Interpretation of time constant and electrotonic length estimates in multicylinder or branched neuronal structures

1992 ◽  
Vol 68 (4) ◽  
pp. 1401-1420 ◽  
Author(s):  
W. R. Holmes ◽  
I. Segev ◽  
W. Rall
Keyword(s):  
Time Constant ◽  
Algebraic Approach ◽  
Weighted Average ◽  
Analytic Solutions ◽  
The Other ◽  
Geometric Complexity ◽  
Time Constants ◽  
Voltage Transients ◽  
Branched Structures ◽  
Current Transients

1. We have investigated the theoretical and practical problems associated with the interpretation of time constants and the estimation of electrotonic length with equivalent cylinder formulas for neurons best represented as multiple cylinders or branched structures. Two analytic methods were used to compute the time constants and coefficients of passive voltage transients (and time constants of current transients under voltage clamp). One method, suitable for simple geometries, involves analytic solutions to boundary value problems. The other, suitable for neurons of any geometric complexity, is an algebraic approach based on compartmental models. Neither of these methods requires the simulation of transients. 2. We computed the time constants and coefficients of voltage transients for several hypothetical neurons and also for a spinal motoneuron whose morphology was characterized from serial reconstructions. These time constants and coefficients were used to generate voltage transients. Then exponential peeling, nonlinear regression, and transform methods were applied to these transients to test how well these procedures estimate the underlying time constants and coefficients. 3. For a serially reconstructed motoneuron with 732 compartments, we found that the theoretical and peeled tau 0 values were nearly equal, but the theoretical tau 1 was much larger than the peeled tau 1. The theoretical tau 1 could not be peeled because it was associated with a coefficient, C1, that had a very small value. In fact, there were 156 time constants between 1.0 and 6.0 ms, most of which had very small coefficients; none had a coefficient larger than 2% of the signal. The peeled value of tau 1 (called tau 1 peel) can be viewed as some sort of a weighted average of the time constants having the largest coefficients. 4. We studied simple hypothetical neurons to determine what interpretation could be applied to the multitude of theoretical time constants. We found that after tau 0, there was a group of time constants associated with eigenfunctions that were odd (or approximately odd) functions with respect to the soma. These time constants could be interpreted as "equalizing" time constants along particular paths between different pairs of dendritic terminals in the neuron. After this group of time constants, there was one that we call tau even because it was associated with an eigen-function that was approximately even with respect to the soma. This tau even could be interpreted as an equalizing time constant for charge equalization between proximal membrane (soma and proximal dendrites) and distal membrane (including all distal dendrites).4=

Why is the perceptual octave stretched? An account based on mismatched time constants within the auditory brainstem

2021 ◽  
Author(s):  
Alain de Cheveigné
Keyword(s):  
Time Constant ◽  
Auditory Brainstem ◽  
The Other ◽  
Inhibitory Synapses ◽  
Coincidence Counting ◽  
Time Constants ◽  
Direct Pathway ◽  
Lower Tone ◽  
Excitatory And Inhibitory Synapses

This paper suggests an explanation for listener’s greater tolerance to positive than negative mistuning of the higher tone within an octave pair. It hypothesizes a neu- ral circuit tuned to cancel the lower tone, that also cancels the higher tone if that tone is in tune. Imperfect cancellation is the cue to mistuning of the octave. The circuit involves two pathways, one delayed with respect to the other, that feed a coincidence-counting neuron via excitatory and inhibitory synapses. A mismatch between the time constants of these two synapses results in an asymmetry in sen- sitivity to mismatch. Specifically, if the time constant of the delayed pathway is greater than that of the direct pathway, there is a greater tolerance to positive than to negative mistuning, which can lead to a perceptual“stretch” of the octave. The model is applicable to both harmonic and – with qualification – melodic oc- taves. The paper describes the model and reviews the evidence from auditory psychophysics and physiology in favor – or against – it.

Electrotonic length estimates in neurons with dendritic tapering or somatic shunt

1992 ◽  
Vol 68 (4) ◽  
pp. 1421-1437 ◽  
Author(s):  
W. R. Holmes ◽  
W. Rall
Keyword(s):  
Voltage Clamp ◽  
Exact Estimate ◽  
Exponential Fitting ◽  
Robust Estimator ◽  
Neuron Models ◽  
Time Constants ◽  
A Cell ◽  
Voltage Transients ◽  
Conductance Ratio ◽  
Current Transients

