Voltage Fluctuations of Neural Membrane

Verveen, A. A.; Derksen, H. E.; Schick, Kenneth L.

doi:10.1038/216588a0

Cited by 33 publications

(14 citation statements)

References 5 publications

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“…Fluctuations of the membrane potentials at the nodes of Ranvier of myelinated fibers have been shown to be approximately normally distributed [31]. Accordingly, the threshold current, I th , which bridges the gap between resting membrane potential and threshold (assuming a constant threshold, cf.…”

Section: Methodsmentioning

confidence: 99%

“…2)" rend="display" xml:id="FD2">

\begin{matrix} right & left p (I_{c}, I_{t h 50}; G, σ) = \int_{- \infty}^{I_{z}} \frac{1}{\sqrt{2 π}} e^{\frac{z^{2}}{2}} d z \\ right & left with I_{z} = \frac{G \cdot I_{c} - I_{t h 50}}{σ} \end{matrix}

where I c is the ICMS current, G is a gain parameter, and I th 50 is the mean threshold current, that is, the current that causes the neuron to fire with a probability of 50%. Because the standard deviation of the membrane potential increases approximately linearly with its mean, the standard deviation of the threshold current is also a linear function of its mean σ = sI th 50 [28, 31, 32], where s is the “relative spread.” After each spike, the threshold current I th jumps up then decays exponentially along a time course that tracks absolute and relative refractoriness [28]:

I_{t h 50} (t; I_{0}, τ_{r}) = \begin{matrix} \infty, & t \leq t_{a b s} \\ I_{0} \cdot true(1 + γ e^{\frac{(t - t_{a b s})}{τ_{r e f}}} true), & t > t_{a b s} \end{matrix}

where t abs represents an absolute refractory period (fixed at 1 ms) during which the firing probability equals zero (see Eqs 2,3); γ and τ ref reflect the spike-triggered conductance change and its decay time constant, respectively.…”

Section: Methodsmentioning

confidence: 99%

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A computational model that predicts behavioral sensitivity to intracortical microstimulation

2016

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Objective Intracortical microstimulation (ICMS) is a powerful tool to investigate the neural mechanisms of perception and can be used to restore sensation for patients who have lost it. While sensitivity to ICMS has previously been characterized, no systematic framework has been developed to summarize the detectability of individual ICMS pulse trains or the discriminability of pairs of pulse trains. Approach We develop a simple simulation that describes the responses of a population of neurons to a train of electrical pulses delivered through a microelectrode. We then perform an ideal observer analysis on the simulated population responses to predict the behavioral performance of non-human primates in ICMS detection and discrimination tasks. Main results Our computational model can predict behavioral performance across a wide range of stimulation conditions with high accuracy (R2 = 0.97) and generalizes to novel ICMS pulse trains that were not used to fit its parameters. Furthermore, the model provides a theoretical basis for the finding that amplitude discrimination based on ICMS violates Weber's law. Significance The model can be used to characterize the sensitivity to ICMS across the range of perceptible and safe stimulation regimes. As such, it will be a useful tool for both neuroscience and neuroprosthetics.

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Section: Methodsmentioning

confidence: 99%

“…2)" rend="display" xml:id="FD2">

\begin{matrix} right & left p (I_{c}, I_{t h 50}; G, σ) = \int_{- \infty}^{I_{z}} \frac{1}{\sqrt{2 π}} e^{\frac{z^{2}}{2}} d z \\ right & left with I_{z} = \frac{G \cdot I_{c} - I_{t h 50}}{σ} \end{matrix}

I_{t h 50} (t; I_{0}, τ_{r}) = \begin{matrix} \infty, & t \leq t_{a b s} \\ I_{0} \cdot true(1 + γ e^{\frac{(t - t_{a b s})}{τ_{r e f}}} true), & t > t_{a b s} \end{matrix}

Section: Methodsmentioning

confidence: 99%

A computational model that predicts behavioral sensitivity to intracortical microstimulation

2016

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“…The effects of intrinsic noise in neuronal membranes have been studied for a long time, with pioneering studies by Pecher (1939), Katz (1950, 1952), Derksen and Verveen (1966), Verveen et al (1967), and numerous others (Fishman, 1973;Wanke et al, 1974;Fishman et al, 1975a,b; for a thorough review, see DeFelice, 1981). More recently, there has been a reinvigoration of interest in the field.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Noise in Cultured Hippocampal Neurons: Experiment and Modeling

2004

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Ion channels open and close stochastically. The fluctuation of these channels represents an intrinsic source of noise that affects the input-output properties of the neuron. We combined whole-cell measurements with biophysical modeling to characterize the intrinsic stochastic and electrical properties of single neurons as observed at the soma. We measured current and voltage noise in 18 d postembryonic cultured neurons from the rat hippocampus, at various subthreshold and near-threshold holding potentials in the presence of synaptic blockers. The observed current noise increased with depolarization, as ion channels were activated, and its spectrum demonstrated generalized 1/f behavior. Exposure to TTX removed a significant contribution from Na ϩ channels to the noise spectrum, particularly at depolarized potentials, and the resulting spectrum was now dominated by a single Lorentzian (1/f 2 ) component. By replacing the intracellular K ϩ with Cs ϩ , we demonstrated that a major portion of the observed noise was attributable to K ϩ channels. We compared the measured power spectral densities to a 1-D cable model of channel fluctuations based on Markov kinetics. We found that a somatic compartment, in combination with a single equivalent cylinder, described the effective geometry from the viewpoint of the soma. Four distinct channel populations were distributed in the membrane and modeled as Lorentzian current noise sources. Using the NEURON simulation program, we summed up the contributions from the spatially distributed current noise sources and calculated the total voltage and current noise. Our quantitative model reproduces important voltage-and frequency-dependent features of the data, accounting for the 1/f behavior, as well as the effects of various blockers.

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“…Much is also understood about the importance of ion channel fluctuations. For example, a quantity called relative spread of threshold has been defined to describe the coefficient of variation of nerve firing probability versus normalized stimulus intensity [Verveen et al, 1967]. Modeling studies have shown that this quantity can be predicted from the expected stochastic fluctuations in ion channel gating [Clay and DeFelice, 1983;Rubenstein, 1995].…”

Section: Introductionmentioning

confidence: 99%

Membrane potential and time requirements for detection of weak signals by voltage-gated ion channels

Gailey¹

1999

Bioelectromagnetics

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Voltage Fluctuations of Neural Membrane

Cited by 33 publications

References 5 publications

A computational model that predicts behavioral sensitivity to intracortical microstimulation

A computational model that predicts behavioral sensitivity to intracortical microstimulation

Intrinsic Noise in Cultured Hippocampal Neurons: Experiment and Modeling

Membrane potential and time requirements for detection of weak signals by voltage-gated ion channels

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