The Experts below are selected from a list of 537 Experts worldwide ranked by ideXlab platform
Carmen C. Canavier - One of the best experts on this subject based on the ideXlab platform.
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Bifurcation structure of adaptation versus depolarization block
BMC Neuroscience, 2012Co-Authors: Kun Qian, Marco Antonio Huertas Chacon, Carmen C. CanavierAbstract:Midbrain dopamine neurons fire in a pacemaker-like fashion in vitro where they are deprived of most afferent input. In vivo, these neurons can emit a burst of action potentials with fast (~50 Hz) frequencies [1]. However, simple somatic depolarization of these neurons does not elicit such rapid firing because the neurons cease firing at levels of depolarizing somatic current injection stronger than those that elicit repetitive firing at about 10 Hz [2]. Here we argue that in the case of simple somatic current injection, firing ceases due to adaptation rather than depolarization block. We hypothesize that the primary adaptation mechanism is the slow inactivation of the fast sodium current [3], which causes the spike threshold to become more depolarized with each spike until spiking fails. We contrast the bifurcation structure of a simple 3 variable model that ceases to fire via this mechanism with a two variable model that fails by going into depolarization block. In both cases, spontaneous firing is characterized by an N shaped voltage Nullcline with two stable branches. For the depolarization block, firing ceases when the fixed point moves from the unstable to the stable branch at the knee of the Nullcline (Fig.(Fig.1).1). The action potentials decrease in amplitude both at the peak and the trough, and the resulting stable potential is much more depolarized than the spike threshold for the adaptation case. In contrast, for the adaptation case, only the peaks of the action potential decrease slightly, and the final stable potential is at the spike threshold. As slow inactivation proceeds, the voltage Nullcline loses the unstable middle branch, and the two stable branches merge. Spiking fails when the trajectory no longer crosses the unstable middle branch (the spike threshold) because the increasing ISI length allows for more fast inactivation. The two mechanisms can be differentiated experimentally: an additional depolarizing square pulse of current applied just after the last spike should evoke an additional action potential for adaptation, but not depolarization block. Figure 1 Spike Failure via Adaptation. (A) Time course of the membrane potential (top) and slow Na+ channel inactivation, middle), during spike failure after a depolarizing current step (bottom). (B) Phase plane for fast/slow analysis. The N shaped voltage Nullcline ...
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Reciprocal excitatory synapses convert pacemaker-like firing into burst firing in a simple model of coupled neurons
Neurocomputing, 2000Co-Authors: Carmen C. CanavierAbstract:Abstract Model neurons that are intrinsically capable of only repetitive single-spike firing can fire in bursts when reciprocally coupled via excitatory chemical synapses. The bursting mechanism is analyzed using a phase portrait consisting of Nullclines both in the presence and in the absence of a fully activated synaptic current. The system of coupled relaxation oscillators is symmetric, and the trajectory can be described by simultaneous jumps between the free and excited potential Nullclines for each oscillator. A new variant of the synaptic release mechanism for both excitation and inhibition emerges in which spike frequency adaptation terminates the synaptic coupling.
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Analysis of Neuromodulator and Bursting Mechanisms a Model of Aplysia Neuron R15
IFAC Proceedings Volumes, 1994Co-Authors: Robert J. Butera, John W. Clark, Carmen C. Canavier, John H. ByrneAbstract:Abstract We have improved and extended an equivalent circuit model of the bursting neuron R15 in Aplysia and have simulated the neuromodulatory effects of serotonin (5-HT) and dopamine (DA), incorporating previously proposed mechanisms. The model produces dynamic model behavior consistent with the observed behavior of R15 in vitro , demonstrating the sufficiency of the proposed mechanisms. Responses of the model to extrinsic stimuli reveal that some of the seemingly paradoxical results can be attributed to the increase in conductance of two opposing currents, providing insight into the complex effects of the neuromodulation of multiple currents by a single neurotransmitter. These simulation results also suggest that neuromodulatory agents and second messengers act not only directly upon channel conductances, but also indirectly through the subsequent regulation of intracellular Ca 2+ concentrations. A Nullcline and bifurcation analysis of reduced fast and slow subsystems of the model is employed to investigate the mathematical mechanism of bursting and neuromodulation. The slow processes define a steady-state manifold upon which the burst trajectory lies upon during the silent phase of the burst. The active (spiking) phase of the burst occurs as the slow system variables sweep into an oscillatory branch of the solution space of the fast subsystem via a homoclinic transition. The neuromodulatory effects of 5-HT and DA are examined by analyzing their effects upon the slow subsystem. Changes in behavioral modes (silence, bursting, beating) of the model are related to the occurence of subcritical Hopf bifurcations in the slow subsystem. Theses bifurcations are caused by the modulation of the shape of both the Nullclines and manifold of the slow subsystem by 5-HT and DA.
Eckehard Schöll - One of the best experts on this subject based on the ideXlab platform.