1. Compartmental models were used to compute the time constants and coefficients of voltage and current transients in hypothetical neurons having tapering dendrites or soma shunt and in a serially reconstructed motoneuron with soma shunt. These time constants and coefficients were used in equivalent cylinder formulas for the electrotonic length, L, of a cell to assess the magnitude of the errors that result when the equivalent cylinder formulas are applied to neurons with dendritic tapering or soma shunt. 2. Of all the formulas for a cylinder (with sealed ends), the most commonly used formula, which we call L tau 0/tau 1 (the formula uses the current-clamp time constants tau 0 and tau 1), was the most robust estimator of L in structures that tapered linearly. When the diameter at the end of the cylinder was no less than 20% of the initial diameter, L tau 0/tau 1 underestimated the actual L by at most 10%. 3. The equivalent cylinder formulas for a cylinder were applied to neurons modeled as a cylinder with a shunted soma at one end. The formula for L based solely on voltage-clamp time constants gave an exact estimate of L. However, the second voltage-clamp time constant cannot be reliably obtained experimentally for neurons studied thus far. Of the remaining formulas, L tau 0/tau 1 was again the most robust estimator of L. This formula overestimated L with the size of the overestimates depending on beta, rho beta = 1, and the actual L of the cylinder, where beta is the soma shunt factor, and rho beta = 1 is the dendritic-to-somatic conductance ratio when beta = 1 (no shunt). When the actual L was 0.5 and the soma shunt was large, this formula overestimated L by two- to threefold, but when the actual L was 1.5, the overestimate was only 10-15% regardless of the size of the shunt. 4. In neurons modeled as two cylinders with soma shunt, the L tau 0/tau 1 value computed with the actual tau 0 and tau 1 values overestimated the average L by two to six times when soma shunt was large. However, the L tau 0/tau 1 estimates computed with tau 0 and tau 1 values estimated with the exponential fitting program DISCRETE from voltage transients computed for these neuron models were never this large because of inherent problems in estimating closely spaced time constants from data.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Analysis of CO2 kinetics in Na,Cs-Rho crystals using the zero length column: a case study for slow systems

2021 ◽  
Author(s):  
Enzo Mangano ◽  
Stefano Brandani
Keyword(s):  
Time Constant ◽  
Transport Process ◽  
Diffusion Path ◽  
The Other ◽  
Experimental Measurements ◽  
Time Constants ◽  
Adsorption Processes ◽  
Concentration Dependent Diffusivity

AbstractExperimental measurements of systems with slow gas transport kinetics are generally considered a relatively easier task when compared to the challenges of measurements of very fast systems. On the other hand, when the transport process goes towards time constants of the order of several hours, not only the measurements, but also the analysis and interpretation of the data offer challenges which make the assessment of the correct time constant of the process non trivial. In this work we used the measurements of CO2 diffusion in Na,Cs-Rho crystals, carried out using the zero length column (ZLC) technique, as a case study for the use of the technique for very slow adsorption processes. The system, which has a time constant of the order of 8 h, shows the importance of using the partial loading approach for the determination of an unambiguous time constant from the analysis of the ZLC desorption curves. The traditional analysis is refined by using the nonlinear ZLC model to take into account the isotherm nonlinearity that results in a concentration dependent diffusivity. Finally, the method proposed by Cavalcante is used to confirm the 3-D diffusion path of the system.

scholarly journals Individual motion perception parameters and motion sickness frequency sensitivity in fore-aft motion

2021 ◽  
Author(s):  
Tugrul Irmak ◽  
Ksander N. de Winkel ◽  
Daan M. Pool ◽  
Heinrich H. Bülthoff ◽  
Riender Happee
Keyword(s):  
Motion Sickness ◽  
Motion Perception ◽  
Time Constant ◽  
Storage Time ◽  
Velocity Storage ◽  
Strong Positive Correlation ◽  
Subjective Vertical ◽  
Time Constants ◽  
Frequency Sensitivity ◽  
Observer Model

AbstractPrevious literature suggests a relationship between individual characteristics of motion perception and the peak frequency of motion sickness sensitivity. Here, we used well-established paradigms to relate motion perception and motion sickness on an individual level. We recruited 23 participants to complete a two-part experiment. In the first part, we determined individual velocity storage time constants from perceived rotation in response to Earth Vertical Axis Rotation (EVAR) and subjective vertical time constants from perceived tilt in response to centrifugation. The cross-over frequency for resolution of the gravito-inertial ambiguity was derived from our data using the Multi Sensory Observer Model (MSOM). In the second part of the experiment, we determined individual motion sickness frequency responses. Participants were exposed to 30-minute sinusoidal fore-aft motions at frequencies of 0.15, 0.2, 0.3, 0.4 and 0.5 Hz, with a peak amplitude of 2 m/s2 in five separate sessions, approximately 1 week apart. Sickness responses were recorded using both the MIsery SCale (MISC) with 30 s intervals, and the Motion Sickness Assessment Questionnaire (MSAQ) at the end of the motion exposure. The average velocity storage and subjective vertical time constants were 17.2 s (STD = 6.8 s) and 9.2 s (STD = 7.17 s). The average cross-over frequency was 0.21 Hz (STD = 0.10 Hz). At the group level, there was no significant effect of frequency on motion sickness. However, considerable individual variability was observed in frequency sensitivities, with some participants being particularly sensitive to the lowest frequencies, whereas others were most sensitive to intermediate or higher frequencies. The frequency of peak sensitivity did not correlate with the velocity storage time constant (r = 0.32, p = 0.26) or the subjective vertical time constant (r = − 0.37, p = 0.29). Our prediction of a significant correlation between cross-over frequency and frequency sensitivity was not confirmed (r = 0.26, p = 0.44). However, we did observe a strong positive correlation between the subjective vertical time constant and general motion sickness sensitivity (r = 0.74, p = 0.0006). We conclude that frequency sensitivity is best considered a property unique to the individual. This has important consequences for existing models of motion sickness, which were fitted to group averaged sensitivities. The correlation between the subjective vertical time constant and motion sickness sensitivity supports the importance of verticality perception during exposure to translational sickness stimuli.

