling approach to determine plausible ionic mechanisms of GABAA-dependent excitation in isolated post-synaptic CA1 hippocampal neurons because it may constitute a trigger for pathological synchronous epileptiform discharge. In particular, the interplay intracellular chloride accumulation via the GABAA receptor and extracellular potassium accumulation via the K/Cl co-transporter KCC2 in promoting GABAA-mediated excitation is complex. ..." | |

Persistent synchronized bursting activity in cortical tissues (Golomb et al 2005) | |

The program simulates a one-dimensional model of a cortical tissue with excitatory and inhibitory populations. | |

Perturbation sensitivity implies high noise and suggests rate coding in cortex (London et al. 2010) | |

"... The network simulations were also based on a previously published model(Latham et al. 2000), but with modifications to allow the addition and detection of extra spikes (see Supplementary Information, section 7)." | |

Rate model of a cortical RS-FS-LTS network (Hayut et al. 2011) | |

A rate model of cortical networks composed of RS, FS and LTS neurons. Synaptic depression is modelled according to the Tsodyks-Markram scheme. | |

Region-specific atrophy in dendrites (Narayanan, Narayan, Chattarji, 2005) | |

...in this study, we develop an algorithm that uses statistics from precise morphometric analyses to systematically remodel neuronal reconstructions. We use the distribution function of the ratio of two normal distributed random variables to specify the probabilities of remodeling along various regions of the dendritic arborization. We then use these probabilities to drive an iterative algorithm for manipulating the dendritic tree in a region-specific manner. As a test, we apply this framework to a well characterized example of dendritic remodeling: stress-induced dendritic atrophy in hippocampal CA3 pyramidal cells. We show that our pruning algorithm is capable of eliciting atrophy that matches biological data from rodent models of chronic stress.
| |

Relative spike time coding and STDP-based orientation selectivity in V1 (Masquelier 2012) | |

Phenomenological spiking model of the cat early visual system. We show how natural vision can drive spike time correlations on sufficiently fast time scales to lead to the acquisition of orientation-selective V1 neurons through STDP. This is possible without reference times such as stimulus onsets, or saccade landing times. But even when such reference times are available, we demonstrate that the relative spike times encode the images more robustly than the absolute ones. | |

Robust Reservoir Generation by Correlation-Based Learning (Yamazaki & Tanaka 2008) | |

"Reservoir computing (RC) is a new framework for neural computation. A reservoir is usually a recurrent neural network with fixed random connections. In this article, we propose an RC model in which the connections in the reservoir are modifiable. ... We apply our RC model to trace eyeblink conditioning. The reservoir bridged the gap of an interstimulus interval between the conditioned and unconditioned stimuli, and a readout neuron was able to learn and express the timed conditioned response." | |

Simulation study of Andersen-Tawil syndrome (Sung et al 2006) | |

Patients with Andersen-Tawil syndrome (ATS) mostly have mutations on the KCNJ2 gene producing loss of function or dominant-negative suppression of the inward rectifier K(+) channel Kir2.1. However, clinical manifestations of ATS including dysmorphic features, periodic paralysis (hypo-, hyper-, or normokalemic), long QT, and ventricular arrhythmias (VA) are considerably variable. Using a modified dynamic Luo-Rudy simulation model of cardiac ventricular myocyte, we elucidate the mechanisms of VA in ATS. We adopted a kinetic model of KCNJ2 in which channel block by Mg(+2) and spermine was incorporated. In this study, we attempt to examine the effects of KCNJ2 mutations on the ventricular action potential (AP), single-channel Markovian models were reformulated and incorporated into the dynamic Luo-Rudy model for rapidly and slowly delayed rectifying K(+) currents and KCNJ2 channel. During pacing at 1.0 Hz with [K(+)]o at 5.4 mM, a stepwise 10% reduction of Kir2.1 channel conductance progressively prolonged the terminal repolarization phase of AP along with gradual depolarization of the resting membrane potential (RMP). At 90% reduction, early after- depolarizations (EADs) became inducible and RMP was depolarized to -55.0 mV (control: -90.1 mV) followed by emergence of spontaneous action potentials (SAP). Both EADs and SAP were facilitated by a decrease in [K(+)]o and suppressed by increase in [K(+)]o. beta-adrenergic stimulation enhanced delayed after-depolarizations (DADs) and could also facilitate EADs as well as SAP in the setting of low [K(+)]o and reduced Kir2.1 channel conductance. In conclusion, the spectrum of VA in ATS includes (1) triggered activity mediated by EADs and/or DADs, and (2) abnormal automaticity manifested as SAP. These VA can be aggravated by a decrease in [K(+)]o and beta-adrenergic stimulation, and may potentially induce torsades de pointes and cause sudden death. In patients with ATS, the hypokalemic form of periodic paralysis should have the highest propensity to VA especially during physical activities. | |

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. | |

Sleep-wake transitions in corticothalamic system (Bazhenov et al 2002) | |

The authors investigate the transition between sleep and awake states with intracellular recordings in cats and computational models. The model describes many essential features of slow wave sleep and activated states as well as the transition between them. | |

Squid axon: Bifurcation analysis of mode-locking (Lee & Kim 2006) (Gangal et al. under preparation) | |