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Pulse-train solutions and excitability in an optoelectronic oscillator
EPL (Europhysics Letters), 2011Co-Authors: David P. Rosin, Kristine Callan, Daniel J. Gauthier, Eckehard SchöllAbstract:We study an optoelectronic time-delay oscillator with bandpass filtering for different values of the filter bandwidth. Our experiments show novel pulse-train solutions with pulse widths that can be controlled over a three-order-of-magnitude range, with a minimum pulse width of ∼ 150 ps. The equations governing the dynamics of our optoelectronic oscillator are similar to the FitzHugh-Nagumo model from neurodynamics with delayed feedback in the excitable and oscillatory regimes. Using a Nullclines analysis, we derive an analytical proportionality between pulse width and the low-frequency cutoff of the bandpass filter, which is in agreement with experiments and numerical simulations. Furthermore, the Nullclines help to describe the shape of the waveforms. Copyright c � EPLA, 2011
John Rinzel - One of the best experts on this subject based on the ideXlab platform.
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Nullclines in the V2-h plane for fixed values of V1.
2019Co-Authors: Joshua H. Goldwyn, Michiel W. H. Remme, John RinzelAbstract:The V2-Nullclines (colored curves) are sections of three-dimensional nullsurfaces at fixed values of V1: the resting value (V1 = −58 mV for blue curve) and two depolarized values (V1 = −40 mV for red curve, V1 = −30 mV for orange curve). The h-Nullcline is identical in all models (black curve) and given by h = h∞(V2). Coupling configurations are, from left to right, A: weakly-coupled, B: forward-coupled, and C: strongly-coupled. Notice that V1-dependent fixed point moves from the left to middle branch of the V2-Nullcline for the weakly-coupled model. This marks the transition to tonic firing that is absent in the forward-coupled and strongly-coupled models. The V2-Nullclines have cubic shapes typical for excitable dynamics as can be seen in the insets of each panel that show the Nullclines over a larger range of V2 and h values.
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Nullclines in the V2-h plane for fixed values of V1 and trajectory of response to pair of EPSGs.
2019Co-Authors: Joshua H. Goldwyn, Michiel W. H. Remme, John RinzelAbstract:The V2-Nullclines (colored curves) are sections of three-dimensional nullsurfaces at fixed values of V1: the resting value (V1 = −58 mV for blue curve) and a depolarized value of V1 = −42 mV (red curve) chosen to roughly represent the effect of an EPSG input with amplitude three times that of a unitary event from the auditory nerve model. The h-Nullcline is identical in all models (black curve) and given by h = h∞(V2). Coupling configurations are, from left to right, A: weakly-coupled, B: forward-coupled, and C: strongly-coupled. In these simulations we set . The green trajectory is the response of the model to a pair of EPSGs with time delay of 1.5 ms and amplitude three times that of a unitary auditory nerve fiber input. The onsets of the EPSG events are marked by the green dot (first event) and triangle (second event). The arrows in (A) indicate the direction of the trajectory through the phase plane, and the green stars mark spikes (x-axis ends at -20 mV, so trajectory of the spike is out of view). Only the forward-coupled model fires in response to both events in these simulations (B). The forward-coupled model has the shortest refractory period because excitatory inputs recruit sodium activation to decrease the height of the left knee of the V2-Nullcline, and the post-spike dynamics of this model allow sodium inactivation (h gating variable) to recover rapidly.
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Increase in sine- with stimulus amplitude can be explained by differences in IKLT activation.
2016Co-Authors: Jason Mikiel-hunter, Vibhakar Kotak, John RinzelAbstract:(A) Graph of sine- versus stimulus amplitude for a reduced nonlinear model where only w-gating is free (Control voltage-gated τw (red); Frozen τw (black)). Sine- increased to a maximum of 321Hz at 3nA when τw was voltage-gated but plateaued at 254Hz when τw was frozen at a Vrest. (B, C) Phase plane representation of dynamical responses (see Methods). V-w4 phase plane trajectories for 0.1nA (B) and (C) 3nA sinusoidal inputs presented to the reduced nonlinear model above. Stimulus frequencies shown are: 10Hz (green); 245Hz (turquoise); 321Hz (golden) and 1000Hz (black). V-Nullcline at rest (solid red) i.e. when I(t) = 0nA; V-Nullcline at minimum sinusoidal currents (large dashed red) i.e. when ; V Nullcline at maximum sinusoidal current (mixed dash red) i.e. when I(t) = A and w-Nullcline (blue).
Glenn Vinnicombe - One of the best experts on this subject based on the ideXlab platform.