scholarly journals Voltage-gated transient currents in bovine adrenal fasciculata cells. I. T-type Ca2+ current.

1993 ◽  
Vol 102 (2) ◽  
pp. 217-237 ◽  
Author(s):  
B Mlinar ◽  
B A Biagi ◽  
J J Enyeart
Keyword(s):  
Time Constant ◽  
Low Voltage ◽  
Zona Fasciculata ◽  
Patch Clamp Technique ◽  
Time Constants ◽  
Voltage Gated ◽  
Wide Range ◽  
Boltzmann Function ◽  
Voltage Dependent ◽  
Ca2 Channels

The whole cell version of the patch clamp technique was used to identify and characterize voltage-gated Ca2+ channels in enzymatically dissociated bovine adrenal zona fasciculata (AZF) cells. The great majority of cells (84 of 86) expressed only low voltage-activated, rapidly inactivating Ca2+ current with properties of T-type Ca2+ current described in other cells. Voltage-dependent activation of this current was fit by a Boltzmann function raised to an integer power of 4 with a midpoint at -17 mV. Independent estimates of the single channel gating charge obtained from the activation curve and using the "limiting logarithmic potential sensitivity" were 8.1 and 6.8 elementary charges, respectively. Inactivation was a steep function of voltage with a v1/2 of -49.9 mV and a slope factor K of 3.73 mV. The expression of a single Ca2+ channel subtype by AZF cells allowed the voltage-dependent gating and kinetic properties of T current to be studied over a wide range of potentials. Analysis of the gating kinetics of this Ca2+ current indicate that T channel activation, inactivation, deactivation (closing), and reactivation (recovery from inactivation) each include voltage-independent transitions that become rate limiting at extreme voltages. Ca2+ current activated with voltage-dependent sigmoidal kinetics that were described by an m4 model. The activation time constant varied exponentially at test potentials between -30 and +10 mV, approaching a voltage-independent minimum of 1.6 ms. The inactivation time constant (tau i) also decreased exponentially to a minimum of 18.3 ms at potentials positive to 0 mV. T channel closing (deactivation) was faster at more negative voltages; the deactivation time constant (tau d) decreased from 8.14 +/- 0.7 to 0.48 +/- 0.1 ms at potentials between -40 and -150 mV. T channels inactivated by depolarization returned to the closed state along pathways that included two voltage-dependent time constants. tau rec-s ranged from 8.11 to 4.80 s when the recovery potential was varied from -50 to -90 mV, while tau rec-f decreased from 1.01 to 0.372 s. At potentials negative to -70 mV, both time constants approached minimum values. The low voltage-activated Ca2+ current in AZF cells was blocked by the T channel selective antagonist Ni2+ with an IC50 of 20 microM. At similar concentrations, Ni2+ also blocked cortisol secretion stimulated by adrenocorticotropic hormone. Our results indicate that bovine AZF cells are distinctive among secretory cells in expressing primarily or exclusively T-type Ca2+ channels.(ABSTRACT TRUNCATED AT 400 WORDS)

Identification of Time-Varying Time Constants of Thermocouple Sensors and Its Application to Temperature Measurement

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Kenneth Kar ◽  
Akshya K. Swain ◽  
Robert Raine
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Time Constant ◽  
Identification Problem ◽  
Basis Functions ◽  
New Technique ◽  
Ratio Test ◽  
Time Varying ◽  
Time Constants ◽  
Orthogonal Least Squares

The present study addresses the problem of estimating time-varying time constants associated with thermocouple sensors by a set of basis functions. By expanding each time-varying time constant onto a finite set of basis sequences, the time-varying identification problem reduces to a parameter estimation problem of a time-invariant system. The proposed algorithm, to be called as orthogonal least-squares with basis function expansion algorithm, combines the orthogonal least-squares algorithm with an error reduction ratio test to include significant basis functions into the model, which results in a parsimonious model structure. The performance of the method was compared with a linear Kalman filter. Simulations on engine data have demonstrated that the proposed method performs satisfactorily and is better than the Kalman filter. The new technique has been applied in a Stirling cycle compressor. The sinusoidal variations in time constant are tracked properly using the new technique, but the linear Kalman filter fails to do so. Both model validation and thermodynamic laws confirm that the new technique gives unbiased estimates and that the assumed thermocouple model is adequate.