The model was built with the purpose of finding mode lockings between the input sinusoidal current frequency and the output frequency. Phase plase plane analysis, spike statistics, mode locking formulation etc. can be done with the help of the model. Any additional functionality can be added as the base code return the correct action potential values. | |

STDP promotes synchrony of inhibitory networks in the presence of heterogeneity (Talathi et al 2008) | |

"Recently Haas et al. (J Neurophysiol 96: 3305–3313, 2006), observed a novel form of spike timing dependent plasticity (iSTDP) in GABAergic synaptic couplings in layer II of the entorhinal cortex. Depending on the relative timings of the presynaptic input at time tpre and the postsynaptic excitation at time tpost, the synapse is strengthened (delta_t = tpost − tpre > 0) or weakened (delta_t < 0). The temporal dynamic range of the observed STDP rule was found to lie in the higher gamma frequency band (≥40 Hz), a frequency range important for several vital neuronal tasks. In this paper we study the function of this novel form of iSTDP in the synchronization of the inhibitory neuronal network. In particular we consider a network of two unidirectionally coupled interneurons (UCI) and two mutually coupled interneurons (MCI), in the presence of heterogeneity in the intrinsic firing rates of each coupled neuron. ..." | |

Studies of stimulus parameters for seizure disruption using NN simulations (Anderson et al. 2007) | |

Architecturally realistic neocortical model using seven classes of excitatory and inhibitory single compartment Hodgkin-Huxley cells. Wiring is adapted to minicolumn hypothesis and incorporates visual and neocortical data. Simulation demonstrates spontaneous bursting onset and cessation, and activity can be altered with external electric field. | |

Temperature-Dependent Pyloric Pacemaker Kernel (Caplan JS et al., 2014) | |

Temporal decorrelation by intrinsic cellular dynamics (Wang et al 2003) | |

"... Recent investigations in primary visual (V1) cortical neurons have demonstrated that adaptation to prolonged changes in stimulus contrast is mediated in part through intrinsic ionic currents, a Ca2+ activated K+ current (IKCa) and especially a Na+ activated K+ current (IKNa). The present study was designed to test the hypothesis that the activation of adaptation ionic currents may provide a cellular mechanism for temporal decorrelation in V1. A conductance-based neuron model was simulated, which included an IKCa and an IKNa. We show that the model neuron reproduces the adaptive behavior of V1 neurons in response to high contrast inputs. ...". See paper for details and more. | |

Temporal integration by stochastic recurrent network (Okamoto et al. 2007) | |

"Temporal integration of externally or internally driven information is required for a variety of cognitive processes. This computation is generally linked with graded rate changes in cortical neurons, which typically appear during a delay period of cognitive task in the prefrontal and other cortical areas. Here, we present a neural network model to produce graded (climbing or descending) neuronal activity. Model neurons are interconnected randomly by AMPA-receptor–mediated fast excitatory synapses and are subject to noisy background excitatory and inhibitory synaptic inputs. In each neuron, a prolonged afterdepolarizing potential follows every spike generation. Then, driven by an external input, the individual neurons display bimodal rate changes between a baseline state and an elevated firing state, with the latter being sustained by regenerated afterdepolarizing potentials. ..." | |

Theta phase precession in a model CA3 place cell (Baker and Olds 2007) | |

"... The present study concerns a neurobiologically based computational model of the emergence of theta phase precession in which the responses of a single model CA3 pyramidal cell are examined in the context of stimulation by realistic afferent spike trains including those of place cells in entorhinal cortex, dentate gyrus, and other CA3 pyramidal cells. Spike-timing dependent plasticity in the model CA3 pyramidal cell leads to a spatially correlated associational synaptic drive that subsequently creates a spatially asymmetric expansion of the model cell’s place field. ... Through selective manipulations of the model it is possible to decompose theta phase precession in CA3 into the separate contributing factors of inheritance from upstream afferents in the dentate gyrus and entorhinal cortex, the interaction of synaptically controlled increasing afferent drive with phasic inhibition, and the theta phase difference between dentate gyrus granule cell and CA3 pyramidal cell activity." | |

Two Models for synaptic input statistics for the MSO neuron model (Jercog et al. 2010) | |

The model is a point neuron model with ionic currents from Rothman & Mannis (2003) and with an update of the low threshold potassium current (IKLT) measured in-vitro by Mathews & Jercog et al (2010). This model in conjunction with the synaptic input models presented here has been used to gain insight into mechanisms that account for experimentally observed asymmetries in ITD tuning (Brand et al, 2002). Asymmetry and displacement of the ITD response function is achieved in the model by the interplay between asymmetry of the excitatory inputs arriving from the two sides and the precise voltage dependent activation of IKLT. In Jercog et al (2010) we propose two different mathematical ways, physiologically plausible scenarios, of generating the asymmetry in the bilateral synaptic input events. Here, we present two models for simulating the stochastic synaptic input trains. | |

Wang-Buzsaki Interneuron (Talathi et al., 2010) | |

The submitted code provides the relevant C++ files, matlabfiles and the data files essential to reproduce the figures in the JCNS paper titled Control of neural synchrony using channelrhodopsin-2: A computational study. |

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