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understanding the discrete genetic toggle switch phenomena using a discrete Nullcline construct inspired by the markov chain tree theorem
Conference on Decision and Control, 2017Co-Authors: Andreas Petrides, Glenn VinnicombeAbstract:Nullclines provide a convenient way of characterising and understanding the behaviour of low dimensional nonlinear deterministic systems, but are, perhaps not unsurprisingly, a poor predictor of the behaviour of discrete state stochastic systems in the low numbers regime. Such models are appropriate in many biological systems. In this paper we propose a graphical discrete ‘Nullcline-like’ construction, inspired by the Markov chain tree theorem, and investigate its application to the original genetic toggle switch, which is a feedback interconnection of two mutually repressing genes. When the feedback gain (the ‘cooperativity’) is sufficiently large, the deterministic system exhibits bistability, which shows itself as a bimodal stationary distribution in the discrete stochastic system for sufficiently large numbers. However, at small numbers a third mode appears corresponding to roughly equal numbers of each molecule. Without cooperativity, on the other hand (i.e. low feedback gain), the deterministic system has just one stable equilibrium. Nevertheless, the stochastic system can still exhibit bimodality. In this paper, we illustrate that the discrete ‘Nullclines’ proposed can, without the need to calculate the steady state distribution, provide an efficient graphical way of predicting the shape of the stationary probability distribution in different parameter regimes, thus allowing for greater insights in the observed behaviours.
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CDC - Understanding the discrete genetic toggle switch phenomena using a discrete ‘Nullcline’ construct inspired by the Markov chain tree theorem
2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017Co-Authors: Andreas Petrides, Glenn VinnicombeAbstract:Nullclines provide a convenient way of characterising and understanding the behaviour of low dimensional nonlinear deterministic systems, but are, perhaps not unsurprisingly, a poor predictor of the behaviour of discrete state stochastic systems in the low numbers regime. Such models are appropriate in many biological systems. In this paper we propose a graphical discrete ‘Nullcline-like’ construction, inspired by the Markov chain tree theorem, and investigate its application to the original genetic toggle switch, which is a feedback interconnection of two mutually repressing genes. When the feedback gain (the ‘cooperativity’) is sufficiently large, the deterministic system exhibits bistability, which shows itself as a bimodal stationary distribution in the discrete stochastic system for sufficiently large numbers. However, at small numbers a third mode appears corresponding to roughly equal numbers of each molecule. Without cooperativity, on the other hand (i.e. low feedback gain), the deterministic system has just one stable equilibrium. Nevertheless, the stochastic system can still exhibit bimodality. In this paper, we illustrate that the discrete ‘Nullclines’ proposed can, without the need to calculate the steady state distribution, provide an efficient graphical way of predicting the shape of the stationary probability distribution in different parameter regimes, thus allowing for greater insights in the observed behaviours.
David P. Rosin - One of the best experts on this subject based on the ideXlab platform.
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Pulse-train solutions and excitability in an optoelectronic oscillator
EPL (Europhysics Letters), 2011Co-Authors: David P. Rosin, Kristine Callan, Daniel J. Gauthier, Eckehard SchöllAbstract:We study an optoelectronic time-delay oscillator with bandpass filtering for different values of the filter bandwidth. Our experiments show novel pulse-train solutions with pulse widths that can be controlled over a three-order-of-magnitude range, with a minimum pulse width of ∼ 150 ps. The equations governing the dynamics of our optoelectronic oscillator are similar to the FitzHugh-Nagumo model from neurodynamics with delayed feedback in the excitable and oscillatory regimes. Using a Nullclines analysis, we derive an analytical proportionality between pulse width and the low-frequency cutoff of the bandpass filter, which is in agreement with experiments and numerical simulations. Furthermore, the Nullclines help to describe the shape of the waveforms. Copyright c � EPLA, 2011
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Pulse train solutions in a time-delayed opto-electronic oscillator
2011Co-Authors: David P. RosinAbstract:In this master’s thesis, we study an optoelectronic time-delay oscillator. In its optical part, the light of a semiconductor laser passes a Mach-Zehnder modulator and shines on a photodiode to produce a radio frequency signal that is filtered and amplified in the electronic part. This voltage in return controls the optical part through the Mach-Zehnder modulator. The major part of the time-delay is due to an optical delay line that produces time-delayed feedback, implying rich dynamics, the topic of this thesis. For this optoelectronic oscillator, we find novel pulse train solutions that appear when the oscillator is first seeded with an initial pulse at certain parameter values. We are able to control the width of the pulses over a range of three orders-of-magnitude with a minimum pulse width of 150 ps by adjusting the bandpass filter characteristics in the experiment. Furthermore, the dynamic equations in the pulsing regime show strong similarities to the delayed feedback FitzHugh-Nagumo system in neuroscience, which is a generic model for excitability. The analogy goes so far that both systems show similar Nullclines and the same bifurcation mechanism between oscillatory and excitable regimes. These Nullclines help to describe the shape of the waveforms in the pulsing and oscillatory regime as well as the shape of the trajectory on its way to chaos for high feedback gains. Furthermore, they help to derive analytic expressions for the pulse width and the oscillation period as a function of the low-frequency cutoff of the bandpass filter, a finding that is in agreement with experiments and numerical simulations. Using the Nullclines, we can derive the Hopf bifurcation point between the excitable and oscillatory regimes exactly, a feature which was only approximately possible in previous works.