Voltage Dependence of the Glycine Receptor–Channel Kinetics in the Zebrafish Hindbrain

1999 ◽  
Vol 82 (5) ◽  
pp. 2120-2129 ◽  
Author(s):  
Pascal Legendre
Keyword(s):  
Time Constant ◽  
Rise Time ◽  
Time Course ◽  
Voltage Dependence ◽  
Good Description ◽  
Glycine Receptor ◽  
Relative Amplitude ◽  
Time Constants ◽  
Low Concentration ◽  
Voltage Dependent

Electrophysiological recordings of outside-out patches to fast-flow applications of glycine were made on patches derived from the Mauthner cells of the 50-h-old zebrafish larva. As for glycinergic miniature inhibitory postsynaptic currents (mIPSCs), depolarizing the patch produced a broadening of the transient outside-out current evoked by short applications (1 ms) of a saturating concentration of glycine (3 mM). When the outside-out patch was depolarized from −50 to +20 mV, the peak current varied linearly with voltage. A 1-ms application of 3 mM glycine evoked currents that activated rapidly and deactivated biexponentially with time constants of ≈5 and ≈30 ms (holding potential of −50 mV). These two decay time constants were increased by depolarization. The fast deactivation time constant increased e-fold per 95 mV. The relative amplitude of the two decay components did not significantly vary with voltage. The fast component represented 64.2 ± 2.8% of the total current at −50 mV and 54.1 ± 10% at +20 mV. The 20–80% rise time of these responses did not show any voltage dependence, suggesting that the opening rate constant is insensitive to voltage. The 20–80% rise time was 0.2 ms at −70 mV and 0.22 ms at +20 mV. Responses evoked by 100–200 ms application of a low concentration of glycine (0.1 mM) had a biphasic rising phase reflecting the complex gating behavior of the glycine receptor. The time constant of these two components and their relative amplitude did not change with voltage, suggesting that modal shifts in the glycine-activated channel gating mode are not sensitive to the membrane potential. Using a Markov model to simulate glycine receptor gating behavior, we were able to mimic the voltage-dependent change in the deactivation time course of the responses evoked by 1-ms application of 3 mM glycine. This kinetics model incorporates voltage-dependent closing rate constants. It provides a good description of the time course of the onset of responses evoked by the application of a low concentration of glycine at all membrane potentials tested.

scholarly journals Alexander- and Markov-type theorems for virtual trivalent braids

2019 ◽  
Vol 28 (01) ◽  
pp. 1950003 ◽  
Author(s):  
Carmen Caprau ◽  
Abigayle Dirdak ◽  
Rita Post ◽  
Erica Sawyer
Keyword(s):  
Type Theorem ◽  
Algebraic Approach ◽  
The Other ◽  
Markov Type ◽  
Trivalent Graphs

We prove Alexander- and Markov-type theorems for virtual spatial trivalent graphs and virtual trivalent braids. We provide two versions for the Markov-type theorem: one uses an algebraic approach similar to the case of classical braids and the other one is based on [Formula: see text]-moves.

scholarly journals On the convection of ionospheric density features

2019 ◽  
Vol 37 (2) ◽  
pp. 201-214
Author(s):  
John D. de Boer ◽  
Jean-Marc A. Noël ◽  
Jean-Pierre St.-Maurice
Keyword(s):  
Collision Frequency ◽  
Analytic Solutions ◽  
The Other ◽  
Density Difference ◽  
Density Gradients ◽  
Scale Invariant ◽  
The Real ◽  
Altitude Dependence ◽  
Density Enhancement ◽  
Auroral Arcs

Abstract. We investigate whether the boundaries of an ionospheric region of different density than its surroundings will drift relative to the background E×B drift and, if so, how the drift depends on the degree of density enhancement and the altitude. We find analytic solutions for discrete circular features in a 2-D magnetised plasma. The relative drift is proportional to the density difference, which suggests that where density gradients occur they should tend to steepen on one side of a patch while they are weakened on the other. This may have relevance to the morphology of polar ionospheric patches and auroral arcs, since the result is scale-invariant. There is also an altitude dependence which enters through the ion-neutral collision frequency. We discuss how the 2-D analytic result can be applied to the real ionosphere.

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

Sign in / Sign up

Export Citation Format

Share Document